Cognitive load when learning mathematics: Difference between revisions

Revision as of 23:08, 4 August 2018

This page lists some math-specific stuff relating to cognitive load.

Some things that increase strain on working memory:

If a proof has steps $P_{1},P_{2},P_{3},\ldots ,P_{n}$ the proof is much easier to follow when the justifications for a step $P_{j}$ are close to $P_{j}$ . When much earlier stages of the proof are required to understand the current step, the reader has to go back to remember what was done early on. If $J(j)$ is the set of justification numbers used on step $P_{j}$ (e.g. maybe $J(5)=\{1,3\}$ ), then the quantity of interest is something like $\max _{j\in \{1,\ldots ,n\}}(j-\min J(j))$ , which is the most number of steps the proof stretches backwards.
Level of nesting: nested sums, nested products, nested quantifiers, nested loops, combinations of nesting.

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 Some things that increase strain on working memory:
-* If a proof has steps <math>P_1, P_2, P_3, \ldots, P_n</math> the proof is much easier to follow when the justifications for a step <math>P_j</math> are close to <math>P_j</math>. When much earlier stages of the proof are required to understand the current step, the reader has to go back to remember what was done early on. If <math>J(j)</math> is the set of justification numbers used on step <math>P_j</math> (e.g. maybe <math>J(5) = \{1,3\}</math>), then the quantity of interest is something like <math>\max(j - \min J(j))</math>, which is the most number of steps the proof stretches backwards.
+* If a proof has steps <math>P_1, P_2, P_3, \ldots, P_n</math> the proof is much easier to follow when the justifications for a step <math>P_j</math> are close to <math>P_j</math>. When much earlier stages of the proof are required to understand the current step, the reader has to go back to remember what was done early on. If <math>J(j)</math> is the set of justification numbers used on step <math>P_j</math> (e.g. maybe <math>J(5) = \{1,3\}</math>), then the quantity of interest is something like <math>\max_{j\in \{1,\ldots,n\}}(j - \min J(j))</math>, which is the most number of steps the proof stretches backwards.
 * Level of nesting: nested sums, nested products, nested quantifiers, nested loops, combinations of nesting.