Encouraging Mathematical Thinking


 Abstract
 Introduction

 Discourse
 Interventions
  - Approaches
  - Leading Q's
  - Non-leading Q's
  - Paraphrasing
  - Summarizing
  - Listening
 Decisions

 Cylinder Problem
 Lesson Reflections
 Student Predictions

 Project Reflections
 Conclusion

 References
 Acknowledgments
 Teacher Resources



Authors'
Biographies

Table of Contents


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Interventions: Summarizing



We have also begun to think together about brief restatements of main points, or summarizing, as a means of facilitating student thinking. We have seen that summarizing can serve several purposes. It can help to bring a sense of temporary closure to a discussion by letting the class take stock of where it has been in the preceding conversation (Schoenfeld, 1987). It can also be used to distill, clarify, and/or illuminate ideas that students have raised, particularly when a discussion has covered many concepts and questions.

If summarizing is to support inquiry, it helps when a teacher remembers to acknowledge those whose ideas are being summarized, and reflects the language and flow of the conversation as it took place. The goal is to provide students with a compact record of their thinking that is easily used and returned to. The more the summary connects to their experience of the conversation and hooks into embedded meanings and memories of the situation, the easier it will be to make a useful transition to the next area of study.

Acknowledgement also affirms students' ideas and participation, reinforcing their roles in the conversation. In this clip, John McKinstry summarizes in order to set up a transition to the next question, while also bringing the current line of thinking into sharp focus.

  [view clip]


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