Cognitive load when learning mathematics

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 $\max(j-\min J(j))$, 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.