What's the best way to learn complex skills, like problem solving, for example? Looking at the way homework problems are typically laid out in textbooks and often assigned by teachers, the answer would appear to be by giving students problem sets that focus on one kind of problem at a time. The next homework set gives students practice working a different kind of problem.

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What's the best way to learn complex skills, like problem solving, for example? Looking at the way homework problems are typically laid out in textbooks and often assigned by teachers, the answer would appear to be by giving students problem sets that focus on one kind of problem at a time. The next homework set gives students practice working a different kind of problem. As the name implies, in distributed practice students work homework sets featuring a new type of problem but also including some problems from previous sets so that the review of all kinds of problems is ongoing.
“Mass” practice, doing all the review at once, promotes short-term but not long-term retention. “The student develops a false sense of confidence in her abilities as she finds she is able to correctly work several problems on the same topic in one sitting, and thus concludes she has mastered the content.” (p. 2) In the course where this study of distributed practice occurred, the instructor-researcher offers an example of what happens when students don't review material they believe they've mastered. “By the time of the final exam, students may not have worked a problem requiring expected value and standard deviation for discrete random variables in over a month.” (p. 2) So, when students face a final with problems from all parts of the course, it feels like an extraordinarily hard exam, which is probably why students would rather not have cumulative finals.
Distributed practice provides regular, ongoing review. Its efficacy has been documented by extensive research in cognitive psychology, mostly conducted in labs, but across a wide range of skills, not just problem solving. Distributed practice works because each time the skill is revisited, retrieving it is easier, more of it is remembered, and a growing familiarity results from these encounters spaced across time.
The problem, of course, is that distributed practice makes learning harder work. When all the problems are the same type, there's no need to retrieve anything learned previously. It's easier, and that's why students so relentlessly badger teachers for unit tests, on only what's been covered since the last exam. But if every quiz and exam is cumulative, then review is ongoing and everything on the final looks familiar.
The comparison of mass and distributed practices reported in this study occurred in three sections of a business statistics course. Students were randomly assigned 10 massed homework problems or 10 homework problems, five review problems, and five of the new problems. In both cases the 27 homework assignments counted for 5 percent of the course grade. All students took the same two exams and final. “While mean scores on all the outcome variables [all three exam scores, data assignments, lab activities, and homework] were higher in the DP [distributed practice] group than the MP [mass practice] group, the difference was not statistically significant on the final exam scores.” (p. 11) The difference was clearly significant on exam one. Due to circumstances beyond the researcher/instructor's control, a third instructor assumed responsibility for one of the three sections after the course had started and it could not be determined whether that influenced the results.
Because distributed practice is a harder way to learn, selling students on the idea is not easy. Many students still mistakenly believe that the best learning is easy learning. However, one of the enduring lessons of college should be that most learning isn't easy. If the learning is to be deep and lasting, not memorized for the test tomorrow but gone the day after, that requires different approaches to study. Students do pay attention when there's evidence that something improves exam scores, and this study is one of many documenting the benefits of distributed practice. This research can be shared with students; maybe a quasi experiment can be conducted in class and certainly individual students can be challenged to try the approach for themselves. They should regularly review previous problems and see whether that makes understanding the problems easier and scores on exams higher.Reference: Crissinger, B.R., (2015). The effect of distributed practice in undergraduate statistic homework sets: A randomized trial. Journal of Statistics Education, 23 (3), 1-22.