2021 Volume 26 Issue 2 Pages 45-57
The purpose of this research is to clarify the actual conditions of learning by conducting a case study dealing with the condition for the formation of triangles in the introduction of the unit “triangle” in the third grade of elementary school. This case study focuses on one extracted child and qualitatively analyzes the learning aspects. The qualitative analysis uses the theory of geometric discourse development (Wang, 2016). The basis of this theory is van Hiele’s theory of learning levels of geometry (van Hiele, 1986) and the theory of commognition (Sfard, 2008). The development of geometric discourse is divided into four levels. The emphasis is placed on geometric objects and its routines that support the transformation of discourse.
In lesson study, there were three group interactions and three whole-class interactions. Then from the utterance record and video record of the extracted child in lesson study, the mathematical use of the extracted child and its routine were interpreted. As a result, the following three points were clarified, and it was demonstrated that it is possible to learn the condition for forming triangles in the third grade of elementary school.
1: The geometric discourse of the extracted child changed from level 1 to level 2.
2: The possibility of realizing discourse using deductive reasoning was suggested.
3: The level 3 discourse was partially realized by using a slightly abstract object as the object of inference and a common narrative.
