I think this is a really good thing.

This is the whole issue with Common Core, and indeed every attempt at reforming math education in the USA. The problem is that this method of teaching hasn't been taught and supported to the educators and so (I can vouch) it's very stressful on the students (aka, Matilda).

Theoretically this is how you want to teach math. In reality, the teachers get thrown out with poorly designed materials and little support and the kids FLIP OUT. (cf., Louis CK's rant on this subject.)

I suffered with lack of mathiness in college. Memorized, memorized, memorized. I spent 12-15 hours a week studying and going over the same stuff repeatedly. Although I got straight As, I never knew how I did on a test until it was returned because I had absolutely no understanding of what I was doing. The professor thought it was funny how I would hang out to see how I did when I always had such great grades. I had no way of knowing how I did.

And people think I am mathy! My kids are better off than me that way, apparently they got their dad's math sense.

I don't know if being taught differently early on would have helped, but that ship has sailed.

A lot of teachers don't, themselves, really understand the math, especially at the lower el levels (I know our Aims to be an exception to this, and have met some others). It's basically impossible to teach a proper understanding of math you don't, yourself, understand.

The weird thing about calculus for me (and some others) is when I was studying it, all of a sudden it just clicked in my brain and made perfect sense. This happened to me for both differential and integral calculus.

I'm guessing this never happens for some people. I don't know what teaching methods could be used to get more students to have this understanding.

I don't think throwing the kids into the deep end of the math pool without teaching them the concepts first is necessarily a good thing, nor do I think rote memorization and drilling is necessarily a good thing, much less a better thing. I kind of wish the US would learn the value of a pragmatic approach to pedagogy rather than adherence to an ideological principle. Actually, not just in math, in a great many realms I think the US would be better off if we didn't try to be so ideologically rigid.

If I were trying to teach CC I would spend a day going over concepts and formulas and give the class exercises where the expectations were clear, and explain the answers. The next day I'd give them the problem sets that apply those concepts and let them try out the "sink or swim" approach. It seems pretty challenging to me to expect students to, at least in the 6th grade curriculum, intuit concepts like the formula for calculating the area of 3 dimensional object, or that they can solve a certain problem by multiplying both sides of the equation by the same amount.

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.