How to Study Math with Flashcards (Without Just Memorizing)

Math has a reputation as the one subject you can't memorize your way through, and that reputation is mostly deserved. You learn math by understanding ideas and solving problems, not by reciting facts. So where do flashcards fit?

In the background of every problem. Solving an equation leans on exponent rules you have to remember. A related-rates question needs the derivative rules. A statistics question needs the right formula and the conditions for using it. When those pieces come to mind instantly, your attention goes to the actual problem. When they don't, you stall before you start.

This guide covers what belongs on math flashcards, what doesn't, and how to combine cards with the problem practice that does the heavy lifting.

Why Flashcards Help With Math

Your working memory can only juggle a few things at once. If part of it is busy trying to remember whether the derivative of cos x is sin x or −sin x, there's less left for figuring out how to set up the problem. Facts you can recall instantly free that space up.

Two of the best-supported study techniques are built into flashcards. In a large review of learning techniques, Dunlosky and colleagues (2013) rated practice testing and distributed practice as the only two with "high utility": they help learners of different ages and abilities across many subjects. A flashcard is a practice test, and spaced repetition is distributed practice with the timing worked out for you.

What to Put on Math Flashcards

Formulas, with what they mean. The formula itself on one side, and a prompt that makes you produce it on the other. Write it in real notation, so you're recalling the formula as it appears on the page.

Definitions and theorems, with their conditions. Many exam mistakes come from using a theorem where it doesn't apply. Put the conditions on the card, not just the conclusion.

First steps. You can't put a whole problem on a card, but you can put the decision that unlocks it: which method to use, and how to start.

Your own common mistakes. If you keep making the same error, turn it into a card. Seeing the wrong version and correcting it is surprisingly effective.

What to Leave Off

Multi-step problems. A card should have one short answer you can check at a glance. A ten-line solution is a practice problem, and it belongs in a problem set.

Long derivations. Learn why a formula is true from your notes or textbook. The card is for recalling the result once you understand it.

Cards you answer by recognizing the card. If you only know the answer because you remember what the card looks like, rewrite the question so it makes you think, or ask it the other way around.

Mix Your Practice

Spacing isn't the only timing trick that helps math. Most textbooks give you a block of problems on the lesson you just learned, all solved the same way. Research by Doug Rohrer and colleagues suggests mixing problem types works better.

In Rohrer and Taylor (2007), students who practiced with shuffled problems did far better on a test a week later than students who practiced the same problems in blocks. A later classroom study, Rohrer, Dedrick and Stershic (2015), followed 126 seventh-graders over three months and found that interleaved practice beat blocked practice on both an immediate and a delayed test, with the bigger advantage on the delayed one. The likely reason: when problems are mixed, you have to work out which method each one needs, which is exactly what an exam asks you to do.

You can use the same idea with flashcards. In Space Repeat, put your math decks in one folder and study the folder: the due cards from every deck in it come up shuffled, so derivatives, integrals and limits arrive mixed instead of in neat blocks. For problem sets, add a few problems from earlier chapters to each session.

Writing Math on Your Cards

Plain text works for a lot of math, but formulas are much easier to read, and to remember, when they look the way they do in your textbook. In Space Repeat you put math between dollar signs and it's rendered with LaTeX, the notation math is written in: $\frac{a}{b}$ becomes a real fraction, and $x^2$ a real exponent. Double dollar signs put a formula on its own line.

If LaTeX is new to you, open the Math & code toolbar under any card field. It inserts fractions, roots, exponents, integrals, sums and Greek letters, and shows a live preview of the card. New accounts can also start from ready-made decks, from pre-algebra to calculus, and edit them to match their course. See Math flashcards and Calculus flashcards for more examples.

A Simple Routine

After each class, write three to five cards for the formulas, definitions and first steps you met that day. It takes a few minutes, and it's already your first review.

Every day, before homework, do your due cards. Ten minutes is usually enough, and it warms up exactly the facts the homework needs.

Once a week, do a short mixed problem set with problems from older chapters. That's where you check that the facts on your cards turn into working skills.

Keep the number of new cards modest so the daily reviews stay short. How Many Flashcards Should You Study Each Day has the numbers.

The Bottom Line

Flashcards won't teach you math, and they don't replace solving problems. What they do is make the building blocks automatic: formulas, definitions, theorem conditions and first moves. Put one idea on each card, write it in real notation, review on a schedule, and mix your practice. The problems get easier when you're not fighting to remember the tools. For formulas in particular, see How to Memorize Formulas.