Visualization techniques for proofs : implications for enhancing conceptualization and understanding in mathematical analysis

Loading...
Thumbnail Image

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

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.