Yeah, the "intuit the answer" approach just pissed me off when they tried it in our physics class. I'd totally go for Burrell's approach, but otherwise you end up with people "intuiting" the wrong answer and not remembering whether the right way was their guess, someone else's, or some other thing entirely.

I'm also cranky right now because my daughter is flailing in her math class, so my comments should be read with that in mind. As her teacher has told me more than once, other kids are getting the concepts just fine and doing just fine. My kid is CLEARLY the problem here, not his teaching methods. (Grrr)

I'm also cranky right now because my daughter is flailing in her math class, so my comments should be read with that in mind.

What grade is she in now? Fifth or so? I've known people who've had good experiences supplementing the curriculum with Singapore Math, but that would mean getting her to do extra math work, which might be a tough sell. (I like the Singapore Math approach for the younger grades. Each new topic is introduced in three stages -- first, the students do some activities with actual objects, building things or counting things or separating things into groups or things like that, to get the general idea of what's going on. Then, they do the same thing by drawing pictures (and there are a couple of specific standard ways of doing that, so that they don't need to reinvent the wheel for every problem.) Then, once they get how it works as a picture, they start doing it with numbers. Doing it that way kind of forces them to get the concept, since they can't fall back on memorizing number rules. Although there is still the issue of "I know they're going to teach me the number rules later, so why do I have to draw this picture now?" but, from what I've seen, they usually don't start asking that until middle school or so, unless they've been hearing it from their parents.)

Children are expected to intuit and/or reason out mathematical concepts and are not given formulas beforehand to plug into the problems and figure out the answer.

Which is why I discovered that when in doubt x = 8 will give you a "C" average in algebra. By the time my teachers got around to explaining the formulas and concepts, I was so frustrated that I just gave up.

(Of course, hindsight also shows that I almost certainly suffer from wicked dyscalculia, so my nope, doesn't make sense, don't wanna deal with this freak-outs were semi-justified, instead of it being that I was dumb and couldn't math.)

I did really well in algebra, but beyond that I was completely lost.

Isn't the whole point of math and science to not intuit things?

Isn't the whole point of math and science to not intuit things?

How else would you come up with a hypothesis, or know if your answer makes sense?

Or what kind of experiment to run.

On intuiting, I have enough number sense that if I try to multiply two large numbers (by hand), say 27 times 145, and I get an answer that's off by an order of magnitude (say, 450), I can kind of tell it's wrong. My 6th grader? No clue. They try and teach this - what they teach is to test yourself by rounding - in my example, try 30 x 150 and see if what you got is close to that - but it's not sticking with my kid too easily. (My 3rd grader seems to have better instincts.)

My daughter is in 6th, and was grouped in advanced math up through 4th grade. That's part of the reason this drop is so frustrating for me.