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Mathematics

In maths, what you memorise is definitions, theorems with their conditions, formulas and the steps of a method. Lumi makes you pull them out of your head instead of showing them again, and that effort is what makes them stick.

How to turn this subject into cards

In maths, split your notes by topic and then by type of knowledge. One card set for definitions, one for theorems with their conditions, one for formulas you need cold, one for methods written as steps. Lumi quizzes you on what really has to be remembered, the statement of a theorem, an identity, the shape of a standard answer. The classic trap is reading a worked solution and believing you could redo it. Following a proof is not the same as producing one. Mixing problem types helps you spot which method to use, and that idea was tested on maths problems (Rohrer and Taylor, 2007). Lumi helps you remember definitions, formulas, theorems and method steps.

Example card

Try it, Lumi turns it into fill in the blank questions in your browser.

study-card.txt

Mathematics · teach this card to Lumi

Pythagoras’ theorem says that in a right-angled triangle the square of the hypotenuse equals the sum of the squares of the other two sides. The roots of a quadratic depend on its discriminant, which is b squared minus 4ac. The angles in a triangle add up to 180 degrees. The derivative of x squared is 2x.

Lumi’s question

Pythagoras’ theorem says that in a right-angled triangle the square of the _____ equals the sum of the squares of the other two sides.

Pick the missing word

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Levels where Lumi offers this subject

Active recall, why quizzing yourself beats rereadingReading once then quizzing three times gave 61% of ideas recalled after a week, against 40% for rereading four times (Roediger, 2006).Does interleaving, or mixed practice, really help you study?Mixing exercise types instead of grouping them. What Rohrer and Taylor (2007) and the Dunlosky review (2013) show.How to study effectively, according to the researchTen study techniques compared in a 2013 review. Two earned a high rating, practice testing and spacing. Here is how to use them.

Teach this to Lumi

Give Lumi your mathematics notes, it gives them back as questions at the right moment.

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