SUBJECT CONCEPTIONS AND INSTRUCTIONAL PRACTICES
R. Geoffrey Roulet
Ontario Institute for Studies in Education of the
University of Toronto
Theoretical links between conceptions of mathematics and teaching practice have been postulated and research exploring these conjectures has been conducted at the elementary school level and to a limited extent with selected secondary school mathematics topics. Studies have shown that instrumentalist images of mathematics are carried into transmissive modes of instruction, but the few teachers with social constructivist views have troubles bringing their visions to practice. This study involving two exemplary secondary school mathematics teachers, that is teachers who are working to implement mathematics education reform, extends this line of research, exploring: their conceptions of mathematics, teaching practices, and the struggles they experience in bringing subject images to the classroom.
Qualitative methods were used to explore conceptions of mathematics and teaching practice. The teachers' subject images were examined through personal writing on the nature of mathematics, repertory grid technique, and the construction of concept maps, and interviews analysing these products. Participant observation was employed to gather data on mathematics teaching and lessons were analysed from a sociological and epistemological perspective. In two case studies, using alternating sections presenting subject image themes and narratives of related teaching, links are built between practice and epistemology.
In this study, one teacher with a well developed social constructivist image of mathematics managed to struggle against pupil and administrative opposition and put his personal subject philosophy into practice. The second teacher, with a more mixed subject conception, one that was undergoing transition and reconstruction, had difficulties translating his epistemology into practice and when confronted with opposition turned to traditional transmissive modes of instruction. His emerging constructivist views showed through in activities provided beyond the core of his lessons.
Obstacles that the two teachers faced in attempting to implement their personal philosophies are examined and sources of support are identified. For both teachers, links to university faculty that provided opportunities for mathematical explorations beyond the school curriculum were valuable. The development of the stronger teacher's more complete and consistent image was helped by a professional network that provided opportunities for discussion of philosophical matters.
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