Examining the Tasks of Teaching When Using Students' Mathematical Thinking
 Helen M. Doerr
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Recent research suggests that the examination of students' work may lead to changes in teaching practice that are more effective in terms of students' mathematical learning. However, the link between the examination of students' work and the teachers' actions in the classroom is largely unexamined, particularly at the secondary level. In this paper, I present the results of a study in which teachers had extensive opportunities to examine the development of students' conceptual models of exponential growth in the context of their own classrooms. I describe two related aspects of the practice of one teacher: (a) how she listened to students' alternative solution strategies and (b) how she responded to these strategies in her practice. The results of the analysis suggest that as the teacher listened to her students, she developed a sophisticated schema for understanding the diversity of student thinking. The actions of the teacher supported extensive student engagement with the task and led the students to revise and refine their own mathematical thinking. This latter action reflects a significant shift in classroom practice from the role of the teacher as evaluator of student ideas to the role of students as selfevaluators of their emerging ideas.
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 Title
 Examining the Tasks of Teaching When Using Students' Mathematical Thinking
 Journal

Educational Studies in Mathematics
Volume 62, Issue 1 , pp 324
 Cover Date
 20060501
 DOI
 10.1007/s1064900644379
 Print ISSN
 00131954
 Online ISSN
 15730816
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 functions
 problem solving
 secondary mathematics teaching
 subject matter knowledge
 teacher knowledge
 teaching practice
 Authors

 Helen M. Doerr ^{(1)}
 Author Affiliations

 1. Mathematics Department, Syracuse University, 215 Carnegie Hall, Syracuse, NY, 13244, USA