| Students who are best able to understand, communicate, reason, and problem-solve are those who learn through the process of problem solving. However, while American mathematics teachers at times promote student problem solving, they commonly minimize or eliminate the need for students to use their own ideas and judgments in the course of the problem discussion, particularly when the students experience difficulties. We need to understand why teachers respond as they do, to determine both the appropriateness and the means for encouraging changes in their practices.; This study contributes to formation of such understanding by examining practices of three middle-school mathematics teachers. Teachers' responses to student difficulties during problem solving were recorded and coded as either Eliciting Responses or Non-Eliciting Responses, depending on whether or not they elicited students' ideas and judgments. The teachers were then asked during interviews why they responded as they did, and their reasons were unified into categories containing similar objectives.; The findings of the study revealed that (1) whether or not teachers maintained a shift of cognitive responsibilities toward students depended upon the teachers' objectives, and (2) the teachers' objectives were shaped by the teachers' assessments of their students' ability to effectively take on the cognitive responsibilities of problem solving. To the extent that these conditions hold for other teachers, instructional reform efforts must be prepared to help teachers address perceived weaknesses in their students, and to align teachers' objectives with the reform objectives, in order to effect changes in practice. |
