I'm currently working through calculus. I picked up Spivak's and Apostol's books-- probably the most recommended calc books on the internet. Aaaand... they're ok. There are many parts that are confusing, not because calculus is "hard", but because the authors didn't do any user testing. If they actually reworked the books to minimize real students struggling, the books would have been much much easier to self-study from.
I eventually found David Galvin's calculus notes[1] from University of Notre Dame. He basically follows Spivak closely, but reorganized the material a bit in response to user testing. The notes aren't perfect, but much much easier to follow. Same experience with Terence Tao's linear algebra notes[2].
I think book authors, even very highly respect ones, often kind of suck because they optimize for writing a beautiful book, not for minimizing student confusion. Once you struggle through the confusing parts, yes, the book is beautiful. But it's supposed to be written for people to learn, not for experts to appreciate! Notes written by professors who teach smart kids, optimize for minimizing confusion, and do real user testing are often much better than the best books, in my experience.
Exactly. It's very hard to judge how hard it is to understand something when you already understand it. This is also why video games with puzzles need extensive play testing. Because the puzzle designer, already understanding how to solve the puzzle, is terrible at judging how hard it is to understand the puzzle.
It seems that our counterfactual reasoning ability largely breaks down when it comes to understanding. For some reason we can't evaluate the question "what would I think if I didn't already understand this?"
> Notes written by professors who teach smart kids, optimize for minimizing confusion, and do real user testing are often much better than the best books, in my experience.
Yeah. Though smart kids get confused less easily, which means lecture notes written to teach dumb kids are even less confusing.
I eventually found David Galvin's calculus notes[1] from University of Notre Dame. He basically follows Spivak closely, but reorganized the material a bit in response to user testing. The notes aren't perfect, but much much easier to follow. Same experience with Terence Tao's linear algebra notes[2].
I think book authors, even very highly respect ones, often kind of suck because they optimize for writing a beautiful book, not for minimizing student confusion. Once you struggle through the confusing parts, yes, the book is beautiful. But it's supposed to be written for people to learn, not for experts to appreciate! Notes written by professors who teach smart kids, optimize for minimizing confusion, and do real user testing are often much better than the best books, in my experience.
[1] https://www3.nd.edu/~andyp/teaching/2020FallMath10850/Galvin...
[2] https://terrytao.wordpress.com/wp-content/uploads/2016/12/li...