Thursday, August 04, 2005

Is It Fact or Process?

A friend of mine and I were recently discussing some aspect of mathematics instruction. I wanted to talk about the "number line" and he wanted to talk about "math facts". Perhaps I was being a bit ornery (quite contrary actually), but I looked at him with a blank stare and asked what he meant by "facts." He said, "You know...facts, like two times two is equal to four." Since I started down this path, I continued. So I replied, "Well, actually, two times two is really a concept. The concept of the successive addition of two for a total of two cycles." He became quite agitated and said, "No! It is a fact, you either know it or you don't." That is when I drew a matrix of 1-9 across the top of a piece of paper and 1-9 down the side and showed him how this matrix provided the "facts" he claimed without really "knowing" anything (other than how to draw the matrix). My friend then noticed that I was trying to teach him about process and he was trying to teach me about facts, and that we were getting no where fast. As such, he changed the topic to history, which I am sure he thought was a safe subject. "Math is no different than history," he said. "It's all about knowing the facts and sequencing them correctly." I said, "Really? Then if you list the League of Nations before the United Nations on some timeline you have demonstrated knowledge of history?" My friend was skeptical (and annoyed) and did not answer. I told him that in reality, it might very well be important to understand the impact the League of Nations had on the development of the United Nations if you were going to use history to help understand current events and/or future events.

At this point we decided to end the conversation before anyone got really mad. In departing, he did take one last shot. He said, "It's just like with testing...all you have to do is figure out if the kids know the facts." And I asked him, "Perhaps, but what process do you want to use? Multiple-choice, short answer, essay...?"

Perhaps the next time I see my friend we will talk will likely lead to a simpler discussion!

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