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All Journal JRAMathEdu (Journal of Research and Advances in Mathematics Education) International Journal of Review in Mathematics Education
Mangwende, Edmore
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Mathematics

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An APOS analysis of preservice mathematics teachers’ understanding of limits of trigonometric functions Mangwende, Edmore; Chirume, Silvanos
JRAMathEdu (Journal of Research and Advances in Mathematics Education) Volume 10, Issue 4, October 2025
Publisher : Lembaga Pengembangan Publikasi Ilmiah dan Buku Ajar, Universitas Muhammadiyah Surakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.23917/jramathedu.v10i4.10440

Abstract

This paper reports on an APOS analysis of first year undergraduate pre-service mathematics student teachers’ understanding of the Sine Limit Identity(SLI), , and its application in computing limits of trigonometric functions. It was a case study of sixty-eight pre-service mathematics teachers. The student teachers explored various ways of computing . They also learnt how to apply the SLI in evaluating limits of other trigonometric functions. In order to determine the participants’ level of understanding, the researchers analysed the participants’ responses to given test items, against a constructed genetic decomposition. The results of the study revealed that although more than half of the students could evaluate the sine limit, three quarters of them made some procedural, conceptual and extrapolation errors when applying the SLI in computing limits of related trigonometric functions. Based on the findings, the researchers recommended inclusion of visual computer applications like Geogebra as teaching tools for teaching limits of trigonometric functions. Such applications allow students to visualise relationships among variables. The researchers also recommended further research on teaching strategies that aim at improving the teaching of limits of trigonometric functions.
Social Constructivism: Principles and Implications to Mathematics Learning Mangwende, Edmore
International Journal of Review in Mathematics Education Volume 1 No. 1: March 2026
Publisher : Universitas Muhammadiyah Surakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.23917/ijrime.15221

Abstract

This paper examines social constructivism as a learning theory and its implications in mathematics learning. The study followed a conceptual qualitative paradigm. The researcher used secondary data obtained from journal articles, e-books, periodicals and websites. Social constructivism emphasizes active construction of knowledge by learners through interaction with others and the environment. According to the theory, the learner understands the world through experiencing it. Reality is socially constructed and it depends on individual interpretation. In mathematics learning, the theory implies that mathematics tasks make sense to the learners if they solve real life problems. Mathematics learners should not simply memorise concepts, but should critically analyse their own and other people’s mathematical perspectives. More marks should be awarded for the thought process than for the final solution to a mathematical task.   Mathematics learning should be taken beyond the classroom. Formal mathematics learning can be built atop the knowledge gained by the learners through culturally performed tasks. The mathematics learners should view their teacher as a facilitator, co-learner, co-explorer and co-constructor of knowledge. Teaching strategies that promote collaboration and active participation of learners are desirable. Peer and self assessment help to foster active and interactive mathematics learning.
Co-Authors Chirume, Silvanos