Teachers who participate in their “Kounai-kenshu” are necessary to understand the qualitative changes of children’s thinking in the teaching and learning process. So, they need their viewpoints to grasp the process objectively.
We have two purposes of this paper: one is to develop the viewpoints to grasp the qualitative changes in the children’s thinking by focusing on inductive activities in mathematics classes by an elementary school teacher in her 2nd graders’ class, which was conducted in the “School Support Project” improving the “Didactical Situation Model;” the other is to answer the following research questions: How can we grasp the development of children’s thinking in the teaching and learning process?; How do the teacher and the children make their qualitative development of the inductive activities?; What makes the qualitative changes in the interaction process?
To achieve the two purposes, we constructed the “Variable-detailed Version of Didactical Situation Model” based on the “Didactical Situation Model” and the “Type of MATOME” to grasp the qualitative changes of the children’s thinking more precisely. We have made protocol analyses of 20 class-hours conducted by the teacher from the viewpoints of the new model and the “Mathematics as the Science of Patterns.”
As the results of these analyses, it was revealed what the qualitative changes of the children’s thinking is and what makes these changes. It was also suggested that the viewpoints of the suggestive and supporting contacts and the quality of what they are looking for in their inductive activities could be the practical viewpoints in which to grasp the qualitative development of children’s thinking in the inductive activities.
