Characterizing Experienced Teachers’ Questioning in Mathematics Classrooms: Questioning as a Window for Examining Quality Teaching

• In Event: Culturally Specific Perspectives on Quality Mathematics Teaching

Abstract

This research analyzed two mathematics lessons collected in the Learner’s Perspective Study (Clarke, Keitel & Shimizu, 2006), taught by experienced “competent” teachers in Germany and Japan. One class was on simultaneous equations in a public junior high school in Tokyo (J3), and the other was on complex mathematical expressions in gymnasium in West Berlin (G2). These lessons were selected to minimize the differences in teaching method due to differences in content, involved introducing mathematical concepts and were located at a critical point in the lesson sequence.

The focus of our analysis was the teacher’s questioning recorded in the classroom video material (Clarke, 2006). Episodes were identified in G2 and J3 that started with posing a task related to learning new things for the student and ended with tasks for practice. Teacher questioning was compared in those episodes. The tasks treated in both J3 and G2 involved transforming algebraic expressions to a previously-learned form.

Our analysis revealed similarities in the teachers’ questioning between the Japanese and the German classrooms, while the student outcomes afforded by the teachers’ questions were different. In both the German and Japanese lessons, the teacher asked the students for suggestions and then developed the solution based on the students’ responses. However, the German teacher developed the procedure in an “elicitation-response” sequence, while the Japanese teacher used an extended time period between posing a task and sharing and discussing the students’ solutions.

As reported in the TIMSS-1995 videotape study, both the German and the Japanese teachers developed the lesson by incorporating students’ responses into the classroom process during the phase of learning new things. Similar conversations occurred in both classrooms, in which the teachers asked students about strategies and calculating processes. However, the G2 teacher constituted the learning process through the teacher-student conversation after the teacher had presented the tasks, while the J3 teacher set individual activity after presenting the task and then conducted a discussion based on the concepts and procedures generated in the students’ individual activity.

For that reason, the things that the teacher’s questions required of the student were superficially similar, but the function for the German students was to guide and cue students to think about the current task in the G2 lesson, while the teacher’s questions functioned for Japanese students as reminders of the things that they had generated in individual activity in the J3 lesson. The G2 teacher broke the task into small parts, focused on each step and developed a more general procedure by aggregation, while the J3 teacher expected the students to find a strategy and solution through individual activity and questioning regarding the processes they generated.

Comparative analyses, such as the one reported here, illustrate what is valued as quality mathematics teaching in each education system. The teachers’ questions were seemingly similar, but, in fact, the consequence of the questions for the students were different. The result of the analysis reveals that the quality teaching for the same purpose can take different forms in each educational setting.

Authors

• Yoshinori Shimizu, University of Tsukuba

• Yuka Koizumi, University of Tsukuba