On the interplay of cognitive, tactile, and computational approaches to number theory in teacher education

Sergei Abramovich

doi:10.59400/fes.v1i1.201

On the interplay of cognitive, tactile, and computational approaches to number theory in teacher education

Sergei Abramovich State University of New York at Potsdam, Potsdam, NY 13676, United States

Ariticle ID: 201

1219 Views, 81 PDF Downloads

DOI: https://doi.org/10.59400/fes.v1i1.201

Keywords: number theory; visualization; polygonal numbers; trapezoidal numbers; Maple; Wolfram Alpha; teacher education

Abstract

This paper focuses on topics from elementary number theory used by the author in the mathematical preparation of K-12 teacher candidates by juxtaposing concrete materials, digital technology, and formal reasoning. The topics include triangular numbers, their connection to trapezoidal numbers, and their extension to other figurate numbers. The paper shows how problem solving may be based on the integration of modern-day approaches to mathematics supported by the creation of images, their numeric interpretation, followed by algebraic generalization, and computational verification of general statements in symbolic form. Digital tools used in the paper include spreadsheets, Wolfram Alpha, and Maple. Solicited comments by teacher candidates about their use of digital tools are shared.

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Published

2023-12-26

How to Cite

Abramovich, S. (2023). On the interplay of cognitive, tactile, and computational approaches to number theory in teacher education. Forum for Education Studies, 1(1), 201. https://doi.org/10.59400/fes.v1i1.201

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