On this page
Most textbook practice looks the same: a lesson, then twenty problems on that lesson. The answers come out right and it feels like learning. A 2007 experiment suggests that rhythm hides a gap, and the fix costs no extra problems.
What is interleaved practice?
Blocked practice means doing all problems of one type together, such as ten substitution integrals and then ten by parts. Interleaved (mixed) practice shuffles the same problems, so you cannot predict which method comes next.
That matters because an exam is mixed. In a block, the chapter heading tells you the method. In a paper, you have to work it out from the question.
What did Rohrer and Taylor (2007) find?
Doug Rohrer and Kelli Taylor at the University of South Florida tested this directly in The shuffling of mathematics problems improves learning, published in Instructional Science. In their second experiment, 18 undergraduates learned to find the volume of four unfamiliar solids, such as a wedge and a half cone. Everyone worked the same 16 practice problems in each of two sessions a week apart. One group did them blocked, four of one solid then four of the next; the other group did them shuffled.
During practice, the blocked group did better: 89% correct against 60% for the mixed group, according to the paper. One week after the last session, both groups sat a test of eight new problems. The mixed group scored 63% and the blocked group 20%.
Almost every test error came from choosing the wrong formula, not from using the right one badly. The blocked group knew how to solve each type; they had not learned which method went with which problem.
The authors list the limits themselves: college students, a lab rather than a classroom, procedural tasks, and test problems close to the practice ones. Treat the size of the gap as an illustration, not a promise.
Does interleaving work for physics too?
A later classroom study suggests it does. Joshua Samani and Steven Pan ran an 8-week study in an undergraduate introductory physics course, published in npj Science of Learning in 2021. Students in two lecture sections did thrice-weekly homework in which problems were either interleaved or arranged one topic at a time. On two surprise tests with new and more challenging problems, students did better after interleaved practice, with median improvements of 50% on the first test and 125% on the second.
Students rated interleaving as harder and wrongly believed they had learned less from it. Our post on why learning that feels hard sticks explains the wider idea, and why rereading feels like learning covers the same trap from another side.
How do you interleave maths and physics practice?
Interleave topics you have already been taught; it is a way to practise, not to learn a chapter for the first time. Here is a two-week plan for a Class 11 or 12 student. Pick three types in each subject, for example:
Maths: integration by substitution, integration by parts, partial fractions
Physics: projectile motion, connected blocks with Newton's laws, work-energy problems
Week 1:
Days 1-2: a short blocked refresher. Three problems of each type, checking each method against your notes.
Days 3-6: one shuffled set a day of 12 problems, four of each type, alternating maths and physics days. Copy problems onto a sheet without chapter names.
Before solving, write the method in the margin, such as "by parts" or "energy, no friction".
Day 7: a timed mixed test of eight new problems, four per subject, no notes.
Week 2:
Days 8-13: add a fourth type to each subject (say definite integral properties and circular motion) and keep mixing all four.
Day 14: another timed mixed test of eight new problems, then compare with Day 7.
After each test, mark every wrong answer as either wrong method chosen or right method with a slip in the working. Mostly the first kind: keep mixing. Mostly the second: slow down on those types. Mixing also spaces out each type; our 4-week spaced revision schedule shows how to keep that going after the plan ends.
What if you keep picking the wrong method?
Put one problem of each confusing type side by side and write one line on what in the question points to each method. If the error is in the working, the Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning rather than printing an answer, so you can compare each step with your own working. If you are unsure why a method applies at all, the Fermi Concept Library has a lesson for each concept in physics and mathematics.
Start with tomorrow's practice: take the problems you would have done anyway, and shuffle them.
