Math Can Be Visual—Teaching and Understanding Arithmetical Functions through Visualization

Szilárd Svitek, Norbert Annuš and Ferdinánd Filip
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Szilárd Svitek: Department of Mathematics, J. Selye University, 945 01 Komárno, Slovakia
Norbert Annuš: Department of Informatics, J. Selye University, 945 01 Komárno, Slovakia
Ferdinánd Filip: Department of Mathematics, J. Selye University, 945 01 Komárno, Slovakia

Mathematics, 2022, vol. 10, issue 15, 1-14

Abstract: Number theory is an area of mathematics not unknown to students majoring in mathematics teaching. As early as in junior high, they may encounter basic number theory concepts such as prime numbers, multiples, divisors, or even the fundamental theorem of arithmetic—the proof of which, however, will only be included in the university curriculum of mathematics teacher students. When teaching number theory, in addition to inspiring and motivating students, it is important to have them ask the right questions. Proofs are important, but so is the proper formulation of mathematical conjectures, not to mention intuitions regarding mathematical properties and relationships. These processes are facilitated by the software used, developed to visualize functions related to number theory. Our study aims to assess the relevance of visualization in the teaching and understanding of certain arithmetic functions among mathematics teacher students. Furthermore, we aim to investigate the practical usability of our visualization software, relying on student feedback. According to our results, students found the software useful, as it helped them to discover previously unknown relationships in the examined arithmetic functions. We may conclude our software fills a niche, with student feedback indicating its usefulness.

Keywords: visualization; number theory; teacher training; formulation of conjecture; arithmetic function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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