"Problem solving, which is preferred, occurs when students are not able to apply a mechanical, memorized response, but rather have to figure out what to do in a new situation."Kids who know math can look at a problem and apply a straightforward, mathematical solution. For kids who know squat, EVERYTHING is a problem that has to be figured out. That is not a good thing. The route to complex problem solving does not bypass mastery of the basics.
Discovery learning in math (pdf file)
This reminds me of the parent uprising that took place here a few years back.
Kids in the accelerated math course at the middle school were doing so badly on their tests, and the tests were so different from what had been taught in class, that the district was finally forced to hold a public meeting to discuss the situation.
The then math chair, by way of explanation, told us that the reason kids were struggling was that the course goal wasn't just to teach math. "I want your children to be able to solve problems," she said.
She elaborated on this point: there was something about astronauts, as I recall. She wanted our kids to be able to use math to solve the kinds of problems an astronaut might have to solve. Something out of the ordinary.
That was the goal.
Ergo: hard course, 6th grade children weeping over their homework, and parents hiring tutors. Specifically: parents hiring math tutors already employed by the district as math teachers.
Later, a parent standing in the back of the room raised his hand and when called on observed that students hadn't done so well on measurement in the last round of state tests.
The department chair said emphatically, a hint of triumph in her voice, "Your children can't measure!" She seemed to relish this factoid. Your children!
A friend of mine heard from the administration just the other day that kids did badly on the measurement scale again this year.
So I guess the 4 intervening years of Math Trailblazers hasn't done the trick.