**Presenting students with different types of interleaved (interspersed) problems instead of grouping them by topic benefits their memorization of concepts and their ability to solve more difficult problems on future tests. A recent study demonstrates these results in a classroom context, with college students in a physics class.**

The practice of alternating retrieval practice—testing knowledge on different topics in an interspersed mode—increases memory and the ability to solve problems. This is the conclusion of a study published in the journal *Nature* in November 2021. Conducted by Joshua Samani and Steven Pan of the Departments of Physics and Astronomy and psychology at the University of California, Los Angeles, this research reinforces the idea that studying topics alternately improves learning.

The researchers tested 286 college students in a physics class for eight weeks, using the regular study materials. After each lesson, it was customary for students to be given nine problems to do at home, grouped by topic, in block (A-A-A-B-B-B-C-C-C). In the study, during the first four weeks half of the students continued to receive the problems blocked, while the other half received them interspersed (A-B-C-A-B-C-A-B-C). Over the next four weeks, the conditions were reversed to avoid harming a group of students if learning with blocked problems differed from learning with interspersed problems.

To measure the effects of interleaved practice after each four-week period, Samani and Pan gave students surprise quizzes, to minimize effects that could contaminate the results. These tests included three more difficult problems than those included in the homework assignments. Two of them required the integration of concepts and procedures from different topics, and the third required the application of one of the topics studied to a new scenario.

Results indicated that the **students’ performance in the homework problems was worse in the interleaved problems than in the blocked problems.** The students themselves **recognized the increased difficulty** when solving the interleaved problems, which upon completion they classified as "more difficult". In the same sense, **participants also estimated that they had learned less after solving interleaved problems.**

However, in the surprise tests, **students who solved interleaved problems performed much better than their peers who received blocked problems**: the median score in the first test was 50% higher for interleavedproblems than for blocked problems; in the second test, this improvement was 125%.

Analyzing the results in the two types of problems in the surprise tests, the researchers found that students who solved interleaved exercises **had more effectively memorized** the formulas necessary to solve the problems in the test and **gave 100% correct answers more often** than students who solved blocked problems.

It should be noted that **in the mid-semester exams for the class, all students had similar results**. However, questionnaires conducted after the exams indicated that most of the students had done an intense previous study; in addition, the surprise tests may have functioned as an excellent learning opportunity, contributing to the homogeneity of the results.

In sum, **students who solved interleaved problems performed worse while solving them, experienced more difficulties, and underestimated their learning**, than students who solved blocked problems. **This pattern reversed when students took surprise tests**: those who had solved interleaved problems performed better and were able to apply knowledge to new scenarios and integrate concepts and procedures from different topics.

Different theories may explain these results. According to a 2021 study led by Alice Latimier, **interleaved practice implies spaced practice** which, **as we have already seen in other articles, increases learning**. Another theory, presented in 2012 by two groups of researchers, assumes that **interleaved practice leads students to infer the abstract characteristics of various types of problems** rather than focusing on their superficial characteristics. Thus, they can identify the categories of problems in the test better than the students who studied blocked problems.

Another possible explanation, put forward by John Dunlosky and other researchers in 2013, is that **interleaved practice gives students the opportunity to compare different types of problems**. This allows them to understand the similarities and relationships between the problems, which potentially increases their ability to integrate concepts to solve exercises that require combining several types of problems. Finally, according to a 2011 article by Elizabeth and Robert Bjork, the fact that interleaved problems are more difficult to solve can become a **"desirable difficulty," which leads students to form more connections between materials**. This explanation also sheds light on why students performed worse on interleaved homework and felt they learned less.

It should be noted that these explanations for the benefits of interleaved practice are not mutually exclusive. All can contribute to the observed benefits. In any case, the conclusion of this study is that a small change in the way homework is presented to students can improve learning, not only in terms of memorization but also in problem solving.

### References

Bjork, E. L., & Bjork, R. A. (2011). Making things hard on yourself, but in a good way: Creating desirable difficulties to enhance learning. *Psychology and the real world: Essays illustrating fundamental contributions to society*, *2*(59-68).

Dunlosky, J., Rawson, K. A., Marsh, E. J., Nathan, M. J., & Willingham, D. T. (2013). Improving students’ learning with effective learning techniques: Promising directions from cognitive and educational psychology. *Psychological Science in the Public Interest*, *14*(1), 4-58. https://doi.org/10.1177/1529100612453266

Kang, S. H., & Pashler, H. (2012). Learning painting styles: Spacing is advantageous when it promotes discriminative contrast. *Applied Cognitive Psychology*, *26*(1), 97-103. https://doi.org/10.1016/j.jarmac.2014.05.006

Kornell, N., & Bjork, R. A. (2008). Learning concepts and categories: Is spacing the “enemy of induction”?. *Psychological Science*, *19*(6), 585-592. https://doi.org/10.1111/j.1467-9280.2008.02127.x

Latimier, A., Peyre, H., & Ramus, F. (2021). A meta-analytic review of the benefit of spacing out retrieval practice episodes on retention. *Educational Psychology Review*, *33*(3), 959-987. https://doi.org/10.1007/s10648-020-09572-8

Samani, J., & Pan, S. C. (2021). Interleaved practice enhances memory and problem-solving ability in undergraduate physics. *NPJ Science of Learning*, *6*(1), 1-11. https://doi.org/10.1038/s41539-021-00110-x

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