

Here are some ways in which our videopaper has been used by our readers:
 Hollylynne Drier of North Carolina State University has used the videopaper with her preservice teachers to provide examples of reflections written by teachers in her Teaching Mathematics with Technology course.
 Barbara Donner, Math Department Chair of Chadwick School in California is thinking of using the videopaper in the next k12 math department day. She is thinking that teachers would do a webbased inquiry which would involve researching answers to questions based on "Encouraging Mathematical Thinking" Videopaper. She mentioned that this would be beneficial exercise on so many levels. For example, they would be experiencing activities that they can use for their students while raising their own awareness of good teaching techniques, and modeling them in their own discussions of the exercise.
 Brian Rick and Bev Neitzel of Bellingham Public Schools, Bellingham, Washington, and Jerry Johnson of Western Washington University coordinated the development of a workshop in which they referenced the Encouraging Mathematical Thinking videopaper. They shared some of the lessons and learning from it with a group of teachers attending "Geometry, Problem Solving, and Communication: A K12 Perspective." The part of this workshop in which our videopaper was presented, had to do with research to support problem solving and communication.


What kinds of norms need to be established in the classroom in order to
enable students to think about and share their confusions about mathematics?
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How do I judge whether to probe for a misconception, or let classmates be responsible for sensemaking and validation?
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When should I summarize in order to move on, and when should I encourage my students to play out their thinking?
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How do I know when it would help to wait, rather than ask a question or volunteer more information?
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