Gifted Issues Discussion homepage Forums Learning Environments Woe is DD

I've heard of classrooms with "fraction means divide!" as a mantra - wonder whether that might be the root of this mistake? Glad it's sorted, anyway!

Learning by epiphany, blocks - does this indicate too great a tolerance for not understanding the first time a mistake is made?

I have too low a tolerance for not understanding, which (used to) get(s) me into trouble in situations where a lot of information is dumped on me at once too fast to understand it. I had trouble with my first hard university maths lectures, because I'd get stuck at the first line I didn't understand and get nothing from the rest of the lecture. These days, I have a special mode I go into in seminars after the point of nonunderstanding, that lets me still get something, but it was hard to develop. But on the plus side, it means I rarely make the same mistake twice in technical matters, so your workpapers/change entries example is strange to me: I can't quite imagine having let the first instance go before having understood what was going on enough to never make that mistake again.

There must be a happy medium somewhere. Maybe a chat about a mistake being a sign of a learning opportunity, which should be taken full advantage of, is in order?

Related, come to think of it: DS was getting frustrated early in the AoPS geometry course with repeatedly not being able to see immediately what to do. I encouraged him to make a list of useful techniques (assign variables to things of interest; angle chase; find similar triangles; drop a perpendicular, etc.). Now he (mentally or actually) consults the list as needed, and after each problem that he finds hard I encourage him to consider why it was hard; does something need to be added to the list, or were the right techniques there but hard to pick out?