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Mathematics Teachers as Applied Mathematicians: Advancing Teacher Education in the Age of Technology

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two-variable polynomials disintegrate
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Submitted   Sep 1, 2025
Published   Dec 10, 2025
Issue    Vol 6 No 1 (2025)
DOI   10.25082/AERE.2025.01.004

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Sergei Abramovich corresponding author
School of Education and Professional Studies, State University of New York, Potsdam, NY 13676, USA

Abstract

Applied mathematics represents a blend of methods of pure mathematics and knowledge of problems from a field to which those methods can be applied toward the advancement of the field. Notably, the fields of engineering and life sciences have been significantly advanced by formulating their problems in the language of mathematics and using rigorous mathematical methods to enable intuitive thinking to be replaced by exact models to which formally proved mathematical propositions can be applied. This paper suggests that among the fields to which knowledge and methods of mathematics can be applied, especially in the age of technology which supports experimental problem solving, is mathematics teacher education. The paper builds on the ideas about mathematics as an experimental science that span from ancient to modern times. It provides three major illustrations of different levels of contextual and conceptual intricacy reflecting on the author’s work as a mathematician-teacher educator. This conceptual reflection alludes to a case in point that seeing mathematics pedagogy through technology-enhanced lens can sometimes give way for the emergence of new mathematical knowledge through learners’ unwitting entry into the substance of the discipline. Examples of such unexpected entries provided in the paper include the discovery of generalized Golden Ratios as strings of numbers of different lengths, Fibonacci-like polynomials stemming from a rearranged Pascal’s triangle, and symmetrical vs. asymmetrical location of the roots of the polynomials depending on the sums of their coefficients.

Keywords
applied mathematics, teacher education, computational experiment, trial and error, early algebra

Article Details

How to Cite
Abramovich, S. (2025). Mathematics Teachers as Applied Mathematicians: Advancing Teacher Education in the Age of Technology. Advances in Educational Research and Evaluation, 6(1), 345-361. https://doi.org/10.25082/AERE.2025.01.004
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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

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