International Portal of Teacher Education

Source: Journal of Mathematics Teacher Education, 14(1), p. 5–23. (February, 2011) .
(Reviewed by the Portal Team)

In this article, the authors were interested to explore how teachers can effectively facilitate classroom discussions in the ways that elicit negotiation of meaning and maximize the potential of mathematical inquiry activities.

In the neriage stage, Japanese teachers encourage students to listen to other students’ ideas carefully and consider the strengths and weaknesses of different problem-solving strategies. Then the teachers facilitate discussions to co-determine which strategy is the most reasonable and efficient one.
This article introduces a video-based lesson study that explored how a group of U.S. teachers could successfully implement consensus building discussions (or neriage) in their mathematics classrooms.
Video-based lesson study
For this project, six 4th and 5th grade teachers were recruited from the San Diego.
To ground the lesson study in the Japanese inquiry approach, three experienced Japanese teachers at a local Japanese school agreed to participate in the lesson study as advisors. The Japanese teachers were trained in Japan and had gone through a number of lesson studies that focused on the neriage stage of inquiry lessons.

The Japanese teachers were asked to play the role of advice-givers to the US teachers in the meetings in case they had questions or seemed to struggle with implementing neriage in their lessons.

This lesson study project particularly focused on how to elicit negotiation and social construction of meaning through consensus building discussions in inquiry-based problem-solving activities.

The study identified different sets of ‘‘tacit knowledge’’ that the participating teachers need to know at various points in planning and delivering mathematical inquiry lessons.
1. Know what you are asking:
Teachers need to be clear about specific points that they want their students to notice, discover, or realize in the lesson (kizuki) in relation to the lesson goal and the curriculum map, before initiating the consensus building discussions.

2. Anticipate students’ responses during lesson planning:
In the videotaped discussions, there were many instances where students presented diverse strategies and the teacher did not know how to respond.

3. Releasing control to students:
The group agreed on the importance of releasing control to their students so that the students could freely compare and contrast different problem-solving strategies from multiple angles.

4. Don’t hesitate to provide traffic control:
Sometimes students’ explanations of their mathematical reasoning are too quick or inaudible to the whole class. In such cases, repeat or rephrase the students’ answers slowly and in a concise, step-by-step manner.

5. Always follow-up:
Generalize the mathematical principles agreed in the consensus building discussions to different cases of problem solving at the end of the lesson and possibly incorporate exercises of similar problems so that children can see the value of their discussions as leading to accurate, efficient problem solving.

This study reveals that acquiring the aforementioned set of tacit knowledge changed the six US teachers’ view of mathematical inquiry lessons.

All of the US teachers initially viewed teaching inquiry activities as risky and time-consuming. However, at the end of the lesson study, they indicated that if they considered the aforementioned points when planning and delivering inquiry activities, it can be a ‘‘easier and faster’’ way to teach mathematical algorithms and techniques, building on students’ deep understanding of the mathematical concepts and the rationale behind the algorithm established in the consensus building.

To conclude, this lesson study project highlights the potential for improving the quality of mathematical inquiry lessons using video-based, cross-cultural lesson study in non-Japanese contexts.