theme based real world problem solving challenge

New Designs for School From Teacher to Teammate: Real-World Projects Challenge Students and Teachers Alike

Elizabeth Luna (she/her) Teacher and Department Chair Athens Drive Magnet High School in Raleigh, North Carolina

We’ve all had the experience of truly purposeful, authentic learning and know how valuable it is. Educators are taking the best of what we know about learning, student support, effective instruction, and interpersonal skill-building to completely reimagine schools so that students experience that kind of purposeful learning all day, every day.

Community-based projects are a game-changer in the classroom, when students learn to use design thinking to solve problems, address community needs, and make an impact... and teachers become partners in learning.

After 12 years of teaching, I thought I had mastered connecting curriculum to student interest. However, during the pandemic, the problem of student engagement became glaring as students struggled to find purpose. Faced with learning on their own, they encountered the daunting task of finding meaning in standards that were disconnected from “real life.”

While students struggled to find motivation and purpose, I also faced the need to rethink my view of teaching and learning. There were a lot of questions that ran through my mind. The main one that continued to resurface was, “What actually matters?” With shortened teaching time, on top of the disengagement, I encountered the formidable moment of figuring out the goal of my courses and what I truly wanted students to learn/know. For years, the county and the state have been telling teachers what matters most through the curriculums provided. This pandemic shined a light on the fact that the standards weren’t cutting it.

When I reflected on what my design courses had lost in the online transition, I realized that the community connections and design thinking that I had built in my first few years of teaching had vanished. Classes became flat and task driven, and my students couldn’t “think big” anymore because they didn’t have the space to do so. The new tech standards weren’t enough for my students, and they didn’t work for me either. Teaching a student how to click buttons in an ever-changing and evolving technology-filled world felt pointless and went against every virtue taught to me within my design degree. I needed more and so did they.

“What actually matters?” is a tough question to answer. Upon some reflection, I realized that I have two major goals within my classroom.

First, I want students to become proficient in the design programs so that they can create.

Second, I need students to understand how to use these skills to solve problems, address community needs, and thus, make an impact.

The base curriculum covered the first goal, but the second part was on me to create and develop.

A Design Thinking Classroom

The design process is a procedure with which everyone needs to become familiar in the 21st century and is a necessity to achieve my second goal. My graphic design degree from North Carolina State University taught me the importance of design thinking and its impact on creating change. As a teacher, this training is implemented within my classroom. I explain to students that no matter what subject area they are interested in, the process is applicable. You will always be solving problems and inventing solutions whether they are designed products, business plans, or vaccines; your life is about problem-solving and innovating. There are a lot of design processes out there, from simple to complex, but they all move you through the same base steps.

• Empathizing with the user/ Gathering information
• Defining the problem
• Ideating/ Finding solutions
• Creating and evaluating solutions: Sharing out and receiving critique
• Refining and adjusting those solutions

These steps were the guiding process in my classroom before the pandemic and needed to be reinstated at the forefront of my classroom as students returned to school this year. Rather than teaching the five step process to students as a discrete skill, I recognized the importance of integrating the five steps into every project and assignment, to teach through the five steps. Transforming a classroom to incorporate this type of thinking is complex and time consuming. It forced me to break away from the provided curriculum and enhance it. I had to carve out time within my classes for students to think deeply around problems, to debate, and to develop and express opinions.

For the first time in a long time I saw growth as students pulled away from a task-completion mindset and, instead, focused on seeking feedback and refining ideas. Allowing time for thought and exploration was key to moving students toward being problem-solvers. Students began to turn to each other for opinions and, instead of rejecting the other person’s thoughts, they sought to understand another viewpoint. When they fell short on a technical skill, they didn’t shut down. Instead, they asked for help from me or another student, searched on the internet for support, etc. Because the assignments were structured in a more open-ended manner, students were no longer worried about being seen as “right.” Instead, they focused on creating the best result possible for them at that time.

Building a creative thought process was only half the battle, though. I needed to connect students to the community to engage in purposeful ways. In the past, I have connected to community members that needed graphic design work done. I knew that my students responded better to real-world projects than any construct I could mimic. But as a teacher, I was overwhelmed by the time required to track down community members in need, connect them with students, and figure out the direction and goal of the project. I needed community connection to help my students build their purpose, but figuring out how to make that happen was a roadblock. Then Project Invent came along.

Project Invent would impact my classroom in ways that I did not understand immediately, challenging me as an educator while also providing structure and opportunities for my students. Project Invent was a tangible organization that took the design process I had been working so hard to embed in my classroom and connected it to problem-solving within the community. They were the bridge that I needed to make my second goal come to fruition.

Get the learner perspective on real-world projects from a former student in Ms. Luna’s class! Rethinking Education: Prioritizing Creativity and People over Grades and Rubrics

Real-World Context Is Everything to a Student

My students need connection. I was inundated with statements like, “I am most excited about being able to apply design to group projects and work towards making an impact for someone,” and “getting to do something real.” Project Invent partnered us with two community members that matched our school’s magnet theme. We have a global health theme at our school that teachers are supposed to integrate into curriculum, and some students take part in a STEM Academy which focuses on sustainability. My community partners targeted both of these areas, one from the North Carolina Forestry Division and another with a son that struggled with microcephaly amongst other medical conditions.

In order for students to take full ownership, I handed the reins to them immediately. We reviewed some basic interview etiquette, students did some background research, and then we scheduled our first interview. My students met with the community partners and controlled the interactions from the start. The interviews brought a deeper engagement. I often work to mimic projects and requests they would receive in the workforce so my students are used to getting a ‘real’ project brief that I create for them. However, I have never before put them in front of someone and asked them to listen to everything that person has to say and attempt to deconstruct the client’s biggest needs. In this situation, they were tasked with figuring out what the client’s problems were, empathizing with them, and defining their direction of work. Meeting our clients was a game-changing experience for students. They left their interview sessions discussing every statement said, went back and analyzed the transcripts, and argued about what was most important and what should be the focus. Their passion bloomed before my eyes as these excited students became invested in the people sitting across from them.

Visiting a Site Creates Opportunities to Learn and Understand

Visiting the site of a problem or seeing a situation in-person is essential for kids to "feel" what is going on. Encouraging students to venture out to a space or physically research and experiment with a problem is the key to better understanding. Students come up with more accurate solutions and/or develop new ways to look at things when they can experience the space or problem first hand. My students were sure their solution direction was the right way to go, until they had an opportunity to visit the site of concern. After walking the space, experiencing the different areas, and hearing more from the client, they agreed they’d have to pivot their ideas and throw out their plans. It turns out, they had not solved the most essential problems and they knew their plans weren’t accurate anymore. The feedback from their partner and the chance to immerse themselves into a situation made students aware of possibilities they had not imagined based on their own experiences.

Team Assignments and Collaboration Support Change-Making

I wanted students to self-select the design challenges most interesting to them.Interviews, breakdowns, and problem analysis were done with all students in randomly assigned small groups as well as a whole class. This ensured a basic understanding of both clients for all and would foster a better creative environment as our class progressed through the year. If every student understood the problems at hand, every one could provide valuable feedback and be active supporters in the invention process. As research and problem definition progressed, students began to really gravitate toward one client over the other; natural separations started to form within the classroom.

Even with the class splitting, groups were still too large for each student to have an active voice. They worked through a variety of ideation charts as they narrowed their points of interest with the client, thus further dividing themselves into smaller cohorts. I also began surveying students around different skill sets to ensure that groups were balanced with knowledge/ability as much as possible. However, one student pointed out, “It’s more important that I am passionate about what I am working on and who I am working with than having a technically skilled team. I want to be invested in this.” His statement reminded me that the point of the teams was to push student-passion forward; I needed to be careful about balancing a team around skill and needed to focus more on dedication and client-based interest.

Community Engagement Can Fill the Knowledge/Skill Gap of the Teacher

“I don’t know how” might be the most common phrase uttered by students and myself this year. I vividly remember the point where I looked at my students and said we had hit the point where I no longer had the knowledge base to support them. I am a graphic designer. I like to make things look good and I enjoy the challenge of communication. When we hit questions around feasibility and the prototyping stage, I was way out of my league. I openly admitted this to my students. That moment was transformative as the playing field was leveled. My job was to support them and help them problem-solve. I couldn’t tell them what was right or wrong and, as students realized this, we entered a space where trial and error would lead to a lot of failure and, hopefully, some success. The rhythm of the class changed.

Already engaging with community members as clients, it occurred to me that I could use community members to support my students where my knowledge was scant. I sought help from teachers, friends, college students, and local businesses. Since virtual meetings are so prominent now, the challenge of getting students and professionals together was almost non-existent. It became a natural process: students would hit a question that we genuinely couldn’t answer, we’d debate about what type of person would be able to support us, and I would work alongside my magnet coordinator to find a professional that could help. Product developers could understand their idea and talk to students about feasibility, often giving them parts to look up or products to learn about. Engineers talked about intricate electronic concepts, pointing students to a type of relay or remote. Gardeners and landscapers discussed invasive species and methods of removal, directing us back to specific research articles and studies completed.

Honest and purposeful feedback is absolutely vital for students to know whether an idea is successful, possible, or should be pursued further. Real feedback from invested clients and business professionals encourages students’ refining and adjusting solutions for the benefit of the project. Without client and community insight, the initial design may be "good" but not fulfill all the essential needs. Since feedback came from multiple volunteers spanning different backgrounds, students were exposed to a variety of viewpoints. They learned how to sift through reviews and pull the most essential information. Designers need to take feedback as a gift of new possibilities, not a "put down" of their ideas.

Every conversation a student had, even when it was filled with critique, led to more energy and motivation. Students pivoted concepts, considered issues they hadn’t previously thought about, and had moments of confirmation that I couldn’t give them. Every time, they came back and asked for more. I realized that the engagement with outsiders filled the knowledge gap I faced while also giving the kids meaningful experience with experts in a variety of fields. The cool part was, they came back to me to share their excitement, their success, their questions and concerns. I was now a member of each team; instead of being the one with the answers, I was getting to be part of their support system. I was working alongside them to hypothesize and decide on their next steps as an equal, which so rarely happens in the classroom.

Local professionals want to work with students and, when asked to engage actively and not just as a speaker, they are as fulfilled as the kids. The experience benefits everyone involved. Making time for those interactions is key to keeping students engaged in their work. ‘Rejuvenating’ was the word many community members used. The students brought new hope and excitement to their lives. One professional said, “Your students’ passion is electrifying. I am so impressed with their concepts and work. They will change the world and have the ability to do that because of the opportunities you’re providing them.” His excitement reminded me of what many professionals have said over the years, “Students are the future and I want to work with them and inspire them to create.”

Student Success Is So Much More than Test Scores

As a teacher, my job has been consistently broken down into teaching students standards and technical skills. Because of a need to ‘test’ students to prove their success, my curriculum has lost the applicability, creative thinking, and all of the upper-level verbs in Bloom’s Taxonomy. I’ve come to believe that focusing on new high-tech skills is an archaic choice. The world is continuously evolving and shifting; my job is not to teach a skill that will be outdated in a year to come, but use the skills as a means of production and creation.

With this mindset, students learn by necessity and naturally gain ability as they apply themselves to larger tasks. It is not going to be equal. Every student will not develop success in the same area. Some students end up gaining coding knowledge, others focus on design, some find out their success is in presentation, but all grow in areas that interest them and help direct them in future career choices. Amongst individual accomplishment, there is also a level of success that comes from having to work closely in a team. They’ve learned how to hold each other accountable, how to manage peers and time, and how to celebrate each small victory.

I have enhanced the learning experience to wrap around a student and their natural abilities by building creative spaces, community connection, and providing opportunities in which everyone learns from each other. Beyond the student, I have enhanced my teaching experience, challenging myself to be comfortable with students working on a variety of skills, with non-traditional ways to measure success, and with not always having the control over learning direction. The environment that forms from client-driven projects and community engagement is life-giving to community members, teachers, and students alike.

The Portrait of a Graduate in Practice

New from NGLC! The outcomes that Elizabeth Luna sees from real-world projects are often the competencies expressed in a school or district's graduate portrait. Find out how portraits are inspiring system-wide change where this kind of teaching and learning can thrive.

All photos courtesy of the author.

Elizabeth Luna (she/her)

Teacher and department chair, athens drive magnet high school.

Elizabeth Luna is a graphic design teacher and career tech education department chair at Athens Drive Magnet High School, Center for Medical Sciences and Global Health Initiatives. She also coaches four teams of students through Project Invent . She has led work at the county and school level focused on implementing design thinking in the classroom.

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31 Examples of Real-World Math Problems

• • Published: April 23, 2024
• • Last update: May 22, 2024
• • Grades: All grades

Introduction

8th grade algebra problem:

Farmer Alfred has three times as many chickens as cows. In total, there are 60 legs in the barn. How many cows does Farmer Alfred have? [1]

Does this sound like a real-world math problem to you? We’ve got chickens, cows, and Farmer Alfred – it’s a scenario straight out of everyday life, isn’t it?

But before you answer, let me ask you something: If you wanted to figure out the number of cows, would you:

• Count their legs, or
• Simply count their heads ( or even just ask Farmer Alfred, “Hey Alfred, how many cows do you have?” )

Chances are, most people would go with option B.

So, why do our math books contain so many “real-world math problems” like the one above?

In this article, we’ll dive into what truly makes a math problem a real-world challenge.

Understanding 'Problems' in Daily Life and Mathematics

The word “problem” carries different meanings in everyday life and in the realm of mathematics, which can sometimes lead to confusion. In our daily lives, when we say “ I have a problem ,” we typically mean that something undesirable has occurred – something challenging to resolve or with potential negative consequences.

For instance:

• “I have a problem because I’ve lost my wallet.”
• “I have a problem because I forgot my keys at home, and I won’t be able to get into the house when I return from school.”
• “I have a problem because I was sick and missed a few weeks of school, which means I’ll likely fail my math test.”

These are examples of everyday problems we encounter. However, once the problem is solved, it often ceases to be a problem:

• “I don’t have a problem getting into my house anymore because my mom gave me her keys.”

In mathematics, the term “problem” takes on a different meaning. According to the Cambridge dictionary [2], it’s defined as “ a question in mathematics that needs an answer. “

Here are a few examples:

• If x + 2 = 4, what is the value of x?
• How do you find the common denominator for fractions 1/3 and 1/4?
• What is the length of the hypotenuse in a right triangle if two legs are 3 and 4 feet long?

These are all examples of math problems.

It’s important to note that in mathematics, a problem remains a problem even after it’s solved. Math problems are universal, regardless of who encounters them [3]. For instance, both John and Emma could face the same math problem, such as “ If x + 2 = 4, then what is x? ” After they solve it, it still remains a math problem that a teacher could give to somebody else.

Understanding Real-World Math Problems

So, what exactly is a “real-world math problem”? We’ve established that in our daily lives, we refer to a situation as a “problem” when it could lead to unpleasant consequences. In mathematics, a “problem” refers to a mathematical question that requires a mathematical solution.

With that in mind, we can define a real-world math problem as:

A situation that could have negative consequences in real life and that requires a mathematical solution (i.e. mathematical solution is preferred over other solutions).

Consider this example:

Could miscalculating the flour amount lead to less-than-ideal results? Absolutely. Messing up the flour proportion could result in a less tasty cake – certainly an unpleasant consequence.

Now, let’s explore the methods for solving this. While traditional methods, like visually dividing the flour or measuring multiple times, have their place, they may not be suitable for larger-scale events, such as catering for a wedding with 250 guests. In such cases, a mathematical solution is not only preferred but also more practical.

By setting up a simple proportion – 1 1/2 cups of flour for 8 people equals x cups for 20 people – we can quickly find the precise amount needed: 3 3/4 cups of flour. In larger events, like the wedding, the mathematical approach provides even more value, yielding a requirement of nearly 47 cups of flour.

This illustrates why a mathematical solution is faster, more accurate, and less error-prone, making it the preferred method. Coupled with the potential negative consequences of inaccuracies, this makes the problem a real-world one, showcasing the practical application of math in everyday scenarios.

Identifying Non-Real-World Math Problems

Let’s revisit the example from the beginning of this article:

Farmer Alfred has three times as many chickens as cows. In total, there are 60 legs in the barn. How many cows does Farmer Alfred have?

3rd grade basic arithmetic problem:

Noah has $56, and Olivia has 8 times less. How much money does Olivia have?

Once more, in our daily routines, do we handle money calculations this way? Why would one prefer to use mathematical solution ($56 : 8 =$7). More often than not, we’d simply ask Olivia how much money she has. While the problem can theoretically be solved mathematically, it’s much more practical, efficient, and reliable to resolve it by directly asking Olivia.

Examples like these are frequently found in math textbooks because they aid in developing mathematical thinking. However, the scenarios they describe are uncommon in real life and fail to explicitly demonstrate the usefulness of math. In essence, they don’t showcase what math can actually be used for. Therefore, there are two crucial aspects of true real-world math problems: they must be commonplace in real life, and they must explicitly illustrate the utility of math.

To summarize:

Word problems that are uncommon in real life and fail to convincingly demonstrate the usefulness of math are not real-world math problems.

Real-World Math Problems Across Professions

Many professions entail encountering real-world math problems on a regular basis. Consider the following examples:

Nurses often need to calculate accurate drug dosage amounts using proportions, a task solved through mathematical methods. Incorrect dosage calculations can pose serious risks to patient health, leading to potentially harmful consequences.

Construction engineers frequently need to determine whether a foundation will be sturdy enough to support a building, employing mathematical solving techniques and specialized formulas. Errors in these calculations can result in structural issues such as cracks in walls due to foundation deformation, leading to undesirable outcomes.

Marketers often rely on statistical analysis to assess the performance of online advertisements, including metrics like click-through rates and the geographical distribution of website visitors. Mathematical analysis guides decision-making in this area. Inaccurate analyses may lead to inefficient allocation of advertisement budgets, resulting in less-than-optimal outcomes.

These examples illustrate real-world math problems encountered in various professions. While there are numerous instances of such problems, they are often overlooked in educational settings. At DARTEF, we aim to bridge this gap by compiling a comprehensive list of real-world math problems, which we’ll explore in the following section.

31 Genuine Real-World Math Problems

In this section, we present 31 authentic real-world math problems from diverse fields such as safety and security, microbiology, architecture, engineering, nanotechnology, archaeology, creativity, and more. Each of these problems meets the criteria we’ve outlined previously. Specifically, a problem can be classified as a real-world math problem if:

• It is commonly encountered in real-life scenarios.
• It has the potential for undesirable consequences.
• A mathematical solution is preferable over alternative methods.
• It effectively illustrates the practical utility of mathematics.

All these problems stem from actual on-the-job situations, showcasing the application of middle and high school math in various professions.

Math Problems in Biology

Real-world math problems in biology often involve performing measurements or making predictions. Mathematics helps us understand various biological phenomena, such as the growth of bacterial populations, the spread of diseases, and even the reconstruction of ancient human appearances. Here are a couple of specific examples:

1. Reconstructing Human Faces Using Parallel and Perpendicular Lines:

Archeologists and forensic specialists often reconstruct human faces based on skeletal remains. They utilize parallel and perpendicular lines to create symmetry lines on the face, aiding in the recovery of facial features and proportions. Our article, “ Parallel and Perpendicular Lines: A Real-Life Example (From Forensics and Archaeology) ,” provides a comprehensive explanation and illustrates how the shape of the nose can be reconstructed using parallel and perpendicular lines, line segments, tangent lines, and symmetry lines.

2. Measuring Bacteria Size Using Circumference and Area Formulas:

Microbiology specialists routinely measure bacteria size to monitor and document their growth rates. Since bacterial shapes often resemble geometric shapes studied in school, mathematical methods such as calculating circumference or area of a circle are convenient for measuring bacteria size. Our article, “ Circumference: A Real-Life Example (from Microbiology) ,” delves into this process in detail.

Math Problems in Construction and Architecture

Real-world math problems are abundant in architecture and construction projects, where mathematics plays a crucial role in ensuring safety, efficiency, and sustainability. Here are some specific case studies that illustrate the application of math in these domains:

3. Calculating Central Angles for Safe Roadways:​

Central angle calculations are a fundamental aspect of roadway engineering, particularly in designing curved roads. Civil engineers use these calculations to determine the degree of road curvature, which significantly impacts road safety and compliance with regulations. Mathematical concepts such as radius, degrees, arc length, and proportions are commonly employed by civil engineers in their daily tasks. Our article, “ How to Find a Central Angle: A Real-Life Example (from Civil Engineering) ,” provides further explanation and demonstrates the calculation of central angles using a real road segment as an example.

4. Designing Efficient Roofs for Solar Panels Using Angle Geometry:

Mathematics plays a crucial role in architecture, aiding architects and construction engineers in designing energy-efficient building structures. For example, when considering the installation of solar panels on a building’s roof, understanding geometric properties such as adjacent and alternate angles is essential for maximizing energy efficiency . By utilizing mathematical calculations, architects can determine the optimal angle for positioning solar panels and reflectors to capture maximum sunlight. Our article, “ A Real-Life Example of How Angles are Used in Architecture ,” provides explanations and illustrations, including animations.

5. Precision Drilling of Oil Wells Using Trigonometry:

Petroleum engineers rely on trigonometric principles such as sines, cosines, tangents, and right-angle triangles to drill oil wells accurately. Trigonometry enables engineers to calculate precise angles and distances necessary for drilling vertical, inclined, and even horizontal wells. For instance, when drilling at an inclination of 30°, engineers can use trigonometry to calculate the vertical depth corresponding to each foot drilled horizontally. Our article, “ CosX: A Real-Life Example (from Petroleum Engineering) ,” provides examples, drawings of right triangle models, and necessary calculations.

6. Calculating Water Flow Rate Using Composite Figures:

Water supply specialists frequently encounter the task of calculating water flow rates in water canals, which involves determining the area of composite figures representing canal cross-sections . Many canal cross-sections consist of composite shapes, such as rectangles and triangles. By calculating the areas of these individual components and summing them, specialists can determine the total cross-sectional area and subsequently calculate the flow rate of water. Our article, “ Area of Composite Figures: A Real-Life Example (from Water Supply) ,” presents necessary figures, cross-sections, and an example calculation.

Math Problems in Business and Marketing

Mathematics plays a crucial role not only in finance and banking but also in making informed decisions across various aspects of business development, marketing analysis, growth strategies, and more. Here are some real-world math problems commonly encountered in business and marketing:

7. Analyzing Webpage Position in Google Using Polynomials and Polynomial Graphs:

Polynomials and polynomial graphs are essential tools for data analysis. They are useful for a wide variety of people, not only data analysts, but literally everyone who ever uses Excel or Google Sheets. Our article, “ Graphing Polynomials: A Real-World Example (from Data Analysis) ,” describes this and provides an authentic case study. The case study demonstrates how polynomials, polynomial functions of varying degrees, and polynomial graphs are used in internet technologies to analyze the visibility of webpages in Google and other search engines.”

8. Making Informed Business Development Decisions Using Percentages:

In business development, math problems often revolve around analyzing growth and making strategic decisions. Understanding percentages is essential, particularly when launching new products or services. For example, determining whether a startup should target desktop computer, smartphone, or tablet users for an app requires analyzing installation percentages among user groups to gain insights into consumer behavior. Math helps optimize marketing efforts, enhance customer engagement, and drive growth in competitive markets. Check out our article “ A Real-Life Example of Percent Problems in Business ” for a detailed description of this example.

9. Analyzing Customer Preferences Using Polynomials:

Marketing involves not only creative advertising but also thorough analysis of customer preferences and marketing campaigns. Marketing specialists often use simple polynomials for such analysis, as they help analyze multiple aspects of customer behavior simultaneously. For instance, marketers may use polynomials to determine whether low price or service quality is more important to hotel visitors. Smart analysis using polynomials enables businesses to make informed decisions. If you’re interested in learning more, our article “ Polynomials: A Real Life Example (from Marketing) ” provides a real-world example from the hotel industry.

10. Avoiding Statistical Mistakes Using Simpson’s Paradox:

Data gathering and trend analysis are essential in marketing, but a good understanding of mathematical statistics helps avoid intuitive mistakes . For example, consider an advertising campaign targeting Android and iOS users. Initial data may suggest that iOS users are more responsive. However, a careful statistical analysis, as described in our article “ Simpson’s Paradox: A Real-Life Example (from Marketing) ,” may reveal that Android users, particularly tablet users, actually click on ads more frequently. This contradiction highlights the importance of accurate statistical interpretation and the careful use of mathematics in decision-making.

Math Problems in Digital Agriculture

In the modern era, agriculture is becoming increasingly digitalized, with sensors and artificial intelligence playing vital roles in farm management. Mathematics is integral to this digital transformation, aiding in data analysis, weather prediction, soil parameter measurement, irrigation scheduling, and more. Here’s an example of a real-world math problem in digital agriculture:

11. Combatting Pests with Negative Numbers:

Negative numbers are utilized in agriculture to determine the direction of movement, similar to how they’re used on a temperature scale where a plus sign indicates an increase and a minus sign indicates a decrease. In agricultural sensors, plus and minus signs may indicate whether pests are moving towards or away from plants. For instance, a plus sign could signify movement towards plants, while a minus sign indicates movement away from plants. Understanding these directional movements helps farmers combat pests effectively. Our article, “ Negative Numbers: A Real-Life Example (from Agriculture) ,” provides detailed explanations and examples of how negative numbers are applied in agriculture.

Math Problems in DIY Projects

In do-it-yourself (DIY) projects, mathematics plays a crucial role in measurements, calculations, and problem-solving. Whether you’re designing furniture, planning home renovations, crafting handmade gifts, or landscaping your garden, math provides essential tools for precise measurements, material estimations, and budget management. Here’s an example of a real-world math problem in DIY:

12. Checking Construction Parts for Right Angles Using the Pythagorean Theorem:

The converse of the Pythagorean theorem allows you to check whether various elements – such as foundations, corners of rooms, garage walls, or sides of vegetable patches – form right angles. This can be done quickly using Pythagorean triples like 3-4-5 or 6-8-10, or by calculating with square roots. This method ensures the creation of right angles or verifies if an angle is indeed right. Our article, “ Pythagorean Theorem Converse: A Real-Life Example (from DIY) ,” explains this concept and provides an example of how to build a perfect 90° foundation using the converse of the Pythagorean theorem.

Math Problems in Entertainment and Creativity

Mathematics plays a surprisingly significant role in the creative industries, including music composition, visual effects creation, and computer graphic design. Understanding and applying mathematical concepts is essential for producing engaging and attractive creative works. Here’s an example of a real-world math problem in entertainment:

13. Controlling Stage Lamps with Linear Functions:

Linear and quadratic functions are essential components of the daily work of lighting specialists in theaters and event productions. These professionals utilize specialized software and controllers that rely on algorithms based on mathematical functions. Linear functions, in particular, are commonly used to control stage lamps, ensuring precise and coordinated lighting effects during performances. Our article, “ Linear Function: A Real-Life Example (from Entertainment) ,” delves into this topic in detail, complete with animations that illustrate how these functions are applied in practice.

Math Problems in Healthcare

Mathematics plays a crucial role in solving numerous real-world problems in healthcare, ranging from patient care to the design of advanced medical devices. Here are several examples of real-world math problems in healthcare:

14. Calculating Dosage by Converting Time Units:

Nurses frequently convert between hours, minutes, and seconds to accurately administer medications and fluids to patients. For example, if a patient requires 300mL of fluid over 2.5 hours, nurses must convert hours to minutes to calculate the appropriate drip rate for an IV bag. Understanding mathematical conversions and solving proportions are essential skills in nursing. Check out our article, “ Converting Hours to Minutes: A Real-Life Example (from Nursing) ,” for further explanation.

15. Predicting Healthcare Needs Using Quadratic Functions:

Mathematical functions, including quadratic functions, are used to make predictions in public health. These predictions are vital for estimating the need for medical services, such as psychological support following traumatic events. Quadratic functions can model trends in stress symptoms over time, enabling healthcare systems to anticipate and prepare for increased demand. Our article, “ Parabola Equation: A Real-Life Example (from Public Health) ,” provides further insights and examples.

16. Predicting Healthcare Needs Using Piecewise Linear Functions:

Piecewise linear functions are useful for describing real-world trends that cannot be accurately represented by other functions. For instance, if stress symptoms fluctuate irregularly over time, piecewise linear functions can define periods of increased and decreased stress levels. Our article, “ Piecewise Linear Function: A Real-Life Example (From Public Health) ,” offers an example of how these functions are applied.

17. Designing Medical Prostheses Using the Pythagorean Theorem:

The Pythagorean theorem is applied in the design of medical devices , particularly prostheses for traumatic recovery. Components of these devices often resemble right triangles, allowing engineers to calculate movement and placement for optimal patient comfort and stability during rehabilitation. For a detailed explanation and animations, see our article, “ The 3-4-5 Triangle: A Real-Life Example (from Mechatronics) .”

18. Illustrating Disease Survival Rates Using Cartesian Coordinate Plane:

In medicine, Cartesian coordinate planes are utilized for analyzing historical data, statistics, and predictions. They help visualize relationships between independent and dependent variables, such as survival rates and diagnostic timing in diseases like lung cancer. Our article, “ Coordinate Plane: A Real-Life Example (from Medicine) ,” offers a detailed exploration of this concept, including analyses for both non-smoking and smoking patients.

Math Problems in Industry

Mathematics plays a vital role in solving numerous real-world problems across various industries. From designing industrial robots to analyzing production quality and planning logistics, math is indispensable for optimizing processes and improving efficiency. Here are several examples of real-world math problems in industry:

19. Precise Movements of Industrial Robots Using Trigonometry:

Trigonometry is extensively utilized to direct and control the movements of industrial robots. Each section of an industrial robot can be likened to a leg or hypotenuse of a right triangle, allowing trigonometry to precisely control the position of the robot head. For instance, if the robot head needs to move 5 inches to the right, trigonometry enables calculations to ensure each section of the robot moves appropriately to achieve the desired position. For detailed examples and calculations, refer to our article, “ Find the Missing Side: A Real-life Example (from Robotics) .”

20. Measuring Nanoparticle Size via Cube Root Calculation:

Mathematics plays a crucial role in nanotechnology, particularly in measuring the size of nanoparticles. Cube roots are commonly employed to calculate the size of cube-shaped nanoparticles. As nanoparticles are extremely small and challenging to measure directly, methods in nanotechnology determine nanoparticle volume, allowing for the calculation of cube root to determine the size of the nanoparticle cube side. Check out our article, “ Cube Root: A Real-Life Example (from Nanotechnology) ,” for explanations, calculations, and insights into the connection between physics and math.

21. Understanding Human Emotions Using Number Codes for Robots:

Mathematics is employed to measure human emotions effectively, which is essential for building smart robots capable of recognizing and responding to human emotions. Each human emotion can be broken down into smaller features, such as facial expressions, which are assigned mathematical codes to create algorithms for robots to recognize and distinguish emotions. Explore our article, “ Psychology and Math: A Real-Life Example (from Smart Robots) ,” to understand this process and its connection to psychology.

22. Systems of Linear Equations in Self-Driving Cars:

In the automotive industry, mathematics is pivotal for ensuring the safety and efficiency of self-driving cars. Systems of linear equations are used to predict critical moments in road safety, such as when two cars are side by side during an overtaking maneuver. By solving systems of linear equations, self-driving car computers can assess the safety of overtaking situations. Our article, “ Systems of Linear Equations: A Real-Life Example (from Self-Driving Cars) ,” provides a comprehensive explanation, including animated illustrations and interactive simulations, demonstrating how linear functions and equations are synchronized with car motion.

Math Problems in Information Technology (IT)

Mathematics serves as a fundamental tool in the field of information technology (IT), underpinning various aspects of software development, cybersecurity, and technological advancements. Here are some real-world math problems encountered in IT:

23. Selecting the Right Word in Machine Translation Using Mathematical Probability:

Theoretical probability plays a crucial role in AI machine translation systems, such as Google Translate, by aiding in the selection of the most appropriate words. Words often have multiple translations, and theoretical probability helps analyze the frequency of word appearances in texts to propose the most probable translation. Dive deeper into this topic in our article, “ Theoretical Probability: A Real-Life Example (from Artificial Intelligence) .”

24. Creating User-Friendly Music Streaming Websites Using Mathematical Probability:

Probability is utilized in user experience (UX) design to enhance the usability of digital products , including music streaming websites. Recommendation algorithms calculate theoretical probability to suggest songs that users are likely to enjoy, improving their overall experience. Learn more about this application in our article, “ Theoretical Probability: A Real-Life Example (from Digital Design) .”

25. Developing Realistic Computer Games with Vectors:

Mathematics is essential in animating objects and simulating real-world factors in computer games. Vectors enable game developers to incorporate realistic elements like gravity and wind into the gaming environment. By applying vector addition, developers can accurately depict how external forces affect object trajectories, enhancing the gaming experience. Explore this concept further in our article, “ Parallelogram Law of Vector Addition: A Real-Life Example (from Game Development) .”

26. Detecting Malicious Bots in Social Media Using Linear Inequalities:

Mathematical inequalities are valuable tools in cybersecurity for identifying malicious activity on social media platforms. By analyzing behavioral differences between real users and bots—such as friend count, posting frequency, and device usage—cybersecurity experts can develop algorithms to detect and block suspicious accounts. Discover more about this application in our article, “ How to Write Inequalities: A Real-life Example (from Social Media) .”

27. Increasing Computational Efficiency Using Algebraic and Rational Expressions

Algebraic and rational expressions are crucial in computer technology for increasing computational efficiency . Every step in a computer program’s algorithm requires valuable time and energy for execution. This is especially important for programs used in various safety and security systems. Simplifying these expressions helps boost computational performance. Our article, “ Algebraic and Rational Expressions: A Real-Life Example (from Computer Technology) ,” explains this in detail.

Math Problems in Legal Issues

In legal proceedings, mathematics plays a crucial role in analyzing data and making informed decisions. Here’s a real-world math problem encountered in legal work:

28. Proving the Reliability of Technology in Court Using Percentages:

In certain court cases, particularly those involving new technologies like autonomous cars, lawyers may need to employ mathematical methods to justify evidence. Percentage analysis can be utilized to assess the reliability of technology in court. For instance, in cases related to self-driving cars, lawyers may compare the percentage of errors made by autonomous vehicles with those made by human drivers to determine the technology’s safety. Delve deeper into this topic in our article, “ Solving Percent Problems: A Real-Life Example (from Legal) .”

Math Problems in Safety and Security

In the realm of safety and security, mathematics plays a vital role in protecting people, nature, and assets. Real-world math problems in this field can involve reconstructing crime scenes, analyzing evidence, creating effective emergency response plans, and predicting and responding to natural disasters. Here are two examples:

29. Reconstructing a Crime Scene with Inverse Trigonometry:

Forensic specialists rely on mathematical methods, such as inverse trigonometry, to uncover details of crimes long after they’ve occurred. Inverse trigonometric functions like arcsin, arccos, and arctan enable forensic specialists to calculate precise shooting angles or the trajectory of blood drops at crime scenes. Dive into this topic in our article, “ Arctan: A Real-Life Example (from Criminology) .”

30. Responding to Wildfires with Mathematical Variables:

Variables in mathematical language are also prevalent in real-world scenarios like firefighting. For instance, when dealing with wildfires, independent variables like forest type, wind speed and direction, rainfall, and terrain slope influence fire spread speed (dependent variable) . By utilizing specialized formulas incorporating these variables, fire protection specialists can accurately predict fire paths and optimize firefighting efforts. Explore this practical application in our article, “ Dependent and Independent Variables: A Real-Life Example (from Fire Protection) .”

Math Problems in Weather and Climate

In the realm of weather and climate, mathematics is crucial for creating mathematical models of Earth’s atmosphere, making weather forecasts, predicting weather patterns, and assessing long-term climate trends. Here’s an example:

31. Forecasting Thunderstorms with Negative Numbers:

Negative numbers play a significant role in forecasting thunderstorms. The probability of thunderstorms is closely tied to the temperature differences between air masses in the atmosphere. By subtracting negative numbers (representing temperature values) and analyzing the results, meteorologists can forecast the likelihood of thunderstorms based on the temperature differentials. Dive deeper into this concept in our article, “ Subtracting Negative Numbers: A Real-Life Example (from Weather Forecast). “

Conclusions

Many students perceive math as disconnected from the real world, leading them to question its relevance. Admittedly, maintaining this relevance is no easy feat—it requires collective effort. Farmer Alfred can’t tackle this challenge alone. However, introducing more real-world math examples into the school curriculum is a crucial step. Numerous studies have demonstrated that such examples significantly enhance students’ motivation to learn math. Our own pilot tests confirm this, showing that a clear connection between real-world problems and math education profoundly influences how young people view their future careers.

Therefore, to increase the overall relevance of math education and motivate students, we must prioritize the integration of real-world examples into our teaching practices. At DARTEF, we are dedicated to this cause, striving to bring authenticity to mathematics education worldwide.

• Vos, Pauline. ““How real people really need mathematics in the real world”—Authenticity in mathematics education.” Education Sciences  8.4 (2018): 195.
• Cambridge dictionary, Meaning of problem in English.
• Reif, Frederick.  Applying cognitive science to education: Thinking and learning in scientific and other complex domains . MIT press, 2008.

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65+ Real-World Project-Based Learning Ideas for All Ages and Interests

Find and implement solutions to real-world problems.

Project-based learning is a hot topic in many schools these days, as educators work to make learning more meaningful for students. As students conduct hands-on projects addressing real-world issues, they dig deeper and make personal connections to the knowledge and skills they’re gaining. But not just any project fits into this concept. Learn more about strong project-based learning ideas, and find examples for any age or passion.

What is project-based learning?

Project-based learning (PBL) uses real-world projects and student-directed activities to build knowledge and skills. Kids choose a real-world topic that’s meaningful to them (some people call these “passion projects”), so they’re engaged in the process from the beginning. These projects are long-term, taking weeks, months, or even a full semester or school year. Students may complete them independently or working in small groups. Learn much more about project-based learning here.

What makes a good PBL project?

In many ways, PBL is more like the work adults do in their daily jobs, especially because student efforts have potential real-world effects. A strong PBL project:

• Addresses a real-world issue or problem
• Requires sustained and independent inquiry, in and out of the classroom
• Allows students voice and choice throughout the project
• Combines elements of many disciplines
• Includes collaboration with public partners, such as universities, community organizations, or businesses
• Produces a public product that is seen by those outside the school community
• Covers a complete process, including activities like research, design, production, marketing or public awareness, and enlisting supporters or investors

Outdoor Project-Based Learning Ideas

• Create a new local park, or improve an existing one by adding new features or providing needed maintenance.
• Plant a community garden to provide food for a soup kitchen, food pantry, or other organization.
• Design and create a butterfly, pollinator, or other wildlife garden to support the local ecosystem.
• Build a new walking or biking trail that’s safe for people of all ages to use.
• Devise and implement a way to reduce litter in your community.
• Set up and manage a school or community compost pile, and distribute the resulting soil to those who need it most.
• Find and help the public use a new way to grow food that requires less soil, water, or fertilizers, which are in short supply in some parts of the world.
• Design, build, and install a completely unique piece of playground equipment that serves a specific purpose or need.

School Community Project-Based Learning Ideas

• Start a comprehensive recycling program at school, or substantially improve participation in an existing one.
• Add collaborative artwork like murals or other displays to school hallways, bathrooms, or grounds.
• Determine a location or program at your school that needs improvement, then make a plan, raise the funds, and implement your ideas.
• Come up with ways to celebrate your school’s diversity and improve relationships between all students.
• Start and run a school store , including inventory, financial plans, and marketing.
• Write a school handbook for new students, with tips and tricks for helping them feel at home.
• Figure out how to offer healthier, better-tasting meals and snacks in the school cafeteria.
• Implement a mentoring program for older students to help younger students, with planned activities and appropriate training for older students.
• Design and propose a new style of grading system that ensures equity.
• Find ways to improve the indoor recess experience at your school.
• Set up and run a new school newspaper, magazine, podcast, video channel, etc.

Greater Community Project-Based Learning Ideas

• Coordinate a community art project in a central location to celebrate local culture or artists.
• Set up a program for schoolkids to socialize with senior citizens in nursing homes, hospitals, or retirement communities.
• Create a program to offer free translation services for ESL families in the community.
• Help a local animal shelter improve its facilities, or find new ways to match homeless pets with their forever families.
• Build and maintain Little Free Libraries around your community, especially in underserved areas.
• Help local businesses become more environmentally conscious, increasing sustainability and decreasing waste.
• Create and lead a walking tour of your community, highlighting its culture, history, landmarks, and more.
• Find a way to record and celebrate local voices in your community’s history.
• Come up with ideas for welcoming immigrants and other newcomers to your community.
• Set up a series of events that will encourage the community to mix and experience each others’ foods, cultures, and more.
• Create and implement a new program to inspire a love of books and reading in preschool students.
• Set up and help run a new charitable organization your community needs.

Social Issues Project-Based Learning Ideas

• Start an awareness campaign on a topic that’s important to you, like anti-bullying, healthy living, protecting the environment, civil rights, equality and equity, etc.
• Come up with and implement ways to increase voter turnout in your community, especially among younger voters.
• Write, record, and share with a wider audience your own TED Talk–style video on an issue that hasn’t been covered yet or on which you have a unique perspective.
• Devise and implement ways for unheard voices to be amplified in your school or community.
• Write and publicly perform a play that highlights a social issue that’s important to you.
• Look for areas in your community that present challenges to those with disabilities, and help to improve them to overcome those challenges.
• Research, write, and publicly present and defend a position paper on an issue that’s important to your community.
• Choose a real court case, then research the law and work with legal experts to prepare and present your own case as you would in a courtroom.
• Write, edit, seek, and incorporate real-world feedback, and publish or publicly present your own book, poem, or song on an issue that’s important to you.
• Start a program to teach a specific group (e.g., preschoolers, senior citizens, business owners) to care for and protect the environment.
• Plan and hold a fundraiser to support an issue you care about.
• Choose a law you feel is unjust, and write, research, and publicly present and defend a position paper about your desired change.

STEM Project-Based Learning Ideas

• Create an app that meets a specific purpose for a specific audience.
• Invent something new that the world needs, and then fund, create, and sell your product in the community.
• Design a game to help students learn important STEM concepts.
• Find a simple way to improve an existing product, especially if it cuts costs or improves environmental sustainability.
• Explore ways to reduce the amount of waste we produce, especially plastic and other landfill-bound items.
• Write a book or graphic novel that’s entertaining but also teaches kids about science or math.
• Devise new ways to provide clean drinking water to communities where water is scarce.
• Build an effective solar oven people can use to cook during extended power outages, or in areas where electricity isn’t available.
• Work with a university or STEM organization to gather, analyze, and present real-world scientific data.
• Design a building to fit a specific purpose or need, including researching the requirements and zoning laws, accurately drafting a plan, determining the costs, and presenting the plan to the proposed client.
• Create an interactive hands-on exhibit to teach people about STEM concepts.
• Determine a type of website you believe is missing, then research, build, and publish the site you envision.

Creative Arts Project-Based Learning Ideas

• Organize an art show for the community, seeking out those who ordinarily might not have a chance to display their work.
• Create and teach an art class in your area of expertise to children, the elderly, or another segment of the population.
• Design a mural for an area in your community that needs beautification, and seek funding or other assistance from community members to install it.
• Write a play about a topic that’s meaningful to you or your community. Work with the community to stage a performance for all to attend.
• Invite local dancers to perform at a school or community Festival of Dance, highlighting a variety of cultures and dance styles.
• Start a regular writer’s workshop where community writers can come together to share and seek feedback. Invite local authors or publishing experts to speak as guests.
• Collect stories, poems, and essays from local authors, and put them together into a book. Sell the book to raise money for a cause that’s important to local writers.
• Gather singers or instrumentalists from your community into a choir or band. Put on a concert to raise money for a special cause, or take your choir on tour to local retirement homes, hospitals, etc.
• Write a song about a person or cause that’s important to you. Produce and record the song, then find a way to share it with others.
• Make a short film about a local hero, community event, or local place. Invite others to do the same, and organize a local film festival.

What are some your favorite project-based learning ideas? Come share your thoughts in the We Are Teachers HELPLINE group on Facebook !

Plus, meaningful service learning projects for kids and teens ..

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What Is Project-Based Learning and How Can I Use It With My Students?

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Immerse your students in creative, real-world problem solving with Mindsets

Educators will be introduced to the best practices around planning, integrating, and facilitating real-world learning in their classroom through the Mindsets Learning instructional platform.

Learning objectives

In this module, you will:

• Describe how to use key components of a Mindsets Challenge
• Identify sequencing and timing options for Mindsets Challenges
• Plan for using a Mindsets Challenge
• List best practices around facilitating a Mindsets Challenge
• Plan to implement a project-based extension of a Mindsets Challenge

ISTE Standards for Educators :

• Educator - Facilitator
• Educator -Collaborator
• Leaders - Connected Learner

Prerequisites

• Introduction min
• What are the key components of a Mindsets Challenge? min
• What are sequencing and timing options for Mindsets Challenges? min
• How to prepare for a Mindsets Challenge min
• How to facilitate a Mindsets Challenge min
• How to extend the Mindsets Challenge experience min
• Knowledge check min
• Summary min

Creative Problem Solving Examples That Solved Real World Problems

Not all problems have simple, straightforward solutions. And the more we try to solve these problems with basic techniques, the worse the problems get. Real-world problems are messy and complicated, and they require a creative approach to problem solving. In this post, we’ll share a range of real-world creative problem solving examples from the human-centred design work of Overlap Associates.

When there isn’t a straightforward answer, it’s time for another approach—one that puts all of the people involved at the forefront of decision making.

What is Creative Problem Solving?

Creative problem solving applies human-centred design principles, practices, and tools to complex problems, enabling individuals, teams, and organizations to unlock innovation and navigate uncertainty in a rapidly changing world. It’s all about tapping into the unknown to uncover brand new solutions—ones you’ve never thought of before or didn’t know were possible.

The more complex a problem is, the more nuanced and layered the solution needs to be. Creative problem solving requires that you separate divergent thinking (idea generation and brainstorming) from convergent thinking (idea evaluation and decision making) as opposed to trying to do both at once. 

Creative problem solving involves gathering observations, asking questions, and considering a wide range of perspectives.

Let’s discuss complex, real-world problems that were solved using creative problem solving and human-centred design techniques. 

Creative Problem Solving Examples

Example #1: adapting customer service to evolving customer expectations and needs.

The Complex Problem:

Customer service always has room for improvement, and the insurance industry is no exception. Tensions run high when receiving claims, and it is critical that customers feel both comfortable and satisfied with the claims experience. Gore Mutual was at a standstill with a 97% customer satisfaction rating, but the company wanted to do more. As customer expectations and needs continue to evolve, how can customer service continue to improve?

Creative Problem Solving Methods:

In order to improve customer satisfaction, Gore Mutual first needed to understand the experiences of all relevant stakeholders in the claims process, which included customers, brokers, and service providers. Acknowledging the role of each group in the overall claims experience would create a clear customer journey.

Overlap led a series of engagement sessions and gathered feedback from all groups involved in the customer journey to better understand where the journey could be improved. Methods of information gathering included in-person interviews, interactive Stakeholder Lab workshops, and observational research of spaces, such as dispatch centres, digital platforms, contractors’ shops, and customer meetings. 

This thorough approach went beyond simple satisfaction surveys to paint a detailed picture of the entire customer journey. A Journey Map , a design tool for capturing new ways of looking at someone’s experience, was used to guide research collection. 

In the end, a nuanced insights report was created to outline the current and ideal future state of navigating the claims process. With this ideal claims journey in mind, Gore Mutual established ClaimCare, a new approach to claims processing, which included improvements such as a Concierge for inquiries, a Mobile Response Team, and a Mobile Response Centre for catastrophes.

Learn more about the Service Design Project with Gore Mutual Insurance .

Example #2: Developing Inclusive Online Facilitation in the Midst of a Pandemic

The Complex Problem: 

The beginning of the pandemic left businesses scrambling to find inventive ways to hold in-person meetings and events. How do you create engaging facilitation without experiencing the intangible moments that come with face-to-face, in-person connection? How do you develop online facilitation that’s engaging and accessible to everyone in the midst of overwhelming Zoom fatigue? How do you implement technology in order to be effective while also not alienating those who are unfamiliar or struggle with new technology? 

Like many businesses, The Schlegel-UW Research Institute for Aging (RIA) was caught in the dramatic shift to online methods that occurred in the early days of the pandemic. They knew they needed to adopt new technology in order to thrive—or even survive—but they didn’t want engagement to suffer or for those less technologically inclined to be left behind. 

Using the lens of creative problem solving and human-centred design techniques, RIA was able to translate all they previously knew about facilitation into an adaptive and inclusive online approach. It was essential to find tools and solutions that were simple to navigate and accessible to everyone on the RIA team, as well as those RIA works with. 

Overlap provided these tools and the training required to implement online facilitation quickly and effectively while sharing insight into how to spot unconscious bias, how to lead an accessible session, and how to apply diversity, equity, and inclusion across all online communication. Keeping human-centred design principles top-of-mind ensured all voices were heard, and no one was left behind in the transition. 

Learn more about Developing New Training for Great Online Facilitation .

Example #3: Improving the Experiences of Aging Adults

Aging is a deeply personal and challenging experience. How can caregivers better understand the experiences of older adults? Instead of grouping every senior together, how can care be designed to meet the needs of all subgroups of aging adults? For example, newcomers, people who identify as LGBTQ+, and people with dementia may require or prefer different methods of service.

To solve this complex problem, Overlap deployed design teams to complete high-touch, day-long ethnography as well as low-touch, three-minute surveys to gather a wealth of data that could inform decision making. Overlap used the findings and insights to develop a thorough and wide-ranging set of design principles for serving older adults.

A comprehensive toolkit was designed to help service providers co-design alongside older adults. The toolkit included practical, creative problem solving techniques and guided design thinking practices to ensure everyone affected was involved in the process. In addition to the toolkit, training was provided directly to caregivers to ensure all gaps in service and understanding were bridged.

Directly involving aging adults from all walks of life, their loved ones, and their caregivers meant the decision making process was thoroughly informed, which enabled care to be adapted to meet the needs of all individuals. 

Learn more about the Aging By Design Project in New York State .

Learning More About the Design Thinking Process

Overlap has a suite of courses that have been carefully designed to bring design thinking training to anyone ready to learn. We share tools and strategies that will help you and your team make better decisions. 

Our wide range of courses include practical and engaging materials that will help you work better together, understand your customers, and navigate complex challenges. 

The Exploring Complex Problems course focuses on how to solve complex, real world problems using creative problem solving methods. It’s a deep dive into the Define and Research phases of the human-centred design cycle and demonstrates why remaining in the problem space and iterating between these two phases creates a strong foundation for ideation. 

Learn more: Why Every Team Needs Human-Centred Design Training .

If you want to continue developing your creative problem solving skills, follow us on social media and sign up for our monthly newsletter to stay informed about our latest training schedule, new courses, and free resources!

An Introduction to Complex Problem Solving

Why every team needs human-centred design training.

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Unfulfilled Promise: The Forty-Year Shift from Print to Digital and Why It Failed to Transform Learning

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Focusing on how making a difference has emerged as one of the most powerful learning experiences.

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This campaign will serve as a road map to the new architecture for American schools. Pathways to citizenship, employment, economic mobility, and a purpose-driven life.

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We share stories that highlight best practices, lessons learned and next-gen teaching practice.

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About Getting Smart

Getting smart collective, impact update, 4 tools to connect students to real world math, yummymath.com.

This awesome website provides teachers with ready to use lessons and resources to bring real-life math into the classroom. Authored by real math teachers, Brian Marks and Leslie Lewis , the creative team at YummyMath is working hard to publish new activities every week to help teachers and students explore math in interesting and familiar real world contexts. The lessons are aligned to Common Core Standards and organized by strands, genres, grade level, and categories. The activities are designed to engage students and encourage them to reason, think critically and communicate. No special tech expertise is needed to access the activities and use them with students.

GetTheMath.org

GetTheMath.org, by thirteen.org, uses short videos to demonstrate how algebra is used in the real world.  The videos introduce students to real world professions that require the use of algebra. The videos explore a number of fields including music, fashion, video games, and basketball, and they feature professionals in non-traditional roles. The videos are are fun, engaging and designed to speak to students by using an interactive video game format. Each video includes a problem-solving challenge for students to complete and it also provides extended learning opportunities. The website also includes lesson plans and professional development videos for teachers. Use this site to capture the interest of middle school and high school students.

TedEd The popular YouTube based learning platform supports a growing video library of amazing educational videos, with a series titled   Math in Real Life .  The “Find and Flip” feature of TedED allows users to easily create customized lesson around any YouTube video. Teachers can add a variety of questions, notes, discussion starters and resources to help students dig deeper into the content presented. Start by exploring some of the lessons created by other educators, then explore videos available in YouTube and use the TedED tools to create your own connected math videos. Share your flipped videos through a variety of social media platforms or by embedding them into a website or online learning platform.

RealWorldMath.org

This outstanding resource explores real world math through challenges and concepts presented in the the virtual world of Google Earth, with occasional help from SketchUp. The lessons build on traditional classroom instruction by providing students with real world scenarios that engage them in the application of concepts combined with problem-solving. The lessons are technology based, so they can be used in the classroom or completed at home. There are a variety of different types of lessons to choose from.

• Concept lessons are designed to target specific math concepts, often in real world settings and situations.
• Measurement lessons demonstrate how linear measurement can be applied to real world problems.
• Project-Based Learning activities are intended to build upon previous knowledge and offer opportunities to utilize it.
• Exploratory lessons go beyond traditional textbook mathematics that focus arithmetic, algebra, and geometry to include a wide range of investigations into math topics that are utilized in the real world.
• Space lessons connect math with science and extend the learning to outer space through the use of Google Sky, Moon and Mars.

Final Thoughts

When we help students understand how the work we do in school is related to their own world, we personalize learning. When we provide students with opportunities to apply the learning and use the acquired skills for reasons beyond passing a test or getting a good grade, we inspire them to love learning!

SusanOxnevad

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Kalonde harrington.

I wanted to know how children apply mathematics when they are shopping, playing games, sharing things, traveling and farming.

Thank you very much for the websites ....

We've recently launched Panjango which shows young people how their knowledge of maths (and English and science) is applied in the world of work. Panjango is free to use for young people and schools. Check it out at panjango.online. The platform also helps young people develop the skills they need to thrive in life after school - and to explore the world of work in a more fun, interactive and meaningful way.

I look for ways to teach math to kids in a fun way where kids really enjoy math. I include whatever I get, from props to culture, from activities to worksheets, from stories to games. Like I loved these worksheets on Halloween themes (https://logicroots.com/math-worksheets/halloween-theme/) and my kids enjoyed the stories with math. These are free resource and a great help for me.

Miryam Hernandez

Thank you for the information.

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PBL Projects

Engaging Students in STEM with Problem Based Learning

Introduction to PBL

What is pbl.

Problem Based Learning (PBL) is an educational method that engages students in inquiry-based “real world” problem-solving. Used extensively in medical education since the 1970s, PBL is an instructional approach that teaches students “what to do when you don’t know what to do” by collaboratively solving authentic open-ended problems. While already adopted in fields including business and law, it is only beginning to emerge in science, technology, engineering and mathematics (STEM) education.

PBL is an exciting and challenging alternative to traditional lecture-based instruction, providing students with learning experiences that engage them directly in the types of problems and situations they will encounter in the 21st century workplace. Students of PBL become active participants in their own learning as they encounter new and unfamiliar learning situations where problem parameters are ill-defined and ambiguous —just like in the real world.

PBL can be implemented in many ways but there are elements common to all:

• Problems are presented before any formal instruction; the problem itself drives the learning of new information.
• Students work collaboratively in teams to frame the problem, research necessary information and propose and present solutions.
• The instructor acts as a facilitator who provides instruction to teams as needed and guides students as necessary to keep them on track.

Research shows that compared with traditional lecture-based instruction, PBL improves:

• Student understanding and retention of ideas.
• Critical thinking and problem-solving skills.
• Motivation and learning engagement.
• The ability to work in teams.
• The ability to successfully apply skills and knowledge to new situations.

The PBL Challenge model is designed to scaffold student learning by acclimating students to PBL through their own learned experience. Instructors have the ability to choose an implementation approach ranging from highly structured( instructor led , least student autonomy)to open-ended (instructor as facilitator , most student autonomy) based on students’ experience with PBL.

What Students Say About the PBL Challenges

PBL was a very rewarding experience for me. It was way different from normal learning. I felt like an actual scientist instead of just a student in high school. If PBL was an every day or weekly activity it would help kids a lot, because when you are just sitting at a desk and teachers are giving you information it’s really boring, but when I have to find the information on my own it sticks with me.” –Taft Union High School, CA

Now, I feel that manufacturing isn’t just about making/building products, it is about quality, efficiency, productivity, and also taking the products that are already manufactured and redesign[ing] them with the latest technology.” –Taconic High School, MA

Initially, I was overwhelmed by all the technical aspects considering I am not from any sort of science/math/tech background, and didn’t really feel I had any solutions to contribute. But the combined effort and brainpower of the whole group was really helpful and I think I learned a lot.” –Three Rivers Community College, CT

I enjoyed the problem-based aspect of everything. It got my mind thinking in a way I have never used it!” –Rhode Island College, RI

PBL teaches you what to do when you don’t know what to do. First, by process of elimination, you learn what you do know and then it gives you clear steps on how to go about researching the parts that you don’t know. The ‘Whiteboards’ helped me with time management, taught me what to do, when to do it, and helped me not to be afraid of a problem, to tackle a problem that I had never seen before and to come up with an answer that was at least close to the mark. That was very valuable.” –Springfield Technical Community College, MA

What Instructors Say About the PBL Challenges

It’s never too early for our students to begin problem-solving. By the time they’ve reached fifth grade, they’ve already started to learn the game of school—they’ve learned that if they just memorize some stuff, regurgitate it back on a piece of paper, they’re going to skate by and be fine. But if they’re given some kind of problem that requires them to come up with their own solution, that’s where they struggle.” –Sharon Center School, CT

Problem-based learning allows students an opportunity for collaboration and problem solving that will develop critical thinking skills, reading and research skills, argumentation and presentation skills. Awesome projects!” –CREC Magnet Middle School, CT

I enjoy using PBL in my classes because I can see how it gives the students a good framework to solving any problem they encounter. I like having the Whiteboards for the students to use as an organizer for all the information they need. I really enjoy watching the students present their solutions to the class. I have had a positive experience with the PBL Challenges and I plan on using and developing more of them in the future.” –Ponaganset High School, RI

Students seemed to like problem-based learning! They were engaged in solving the problem, and most pushed themselves and their teammates to better understand the issues. I found that they were nervous about defining the problem incorrectly at first, but that they got past this trepidation as they dug deeper into the possible solutions. I was impressed with the solutions the student teams developed.” –Stonehill College, MA

PBL forces us to slow down and get a lot more quality into our lesson, to dig deeper into the materials rather than get this thing done and move on to the next.” –Central Connecticut State University, CT

What Industry Partners Say About the PBL Challenges

Problem-based learning is such an important aspect of career development.It is something that is not fully utilized in the classroom setting since students don’t always understand how the practical aspects of what they are doing—like math—connect to what they will be doing in the workforce. Without PBL, that disconnect continues, and it also impedes the interest a lot of people might have to moving into certain careers. They might say ‘Well I am not good at math, so I can’t do that’, but when they understand how they’re connected, it might peak that level of interest and make them realize they can overcome some of the ideas they have of themselves.” –CEO, Sound Manufacturing, CT

Because we need good, quality technical personnel, anything that we can contribute to science education and particularly to local science and engineering education is valuable to us.” –Senior Director of Special Programs, Cirtec, MA

Our clients expect us to be strong problem-solvers and it’s important that our employees and our management system aligns to strong problem-solving.” –Manufacturing & Operations Director, Global Foundries (formerly IBM), VT

When I started here, we would approach problem-solving in a much different way than we do now—we would essentially jump to conclusions, jump to what we thought was the answer and sometimes the problems would re-occur because we really didn’t get to the true root cause. By following the structure of problem-solving, it forces the discipline…to gather data. It’s really a powerful process that we’ve seen work exceptionally well. I wish I had it in my career thirty years ago.” –Core Team Member, Global Foundries (formerly IBM), VT

PBL actively engages students in the problem-solving process with problems that have real applications and many times aren’t as well structured as end of chapter problems found in lecture-based textbooks…Once our company learned of STEM PBL, we realized it was the vehicle to provide problem-based learning to a larger audience of students without compromising our company’s productivity. Collaborating with STEM PBL is an investment in the future. As these students complete their education and enter the work force, their ability to critically think and solve real-world problems will be an asset for any company.” –Technology Company, STEM PBL

Engaging Problem Solving Activities For High School Students

In today’s world, strong problem solving skills are more important than ever before. Employers highly value candidates who can think critically and creatively to overcome challenges. If you’re looking for ways to sharpen your high school student’s problem solving abilities, you’ve come to the right place.

Here’s a quick overview of the top problem solving activities we’ll cover in this guide: group challenges like escape rooms, individual logic puzzles and riddles, project-based learning through coding and engineering tasks, and conversational problem solving through Socratic seminars.

Group Challenges and Escape Rooms

Engaging high school students in problem-solving activities is crucial for their cognitive development and critical thinking skills. One popular and effective approach is through group challenges and escape rooms.

These activities not only promote teamwork and collaboration but also provide an exciting and immersive learning experience.

What Are Escape Rooms and Why Are They Effective?

Escape rooms are physical adventure games where participants are “locked” in a room and must solve puzzles and find clues to escape within a set time limit. These rooms are designed to challenge participants’ problem-solving abilities, logical thinking, and decision-making skills.

            View this post on Instagram                         A post shared by NoWayOut Premium Escape Rooms (@nowayout_dubai)

The immersive nature of escape rooms creates an exciting and high-stakes environment that motivates students to think creatively and work together as a team.

Research has shown that escape rooms are highly effective in improving students’ problem-solving and critical-thinking skills.

According to a study from BMC Medical Education , escape rooms improve student engagement and learning. This activity can increase motivation and enhance teamwork skills.

The challenging and interactive nature of escape rooms makes them a valuable tool for engaging high school students in problem-solving activities.

Tips for Creating Your Own Escape Room

If you want to create your own escape room for high school students, here are some tips to make it a memorable and effective experience:

• Theme and Storyline: Choose an engaging theme or storyline that will capture the students’ interest and make the experience more immersive.
• Puzzles and Challenges: Design a variety of puzzles and challenges that require critical thinking, problem-solving, and teamwork to solve.
• Time Limit: Set a reasonable time limit to create a sense of urgency and keep the students engaged throughout the activity.
• Feedback and Reflection: Provide feedback and encourage students to reflect on their problem-solving strategies and teamwork skills after completing the escape room.

Other Group Challenges and Problem Solving Activities

In addition to escape rooms, there are various other group challenges and problem-solving activities that can be implemented in high school settings . These activities can range from outdoor team-building exercises to classroom-based problem-solving tasks.

Outdoor activities such as scavenger hunts, obstacle courses, and ropes courses can foster teamwork, communication, and problem-solving skills. Classroom-based activities like brainstorming sessions, case studies, and simulation games can also provide opportunities for students to think critically and solve complex problems.

It is important for educators to select activities that align with the learning objectives and interests of their students. By incorporating these engaging group challenges and problem-solving activities into high school curricula, educators can empower their students to develop essential skills that will benefit them in their academic and professional lives.

Individual Logic Puzzles and Riddles

Benefits of logic puzzles.

Logic puzzles are a great way to engage high school students in problem-solving activities. These puzzles require students to think critically, analyze information, and use deductive reasoning to find solutions.

They help develop cognitive skills such as logical thinking, attention to detail, and problem-solving abilities. By solving these puzzles individually, students also learn to work independently and trust their own reasoning abilities.

According to Psychology Today , logic puzzles can improve memory, enhance problem-solving skills, and boost overall brain health. They provide mental stimulation and challenge students to think outside the box.

Moreover, logic puzzles are a fun and engaging way to learn, making the learning process enjoyable and captivating for high school students.

Examples of Engaging Logic Puzzles

There are various types of logic puzzles and riddles that high school students can enjoy. Here are a few examples:

• Grid-based puzzles: These puzzles require students to fill in a grid by using clues to determine the correct arrangement of elements. Sudoku is a popular example of a grid-based logic puzzle.
• Number series puzzles: In these puzzles, students need to find the missing number or the pattern in a given series of numbers. This helps develop numerical reasoning and pattern recognition skills.
• Mystery riddles: These riddles present a scenario or a problem that students need to solve by using logic and deduction. They often involve a crime or a mysterious situation that requires careful analysis to find the solution.

These examples are just a starting point, and there are countless logic puzzles and riddles available online or in puzzle books that can keep high school students engaged and challenged.

Tips for Using Riddles and Brain Teasers

When using riddles and brain teasers as problem-solving activities, it’s important to keep a few things in mind:

• Start with easier puzzles: Begin with puzzles that are relatively easy to solve, and gradually increase the difficulty level. This allows students to build confidence and develop their problem-solving skills.
• Encourage collaboration: While individual puzzles are beneficial, group activities can foster teamwork and collaboration. Consider incorporating group discussions or competitions to promote collaboration and peer learning.
• Provide hints and guidance: If students get stuck, offer hints or guidance to help them move forward. This prevents frustration and keeps the learning process enjoyable.
• Reflect on the solution: After solving a puzzle, encourage students to reflect on the problem-solving process. Discuss the strategies they used, the challenges they faced, and the lessons they learned. This promotes metacognition and helps students improve their problem-solving skills.

By incorporating individual logic puzzles and riddles into problem-solving activities, high school students can have a great time while developing essential cognitive skills and enhancing their ability to think critically and analytically.

Project-Based Learning Through STEM

Project-Based Learning (PBL) is an effective teaching method that encourages students to actively engage in real-world problem-solving . When combined with the subjects of Science, Technology, Engineering, and Mathematics (STEM), it creates a powerful learning experience for high school students.

PBL through STEM not only helps students develop critical thinking and problem-solving skills, but also fosters creativity, collaboration, and communication abilities.

            View this post on Instagram                         A post shared by SOAR STEM Schools (@soarstemschools)

Coding Challenges

Coding challenges are an excellent way to introduce high school students to the world of computer programming. These challenges allow students to apply their logical thinking and problem-solving skills to create programs or solve coding problems.

Online platforms like Codecademy provide a wide range of coding challenges and tutorials for students to enhance their coding abilities. These challenges can be related to creating games, building websites, or developing mobile applications.

By engaging in coding challenges, students not only learn coding languages but also gain an understanding of the importance of computational thinking in today’s technology-driven world.

Engineering and Design Thinking Projects

Engineering and design thinking projects involve hands-on activities that allow high school students to apply their knowledge of engineering principles and design concepts. These projects can range from building simple structures using everyday materials to constructing complex machines and systems.

Websites like TeachEngineering provide a plethora of project ideas and resources for educators and students. By engaging in these projects, students learn to think critically, analyze problems, and develop innovative solutions.

They also develop essential skills such as teamwork, communication, and time management.

Science Investigation and Experiments

Science investigation and experiments are fundamental to STEM education as they enable high school students to explore scientific concepts through hands-on experiences. These activities involve formulating hypotheses, conducting experiments, collecting data, and analyzing results.

Websites like Science Buddies offer a vast collection of science project ideas and resources for students of all ages. By engaging in scientific investigations and experiments, students not only deepen their understanding of scientific concepts but also develop skills such as observation, data analysis, and critical thinking .

Socratic Seminars

Socratic Seminars are a valuable tool for engaging high school students in problem-solving activities. Originating from the Socratic method of teaching, these seminars encourage students to think critically and engage in thoughtful discussions.

The goal of a Socratic Seminar is to delve deeper into a particular topic or text by asking open-ended questions and encouraging students to analyze and evaluate different perspectives. This method promotes active listening, respectful dialogue, and the development of critical thinking skills.

            View this post on Instagram                         A post shared by Gloucester City High School (@gloucester_highschool_lions)

One of the key aspects of a successful Socratic Seminar is the preparation of thought-provoking discussion questions. These questions should be open-ended and encourage students to think deeply about the topic being discussed.

A well-prepared question can spark lively and insightful conversations, allowing students to explore different viewpoints and develop their own ideas. It is important for the facilitator or teacher to carefully select questions that will challenge the students and promote critical thinking.

When preparing discussion questions for a Socratic Seminar, it can be helpful to consider the following:

• What are the main themes or concepts that you want students to explore?
• How can you frame questions that will encourage students to analyze and evaluate different perspectives?
• Are there any current events or real-life examples that can be incorporated into the discussion?

During a Socratic Seminar, the facilitator plays a crucial role in guiding the conversation and ensuring that all students have the opportunity to participate. The facilitator should create a safe and inclusive environment where students feel comfortable sharing their thoughts and opinions.

It is important to establish ground rules for respectful dialogue, such as using evidence to support arguments and actively listening to others.

The facilitator can also help steer the conversation by asking follow-up questions, summarizing key points, and encouraging students to elaborate on their ideas. By actively listening and responding to student contributions, the facilitator can foster a dynamic and engaging discussion that encourages problem-solving and critical thinking.

Socratic Seminars are a powerful tool for engaging high school students in problem-solving activities. By promoting critical thinking, active listening, and respectful dialogue, these seminars provide an opportunity for students to develop their analytical skills and engage in meaningful conversations.

Whether discussing a literary text or a current event, Socratic Seminars offer a platform for students to explore complex issues and find innovative solutions.

Problem solving abilities will serve students well both in academics and in life after school. The activities discussed give teens a chance to flex their critical thinking muscles in a hands-on, engaging way.

Group challenges teach teamwork and collaboration skills, while individual puzzles help sharpen logic and reasoning. Real-world projects allow students to creatively apply STEM concepts, and seminars provide conversational problem solving practice.

The next time your high schooler seems bored or disengaged, try one of these stimulating problem solving activities! With consistent practice, teens will develop stronger skills to overcome obstacles and achieve success.

Maria Sanchez is the founder of the Save Our Schools March blog. As a former teacher and parent, she is passionate about equitable access to quality public education. Maria created the blog to build awareness around education issues and solutions after organizing a local march for public schools.

With a Master's in Education, Maria taught high school English before leaving her career to raise a family. As a parent, she became concerned about underfunded schools and over-testing. These experiences drove Maria to become an education advocate.

On the blog, Maria provides resources and policy insights from the dual perspective of an informed parent and former teacher. She aims to inspire others to join the movement for quality, equitable public education. Maria lives with her family in [city, state].

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• STEM By Design / STEM Lessons

STEM Lessons Sparked by Real World Problems

by Anne Jolly · Published 08/27/2019 · Updated 11/12/2019

A MiddleWeb Blog

So STEM teachers often face a recurring problem when designing  lessons for their classroom or school lab: Just how do you DO that? How do you build a STEM lesson around a real-world challenge?

That’s not always an easy thing to figure out. While there’s no single  answer for that, I can give you an example of a STEM lesson that math colleague Judy Duke co-created with me (I was the science teacher in the mix), designed around a local environmental challenge. Here’s how we proceeded:

We started with a problem that students were interested in. One particularly painful problem in our area involved sand and clay from a large road construction project washing into streams. These muddy streams fed into the city reservoir, polluting it with excess sediments.

Local news reports showing a muddy reservoir fueled students’ indignation and they wanted to know how to stop those sediments from washing into the streams. That student question became the real-world problem for a great STEM project.

After some discussion we arrived at this STEM challenge: Reduce the rate at which sediment is being discharged from Spring Creek (a nearby creek) into a stream feeding the reservoir. We titled the project “Don’t Go with the Flow.”

We formulated ideas for how kids might conduct this project. We involved students in thinking this through with us, making sure that the process we decided on was doable and affordable. The process involved teams in designing and constructing a system of barriers in model stream beds, while following specific criteria and constraints. They would test their barrier systems, calculate the sediment discharge rates, redesign as needed, and document their results on Excel spreadsheets for class analysis.

We gathered and set up materials and equipment . What materials would teams need to set up streambed prototypes, construct barriers, and control the amount of water? What sediment would they use in their modeling? How would they collect and measure the sediment discharge? What would they do with left-over sediment and water?

Those are just a few questions we had to consider. Each team needed its own set of materials to simulate this sediment problem, so materials had to be inexpensive and easily accessible.

We planned our project facilitation process. We used a project-based learning approach for all STEM projects, including this one. Students would use an iterative engineering design process (EDP) to guide them in coming up with multiple ideas for solving the sediment problem.

As with all of our STEM projects, each team would work out its own design and approach. Our primary function as teacher-facilitators was to provide guidance with steps of the EDP and with teamwork .

Students worked diligently to find solutions for the sediment problem.   All teams discussed, selected, sketched, and constructed their respective barrier systems. To test its system, each team released a liter of water at a precise rate down the model streambed. Teams then measured the amount of sediment that got past the barriers and entered the stream (a bucket at the end of the streambed). They also clocked the amount of time this took. Team members used this data to calculate the sediment flow rate and decide whether to redesign the barrier system to hold back more sediment before recording their results.

Redesign is generally in order. Predictably, most barrier systems did not work well. That always provided important learning opportunities. After losing to Clemson in the 2019 National Championship game, Alabama coach Nick Saban directed his team, “Don’t waste a failure.” This STEM project offered abundant opportunities for our students to learn the benefit of failure and the skill of persistence.

The project lasted 5 class days. Obviously, I didn’t do full-blown STEM projects every week, but I tried to do at least one such project per quarter. In between big projects, the kids worked on their subject matter and on specific STEM skills – things like teamwork, using specific digital technology, suggesting multiple solutions for a problem, and so on. STEM skills fit seamlessly into our everyday curriculum.

Where to look for more real-world problems

That, in a nutshell, gives you a starting point for designing a STEM lesson/unit around a real-world topic. If you’d like more information about designing STEM lessons, check out chapters 7-8 of my STEM By Design  book and/or visit my book website for plenty of free materials and tips. This design tools page at the book site includes both teacher tips and student handouts – like this one about teaming .)

Here’s a parting tip: If you want to know more about real world problems, you can overview some of the big challenges at a couple of sites: Global Goals and Grand Challenges for Engineering .  As an FYI, I edited the Grand Challenges to make them more middle school friendly, with approval from the National Academy of Engineers. You can download my version here.

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Anne Jolly began her career as a lab scientist, caught the science teaching bug and was recognized as an Alabama Teacher of the Year during her long career as a middle grades science teacher. From 2007-2014 Anne was part of an NSF-funded team that developed middle grades STEM curriculum modules and teacher PD. In 2020-2021 Anne teamed with Flight Works Alabama to develop a workforce-friendly middle school curriculum and is now working on an elementary version. Her book STEM By Design: Strategies & Activities for Grades 4-8 is published by Routledge/EOE in partnership with MiddleWeb.

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Tackling a real-world maths problem

In the final instalment of our three part series on the International Mathematical Modelling Challenge (IMMC), Ross Turner outlines the mathematical modelling framework and provides some practical advice on approaching the ‘jet lag' problem set for the 2017 challenge.

Strengthening the connection between mathematical knowledge and skills, and the ways in which they can be used, is a central objective of many approaches to mathematics teaching and learning.

The IMMC provides a very direct opportunity to develop the relevant capabilities. It's a team-based competition where up to four students from the same school are given five days to work on a modelling task (located in a real-world setting), write a report and submit it for evaluation.

Australia's participation in the IMMC has been led and overseen by the Australian Council for Educational Research (ACER). An overarching objective of the challenge is to encourage and facilitate change in some of the classroom practices of mathematics teachers and learners.

What is the mathematical modelling framework?

The aim of IMMC is to produce students who can identify and effectively solve real-world problems. The following seven-step framework – which can be found on the Australian Challenge website – helps students take a systematic approach to devising solutions.

• Describe the real-world problem. Identify and understand the practical aspects of the situation.
• Specify the mathematical problem. Frame the real-world scenario as an appropriate, related mathematical question(s).
• Formulate the mathematical model. Make simplifying assumptions, choose variables, estimate magnitudes of inputs, justify decisions made.
• Solve the mathematics.
• Interpret the solution. Consider mathematical results in terms of their real-world meanings.
• Evaluate the model. Make a judgment as to the adequacy of the solution to the original question(s). Modify the model as necessary and repeat the cycle until an adequate solution has been found.
• Report the solution. Communicate clearly and fully your suggestions to address the real-world problem.

Students may need to repeat four of the steps (formulate, solve, interpret and evaluate) several times before they reach a successful solution.

The IMMC ‘jet lag' problem

The ‘jet lag' problem set for the 2017 challenge began: “Organizing international meetings is not easy in many ways, including the problem that some of the participants may experience the effects of jet lag after recent travel from their home country to the meeting location which may be in a different time-zone, or in a different climate and time of year, and so on. All these things may dramatically affect the productivity of the meeting.”

Student teams were tasked with creating an algorithm to produce a list of recommended places to hold a meeting, with the aim being to maximise overall productivity. They were asked to test their algorithm on two datasets:

Scenario 1 “Small Meeting”. Time: mid-June. Six individual participants from: Monterey CA, USA; Zutphen, Netherlands; Melbourne, Australia; Shanghai, China; Hong Kong (SAR), China; Moscow, Russia

Scenario 2 “Big meeting”. Time: January. Eleven individual participants from: Boston MA, USA (2 people); Singapore; Beijing, China; Hong Kong (SAR), China (2 people); Moscow, Russia; Utrecht, Netherlands; Warsaw, Poland; Copenhagen, Denmark; Melbourne, Australia.

The modelling process

An essential starting point is to clarify exactly what the IMMC problem required. The problem statement asks teams to develop an algorithm and test it on at least two given scenarios. It is worthwhile emphasising that the question does not ask where those two meetings should be held, but asks for a systematic process (an algorithm) that could be followed to determine a location for a meeting of participants from different home locations that maximises productivity of the participants, especially in relation to the effects of jet lag.

A further essential step in an effective modelling activity is to transform the statement of what is required in relation to the problem statement and its real-world setting, into a mathematical objective. As well as developing a clear understanding of what would constitute an answer to the question in the context from which it came, the goals of the exercise must also be expressed in clear mathematical terms. For example, the mathematical objective could be to minimise total distance travelled by the meeting participants, or time spent travelling, and so on.

The end-point of the modelling process is to communicate the results of the modelling work in a form that can be understood and used by its intended audience. The form of the product required for the IMMC comprises three parts: a one-page summary sheet, a report of the solution, and appendices including references used. However, the exact way a report is constructed should be determined in light of its purpose and audience. A modelling report is not the same thing as a school mathematics assignment. It might often take the form of a recommendation or set of recommendations to a committee, together with an explanation and justification of the recommendations.

In between the beginning process of defining the goals of the task and defining that in mathematical terms, and the end process of writing a report, the processes of model formulation, mathematical processing, and model evaluation take place. Those processes would often occur multiple times, since a first attempt at solving the problem might expose further issues that should be taken more effectively into account to provide the best possible solution to the problem at hand. A better mathematical formulation might be needed, an adjusted model might then be required, a different kind of mathematical processing could assist, and an updated interpretation of the results and evaluation of the outcomes would then be needed.

Approaches taken by Australian teams

Identifying relevant variables . Some factors that were said to be important included: time zone changes; climate; weather; characteristics of the destination city; hours of sunlight; optimal working conditions; and activities outside of the meeting. A key issue then was the extent to which factors said to be important were treated effectively in the solution rocess.

Identifying assumptions, and other factors . A key feature of mathematical modelling is the need to identify assumptions that are made, and to explain why they are made; also to consider how the assumptions made influence the solution found, and how changing assumptions might affect the solution. Other factors that could be considered include: the difference in jet lag effect between travel towards the east and west; the added impact of travel fatigue; and the possible addition of consideration of cost-related factors.

How ‘distance travelled' was treated . Some of the considerations that were important here were: considering ‘as the crow flies' versus plausible flight routes; whether minimising distance travelled would alone solve the problem; consideration of journey time (for example, whether direct or multiple flights might be needed); accuracy of complex distance calculations.

How time zones were treated . Relevant factors here were: it was essential to use some absolute reference system – most teams used Universal Coordinated Time (UTC) as a reference; the degree of overlap of ‘alert' periods for participants; accuracy in calculations of time zones for different locations and different times of the year; and the treatment of ‘recovery time'.

Sensitivity analysis, solution evaluation . Finally, no modelling process is complete without an evaluation of the solution proposed. Does the proposed solution answer the question? How would a change in the assumptions or starting conditions affect the solution found? What additional factors could be taken into account to make the solution work in a wider variety of circumstances? Very few of the IMMC 2017 reports considered the extent to which their solution was ‘best' and what other possible solutions might have been equally or almost as good. Very few teams showed that their solution would apply to completely different scenarios from the two cases given in the problem statement.

The IMMC Australian website includes free resources for teachers. Educators can download example problems for general use in maths teaching.

Think about an upcoming topic you’re teaching. How can you incorporate classroom activities that reflect real-life situations?

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• STEM EDUCATION ARTICLES & OPINIONS
• How STEM is Actively Solving Real-World Problems

STEM education has been a topic of hot debate for a few years now and its existence is under unending scrutiny. At a first glance this “third-degree” may feel like an annoying, rude, and uneducated attack on what is arguably one of the most progressive ideas to be set into action in schools in over 100 years. However, this scrutiny is actually proof that STEM is making its intended impact on the future generation of innovative, thoughtful, and resourceful leaders. Science, technology, engineering, and mathematics all require that individuals employ critical thinking skills in a variety of settings to accomplish tasks both big and small. You may thank those in the STEM fields for everything from shoes that protect your feet from whatever is on the ground to the mobile device that you have likely used at least once today for your own personal purposes. Beyond these useful, but not vital, components in your everyday life, STEM is actively being used to help solve some of the world’s greatest and most demanding problems.

Taming World Hunger

World hunger is an issue that is facing thousands of communities all over the world. Entire villages, towns, and cities are facing food shortages for various reasons including: dry seasons, climate change, changes in the environment, animal disturbances in farms and gardens, and simply lack of money. STEM is stepping up and solving these problems on a regular basis by teaching individuals how to grow gardens and providing communities in adverse situations with greenhouses and farming technology to help combat this very real problem.

Facilitating Worldwide Communications

If you are using a computer, tablet, smartphone, or other mobile device to view this page, then you are witnessing first-hand how the internet is connecting you with people, places, businesses, and products all over the world. The device that you are using to view this material is a prime example of how technology has been used to facilitate worldwide communication efforts around the world. This helps to inform individuals of disasters, politics, travel, and social situations across the world without physically having to travel. It is a much cheaper, faster, and more efficient way to spread important information than what was used just a few decades ago.

Safer World Travel

Have you ever booked a flight only to have it canceled or delayed by a winter storm? Not only are you annoyed, upset, or concerned about having to wait to get wherever you are going, you are actually facing the reality that you could be entering into a dangerous situation once you finally do board that plane. Why? Planes that fly in wintery, frozen precipitation accumulate ice on the wings. To combat this problem, flights are delayed, and the plane is sprayed down with an antifreeze-type substance to keep ice from forming on the wings. Unfortunately, this substance wears down and some planes are forced into emergency landings. Science is currently researching the possibility of planes releasing this anti-freezing liquid in mid-air and making travel a safer experience for all involved.

Life Saving Medicine

All areas of STEM education are currently working together to research the medical procedures and medications that are given to individuals in order to save their lives. Vaccines for conditions like Polio have nearly eradicated these deadly diseases. Heart, lung, and kidney transplants have literally saved lives thanks to the efforts made by individuals in STEM-related fields. Researchers have an entire list of diseases and conditions that they are working on tackling in the future as new and bright minds enter these STEM careers.

Decreasing Homelessness

3D printing is one of the newest, most innovative, and relatively inexpensive methods of providing strong homes for people in areas of the world that are highly populated. These homes can be built in as little as one day and can be customized to meet all of the requirements that an individual could ever need or want. These homes are sturdy, readily available, and incredibly affordable. Communities in places like Japan are already utilizing these 3D printed homes and efforts around the world have taken place to raise the money necessary to build such homes for the truly homeless to use.

Saving Wildlife

In places like New York City where skyscrapers are plentiful and glass walls are everywhere, birds and other flying animals are dying in the thousands. These animals do not see the glass and will literally fly into it, fall to the ground, and die either from the impact of flying into the glass or from the impact of hitting the ground from such a high altitude. Researchers are currently testing different types of glass with different patterns in an effort to design an aesthetically pleasing glass that birds can see and avoid. As of now, there STEM researchers have discovered that birds do see certain patterns in glass and the journey to providing these types of glass at an affordable price to the public is moving forward.

Providing Fresh Water

Dry, hot, and barren areas of the world are constantly faced with a lack of quality, clean, drinking water. It is often easier to access saltwater than freshwater in these areas, and the little freshwater that is available is usually too dirty to consume. To solve this issue, researchers are actively working on technology that can desalinate saltwater for the purpose of turning it into safe drinking water.

Creating “Green” Alternative, Renewable Energy Sources

You have probably heard that you have what is called a “carbon footprint”. This means that a portion of your daily life is made possible by the burning of limited carbon resources like coal. Individuals in the STEM field have committed their time to finding resources that can replace carbon-based fossil fuels without harsh negative ecological effects. Once a viable source has been discovered [such as water or wind sources], it takes an entire crew of people to develop the technology necessary to harness that energy and distribute it to communities all around the world. Not only are these resources viable "green" alternatives, but they are renewable and therefore feasibly sustainable methods of powering everyday life.

STEM is providing young generations with the incentive to tackle world problems like those listed above. While it is impossible to get everyone on the same page with agreeing opinions of its structure, it is worth noting that STEM-oriented individuals are making a difference in the world.

For those that question whether a STEM education is worth pursuing because of its exclusion of other important topics like arts, physical education, history, and language arts, try and point out to them that every STEM career can incorporate those subjects and their lessons. No topic in life is ever as cut and dry as it may seem on the surface. All subjects are important in making students well-rounded and active citizens in their communities, but STEM-oriented students simply choose to focus more of their attention to the areas of science, technology, engineering, and mathematics than in other areas.

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11 Activities That Promote Critical Thinking In The Class

52 Critical Thinking Flashcards for Problem Solving

Critical thinking activities encourage individuals to analyze, evaluate, and synthesize information to develop informed opinions and make reasoned decisions. Engaging in such exercises cultivates intellectual agility, fostering a deeper understanding of complex issues and honing problem-solving skills for navigating an increasingly intricate world. Through critical thinking, individuals empower themselves to challenge assumptions, uncover biases, and constructively contribute to discourse, thereby enriching both personal growth and societal progress.

Critical thinking serves as the cornerstone of effective problem-solving, enabling individuals to dissect challenges, explore diverse perspectives, and devise innovative solutions grounded in logic and evidence. For engaging problem solving activities, read our article problem solving activities that enhance student’s interest.

What is Critical Thinking?

Critical thinking is a 21st-century skill that enables a person to think rationally and logically in order to reach a plausible conclusion. A critical thinker assesses facts and figures and data objectively and determines what to believe and what not to believe. Critical thinking skills empower a person to decipher complex problems and make impartial and better decisions based on effective information.

More Articles from Educationise

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Critical thinking skills cultivate habits of mind such as strategic thinking, skepticism, discerning fallacy from the facts, asking good questions and probing deep into the issues to find the truth.

Importance of Acquiring Critical Thinking Skills

Acquiring critical thinking skills was never as valuable as it is today because of the prevalence of the modern knowledge economy. Today, information and technology are the driving forces behind the global economy. To keep pace with ever-changing technology and new inventions, one has to be flexible enough to embrace changes swiftly.

Read our article: How to Foster Critical Thinking Skills in Students? Creative Strategies and Real-World Examples

Today critical thinking skills are one of the most sought-after skills by the companies. In fact, critical thinking skills are paramount not only for active learning and academic achievement but also for the professional career of the students. The lack of critical thinking skills catalyzes memorization of the topics without a deeper insight, egocentrism, closed-mindedness, reduced student interest in the classroom and not being able to make timely and better decisions.

Benefits of Critical Thinking Skills in Education

Certain strategies are more eloquent than others in teaching students how to think critically. Encouraging critical thinking in the class is indispensable for the learning and growth of the students. In this way, we can raise a generation of innovators and thinkers rather than followers. Some of the benefits offered by thinking critically in the classroom are given below:

• It allows a student to decipher problems and think through the situations in a disciplined and systematic manner
• Through a critical thinking ability, a student can comprehend the logical correlation between distinct ideas
• The student is able to rethink and re-justify his beliefs and ideas based on facts and figures
• Critical thinking skills make the students curious about things around them
• A student who is a critical thinker is creative and always strives to come up with out of the box solutions to intricate problems
• Critical thinking skills assist in the enhanced student learning experience in the classroom and prepares the students for lifelong learning and success
• The critical thinking process is the foundation of new discoveries and inventions in the world of science and technology
• The ability to think critically allows the students to think intellectually and enhances their presentation skills, hence they can convey their ideas and thoughts in a logical and convincing manner
• Critical thinking skills make students a terrific communicator because they have logical reasons behind their ideas

Critical Thinking Lessons and Activities

11 Activities that Promote Critical Thinking in the Class

We have compiled a list of 11 activities that will facilitate you to promote critical thinking abilities in the students. We have also covered problem solving activities that enhance student’s interest in our another article. Click here to read it.

1. Worst Case Scenario

Divide students into teams and introduce each team with a hypothetical challenging scenario. Allocate minimum resources and time to each team and ask them to reach a viable conclusion using those resources. The scenarios can include situations like stranded on an island or stuck in a forest. Students will come up with creative solutions to come out from the imaginary problematic situation they are encountering. Besides encouraging students to think critically, this activity will enhance teamwork, communication and problem-solving skills of the students.

Read our article: 10 Innovative Strategies for Promoting Critical Thinking in the Classroom

2. If You Build It

It is a very flexible game that allows students to think creatively. To start this activity, divide students into groups. Give each group a limited amount of resources such as pipe cleaners, blocks, and marshmallows etc. Every group is supposed to use these resources and construct a certain item such as building, tower or a bridge in a limited time. You can use a variety of materials in the classroom to challenge the students. This activity is helpful in promoting teamwork and creative skills among the students.

It is also one of the classics which can be used in the classroom to encourage critical thinking. Print pictures of objects, animals or concepts and start by telling a unique story about the printed picture. The next student is supposed to continue the story and pass the picture to the other student and so on.

4. Keeping it Real

In this activity, you can ask students to identify a real-world problem in their schools, community or city. After the problem is recognized, students should work in teams to come up with the best possible outcome of that problem.

5. Save the Egg

Make groups of three or four in the class. Ask them to drop an egg from a certain height and think of creative ideas to save the egg from breaking. Students can come up with diverse ideas to conserve the egg like a soft-landing material or any other device. Remember that this activity can get chaotic, so select the area in the school that can be cleaned easily afterward and where there are no chances of damaging the school property.

6. Start a Debate

In this activity, the teacher can act as a facilitator and spark an interesting conversation in the class on any given topic. Give a small introductory speech on an open-ended topic. The topic can be related to current affairs, technological development or a new discovery in the field of science. Encourage students to participate in the debate by expressing their views and ideas on the topic. Conclude the debate with a viable solution or fresh ideas generated during the activity through brainstorming.

7. Create and Invent

This project-based learning activity is best for teaching in the engineering class. Divide students into groups. Present a problem to the students and ask them to build a model or simulate a product using computer animations or graphics that will solve the problem. After students are done with building models, each group is supposed to explain their proposed product to the rest of the class. The primary objective of this activity is to promote creative thinking and problem-solving skills among the students.

8. Select from Alternatives

This activity can be used in computer science, engineering or any of the STEM (Science, Technology, Engineering, Mathematics) classes. Introduce a variety of alternatives such as different formulas for solving the same problem, different computer codes, product designs or distinct explanations of the same topic.

Form groups in the class and ask them to select the best alternative. Each group will then explain its chosen alternative to the rest of the class with reasonable justification of its preference. During the process, the rest of the class can participate by asking questions from the group. This activity is very helpful in nurturing logical thinking and analytical skills among the students.

9. Reading and Critiquing

Present an article from a journal related to any topic that you are teaching. Ask the students to read the article critically and evaluate strengths and weaknesses in the article. Students can write about what they think about the article, any misleading statement or biases of the author and critique it by using their own judgments.

In this way, students can challenge the fallacies and rationality of judgments in the article. Hence, they can use their own thinking to come up with novel ideas pertaining to the topic.

10. Think Pair Share

In this activity, students will come up with their own questions. Make pairs or groups in the class and ask the students to discuss the questions together. The activity will be useful if the teacher gives students a topic on which the question should be based.

For example, if the teacher is teaching biology, the questions of the students can be based on reverse osmosis, human heart, respiratory system and so on. This activity drives student engagement and supports higher-order thinking skills among students.

11. Big Paper – Silent Conversation

Silence is a great way to slow down thinking and promote deep reflection on any subject. Present a driving question to the students and divide them into groups. The students will discuss the question with their teammates and brainstorm their ideas on a big paper. After reflection and discussion, students can write their findings in silence. This is a great learning activity for students who are introverts and love to ruminate silently rather than thinking aloud.

Finally, for students with critical thinking, you can go to GS-JJ.co m to customize exclusive rewards, which not only enlivens the classroom, but also promotes the development and training of students for critical thinking.

Read our next article: 10 Innovative Strategies for Promoting Critical Thinking in the Classroom

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Thanks for the great article! Especially with the post-pandemic learning gap, these critical thinking skills are essential! It’s also important to teach them a growth mindset. If you are interested in that, please check out The Teachers’ Blog!

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Grappling With Real-World Problems

Project-based learning can focus on real community issues to combine content and student interests.

Problem-based learning (PBL) is integrated at Two Rivers Public Charter School in Washington, DC, at every grade level—pre-K through eighth grade. Students are presented with a real-world problem, undertake a series of investigations, and create a product that they present to an authentic audience as part of the Expeditionary Learning (EL) Education framework. 

PBL enables the school to reach all learners. “There are multiple entry points,” explains Julia Tomasko, a fourth-grade teacher. “It’s easy to scaffold [PBL] for students who need more support, and the sky’s the limit for extensions.”

In Tomasko’s problem-based unit covering Jamestown, her class looked through primary resources like John Smith’s diary. They discussed representation and how all the primary resources are from the English settlers. Tomasko recalls one of her students asking, “‘Out of all the cultures in the world, which culture do you think needs to have its story told more and have its voice heard?’ I was blown away. That’s not typical fourth-grade thinking, but she was clearly thinking through these ideas in a deep way and wondering how [they] can apply to other things.”

How It's Done

1. Backwards plan. Jeff Heyck-Williams, the director of curriculum and instruction, believes that the perfect problem connects content, student interest, and an authentic context. To guide your planning, he suggests asking:

• What content and skills do my students need to learn?
• What would be proof of their understanding?
• In what contexts will they develop understanding?
• What are my students interested in?
• What are real problems that people in my field—ecology, biology, local history—grapple with that are related to the content I need to teach?
• What is the problem that I want my kids to solve?
• What product will my students create?

“Once you have those big pieces in place, you can start to plan: ‘What are the day-to-day things that I'm going to do to get them to face that problem and then move towards an ultimate solution?’” says Heyck-Williams.

2. Find a problem that’s relevant to your students’ interests and appropriate for their age. “Our youngest kids are working on problems that speak to things in their immediate environment,” explains Heyck-Williams, “but as kids move forward, they work with more philosophical problems outside of their direct community.”

First-grade students roamed school fields to investigate spiders. To discover the truth about spiders and help reduce people’s fear of them, each student created a scientific drawing of a spider and wrote a book exploring their characteristics, like eating mosquitos or bugs that harm people’s gardens. Fourth-grade students were asked how they could improve the quality of their local, polluted river. They created a website to teach kids how to take care of it. Eighth-grade students learned about gene editing, explored the ethics around it, and presented policy briefs to the National Academies of Sciences, Engineering, and Medicine. (See 4 Tips on Teaching Problem Solving [From a Student] .)

3. Be flexible with the product. It’s good to have a product in mind that you can guide your students towards, like creating a book, website, or policy brief. If you want your students to create a website, you can introduce websites as great resources in prior lessons. But the product isn’t the learning goal. Solving the problem and understanding the content is. The product is just the avenue to get there. If your students are excited about another product idea, go with it. When planning, think about the variety of products that your students might come up with to solve the problem, suggests Tomasko. Plan for flexibility.

4. Some lessons will be a flop, and that’s OK. “You think that you’re guiding your kids towards a certain idea,” reflects Tomasko, “and not only do they not come up with that, but sometimes they don’t come up with anything.” When this happens, go back to the planning board and think about how you can reteach that content another way. (See 3 Ways Lesson Plans Flop—and How to Recover .)

5. Start small. “When we first started problem-based learning, it was important for people to see that they could do this in small ways,” says Jessica Wodatch, the executive director of Two Rivers Public Charter School. “It’s really about taking your daily routine and thinking, ‘Where could kids have input? Where could kids be asked to solve a problem?’”

Instead of giving your students directions for an in-class assignment, ask them what they should do. If your students are lining up and it’s noisy, tell them what’s not working and ask them how they can solve it. If you create a birthday chart every year, have your students create it.

“It doesn’t need to be a three-week unit. It can be a little part of your day,” says Wodatch. “Part of the shift is thinking, ‘What can I hand to them? What am I deciding for them that I don’t need to?’ It’s about giving them some of that decision-making power, authority, and choice, and that is where we start to see the problem-based learning live.”

6. Use KWI to help your students problem solve. K: What do your kids already know about the problem? W: What do they need to know in order to solve the problem? I: What ideas do your students have to solve the problem? “Even if your students are solving an open-ended math problem, they can think through: What do they know about the problem, what’s being asked, and what different ideas do they have to solve it? Then you can apply that same structure to a more long-term project like a learning expedition,” says Tomasko.

Allowing students to explore ideas and make mistakes is a key element of problem-based learning at Two Rivers Public Charter School. Wodatch explains, “We want kids getting in the practice of weighing information, grappling with difficult problems that don’t have clear answers, considering different points of view and data, asking for expert opinions, and ultimately coming up with the solution. Those are things that we all do every day of our lives, and we want our kids to do that.”

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Hypothesis and theory article, real world problem-solving.

• Human-Robot Interaction Laboratory, Department of Computer Science, Tufts University, Medford, MA, United States

Real world problem-solving (RWPS) is what we do every day. It requires flexibility, resilience, resourcefulness, and a certain degree of creativity. A crucial feature of RWPS is that it involves continuous interaction with the environment during the problem-solving process. In this process, the environment can be seen as not only a source of inspiration for new ideas but also as a tool to facilitate creative thinking. The cognitive neuroscience literature in creativity and problem-solving is extensive, but it has largely focused on neural networks that are active when subjects are not focused on the outside world, i.e., not using their environment. In this paper, I attempt to combine the relevant literature on creativity and problem-solving with the scattered and nascent work in perceptually-driven learning from the environment. I present my synthesis as a potential new theory for real world problem-solving and map out its hypothesized neural basis. I outline some testable predictions made by the model and provide some considerations and ideas for experimental paradigms that could be used to evaluate the model more thoroughly.

1. Introduction

In the Apollo 13 space mission, astronauts together with ground control had to overcome several challenges to bring the team safely back to Earth ( Lovell and Kluger, 2006 ). One of these challenges was controlling carbon dioxide levels onboard the space craft: “For 2 days straight [they] had worked on how to jury-rig the Odysseys canisters to the Aquarius's life support system. Now, using materials known to be available onboard the spacecraft—a sock, a plastic bag, the cover of a flight manual, lots of duct tape, and so on—the crew assembled a strange contraption and taped it into place. Carbon dioxide levels immediately began to fall into the safe range” ( Team, 1970 ; Cass, 2005 ).

The success of Apollo 13's recovery from failure is often cited as a glowing example of human resourcefulness and inventiveness alongside more well-known inventions and innovations over the course of human history. However, this sort of inventive capability is not restricted to a few creative geniuses, but an ability present in all of us, and exemplified in the following mundane example. Consider a situation when your only suit is covered in lint and you do not own a lint remover. You see a roll of duct tape, and being resourceful you reason that it might be a good substitute. You then solve the problem of lint removal by peeling a full turn's worth of tape and re-attaching it backwards onto the roll to expose the sticky side all around the roll. By rolling it over your suit, you can now pick up all the lint.

In both these examples (historic as well as everyday), we see evidence for our innate ability to problem-solve in the real world. Solving real world problems in real time given constraints posed by one's environment are crucial for survival. At the core of this skill is our mental capability to get out of “sticky situations” or impasses, i.e., difficulties that appear unexpectedly as impassable roadblocks to solving the problem at hand. But, what are the cognitive processes that enable a problem solver to overcome such impasses and arrive at a solution, or at least a set of promising next steps?

A central aspect of this type of real world problem solving, is the role played by the solver's surrounding environment during the problem-solving process. Is it possible that interaction with one's environment can facilitate creative thinking? The answer to this question seems somewhat obvious when one considers the most famous anecdotal account of creative problem solving, namely that of Archimedes of Syracuse. During a bath, he found a novel way to check if the King's crown contained non-gold impurities. The story has traditionally been associated with the so-called “Eureka moment,” the sudden affective experience when a solution to a particularly thorny problem emerges. In this paper, I want to temporarily turn our attention away from the specific “aha!” experience itself and take particular note that Archimedes made this discovery, not with his eyes closed at a desk, but in a real-world context of a bath 1 . The bath was not only a passive, relaxing environment for Archimedes, but also a specific source of inspiration. Indeed it was his noticing the displacement of water that gave him a specific methodology for measuring the purity of the crown; by comparing how much water a solid gold bar of the same weight would displace as compared with the crown. This sort of continuous environmental interaction was present when the Apollo 13 engineers discovered their life-saving solution, and when you solved the suit-lint-removal problem with duct tape.

The neural mechanisms underlying problem-solving have been extensively studied in the literature, and there is general agreement about the key functional networks and nodes involved in various stages of problem-solving. In addition, there has been a great deal of work in studying the neural basis for creativity and insight problem solving, which is associated with the sudden emergence of solutions. However, in the context of problem-solving, creativity, and insight have been researched as largely an internal process without much interaction with and influence from the external environment ( Wegbreit et al., 2012 ; Abraham, 2013 ; Kounios and Beeman, 2014 ) 2 . Thus, there are open questions of what role the environment plays during real world problem-solving (RWPS) and how the brain enables the assimilation of novel items during these external interactions.

In this paper, I synthesize the literature on problem-solving, creativity and insight, and particularly focus on how the environment can inform RWPS. I explore three environmentally-informed mechanisms that could play a critical role: (1) partial-cue driven context-shifting, (2) heuristic prototyping and learning novel associations, and (3) learning novel physical inferences. I begin first with some intuitions about real world problem solving, that might help ground this discussion and providing some key distinctions from more traditional problem solving research. Then, I turn to a review of the relevant literature on problem-solving, creativity, and insight first, before discussing the three above-mentioned environmentally-driven mechanisms. I conclude with a potential new model and map out its hypothesized neural basis.

2. Problem Solving, Creativity, and Insight

2.1. what is real world problem-solving.

Archimedes was embodied in the real world when he found his solution. In fact, the real world helped him solve the problem. Whether or not these sorts of historic accounts of creative inspiration are accurate 3 , they do correlate with some of our own key intuitions about how problem solving occurs “in the wild.” Real world problem solving (RWPS) is different from those that occur in a classroom or in a laboratory during an experiment. They are often dynamic and discontinuous, accompanied by many starts and stops. Solvers are never working on just one problem. Instead, they are simultaneously juggling several problems of varying difficulties and alternating their attention between them. Real world problems are typically ill-defined, and even when they are well-defined, often have open-ended solutions. Coupled with that is the added aspect of uncertainty associated with the solver's problem solving strategies. As introduced earlier, an important dimension of RWPS is the continuous interaction between the solver and their environment. During these interactions, the solver might be inspired or arrive at an “aha!” moment. However, more often than not, the solver experiences dozens of minor discovery events— “hmmm, interesting…” or “wait, what?…” moments. Like discovery events, there's typically never one singular impasse or distraction event. The solver must iterate through the problem solving process experiencing and managing these sorts of intervening events (including impasses and discoveries). In summary, RWPS is quite messy and involves a tight interplay between problem solving, creativity, and insight. Next, I explore each of these processes in more detail and explicate a possible role of memory, attention, conflict management and perception.

2.2. Analytical Problem-Solving

In psychology and neuroscience, problem-solving broadly refers to the inferential steps taken by an agent 4 that leads from a given state of affairs to a desired goal state ( Barbey and Barsalou, 2009 ). The agent does not immediately know how this goal can be reached and must perform some mental operations (i.e., thinking) to determine a solution ( Duncker, 1945 ).

The problem solving literature divides problems based on clarity (well-defined vs. ill-defined) or on the underlying cognitive processes (analytical, memory retrieval, and insight) ( Sprugnoli et al., 2017 ). While memory retrieval is an important process, I consider it as a sub-process to problem solving more generally. I first focus on analytical problem-solving process, which typically involves problem-representation and encoding, and the process of forming and executing a solution plan ( Robertson, 2016 ).

2.2.1. Problem Definition and Representation

An important initial phase of problem-solving involves defining the problem and forming a representation in the working memory. During this phase, components of the prefrontal cortex (PFC), default mode network (DMN), and the dorsal anterior cingulate cortex (dACC) have been found to be activated. If the problem is familiar and well-structured, top-down executive control mechanisms are engaged and the left prefrontal cortex including the frontopolar, dorso-lateral (dlPFC), and ventro-lateral (vlPFC) are activated ( Barbey and Barsalou, 2009 ). The DMN along with the various structures in the medial temporal lobe (MTL) including the hippocampus (HF), parahippocampal cortex, perirhinal and entorhinal cortices are also believed to have limited involvement, especially in episodic memory retrieval activities during this phase ( Beaty et al., 2016 ). The problem representation requires encoding problem information for which certain visual and parietal areas are also involved, although the extent of their involvement is less clear ( Anderson and Fincham, 2014 ; Anderson et al., 2014 ).

2.2.1.1. Working memory

An important aspect of problem representation is the engagement and use of working memory (WM). The WM allows for the maintenance of relevant problem information and description in the mind ( Gazzaley and Nobre, 2012 ). Research has shown that WM tasks consistently recruit the dlPFC and left inferior frontal cortex (IC) for encoding an manipulating information; dACC for error detection and performance adjustment; and vlPFC and the anterior insula (AI) for retrieving, selecting information and inhibitory control ( Chung and Weyandt, 2014 ; Fang et al., 2016 ).

2.2.1.2. Representation

While we generally have a sense for the brain regions that are functionally influential in problem definition, less is known about how exactly events are represented within these regions. One theory for how events are represented in the PFC is the structured event complex theory (SEC), in which components of the event knowledge are represented by increasingly higher-order convergence zones localized within the PFC, akin to the convergence zones (from posterior to anterior) that integrate sensory information in the brain ( Barbey et al., 2009 ). Under this theory, different zones in the PFC (left vs. right, anterior vs. posterior, lateral vs. medial, and dorsal vs. ventral) represent different aspects of the information contained in the events (e.g., number of events to be integrated together, the complexity of the event, whether planning, and action is needed). Other studies have also suggested the CEN's role in tasks requiring cognitive flexibility, and functions to switch thinking modes, levels of abstraction of thought and consider multiple concepts simultaneously ( Miyake et al., 2000 ).

Thus, when the problem is well-structured, problem representation is largely an executive control activity coordinated by the PFC in which problem information from memory populates WM in a potentially structured representation. Once the problem is defined and encoded, planning and execution of a solution can begin.

2.2.2. Planning

The central executive network (CEN), particularly the PFC, is largely involved in plan formation and in plan execution. Planning is the process of generating a strategy to advance from the current state to a goal state. This in turn involves retrieving a suitable solution strategy from memory and then coordinating its execution.

2.2.2.1. Plan formation

The dlPFC supports sequential planning and plan formation, which includes the generation of hypothesis and construction of plan steps ( Barbey and Barsalou, 2009 ). Interestingly, the vlPFC and the angular gyrus (AG), implicated in a variety of functions including memory retrieval, are also involved in plan formation ( Anderson et al., 2014 ). Indeed, the AG together with the regions in the MTL (including the HF) and several other regions form a what is known as the “core” network. The core network is believed to be activated when recalling past experiences, imagining fictitious, and future events and navigating large-scale spaces ( Summerfield et al., 2010 ), all key functions for generating plan hypotheses. A recent study suggests that the AG is critical to both episodic simulation, representation, and episodic memory ( Thakral et al., 2017 ). One possibility for how plans are formulated could involve a dynamic process of retrieving an optimal strategy from memory. Research has shown significant interaction between striatal and frontal regions ( Scimeca and Badre, 2012 ; Horner et al., 2015 ). The striatum is believed to play a key role in declarative memory retrieval, and specifically helping retrieve optimal (or previously rewarded) memories ( Scimeca and Badre, 2012 ). Relevant to planning and plan formation, Scimeca & Badre have suggested that the striatum plays two important roles: (1) in mapping acquired value/utility to action selection, and thereby helping plan formation, and (2) modulation and re-encoding of actions and other plan parameters. Different types of problems require different sets of specialized knowledge. For example, the knowledge needed to solve mathematical problems might be quite different (albeit overlapping) from the knowledge needed to select appropriate tools in the environment.

Thus far, I have discussed planning and problem representation as being domain-independent, which has allowed me to outline key areas of the PFC, MTL, and other regions relevant to all problem-solving. However, some types of problems require domain-specific knowledge for which other regions might need to be recruited. For example, when planning for tool-use, the superior parietal lobe (SPL), supramarginal gyrus (SMG), anterior inferior parietal lobe (AIPL), and certain portions of the temporal and occipital lobe involved in visual and spatial integration have been found to be recruited ( Brandi et al., 2014 ). It is believed that domain-specific information stored in these regions is recovered and used for planning.

2.2.2.2. Plan execution

Once a solution plan has been recruited from memory and suitably tuned for the problem on hand, the left-rostral PFC, caudate nucleus (CN), and bilateral posterior parietal cortices (PPC) are responsible for translating the plan into executable form ( Stocco et al., 2012 ). The PPC stores and maintains “mental template” of the executable form. Hemispherical division of labor is particularly relevant in planning where it was shown that when planning to solve a Tower of Hanoi (block moving) problem, the right PFC is involved in plan construction whereas the left PFC is involved in controlling processes necessary to supervise the execution of the plan ( Newman and Green, 2015 ). On a separate note and not the focus of this paper, plan execution and problem-solving can require the recruitment of affective and motivational processing in order to supply the agent with the resolve to solve problems, and the vmPFC has been found to be involved in coordinating this process ( Barbey and Barsalou, 2009 ).

2.3. Creativity

During the gestalt movement in the 1930s, Maier noted that “most instances of “real” problem solving involves creative thinking” ( Maier, 1930 ). Maier performed several experiments to study mental fixation and insight problem solving. This close tie between insight and creativity continues to be a recurring theme, one that will be central to the current discussion. If creativity and insight are linked to RWPS as noted by Maier, then it is reasonable to turn to the creativity and insight literature for understanding the role played by the environment. A large portion of the creativity literature has focused on viewing creativity as an internal process, one in which the solvers attention is directed inwards, and toward internal stimuli, to facilitate the generation of novel ideas and associations in memory ( Beaty et al., 2016 ). Focusing on imagination, a number of researchers have looked at blinking, eye fixation, closing eyes, and looking nowhere behavior and suggested that there is a shift of attention from external to internal stimuli during creative problem solving ( Salvi and Bowden, 2016 ). The idea is that shutting down external stimuli reduces cognitive load and focuses attention internally. Other experiments studying sleep behavior have also noted the beneficial role of internal stimuli in problem solving. The notion of ideas popping into ones consciousness, suddenly, during a shower is highly intuitive for many and researchers have attempted to study this phenomena through the lens of incubation, and unconscious thought that is internally-driven. There have been several theories and counter-theories proposed to account specifically for the cognitive processes underlying incubation ( Ritter and Dijksterhuis, 2014 ; Gilhooly, 2016 ), but none of these theories specifically address the role of the external environment.

The neuroscience of creativity has also been extensively studied and I do not focus on an exhaustive literature review in this paper (a nice review can be found in Sawyer, 2011 ). From a problem-solving perspective, it has been found that unlike well-structured problems, ill-structured problems activate the right dlPFC. Most of the past work on creativity and creative problem-solving has focused on exploring memory structures and performing internally-directed searches. Creative idea generation has primarily been viewed as internally directed attention ( Jauk et al., 2012 ; Benedek et al., 2016 ) and a primary mechanism involved is divergent thinking , which is the ability to produce a variety of responses in a given situation ( Guilford, 1962 ). Divergent thinking is generally thought to involve interactions between the DMN, CEN, and the salience network ( Yoruk and Runco, 2014 ; Heinonen et al., 2016 ). One psychological model of creative cognition is the Geneplore model that considers two major phases of generation (memory retrieval and mental synthesis) and exploration (conceptual interpretation and functional inference) ( Finke et al., 1992 ; Boccia et al., 2015 ). It has been suggested that the associative mode of processing to generate new creative association is supported by the DMN, which includes the medial PFC, posterior cingulate cortex (PCC), tempororparietal juntion (TPJ), MTL, and IPC ( Beaty et al., 2014 , 2016 ).

That said, the creativity literature is not completely devoid of acknowledging the role of the environment. In fact, it is quite the opposite. Researchers have looked closely at the role played by externally provided hints from the time of the early gestalt psychologists and through to present day studies ( Öllinger et al., 2017 ). In addition to studying how hints can help problem solving, researchers have also looked at how directed action can influence subsequent problem solving—e.g., swinging arms prior to solving the two-string puzzle, which requires swinging the string ( Thomas and Lleras, 2009 ). There have also been numerous studies looking at how certain external perceptual cues are correlated with creativity measures. Vohs et al. suggested that untidiness in the environment and the increased number of potential distractions helps with creativity ( Vohs et al., 2013 ). Certain colors such as blue have been shown to help with creativity and attention to detail ( Mehta and Zhu, 2009 ). Even environmental illumination, or lack thereof, have been shown to promote creativity ( Steidle and Werth, 2013 ). However, it is important to note that while these and the substantial body of similar literature show the relationship of the environment to creative problem solving, they do not specifically account for the cognitive processes underlying the RWPS when external stimuli are received.

2.4. Insight Problem Solving

Analytical problem solving is believed to involve deliberate and conscious processing that advances step by step, allowing solvers to be able to explain exactly how they solved it. Inability to solve these problems is often associated with lack of required prior knowledge, which if provided, immediately makes the solution tractable. Insight, on the other hand, is believed to involve a sudden and unexpected emergence of an obvious solution or strategy sometimes accompanied by an affective aha! experience. Solvers find it difficult to consciously explain how they generated a solution in a sequential manner. That said, research has shown that having an aha! moment is neither necessary nor sufficient to insight and vice versa ( Danek et al., 2016 ). Generally, it is believed that insight solvers acquire a full and deep understanding of the problem when they have solved it ( Chu and Macgregor, 2011 ). There has been an active debate in the problem solving community about whether insight is something special. Some have argued that it is not, and that there are no special or spontaneous processes, but simply a good old-fashioned search of a large problem space ( Kaplan and Simon, 1990 ; MacGregor et al., 2001 ; Ash and Wiley, 2006 ; Fleck, 2008 ). Others have argued that insight is special and suggested that it is likely a different process ( Duncker, 1945 ; Metcalfe, 1986 ; Kounios and Beeman, 2014 ). This debate lead to two theories for insight problem solving. MacGregor et al. proposed the Criterion for Satisfactory Progress Theory (CSPT), which is based on Newell and Simons original notion of problem solving as being a heuristic search through the problem space ( MacGregor et al., 2001 ). The key aspect of CSPT is that the solver is continually monitoring their progress with some set of criteria. Impasses arise when there is a criterion failure, at which point the solver tries non-maximal but promising states. The representational change theory (RCT) proposed by Ohlsson et al., on the other hand, suggests that impasses occur when the goal state is not reachable from an initial problem representation (which may have been generated through unconscious spreading activation) ( Ohlsson, 1992 ). In order to overcome an impasse, the solver needs to restructure the problem representation, which they can do by (1) elaboration (noticing new features of a problem), (2) re-encoding fixing mistaken or incomplete representations of the problem, and by (3) changing constraints. Changing constraints is believed to involve two sub-processes of constraint relaxation and chunk-decomposition.

The current position is that these two theories do not compete with each other, but instead complement each other by addressing different stages of problem solving: pre- and post-impasse. Along these lines, Ollinger et al. proposed an extended RCT (eRCT) in which revising the search space and using heuristics was suggested as being a dynamic and iterative and recursive process that involves repeated instances of search, impasse and representational change ( Öllinger et al., 2014 , 2017 ). Under this theory, a solver first forms a problem representation and begins searching for solutions, presumably using analytical problem solving processes as described earlier. When a solution cannot be found, the solver encounters an impasse, at which point the solver must restructure or change the problem representation and once again search for a solution. The model combines both analytical problem solving (through heuristic searches, hill climbing and progress monitoring), and creative mechanisms of constraint relaxation and chunk decomposition to enable restructuring.

Ollingers model appears to comprehensively account for both analytical and insight problem solving and, therefore, could be a strong candidate to model RWPS. However, while compelling, it is nevertheless an insufficient model of RWPS for many reasons, of which two are particularly significant for the current paper. First, the model does explicitly address mechanisms by which external stimuli might be assimilated. Second, the model is not sufficiently flexible to account for other events (beyond impasse) occurring during problem solving, such as distraction, mind-wandering and the like.

So, where does this leave us? I have shown the interplay between problem solving, creativity and insight. In particular, using Ollinger's proposal, I have suggested (maybe not quite explicitly up until now) that RWPS involves some degree of analytical problem solving as well as the post-impasse more creative modes of problem restructuring. I have also suggested that this model might need to be extended for RWPS along two dimensions. First, events such as impasses might just be an instance of a larger class of events that intervene during problem solving. Thus, there needs to be an accounting of the cognitive mechanisms that are potentially influenced by impasses and these other intervening events. It is possible that these sorts of events are crucial and trigger a switch in attentional focus, which in turn facilitates switching between different problem solving modes. Second, we need to consider when and how externally-triggered stimuli from the solver's environment can influence the problem solving process. I detail three different mechanisms by which external knowledge might influence problem solving. I address each of these ideas in more detail in the next two sections.

3. Event-Triggered Mode Switching During Problem-Solving

3.1. impasse.

When solving certain types of problems, the agent might encounter an impasse, i.e., some block in its ability to solve the problem ( Sprugnoli et al., 2017 ). The impasse may arise because the problem may have been ill-defined to begin with causing incomplete and unduly constrained representations to have been formed. Alternatively, impasses can occur when suitable solution strategies cannot be retrieved from memory or fail on execution. In certain instances, the solution strategies may not exist and may need to be generated from scratch. Regardless of the reason, an impasse is an interruption in the problem solving process; one that was running conflict-free up until the point when a seemingly unresolvable issue or an error in the predicted solution path was encountered. Seen as a conflict encountered in the problem-solving process it activates the anterior cingulate cortex (ACC). It is believed that the ACC not only helps detect the conflict, but also switch modes from one of “exploitation” (planning) to “exploration” (search) ( Quilodran et al., 2008 ; Tang et al., 2012 ), and monitors progress during resolution ( Chu and Macgregor, 2011 ). Some mode switching duties are also found to be shared with the AI (the ACC's partner in the salience network), however, it is unclear exactly the extent of this function-sharing.

Even though it is debatable if impasses are a necessary component of insight, they are still important as they provide a starting point for the creativity ( Sprugnoli et al., 2017 ). Indeed, it is possible that around the moment of impasse, the AI and ACC together, as part of the salience network play a crucial role in switching thought modes from analytical planning mode to creative search and discovery mode. In the latter mode, various creative mechanisms might be activated allowing for a solution plan to emerge. Sowden et al. and many others have suggested that the salience network is potentially a candidate neurobiological mechanism for shifting between thinking processes, more generally ( Sowden et al., 2015 ). When discussing various dual-process models as they relate to creative cognition, Sowden et al. have even noted that the ACC activation could be useful marker to identify shifting as participants work creative problems.

3.2. Defocused Attention

As noted earlier, in the presence of an impasse there is a shift from an exploitative (analytical) thinking mode to an exploratory (creative) thinking mode. This shift impacts several networks including, for example, the attention network. It is believed attention can switch between a focused mode and a defocused mode. Focused attention facilitates analytic thought by constraining activation such that items are considered in a compact form that is amenable to complex mental operations. In the defocused mode, agents expand their attention allowing new associations to be considered. Sowden et al. (2015) note that the mechanism responsible for adjustments in cognitive control may be linked to the mechanisms responsible for attentional focus. The generally agreed position is that during generative thinking, unconscious cognitive processes activated through defocused attention are more prevalent, whereas during exploratory thinking, controlled cognition activated by focused attention becomes more prevalent ( Kaufman, 2011 ; Sowden et al., 2015 ).

Defocused attention allows agents to not only process different aspects of a situation, but to also activate additional neural structures in long term memory and find new associations ( Mendelsohn, 1976 ; Yoruk and Runco, 2014 ). It is believed that cognitive material attended to and cued by positive affective state results in defocused attention, allowing for more complex cognitive contexts and therefore a greater range of interpretation and integration of information ( Isen et al., 1987 ). High attentional levels are commonly considered a typical feature of highly creative subjects ( Sprugnoli et al., 2017 ).

4. Role of the Environment

In much of the past work the focus has been on treating creativity as largely an internal process engaging the DMN to assist in making novel connections in memory. The suggestion has been that “individual needs to suppress external stimuli and concentrate on the inner creative process during idea generation” ( Heinonen et al., 2016 ). These ideas can then function as seeds for testing and problem-solving. While true of many creative acts, this characterization does not capture how creative ideas arise in many real-world creative problems. In these types of problems, the agent is functioning and interacting with its environment before, during and after problem-solving. It is natural then to expect that stimuli from the environment might play a role in problem-solving. More specifically, it can be expected that through passive and active involvement with the environment, the agent is (1) able to trigger an unrelated, but potentially useful memory relevant for problem-solving, (2) make novel connections between two events in memory with the environmental cue serving as the missing link, and (3) incorporate a completely novel information from events occuring in the environment directly into the problem-solving process. I explore potential neural mechanisms for these three types of environmentally informed creative cognition, which I hypothesize are enabled by defocused attention.

4.1. Partial Cues Trigger Relevant Memories Through Context-Shifting

I have previously discussed the interaction between the MTL and PFC in helping select task-relevant and critical memories for problem-solving. It is well-known that pattern completion is an important function of the MTL and one that enables memory retrieval. Complementary Learning Theory (CLS) and its recently updated version suggest that the MTL and related structures support initial storage as well as retrieval of item and context-specific information ( Kumaran et al., 2016 ). According to CLS theory, the dentate gyrus (DG) and the CA3 regions of the HF are critical to selecting neural activity patterns that correspond to particular experiences ( Kumaran et al., 2016 ). These patterns might be distinct even if experiences are similar and are stabilized through increases in connection strengths between the DG and CA3. Crucially, because of the connection strengths, reactivation of part of the pattern can activate the rest of it (i.e., pattern completion). Kumaran et al. have further noted that if consistent with existing knowledge, these new experiences can be quickly replayed and interleaved into structured representations that form part of the semantic memory.

Cues in the environment provided by these experiences hold partial information about past stimuli or events and this partial information converges in the MTL. CLS accounts for how these cues might serve to reactivate partial patterns, thereby triggering pattern completion. When attention is defocused I hypothesize that (1) previously unnoticed partial cues are considered, and (2) previously noticed partial cues are decomposed to produce previously unnoticed sub-cues, which in turn are considered. Zabelina et al. (2016) have shown that real-world creativity and creative achievement is associated with “leaky attention,” i.e., attention that allows for irrelevant information to be noticed. In two experiments they systematically explored the relationship between two notions of creativity— divergent thinking and real-world creative achievement—and the use of attention. They found that attentional use is associated in different ways for each of the two notions of creativity. While divergent thinking was associated with flexible attention, it does not appear to be leaky. Instead, selective focus and inhibition components of attention were likely facilitating successful performance on divergent thinking tasks. On the other hand, real-world creative achievement was linked to leaky attention. RWPS involves elements of both divergent thinking and of real-world creative achievement, thus I would expect some amount of attentional leaks to be part of the problem solving process.

Thus, it might be the case that a new set of cues or sub-cues “leak” in and activate memories that may not have been previously considered. These cues serve to reactivate a diverse set of patterns that then enable accessing a wide range of memories. Some of these memories are extra-contextual, in that they consider the newly noticed cues in several contexts. For example, when unable to find a screwdriver, we might consider using a coin. It is possible that defocused attention allows us to consider the coin's edge as being a potentially relevant cue that triggers uses for the thin edge outside of its current context in a coin. The new cues (or contexts) may allow new associations to emerge with cues stored in memory, which can occur during incubation. Objects and contexts are integrated into memory automatically into a blended representation and changing contexts disrupts this recognition ( Hayes et al., 2007 ; Gabora, 2016 ). Cue-triggered context shifting allows an agent to break-apart a memory representation, which can then facilitate problem-solving in new ways.

4.2. Heuristic Prototyping Facilitates Novel Associations

It has long been the case that many scientific innovations have been inspired by events in nature and the surrounding environment. As noted earlier, Archimedes realized the relationship between the volume of an irregularly shaped object and the volume of water it displaced. This is an example of heuristic prototyping where the problem-solver notices an event in the environment, which then triggers the automatic activation of a heuristic prototype and the formation of novel associations (between the function of the prototype and the problem) which they can then use to solve the problem ( Luo et al., 2013 ). Although still in its relative infancy, there has been some recent research into the neural basis for heuristic prototyping. Heuristic prototype has generally been defined as an enlightening prototype event with a similar element to the current problem and is often composed of a feature and a function ( Hao et al., 2013 ). For example, in designing a faster and more efficient submarine hull, a heuristic prototype might be a shark's skin, while an unrelated prototype might be a fisheye camera ( Dandan et al., 2013 ).

Research has shown that activating the feature function of the right heuristic prototype and linking it by way of semantic similarity to the required function of the problem was the key mechanism people used to solve several scienitific insight problems ( Yang et al., 2016 ). A key region activated during heuristic prototyping is the dlPFC and it is believed to be generally responsible for encoding the events into memory and may play an important role in selecting and retrieving the matched unsolved technical problem from memory ( Dandan et al., 2013 ). It is also believed that the precuneus plays a role in automatic retrieval of heuristic information allowing the heuristic prototype and the problem to combine ( Luo et al., 2013 ). In addition to semantic processing, certain aspects of visual imagery have also been implicated in heuristic prototyping leading to the suggestion of the involvement of Broadman's area BA 19 in the occipital cortex.

There is some degree of overlap between the notions of heuristic prototyping and analogical transfer (the mapping of relations from one domain to another). Analogical transfer is believed to activate regions in the left medial fronto-parietal system (dlPFC and the PPC) ( Barbey and Barsalou, 2009 ). I suggest here that analogical reasoning is largely an internally-guided process that is aided by heuristic prototyping which is an externally-guided process. One possible way this could work is if heuristic prototyping mechanisms help locate the relevant memory with which to then subsequently analogize.

4.3. Making Physical Inferences to Acquire Novel Information

The agent might also be able to learn novel facts about their environment through passive observation as well as active experimentation. There has been some research into the neural basis for causal reasoning ( Barbey and Barsalou, 2009 ; Operskalski and Barbey, 2016 ), but beyond its generally distributed nature, we do not know too much more. Beyond abstract causal reasoning, some studies looked into the cortical regions that are activated when people watch and predict physical events unfolding in real-time and in the real-world ( Fischer et al., 2016 ). It was found that certain regions were associated with representing types of physical concepts, with the left intraparietal sulcus (IPS) and left middle frontal gyrus (MFG) shown to play a role in attributing causality when viewing colliding objects ( Mason and Just, 2013 ). The parahippocampus (PHC) was associated with linking causal theory to observed data and the TPJ was involved in visualizing movement of objects and actions in space ( Mason and Just, 2013 ).

5. Proposed Theory

I noted earlier that Ollinger's model for insight problem solving, while serving as a good candidate for RWPS, requires extension. In this section, I propose a candidate model that includes some necessary extensions to Ollinger's framework. I begin by laying out some preliminary notions that underlie the proposed model.

5.1. Dual Attentional Modes

I propose that the attention-switching mechanism described earlier is at the heart of RWPS and enables two modes of operation: focused and defocused mode. In the focused mode, the problem representation is more or less fixed, and problem solving proceeds in a focused and goal directed manner through search, planning, and execution mechanisms. In the defocused mode, problem solving is not necessarily goal directed, but attempts to generate ideas, driven by both internal and external items.

At first glance, these modes might seem similar to convergent and divergent thinking modes postulated by numerous others to account for creative problem solving. Divergent thinking allows for the generation of new ideas and convergent thinking allows for verification and selection of generated ideas. So, it might seem that focused mode and convergent thinking are similar and likewise divergent and defocused mode. They are, however, quite different. The modes relate less to idea generation and verification, and more to the specific mechanisms that are operating with regard to a particular problem at a particular moment in time. Convergent and divergent processes may be occurring during both defocused and focused modes. Some degree of divergent processes may be used to search and identify specific solution strategies in focused mode. Also, there might be some degree of convergent idea verification occuring in defocused mode as candidate items are evaluated for their fit with the problem and goal. Thus, convergent and divergent thinking are one amongst many mechanisms that are utilized in focused and defocused mode. Each of these two modes has to do with degree of attention placed on a particular problem.

There have been numerous dual-process and dual-systems models of cognition proposed over the years. To address criticisms raised against these models and to unify some of the terminology, Evans & Stanovich proposed a dual-process model comprising Type 1 and Type 2 thought ( Evans and Stanovich, 2013 ; Sowden et al., 2015 ). Type 1 processes are those that are believed to be autonomous and do not require working memory. Type 2 processes, on the other hand, are believed to require working memory and are cognitively decoupled to prevent real-world representations from becoming confused with mental simulations ( Sowden et al., 2015 ). While acknowledging various other attributes that are often used to describe dual process models (e.g., fast/slow, associative/rule-based, automatic/controlled), Evans & Stanovich note that these attributes are merely frequent correlates and not defining characteristics of Type 1 or Type 2 processes. The proposed dual attentional modes share some similarities with the Evans & Stanovich Type 1 and 2 models. Specifically, Type 2 processes might occur in focused attentional mode in the proposed model as they typically involve the working memory and certain amount of analytical thought and planning. Similarly, Type 1 processes are likely engaged in defocused attentional mode as there are notions of associative and generative thinking that might be facilitated when attention has been defocused. The crucial difference between the proposed model and other dual-process models is that the dividing line between focused and defocused attentional modes is the degree of openness to internal and external stimuli (by various networks and functional units in the brain) when problem solving. Many dual process models were designed to classify the “type” of thinking process or a form of cognitive processing. In some sense, the “processes” in dual process theories are characterized by the type of mechanism of operation or the type of output they produced. Here, I instead characterize and differentiate the modes of thinking by the receptivity of different functional units in the brain to input during problem solving.

This, however, raises a different question of the relationship between these attentional modes and conscious vs. unconscious thinking. It is clear that both the conscious and unconscious are involved in problem solving, as well as in RWPS. Here, I claim that a problem being handled is, at any given point in time, in either a focused mode or in a defocused mode. When in the focused mode, problem solving primarily proceeds in a manner that is available for conscious deliberation. More specifically, problem space elements and representations are tightly managed and plans and strategies are available in the working memory and consciously accessible. There are, however, secondary unconscious operations in the focused modes that includes targeted memory retrieval and heuristic-based searches. In the defocused mode, the problem is primarily managed in an unconscious way. The problem space elements are broken apart and loosely managed by various mechanisms that do not allow for conscious deliberation. That said, it is possible that some problem parameters remain accessible. For example, it is possible that certain goal information is still maintained consciously. It is also possible that indexes to all the problems being considered by the solver are maintained and available to conscious awareness.

5.2. RWPS Model

Returning to Ollinger's model for insight problem solving, it now becomes readily apparent how this model can be modified to incorporate environmental effects as well as generalizing the notion of intervening events beyond that of impasses. I propose a theory for RWPS that begins with standard analytical problem-solving process (See Figures 1 , 2 ).

Figure 1 . Summary of neural activations during focused problem-solving (Left) and defocused problem-solving (Right) . During defocused problem-solving, the salience network (insula and ACC) coordinates the switching of several networks into a defocused attention mode that permits the reception of a more varied set of stimuli and interpretations via both the internally-guided networks (default mode network DMN) and externally guided networks (Attention). PFC, prefrontal cortex; ACC, anterior cingulate cortex; PCC, posterior cingulate cortex; IPC, inferior parietal cortex; PPC, posterior parietal cortex; IPS, intra-parietal sulcus; TPJ, temporoparietal junction; MTL, medial temporal lobe; FEF, frontal eye field.

Figure 2 . Proposed Model for Real World Problem Solving (RWPS). The corresponding neural correlates are shown in italics. During problem-solving, an initial problem representation is formed based on prior knowledge and available perceptual information. The problem-solving then proceeds in a focused, goal-directed mode until the goal is achieved or a defocusing event (e.g., impasse or distraction) occurs. During focused mode operation, the solver interacts with the environment in directed manner, executing focused plans, and allowing for predicted items to be activated by the environment. When a defocusing event occurs, the problem-solving then switches into a defocused mode until a focusing event (e.g., discovery) occurs. In defocused mode, the solver performs actions unrelated to the problem (or is inactive) and is receptive to a set of environmental triggers that activate novel aspects using the three mechanisms discussed in this paper. When a focusing event occurs, the diffused problem elements cohere into a restructured representation and problem-solving returns into a focused mode.

5.2.1. Focused Problem Solving Mode

Initially, both prior knowledge and perceptual entities help guide the creation of problem representations in working memory. Prior optimal or rewarding solution strategies are obtained from LTM and encoded in the working memory as well. This process is largely analytical and the solver interacts with their environment through focused plan or idea execution, targeted observation of prescribed entities, and estimating prediction error of these known entities. More specifically, when a problem is presented, the problem representations are activated and populated into working memory in the PFC, possibly in structured representations along convergence zones. The PFC along with the Striatum and the MTL together attempt at retrieving an optimal or previously rewarded solution strategy from long term memory. If successfully retrieved, the solution strategy is encoded into the PPC as a mental template, which then guides relevant motor control regions to execute the plan.

5.2.2. Defocusing Event-Triggered Mode Switching

The search and solve strategy then proceeds analytically until a “defocusing event” is encountered. The salience network (AI and ACC) monitor for conflicts and attempt to detect any such events in the problem-solving process. As long as no conflicts are detected, the salience network focuses on recruiting networks to achieve goals and suppresses the DMN ( Beaty et al., 2016 ). If the plan execution or retrieval of the solution strategy fails, then a defocusing event is detected and the salience network performs mode switching. The salience network dynamically switches from the focused problem-solving mode to a defocused problem-solving mode ( Menon, 2015 ). Ollinger's current model does not account for other defocusing events beyond an impasse, but it is not inconceivable that there could be other such events triggered by external stimuli (e.g., distraction or an affective event) or by internal stimuli (e.g., mind wandering).

5.2.3. Defocused Problem Solving Mode

In defocused mode, the problem is operated on by mechanisms that allow for the generation and testing of novel ideas. Several large-scale brain networks are recruited to explore and generate new ideas. The search for novel ideas is facilitated by generally defocused attention, which in turn allows for creative idea generation from both internal as well as external sources. The salience network switches operations from defocused event detection to focused event or discovery detection, whereby for example, environmental events or ideas that are deemed interesting can be detected. During this idea exploration phase, internally, the DMN is no longer suppressed and attempts to generate new ideas for problem-solving. It is known that the IPC is involved in the generation of new ideas ( Benedek et al., 2014 ) and together with the PPC in coupling different information together ( Simone Sandkühler, 2008 ; Stocco et al., 2012 ). Beaty et al. (2016) have proposed that even this internal idea-generation process can be goal directed, thereby allowing for a closer working relationship between the CEN and the DMN. They point to neuroimaging evidence that support the possibility that the executive control network (comprising the lateral prefrontal and inferior parietal regions) can constrain and direct the DMN in its process of generating ideas to meet task-specific goals via top down monitoring and executive control ( Beaty et al., 2016 ). The control network is believed to maintain an “internal train of thought” by keeping the task goal activated, thereby allowing for strategic and goal-congruent searches for ideas. Moreover, they suggest that the extent of CEN involvement in the DMN idea-generation may depend on the extent to which the creative task is constrained. In the RWPS setting, I would suspect that the internal search for creative solutions is not entirely unconstrained, even in the defocused mode. Instead, the solver is working on a specified problem and thus, must maintain the problem-thread while searching for solutions. Moreover, self-generated ideas must be evaluated against the problem parameters and thereby might need some top-down processing. This would suggest that in such circumstances, we would expect to see an increased involvement of the CEN in constraining the DMN.

On the external front, several mechanisms are operating in this defocused mode. Of particular note are the dorsal attention network, composed of the visual cortex (V), IPS and the frontal eye field (FEF) along with the precuneus and the caudate nucleus allow for partial cues to be considered. The MTL receives synthesized cue and contextual information and populates the WM in the PFC with a potentially expanded set of information that might be relevant for problem-solving. The precuneus, dlPFC and PPC together trigger the activation and use of a heuristic prototype based on an event in the environment. The caudate nucleus facilitates information routing between the PFC and PPC and is involved in learning and skill acquisition.

5.2.4. Focusing Event-Triggered Mode Switching

The problem's life in this defocused mode continues until a focusing event occurs, which could be triggered by either external (e.g., notification of impending deadline, discovery of a novel property in the environment) or internal items (e.g., goal completion, discovery of novel association or updated relevancy of a previously irrelevant item). As noted earlier, an internal train of thought may be maintained that facilitates top-down evaluation of ideas and tracking of these triggers ( Beaty et al., 2016 ). The salience network switches various networks back to the focused problem-solving mode, but not without the potential for problem restructuring. As noted earlier, problem space elements are maintained somewhat loosely in the defocused mode. Thus, upon a focusing event, a set or subset of these elements cohere into a tight (restructured) representation suitable for focused mode problem solving. The process then repeats itself until the goal has been achieved.

5.3. Model Predictions

5.3.1. single-mode operation.

The proposed RWPS model provides several interesting hypotheses, which I discuss next. First, the model assumes that any given problem being worked on is in one mode or another, but not both. Thus, the model predicts that there cannot be focused plan execution on a problem that is in defocused mode. The corollary prediction is that novel perceptual cues (as those discussed in section 4) cannot help the solver when in focused mode. The corollary prediction, presumably has some support from the inattentional blindness literature. Inattentional blindness is when perceptual cues are not noticed during a task (e.g., counting the number of basketball passes between several people, but not noticing a gorilla in the scene) ( Simons and Chabris, 1999 ). It is possible that during focused problem solving, that external and internally generated novel ideas are simply not considered for problem solving. I am not claiming that these perceptual cues are always ignored, but that they are not considered within the problem. Sometimes external cues (like distracting occurrences) can serve as defocusing events, but the model predicts that the actual content of these cues are not themselves useful for solving the specific problem at hand.

When comparing dual-process models Sowden et al. (2015) discuss shifting from one type of thinking to another and explore how this shift relates to creativity. In this regard, they weigh the pros and cons of serial vs. parallel shifts. In dual-process models that suggest serial shifts, it is necessary to disengage one type of thought prior to engaging the other or to shift along a continuum. Whereas, in models that suggest parallel shifts, each of the thinking types can operate in parallel. Per this construction, the proposed RWPS model is serial, however, not quite in the same sense. As noted earlier, the RWPS model is not a dual-process model in the same sense as other dual process model. Instead, here, the thrust is on when the brain is receptive or not receptive to certain kinds of internal and external stimuli that can influence problem solving. Thus, while the modes may be serial with respect to a certain problem, it does not preclude the possibility of serial and parallel thinking processes that might be involved within these modes.

5.3.2. Event-Driven Transitions

The model requires an event (defocusing or focusing) to transition from one mode to another. After all why else would a problem that is successfully being resolved in the focused mode (toward completion) need to necessarily be transferred to defocused mode? These events are interpreted as conflicts in the brain and therefore the mode-switching is enabled by the saliency network and the ACC. Thus, the model predicts that there can be no transition from one mode to another without an event. This is a bit circular, as an event is really what triggers the transition in the first place. But, here I am suggesting that an external or internal cue triggered event is what drives the transition, and that transitions cannot happen organically without such an event. In some sense, the argument is that the transition is discontinuous, rather than a smooth one. Mind-wandering is good example of when we might drift into defocused mode, which I suggest is an example of an internally driven event caused by an alternative thought that takes attention away from the problem.

A model assumption underlying RWPS is that events such as impasses have a similar effect to other events such as distraction or mind wandering. Thus, it is crucial to be able to establish that there exists of class of such events and they have a shared effect on RWPS, which is to switch attentional modes.

5.3.3. Focused Mode Completion

The model also predicts that problems cannot be solved (i.e., completed) within the defocused mode. A problem can be considered solved when a goal is reached. However, if a goal is reached and a problem is completed in the defocused mode, then there must have not been any converging event or coherence of problem elements. While it is possible that the solver arbitrarily arrived at the goal in a diffused problem space and without conscious awareness of completing the task or even any converging event or problem recompiling, it appears somewhat unlikely. It is true that there are many tasks that we complete without actively thinking about it. We do not think about what foot to place in front of another while walking, but this is not an instance of problem solving. Instead, this is an instance of unconscious task completion.

5.3.4. Restructuring Required

The model predicts that a problem cannot return to a focused mode without some amount of restructuring. That is, once defocused, the problem is essentially never the same again. The problem elements begin interacting with other internally and externally-generated items, which in turn become absorbed into the problem representation. This prediction can potentially be tested by establishing some preliminary knowledge, and then showing one group of subjects the same knowledge as before, while showing the another group of subjects different stimuli. If the model's predictions hold, the problem representation will be restructured in some way for both groups.

There are numerous other such predictions, which are beyond the scope of this paper. One of the biggest challenges then becomes evaluating the model to set up suitable experiments aimed at testing the predictions and falsifying the theory, which I address next.

6. Experimental Challenges and Paradigms

One of challenges in evaluating the RWPS is that real world factors cannot realistically be accounted for and sufficiently controlled within a laboratory environment. So, how can one controllably test the various predictions and model assumptions of “real world” problem solving, especially given that by definition RWPS involves the external environment and unconscious processing? At the expense of ecological validity, much of insight problem solving research has employed an experimental paradigm that involves providing participants single instances of suitably difficult problems as stimuli and observing various physiological, neurological and behavioral measures. In addition, through verbal protocols, experimenters have been able to capture subjective accounts and problem solving processes that are available to the participants' conscious. These experiments have been made more sophisticated through the use of timed-hints and/or distractions. One challenge with this paradigm has been the selection of a suitable set of appropriately difficult problems. The classic insight problems (e.g., Nine-dot, eight-coin) can be quite difficult, requiring complicated problem solving processes, and also might not generalize to other problems or real world problems. Some in the insight research community have moved in the direction of verbal tasks (e.g., riddles, anagrams, matchstick rebus, remote associates tasks, and compound remote associates tasks). Unfortunately, these puzzles, while providing a great degree of controllability and repeatability, are even less realistic. These problems are not entirely congruent with the kinds of problems that humans are solving every day.

The other challenge with insight experiments is the selection of appropriate performance and process tracking measures. Most commonly, insight researchers use measures such as time to solution, probability of finding solution, and the like for performance measures. For process tracking, verbal protocols, coded solution attempts, and eye tracking are increasingly common. In neuroscientific studies of insight various neurological measures using functional magnetic resonance imaging (fMRI), electroencephalography (EEGs), transcranial direct current stimulation (tDCS), and transcranial magnetic stimulation (tMS) are popular and allow for spatially and temporally localizing an insight event.

Thus, the challenge for RWPS is two-fold: (1) selection of stimuli (real world problems) that are generalizable, and (2) selection of measures (or a set of measures) that can capture key aspects of the problem solving process. Unfortunately, these two challenges are somewhat at odds with each other. While fMRI and various neuroscientific measures can capture the problem solving process in real time, it is practically difficult to provide participants a realistic scenario while they are laying flat on their back in an fMRI machine and allowed to move nothing more than a finger. To begin addressing this conundrum, I suggest returning to object manipulation problems (not all that different from those originally introduced by Maier and Duncker nearly a century ago), but using modern computing and user-interface technologies.

One pseudo-realistic approach is to generate challenging object manipulation problems in Virtual Reality (VR). VR has been used to describe 3-D environment displays that allows participants to interact with artificially projected, but experientially realistic scenarios. It has been suggested that virtual environments (VE) invoke the same cognitive modules as real equivalent environmental experience ( Foreman, 2010 ). Crucially, since VE's can be scaled and designed as desired, they provide a unique opportunity to study pseudo-RWPS. However, a VR-based research approach has its limitations, one of which is that it is nearly impossible to track participant progress through a virtual problem using popular neuroscientific measures such as fMRI because of the limited mobility of connected participants.

Most of the studies cited in this paper utilized an fMRI-based approach in conjunction with a verbal or visual task involving problem-solving or creative thinking. Very few, if any, studies involved the use physical manipulation, and those physical manipulations were restricted to limited finger movements. Thus, another pseudo-realistic approach is allowing subjects to teleoperate robotic arms and legs from inside the fMRI machine. This paradigm has seen limited usage in psychology and robotics, in studies focused on Human-Robot interaction ( Loth et al., 2015 ). It could be an invaluable tool in studying real-time dynamic problem-solving through the control of a robotic arm. In this paradigm a problem solving task involving physical manipulation is presented to the subject via the cameras of a robot. The subject (in an fMRI) can push buttons to operate the robot and interact with its environment. While the subjects are not themselves moving, they can still manipulate objects in the real world. What makes this paradigm all the more interesting is that the subject's manipulation-capabilities can be systematically controlled. Thus, for a particular problem, different robotic perceptual and manipulation capabilities can be exposed, allowing researchers to study solver-problem dynamics in a new way. For example, even simple manipulation problems (e.g., re-arranging and stacking blocks on a table) can be turned into challenging problems when the robotic movements are restricted. Here, the problem space restrictions are imposed not necessarily on the underlying problem, but on the solver's own capabilities. Problems of this nature, given their simple structure, may enable studying everyday practical creativity without the burden of devising complex creative puzzles. Crucial to note, both these pseudo-realistic paradigms proposed demonstrate a tight interplay between the solver's own capabilities and their environment.

7. Conclusion

While the neural basis for problem-solving, creativity and insight have been studied extensively in the past, there is still a lack of understanding of the role of the environment in informing the problem-solving process. Current research has primarily focused on internally-guided mental processes for idea generation and evaluation. However, the type of real world problem-solving (RWPS) that is often considered a hallmark of human intelligence has involved both a dynamic interaction with the environment and the ability to handle intervening and interrupting events. In this paper, I have attempted to synthesize the literature into a unified theory of RWPS, with a specific focus on ways in which the environment can help problem-solve and the key neural networks involved in processing and utilizing relevant and useful environmental information. Understanding the neural basis for RWPS will allow us to be better situated to solve difficult problems. Moreover, for researchers in computer science and artificial intelligence, clues into the neural underpinnings of the computations taking place during creative RWPS, can inform the design the next generation of helper and exploration robots which need these capabilities in order to be resourceful and resilient in the open-world.

Author Contributions

The author confirms being the sole contributor of this work and approved it for publication.

The research for this Hypothesis/Theory Article was funded by the authors private means. Publication costs will be covered by my institution: Tufts University, Medford, MA, USA.

Conflict of Interest Statement

The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Acknowledgments

I am indebted to Professor Matthias Scheutz, Professor Elizabeth Race, Professor Ayanna Thomas, and Professor. Shaun Patel for providing guidance with the research and the manuscript. I am also grateful for the facilities provided by Tufts University, Medford, MA, USA.

1. ^ My intention is not to ignore the benefits of a concentrated internal thought process which likely occurred as well, but merely to acknowledge the possibility that the environment might have also helped.

2. ^ The research in insight does extensively use “hints” which are, arguably, a form of external influence. But these hints are highly targeted and might not be available in this explicit form when solving problems in the real world.

3. ^ The accuracy of these accounts has been placed in doubt. They often are recounted years later, with inaccuracies, and embellished for dramatic effect.

4. ^ I use the term “agent” to refer to the problem-solver. The term agent is more general than “creature” or “person” or “you" and is intentionally selected to broadly reference humans, animals as well as artificial agents. I also selectively use the term “solver.”

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Keywords: creativity, problem-solving, insight, attention network, salience network, default mode network

Citation: Sarathy V (2018) Real World Problem-Solving. Front. Hum. Neurosci . 12:261. doi: 10.3389/fnhum.2018.00261

Received: 03 August 2017; Accepted: 06 June 2018; Published: 26 June 2018.

Reviewed by:

Copyright © 2018 Sarathy. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Vasanth Sarathy, [email protected]

Project-Based Learning: Preparing Students for Real-World Challenges

Source: https://unsplash.com/photos/man-in-blue-long-sleeve-shirt-holding-smartphone-v89zhr0iBFY  

Homework is a major part of education. Yet some institutions tackle it in a more exciting way. Taking a more hands-on approach to learning can lead to numerous benefits for students, teachers and the educational institution as a whole. 

Some people still think that only the younger generation of learners can benefit from this learning model. However, the truth is, it can be great for everyone – from preschoolers to college goers.

Why use PBL?

Studies performed by the Lucas Education Research in 2021 give valid proof that implementing project-based learning can improve equity in schools and increase student’s overall performance. 

For students, it can have multiple benefits, such as: 

• Better motivation
• Enhanced engagement
• Development of problem-solving & critical-thinking skills
• Improved retention & understanding
• Self-organization
• Research skills
• Prep for future careers

For modern students, project-based learning is especially important. Whether they are writing essays with EssayPro or cramming all night prepping for a test, it’s hard to find motivation. Due to the accessibility of technology and easily available answers to every question, many students don’t see the need for homework. Using a PBL approach may help them understand the importance and relevance of it and nurture self-motivation skills. 

The main difference of PBL from a traditional learning setting is the relevance in the real world. It can be hard for students to understand why they need to solve math problems. Luckily for them, services like https://do-my-math.com/college-homework-help/ prove very helpful. 

Project-based learning also places more responsibility on the student. Rather than being taught, they take an active part in their education. This added responsibility can also help students who struggle with self-motivation.

Elements of Project-Based Learning

Every assignment presented to the students must contain several key elements for it to fit the PBL philosophy. 

A project must propose a challenge or a question to be solved or answered. This helps students apply their knowledge in the real world, rather than seeing learning as a collection of rules or formulae. Exploring a real-world scenario ensures that students understand the implications of their project and its relevance. It also focuses on developing modern, currently relevant skills rather than studying obsolete abstract concepts.

An inquiry-based process helps facilitate research and deeper understanding of the subject. A student is encouraged to ask as many questions as possible and perform in-depth research.

Students are encouraged to use their voice and make executive decisions. This fosters independence, helps enhance communication skills and teaches students to collaborate. Direct ownership of the project also affects the sense of responsibility and pushes students to work harder. 

One should also have some time for reflection. Both students and teachers should reflect on the project, see what they’ve learnt and how. Reflecting on whether the methods chosen for the project were effective ensures that fewer mistakes are made in the future.

Having space for feedback and revisions is essential for PBL. Getting feedback from the teacher and implementing it will help improve the final project. Critiquing other students’ work is also a helpful tool for collaboration and healthy competition.

Presenting the final project to the class, or sometimes even beyond it fosters responsibility and ownership. It also ensures that students are confident in their work and feel good enough to present it.

Source: https://unsplash.com/photos/person-using-microsoft-surface-laptop-on-lap-with-two-other-people-w79mIrYKcK4  

Preparation For Future Careers

Even though PBL is mostly practiced among younger children, it is still a great tool for career prep. Knowing who you want to be and how you are going to achieve it is extremely valuable for learners since they will have more time to focus on their professional growth. 

Being aware of the current problems can help bring up a more conscious and responsible generation of students. A person who knows what they want to be from a young age and has the ability to self-organize and motivate can be a prominent addition to the workplace. Besides, choosing a career with real, relevant problems in mind will ensure that the person is happy and fulfilled in their work.

Fostering Creativity

Project-based learning relies on students to choose their own assignments, organize them the way they see fit, research using any available sources and present their work. This, whether done alone or in collaboration with other students, requires creativity in both research and presentation. 

The problems facing society at the moment can’t be solved without creative and innovative decisions. PBL relies on creative, critical thinking to foster innovative solutions. A young students’ fresh approach may lead to new ideas that haven’t been proposed before, or a different way of approaching a situation. 

Examples of PBL

Project-based learning may sound complicated, especially with all the conditions and problem-solving. But the truth is, many assignments we all did at school technically fall into the PBL category. 

Remember that solar system model we all had to build? That’s the simplest example of PBL. Researching your heritage and the history of your last name or ancestry, as far as possible, is also a PBL project many of us had to do in school.

Sure, some schools, like High Tech High in San Diego, California have robotics projects and compete in an exhibition. But that just goes to show how many different purposes PBL can fulfill.

Wrapping up

A project-based curriculum can be an incredibly valuable addition to any school or educational institution. Teaching student life skills and solving real problems will help foster communication, responsibility, deeper learning and retention and higher motivation. 

Projects can vary widely, from simple assignments for preschoolers, to complex robotics projects. But that only shows how diverse and widely applicable PBL can be.

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• Published: 24 August 2018

Making sense of “STEM education” in K-12 contexts

• Tamara D. Holmlund   ORCID: orcid.org/0000-0001-6132-7873 1 ,
• Kristin Lesseig 1 &
• David Slavit 1  

International Journal of STEM Education volume  5 , Article number:  32 ( 2018 ) Cite this article

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Despite increasing attention to STEM education worldwide, there is considerable uncertainty as to what constitutes STEM education and what it means in terms of curriculum and student outcomes. The purpose of this study was to investigate the commonalities and variations in educators’ conceptualizations of STEM education. Sensemaking theory framed our analysis of ideas that were being selected and retained in relation to professional learning experiences in three contexts: two traditional middle schools, a STEM-focused school, and state-wide STEM professional development. Concept maps and interview transcripts from 34 educators holding different roles were analyzed: STEM and non-STEM teachers, administrators, and STEM professional development providers.

Three themes were included on over 70% of the 34 concept maps: interdisciplinary connections; the need for new, ambitious instructional practices in enacting a STEM approach; and the engagement of students in real-world problem solving. Conceptualizations of STEM education were related to educational contexts, which included the STEM education professional development activities in which educators engaged. We also identified differences across educators in different roles (e.g., non-STEM teacher, administrator). Two important attributes of STEM education addressed in the literature appeared infrequently across all contexts and role groups: students’ use of technology and the potential of STEM-focused education to provide access and opportunities for all students’ successful participation in STEM.

Conclusions

Given the variety of institutionalized practices and school contexts within which STEM education is enacted, we are not convinced that a single worldwide definition of STEM education is critical. What we do see as essential is that those working in the same system explore the common elements that are being attributed to STEM education and co-construct a vision that provides opportunities for all their students to attain STEM-related goals. This is especially important in the current reform contexts related to STEM education. We also see that common conceptions of STEM education appear across roles and contexts, and these could provide starting points for these discussions. Explicitly identifying the ideas educators are and are not selecting and retaining can inform professional learning activities at local and larger scales.

Across the world, STEM receives tremendous attention in education reform efforts and in popular media. The International Council of Associations for Science Educators (ICASE 2013 ) recently urged member countries to work together to improve access to, and the quality of, STEM education in order to prepare all students for global citizenry. In the USA, the National Science Foundation (NSF) has played a significant role in the STEM education movement by calling for research related to science, mathematics, engineering, and technology. While the NSF first used the term “SMET,” this was revised into the more euphonic “STEM” in the early 2000s (Patton 2013 ). Shortly thereafter, the US government issued several studies on the state of STEM learning, and the number of schools designated as STEM-focused increased. Numerous legislative actions also emerged at this time related to computer science, STEM teachers, and STEM as career and technology (CTE) education (Gonzalez and Kuenzi 2012 ; Kuenzi 2008 ).

The NSF continues to use the STEM as an overarching title—for example, in requests for proposals—and activity within any one of the four disciplines can fit into the STEM category. For example, engaging elementary children in engineering and design, developing middle-level mathematics curriculum, or studying high school biology students’ understandings about evolution are all STEM activities. However, in the general public and among K-12 educators, “STEM education” is being increasingly viewed as a new concept, one that somehow brings all four disciplines together. One definition that illustrates an integrated perspective of STEM education comes from work in southwest Pennsylvania:

STEM education is an interdisciplinary approach to learning where rigorous academic concepts are coupled with real world lessons as students apply science, technology, engineering, and mathematics in contexts that make connections between school, community, work, and the global enterprise enabling the development of STEM literacy and with it the ability to compete in the new economy. (Southwest Regional STEM Network 2009 , p. 3)

Despite the increasingly common use of the term “STEM education,” there is still uncertainty as to what constitutes STEM education and what it means in terms of curriculum and student outcomes (Breiner et al. 2012 ; Lamberg and Trzynadlowski 2015 ). STEM education can be considered a single or multi-disciplinary field, and in the case of the latter, no clear consensus exists on the nature of the content and pedagogic interplay among the STEM fields. While science and mathematics education are well-defined (though separate) entities across elementary and secondary schools worldwide, engineering education has largely been a function of higher education in the USA. And technology education has traditionally been delegated to vocational education (now called CTE), when included at all in secondary schooling. Given that policymakers, parents, and business communities are calling for STEM education across grade levels and that STEM literacy is viewed as critical for the economic success and health of individuals and nations worldwide (National Science Board 2015 ; STEM Education Coalition 2014 ), it is important to consider the varied meanings that different groups may have for STEM and STEM education. While it may not be necessary, or even feasible, to coalesce around one common definition of STEM education, we argue that without some shared understandings across a system, it is difficult to design and implement curriculum and instruction to promote successful STEM learning for all students.

In this study, we investigated the conceptualizations of STEM education among educators who work in STEM-focused settings. Our analysis centered on identifying the themes that arise in these educators’ conceptualizations. We also looked for possible relationships between these conceptualizations and (a) their professional work context, including relevant supports for professional learning (referred to as context group ), as well as (b) their professional roles (referred to as role group ).

Conceptualizing STEM education

Consistent with many international recommendations, two National Research Council (NRC) reports on successful K-12 STEM programs in the USA described three major and inclusive goals for STEM education: (a) increase the number of STEM innovators and professionals, (b) strengthen the STEM-related workforce, and (c) improve STEM literacy in all citizens (National Research Council 2011a , 2013 ). But what does it mean, at the classroom level, to implement STEM education? Current research suggests that STEM education is an innovation with various instructional models and emphases that are shaping reform in many educational systems (Bybee 2013 ; National Academy of Engineering and National Research Council 2014 ; Wang et al. 2011 ). Emerging research shows a lack of consensus on the content and instructional practices associated with STEM education, with various models being promoted. These include the incorporation of an engineering design process into the curriculum (Lesseig et al. 2017 ; Ring et al. 2017 ; Roehrig et al. 2012 ), a thematic approach centered around contemporary issues or problems that integrates two or more STEM areas (Bybee 2010 ; Zollman 2012 ), and maker-oriented programs such as robotics, coding, and Maker Faires, which may occur outside of the regular school curriculum (Bevan et al. 2014 )).

However, while various models have emerged, an analysis of STEM education does reveal an emerging consensus on the global attributes associated with this innovation. For example, Peters-Burton et al. ( 2014 ) compiled ten “critical components” of STEM high schools, and LaForce et al. ( 2014 ) identified eight “core elements” of STEM schools. At the classroom level, Kelley and Knowles ( 2016 ) provide a conceptual framework for secondary STEM education efforts. As these and other reports informed the content of the professional development for the participants in this study and our a priori coding categories, we next provide brief descriptions of common elements of STEM education.

One significant attribute of STEM-focused schools is the attention to instructional practices that actively engage and support all students in learning rigorous science and mathematics (Kloser 2014 ; LaForce et al. 2014 ; Lampert and Graziani 2009 ; Newmann and Associates 1996 ). These instructional practices are beginning to be known as a core or ambitious teaching (Kloser 2014 ; Whitcomb et al. 2009 ), and professional development that helps teachers develop these practices along with disciplinary content knowledge is often recommended for STEM-focused learning contexts. Other attributes of STEM-focused schools are student learning experiences that incorporate multiple disciplines (an interdisciplinary, integrated, or trans-disciplinary approach) and often include a project- or problem-based approach tied to authentic or real-world contexts (LaForce et al. 2014 ; Peters-Burton et al. 2014 ). Inherent in problem- and project-based learning are opportunities for student growth in twenty-first century skills such as collaboration, critical thinking, creativity, accountability, persistence, and leadership (Buck Institute 2018 ; Partnership for 21st Century Skills 2013 ). These projects often encompass partnerships with STEM professionals and other community members who can help students make connections between school learning, problem solving, and careers. Another important attribute is students’ use of appropriate and innovative technologies in their inquiries, research, and communication. In this study, we explore the extent to which these characteristics or any others were part of educators’ conceptions of STEM education.

Research questions

Our interest in how educators conceptualize STEM education is grounded in our research on STEM schools and our participation as STEM professional development providers. We framed our study around the following question:

What sense have educators made of STEM education after implementing and/or supporting STEM learning experiences?

We were also interested in possible relationships between participants’ professional work contexts or professional roles and the themes they associated with STEM education. Thus, we addressed the following sub-questions in our analysis:

What themes emerge in the conceptualizations of STEM education among educators in a given professional context? What relationships might exist between an individual’s conceptualization of STEM education and the professional context in which she/he works?

What themes emerge in the conceptualizations of STEM education among educators in a given role group? What relationships might exist between an individual’s conceptualization of STEM education and his/her professional role?

Theoretical framework

Understanding the intentions of reform proposals requires implementers to interpret what is meant and foresee implications on curriculum and instruction (Spillane et al. 2002 ). Because we are interested in the ways in which individuals are navigating the complex and novel ideas inherent in STEM education, we use sensemaking as our theoretical framework. Sensemaking theory attends to both the individual processing and the socially interactive work that occurs when a person encounters a gap in or discontinuity between what exists and a proposed change or innovation (Dervin 1992 ). Grounded in cognitive learning theory, sensemaking is a dynamic process where each person draws upon existing knowledge, beliefs, values, experiences, and identity to accommodate or assimilate new concepts (Weick 1995 ).

Sensemaking begins with a real or perceived disruption to the status quo, which may range from a fairly routine change, such as a schedule revision, to radical innovation in curriculum and instruction. Sensemaking involves a continuous cycle of enacting actions to address the disruption, noticing and categorizing aspects of the enactment, selecting elements that are plausible, and retaining those in future actions (see Fig.  1 ). Feedback from multiple sources shapes all these processes (Weick et al. 2005 ). The creation of a “plausible story” (Weick et al. 2005 , p. 410) provides the implementer a way to reconcile the varied requirements, standards, and other ideas associated with a proposal for change within their current situation.

Sensemaking cycle (adapted from Weick et al. 2005 , p. 414)

Sensemaking is situated within social and contextual components that influence the individual (Coburn 2001 ; Spillane et al. 2002 ). Any one person’s conceptualization can be “talked into existence” (Weick et al. 2005 , p. 413), as it is shaped through dialog with others, by the constraints and affordances of the environment, and sometimes by the influence of leaders. Both individual and collective sensemaking can result in a range of meanings. While multiple perspectives are useful in generating ideas, this can also be problematic in terms of how new ideas are implemented. For example, there are numerous accounts of the challenges inherent in translating educational innovations or policies for reform into mathematics and science classrooms due to contrasting vision (Allen and Penuel 2015 ; Fishman and Krajcik 2003 ; Spillane 2001 ). Therefore, in this study, we are most interested in the current status and result of the participants’ sensemaking process rather than documenting the sensemaking process itself. Understanding how various stakeholders conceptualize new curricular or instructional ideas can inform the conversation needed to support professional learning and alleviate challenges to reform.

Research design

“The assumptions and propositions of sensemaking, taken together, provide methodological guidance for framing research questions, for collecting data, and for charting analyses” (Dervin 1992 , p.62). To understand what sense participants made of the information encountered and experiences they had about STEM education, we elicited each participant’s thinking through concept maps and interviews. Concept maps can show the “structure of knowledge” (Novak 1995 , p. 79) by making explicit one’s ideas within a specific domain. Map creators identify ideas associated with the given domain and arrange these in a way to designate which are most salient and which are related but less significant. These main and subordinate ideas are called “nodes.” Connecting lines, arrows, and words written on these connecting lines can be used to show the interrelationships between the major and less significant nodes (Novak and Cañas 2008 ). As learning is contextual and informed by a learner’s previous knowledge (Bruner 1990 ), any two concept maps typically differ in multiple ways.

Concept maps have been used in K-20 education and in professional development to provide insight into how learners are structuring new ideas with existing understandings (Adesope and Nesbit 2009 ; Besterfield-Sacre et al. 2004 ; Greene et al. 2013 ; Markham et al. 1994 ). The act of map creation requires reflection on events, experiences, and ideas and, thus, is a sensemaking activity: “How can I know what I think until I see what I say?” (Weick et al. 2005 , p. 416). In addition, concept maps allow participants time to make sense of what they think. The maps can then be used in interviews to provide focal points for further sensemaking (Linderman et al. 2011 ), with opportunities for the creator to elaborate and clarify the components and structures of the map.

While sensemaking is ultimately individualistic, the ideas and experiences that contribute to this occur in the context of organizations, conversation, shared activity, and feedback loops (Weick et al. 2005 ).

Sense-making does assume that the individual is situated in cultural/historical moments in time-space and that culture, history, and institutions define much of the world within which the individual lives . . . the individual’s relationship to these moments and the structures that define them is always a matter of self-construction. (Dervin 1992 , p. 67)

In line with this theoretical perspective, the unit of analysis for our study is the individual. We report on this analysis to answer our first research question. We also recognize that each individual has a professional role and is situated within particular institutional structures and cultures and that both the responsibilities of one’s role and the context inform one’s conceptualization of STEM education. As such, we also noted the roles of each participant and developed rich descriptions of the professional contexts in which participants worked. These descriptions, in conjunction with participants’ concept maps and interviews, allowed us to look for relationships among participants’ conceptualizations of STEM education, their professional contexts (sub-question A), and their professional roles and responsibilities (sub-question B).

Participants

Thirty-four people participated in this study. Each was affiliated with STEM education endeavors in one of three context groups . Thirteen participants were teachers and administrators at an inclusive, STEM-focused secondary school (Ridgeview STEM Academy Footnote 1 ). Another 12 were teachers from two traditional middle schools who participated in a 2-year professional development project that supported their implementation of engineering design challenges with their students. Nine were STEM educators and stakeholders participating as faculty in a statewide professional development (PD) institute designed to assist district or school teams with the creation of a STEM education implementation plan. The professional roles of each participant are shown in Table  1 .

Some participants in each context group held dual roles (e.g., Shawn was both a science and an engineering/CTE teacher; Will and Michelle were both non-STEM teachers and administrators). For the purpose of this analysis, the role they most strongly identified with at the time they completed the concept map was used to determine the role groups . The selection of these participants from the larger pool of teachers and administrators at all three schools was based on their participation in two larger research projects. The professional development faculty were included as participants to provide data from a group with very different contexts and, possibly, perspectives. Given the frequent lack of communication and difference in vision among groups associated with reform efforts (Spillane et al. 2002 ), it was important to get a snapshot of the thinking of a group situated outside of classrooms and schools.

Professional work contexts

We describe the professional work contexts of each of our participants. With regard to the participants from Ridgeview STEM Academy and from the two traditional middles schools, we focus on the characteristics of the school and the supports teachers received for their professional learning. In the case of the statewide PD faculty, we focus primarily on their leadership roles in the context of a statewide STEM education leadership institute.

Ridgeview STEM Academy

The participants in this context group were from Ridgeview STEM Academy (RSA), an inclusive STEM-focused school that opened in 2012 with nine teachers and students in grades 6, 7, and 9. The student population was intended to mirror the demographics of the district, and admission was obtained through a lottery by zip code. During the focus year of this study, RSA had approximately 400 students in grades 6–12 and 22 teachers. District-provided professional development associated with learning about the school vision, culture, and practices has been provided since the opening of the school, but teachers have predominantly made sense of STEM education as they implement it. The RSA vision statement described the student learning experience as one that would support the student as a “learner, collaborator, designer, and connector” and the faculty nurtured the growth of a school identity as a place where students had “voice and choice.” STEM learning was viewed as possible for all students, and the curriculum was envisioned as a project- or problem-based (Buck Institute 2018 ) and connected to “the real world of business and research.”

Teachers collaborated across the school year to develop their own interdisciplinary, project-based curricula and used overarching themes to integrate the humanities and STEM disciplines. They accessed a variety of resources as they experimented with the types of instructional practices needed to enact the school vision in the context of the Common Core State Standards (CCSS) (National Governors Association 2010 ) and the Next Generation Science Standards (NGSS) (Achieve 2013 ). Teachers explicitly supported building student skills and attitudes, such as persistence in problem solving, curiosity and a willingness to learn from failure, creative thinking, and the ability to work independently and collaboratively. The technology received attention from the start. Each student was provided a laptop loaded with design, research, and communication tools, and the school offered specific classes dedicated to the use of this technology. Bringing STEM professionals into the school and taking students out to explore STEM careers and work was an explicit focus, with a half-time position created to develop partnerships to support this. The administration assisted teachers in curriculum development by encouraging curricular risk-taking and continuous improvement.

The first and third authors conducted research at this school over a 5-year period (Slavit et al. 2016 ). We invited teachers who participated in our long-term study on STEM schools to participate in this investigation about sensemaking of STEM education. Interviews for this study were conducted with 13 RSA teachers and administrators over an 18-month period.

Traditional Middle Schools (TrMS)

This context group was composed of teachers from two middle schools (Rainier and Hood) in a large suburban school district. Both schools had traditional approaches to education, including a seven-period day and distinct courses for each content area (e.g., physical science, algebra, state history). Limited structures for teacher collaboration existed, and teachers’ interactions typically were by discipline and grade level. Each school had approximately 850 students in grades 6–8; 50% of these students came from low-income households, as determined by their qualification for free or reduced-price lunch.

Thirty-four science, mathematics, special education, and English language teachers from these two schools participated in Teachers Exploring STEM Integration (TESI), a 2-year professional development project that included a 2-week summer institute and ongoing support throughout the school years. Twelve of the 34 teachers participated in this study. TESI focused on the integration of STEM design challenges (DCs) into the existing middle school curriculum (Lesseig et al. 2016 ). An interdisciplinary team composed of scientists, mathematicians, and educators from a local university, community college, and school district developed several DCs that could be incorporated into the district’s existing mathematics and science curricula. The professional learning experiences in TESI were explicitly designed to model integrated STEM curricula aligned with math, science, and ELA standards. Authentic mathematical, scientific, and engineering practices received specific and ongoing attention, especially the identification and clarification of the problem; the importance of research, solution testing, failure, and feedback; and the development of evidence-based explanations. Teachers were provided with the literature about and video examples of core instructional practices (e.g., https://ambitiousscienceteaching.org ) specific to mathematics and science. Teachers were also supported in making sense of an engineering design cycle and reflecting on the attributes of a strong design challenge in relation to the student learning experience. The need for and value of STEM learning was also contextualized in terms of twenty-first century challenges and opportunities for innovation.

During the first week of each summer session, teachers engaged in STEM DCs to support their learning about the relevant disciplinary content and to gain familiarity with the engineering design process. During the second summer week, middle school students identified by their teachers as struggling in mathematics or science were invited to attend each morning session; teachers worked alongside the students to solve a design challenge. Engineering, mathematics, and science professors from the university and a variety of other professionals (e.g., a prosthetics designer, a government climate scientist) interacted with the teachers and students. Teachers spent the afternoons reflecting on the students’ engagement, analyzing instructional practices, and planning for the implementation of design challenges in their classrooms. While undertaking design challenges, teachers and students were involved in collaborative and creative problem solving, communication, and critical thinking. The use of various forms of technology was modeled during the professional development summer institutes. The recognition that every student could be a successful contributor to solving a design challenge was also an explicit element of the TESI project.

The second author was the PI for TESI, and the other two authors were involved in the planning and advisory committees. The teachers interviewed for this study were in the TESI project for 2 years and also participated in a study of the implementation of ideas from that project. Participants from one school included eight eighth-grade mathematics, science, STEM, English as a second language, and special education teachers. Participants from the second school included four sixth-grade teachers of mathematics, science, STEM, and special education (see Table  1 ). All were interviewed in the fall of the second year of the project.

Statewide professional development faculty

The professional work context for each of these nine participants was different than that of the TrMS and RSA educators. All shared a common experience as leaders in a statewide STEM education leadership institute. Yet, each came from a different professional context, and they collectively held a variety of professional roles (see Table  1 ).

The PD faculty were responsible for developing and implementing a week-long summer institute on STEM education and leadership for school and district teams from across the state. The institute focused on the development of and leadership for an implementation plan for STEM education. The content of the institute was grounded in the NGSS, CCSS, and CTE standards ( https://careertech.org ) and informed by the NRC ( 2011a , 2011b ) reports on STEM education. In addition, each faculty member brought a wealth of expertise relevant to STEM education from their professional roles external to this initiative; for example, one was a principal of an elementary STEM school and another a scientist at a national laboratory (see Table  1 ). Many were involved with science and mathematics PD at local and regional levels. Across the year, these institute faculty members developed a list of relevant resources that could be useful to institute participants, including model STEM schools, websites, research and practitioner literature, curricula, and STEM activities. Across multiple meetings, the faculty drew upon these resources and their own expertise to develop sessions for the summer institute. Various sessions focused on the meaning and value of STEM education, including how to integrate isolated school subjects and provide connections to the real-world needs and careers, the importance of partnerships between STEM educators and STEM professionals, equity in STEM learning opportunities, and how to anticipate and address common challenges associated with change. Thus, preparation for and implementation of the various sessions in this institute provided opportunities for all faculty members to share their expertise and clarify key ideas about STEM education.

The PD faculty were invited to participate in this study as their perspectives give us insight into how educators who are promoting the innovation are conceptualizing it, what they identify as important, and the extent to which the messages they convey are coherent and consistent. They created their concept maps during the first of a 2-day planning meeting for the summer STEM education institute. The first author was a member of this faculty and had worked with all but two of the members for at least 5 years.

Data collection

Based on our long-term work within each of the three contexts, we had in-depth information about the STEM-relevant contexts for each of the three participant groups, and the actions group members were asked to take. The above descriptions of each of these contexts were developed in order to address sub-question A about potential relationships between contextual elements and participants’ sensemaking about STEM education.

To capture participants’ conceptualizations of STEM education, we asked them to construct concept maps and used follow-up interviews to clarify the meaning of map elements. At the time of the interviews, each participant had implemented some kind of STEM education-related action multiple times and had opportunities to individually and collectively make sense (envision, enact, select, retain) of STEM education. Initially, each participant was asked if they were familiar with concept mapping and, if needed, given a brief overview about representing concepts and sub-concepts hierarchically. They were asked to construct a concept map in response to two questions: “What is your understanding or conception of STEM education? and What do you see as the most important ideas and sub-ideas?” Due to contextual constraints, participants created their concept maps in varied settings. The participants from the three schools were invited to meet with researchers in pairs or individually at a time convenient to them. The PD faculty developed their concept maps individually while all were in the same room. Each person was given as much time as needed to develop her/his map. The researcher read or wrote while participants were constructing their maps to alleviate potential discomfort. Participants were not held to using a traditional hierarchical structure in their mapping; as such, map formats ranged widely (Figs.  2 and 3 ).

Hierarchically arranged concept map from Hunter, RSA

Non-traditional concept map, Bridget, PD faculty

After concept mapping, semi-structured interviews were used to provide participants with another opportunity to make sense of their ideas about STEM education and inform the research findings. TrMS and RSA participants were interviewed immediately after constructing their maps. Due to time constraints, clarification of the maps of the PD faculty was done informally over the duration of the faculty meeting rather than with semi-structured interviews. However, for three PD faculties who constructed non-traditional concept maps (e.g., Fig.  3 ), semi-structured telephone interviews were conducted. Participants were asked to “talk us through” their concept maps. The interviewer would then follow up on a particular idea or ask a participant to elaborate on specific ideas they brought up. The researcher also asked what, if any, questions participants had about STEM education, and what supported them in coming to these particular views of STEM education. In cases where interviews were conducted in pairs, participants were asked to compare and contrast their maps or to comment on specific ideas that may have appeared on a colleagues’ map. For some participants, the interview prompted them to make modifications to the map or express additional ideas that were not on the map. For others, the interview did not result in additional information. In explaining the components of the map, participants could notice what they had included (or not) and how they had portrayed relationships between ideas.

Data analysis

Concept maps can be analyzed quantitatively and qualitatively (Greene et al. 2013 ). A quantitative analysis involves counting nodes (concepts), hierarchies (chains of sub-concepts out of one node), and cross-links between hierarchies to infer the complexity of the map creator’s understanding of the concept being represented. However, because we allowed each participant to represent their thinking in whatever way it made personal sense, some of the participants’ maps did not readily translate to quantitative analyses (e.g., did not include identifiable nodes or were global in nature, see Fig.  3 ). We chose to analyze the concept maps qualitatively and analyzed the interview data concurrently to aid our interpretation of the concept maps. We looked at the maps holistically, attending to the overall structure, the words used as nodes, and words used as cross-links. These analyses led to our primary results on the participants’ views of STEM education, including the emergence of our themes, and a secondary quantitative synthesis of each theme’s frequency across the participants’ context groups and role groups.

Generating themes

We drew on current research on STEM education as well as a grounded approach based on our interviews with teachers to generate our initial themes (Breiner et al. 2012 ; LaForce et al. 2014 ; Peters-Burton et al. 2014 ; Sanders 2009 ). We developed nine initial themes and added three others as the coding progressed. The initial themes were a synthesis of the way participants represented or talked about the attributes of STEM education and the major attributes that are described across the literature. For example, because project- or problem-based learning (PBL) tends to be situated in real-world contexts, we originally had one theme for PBL that included real-world connections. However, on a majority of concept maps, there were distinct nodes for real-world problem solving and others for attributes that characterized the student learning experience, regardless of whether it was within a PBL approach. Thus, we created different themes for these two distinct aspects of STEM education (RWPS, StLE; see Table  2 ).

The three codes (Val, TchNd, ChPrb in Table  2 ) were added later in the coding process to better capture significant themes that emerged in our analysis. For example, when we began coding the concept maps of the PD faculty, we saw ideas that related to opportunities to practice twenty-first century skills through PBL but also referred more generally to creating a STEM-literate citizenry. Thus, we created a separate theme to capture this more global perspective. Specifically, we coded nodes that focused predominantly on the abilities and dispositions of each student to communicate, work collaboratively, think creatively, or persevere in problem solving as “twenty-first century skills” (21CS). Nodes that reflected a broader conceptualization related to global citizenship and STEM literacy as having economic and other societal benefits were recoded as “value of STEM literacy” (Val).

We also developed two themes to reflect nodes associated with the conditions needed for implementing STEM-oriented teaching or curriculum. Ideas associated with what teachers might need in order to implement STEM education such as content knowledge and time for collaborative planning were coded as “teacher needs” (TchNd). Challenges and problems in implementing STEM education (ChPrb) showed up on some concept maps or, more frequently, emerged during the interviews. These responses ranged from structural constraints, such as lack of collaborative planning time or students in one class not having the same mathematics and science teachers (preventing extending projects across two class periods), to the politicization of STEM education.

Thematic analysis

In January 2015, the first author analyzed each map from the TrMS and RSA participants, generating themes based on the words participants used as nodes (concepts and sub-concepts) and cross-links (e.g., a line labeled “supplement each other” drawn between the nodes for “science” and “math” would be coded as IntDis for integration). Coding rules were developed and used to clarify the coding themes. In August 2015, PD institute faculty maps were obtained and coded by the first author, and coding rules were further elaborated. In September 2015, the second two authors and a research assistant coded six concept maps. After discussions with the first author, coding rules were further clarified and made more specific, especially to distinguish between student learning experiences and instructional practices. To check the reliability of our thematic coding on complex, non-traditional maps, the first author conducted follow-up interviews with three of the PD faculty and found that the initial coding accurately represented the mapmaker’s intentions. Based on the revised and/or clarified coding rules, the first author recoded all 34 concept maps, using the interview transcripts and concept maps concurrently. As the interview protocol probed for explanations about each map element, the transcripts helped clarify meanings or validate interpretations of cross-links and nodes.

Quantifying the themes

We coded 34 concept maps as described above and then counted how many people included each theme in their concept maps. After all maps were coded for the themes, we counted the occurrence of each theme, recorded these for each individual, and compiled the total inclusion of each theme. This allowed us to respond to our main research question. To address our two sub-questions, we then looked at the frequency of theme inclusion for each context group (RSA, TrMS, PD faculty) and also determined the frequency of inclusion of each theme by general role groups: STEM teachers (18 secondary math, science, technology, engineering, CTE teachers), non-STEM teachers (5 secondary special education or ELL teachers), school or district administrators (5), and non-school-based external partners (6 partners from businesses or organizations or regional PD providers). We present a discussion of our analyses in the next section.

Limitations

The use of concept maps to elicit conceptualizations of STEM education has multiple limitations. Although we allowed participants to construct their maps in non-traditional ways, including writing a paragraph instead of mapping, some may have felt uncomfortable portraying their ideas using this type of representation or may not have included all their ideas. While the interviews provided an opportunity for participants to add to or expand upon their representations, participants may have held ideas they did not want to share, lacked the ability or language to represent, or perhaps were not considering at the time of the interview. Moreover, participants may not have mentioned certain ideas they perceived as obvious, such as the inclusion of all students in STEM experiences. There are also limitations related to the participant pool. There were limited numbers of non-STEM teachers (5), administrators (5), and external partners (6) in comparison with the number of STEM teachers (18) who participated. However, the concept maps and interviews with all participants provide insight into the variation that is possible in making sense of STEM education.

We address our main research question by showing the frequency of the various themes relevant to STEM education (coding categories) that were included in individual concept maps (Table  3 ) and providing examples that show different individual’s conceptualizations of the theme at the time. We then address sub-question A by showing the frequency of theme inclusion by context group (Table  4 ) and examining relationships between the conceptualizations of STEM education and the context in which participants implemented STEM education activities. Finally, we address sub-question B by organizing the themes by role group (Table  5 ) and discussing potential relationships between the responsibilities inherent in specific roles and the elements of STEM education that surfaced in the concept maps among participants in that role. Our data suggest that certain aspects of STEM education are more salient in participants’ conceptions, and both context and role group contribute to these conceptions.

Making sense of STEM education

We first tabulated the inclusion of theme by individuals and calculated the percentage of participants who included each theme. As shown in Table  3 , there were three common themes on the concept maps: a connection across disciplinary subjects (IntDis), a focus on what teachers must attend to instructionally (InstPrac) when implementing a STEM approach, and explicit connections between in-school content and out-of-school problems or contexts (RWPS).

Interview data provided detail on how each participant conceptualized these themes. For example, when asked what her inclusion of the word “integration” meant (IntDis), a special education teacher from the TrMS group explained:

The reading, the writing, the art, the creativity. You know? You’re using computer skills. You’re using building skills. … So it makes [students] use everything. And the cool thing is they don’t know they’re using all that. (Brenda, interview, January 29, 2015)

A member of the PD faculty who was also the principal of an elementary STEM school talked about how real-world problems helped the teachers develop integrated curricula:

What we do is intentionally interweave the S, the T, the E, the M into instruction. So, at a typical elementary or middle school, often subjects are segmented and segregated, kind of siloed. Our commitment is that our students are doing STEM every day … . We intentionally plan STEM … we take the standards and cut them all apart and then piece them all together so we have consistent themes or overarching problems for students to solve. (Bridget interview, September 30, 2015)

A middle school science teacher from RSA also included real-world connections and instructional decision-making on his map. In his interview, he explained why real-world connections were important and how he developed these:

And so I started with real world scenarios, just because to me the science, technology, engineering and mathematics, kind of the end goal is getting students more fully prepared for real life. And so having them deal with real world scenarios helps them to do that. Couple of different ways to do that, one I had input from professionals … .And then opportunities to see and experience that real world, or real work, environment or conditions. (Hunter interview, November 4, 2014)

Participants represented these three themes (integration, real-world connections, and instructional practices) separately on their maps but, as seen by these comments, often revealed significant relationships among these themes in their interviews.

Over half of all participants included attributes of students’ learning experiences (StLE) and students’ opportunities to develop twenty-first century skills (21CS) as salient features of STEM education. Ideas related to the attributes of the student learning experience were represented on 59% of concept maps. Comments about this often addressed students’ engagement in the authentic practices of each discipline. A high school math teacher at RSA explained that “Kids should be looking for patterns, engaged in the real work of scientists and mathematicians” (Greg, October 19, 2015). A scientist who was a member of the PD faculty described that the student learning experience should involve “designing and developing within constraints [as this] models real world scenarios. .. realizing it is okay to learn from failure and that there isn’t just one right answer all the time” (Sophie interview, September 30, 2015).

The opportunity for students to develop and practice twenty-first century skills and dispositions was also included on over half of the concept maps. Participants listed specific skills, such as collaboration, communication, and perseverance. Expanding on this area in interviews, some connected these skills to career and life opportunities. As a TrMS math teacher described:

I think the end goal, what I would really want is students who can problem solve. … Life problems, work problems, I mean for years I’ve just thought employers just want employees who can think and take care of the problems at hand. Not have to be told, “Do this, do this, do this.” And so if you’re a problem solver you’re going to be a great employee. If you’re a problem solver you’re going to be a great inventor. (Olivia interview, January 26, 2015)

Less than one third of the participants included an explicit reference to STEM education as providing opportunities for all students to participate and be successful (Equ). Also, less than one third included ideas about technology (Tech), other than to write the word “technology” as part of STEM. We further discuss the low representation of these categories in the next section.

Making sense of STEM education in different contexts

In this section, we address sub-question A regarding the themes educators in different professional contexts included in their conceptualizations of STEM education and the possible relationships between an individual’s conception of STEM education and the context in which she/he works. We first calculated the frequency of the inclusion of each theme for each context group. Table  4 shows that within context groups, different categories were more salient than others. We draw from our descriptions of the PD and school environments to consider potential relationships between the attributes of each context group’s STEM education work and the themes that were most or least commonly identified within that group.

Aside from the attributes common across all participants (interdisciplinary, instructional practices, and real-world problem solving), the statewide PD faculty, a group composed of people with a wide variety of backgrounds, commonly focused on broader concepts such as the global, societal value of STEM education (Val). This was also an overall theme of the summer STEM leadership institute developed by the PD faculty. The maps from the PD faculty also highlighted partnerships (Prtnr) between STEM professionals, teachers, and students. Claudia, a regional PD provider, indicated that STEM education benefits from community connections with “professionals in STEM, professionals related to STEM, informal science educators” and “benefits with support from parents, community professionals, and administrators” (Claudia concept map, May 7, 2015). The development of partnerships between schools and STEM professionals was addressed in multiple sessions during the institute, and two thirds of the PD faculty retained ideas about this attribute of STEM education when constructing their concept maps.

Ideas related to technology (Tech) were not commonly included on the PD faculty maps. Three of the four who included technology were people who worked most directly with it: the STEM school principal whose third- through eighth-grade students all had iPod touches or laptops, one of the business partners, and the district-level CTE director. On the fourth map that included technology, the strand of ideas was “STEM education ➔ multiple academic subjects ➔ technology [is] ill-defined” (Abel concept map, May 7, 2015). Abel’s notation is indicative of the confusion around what the T in STEM education means. At the institute, an invited presenter described how K-12 educators are uncertain about whether technology now means computer science, students’ and teachers’ use of information and communication technology (e.g., the internet; word processing and presentation tools), or tools more commonly found in CTE courses, such as 3D printers.

Forty-four percent of the PD faculty included an explicit relationship between STEM education and equitable learning opportunities (Equ), using phrases such as “teaching every child” (Marion concept map, May 7, 2015). Carlton expanded on this perspective: “It’s about the individual kid, not the industrial model of kids [coming through school]” (Carlton interview, September 30, 2015). Equity was a major theme of the institute, including a focused session at the beginning of the week and embedded in multiple sessions throughout.

Only one third of the PD faculty included standards (Stan), although standards received significant attention in a number of sessions during the institute. Also, less than half of this group included ideas about the student learning experience (StLE) or twenty-first century skills (21CS). The nature of the student experience in a STEM learning environment was modeled in a half-day session, although ideas about students’ opportunities to practice and develop twenty-first century skills were more implicit across sessions. The roles of PD faculty outside of the context of the institute might better explain why these three themes were not more frequently included on the concept maps of this group. We will discuss that in a subsequent section.

As shown in Table  4 , 50% or more of the participants in the TrMS group included attributes directly related to curriculum and instruction: interdisciplinary curriculum, ambitious instructional practices, attributes of students’ learning experiences, twenty-first century skills, standards, and real-world problem solving, in that order. These themes directly relate to elements of the professional development the teachers participated in for 2 years, where STEM design challenges were presented as a way to integrate standard-based mathematics and science content into existing curricula.

Over 50% of the participants from these two traditional middle schools also included ideas about various challenges associated with the implementation of STEM education (ChPrb). This reflects the constraints presented by their school contexts, including “time for planning” and “difficulties with creating in-depth integrated math and science problems.” Another challenge related to school structures that inhibited enacting the interdisciplinary, project-based curriculum units they were exploring in the TESI PD project. An eighth-grade science teacher explained:

The way our building is lined up or our schedule is we’re not in teams by any means. I mean my kids go off and see three different math teachers. So if it was ideal they’d have one math teacher, one science teacher, one humanities and we could do a little bit more of that integration, true integration. (Anthony interview, December 9, 2014).

Over 50% of the TrMS participants included references to standards (Stan) on their maps or mentioned these in interviews. Again, the context was important. Many of the comments reflected a negative relationship between the need to address standards and the desire to enact interdisciplinary, project-based curricula. Shawn, an eighth-grade teacher who had developed a new STEM elective course, commented on standards in this way:

I mean [this STEM course] is a great opportunity and I hope others get the chance and embrace it and run with it because I think it’s got a chance to be really successful and get some kids far better prepared for the real world than just learning back again state standards and stuff. I’ve probably been negative about state standards in my comments, and they’re important, but I don’t know that they focus enough on the STEM related skills, the integration of all this stuff to give kids successful opportunities to fulfill roles in business as problem solvers. (Interview, December 9, 2014)

These participants worked in two traditional middle schools in a district and state context where teachers were attempting to understand how to support students in meeting CCSS for mathematics and language arts, as measured by state achievement test data. Teachers were also just becoming familiar with the NGSS, both through the TESI project and other regional and district-level PD events. While the curricular units provided by the TESI project were aligned, the other instructional materials provided by the district were purchased prior to these new standards.

Ideas related to the access and opportunity for all students (Equ) were included on one third of the TrMS participants’ maps. The TESI summer institute was designed to help teachers recognize ways to support all students’ successful participation in STEM learning. For a week, students who had struggled with the content of their math or science courses joined their teachers in tackling engineering design challenges. Only four teachers explicitly identified this as an important feature of STEM education. A sixth-grade math teacher stated: “All kids bring skills, everyone’s good at something, no one’s good at everything” (Regan concept map, January 29, 2015) and a sixth-grade special education teacher constructed this strand on her map: “STEM education ➔ very inclusive ➔ kids of many levels can access something” (Brenda concept map, January 29, 2015). Others may have implied ideas about equity in other aspects of their concept maps, but there were no other explicit words or ideas either on maps or in interviews that we could code for this theme.

Three themes were seldom included or not included at all. Only one person from the TrMS group included ideas related to technology (Tech) and connecting it to “research skills.” This is not too surprising for traditional schools; one teacher pointed out the non-working Wi-Fi router on her classroom ceiling, and others commented that CTE classes were the only places where students could access technological tools. Students’ use of technology in the form of robotics was modeled in the summer PD but received little explicit attention other than that. Partnerships (Prtnr) and a broader value for STEM education (Val) did not appear on any concept maps in the TrMS group. While a variety of STEM professionals contributed to the activities of the summer institute, the development of partnerships in relation to supporting students’ interests in STEM careers and learning opportunities was not an explicit element of the PD.

Similar to the TrMS group, the participants from RSA most frequently included themes directly related to the classroom (IntDis, RWPS, InstPrac, StLE, 21CS; see Table  4 ). Also, over 50% of the RSA participants included partnerships (Prtnr) as an element of STEM education. This reflected a focus of their school philosophy, where building sustainable partnerships was supported with a half-time faculty position dedicated to cultivating business and academic partners to support student learning. The high school art teacher connected “relevance to real-world experiences” to “work-based learning and internships” (Josh concept map, October 15, 2015) and the principal represented this theme with a connection from STEM education to “extended learning opportunities and mentors” (Sandra concept map, June 4, 2015).

Similar to the other context groups, only 5 of the 13 participants from RSA included ideas about technology (Tech), although the technology was an explicit component of the school. A middle school history and language arts teacher who did include technology on his map explained why he positioned it as one of the major nodes: “I feel technology is embedded into everything. Because technology is just something that helps make the job easier” (Jason interview, November 4, 2014). The robotics and pre-engineering teacher discussed her vision for how technology should be integral to a STEM school:

I think for STEM education, space is very important and that’s one thing that we lack here. For maker space, fabrication projects, things like that. I mean both room as well as having the tools available. So C&C machines, we have a 3D printer but we haven’t been trained on using it yet. You know I mean just . . . any type of thing that you can think that a student might want to use to create. (Rachel interview, November 6, 2014)

The technology was of great importance to some of the RSA participants but not considered by the majority.

Ideas related to standards (Stan) were included on less than one third of the concept maps of the participants from RSA. While these teachers worked in the same state context as the TrMS teachers, they were located in a different district. More importantly, their school context differed. Teachers may have been more focused on the need to develop curriculum to address the school vision of interdisciplinary, project-based learning than to align with standards. However, the high school science teacher was very focused on the NGSS and developed two relevant strands on his concept map, one that connected STEM education ➔ integration ➔ 3D teaching ➔ science practices, concepts, and cross-cutting ideas, and another that connected STEM education to the K-12 Framework (National Research Council 2012 ). Alternately, the high school math teacher talked at length about how the pressures from testing specific standards at specific times was a roadblock to project-based learning: “I could develop a four-year program that would get kids to all standards, but the way it’s going now. .. we are trying to fill in skill gaps so how can we get into that real world stuff?” (Greg interview, October 19, 2015).

Finally, few of the RSA participants (15%) included or talked about opportunities for all students in STEM education (Equ). The principal wrote, “Do everything you can to support student success – make it happen” as the overarching concept on her map, and further explained in her interview:

You do everything you can to support student success and you make it happen. That’s what we’re after. Because every child can learn, every child wants to learn and be successful. And we just have practices and things in place in K-12 that separate out, that rank, and we know in our hearts and in our minds that not all students learn everything at the same pace, the same rate. It doesn’t mean they can’t learn or they won’t learn. (Sandra interview, June 4, 2015)

Also, the robotics teacher connected the curriculum ideas on her map to the challenge she faced in getting more girls interested in STEM areas (Rachel interview, November 6, 2014). Others did not specifically reference ideas related to equitable student opportunities. RSA opened as an inclusive STEM school and from conversations with RSA teachers separate from the data collection for this study, we know teachers are well aware of the need to support all kinds of students in STEM learning. However, based on the concept map data and interviews, teachers were not making explicit connections between the “most important ideas about STEM education” and opportunities for all students.

Making sense of STEM education by role group

Given the multiple roles represented by the participants in this study, we next examined whether there would be notable similarities or differences in the conceptualizations of STEM education based on participants’ professional responsibilities (sub-question B; Table  5 ). Table  5 is organized in descending order of the most commonly included concept map themes by individual participants, making for an easy comparison between the global findings (reported in Table  3 ) and the frequency of inclusion by role group. Teachers of STEM-specific courses comprised the largest group, with 18 participants. Thus, it is not surprising that the most commonly included themes by individual and by context group are also those that STEM teachers most commonly included. Science, mathematics, technology, and CTE teachers are directly responsible for implementing the individually and/or collectively constructed vision of STEM education. They must identify or develop interdisciplinary curricula (IntDis) and determine how to bridge from in-school to real-world problems (RWPS). They understand that supporting students in the project- or problem-based learning experiences (StLE) will require instructional approaches that may differ from traditional, teacher-centered practices (InstPrac).

The interdisciplinary nature of STEM learning was by far the most salient feature for non-STEM teachers as well, and a significant focus by the administrators and external partners.

The art teacher from RSA explained:

I added art in there because I feel like that’s important. Turning it into STEAM. But like literally every single thing is intermingled. Like it’s a melting pot. All of it just goes together. Basically no matter what assignment, project, anything you pick you can connect every single one of these STEM or STEAM aspects into one another. (Brittany interview, November 10, 2014).

Real-world problem solving (RWPS) and ideas about instructional practices (InstPrac) were also included by the majority of non-STEM teachers, but the remaining themes were not consistently included. Many of the non-STEM teachers connected the need for an interdisciplinary approach to real-world problem solving yet faced challenges in connecting this approach to the standards they felt necessary to address. A sixth-grade special education teacher in the TrMS group explained that she wanted to bring in “Kind of authentic experiences and real-world [problems]” yet found that “it’s hard to integrate the 6th grade standards with STEM. I wish we had more time.” (Brenda interview, January 29, 2015).

School and district administrators all included ideas related to instructional practices, and most also included ideas about the student learning experience (StLE) and interdisciplinary curricula (IntDis). Administrators largely recognized most of the thematic elements of STEM education, except for the more global value (Val). In comparison, nearly all the external partners (regional PD providers and business or organization partners) included ideas related to this broader value of STEM education (Val) as well as connections to real-world problems (RWPS). Similar to all the role groups, the interdisciplinary nature of STEM curricula (IntDis) was included by most. External partners included external partnerships at a higher frequency than other groups.

As in the case of PD context, there is an indication in these data that the responsibilities of one’s specific job contribute to the elements of STEM education that are retained. Administrators, who tend to have responsibilities that relate to a large number of educational issues, gave explicit attention to numerous elements. Similarly, the broader outlook of the external partners, reflected in their attention to global values of STEM education in their concept maps, is consistent with their duties and responsibilities inside the STEM education system.

The ways in which the teacher participants made sense of STEM education was also consistent with their roles and responsibilities. Most teachers found interdisciplinary and real-world connections to be especially relevant. However, STEM teachers were also more likely to consider content standards, instructional approaches commonly associated with STEM education such as project-based learning, and twenty-first century skills in their conceptions. Non-STEM teachers were much more attentive to more general attributes of instruction, such as student-centered practices, engagement, and participation.

Those working with the implementation of STEM education are well aware that while core elements have been identified (Kelley and Knowles 2016 ; LaForce et al. 2014 ), there are still varying conceptions of what a STEM school or program entails. In this way, enacting STEM education entails innovation and motivates sensemaking. Our research shows that even when educators have similar professional learning experiences and/or work in the same contexts, they may make sense of what this innovation means quite differently. What is seen as most important to attend to or innovate around may differ in relation to professional roles and contexts.

Sensemaking provided a useful framework (Fig.  1 ) for considering the influence of institutional and professional contexts in shaping each educator’s construction of a plausible story of STEM education. Context appears to have some relationship with the ideas about STEM education noticed and retained by participants. This is most apparent in relation to partnerships, a key feature of the PD faculty work and of RSA. The identity of RSA as a STEM school supported teachers’ sensemaking about elements associated with STEM education such as interdisciplinary curricula, project-based learning, inclusion, and partnerships; these were part of the school vision statement. On the other hand, the professional identities of non-STEM teachers (e.g, English or history teachers) and STEM teachers shaped their individual meaning-making in relation to a STEM-focused curriculum. Teachers at the two middle schools were enacting STEM curricula in the context of a traditional middle school, with compartmentalized science and mathematics and a curricular focus aligned with statewide tests. Given these constraints, teachers in a more traditional school context may not take up ideas about STEM education that they encounter in professional learning experiences as readily as those in a STEM school context. The PD faculty worked in various professional contexts, with most in non-school settings. The STEM education ideas most salient to these scientists, business partners, and regional educators differed notably from those of STEM and non-STEM teachers.

In addition to the influence of institutional and organizational contexts, opportunities for collective reflection on the enactment of ideas associated with STEM education also contribute to an individual’s sensemaking (Davis 2003 ). Talking about actions involves “sensegiving,” which serves both to give information or feedback to others as well as an opportunity to “hear what one thinks” and further develop a plausible story (Weick et al. 2005 , p. 416). For the TrMS teachers, there was an ongoing dialog with their colleagues, the PD providers, their instructional coaches, and their administrators. We can imagine that not only the traditional structures of the schools but also the differing ideas about and experiences with curriculum, instruction, and learning held by everyone involved in these conversations influenced the STEM education ideas the TrMS teachers selected and retained. Similarly, the PD faculty came together at least twice per year over 3 years to continually refine and co-construct their understandings about STEM education. Each drew upon relevant experiences from their professional roles and from educational research as they collectively developed a STEM education framework for each summer institute. At RSA, teachers met weekly to jointly develop curriculum and discuss student progress and school development. Teachers and administrators received feedback from the community of STEM professionals, parents, and district administrators, which also informed their conversations and subsequent sensemaking.

As shown in Table  3 , our findings show the majority of educators in this study shared some common ideas about what is important for STEM education. However, identifying attributes and realizing these in practice are very different. For example, the interdisciplinary or integrated curriculum was the most identified theme across all concept maps. However, this may not be easily accomplished at many middle and high schools in the USA, as disciplinary skills and knowledge are often siloed, pacing guides determine time devoted to a given concept, and students move to different teachers in different groups. Opportunities to set up and engage in long-term STEM-related projects are constrained by these institutionalized practices as well as by space and equipment. Addressing this commonly identified attribute of STEM education will require tremendous creativity and resources.

Our analysis revealed other attributes that only a few included. The overall low representation of STEM education as an opportunity for all students is troubling. It may be that this was a concept educators considered but held distinct from STEM education. However, it has been apparent in education that when equity is not explicitly named and addressed, it is overlooked; Rodriguez ( 1997 ) termed this “the dangerous discourse of invisibility.” The inclusion of all students in STEM learning was emphasized in each of the contexts in this study yet failed to be retained as a salient attribute. The development of a STEM-literate citizenry and increased opportunities for all students to pursue STEM-related professions will require educators to explicitly address how students are included in or excluded from meaningful STEM learning.

Our data suggest that professional roles and contexts influence the vision educators develop about STEM education. These results raise questions about the coherence of this innovation when people in the same school or district make sense of it in such different ways. Given the variety of institutionalized practices and contexts across schools, we are not convinced that a single worldwide definition of STEM education is critical. What we do see as essential is that those working in the same system, be it a department, school, or district, explore the common elements that are being attributed to STEM education and co-construct a vision that provides opportunities for all their students to attain STEM-related goals. Visioning, however, is insufficient, as what is envisioned and what is implemented are often very different. Educators must push on the status quo in areas of instruction, curriculum, learning opportunities, assessment, and school structures. Sensemaking as a collaborative, reflective, and iterative process can surface the differences and commonalities in people’s understandings to better ensure consistency in students’ learning opportunities across classrooms.

We propose that collective sensemaking through professional dialog be an explicit and ongoing activity when planning for and implementing STEM education. Supporting dialog among stakeholders from different contexts and professional roles is critical in order to ensure that diverse perspectives about the attributes for STEM teaching, learning, and curricula can be raised and discussed. For example, community members and policymakers may take a more global perspective focused on economic and societal implications. STEM and non-STEM teachers may focus on different aspects of the learning experience. Administrators are positioned to make sense of how individual teachers’ efforts contribute to student opportunities.

While it has been well established that professional development experiences, school vision statements, or readings about an innovation do not directly translate into the classroom and school practices (Penuel et al. 2008 ), explicitly identifying the ideas educators are and are not selecting and retaining can inform professional learning activities at local and larger scales. Further research is needed to understand more specifically what ideas educators notice, select, and retain about STEM education and how to support educators’ construction of plausible stories that promote a consistent vision of STEM education across a system.

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App ideas that solve real-world problems

Grow Solutions

The power of mobile apps in solving real-world problems

Mobile apps have become an integral part of our daily lives, offering convenience, efficiency, and entertainment. However, their potential goes beyond just providing entertainment or convenience. Mobile apps have the power to solve real-world problems and address common challenges that people face in their daily lives.

Mobile apps can leverage the capabilities of smartphones, such as GPS, cameras, sensors, and connectivity, to create innovative solutions for a wide range of problems. Whether it’s improving healthcare, enhancing education, promoting sustainability, or streamlining business processes, mobile apps have the potential to make a significant impact on society.

Identify and address common challenges through app development

To develop an app that solves a real-world problem, it’s important to identify the common challenges that people face in their daily lives. This can be done through market research, surveys, user feedback, and observing trends and patterns in society.

Once the challenges are identified, app developers can brainstorm innovative solutions that leverage the unique capabilities of mobile devices. This could involve creating apps that provide information, facilitate communication, automate tasks, or offer personalized experiences.

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Overview of the importance of problem-solving apps

Problem-solving apps play a crucial role in addressing societal challenges and improving the quality of life for individuals. Here are a few reasons why problem-solving apps are important:

• Efficiency and convenience : Problem-solving apps can streamline processes, automate tasks, and provide convenient access to information and services. It can save time and effort for users, making their lives easier.
• Access to information : Provide valuable information and resources that may not be easily accessible otherwise. It can empower users to make informed decisions and take action to address their challenges.
• Personalization : Offer personalized experiences tailored to the specific needs and preferences of individual users. It can enhance user satisfaction and engagement with the app.
• Social impact : Have the potential to make a positive impact on society by addressing pressing issues such as healthcare, education, environmental sustainability, and social justice. They can contribute to creating a more inclusive and equitable world.
• Innovation and entrepreneurship : Developing problem-solving apps requires creativity, innovation, and entrepreneurial spirit. By encouraging app development, we foster a culture of innovation and entrepreneurship, driving economic growth and job creation.

Healthcare and Wellness App Ideas

Improving access to healthcare services.

Improving access to healthcare services is a crucial aspect of healthcare and wellness. Mobile apps can play a significant role in enhancing access to healthcare by providing the following features:

• Telemedicine : Telemedicine apps allow users to consult with healthcare professionals remotely, eliminating the need for in-person visits. These apps enable users to schedule virtual appointments, have video consultations, and receive medical advice and prescriptions.
• Healthcare provider directories : Apps can provide comprehensive directories of healthcare providers, including doctors, specialists, clinics, and hospitals. Users can search for healthcare providers based on location, specialty, and other criteria, making it easier to find the right healthcare professional.
• Emergency services : Apps can provide information on nearby emergency services, such as hospitals, urgent care centers, and pharmacies. They can also include features like emergency contact numbers and first aid instructions, ensuring quick access to help in critical situations

Appointment scheduling and reminders

Appointment scheduling and reminders are essential for managing healthcare appointments effectively. Mobile apps can offer the following features to help users stay organized:

• Appointment scheduling : Apps can allow users to schedule appointments with healthcare providers directly from their smartphones. Users can view available time slots, select a convenient appointment time, and receive confirmation details.
• Appointment reminders : Send reminders to users about upcoming appointments, ensuring that they don’t miss important healthcare visits. Reminders can be sent via push notifications, SMS, or email, depending on the user’s preference.
• Calendar integration : Integrate with the user’s calendar app, automatically adding healthcare appointments and reminders to their existing schedule. It helps users manage their time effectively and avoid scheduling conflicts.

Fitness and nutrition tracking

Fitness and nutrition tracking apps can help individuals monitor their physical activity, diet, and overall well-being. These apps can include the following features:

• Activity tracking : Apps can use the smartphone’s sensors or connect with wearable devices to track steps, distance, calories burned, and other fitness metrics. Users can set goals, track their progress, and receive personalized recommendations for improving their fitness levels.
• Diet and nutrition tracking : Allow users to log their meals, track calorie intake, and monitor their nutritional intake. They can provide information on the nutritional content of foods, offer meal planning suggestions, and help users make healthier food choices.
• Workout routines : Provide pre-designed workout routines or create personalized workout plans based on the user’s goals and fitness level. They can include instructional videos, timers, and progress tracking to help users stay motivated and achieve their fitness objectives.

Also read: How to Patent an Idea for an App?

Mental health and meditation apps

Mental health and meditation apps can support individuals in managing stress, improving mental well-being, and practicing mindfulness. These apps can offer the following features:

• Guided meditation : Apps can provide a library of guided meditation sessions, allowing users to choose from various themes, durations, and meditation techniques. They can include soothing audio, visual aids, and progress tracking to help users develop a regular meditation practice.
• Stress management tools: Offer tools and techniques for managing stress, such as breathing exercises, relaxation techniques, and mindfulness exercises. These tools can help users reduce anxiety, improve sleep, and enhance overall mental well-being.
• Mood tracking : This allows users to track their moods and emotions over time, helping them identify patterns and triggers. This information can be used to gain insights into mental health and facilitate communication with healthcare professionals if needed.

Education and Learning apps

Remote learning and virtual classrooms.

Remote learning and virtual classrooms have become increasingly popular, especially in recent times. These approaches to education leverage technology to enable students to learn from anywhere, at any time. Here are some key aspects of remote learning and virtual classrooms:

• Online learning platforms : Online learning platforms provide a digital space where students can access course materials, participate in discussions, submit assignments, and interact with instructors and peers. These platforms often include features such as video lectures, interactive quizzes, and discussion forums.
• Live virtual classes : Virtual classrooms allow students and teachers to connect in real time through video conferencing tools. Students can attend lectures, ask questions, and engage in discussions with their classmates and instructors. Virtual classrooms aim to replicate the interactive nature of traditional face-to-face classes.
• Asynchronous learning : Asynchronous learning refers to self-paced learning, where students access pre-recorded lectures, readings, and assignments at their convenience. This approach provides flexibility for students to learn at their own pace and manage their time effectively.
• Collaborative tools : Remote learning often incorporates collaborative tools that enable students to work together on projects, presentations, and group assignments. These tools can include shared documents, online whiteboards, and video conferencing features.

Language learning and translation apps

Language learning and translation apps have revolutionized the way people learn new languages and communicate across language barriers. These apps offer various features to enhance language learning and translation:

• Interactive lessons : Language learning apps provide interactive lessons that cover vocabulary, grammar, pronunciation, and cultural aspects of a language. These lessons often incorporate multimedia elements, such as audio recordings, videos, and interactive exercises.
• Speech recognition and pronunciation practice : Many language learning apps include speech recognition technology to help learners improve their pronunciation. Users can practice speaking and receive feedback on their pronunciation accuracy.
• Translation tools : Language learning apps often include translation features that allow users to translate words, phrases, or entire sentences between different languages. These tools can be useful for understanding unfamiliar words or practicing translation skills.
• Gamification and progress tracking : To make language learning engaging, apps often incorporate gamification elements, such as quizzes, challenges, and rewards. Users can track their progress, set goals, and receive feedback on their language proficiency.

Skill development and online courses

Online courses and skill development platforms offer a wide range of courses to help individuals acquire new skills or enhance existing ones. Here are some key aspects of skill development and online courses:

• Diverse course offerings : Online platforms provide courses on various subjects, including programming, data analysis, marketing, design, and personal development. These courses are often created by industry professionals and experts in their respective fields.
• Flexible learning options : Online courses offer flexibility in terms of scheduling and pace of learning. Learners can access course materials at their convenience and progress through the content at their own speed.
• Certifications and credentials : Many online courses provide certifications or credentials upon completion, which can be valuable for career advancement or showcasing skills to potential employers.
• Interactive learning experiences : Online courses often include interactive elements, such as quizzes, assignments, and discussion forums, to facilitate active learning and engagement. Learners can receive feedback from instructors and interact with peers.

Study aids and educational resources

Study aids and educational resources encompass a wide range of tools and materials that support learning and academic success. Here are some common examples:

• Digital textbooks and e-books : Digital textbooks and e-books offer convenient access to educational content. They often include features like search functionality, highlighting, and note-taking capabilities.
• Educational websites and apps : There are numerous websites and apps that provide educational resources, such as practice exercises, study guides, flashcards, and educational videos. These resources can supplement classroom learning and help students reinforce their understanding of various subjects.
• Online libraries and databases : Online libraries and databases provide access to a vast collection of academic journals, research papers, books, and other scholarly resources. Students can use these resources for research projects, essays, and assignments.
• Study planners and organization tools : Study planners and organization tools help students manage their time effectively, set goals, and stay organized. These tools can include features like task lists, reminders, and progress tracking.

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Transportation and Navigation

Transportation and navigation have become increasingly important in our modern world. With the rise of technology, there are now various platforms and tools available to assist with different aspects of transportation and navigation. Let’s explore some of these areas in more detail:

Ride-sharing and carpooling platforms

Ride-sharing and carpooling platforms have revolutionized the way people travel. These platforms connect drivers with passengers who are heading in the same direction, allowing them to share rides and split the cost of transportation. Examples of popular ride-sharing platforms include Uber , Lyft, and BlaBlaCar. These platforms provide a convenient and cost-effective alternative to traditional taxis and public transportation.

Public transportation and navigation assistance

Public transportation plays a crucial role in urban areas, providing a sustainable and efficient mode of transportation for many people. To make navigating public transportation easier, there are various apps and tools available that provide real-time information on bus and train schedules, routes, and delays. These apps can help users plan their journeys, find the nearest bus or train station, and track the arrival and departure times of public transportation vehicles. Examples of popular public transportation apps include Citymapper , Moovit, and Google Maps.

Parking spot finders and real-time traffic updates

Finding parking in busy urban areas can be a challenge. To address this issue, there are now parking spot finder apps that help users locate available parking spots in real time. These apps provide information on parking garages, lots, and street parking availability, as well as pricing and payment options. Also, real-time traffic update apps can help users avoid traffic congestion and find the fastest routes to their destinations. Examples of popular parking spot finders and real-time traffic update apps include ParkWhiz , SpotHero, and Waze.

Travel planning and itinerary management

When it comes to travel planning, there are numerous tools and platforms available to assist with itinerary management. These tools can help users research and book flights, hotels, and rental cars, as well as plan activities and create personalized travel itineraries. Some platforms even offer features like trip sharing and collaboration, allowing multiple users to contribute to the planning process. Examples of popular travel planning and itinerary management platforms include TripIt , Google Trips, and Airbnb Experiences.

Technology has greatly enhanced transportation and navigation by providing convenient and efficient tools for ride-sharing, public transportation assistance, parking spot finding, real-time traffic updates, and travel planning. These platforms and apps have made it easier for people to navigate their cities, save time and money, and make informed decisions about their transportation options.

Read also: How Much Does App Development Cost?

Sustainability and Environment

Sustainability and environmental awareness have become increasingly important in our efforts to protect the planet and ensure a livable future. Technology has played a significant role in promoting sustainability and providing tools to help individuals and organizations make more environmentally conscious choices. Let’s explore some areas related to sustainability and the environment:

Recycling and waste management apps

Recycling and waste management apps have made it easier for individuals and communities to properly dispose of waste and recycle materials. These apps provide information on recycling centers, collection schedules, and guidelines for recycling different types of materials. Some apps even offer features like barcode scanning to help users identify recyclable items. Examples of popular recycling and waste management apps include RecycleNation , iRecycle, and MyWaste.

Energy consumption tracking and conservation

Tracking energy consumption is crucial for understanding and reducing our environmental impact. Energy consumption tracking apps allow users to monitor their energy usage in real time, providing insights into which appliances or activities are consuming the most energy. These apps often provide tips and recommendations for reducing energy consumption and saving money on utility bills. Examples of popular energy consumption tracking apps include EnergyHub , Sense, and JouleBug.

Eco-friendly product guides and sustainable living tips

Choosing eco-friendly products and adopting sustainable living practices can have a significant positive impact on the environment. Eco-friendly product guides and sustainable living apps provide information on environmentally friendly products, such as organic and fair-trade options, as well as tips for reducing waste, conserving water, and adopting sustainable habits. Examples of popular eco-friendly product guides and sustainable living apps include Good On You, Think Dirty, and Oroeco .

Carbon footprint calculators and environmental awareness platforms

Calculating our carbon footprint is an important step towards understanding our individual impact on the environment. Carbon footprint calculators help users estimate their greenhouse gas emissions based on factors such as transportation, energy usage, and diet. These calculators often provide recommendations for reducing carbon emissions and living a more sustainable lifestyle. Additionally, there are environmental awareness platforms that provide information on environmental issues, news, and ways to get involved in sustainability initiatives. Examples of popular carbon footprint calculators and environmental awareness platforms include Carbon Footprint, Global Footprint Network, and Earth911.

Social Impact and Volunteering

Platforms connecting volunteers with organizations.

Platforms connecting volunteers with organizations have made it easier for individuals to find volunteer opportunities that align with their interests and skills. These platforms provide a database of volunteer opportunities, allowing users to search for opportunities based on location, cause, or specific skills required. They often provide detailed information about the organizations and the specific tasks involved in each opportunity. Examples of popular platforms connecting volunteers with organizations include VolunteerMatch , Idealist, and All for Good.

Donation and fundraising apps

Donation and fundraising apps have revolutionized the way individuals and organizations contribute to social causes. These apps provide a convenient and secure way to donate money to charitable organizations or specific fundraising campaigns. They often offer features like recurring donations, peer-to-peer fundraising, and the ability to track the impact of your donations. Examples of popular donation and fundraising apps include GoFundMe , DonorsChoose, and Charity Navigator.

Social activism and awareness campaigns

Social activism and awareness campaigns play a crucial role in driving social change and raising awareness about important issues. These campaigns leverage social media platforms, online petitions, and offline events to mobilize individuals and communities around specific causes. They often provide resources, educational materials, and opportunities for individuals to get involved and take action. Examples of social activism and awareness campaigns include #BlackLivesMatter, #MeToo, and #ClimateStrike.

Community engagement and support networks

Community engagement and support networks provide a platform for individuals to connect with others who share similar interests or are facing similar challenges. These networks often focus on specific communities or causes and provide a space for individuals to share resources, seek support, and collaborate on initiatives. They may offer forums, online communities, or local meetups to facilitate connections and engagement. Examples of community engagement and support networks include Meetup, Nextdoor, and Reddit communities focused on specific causes or interests.

Read also: How to Publish Apps on Google Play?

Productivity and Time Management

Task management and to-do lists.

Task management and to-do list tools are essential for organizing and prioritizing tasks, ensuring that nothing falls through the cracks. These tools allow you to create and manage tasks, set due dates, assign tasks to team members, and track progress. They often offer features like reminders, task categorization, and collaboration capabilities. Popular task management and to-do list tools include Todoist , Trello, and Microsoft To Do.

Calendar and event planning tools

Calendar and event planning tools help you schedule and manage your time effectively. These tools allow you to create and manage events, set reminders, and view your schedule at a glance. They often integrate with other productivity tools, such as task management apps, to provide a comprehensive view of your commitments. Popular calendar and event planning tools include Google Calendar, Microsoft Outlook Calendar, and Apple Calendar .

Note-taking and document management

Note-taking and document management tools are essential for capturing and organizing information. These tools allow you to take notes, create documents, and store and organize files. They often offer features like tagging, search functionality, and collaboration capabilities. Popular note-taking and document management tools include Evernote , Microsoft OneNote, and Google Keep.

Workflow automation and project management

Workflow automation and project management tools help streamline processes and manage projects efficiently. These tools allow you to automate repetitive tasks, track project progress, collaborate with team members, and manage resources. They often offer features like task dependencies, Gantt charts, and reporting capabilities. Popular workflow automation and project management tools include Asana , Monday.com, and Jira.

By utilizing task management and to-do lists, calendar and event planning tools, note-taking and document management tools, and workflow automation and project management tools, you can enhance your productivity and effectively manage your time and tasks. These tools provide the necessary structure and organization to help you stay focused and achieve your goals.

Mobile applications have the power to address real-world problems and improve various aspects of our lives. Whether it’s healthcare, education, transportation, sustainability, finance, or social impact, there are countless opportunities for app developers to make a positive change. By focusing on solving real-world problems, these app ideas have the potential to make a significant impact and enhance the lives of individuals and communities.

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Problem-Solving Strategies for Real-World Scenarios

In a world filled with complex challenges and ever-changing circumstances, problem-solving strategies become invaluable tools in your arsenal. Whether you're navigating a professional endeavor or facing a personal dilemma, the ability to approach real-world scenarios with a clear and effective problem-solving mindset can make all the difference.

But how do you tackle these situations with confidence and finesse? How can you ensure that your solutions are not only efficient but also innovative?

Join us as we explore a range of problem-solving strategies that will empower you to overcome obstacles and achieve meaningful outcomes.

Key Takeaways

• Clearly define the problem at its core and gather relevant information and data related to the problem.
• Evaluate and prioritize potential solutions based on their effectiveness, feasibility, and alignment with desired outcomes.
• Implement and monitor the chosen solution, seeking feedback from stakeholders and making adjustments as needed.
• Use data-driven decision making, collaborative brainstorming, and diverse perspectives to enhance problem-solving efficiency and effectiveness.

Define the Problem

To effectively solve real-world scenarios, it's crucial to begin by clearly defining the problem at hand. Problem identification is the first step in the problem-solving process. It involves recognizing and understanding the nature of the issue or challenge that needs to be addressed. By properly identifying the problem, you lay the foundation for effective problem analysis and subsequent solution development.

Problem identification requires a systematic approach. Start by gathering relevant information and data related to the problem. This will help you gain a comprehensive understanding of its causes, effects, and potential solutions. Analyze the information collected to identify patterns, trends, and underlying factors contributing to the problem. This analysis allows you to break down complex issues into smaller, more manageable components, making it easier to develop effective strategies for resolution.

Problem analysis is the next step after problem identification. It involves a detailed examination of the problem, its root causes, and its impact on various stakeholders. This analysis helps you gain a deeper understanding of the problem's complexity and scope. By breaking down the problem into its constituent parts, you can identify the underlying factors that contribute to its existence. This understanding is crucial for developing targeted and effective solutions.

Analyze the Situation

To effectively analyze the situation, you must first assess the problem at hand. This involves identifying the key issues and understanding their impact on the larger context.

Once you have a clear understanding of the problem, you can then evaluate possible solutions and their potential outcomes.

Assessing the Problem

In order to effectively solve a problem, it's crucial to carefully analyze the situation at hand. Assessing the problem and identifying obstacles are important steps in this process. Here are five key points to consider when assessing a problem:

• Clearly define the problem : Take the time to understand the issue at its core and determine what needs to be addressed.
• Gather relevant information : Collect all the necessary facts and data to gain a comprehensive understanding of the problem.
• Identify potential obstacles : Identify any barriers or challenges that may impede the problem-solving process.
• Evaluate the impact : Consider the potential consequences and impact of the problem on various aspects of the situation.
• Prioritize and focus : Determine which aspects of the problem need immediate attention and develop a plan for addressing them.

Understanding the Context

Understanding the context is crucial for effectively analyzing the situation and identifying key factors that contribute to the problem at hand. To gain a comprehensive understanding of the context, two important aspects need to be considered: historical context analysis and cultural context examination.

In historical context analysis, you delve into the past events, developments, and trends that have shaped the current situation. By understanding the historical context, you can identify patterns, causes, and potential solutions that may have been overlooked.

On the other hand, cultural context examination involves studying the beliefs, values, norms, and practices of the individuals or groups involved in the problem. Cultural factors play a significant role in shaping people's behaviors and perceptions, which can directly impact the problem-solving process.

By conducting a thorough analysis of the historical and cultural context, you can gain valuable insights that will inform your problem-solving approach and increase the likelihood of finding effective solutions.

Evaluating Possible Solutions

Now that you have gained a comprehensive understanding of the context, it's time to analyze the situation and evaluate possible solutions. This step is crucial in problem-solving as it involves weighing options and comparing alternatives to find the most effective course of action.

Here are some strategies to help you in this process:

• Identify the different solutions available to address the problem.
• Consider the advantages and disadvantages of each solution.
• Evaluate the potential outcomes and impacts of each solution.
• Assess the feasibility and resources required for implementing each solution.
• Prioritize the solutions based on their effectiveness, feasibility, and potential impact.

Generate Possible Solutions

Consider various potential solutions to address the problem at hand. When generating possible solutions, it's important to utilize effective brainstorming techniques and think outside the box with innovative approaches. Start by gathering a diverse group of individuals who can bring different perspectives and expertise to the table. Encourage open and non-judgmental discussions, where all ideas are welcomed. This will help stimulate creativity and generate a wide range of possible solutions.

During the brainstorming process, try to focus on quantity rather than quality. The goal is to generate as many potential solutions as possible, even if some seem far-fetched or unrealistic at first glance. Remember, innovative solutions often arise from seemingly unconventional ideas.

After the brainstorming session, evaluate each potential solution based on its feasibility, effectiveness, and alignment with the desired outcomes. Consider the resources, time, and effort required to implement each solution. Prioritize the solutions that have the highest likelihood of success and the greatest impact on solving the problem.

It is important to keep in mind that generating possible solutions is just the first step in the problem-solving process. Once you have a list of potential solutions, the next step is to evaluate and select the most appropriate one based on the specific context and constraints of the problem at hand.

Evaluate and Select the Best Solution

Now that you have generated possible solutions, it's time to evaluate and select the best one.

This involves considering solution criteria and going through a decision-making process.

Solution Criteria

To evaluate and select the best solution for real-world scenarios, it's crucial to establish clear and objective criteria based on the desired outcomes and the specific needs of the situation. Here are some solution criteria to consider:

• Solution effectiveness : Determine if the solution adequately addresses the problem at hand and achieves the desired results.
• Feasibility : Assess if the solution is realistic and can be implemented within the available resources, such as time, budget, and manpower.
• Sustainability : Evaluate if the solution is sustainable in the long term and doesn't create new problems or dependencies.
• Acceptability : Consider if the solution is acceptable to all stakeholders involved and aligns with their values, preferences, and expectations.
• Flexibility : Examine if the solution is adaptable and can accommodate potential changes or evolving needs in the future.

Decision-making Process

When evaluating and selecting the best solution for real-world scenarios, it's essential to carefully assess the available options based on their alignment with the established solution criteria. To make an informed decision, it's crucial to analyze alternatives using various decision-making models.

One commonly used model is the rational decision-making model, which involves identifying the problem, generating alternatives, evaluating those alternatives based on predetermined criteria, and selecting the best solution.

Another model is the intuitive decision-making model, which relies on gut feelings and past experiences to make decisions quickly.

Whichever model you choose, it's important to consider the pros and cons of each alternative and evaluate them based on their feasibility, effectiveness, and alignment with the desired outcome.

Implement the Chosen Solution

The successful implementation of the chosen solution requires careful planning, effective communication, and diligent execution. Implementing strategies can be challenging, but with the right approach, you can overcome execution challenges and achieve your desired outcomes.

Here are some key steps to consider:

• Clearly define roles and responsibilities : Assign specific tasks to individuals or teams to ensure everyone knows what's expected of them. This helps streamline the implementation process and avoids confusion or duplication of efforts.
• Establish a timeline and milestones : Set clear deadlines and milestones to track progress and keep everyone accountable. This allows for better monitoring of the implementation process and helps identify any potential bottlenecks or delays.
• Communicate regularly and openly : Maintain open lines of communication with all stakeholders involved. Regular updates and transparent communication can help address any concerns, provide clarifications, and foster a collaborative environment.
• Monitor and evaluate progress : Continuously monitor the implementation progress and evaluate the effectiveness of the chosen solution. This allows for timely adjustments or modifications, ensuring that the implementation stays on track and aligns with the desired outcomes.
• Seek feedback and address challenges : Encourage feedback from those involved in the implementation process. Address any challenges or obstacles promptly to maintain momentum and keep the implementation on track.

Monitor and Adjust as Needed

With the implementation of the chosen solution underway, it's crucial to closely monitor progress and make necessary adjustments as needed. Seeking feedback and making adjustments are essential steps in ensuring the success of any problem-solving endeavor.

To effectively monitor progress, establish clear metrics and indicators to measure the outcomes of your solution. Regularly assess these metrics to gauge the effectiveness of your implemented solution. Seek feedback from stakeholders, such as team members, customers, or supervisors, to gain valuable insights into the impact of your solution and identify any potential areas for improvement.

Once you have gathered feedback, analyze it objectively and identify any patterns or recurring issues. Look for opportunities to make adjustments that can enhance the efficiency, effectiveness, or overall impact of your solution. Consider alternative approaches or modifications that could address the identified issues.

When making adjustments, be proactive and agile. Act promptly to address any gaps or shortcomings in your solution. Modify your strategies, processes, or resources as needed to achieve the desired outcomes.

Use Data and Evidence to Inform Decisions

When it comes to making informed decisions, using data and evidence is crucial.

Data-driven decision making allows you to rely on factual information rather than assumptions or opinions.

By analyzing and interpreting data, you can identify patterns, trends, and correlations that can guide your problem-solving process.

Evidence-based problem solving takes this a step further by incorporating scientific research and empirical evidence to support your decisions.

Data-Driven Decision Making

Data-driven decision making is a crucial component of problem-solving in real-world scenarios, allowing you to make informed choices based on evidence and analysis. By incorporating data analysis into your decision-making process, you can ensure that your decisions are grounded in facts and not just assumptions.

Here are five key reasons why data-driven decision making is important:

• Objectivity : Data provides an unbiased view of the situation, helping you avoid personal biases and subjective opinions.
• Accuracy : Data analysis allows you to accurately assess the current state of affairs and predict future outcomes.
• Efficiency : Making decisions based on data saves time and resources, as it eliminates the need for trial and error.
• Transparency : Data-driven decisions are transparent and can be easily communicated and justified to stakeholders.
• Continuous improvement : Data-driven decision making enables you to track progress, identify areas for improvement, and make adjustments accordingly.

Evidence-Based Problem Solving

To effectively solve problems, it's essential to use data and evidence to inform your decisions. Evidence-based decision making involves utilizing objective information and facts to guide your problem-solving techniques. By relying on data and evidence, you can make more informed and rational decisions, minimizing the risk of subjective biases and emotions influencing your choices.

Evidence-based problem solving ensures that your decisions are grounded in reality, rather than being based on assumptions or personal opinions. It allows you to analyze the available information, identify patterns, and draw logical conclusions.

Incorporating evidence into your problem-solving process enhances the effectiveness and accuracy of your decision-making, leading to more successful outcomes. By following evidence-based problem-solving techniques, you can approach challenges with a clear and objective mindset, making informed choices based on reliable data.

Using Facts for Solutions

Using data and evidence to inform your decisions is essential for effective problem-solving. Fact-based decision making allows you to make informed choices that are grounded in reality. By using evidence effectively, you can ensure that your solutions are logical and reliable.

Here are five key reasons why using facts is crucial for problem-solving:

• Accuracy : Facts provide accurate information that can guide your decision-making process.
• Objectivity : Evidence allows you to approach problems in an objective manner, reducing the influence of personal biases.
• Reliability : Facts offer a reliable foundation for decision making, ensuring that your solutions are based on solid information.
• Efficiency : By relying on data, you can streamline the problem-solving process, saving time and resources.
• Effectiveness : Using evidence effectively increases the likelihood of finding successful solutions to the problems you face.

Collaborate and Seek Input From Others

When faced with complex real-world scenarios, collaborating with others and seeking their input can provide valuable insights and solutions. By working together, you can tap into the collective knowledge and experience of a diverse group, which can lead to more innovative and effective problem-solving strategies. One way to facilitate collaboration is through brainstorming techniques, where everyone is encouraged to contribute ideas without judgment. This can be done in problem-solving workshops, where participants can engage in open discussions, share their perspectives, and challenge each other's assumptions. By involving different stakeholders in the process, you can gather a wide range of perspectives and expertise, which can help identify blind spots and uncover new possibilities. To illustrate the benefits of collaboration and seeking input from others, consider the following table:

As you can see, collaborating and seeking input from others can provide numerous advantages when it comes to solving complex real-world problems. It allows you to harness the power of collective intelligence and ensures that diverse perspectives are considered, leading to more robust and effective solutions.

Think Creatively and Outside the Box

Collaborating with others and seeking their input can enhance problem-solving strategies, but to think creatively and outside the box, you must challenge conventional thinking and explore novel approaches. When faced with a problem, it's essential to think critically and question the assumptions that underpin the situation.

Here are five strategies to help you think creatively and identify problems effectively:

• Divergent thinking : Encourage yourself to generate multiple ideas and solutions, without judgment or restriction. This allows for a broader exploration of possibilities.
• Analogical thinking : Look for similarities between seemingly unrelated situations. By drawing connections, you can apply successful solutions from one context to another.
• Reverse thinking : Instead of approaching a problem head-on, try to envision the opposite outcome or consider the problem from a different perspective. This helps break free from traditional problem-solving patterns.
• Mind mapping : Use visual tools like mind maps to organize and connect ideas. This technique helps stimulate creativity and uncover new insights.
• Empathy : Put yourself in the shoes of others involved in the problem. Understanding their perspectives and motivations can lead to innovative solutions.

Reflect and Learn From Past Experiences

To maximize your problem-solving abilities, it is crucial to reflect on and learn from past experiences. Reflecting on mistakes allows you to identify what went wrong and why, enabling you to avoid making the same errors in the future. By analyzing your past failures, you gain valuable insights into the factors that contributed to the problem and can develop strategies to prevent similar issues from arising again. On the other hand, learning from successes helps you understand what worked well and why it was successful. By identifying the key elements that led to a positive outcome, you can replicate those strategies in similar situations. Reflecting on both mistakes and successes provides a comprehensive view of your problem-solving approach and helps you refine your skills.

To further illustrate the importance of reflecting on past experiences, consider the following table:

In conclusion, problem-solving is a crucial skill in navigating real-world scenarios. By defining the problem, analyzing the situation, generating possible solutions, and evaluating and selecting the best one, you can effectively address challenges.

Implementing the chosen solution, using data and evidence to inform decisions, collaborating with others, thinking creatively, and reflecting on past experiences all contribute to successful problem-solving.

As the saying goes, 'A problem shared is a problem halved,' seeking input and collaborating with others can lead to innovative and diverse solutions.

The eSoft Editorial Team, a blend of experienced professionals, leaders, and academics, specializes in soft skills, leadership, management, and personal and professional development. Committed to delivering thoroughly researched, high-quality, and reliable content, they abide by strict editorial guidelines ensuring accuracy and currency. Each article crafted is not merely informative but serves as a catalyst for growth, empowering individuals and organizations. As enablers, their trusted insights shape the leaders and organizations of tomorrow.

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