The idea the math is not simply a set of standard rules and formulas is one of the most radical, maybe even revolutionary, ideas that I have heard. I liked math because I thought it was so structured, so black and white, so clear cut. I thought the objective of math was to get the right answer. I liked it because it did not appear to be subjective. This class has caused me to rethink my ideology. In ways it has pulled my foundation right out from under me. But the interesting thing is that I don’t feel like my world is falling down. Just as quickly as the old ideas are crumbling – or at least let’s say the fallacies and inconsistencies are become apparent – new ideas are forming to replace them.
As I have previously stated, I tried to implement the new constructivist ways (although I didn’t know that’s what it was called at the time), but I also tried to keep the traditional way as well. I wanted to live in both worlds, but that will not work.
A constructivist classroom looks like ordered chaos. Students are engaged in mathematical discussions and activities. Each group may be doing something completely different in their efforts to hash out their ideas. It is such a contract to traditional classroom where at any given moment you should be able to hear a pin down. It is also different because it eliminates the plug-and-chug approach. The importance is not solely on obtaining the correct answer, but obtaining and retaining the key concepts needed to derive the correct answer. Oh, how I long for this in my classroom.
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3 comments:
This response is to "The effects of constructivism on my thinking". Heather I can definiteley relate to what you said in your blog. I had the same concepts of mathematics that influenced my choice to want to teach math. I have had some identical experiences with what you mentioned and it is good to know that through our experiences I am not alone. The good thing is that we are in the process of learning a technique that offers tremendous gains.
I started re-thinking math years ago when I was sitting in a Dynamics class. We had developed two equations because we had two unknowns. I thought the professor was going to use the substitution method. WRONG! He multiplied one equation by a constant number and subtracted one equation from the other. The solution was much easier to solve and I learned there was more than one way to solve simultaneous equations. This was when my structured math world started to crumble. Before, I had been taught there was one and only one way to solve this type of problem.
The look of a constructivist classroom may appear to an outsider as ordered chaos but I think it would probably look like the students would be learning something. The outsider might not think it was a math class.
That is so TRUE! I too thought of math as cut and dry in many ways. Actually for me its even a means to an end. But I like the term 'ordered chaos'. In this new class the kids are the talkers. Good job being open despite the disorientation its causing you.
I think you should consider why you feel the old and the new concepts exist together. I don't have an answer, just the question. :-)
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