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All Journal Journal of Honai Math Studies in Learning and Teaching
Ogbonnaya, Ugorji
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Education Mathematics Social Sciences Other

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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.
Algebraic Question Types in Grade 10 Mathematics Textbook: A Cognitive Perspective Sibiya, Mandlenkosi Richard; Sekao, David; Ogbonnaya, Ugorji
Studies in Learning and Teaching Vol. 6 No. 1 (2025): April
Publisher : CV Sinergi Ilmu dan Publikasi

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46627/silet.v6i1.531

Abstract

Mathematics education depends on textbooks as the primary source of information for both teachers and learners while providing essential tasks that develop cognitive skills. The types of tasks used in these resources directly affect learners’ cognitive growth and show why textbooks must contain various question types. Current research lacks examination of mathematics textbooks in South African schools, even though learners consistently perform poorly in mathematics. This study investigated whether a widely used Grade 10 Mathematics textbook challenged learners to various question types that help build problem-solving skills and high-level thinking. A deductive content analysis approach evaluated 1 360 questions from the textbook’s algebra content, including algebraic expressions, exponents, equations and inequalities, number patterns, and functions. The research results indicated that most questions (62%) required routine calculations while the content lacked questions that required higher-order cognitive skills such as problem-solving, argumentation and interpretation. The assessed textbook appears to fail learners by not adequately developing critical thinking skills that learners need for both future advanced math classes and practical applications. The study recommends more diverse question types in mathematics textbooks to develop learners’ cognitive skills and problem-solving abilities.
Co-Authors Muzangwa, Jonatan Sekao, David Sibiya, Mandlenkosi Richard