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The article mentions "More drill and practice" ... I don't think this is the right way. I believe something happens with math to many/most students which leav

by mlyle 5y ago

The article mentions "More drill and practice" ... I don't think this is the right way. I believe something happens with math to many/most students which leaves them less than fluent in mathematics. Somewhere along the way, they stumble for a few weeks and fall behind. Maybe their family took a vacation. Maybe the teacher's explanations don't make sense to them. And then there's a deficit. Pretty soon, supporting that student through math becomes a whole lot more about drilling and memorizing strategies and understanding is deprioritized. This becomes insurmountable, especially with the "layer cake" model of how math is taught in US schools. Pretty soon you'll never catch up in understanding. But you probably just attribute it to "not being good at math". I'm working with a student right now, who is in precalc and "bad at math." He is actually really bright. Some missing knowledge and intuition about fractions has made everything since much harder. And the problem's never been fixed because he's constantly been in a survival mode in his math classes. These students never end up doing the kinds of things that kids are ahead in math are taught to do to crack free-form problems: - Make a good guess of the answer - Form a mental picture and use it to select strategy - Work a simpler problem and see how this can be extended - Organize your givens ; use dimensional analysis for a hint as to what operations may be required or what picture should be drawn - Look for symmetry and transformations that result in simpler cases - Does positing an incorrect answer reveal any information about the solution? IMO, teaching these things -- strategies-- should be more the goal than doing lots of kinds of applied math work by rote in a way that deeply depends upon previous work.

the_only_law 5y ago
There was another “I’m bad at math” thread a while back I stumbled across and drilling was considered basically the way to get good at math by most people posting. … which is all the more reason I’ll never become good at math. I’d rather drill a hole in my head than subject myself to drilling back to back, contextless, boring problems I don’t care about.
- mlyle 5y ago
  I think there's a few points where drill makes sense. In each case, after you have a good understanding, and you're seeking to become fluid and avoid dumb mistakes. (Even if you have a good understanding, if you're consciously thinking about each step you'll error a fair bit, and on a 20 step problem you can't afford this error rate and slowness) Arithmetic facts, basic algebraic manipulation, big polynomials, derivatives and integrals. But we do much more drill than that. And, worse, it's often as homework, where you can be guaranteed a decent slice of the class is practicing it wrong.

by mlyle 5y ago

the_only_law 5y ago

There was another “I’m bad at math” thread a while back I stumbled across and drilling was considered basically the way to get good at math by most people posting. … which is all the more reason I’ll never become good at math. I’d rather drill a hole in my head than subject myself to drilling back to back, contextless, boring problems I don’t care about.

mlyle 5y ago
I think there's a few points where drill makes sense. In each case, after you have a good understanding, and you're seeking to become fluid and avoid dumb mistakes. (Even if you have a good understanding, if you're consciously thinking about each step you'll error a fair bit, and on a 20 step problem you can't afford this error rate and slowness) Arithmetic facts, basic algebraic manipulation, big polynomials, derivatives and integrals. But we do much more drill than that. And, worse, it's often as homework, where you can be guaranteed a decent slice of the class is practicing it wrong.