Examining the Tasks of Teaching When Using Students' Mathematical Thinking

• Published in: Educational studies in mathematics Vol. 62; no. 1; pp. 3 - 24
• Main Author: Doerr, Helen M.
• Format: Journal Article
• Language: English
• Published: Springer 01.05.2006
• Subjects: Analysis; Cognitive Processes; Education; Educational research; Learning; Mathematical ability; Mathematical constructivism; Mathematical functions; Mathematical knowledge; Mathematical problems; Mathematics; Mathematics education; Mathematics teachers; Methods; Secondary Education; Student Role; Students; Study and teaching; Teacher Attitudes; Teacher Role; Teachers; Teaching Methods; Trajectories; United States
• ISSN: 0013-1954; 1573-0816
• DOI: 10.1007/s10649-006-4437-9

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 self-evaluators of their emerging ideas.