Proficiency needed: ask any carpenter or electrician

Understanding (conceptual) is not superior to Knowing how (proficiency) . In other words I can understand the problem without knowing how to do or solve the problem. Two examples:

1) I understand how to hit a golf ball straight. I understand how I am supposed to stand, what I am to do when I swing the club and where the ball is supposed to go. However, I don't know how to do it. All the understanding in the world does not insure that you can perform the task. Certainly, knowing how to properly swing a golf club is far superior than understanding how you are supposed to swing a golf club.

2) When my car breaks down and I take it in to be fixed it is not enough for the mechanic to understand what is wrong.... the mechanic must know how to fix it.

Ideally, one has both understanding and knowledge of how to solve a problem. However, by far the most important of those two is know-how. Many times students tell me that they understand what the problem is asking....and they understand what they are supposed to do.....but they don't know how to do it. Understanding what division is does not mean that you know how to divide. It may be interesting to understand but unless you know how there is very little value in that understanding. In the real world, it is far superior to know how to do the math than it is to understand why it works.

The natural order of learning is to learn how and then to learn why not the other way around. Reform math would have us believe the opposite. Their claims indict know-how as mindless process while claiming that understanding alone is an ultimate goal. Nothing could be farther from the truth. Understanding is superficial and will not necessarily ever lead to know-how.... .. but know-how often leads to deep understanding. Understanding without knowledge can never be anything but superficial.

Bob Dean
Math Dept Chairman
Evergreen High School
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In math the deep conceptual understanding is difficult to arrive at. It may take years and may not ever occur at a truly deep level for most students.

Traditional math gives students arithmetic, algebraic and geometric skills that can be used, with hopes for eventual deep understanding. Perhaps few arrive at such understanding. Result we have mathematically skilled persons able to live life and be employed.

Reform math plans to develop deep conceptual understanding and the have the math skills emerge from this understanding. The result thus far is a nation increasingly filled with mathematically crippled individuals.

Dan