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

Susan Boone       [Biography]



Over the course of the last year, I have been energized by the encouragement I have received from this project to promote opportunities for discourse in my classroom. I have always wanted students to explore, discuss, and have time to think about problems. I build my lessons around these concepts and I have been generally pleased with the way my lessons go in class. Most importantly, I have fun and students seem to enjoy class. The communication and support I have received from "wrapping" [editor's note: "WRAP" is the acronym for our group, "weaving research and practice"] has reinforced my beliefs and allowed me to develop a classroom environment that is open for discourse.

I place a major emphasis on communicating mathematically. Ninth-grade students are often intimidated in a high school environment. I offer a wide range of opportunities for them to write about mathematics, work on open-ended problems, and work collaboratively with people in a group. I have discovered that my efforts to encourage students to talk more among themselves have allowed me to take a less active part in the "teaching" of lessons.

Putting this paper together has been the epitome of a collaborative effort. Our school has adopted a program that will require all of my students to have a laptop, and as their teacher I am expected to use the technology constructively in my classes. Although the "written" word can never replace actual conversation, I have been inspired by the effectiveness and ease of communicating with fellow "wrappers" over the course of the year. Once again, I have been energized by the prospect of my students having the ability to communicate with each other as well as with other teachers and chosen experts. Although this use of technology was sort of taken for granted in our group, communicating in this manner has given me some wonderful ideas to implement in my classes. This will ultimately improve the discourse among my students, as well as their communication with me.

I have learned a lot by working on this paper. Much more emphasis is placed on the student in my classroom since I have been working with this project. I am a very global person and my teaching style reflects the big picture. The opportunities I have had to discuss my classroom with other colleagues, as well as watching my classes on video, have shown me that students perhaps sometimes need a bit more direction. I have also had wonderful mentors who have shown me other approaches and teaching styles.

The emphasis on discourse has not only altered the environment in my classroom, but I have been much more effective in working with other teachers in my grade level this year. Alas, I may never know whether "I am right", but I have discovered that the real issue is to take risks. What is "right" is creating a classroom environment that is open, friendly, and not threatening, thus allowing students opportunities to be "wrong" on their way to righteousness.

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