When I was in high school, a teacher told us there's two types of math students--those who memorize everything and those who develop a real understanding of what's being taught. He said as math classes get more difficult in college, there's a point where the "memorize everything" technique just stops working and those students who use it can advance no further.

When I was in high school, a teacher told us there's two types of math students--those who memorize everything and those who develop a real understanding of what's being taught. He said as math classes get more difficult in college, there's a point where the "memorize everything" technique just stops working and those students who use it can advance no further.

Yeah. At the point where I'm teaching, "memorize everything" will still get them a B if they're really good at memorizing stuff.

Jason got an aisle seat and he is off to faraway lands. Whew!

I totally freaked out my students today by saying, "There isn't any rule or set of steps to follow here. You just have to look at each individual problem and figure out what's happening."

As far as I can tell, this is now also true of the math my daughter is being taught. Concepts are implied, but no formulas are given. 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.

not given formulas beforehand

I think this is a really good thing. Understanding WHY something works makes you not only more able to figure out when to use it, but also to figure out if you answer makes sense and trouble-shoot if it doesn't.

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.