Building Students' Mathematical Thinking
Watching those videos made me really happy. These kids are real thinkers. They aren't just regurgitating an algorithm. They are creatively solving mathematics challenges. I would love to work in this fashion, but this kind of work takes time. Allowing students to generate their own rules about concepts while on a pacing plan is impossible. Conferencing with each student to analyze their thinking on each concept is a time consuming process. How then do we manage? Teaching students the algorithms often provides more successful interactions at a quicker pace, and when you're playing a numbers game with the district, its often the best approach. We are in a world of efficiency and on demand, does using algorithms produce a solution the quickest and most reliable? Questions I will be examining in my teaching practice this week...
A side note about the student in the article. He made me feel dumb. I couldn't grasp his thinking. I'm not embarrassed to admit it. I just don't think that way. As a teacher, if he were my student, how could I assist him or challenge him if I can't follow his strategy? Oy. Looks like I'm going to be doing that MA project about improving my practice...
Watching those students solve those math problems made me really happy too. It is evident as Bryan pointed out that these students had a deep understanding of mathematical concepts rather than just memorized algorithms. It is very exciting to think that we can develop that same understanding within our own students, but I agree it does take time, far longer than having them memorize an algorithm would.
ReplyDeleteIt would be naive of me to hope that the school district will realize the type of learning students need to have in mathematics now that we are using the CCSS and give us the liberty to allow our students to develop at their own place. It will be up to us to find how we can balance teaching all of the standards with developing mathematical thinking.
I went to a training on Math today. We were told to direct teach them how to do it four days a week, and problem solve one day a week. That is not a constructivist approach. No time is allowed for them to discover a way. They are not discovering, but the focus will be on them using what teachers 'taught' in problem solving. We also got told to teach the standards, and use whatever materials we needed to and then we were referred to four or five different approved curriculum to find each standards material in.
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