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All Journal Indonesian Journal of Science and Mathematics Education MEJ (Mathematics Education Journal) International Journal of Trends in Mathematics Education Research (IJTMER)
Makamure, Chipo
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Education Mathematics Other

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An exploration of grade 2 learners’ experiences in solving addition and subtraction word problems Cheva, G; Makamure, Chipo; Jojo, ZMM
International Journal of Trends in Mathematics Education Research Vol 6, No 3 (2023)
Publisher : SAINTIS Publishing

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.33122/ijtmer.v6i3.214

Abstract

Mathematics has always been a major part of school curricula in most countries. It provides a variety of useful tools that help students to solve problems that they encounter in everyday life. Mathematical tools are considered powerful, as long as one knows how to employ them across a range of suitable situations. However, selecting and using these tools appropriately appear to be challenging for many students. Because of this, word problems have been included in mathematics education to offer practice for students in applying mathematical skills effectively in various problem situations confronted in everyday circumstances. In addition, there is limited research about how learners in the foundation phase (Grades 1-3) solve addition and subtraction word problems. A relatively recent review of South African studies on mathematics education has revealed a paucity of research at the primary school level. This study therefore seeks to explore grade 2 learners’ experiences in solving addition and subtraction word problems. A qualitative research was conducted to describe grade 2 learners experience whilst solving addition and subtraction problems. Only 6 learners in grade 2 were selected to participate in this study. Learners demonstrated a strong preference for paper and pencil methods as well as the standard algorithm, when solving problems in word format. However, little evidence exists within the study that any of the learners conceptually understood the algorithm. The use of base 10 blocks to model the partial sums and partial differences algorithms would help most of the learners to develop a conceptual understanding of addition and subtraction of word problems in mathematics.
Visual-spatial Skills and Mathematics Content Conceptualisation for Pre-service Teachers Makamure, Chipo; Jojo, Zingiswa M
Indonesian Journal of Science and Mathematics Education Vol. 4 No. 3 (2021): Indonesian Journal of Science and Mathematics Education
Publisher : Universitas Islam Negeri Raden Intan Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/ijsme.v4i3.9842

Abstract

Empirical evidence in literature identified significant association between spatial ability and educational performance particularly in science, technology, engineering and mathematics (STEM). The purpose of this study was to explore pre-service teachers’ spatial skills in solving mathematics problems, in the context of coordinate geometry. It is envisaged that spatial skills allow for the perception of visual information and, therefore, spatial cognition has been considered as a key skill in teaching mathematics. However, literature asserts that teachers are ill prepared to teach mathematics, hence there is limited use and misuse of spatial skills in teaching the subject. This study, therefore, examines the spatial orientation of pre-service teachers in teaching coordinate geometry. This is a mixed methods study in which pre-service teachers answered a coordinate geometry test to explore their content knowledge and their ability to interpret, analyse and apply visual spatial models to solve mathematical problems in coordinate geometry. The study established that the spatial orientation skills of pre-service teachers determine their performance in mathematics, especially coordinate geometry.
Students understanding of the basis and dimensions of the solution space using the APOS theory Mutambara, Lillias Hamufari Natsai; Makamure, Chipo
Indonesian Journal of Science and Mathematics Education Vol. 9 No. 1 (2026): Indonesian Journal of Science and Mathematics Education
Publisher : Universitas Islam Negeri Raden Intan Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/ijsme.v9i1.27203

Abstract

The purpose of this study is to explore how in-service mathematics teachers understand the concepts of basis and dimension of the solution space as informed by the APOS theory. The data was obtained from 74 first-year in-service undergraduate mathematics teachers pursuing a Bachelor of Science Education Honours degree through the use of an activity sheet and semi-structured interviews. Employing a qualitative research approach within a case study design, the study was theoretically grounded in the APOS theory, drawing on the constructivist perspective, with the preliminary genetic decomposition serving as the basis for analysis. The study revealed that the lack of prior knowledge and related schema significantly hindered the participants' development of essential mental constructions. Most participants demonstrated a procedural understanding, signifying that a substantial number of in-service mathematics teachers were operating at the action level according to the APOS theory. Analyzing the mental constructions of in-service mathematics teachers can yield essential pedagogical strategies for enhancing understanding of the solution space. This research has implications for understanding that a structured development model based on APOS Theory enables educators to design learning sequences that gradually guide students from physical manipulation to abstract reasoning.
Mathematics Education Undergraduates’ Conceptualisation of Non-Homogeneous Differential Equations Using the Method of Undetermined Coefficients Makamure, Chipo; Jojo, Zingiswa M.; Mkwelie, Nhlanhla
Mathematics Education Journal Vol. 9 No. 1 (2025): MEJ Vol 9 No.1
Publisher : Department of Mathematics Education University of Muhammadiyah Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22219/mej.v9i1.36757

Abstract

The topic of ordinary differential equations (ODEs) is widely covered in higher education institutions, however, understanding non-homogeneous differential equations (NHDEs) poses challenges for students due to its complexity. Limited research in second order NHDEs points to the need for more studies on students’ conceptions and understanding of this topic and its basic concepts. This study delved into the conceptualisation of second order NHDEs and their solutions using the method of undetermined coefficients among Bachelor of Science in Education Mathematics student teachers. Employing the APOS Theory, an in-depth test on NHDE was administered to 60 participants from a university in Zimbabwe to identify their underlying challenges. The study revealed that student teachers encountered difficulties in determining general solutions for NHDEs using the method of undetermined coefficients, largely due to insufficient knowledge of basic ODEs concepts such as differentiation of exponentials, trigonometric ratios, solving quadratic equations, and algebraic skills. The findings indicated that the participants primarily utilised reasoning associated with APOS ‘action’ and less of ‘process’, hindering their engagement with higher-level concepts of solving NHDEs. Consequently, enhancing student teachers’ performance and retention in NHDEs classes therefore requires inventive approaches to instruction.
Co-Authors Cheva, G Jojo, Zingiswa M Jojo, Zingiswa M. Jojo, ZMM Mkwelie, Nhlanhla Mutambara, Lillias Hamufari Natsai