Why chapter by chapter revision can leave you unprepared

You finish the chapter on hypothesis testing. You can follow the worked examples, recognise the notation, and get most of the exercises right. You move on.

Two weeks later, an exam question describes a research problem without naming the method. You hesitate. Is this a test of a mean, a comparison of proportions, or a question about the assumptions behind the model?

Your earlier practice may have taught you the procedure while leaving the choice of procedure largely untested. The chapter heading was doing part of the work.

That is the weakness of treating revision as a second journey through the textbook. Teaching order provides a useful introduction to a subject. Preparing to use that subject independently requires additional decisions about what to revisit, what to mix, and when to remove support.

The help hidden in a problem set

In blocked practice, similar problems appear together. A set on integration by parts tells you the likely method before you inspect the integrand. This can be useful while learning the steps. It also makes successful practice an incomplete test of readiness.

Rohrer, Dedrick and Stershic studied this distinction in 126 seventh-grade mathematics students (Rohrer et al., 2015). Over three months, students encountered the same practice problems arranged in different ways. Interleaved practice produced higher scores on both immediate and delayed tests. The researchers emphasised the need to select a strategy from the problem itself. This was a school mathematics study, so its effect sizes should not be advertised as expected gains in a university course. Its design nevertheless identifies a relevant question: how much help does the arrangement of our practice provide?

Consider three skills in probability: counting possible outcomes, conditioning on information, and calculating an expectation. A student might perform each successfully in its own worksheet. A cumulative set asks an additional question: which representation fits this situation?

You can test that distinction yourself. Before doing any calculation, write down your proposed method and the feature of the problem that justifies it. A wrong choice of method deserves different follow-up from a correct method followed by an arithmetic slip.

The chapter heading was doing part of the work.

Three changes that serve different purposes

Interleaving mixes problem types. Spacing separates encounters with material over time. Retrieval practice asks you to produce an answer from memory. A study session can combine all three, but the terms are not interchangeable.

The timing matters. Cepeda and colleagues' synthesis of distributed-practice experiments found that the useful interval between study sessions depended on the interval before the final test (Cepeda et al., 2006). A schedule designed for tomorrow's quiz need not suit an exam several weeks away. The work primarily concerned verbal recall, which limits how precisely we can translate it into schedules for complex problem solving.

Retrieval adds another change: attempting to answer becomes part of learning. Roediger and Karpicke found that recalling studied passages benefited later retention compared with additional study, even though repeated study could look better on an immediate test (Roediger and Karpicke, 2006). The outcome depended on when learning was measured.

For revision, these findings suggest a practical combination: attempt questions without the solution in view, return to topics after a delay, and include problems whose method has not been announced in advance.

Keep enough depth to learn the method

None of this makes random shuffling a complete study strategy. If you cannot yet interpret a conditional probability, alternating it with five unrelated topics may simply give you six ways to get stuck.

Research on worked examples provides a reason to preserve guidance during early learning. Sweller and Cooper's algebra experiments investigated learning from worked solutions as an alternative to extensive conventional problem solving (Sweller and Cooper, 1985). Their findings support using examples to help establish procedures before expecting independent performance.

A sensible revision session can therefore begin with a focused repair. Study one explanation, work through an example, and attempt a nearby problem unaided. Once the method becomes usable, place it among alternatives. Return later to see whether it survives the delay.

There is no universal number of questions at which to switch. Your errors provide a better guide than the end of a chapter. If you cannot execute the method, deepen. If you can execute it but choose it inappropriately, compare it with neighbouring methods. If it worked last week but fails today, review it.

That is the starting point for Memoza's breadth and depth question. The useful unit of progress is an ability you can demonstrate under relevant conditions. Reaching the last page tells you much less.

How Memoza fits

When you let Memoza choose, your next question does not come from where you are in a syllabus. It scores the concepts you are eligible to practise and serves the one that needs practice most, and two of the seven terms in that score are the ones this article is about: the risk that you have forgotten something, which grows with the days since you last practised it, and a penalty on a concept you have just seen. Whether that ordering beats a fixed schedule is a separate question, and one we have not answered: the machinery for comparing orderings is built, no study has enrolled anyone, and the policy running behind your practice today is the one that restricts nothing.

References

Research types say how each source contributes to the argument. A design framework does not carry the same evidential meaning as a randomised learning-outcome study.

• Cepeda, N. J., Pashler, H., Vul, E., Wixted, J. T., & Rohrer, D. (2006). Distributed practice in verbal recall tasks: A review and quantitative synthesis. Psychological Bulletin, 132(3), 354–380. https://doi.org/10.1037/0033-2909.132.3.354 Meta-analysis.
• Roediger, H. L., III, & Karpicke, J. D. (2006). Test-enhanced learning: Taking memory tests improves long-term retention. Psychological Science, 17(3), 249–255. Experiments.
• Rohrer, D., Dedrick, R. F., & Stershic, S. (2015). Interleaved practice improves mathematics learning. Journal of Educational Psychology, 107(3), 900–908. Classroom experiment.
• Sweller, J., & Cooper, G. A. (1985). The use of worked examples as a substitute for problem solving in learning algebra. Cognition and Instruction, 2(1), 59–89. Experiments.