'Value Creation' Through Mathematical Modeling: Students' Mathematics Dispositions and Identities Developed in a Learning Community

摘要

This study examines how mathematical modeling activities within a collaborative group impact students' `value creation' through mathematics. Creating `value' in this study means to apply one's knowledge in a way that benefits the individual and society, and the notion of `value' was adopted from Makiguchi's theory of `value creation' (1930/1989). With a unified framework of Makiguchi's theory of `value', mathematical disposition, and identity, the study identified three aspects of value-beauty, gains, and social good-using observable evidence of mathematical disposition, identity, and sense of community. Sixty students who enrolled in a college algebra course participated in the study. The results showed significant changes in students' mathematics dispositions after engaging in the modeling activities. Analyses of students' written responses and interview data demonstrated that the modeling tasks associated with students' personal data and social interactions within a group contributed to students' developing their identity as doers of mathematics and creating social value. The instructional model aimed to balance the cognitive aspect and the affective skills of learning mathematics in a way that would allow students to connect mathematical concepts to their personal lives and social lives. As a result of the analysis of this study, there emerged a holistic view of the classroom as it reflects the Makiguchi's educational philosophy. Lastly, implications of this study for research and teaching are discussed.