小集団で数学を考える際に人間関係が与える影響について

抄録

　　The paper focuses on the impact of human relationships in small-group mathematical activities for more effective mathematics learning. The author believes that learning mathematics in small-groups and improving caring competencies, which involves building relationships to care for others and to be cared for by others, are mutual in terms of beneficence. Therefore, the purpose of this paper is to make clear how the improvement of caring competencies contributes to the development of knowledge in small-group mathematics learning in order to comprehend the relationship between mathematics learning and caring competencies.

　　First, the author defined the caring competencies emerged in the mathematics context by reviewing previous studies. Then, by focusing on the small-group activities in which the emergence of 8 graders’ ideas was identified to analyze the situations in which the caring competencies were demonstrated, the author examined how the caring competencies contributed to the development of mathematics knowledge. The results implied that it was difficult for the students to put their own mathematical ideas aside and stand on different viewpoints of other in group members. On the other hand, the interaction with others’ideas while using the caring competencies provided an opportunity for the emergence of mathematical ideas, which updated students’mathematical knowledge.

　　In addition, the author applied the framework developed by Krummheuer (2011) and categorized the students’ statements in small group activities in order to analyze their roles in the group. The results show that it is difficult for the students to state their new ideas in small groups. In order to solve this problem, the research findings suggested that the students in small groups need to switch their roles spontaneously and rebuild new human relationships that enable themselves to care for each other’s statement.

　　The conclusions of this research proved that developing caring competencies can contribute to the following aspects:

● Solving the difficulties to commit others’ideas, which contributes to emerging new ideas.

● Realizing ideal small-group activities where roles are not fixed and students switch roles voluntarily to state.