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Vol. 11 No. 3 (2008): Noviembre

STUDY OF THE EPISTEMOLOGICAL CONCEPT SCHEMAS ASSOCIATED WITH THE HISTORICAL EVOLUTION OF THE INFINITESIMAL NOTION

Published
April 21, 2008

Abstract

This study is part of a research project that analyzes the conceptualization processes of the infinitesimal notion in college students majoring in Mathematics. The research project originates with the interest of understanding the processes of teaching and learning key concepts of Mathematical Analysis such as limit, real numbers and continuity among others. From the mathematical and cognition point of view, these notions are recognized as complex. In order to conceptualize them, student' s intuition of infinitesimal is needed. In this paper we describe, analyze, and characterize the epistemological concept schemas associated with the historical evolution of the infinitesimal notion. We identify seven epistemological concept schemas: the infinitesimal as a ratio, as an indeterminate, as a difference, as an increment, as an arithmetic ratio, as a symbol, and as a function. Furthermore, ideas, methods, representations, and problems that mathematicians use in specific contexts are presented.

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