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

Jon Basden       [Biography]



During my freshman year of college, I was struggling in a chemistry class. I had tried to get help from a good friend of mine who was a stellar math and science student. For some reason, as bright as my friend was, he was unable to help me with one of the topics. It was at that time that another, older student offered me the following advice -- "To get help with this class, try to find someone who just barely understands what is going on. That person will be closer in understanding to where you are, and he or she will be able to help bring you along better than someone who understands the material so well that he or she cannot understand why anyone else could possibly struggle with the material." I often relate this story to my students, reminding them that they are going to learn far more from each other and their informal conversations they have with me than they are from any textbook for formal math lesson. In a parallel manner, I feel that I have gotten the opportunity to learn from and grown with the teachers involved in this project, because the teachers with whom I have interacted are real teachers, teaching real material in real situations where there are real problems. What better collaborators can we possibly have than those who face the same challenges we do, but come at them with a different set of experiences and skills?

In a conversation I had two summers ago with one of the Math Forum staff members, I was mentioning that I felt like most of the mathematics curricula that we have here in the Midwest seemed to be lagging behind that of what I was hearing teachers were doing in other parts of the country. In particular, it sounded as if the movements towards having students engage in more open-ended mathematical problem-solving and offering them opportunities for richer discourse in the classroom were ideas that appeared to be much stronger on the coasts than they were here in Illinois. That Math Forum staff member remarked something to the effect of "Yes, you may feel like some of the newer instructional initiatives are slow to reach you, but there are many unsuccessful educational fads that die out before they get to you there in the Midwest, which makes what you teach more stable."

Since the time that I had the conversation with that Math Forum staff member, the Math Forum has been gracious enough to allow me to participate in a few of their projects, the most recent of which is this, the "Bridging Research and Practice" project. Throughout the project, the opportunity for collaboration with other mathematics educators and opportunity for personal reflection have enriched both my understanding and appreciation of good teaching. If collaborating with our peers and reflecting upon our own work is as helpful as it is to us adults, then why not try to foster the same environment for our students? On a personal level, this project is certainly the best evidence that we should be seeking to promote such relationships, discussions, and cooperation among our students.

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