I help with this stuff all day with people... that problem would completely stump many of my adult learners.

Yea, the goal of lots of math programs is to have them understand what's going on. However, the brutal fact is that sometimes the teacher doesn't. S/he's not going to say it... so s/he follows the book and hopes. I've seen it happen... they have no idea that they're asking a student to solve a quadratic equation.

Then there's when the teacher gets it and doesn't have any idea that while s/he is "teaching" understanding, what the studnets are getting are two things: a complex procedure taht they memorize anyway, because in fact they don't have the background to understand it as it's being taught and b: strong, repeated reinforcement of the idea that they are **supposed** to understand it, and therefore they must Not Be Good At Math because they don't.

It's a bit of a hot button for me 'cause I work with the victims all day...