Another aspect, one that I've encountered many times, is that even when someone has to implement the idea from scratch, they don't work to understand it and ins

Another aspect, one that I've encountered many times, is that even when someone has to implement the idea from scratch, they don't work to understand it and instead just translate pseudocode. I once had an interview where I was asked to explain why a piece of code (that the interviewer wrote) worked, because the interviewer did not know. A benefit of the bottom up approach, of starting with the math and no reference implementation, is that you are less likely to implement it unless you understand it. And I should stress, these are tradeoffs.