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You finally solve a type of problem correctly. Should you do ten more of the same kind right now, or move on? Many students do the ten more, and many maths textbooks are set up that way. Research on "overlearning" suggests that habit buys less than it seems, and that spreading the same practice over time is a better use of your effort.
What is overlearning?
Overlearning means carrying on practising in the same session after you have already got it right. Doug Rohrer and colleagues defined it as further study within the same session once the material has been learnt to one perfect trial.
What did Rohrer and colleagues find?
In a 2005 paper in Applied Cognitive Psychology, Rohrer, Kelli Taylor, Harold Pashler, John Wixted and Nicholas Cepeda had 218 college students learn geography facts or word definitions, practising to different levels. The students returned for a test between one and nine weeks later. At one week, overlearners recalled far more than low learners, but the difference shrank dramatically after that. The authors concluded that overlearning is an inefficient way to remember material over meaningfully long periods.
A follow-up with maths problems made the point sharper. Rohrer and Taylor (2006) had 216 college students learn one kind of maths problem (Applied Cognitive Psychology):
Doing nine practice problems instead of three in one session had no effect on test scores one or four weeks later.
Some students split ten problems across two sessions a week apart instead of doing all ten at once. That made no difference at one week but gave a very large benefit four weeks later.
The authors noted that most maths textbooks use a format that emphasises overlearning and minimises spaced practice.
Does that mean extra practice is useless?
No. An earlier meta-analysis by James Driskell, Ruth Willis and Carolyn Copper in the Journal of Applied Psychology found that overlearning had a moderate effect on retention. The effect depended on how much extra practice was done, the type of task and how long people had to remember. The Rohrer studies add the time dimension: the extra practice helped in the short term, and the gain faded over the following weeks.
So overlearning has a place. If the test is within a few days, more practice now can help. If you need the skill in four months, the same problems spread over weeks are worth more.
How much practice is enough?
Katherine Rawson and John Dunlosky tested this with 533 students learning concepts through retrieval practice (Journal of Experimental Psychology: General, 2011). Their advice for students: practise recalling concepts until you get each one right 3 times in the first session, then relearn them 3 times at widely spaced intervals. Relearning had large effects on long-term retention and cost relatively few extra practice trials.
A plan for a JEE or NEET problem type
Say you have just learnt to solve projectile problems on an inclined plane.
Day 1: work through examples, then solve problems until you get three right without help. Stop there.
Day 3 or 4: two problems of this type, mixed into a set with other mechanics problems.
Week 2: two more, again mixed in.
Weeks 4 to 6: two more inside a timed mixed test.
If you get one wrong in a later review, add one extra correct attempt that day and make the next gap shorter. That is far less total work than 20 problems on day one, and the research suggests spaced returns last longer. For a calendar you can copy, use our 4-week spaced revision schedule. To see why spaced, mixed practice feels harder but works, read about desirable difficulties.
A note on mastery
Getting a problem right once is not mastery. Mastery is getting it right weeks later in a mixed set, without knowing which chapter the question came from. That is the standard to aim for, and you reach it by returning to a skill, not by one long session. Our explainer on mastery learning covers the idea in more detail.
Sometimes you come back to a problem type and cannot remember how to start. The Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning. You can attempt the problem first, then compare your method with the solution step by step.
