Encouraging Mathematical Thinking


 Abstract
 Introduction

 Discourse
 Interventions
 Decisions

 Cylinder Problem
 Lesson Reflections
 Student Predictions

 Project Reflections
 Conclusion

 References
 Acknowledgments
 Teacher Resources



Authors'
Biographies

Table of Contents


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Reflections

Art Mabbott       [Biography]



So seldom are we allowed the luxury of time -- time to spend with our peers to talk to each other, to share with each other in the creation and presentation of a common task. So seldom are we allowed the safety to risk asking for help of our peers. In reflection and after more than a year of interactions with this team of teachers, I have gained much more than I have been able to offer. Several times I have gone to this group of incredible teachers with problems that I was facing in my classroom. Now, I am not a young teacher, having been in this profession for nearly 30 years in both public and private schools, and at all levels 4-16 (elementary through college). Even so, from time to time I get myself into situations with my kids that I need help getting out of, and this year was no exception.

Our team knew that I was making a change this fall back to high school. Early in the fall, someone foolishly asked me how things were going. I have returned to a high school after two years with exceptionally gifted 4th through 8th graders. I have returned to a class of regular, average, normal, run-of-the-mill geometry students -- great kids but definitely not "severely gifted" or even in the honors range. While I physically made the move over the summer, I hadn't made the move educationally -- I walked into class knowing that my new kids would be different but I was not ready to deal with these wonderful kids and their differences. Early this fall, I came to our team complaining about the fact that my kids weren't responding to me. In the past, I would ask my students a question and I'd always get an answer. But this year, I would ask a question and get no response -- nothing, nada, zip. And then Susan Stein and others asked me a really simple question: "Have you talked to them about what you expect? Do they know what it is that you want?" Teach them how to answer a question? Do I really have to do that? I had never thought about that.

So I came back to my kids and talked to them about what it was that I wanted. If I ask a question and get no response, then I don't know what to do. If you answer the question correctly, I know where to go next. But if you answer the question incorrectly, then I know where to make a correction in what I am doing and know where to go next. I also talked about the risks that I was asking them to make in order to answer and possibly be wrong. To do that is very difficult for them as teenagers. Recognizing and validating this for the kids, while not completely solving the problem, went a long way to making my life simpler. Now, at least, they are willing to respond and are willing to take more risks.

This project allowed me the time and the safety to take the same kind of risk that I eventually asked of my kids.

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