Reform math - we need a BALANCE

Recently Spunky wrote about reform math, and I feel I want to say something about it, too.

She was critizing the movement heavily. Some people call reform math 'new new math' or 'fuzzy math' (in a degrading way) - and like you can read in Spunky's post, sometimes when new ideas are implemented, it can cause math to become 'fuzzy' to the children.

But that is not necessarily a fault of the reform on a whole - maybe the teacher in question didn't understand how to implement the methods, or for some reason (unwisely) totally abandoned 'traditional' math fact drills.

I would say not all of the IDEAS that have come from this mathematics education reform are bad.

For example, encouraging kids to explore and investigate mathematical concepts, or discovering their own rules, can be a good thing. Group work CAN be a good thing.

The reformists promote understanding of concepts, problem solving, critical thinking. They try to distance themselves from the "drill ' n' kill" and rote memorization parts of traditional math education.

If kids "learn" math as a set of disconnected rules, they soon forget those since they never learned WHY they worked. (Well that can easily happen. I just witnessed it this past week; a youngster didn't know how to multiply two two-digit numbers since it had been so long that he had done it.)

The key is a BALANCE. Truth is somewhere in the middle. Kids absolutely need to learn their addition facts and memorize their multiplication facts. Otherwise, they're going to go about learning math without a FOUNDATION.

But, I feel it is very important to teach them also WHY the rules and procedures work.

For example, let kids learn how to multiply 2-digit numbers by 2-digit numbers. Let them practice. But also show them what it is based on (distributive property). They need to know that anyway in algebra class!
(For example: 34 x 58 is based on doing it in parts: 4 x 8, 4 x 50, 30 x 8, and 30 x 50, and adding all those. Compare to (x + 1) (2x - 5) which is done using distributive property.)

Learning to estimate and critically look at your final answer is very important, I feel. (For example, 34 x 58 is about 35 x 60, which is same as 70 x 30 = 2100. Exact answer is: 1972. OK.)

Let them SOMETIMES explore and investigate, find real-life connections. Occasional "math labs" can do much good in motivating and showing where math is useful in real life, letting them gain confidence, etc.

But if all the class time is spent on letting the kids find their own division methods and forgetting all about memorization, the pendulum has swung WAY too far to the other direction.

Memorization is needful, very needful. But let us not forget the 'reform' aspects of math altogether.

And like was pointed out in the comments to this post, it is the TEACHER that decides what is done in the math class and how it is done.

I feel the NAME of this reformist website summarizes it all: Mathematically Sane.

P.S. Here's a nice piece Newer Math by Jack Lee about what is going on at Seattle.

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