Date of Award

12-2007

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Dr. Theresa J. Grant

Second Advisor

Dr. Kate Kline

Third Advisor

Dr. Laura Van Zoest

Fourth Advisor

Dr. Ok -Kyeon Kim

Abstract

Research indicates that extending students' mathematical thinking during whole-group discussions is challenging, even for the most experienced teachers. That is, it is challenging for teachers to help students move beyond their initial mathematical observations and solutions during whole-group discussions. To better understand this phenomena, the teaching of six experienced elementary school teachers, who had been teaching aStandards-based curriculum for several years and had participated in a multi-year professional development project focused on that curriculum, is explored in this study. In particular, two issues are addressed: what it looks like to extend student thinking during whole-group discussions and how teachers' beliefs and knowledge support them in their efforts to extend student thinking.

Classrooms were observed as teachers taught an investigation (several connected lessons) on number and operations. Segments of whole-group discussions that had the potential to extend student thinking were analyzed to gain insight into the focus issues. Semi-structured interviews—before, during, and after teaching the investigation—were conducted to gain insight into the teachers' thinking processes relevant to their actions and to understand the relationship between teachers' knowledge/beliefs and their instructional actions.

All six teachers participating in this study created opportunities to extend student thinking during whole-group discussions by engaging students in problematizing mathematics, mathematical reflection, and mathematical reasoning. In creating these discussions, teachers utilized various instructional actions. Some of the least frequently occurring instructional actions, providing counterspeculation and making connections among representations and contexts, may be among the most effective instructional actions as they were found in the most powerful episodes.

The evidence from this study also suggests that the teachers' beliefs about the instructional actions they valued were closely related to the prevalent instructional actions that took place during the extending episodes. However, the presence of tension concerning their role during whole-group discussions seemed to weaken some teachers' ability to extend student thinking. This suggests it may be necessary to have a reasonably harmonious vision to enact these instructional actions in the classroom. Finally, the extent to which the teachers' knowledge was developed had a clear impact on the powerfulness of the extending episodes.

Comments

5th Advisor: Dr. Carol Crumbaugh

Access Setting

Dissertation-Open Access

Download

Share

COinS