Visualization techniques for proofs : implications for enhancing conceptualization and understanding in mathematical analysis
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Date
Authors
Muzangwa, Jonatan
Ogbonnaya, Ugorji Iheanachor
Journal Title
Journal ISSN
Volume Title
Publisher
Universitas Papua
Abstract
Visual images are frequently utilized to elucidate concepts in general mathematics and
geometry; however, their application in mathematical analysis remains uncommon. This paper
demonstrates how visual imagery can enhance the proof of certain theorems in mathematical
analysis. It emphasizes the importance of visualization in the learning and understanding of
mathematical concepts, particularly within mathematical analysis, where diagrams are seldom
employed. The paper focuses on the reasoning processes used by mathematicians in proving
selected fundamental theorems of mathematical analysis. It provides illustrative examples
where visual images are instrumental in performing specific subtasks within proof development
and in completing the proofs. The proofs discussed include the sum of the first n natural
numbers, the sum rule of integration, the mean value theorem for derivatives, the mean value
theorem for integrals, and Young’s Inequality. This paper underscores that visual images serve
not only as persuasive tools but also as bridges between symbolic representations and realworld understanding.
Description
Keywords
Definite integrals, Imagery, Mathematical analysis, Mean value theorem, Visualisation, SDG-04: Quality education, SDG-09: Industry, innovation and infrastructure
Sustainable Development Goals
SDG-04:Quality Education
SDG-09: Industry, innovation and infrastructure
SDG-09: Industry, innovation and infrastructure
Citation
Muzangwa, J., & Ogbonnaya, U. (2024). Visualization techniques for proofs: Implications for enhancing conceptualization and understanding in mathematical analysis. Journal of Honai Math, 7(2), 347–362. https://doi.org/10.30862/jhm.v7i2.603.