At a session I facilitated today, I was going over our old (1996) curriculum as compared to our revised (2010) curriculum. Many of the outcomes are similar, but the big difference is in the wording of the outcomes. I asked the participants to compare the two below.
13. Use the Pythagorean relationship to calculate the measure of the third side, of a right triangle, given the other two sides in 2-D applications.
2. Demonstrate an understanding of the Pythagorean theorem.
The outcomes get at essentially the same thing. In my opinion, though, the big difference is in the word “understanding” in our 2010 curriculum. Back in 1996, we don’t appear to have been too concerned about whether or not the students understood it, as long as they could do it. I threw this thought out in my session, and one person challenged it and said that they were the same thing. He insisted that a student couldn’t do something unless that student actually understood it.
I disagreed, and he claimed I was arguing semantics (which I had to look up later). I had to move on, but I certainly thought about what he had said on my flight home. In the end, though, I stand by my original assertion. I think that too often we ask kids to “do” things in math class without really trying to get at understanding. Some kids imitate our algorithms, score well on tests, without having a true understanding of the math involved.
I tried to think of a real-world example of this distinction, and so far the best one I have come up with is as follows. I know that if I push the gas pedal on my car, it will move forward (if I put that stick thing in the spot marked “D”, which I assume stands for “Go”). This is something I am confident I can do. I do not, however, have any understanding as to why the car goes forward or what is going on to make that happen. I do it without any understanding at all.