Substantive Knowledge and Mindful Use of Logarithms: A Conceptual Analysis for Mathematics Educators

Vagliardo, James J. (2004) Substantive Knowledge and Mindful Use of Logarithms: A Conceptual Analysis for Mathematics Educators. In: Concept Maps: Theory, Methodology, Technology. Proc. of the First Int. Conference on Concept Mapping. Universidad Pública de Navarra, Pamplona, Spain, pp. 611-618. ISBN 84-9769-064-8

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This study uses concept mapping to investigate the logarithm. Empirical evidence documents the extent to which selected instructors and students command substantive knowledge about logarithms and analyzes their ability to make mindful use of their current understanding. Initial mapping reflects inadequacy and provides the basis for an in-depth search of the cultural and historical context that gave rise to the logarithm concept. The author presents a map that incorporates the essence of the concept from a cultural historical perspective as its central structure. This key ideational relationship, the conceptual cross link between arithmetic and geometric sequences discovered by John Napier, precisely identifies the source of weakness in conceptualization empirically evidenced among faculty and students. The improved map visually provides the understanding necessary for corrective intervention and is the prime reference in the development of a pedagogical approach toward more substantive knowledge and mindful use of the logarithm concept. Study results indicate that concept mapping can provide an epistemological tool for sound curricular and instructional development in mathematics education; one that seeks to locate and build on the essence of conceptual foundations. In a scientific discipline, graphically rendering such substantive cognitive structures maximizes the probability of their mindful use in related mathematical reasoning.

Item Type: Book Section
Uncontrolled Keywords: Paper, CMC2004
Subjects: L Education > L Education (General)
Q Science > QA Mathematics
Depositing User: Mr. Ernest Prats
Date Deposited: 17 Aug 2012 20:39
Last Modified: 13 Oct 2012 06:53

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