2020 Volume 44 Issue 4 Pages 271-288
The objective of this paper is to identify, using case examples, how the composition process of revision and refinement of mathematical knowledge relates to changes in the intention behind statements present in mathematical negotiations. To this end, analysis and consideration were conducted to clarify the methodology for the analysis of mathematical negotiations against the theoretical background of agreement constructivism, as well as to plan and conduct experimental lessons on the “division of fraction” unit in the 6th grade of elementary school. In this paper the children’s opinions in that experimental lesson are analyzed and considered by using the analysis frame created by T. Shimomura (in press). The results of the analysis and consideration revealed the following two points. First, differences in the intention behind statements were observed in conjunction with changes in the direction of the process of adapting to the “world” and “oneself” in the composition stage of mathematical knowledge. Second, the intention behind statements used to reach a consensus in the form of mathematical knowledge differed depending on the implications of the existence of others.
