Most of us practise maths the way we were taught: learn one method, then do a page of problems that all use it. It feels smooth. Research suggests three changes that feel a little harder and work better. Here is what each study actually found.
1. Test yourself instead of rereading
In 2013 a team led by John Dunlosky reviewed the evidence for ten popular study techniques. Two came out on top: practice testing (quizzing yourself) and distributed practice (spreading study over time). Rereading, highlighting and summarising were rated low utility (Dunlosky and colleagues, 2013).
A puzzle is a built-in quiz. You cannot reread your way to the answer; you have to pull the method out of your head and use it.
2. Space it out
In the first experiment of Rohrer and Taylor (2007), college students learned one kind of problem. Some did all their practice in one session; others spread the same practice over several sessions. When tested a week later, the spaced group did much better (Rohrer and Taylor, 2007). Same amount of work, better result.
3. Mix the kinds of problem
Most worksheets are blocked: ten problems of one kind, then ten of the next. Because you already know the method before you read each problem, you never practise the hardest part: choosing it. Interleaved practice shuffles the kinds together.
In the second experiment of Rohrer and Taylor (2007), students learned several kinds of problem, then practised them blocked or mixed. One week later, the mixed group did vastly better.
A later classroom study by Rohrer, Dedrick and Burgess followed 140 grade 7 students for nine weeks. Practice was either blocked or interleaved. In an unannounced test two weeks later, material learned by interleaved practice scored 72 percent, against 38 percent for blocked practice (Rohrer, Dedrick and Burgess, 2014).
Interleaving usually feels harder while you do it, so it is easy to think it is not working. The extra effort of choosing the method is the part that sticks.
A ten-minute routine
- Learn it once. Do a few problems of a new kind, with the method in front of you.
- Come back after a gap. A day or two later, try a few from memory before you look anything up.
- Shuffle. Mix new problems with older kinds, so each one needs a decision.
- Check, then fix. A wrong answer is information. Work out why, then try one more.
Where a puzzle adventure fits
Escape the Labyrinth is a puzzle adventure gamebook, so you do not read it in order. Each chamber is a number-pyramid lock, and the kind of lock changes as you travel: its 45 chambers draw on 14 puzzle kinds, among them wrong-brick, ink-blot, symbol and number-path locks. That is a natural shuffle. It is a book of puzzles, not a course, so it will not replace a textbook; it is one way to get mixed practice that feels like a game.
Books mentioned
Escape the Labyrinth
A puzzle adventure gamebook with 45 locked chambers. You choose your road, and the puzzle kind changes from door to door.
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