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All Journal Journal of Honai Math Edumatica: Jurnal Pendidikan Matematika
Muzangwa, Jonatan
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Education Mathematics Social Sciences

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Visualization techniques for proofs: Implications for enhancing conceptualization and understanding in mathematical analysis Muzangwa, Jonatan; Ogbonnaya, Ugorji
Journal of Honai Math Vol. 7 No. 2 (2024): Journal of Honai Math
Publisher : Universitas Papua

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30862/jhm.v7i2.603

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 real-world understanding.
Representasi Visual Mahasiswa S1 Pendidikan Matematika tentang Fungsi Multivariabel Muzangwa, Jonatan; Ogbonnaya, Ugorji I.
Edumatica : Jurnal Pendidikan Matematika Vol 12 No 3 (2022): Edumatica: Jurnal Pendidikan matematika (Desember 2022)
Publisher : Department of Mathematics Education, Faculty of Teacher Training and Education, Universitas Jambi

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22437/edumatica.v12i03.15712

Abstract

Representations of mathematical concepts are very important in the teaching and learning of mathematics. Visual representations are used to present mathematical concepts to solve, explore or explain the concepts. The purpose of this study was to examine undergraduate mathematics education students' visual representations of multivariable functions using matching items tasks. The study was qualitative research conducted with 10 second-year undergraduate mathematics education students at a University in Zimbabwe. The students matched the functions of several variables which are represented in symbolic and graphic forms. The result showed that most of the students were able to match the functions with their graphical representations. However, most of the students had difficulties in communicating mathematical information and these difficulties emanate from language problems and conceptual understanding.
Co-Authors Ogbonnaya, Ugorji Ogbonnaya, Ugorji I.