Yes, exactly. Math is a language for communicating ideas. Reading and writing are key skills here.

Hi Elliot, thanks for the note. For developing psychological safety, I was lucky that I did well enough in elementary through high school that my sense of safety was strong. When I had difficulty my first semester of college, I was able to look back and think “If I’ve come this far, there must be something I need to fix in my approach.”

I think that’s the larger takeaway — over and over again, math concepts that confused experts (like negative numbers, zero) are now taken for granted that anyone can learn. (Even literacy was like this, many thought that a large fraction of the population could never become literate.)

I think using historic examples may help.

Yes, it can be helpful to examine the wrong answers and see where the confusion lies. It’s better than no answer in terms of debugging the thought process.

Hi Denis, great question. In theory, proofs are essentially one person’s explanation of why something is true. But if the proof is unclear (i.e., it’s not simple to see why) it gets tricky. In a way, we’re trying to explain the explanation.

I’d like to give it more thought, but here’s one strategy.

First, try to understand the final conclusion (the Pythagorean theorem) with the ADEPT method. Look for diagrams, examples, etc. and try to convince yourself it’s true (but maybe not why).

Then, go through the proof, but work backwards and see which which part of the proof is confusing. Start with the conclusion [that you know to be true, but perhaps not why], and then look at the step in the proof right before. Does that leap of logic make sense? Then keep going backwards. At that point, you’re finding the step that is confusing.