Number Theory for Mathematics Instruction of Teacher Candidates in the Digital Era
Abstract
The paper presents technology-enhanced activities with triangular, square, and other polygonal numbers arranged in basic geometric shapes — equilateral and isosceles triangles and squares. Computational algorithms for the summation of such numbers within each geometric structure have been developed and discussed. In some cases, algebraic identities between certain numeric entries of the shapes have been formulated and proved computationally. The activities, supported by WolframAlpha, and Maple, are recommended for the use by instructors of technology-motivated mathematics teacher education courses. The paper emphasizes the value of technology-immune/technology-enabled mathematical problem solving in the modern-day teaching topics of elementary number theory across multiple grade levels and educational programs. The paper argues that the power of digital tools allows future teachers of mathematics, in the context of elementary number theory, to appreciate the use of simple algorithms in achieving sophisticated computational outcomes.
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