Epistemologies in Mathematics Education and Their Influences on the Conceptions of Teaching and Learning and Research

Abstract

This study tries to clarify what the epistemologies in mathematics education may influence on the conceptions of teaching and learning and research through examining the historical development of researches of epistemology and drawing the further research tasks. In this paper, we discussed and clarified the followings. First, on the relations between the epistemologies and the teaching practices in the classroom, we showed various paradoxical situations caused by the epistemologies of objectivism, Cartesian dualism, and representational views of mind. Second, on the relations between the epistemologies and the conceptions of the teaching and learning of mathematics, we examined the debates between radical constructivist and socio-cultural researchers. Based on them we clarified that the radical constructivism and the socio-cultural views were approaching with each other, in particular in their conception of "social" and "intersubjectivity", with drawing the view of interactionism with each perspective, and that there was an insurmountable barrier between the mechanism of reflective abstarction and that of internalization in which the social practice in the sense of "thick" may influence on the recognition of the individual. Third, on the relations between the epistemologies and the research methodologies, since they are directly related with each other, it may be necessary to specify the relations. Moreover, we as researchers are requested to cope with the different worlds of reality in the sense of small letter, which is suggested by the metaphor of Bricolage. Lastly, as the future tasks of the epistemology studies, we indicated the problem of coordination or integration between constructivism and socio-cultural views, the problem of characterizing social interactions and cultures in the mathematics classrooms based on the epistemologies, the problem of situating the view of mathematics in each epistemology, the problem of adopting and organizing various perspectives, and clarifying the epistemological bases of Japanese mathematics education. We consider these tasks essential to an establishment of the identity of mathematics education.