Children Engaging with the Nature of Mathematics: The Case of Zeno’s Paradox

By Paul Betts.

Published by The Social Sciences Collection

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Article: Print $US10.00
Article: Electronic $US5.00

Mathematics education is undergoing an era of reform, shifting from behaviourist to constructivist approaches to teaching and learning. Debates within the philosophy of mathematics consider the absolutist versus humanist status of mathematical claims. Given that school math is almost uniformly experienced by teachers and learners as absolute, the content of debates within the philosophy of mathematics could contribute to the reform of mathematics education. This paper considers whether stories from the history of mathematics with philosophical import can generate learning contexts that occasion a greater appreciation of mathematics by school aged children. Zeno’s paradox is one such mathematical/philosophical context, which is used, with some data from children, to explore the above question. By starting with the premise that all school aged children can engage with and generate philosophical ideas, I conclude that the success of this agenda depends on at least two pedagogical considerations: (1) teachers noticing the philosophical thinking of children, which depends on a teachers knowledge of philosophy; and (2) occasioning opportunities for children to engage with philosophy, which is a rejection of the idea that teachers should structure when philosophical thinking will occur.

Keywords: Philosophy of Mathematics, Mathematics Education, Mathematics Appreciation by Children

International Journal of Interdisciplinary Social Sciences, Volume 5, Issue 8, pp.465-476. Article: Print (Spiral Bound). Article: Electronic (PDF File; 655.997KB).

Dr. Paul Betts

Associate Professor, Faculty of Education, University of Winnipeg, Winnipeg, Manitoba, Canada

I taught mathematics in the public school system for seven years before moving into a lecturer position at Brandon University in 1999. While at Brandon, I completed most of my PhD at the University of Regina in mathematics curriculum. I began a position at the University of Winnipeg in 2003 as an Assistant Professor specializing in mathematics education. In 2005, I successfully completed my PhD dissertation, which considered pre-service teachers experiences with the nature of mathematics. I recently earned tenure and promotion at the University of Winnipeg. My current research focuses on (novice) mathematics teacher professional learning and the potential of philosophies of mathematics for the reform of mathematics education.


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