Young Mathematicians at Work Chapters 1 and 2

After reading this first two chapters of this book I began to think about what I have learned about teaching mathematics over the course of this semester. The first chapter focus on the field trip problem which we had worked on in class. It was interesting to see the different ways the children came up with doing the problem. The ways they decided to do the problem were much different that what I had done. I believe this may have been due to my knowledge of mathematics beyond fractions. Both doing this problem and reading about how a classroom of students chose to solve this problem caused me to see the problem in a different light. I gained an understanding of mathematics, how to make things equals, etc. This problem, as I noticed from working on it myself, was a high level thinking problem. When working on the problem I had to think about how to begin to solve the problem, solve it, and then work through my thinking. On the other hand, when reading chapter 2 about the 18/24ths money problem, I saw a huge difference in students thinking. I had not previously done this problem, but I could see from reading the text that the problem was more about the answer than how someone came to get the answer. I also quickly noticed that the problem was confusing. I believe this may have been due to the way it was written, but it also may have been because it is not likely for someone to find out the faction of money they spent.

With all this said, I feel that I have gained a greater ability to pick out high and low mathematical thinking word problems. Before this class I would have never thought that there were differences in the type of word problem which is given to students. Now, when look at the problem children are working on and notice there thinking process I find myself analyzing the type of thinking which is done in the word problem.

The one question is where does this higher-level thinking in word problem correlate with teacher instruction. Do teachers using this framework ever instruct their students other then when they are working on word problems?

I would love to learn more about how mathematics is taught over the course of a week in a classroom which uses higher level thinking word problems.