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Does spaced repetition work for maths?

Yes, if you change what goes on the cards. Definitions alone won’t get you through an exam. Problems, first moves and your own mistakes will.

Updated · 6 min read

Yes. Spaced repetition, reviewing something just before you’d forget it, works for maths as well as for vocabulary. The catch is that maths is a skill, not a list of facts, so cards that only ask for definitions miss the point. Make cards that ask you to do something.

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#The Chain Rule

When one function sits inside another, differentiate the outside, keep the inside, then multiply by the derivative of the inside.

ddxf(g(x))=f′(g(x))⋅g′(x)\frac{d}{dx}f(g(x)) = f'(g(x))\cdot g'(x)
Worked examples
ddxsin⁡(x2)=cos⁡(x2)⋅2x\frac{d}{dx}\sin(x^2) = \cos(x^2)\cdot 2x
ddx(3x+1)5=15(3x+1)4\frac{d}{dx}(3x+1)^5 = 15(3x+1)^4
Every session with Buddy is written into your note, with a summary and review questions.

Four kinds of maths card

  • First-move cards. A problem on the front; on the back, only how to start: “substitute u = x² + 1”. Fast to review, and it trains the hardest part: knowing what to try.
  • Step cards. One line of a worked solution, and the question “why does this step follow?”.
  • Mistake cards. Every error you make on a problem set becomes a card: “What’s the derivative of sin(3x)? (You forgot the 3 last time.)”
  • Re-solve cards. A full problem. Mark it right only if you can set it up and get going without help; you don’t have to grind out the arithmetic.

How often to review

Roughly: a day after you learn it, then about three days, a week, two to three weeks and a couple of months, getting longer each time you remember it. Apps that schedule this for you (Anki is the best-known) do it automatically. Mix topics in a review session rather than doing one chapter at a time: interleaving is harder, and it works better.

What not to put on cards

  • Long derivations to memorise word for word.
  • Anything you don’t understand yet. Understand first, then make the card.
  • Too many cards from one session. Five good ones beat thirty.

Where the cards come from in Pen Buddy

The hardest part is making the cards at all. In Pen Buddy, each study session with Buddy is written into your note: the problem, a short summary and review questions. Buddy turns your notes into review cards with spaced repetition, and can quiz you out loud and tell you how you did. See studying with Buddy.

FAQ

Questions, answered.

Yes, when the cards ask you to do something: start a problem, justify a step, avoid a mistake you’ve made before, or set up a full problem, rather than recite a definition.

Put a problem on the front and only the first move on the back, make a card for each mistake you make, and add a few full problems you mark right only if you can set them up.

Yes, for scheduling: it supports LaTeX, so equations render. The quality of your cards matters more than the app.