Mix your exercises: practise like the exam
You do ten integrals by parts in a row, and you get them all right. Great feeling. Then in the exam, the exercise doesn't say "integration by parts". And that's the whole problem.
Two ways to practise
When you do all the exercises of one type together (all A, then all B, then all C), you already know the method before you read the exercise. You only train applying it.
In the exam, the exercises are mixed. Before you can apply anything, you have to choose: which method is this? That choice is often where the points are lost, and blocked practice never trains it.
Mixing means practising A, C, B, A, B, C… so each exercise starts with the same question as in the exam: "what is this, and how do I solve it?"
What the research shows
In one study (Rohrer & Taylor, 2007), students learned to calculate the volumes of different solids. One group practised by type, the other with the problems mixed. During practice, the mixed group did worse: it felt harder. But one week later, on the test, the mixed group did much better.
To be honest about the science: in Dunlosky's 2013 review, mixing (called interleaving) was rated moderate, because most studies are in maths and in learning to tell similar things apart. That's exactly the situation of most science and engineering exams.
How to mix (the right way)
- Learn each type once first. Mixing is for practice, not for meeting a method for the first time.
- Mix inside one module, with types that can be confused (integration methods, kinds of limits, sorting algorithms…). Mixing Analyse with C programming doesn't help much.
- Before solving, write one line: "Method: … because …". This is the skill the exam tests.
- Use old exams. They are already mixed, in your professor's style.
Try it tonight
Take 3 exercise types from the same module, 2 exercises of each. Shuffle them. For each one, write the method and why before you start solving.
MajorMind does this for you: mixed review shuffles the topics of one module, like the exam, and shows at the end where you were sure but wrong. Free.
Join the betaSources
- Dunlosky, J., Rawson, K. A., Marsh, E. J., Nathan, M. J., & Willingham, D. T. (2013). Improving students' learning with effective learning techniques. Psychological Science in the Public Interest, 14(1), 4–58.
- Rohrer, D., & Taylor, K. (2007). The shuffling of mathematics problems improves learning. Instructional Science, 35(6), 481–498.