The University of Montana
Department of Mathematical Sciences

Technical report #1/2008

Mathematical paradoxes as pathways into beliefs and polymathy

Bharath Sriraman
Dept. of Mathematical Sciences
The University of Montana

Abstract

This paper addresses the role of mathematical paradoxes in fostering polymathy among pre-service elementary teachers. The results of a 3-year study with 120 students are reported with implications for mathematics pre-service education as well as interdisciplinary education. A hermeneutic-phenomenological approach is used to recreate the emotions, voices and struggles of students as they tried to unravel Russellís paradox presented in its linguistic form. Based on the gathered evidence some arguments are made for the benefits and dangers in the use of paradoxes in mathematics pre-service education to foster polymathy, change beliefs, discover structures and open new avenues for interdisciplinary pedagogy.

Keywords: beliefs; interdisciplinarity; paradoxes; pre-service teacher education; polymathy; Russellís paradox

AMS Subject Classification: 97

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Pre-print of paper accepted in ZDM- The International Journal on Mathematics Education, vol.41, no.1, xx-xx