Maybe I was incredibly lucky, but whenever someone rails against how awful the "standard" math education is, and recommends a "better way", I note that the "bet

Maybe I was incredibly lucky, but whenever someone rails against how awful the "standard" math education is, and recommends a "better way", I note that the "better way" was how I was taught. I suspect what happens is that students forget some of the good basic ideas (or is that "basic good ideas" ;-) ) they were taught, and teachers fail to re-emphasize them to keep students on track, and so all they remember is the formal/abstract techniques they spent a login time struggling with. Painful experiences stick in our memort more than smooth easy experiences.