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• Published: 18 June 2024

Effectiveness of spaced repetition for clinical problem solving amongst undergraduate medical students studying paediatrics in Pakistan

• Shazia F. Durrani 1 ,
• Naveed Yousuf 2 ,
• Rahila Ali 2 ,
• Fatima Fakhir Musharraf 3 ,
• Ammara Hameed 1 &
• Hussain Ahmed Raza 2  

BMC Medical Education volume  24 , Article number:  676 ( 2024 ) Cite this article

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Studies using spaced repetition for teaching and learning in undergraduate clinical rotations such as paediatrics are limited, even more so in the South Asian region. Therefore, this study aimed to identify the effectiveness of utilizing spaced repetition compared to traditional learning methods among undergraduate medical students during their paediatric rotation at a medical university in Pakistan.

Bahria University Medical and Dental College (BUMDC) conducted quasii-experimental research in Karachi. Four topics were identified from the Year 5 Pediatrics curriculum to be used in the study, using which the study content was developed along with 50 multiple choice questions (MCQs) for assessment. All BUMDC Year 5 medical students rotating in Pediatrics were included and randomly allocated to the control or intervention group. In the control group, they provided the students with traditional study methods consisting of books and lectures to learn topics. In the intervention group, we created an Anki flashcard deck of the same topics to enable learning via spaced repetition. The researchers conducted a pretest and post test assessment of the 50 MCQs in both groups at the beginning and after the four-week study interval. The data were analysed using SPSS 19.

A total of 115 BUMDC medical students agreed to participate in the study; 70 (59.1%) were in the intervention group, and 45 (41.7%) were in the control group. The pretest mean score of the control group was 27.96 ± 3.70, and the posttest mean score was 27.22 ± 5.02, with no statistically significant difference at the 95% confidence level. The mean score of the pretest for the intervention group was 27.93 ± 4.53, and that of the posttest was 30.8 ± 4.56, with a statistically significant difference at the 95% confidence level. The intervention showed a significant effect size of 0.8.

The use of spaced repetitions resulted in significantly greater scores for medical students studying paediatrics than for those using more traditional methods of learning, compromising medical books and lectures. Considering that medical students need to retain a vast amount of information, using spaced repetition through flashcards can be a more effective learning tool that is more cost-efficient and time-efficient than traditional learning methods.

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Learning in medical school comprises building factual and theoretical knowledge, followed by practical application of that knowledge in a clinical setting. Due to the extensive medical curriculum, undergraduate medical students need help in the long-term retention of knowledge taught in clinical and nonclinical disciplines. Furthermore, medical students are in critical need of efficient self-study teaching and learning methods to help them retain the vast amounts of knowledge and clinical skills required to fulfil medical school competencies [ 1 ]. However, students must be aware of efficient learning strategies that can improve their long-term memory retention [ 2 ].

A study by Gilbert, M. M. (2023), conducted in the Boonshoft School of Medicine, USA, explored techniques that help students improve learning and found that spaced repetition was the best technique for enhancing student learning [ 3 ]. It has already been proven that the retention of factual knowledge is improved by using practice tests and spaced repetition [ 4 ]. Undergraduate and postgraduate medical students globally use spaced repetition despite being a comparatively new concept in medical education. It not only helps individuals attain proficiency but also aids in active recall and the application of clinical knowledge [ 5 ]. Numerous studies have shown evidence of the effectiveness of spaced repetition in long-term memory retention. A study of undergraduate medical students showed better short-term and long-term memory retention using spaced repetition learning [ 6 ].

Flashcards are the most popular method for utilizing spaced repetition learning. Anki. Web consists of flashcard software built on a spaced repetition algorithm. The literature has shown that Anki flashcards are beneficial for learning basic sciences such as anatomy [ 7 ]. Anki has become a popular learning tool in medical schools across the globe since it not only boosts performance on medical licensing exams but also allows most American first-year medical university students to use Anki flashcards to supplement their studies [ 8 , 9 ].

In particular, medical students struggle to learn about numerous volatile topics that require quick recall, such as developmental milestones, immunizations, and integrated management of neonatal and childhood illnesses. Due to difficulty in recalling such minute facts, students will undoubtedly need help to perform well in their paediatric rotations. Furthermore, medical educators have conducted global studies to identify the most effective teaching and learning strategies in medical education. However, data about South Asia, such as Pakistan, still need to be available. Additionally, researchers have yet to perform many studies to determine effective teaching and learning strategies in paediatric rotations for undergraduate medical students. Therefore, this study aimed to identify the effectiveness of the spaced repetition learning strategy compared to traditional learning methods for undergraduate medical students during their paediatrics rotation at a private medical university in Pakistan.

Methodology

Setting and participants.

This quasi experimental study was conducted at Bahria University Medical and Dental College (BUMDC) in Karachi, Pakistan. The total duration of the study was six months, and participant assessments were performed at four-week intervals.

The sample size was the whole population, which included the whole class of BUMDC year 5 medical students rotating in paediatrics. Purposive sampling, where total population sampling was performed.

The inclusion criteria included all BUMDC Year 5 medical students rotating in Pediatrics. The exclusion criteria consisted of five medical students who did not have internet access or who did not consent to participate in the study. The students were randomly divided into two groups: the intervention group and the control group. Each group had an equal number of students who were selected randomly.

Ethical approval

Data collection started after receiving approval from the Ethical Review Committee (ERC) of AKU (2021-6175-19040) and BUHSC (69/2020).

Consent from participants

The AKU-approved consent form was printed, and informed consent was obtained from five medical students of the BUMDC who agreed to participate in the study. Students were informed that their names and results would not be disclosed to anyone (except the students themselves) and that the results would not affect their rotation performance scores. Upon agreement, the students were asked to sign the form that the researcher and principal investigator had already signed. Copies of the form were given to the students after the signatures were completed. The forms are attached as additional file 5 .

Content selection and validation

Four topics were identified from the year 5 pediatrics curriculum to be used in the study for assessing learning in both the intervention and control groups. The topics included developmental milestones, Integrated Management of Neonatal and Childhood Illnesses (IMNCIs), immunizations, and malnutrition. These topics were selected since knowledge of these topics is commonly applied in general paediatric clinics. Furthermore, they encompass a broad range of crucial factual knowledge that is difficult to recall during clinical practice. The learning objectives of these four topics, along with a table of specifications (ToS) with relative weights assigned to each topic for pretest and post test assessments, are provided in additional annexure file 1 .

We identified eight experts who were FCPSs trained or equivalent in pediatrics, had at least five years of teaching experience, and had advanced qualifications in medical education (master’s or advanced diploma or equivalent). All eight experts were sent a request through email to be a member of the expert validation panel for our study to review our learning objectives and weight given to each topic and to select the pretest and post test multiple choice questions (MCQs) for assessment. Five experts responded positively and were included after their approval to participate. The five experts were requested via email to review and rate their agreement with the learning objectives and the weights assigned to each of the four topics we selected from the year 5 Pediatrics curriculum using a structured form with a four-point scale that varied from ‘strongly disagree’ to ‘strongly agree’ (Annexure III). All five experts agreed on the topics’ learning objectives and relative weights (file I). Any minor suggestions provided by the experts were reviewed and incorporated as necessary (Annexure IV).

Spaced repetition and mass learning materials

Anki is a flashcard software built upon a spaced repetition algorithm that allows users to review studied cards after one day, three days, seven days, 14 days, and 28 days. Flashcards are digitally made and appear at intervals depending on user recall. Flashcards are organized into decks, and users review these decks regularly. Based on the algorithm, the card being studied can be a new card not previously created by the user or an older card that reappears after an appropriate interval. Reviewed Anki cards that are difficult to remember reappear after a short interval, whereas quickly recalled cards reappear after a longer interval. This algorithm effectively uses spaced repetition technology and allows users to customize their learning based on their recall power. This spaced repetition learning method ensures revision of all topics provided on the flash cards.

A deck of Pediatrics flashcards was created using the learning objectives of the four selected topics. The flashcards were sent to the expert panel for review and approval. The content of the flashcards was developed using year five medical course books, lectures, and guidelines, with references to their respective sources included. The flashcards were made on the Anki website and were sent to the students in the intervention group. Instructions were given to the students in the intervention group on how to use the Anki website, along with step-by-step instructions on how to use the Pediatrics flashcard deck. If they had any additional queries, the students were also provided with support on WhatsApp regarding how to use the Anki flashcards. Upon request, a few students were guided face-to-face using the Anki website and flash cards.

The control group was requested to follow traditional learning methods used at the university, which consisted of using lecture notes and books that covered the same learning content provided in the flashcards given to the other group.

To eliminate potential confounders and correct the selection of students, intervention group students had to enrol on the Anki website using their emails. The flashcards and download instructions, including the paediatric flashcards deck, were given only to the students in the intervention group, who were given instructions to keep them private. Both groups were added to the respective WhatsApp group chats for daily feedback. This feedback ensured that the intervention group had no trouble using the new Anki flashcards. The total study time given to both groups was four weeks to ensure that all topics were studied thoroughly by both groups, and enough time was given for learning and retaining the provided information.

Development and validation of assessment questions

Seventy-five one-best multiple-choice questions (MCQs) were developed based on the learning objectives of the four topics selected. Particular attention was given to ensuring that all questions not only required factual recall but also involved critical thinking for problem-solving and applying objective knowledge.

A tool for MCQ validation was created for the expert panel to use, consisting of a four-point rating scale for each item assessing the level of agreement (strongly disagree, disagree, agree, strongly agree) based on relevance, content, and clarity. This tool was sent to the expert panel through email for review and validation. After incorporating expert feedback, 50 MCQs were approved and finalized for the pretest and post test assessments. These 50 questions were also validated according to exam weight and learning objectives.

Data collection

The Quizizz online quiz website (quizizz.com) was used for the pretest and post test assessments in both intervention and control groups, which consisted of the 50 validated MCQs.

Participants and faculty members were informed of the date, location, and timing of the pretest assessment along with test instructions via email. On the day of the pretest assessment, the students were asked to sign an attendance sheet and sign up for the test using their names and roll numbers. The pretest was administered through the Quizizz website. Each MCQ was given 90 s to attempt, leading to 1 h and 15 min for the pretest assessment of 50 MCQs. Four faculty members were involved in the invigilation to ensure fair conduct of the examination.

After four weeks of study, a posttest assessment was performed. The participants and faculty members were again informed of the date, location, and timing of the post test assessment along with the test instructions via email. The post test assessment was the same as the pretest assessment. Similarly, each item was given 90 s, and 1 h and 15 min were given for the entire post test. On the day of the post test assessment, the students were told to sign an attendance sheet and sign up for the post test assessment by name and roll number. Four faculty members were involved in the invigilation to ensure fair conduct of the examination.

Ethical considerations

Student names were kept anonymous since coding was used to mask their names. No one had access to the data except the data reviewers. All hard copies of the consent forms were kept in a locked file, and the assessment results were password-protected on a computer. Both assessments were formative and did not affect their rotation performance assessment. After the post test assessment was completed, the Anki flashcard deck and instructions were provided to all the students, including those in the control group, in case they wished to use them later to prepare for their summative assessment.

Data analysis

The Statistical Package for Social Sciences (SPSS) version 19 was used to analyse the data. All inferential analyses were two-sided, and p values < 0.05 (95% confidence level) were considered to indicate statistical significance. For pretest and post test assessment results, quantitative data are reported as the mean ± SD, whereas for qualitative variables, frequencies are reported as percentages. Content validity evidence (ToS) was obtained from content experts (Appendix V). Reliability was determined using Cronbach’s alpha for both pretest and posttest assessments.

An independent sample t test was used to determine the difference between the two groups (intervention versus control) between the pretest and posttest assessments. A paired t test was used to independently measure the differences between the pretest assessment results and posttest assessment results of the two groups (intervention and control). Figure  1 depicts the inferential strategy utilized.

Plan for inferential analysis

Of 145 year 5 BUDMC medical students, 115 agreed to participate in the study for pretest and posttest assessments. Participant characteristics and test results are shown in Table  1 . Among these, 45 (41.7%) were from the control group, and 70 (59.1%) were from the intervention group. Overall, among all participants, 77 (65.8%) were female, and 40 (34.2%) were male.

Overall, for all participants, the mean pretest score was 27.94 ± 4.185, while the posttest score was 29.41 ± 5.04. There was no significant difference in the pretest scores between the intervention and control groups ( p  = 0.973). However, a significant difference was found between the posttest scores between both groups, with the intervention group scoring higher, with a mean score of 30.86 ± 4.56, while the control group scored lower, with a mean score of 27.93 ± 4.53 ( p  < 0.001).

A comparison of the pretest and posttest results using a paired t test is shown in Table  2 . Overall (need info for overall if there was a significant difference). For the control group, there was no significant difference between the pretest and posttest scores ( p  = 0.275). However, for the intervention group, the posttest score was significantly greater, with a mean of 30.86 ± 4.56, than the mean pretest score of 27.93 ± 4.53 ( p  < 0.01). The reliability analysis using Cronbach’s alpha for the pretest was low (0.466), while for the posttest, it was high (0.717).

Effective learning and recall of essential pediatric medicine concepts to perform well in a clinical setting is vital for medical students. Educators and students employ various teaching and learning methods to enable efficient learning and recall of complex concepts. Our study showed that compared to students in the traditional learning methods group, students in the intervention group using spaced repetition performed significantly better on their posttest assessments than on their pretest assessments. Although statistically, posttest scores showed high reliability, pretest scores demonstrated low reliability, which may be due to no or minimal preparation of the students for the pretest assessment.

Our study demonstrated the efficiency of using Anki flashcards for spaced repetition as an effective tool for learning pediatric medicine topics compared to traditional learning methods. Our study revealed that not only does space repetition lead to more effective learning, but students also tend to score higher due to this learning method. A recent blog by Lecturio, a commonly used study platform by medical students, agrees with our findings and states that using flashcards leads to active recall of knowledge, which has been shown to be more advantageous in retaining information than other passive learning methods [ 10 ]. Compared to basic sciences subjects of medicine, which require extensive studies of minute factual details, several studies have also shown flashcards to be practical learning tools for retaining vast amounts of factual knowledge [ 7 , 11 , 12 ]. Interestingly, Lu et al. also found that using Anki flashcards for spaced repetition resulted in higher scores on the United States Medical Licensing Exam (USMLE) Step 1 exam, which is heavily based on fundamental scientific factual knowledge [ 13 ].

Similarly, in clinical fields requiring more application of knowledge than just factual recall, the use of flashcards has also been shown to improve performance scores and retention, such as in the fields of obstetrics and gynaecology, radiology, psychiatry, urology and otolaryngology and internal medicine [ 14 , 15 , 16 , 17 , 18 , 19 ]. With respect to the field of pediatrics in particular, most studies performed to show the effectiveness of spaced repetition have been conducted mainly at the postgraduate and professional levels. For instance, in contrast to our study findings, a study performed on pediatric residency trainees by McConnery et al. using spaced repetition learning did not show improved performance on assessment [ 20 ]. However, they noted that barriers such as limited time and limited participation may have hampered learning. Similarly, in another study related to pediatric acute illness management, after observing 12 critical illness scenario demonstrations, which were spaced fortnightly, learners demonstrated improved pediatric resuscitation skills [ 21 ].

Most studies on spaced repetition tend only to assess direct recall, especially those performed with students from undergraduate medical schools. In comparison, our study made a conscious effort to evaluate students not only for factual recall but also for problem-solving and clinical application of knowledge. Only a few studies in the literature have also assessed the problem-solving skills of students at the undergraduate level. One such study by Tshibwabwa et al. was conducted in second-year preclinical students at the American University of Medicine, in which they used spaced learning in radiology as part of an integrated curriculum. As a result, spatial learning enhances the retention of radiological concepts and improves problem-solving and radiological assessment skills [ 22 ].

Furthermore, with the South Asian region under the spotlight, we found very little research on spaced learning methods in medical education. Of the few studies we observed from the region, two were performed in India and showed improved learning using spaced repetition among undergraduate students [ 23 , 24 ]. However, unfortunately, no study has been conducted in Pakistan, a country with a significantly increasing number of medical students and physicians produced per year [ 25 ]. In Pakistan, medical education in medical universities primarily relies on traditional methods of teaching, such as using medical books and lectures. Although these methods may be good learning tools, medical colleges should integrate spaced repetition into their curriculum to make teaching and learning more effective. In a low- to middle-income country such as Pakistan, using premade digital flashcard decks for various subjects may be a more cost-effective learning tool for medical students than buying expensive medical books to obtain the same information. Furthermore, spaced repetition can also be more time efficient during revision periods since it can help students focus more on key points and revise weak areas rather than the information the student already knows well.

In our study, we also identified specific pediatric topics that are difficult to recall in a clinical setting but are undoubtedly crucial to remember, such as developmental milestones, malnutrition, immunization, and IMNCIs. Our results showed that students using traditional learning methods struggled more to retain this information, as reflected in their posttest assessment scores. Similarly, a cross-sectional study conducted at Sultan Qaboos University, Muscat. Studies on the perceptions of undergraduate medical students toward Integrated Management of Childhood Illness (IMCI) Preservice Education have shown that five-year-old medical students need more knowledge regarding IMNCIs [ 26 ]. Another cross-sectional study aimed at assessing the nutritional knowledge and attitudes of medical students at King Abdul-Aziz University, Jeddah, Saudi Arabia, demonstrated that participants needed better knowledge regarding malnutrition in children [ 27 ]. These findings indicate that medical students struggle to retain critical yet factual concepts related to pediatric health, which will ultimately affect their performance in their clinical rotations and future training. Using improved learning techniques, such as spaced repetition, will aid in retaining minute yet important information and can produce more competent physicians who recognize and promptly address childhood illnesses, improving underfive childhood mortality.

The strengths of our study are that it is the first study of its kind on the use of spaced repetition from Pakistan and the first study of undergraduate medical students studying paediatric medicine. Our sample size included the entire class. An expert panel also validated our assessment content and questions. Both the intervention and control groups were given the same content to study (although in different forms) to ensure fairness in the knowledge provided. We used WhatsApp group chats to ensure that the intervention group completely understood how to use the new learning technology, with daily feedback on several cards reviewed to ensure the completion of cards by the intervention group. Our study also employed pretest and posttest assessments, which enabled us to determine the difference between the two groups under similar testing environments. The MCQs used in the assessment not only involved factual recall but also included critical thinking and problem-solving skills.

Our most significant limitation is that this was a single-institute study, and we could not include a larger sample size, which could have led to a more robust analysis. Furthermore, if we extended the time for learning for more than four weeks, we may have shown improved assessment outcomes. Another limitation of our study is that due to time constraints, we could not study the long-term effects of using spaced repetition on final summative or end-of-year exams. Another limitation was that the students were informed that the assessment scores of the pretest and posttest assessments were formative only. A qualitative aspect of this study could have been included in which students reported their perception of the effectiveness of their respective learning tools. It was also almost impossible to ensure that the intervention group students would not share the flashcards with their friends from the control group. In addition, we did not assess clinical skills using spaced repetition and tested only clinical knowledge.

Currently, there is more literature about the use of spaced repetition in undergraduate medical students, especially in South Asia. Our study, which was conducted in an undergraduate medical program in Pakistan, showed that spaced repetition via Anki flashcards resulted in significantly higher scores for medical students studying paediatrics than for students using more traditional learning methods, compromising medical books and lectures. Considering that medical students need to retain a vast amount of information, using spaced repetition through flashcards can be a more effective learning tool and is more cost-effective and time-efficient than traditional learning methods.

Data availability

The datasets used and analysed during the current study are available from the corresponding author upon reasonable request.

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Department for Pediatrics, Bahria University Medical & Dental College, Karachi, Pakistan

Shazia F. Durrani & Ammara Hameed

Department for Educational Development, The Aga Khan University, Karachi, Pakistan

Naveed Yousuf, Rahila Ali & Hussain Ahmed Raza

Jinnah Sindh Medical University, Karachi, Pakistan

Fatima Fakhir Musharraf

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Contributions

Authors’ contributions: SFD, NY, RA, and FFM contributed to the study concept and design. FFM and AH contributed to data collection and analysis. SFD and NY take responsibility for data integrity and accuracy of the data analysis. HAR and SFD contributed to the visualization and interpretation of data, drafted the work, and substantively revised it. All authors participated in the write-up of the final manuscript.

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Correspondence to Shazia F. Durrani .

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Durrani, S.F., Yousuf, N., Ali, R. et al. Effectiveness of spaced repetition for clinical problem solving amongst undergraduate medical students studying paediatrics in Pakistan. BMC Med Educ 24 , 676 (2024). https://doi.org/10.1186/s12909-024-05479-y

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DOI : https://doi.org/10.1186/s12909-024-05479-y

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Learning Solution-Aware Transformers for Efficiently Solving Quadratic Assignment Problem

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Recently various optimization problems, such as Mixed Integer Linear Programming Problems (MILPs), have undergone comprehensive investigation, leveraging the capabilities of machine learning. This work focuses on learning-based solutions for efficiently solving the Quadratic Assignment Problem (QAPs), which stands as a formidable challenge in combinatorial optimization. While many instances of simpler problems admit fully polynomial-time approximate solution (FPTAS), QAP is shown to be strongly NP-hard. Even finding a FPTAS for QAP is difficult, in the sense that the existence of a FPTAS implies $P = NP$. Current research on QAPs suffer from limited scale and computational inefficiency. To attack the aforementioned issues, we here propose the first solution of its kind for QAP in the learn-to-improve category. This work encodes facility and location nodes separately, instead of forming computationally intensive association graphs prevalent in current approaches. This design choice enables scalability to larger problem sizes. Furthermore, a \textbf{S}olution \textbf{AW}are \textbf{T}ransformer (SAWT) architecture integrates the incumbent solution matrix with the attention score to effectively capture higher-order information of the QAPs. Our model's effectiveness is validated through extensive experiments on self-generated QAP instances of varying sizes and the QAPLIB benchmark.

• Computer Science - Machine Learning;
• Computer Science - Artificial Intelligence

How to think like a programmer — lessons in problem solving

by Richard Reis

If you’re interested in programming, you may well have seen this quote before:

“Everyone in this country should learn to program a computer, because it teaches you to think.” — Steve Jobs

You probably also wondered what does it mean, exactly, to think like a programmer? And how do you do it??

Essentially, it’s all about a more effective way for problem solving .

In this post, my goal is to teach you that way.

By the end of it, you’ll know exactly what steps to take to be a better problem-solver.

Why is this important?

Problem solving is the meta-skill.

We all have problems. Big and small. How we deal with them is sometimes, well…pretty random.

Unless you have a system, this is probably how you “solve” problems (which is what I did when I started coding):

• Try a solution.
• If that doesn’t work, try another one.
• If that doesn’t work, repeat step 2 until you luck out.

Look, sometimes you luck out. But that is the worst way to solve problems! And it’s a huge, huge waste of time.

The best way involves a) having a framework and b) practicing it.

“Almost all employers prioritize problem-solving skills first.

Problem-solving skills are almost unanimously the most important qualification that employers look for….more than programming languages proficiency, debugging, and system design.

Demonstrating computational thinking or the ability to break down large, complex problems is just as valuable (if not more so) than the baseline technical skills required for a job.” — Hacker Rank ( 2018 Developer Skills Report )

Have a framework

To find the right framework, I followed the advice in Tim Ferriss’ book on learning, “ The 4-Hour Chef ”.

It led me to interview two really impressive people: C. Jordan Ball (ranked 1st or 2nd out of 65,000+ users on Coderbyte ), and V. Anton Spraul (author of the book “ Think Like a Programmer: An Introduction to Creative Problem Solving ”).

I asked them the same questions, and guess what? Their answers were pretty similar!

Soon, you too will know them.

Sidenote: this doesn’t mean they did everything the same way. Everyone is different. You’ll be different. But if you start with principles we all agree are good, you’ll get a lot further a lot quicker.

“The biggest mistake I see new programmers make is focusing on learning syntax instead of learning how to solve problems.” — V. Anton Spraul

So, what should you do when you encounter a new problem?

Here are the steps:

1. Understand

Know exactly what is being asked. Most hard problems are hard because you don’t understand them (hence why this is the first step).

How to know when you understand a problem? When you can explain it in plain English.

Do you remember being stuck on a problem, you start explaining it, and you instantly see holes in the logic you didn’t see before?

Most programmers know this feeling.

This is why you should write down your problem, doodle a diagram, or tell someone else about it (or thing… some people use a rubber duck ).

“If you can’t explain something in simple terms, you don’t understand it.” — Richard Feynman

Don’t dive right into solving without a plan (and somehow hope you can muddle your way through). Plan your solution!

Nothing can help you if you can’t write down the exact steps.

In programming, this means don’t start hacking straight away. Give your brain time to analyze the problem and process the information.

To get a good plan, answer this question:

“Given input X, what are the steps necessary to return output Y?”

Sidenote: Programmers have a great tool to help them with this… Comments!

Pay attention. This is the most important step of all.

Do not try to solve one big problem. You will cry.

Instead, break it into sub-problems. These sub-problems are much easier to solve.

Then, solve each sub-problem one by one. Begin with the simplest. Simplest means you know the answer (or are closer to that answer).

After that, simplest means this sub-problem being solved doesn’t depend on others being solved.

Once you solved every sub-problem, connect the dots.

Connecting all your “sub-solutions” will give you the solution to the original problem. Congratulations!

This technique is a cornerstone of problem-solving. Remember it (read this step again, if you must).

“If I could teach every beginning programmer one problem-solving skill, it would be the ‘reduce the problem technique.’

For example, suppose you’re a new programmer and you’re asked to write a program that reads ten numbers and figures out which number is the third highest. For a brand-new programmer, that can be a tough assignment, even though it only requires basic programming syntax.

If you’re stuck, you should reduce the problem to something simpler. Instead of the third-highest number, what about finding the highest overall? Still too tough? What about finding the largest of just three numbers? Or the larger of two?

Reduce the problem to the point where you know how to solve it and write the solution. Then expand the problem slightly and rewrite the solution to match, and keep going until you are back where you started.” — V. Anton Spraul

By now, you’re probably sitting there thinking “Hey Richard... That’s cool and all, but what if I’m stuck and can’t even solve a sub-problem??”

First off, take a deep breath. Second, that’s fair.

Don’t worry though, friend. This happens to everyone!

The difference is the best programmers/problem-solvers are more curious about bugs/errors than irritated.

In fact, here are three things to try when facing a whammy:

• Debug: Go step by step through your solution trying to find where you went wrong. Programmers call this debugging (in fact, this is all a debugger does).

“The art of debugging is figuring out what you really told your program to do rather than what you thought you told it to do.”” — Andrew Singer

• Reassess: Take a step back. Look at the problem from another perspective. Is there anything that can be abstracted to a more general approach?

“Sometimes we get so lost in the details of a problem that we overlook general principles that would solve the problem at a more general level. […]

The classic example of this, of course, is the summation of a long list of consecutive integers, 1 + 2 + 3 + … + n, which a very young Gauss quickly recognized was simply n(n+1)/2, thus avoiding the effort of having to do the addition.” — C. Jordan Ball

Sidenote: Another way of reassessing is starting anew. Delete everything and begin again with fresh eyes. I’m serious. You’ll be dumbfounded at how effective this is.

• Research: Ahh, good ol’ Google. You read that right. No matter what problem you have, someone has probably solved it. Find that person/ solution. In fact, do this even if you solved the problem! (You can learn a lot from other people’s solutions).

Caveat: Don’t look for a solution to the big problem. Only look for solutions to sub-problems. Why? Because unless you struggle (even a little bit), you won’t learn anything. If you don’t learn anything, you wasted your time.

Don’t expect to be great after just one week. If you want to be a good problem-solver, solve a lot of problems!

Practice. Practice. Practice. It’ll only be a matter of time before you recognize that “this problem could easily be solved with <insert concept here>.”

How to practice? There are options out the wazoo!

Chess puzzles, math problems, Sudoku, Go, Monopoly, video-games, cryptokitties, bla… bla… bla….

In fact, a common pattern amongst successful people is their habit of practicing “micro problem-solving.” For example, Peter Thiel plays chess, and Elon Musk plays video-games.

“Byron Reeves said ‘If you want to see what business leadership may look like in three to five years, look at what’s happening in online games.’

Fast-forward to today. Elon [Musk], Reid [Hoffman], Mark Zuckerberg and many others say that games have been foundational to their success in building their companies.” — Mary Meeker ( 2017 internet trends report )

Does this mean you should just play video-games? Not at all.

But what are video-games all about? That’s right, problem-solving!

So, what you should do is find an outlet to practice. Something that allows you to solve many micro-problems (ideally, something you enjoy).

For example, I enjoy coding challenges. Every day, I try to solve at least one challenge (usually on Coderbyte ).

Like I said, all problems share similar patterns.

That’s all folks!

Now, you know better what it means to “think like a programmer.”

You also know that problem-solving is an incredible skill to cultivate (the meta-skill).

As if that wasn’t enough, notice how you also know what to do to practice your problem-solving skills!

Phew… Pretty cool right?

Finally, I wish you encounter many problems.

You read that right. At least now you know how to solve them! (also, you’ll learn that with every solution, you improve).

“Just when you think you’ve successfully navigated one obstacle, another emerges. But that’s what keeps life interesting.[…]

Life is a process of breaking through these impediments — a series of fortified lines that we must break through.

Each time, you’ll learn something.

Each time, you’ll develop strength, wisdom, and perspective.

Each time, a little more of the competition falls away. Until all that is left is you: the best version of you.” — Ryan Holiday ( The Obstacle is the Way )

Now, go solve some problems!

And best of luck ?

Special thanks to C. Jordan Ball and V. Anton Spraul . All the good advice here came from them.

Thanks for reading! If you enjoyed it, test how many times can you hit in 5 seconds. It’s great cardio for your fingers AND will help other people see the story.

If this article was helpful, share it .

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Mathematical Problem-Solving

Peddie’s two-year Mathematical Problem Solving (MPS) sequence offers an innovative integration of algebra and geometry, typically taught in separate Geometry and Algebra II courses. All math classes at Peddie emphasize problem-based learning, but MPS courses are unique in their focus on cultivating problem-solving skills and attitudes that benefit students throughout their academic journey and beyond.

In the MPS classroom, students take the lead, promoting a student-centered learning environment. They are presented with problems and encouraged to work independently and critically to find solutions, while teachers provide guidance and troubleshooting support. This approach allows students to take ownership of the problem-solving process, developing crucial qualities such as courage and persistence.

MPS homework is designed to be different from traditional assignments. It emphasizes persistence, creativity and resilience over merely finding the correct answer. Students are not expected to solve every problem they encounter. Instead, they face challenges that require them to apply their existing knowledge and critical thinking skills without a prescribed method. They document their thought processes in electronic notebooks, which are then discussed in class, further enhancing their understanding and problem-solving abilities.

By engaging with this unique approach to mathematical problem-solving, students at Peddie develop a deep-seated resilience and creativity that prepares them for future mathematical endeavors and life challenges.

To learn more about Peddie’s other math courses and electives, please visit our math department page.

How is an MPS classroom different?

The MPS classroom is a place where everyone is active every day, fostering a sense of belonging and teamwork. Students present their thinking and solutions to their classmates and discuss new problems in collaborative groups. The teacher is always present, leading conversation, suggesting approaches, correcting misunderstanding and reminding students of what they’ve learned. When needed, the teacher will present mathematical ideas and techniques to the class, but the bulk of any class session is devoted to active and engaged student effort.

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• Problem Solving

How to Improve Problem Solving Skills

Last Updated: January 27, 2024 Fact Checked

This article was co-authored by Erin Conlon, PCC, JD . Erin Conlon is an Executive Life Coach, the Founder of Erin Conlon Coaching, and the host of the podcast "This is Not Advice." She specializes in aiding leaders and executives to thrive in their career and personal lives. In addition to her private coaching practice, she teaches and trains coaches and develops and revises training materials to be more diverse, equitable, and inclusive. She holds a BA in Communications and History and a JD from The University of Michigan. Erin is a Professional Certified Coach with The International Coaching Federation. There are 13 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 237,378 times.

The ability to solve problems applies to more than just mathematics homework. Analytical thinking and problem-solving skills are a part of many jobs, ranging from accounting and computer programming to detective work and even creative occupations like art, acting, and writing. While individual problems vary, there are certain general approaches to problem-solving like the one first proposed by mathematician George Polya in 1945. [1] X Research source By following his principles of understanding the problem, devising a plan, carrying out the plan, and looking back, you can improve your problem-solving and tackle any issue systematically.

Define the problem clearly.

• Try to formulate questions. Say that as a student you have very little money and want to find an effective solution. What is at issue? Is it one of income – are you not making enough money? Is it one of over-spending? Or perhaps you have run into unexpected expenses or your financial situation has changed?

State your objective.

• Say that your problem is still money. What is your goal? Perhaps you never have enough to go out on the weekend and have fun at the movies or a club. You decide that your goal is to have more spending cash. Good! With a clear goal, you have better defined the problem.

Gather information systematically.

• To solve your money shortage, for example, you would want to get as detailed a picture of your financial situation as possible. Collect data through your latest bank statements and to talk to a bank teller. Track your earnings and spending habits in a notebook, and then create a spreadsheet or chart to show your income alongside your expenditures.

Analyze information.

• Say you have now collected all your bank statements. Look at them. When, how, and from where is your money coming? Where, when, and how are you spending it? What is the overall pattern of your finances? Do you have a net surplus or deficit? Are there any unexplained items?

Generate possible solutions.

• Your problem is a lack of money. Your goal is to have more spending cash. What are your options? Without evaluating them, come up with possible options. Perhaps you can acquire more money by getting a part-time job or by taking out a student loan. On the other hand, you might try to save by cutting your spending or by lowering other costs.
• Divide and conquer. Break the problem into smaller problems and brainstorm solutions for them separately, one by one.
• Use analogies and similarities. Try to find a resemblance with a previously solved or common problem. If you can find commonalities between your situation and one you've dealt with before, you may be able to adapt some of the solutions for use now.

Evaluate the solutions and choose.

• How can you raise money? Look at expenditures – you aren’t spending much outside of basic needs like tuition, food, and housing. Can you cut costs in other ways like finding a roommate to split rent? Can you afford to take a student loan just to have fun on the weekend? Can you spare time from your studies to work part-time?
• Each solution will produce its own set of circumstances that need evaluation. Run projections. Your money problem will require you to draw up budgets. But it will also take personal consideration. For example, can you cut back on basic things like food or housing? Are you willing to prioritize money over school or to take on debt?

Implement a solution.

• You decide to cut costs, because you were unwilling to take on debt, to divert time away from school, or to live with a roommate. You draw up a detailed budget, cutting a few dollars here and there, and commit to a month-long trial.

Review and evaluate the outcome.

• The results of your trial are mixed. On one hand, you have saved enough during the month for fun weekend activities. But there are new problems. You find that you must choose between spending cash and buying basics like food. You also need a new pair of shoes but can’t afford it, according to your budget. You may need to a different solution.

Adjust if necessary.

• After a month, you decide to abandon your first budget and to look for part-time work. You find a work-study job on campus. Making a new budget, you now have extra money without taking too much time away from your studies. You may have an effective solution.

Do regular mental exercises.

• Word games work great. In a game like “Split Words,” for example, you have to match word fragments to form words under a given theme like “philosophy.” In the game, “Tower of Babel,” you will need to memorize and then match words in a foreign language to the proper picture.
• Mathematical games will also put your problem solving to the test. Whether it be number or word problems, you will have to activate the parts of your brain that analyze information. For instance: “James is half as old now as he will be when he is 60 years older than he was six years before he was half as old as he is now. How old will James be when his age is twice what it was 10 years after he was half his current age?”

Play video games.

• Play something that will force you to think strategically or analytically. Try a puzzle game like Tetris. Or, perhaps you would rather prefer a role-playing or strategy game. In that case, something like “Civilization” or “Sim-City” might suit you better.

Take up a hobby.

• Web design, software programming, jigsaw puzzles, Sudoku, and chess are also hobbies that will force you to think strategically and systematically. Any of these will help you improve your overall problem solving.

Expert Q&A

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• ↑ https://math.berkeley.edu/~gmelvin/polya.pdf
• ↑ https://www.healthywa.wa.gov.au/Articles/N_R/Problem-solving
• ↑ https://asq.org/quality-resources/problem-solving
• ↑ https://ctb.ku.edu/en/table-of-contents/evaluate/evaluate-community-interventions/collect-analyze-data/main
• ↑ https://www.mindtools.com/pages/article/newCT_96.htm
• ↑ https://www.skillsyouneed.com/ips/problem-solving.html
• ↑ Erin Conlon, PCC, JD. Executive Life Coach. Expert Interview. 31 August 2021.
• ↑ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5930973/
• ↑ https://www.theguardian.com/lifeandstyle/2018/oct/13/mental-exercises-to-keep-your-brain-sharp
• ↑ https://www.apa.org/monitor/2014/02/video-game
• ↑ https://www.nature.com/articles/d41586-018-05449-7

About This Article

To improve your problem-solving skills, start by clearly defining the problem and your objective or goal. Next, gather as much information as you can about the problem and organize the data by rewording, condensing, or summarizing it. Then, analyze the information you've gathered, looking for important links, patterns, and relationships in the data. Finally, brainstorm possible solutions, evaluate the solutions, and choose one to implement. For tips on implementing solutions successfully, read on! Did this summary help you? Yes No

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Effective Problem-Solving and Decision-Making

Below are the top discussions from Reddit that mention this online Coursera course from University of California, Irvine .

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Critical thinking – the application of scientific methods and logical reasoning to problems and

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Maybe I'm missing something here...But I clicked on some courses and you still have to apply for financial aid if you want a certificate (or pay), like normal. It's just like it normally is, I see no difference?

For instance, here a random course I just picked that's not on your list: https://www.coursera.org/learn/problem-solving

It also has financial aid available.

Good specialization: [https://www.coursera.org/specializations/career-success]

Good courses within the specialization:

Work Smarter, Not Harder: Time Management [https://www.coursera.org/learn/work-smarter-not-harder]

Effective Problem-Solving and Decision-Making [https://www.coursera.org/learn/problem-solving]

Stopping would be a disservice to yourself.

I understand where you are coming fro. Learning how to program can be difficult and frustrating at times. This is a normal part of the process in learning anything technical. Do not be so hard on yourself and remember that as time goes on, your ability to learn and understand new technical ideas will improve, as will your problem solving skills.

I'd recommend that you try to mostly focus on your own growth and not the growth of other people. Just do you. If you are driven to learn, then you will make progress and improve.

Try different approaches when learning a difficult concept by checking out other resources such as different websites, books, videos, etc. Usually you can find an explanation that makes sense to you and 'clicks' just by spending a little bit of time searching.

Here are 2 other important things that will help:

First, spend some time thinking about the learning process and how you learn best. Many of us have never been taught strong skills used for learning new information and really don't know how to go about doing so in an efficient way. Here is a great course on this subject from Coursera.

https://www.coursera.org/learn/learning-how-to-learn

Second, spend some time learning problem solving skills. Knowing how to approach and break down problems in a logical way is one of the best skills you can have. These skills can be applied to learning as well as to many different areas in your life.

Here are 2 courses on this subject:

This one is aimed at people who are learning programming https://www.mooc-list.com/course/logic-and-computational-thinking-edx

https://www.coursera.org/learn/problem-solving

I hope this helps. Don't worry about your learning speed. You'll know in time whether programming will workout, and it will mostly be dependent on your ambition and how passionate you are about the field. You do not need a higher than average IQ to learn how to code. Instead, you need patience, learning and problem solving skills, focus and most of all, practice, practice, practice.