1. I am not familiar with any empirical work on the subject.
2. Some textbooks give advice in the beginning, esp. about how ideas are organized. (Which can be helpful if you don’t want to read the whole thing—it can explain dependencies between chapters, like 5 requires 1-3, but not 4, etc.)
3. Speculative:
Every subject has basic ‘building blocks’. If a subject builds on an earlier subject, those remain important. Example: For polynomials there’s: 1, x, x^2, x^3, etc. (All the other polynomials can be assembled out of those.) In calculus, there are functions that basically map between them (give or take multiplying/dividing by a constant factor), that are important.
you know times/addition tables? That’s a great format for two dimensional functions that take positive integers as input. (Though f(1-10, 1-10) might not all be necessary if there’s symmetry, and depending on the function, other constants might be more useful to know, like 1, 0, −1, e, pi, the primes, etc. For 3d, you might want to involve color or variables for associations or distinctions.)
These answers are all about how you study a math textbook. Answers based around other people might capture low hanging fruit, for one reason or another.
1. I am not familiar with any empirical work on the subject.
2. Some textbooks give advice in the beginning, esp. about how ideas are organized. (Which can be helpful if you don’t want to read the whole thing—it can explain dependencies between chapters, like 5 requires 1-3, but not 4, etc.)
3. Speculative:
Every subject has basic ‘building blocks’. If a subject builds on an earlier subject, those remain important. Example: For polynomials there’s: 1, x, x^2, x^3, etc. (All the other polynomials can be assembled out of those.) In calculus, there are functions that basically map between them (give or take multiplying/dividing by a constant factor), that are important.
you know times/addition tables? That’s a great format for two dimensional functions that take positive integers as input. (Though f(1-10, 1-10) might not all be necessary if there’s symmetry, and depending on the function, other constants might be more useful to know, like 1, 0, −1, e, pi, the primes, etc. For 3d, you might want to involve color or variables for associations or distinctions.)
These answers are all about how you study a math textbook. Answers based around other people might capture low hanging fruit, for one reason or another.