Shuffling homework problems helps college students learn introductory physics

"Interleaving” between different problem types improves learning

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“How much torque does the force exert on the loop of wire?”  Every day, students taking introductory physics courses—of which there are more than a half-million annually in the U.S. alone—attempt practice problems featuring such questions.  These courses usually cover multiple topics, and for each topic, there may be a homework assignment devoted specifically to it.  For instance, after learning about torque, students might complete an assignment that is comprised of problems focused primarily on torque.   

Concentrating periods of practice on individual topics, which researchers call “blocking,” seems sensible because it allows the learner to focus their cognitive effort on mastering one thing at a time.  That characteristic may explain the popularity of blocking of homework assignments by topic in many science, technology, engineering, and mathematics (STEM) courses.  In such courses, instructors might not even consider organizing practice problems in any other way. 

Over the past decade, however, researchers have begun investigating the potential benefits of an alternative approach known as “interleaving."  This approach involves repeatedly switching between different topics as opposed to concentrating on one topic at a time.  For instance, an “interleaved” physics assignment might contain practice problems addressing torque, acceleration, and magnetism, all shuffled together.   

Is this rather unorthodox approach helpful?  To date, relevant evidence has been lacking.  Although interleaving has shown promise in laboratory studies, those studies have largely involved visual stimuli and not problem solving or other skills that are more commonly learned in actual classrooms.  A prominent exception, however, involves middle-school mathematics, where recent classroom studies have shown benefits from practice problems that are interleaved, as opposed to blocked, by topic.   

In an effort to better understand the effects of interleaving, Joshua Samani and I recently compared interleaving versus blocking in two sections of a large undergraduate physics course.  During each of two four-week periods, one section completed assignments that were interleaved by topic (i.e., containing a random mix of problems such that each successive problem addressed a different topic), whereas the other section completed assignments that were blocked by topic (i.e., containing three problems per topic, presented in succession).  To measure the effectiveness of the two approaches, we administered a surprise problem-solving exam at the end of each period. 

Interleaved versus blocked homework assignments

Interleaved Versus Blocked Homework Assignments
Students in each course section completed up to three assignments per week.  With interleaved assignments, each problem addressed a different topic (subject), whereas with blocked assignments, every three problems addressed the same topic.  In the figure, letters or symbols indicate topics, and subscripts indicate the problem number for that topic. From Samani, J., and Pan, S. C. (2021). npj Science of Learning 6, Article 32.

It was an open question as to which approach would be more helpful.  Among the few studies of interleaving conducted in educational settings, none have involved physics.  Moreover, there might be domains or situations where at least some amount of blocking is necessary or helpful.  The surprise exam results, however, revealed a clear winner: Students that had completed interleaved assignments well outperformed those that had completed blocked assignments (with median improvements of 50% and 125% on the two exams, respectively).  Thus, homework problems that are shuffled by topic, as opposed to blocked by topic, can help college students learn introductory physics.   

In our view, when considered alongside findings for middle-school mathematics, it is possible that interleaving of homework problems by topic can enhance learning in many STEM domains where blocking is currently widespread.  Further research, however, is needed to investigate that possibility.  Additionally, how interleaving improves problem-solving skills remains to be determined.  One possibility is that it promotes learning via the spacing effect, which is the finding that practice opportunities that are spread out in time (as opposed to concentrated together) are more helpful for learning.  Another possibility is that it causes learners to compare different problem types and learn to tell them apart.  Both explanations are currently viable: In our study, the practice problems for each topic were spread out across the interleaved assignments, and within those assignments, there were many opportunities to compare problem types.

For now, the take-home message from our research is clear: The traditional approach of blocking homework assignments by topic need not always be used by default.  Rather, instructors and learners might consider—with the caveat that alternative approaches remain to be thoroughly investigated—using interleaving instead. 

Learn more by reading our research article: Samani, J., and Pan, S. C. (2021). Interleaved practice enhances memory and problem-solving ability in undergraduate physics, published by npj Science of Learning.

Banner image courtesy of Wikimedia Commons/Germanna CC under the CC-BY-2.0 license.

Steven C. Pan

Assistant Professor of Psychology, National University of Singapore