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All Journal Union: Jurnal Ilmiah Pendidikan Matematika Journal of Medives: Journal of Mathematics Education IKIP Veteran Semarang Journal on Mathematics Education
Tatira, Benjamin
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Education Mathematics Social Sciences Other

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Analysis of pre-service mathematics teachers’ proof comprehension through Toulmin’s argumentation model Mukuka, Angel; Tatira, Benjamin
Journal on Mathematics Education Vol. 16 No. 1 (2025): Journal on Mathematics Education
Publisher : Universitas Sriwijaya in collaboration with Indonesian Mathematical Society (IndoMS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jme.v16i1.pp111-130

Abstract

The comprehension of mathematical proofs by preservice mathematics teachers is vital for their ability to effectively teach mathematical reasoning. Despite its importance, existing research reveals a significant gap in preservice teachers’ understanding and application of formal proof methods, especially in the context of mathematical argumentation. This study examined how preservice teachers construct mathematical proofs, using Toulmin’s argumentation model as a framework. A qualitative exploratory case study design was adopted, involving written proofs from 72 third-year preservice teachers at a South African university, supplemented by task-based interviews with nine participants. The findings indicate that 62.5% of the participants were able to construct correct direct proofs, and 61.1% applied the contraposition proof method correctly. However, only 30.6% produced valid proofs using the contradiction method. Further analysis uncovered notable gaps in essential components of proof construction, such as warrants, backing, and rebuttals, particularly when dealing with tasks requiring contraposition and contradiction methods. While many participants (62.5%) demonstrated procedural fluency in direct proofs, 31.9% failed to provide explicit definitions or logical precision, suggesting a superficial engagement with proof construction. These results highlight the need for teacher education programs to emphasize a deeper conceptual understanding of proof structures, which is crucial for preparing preservice mathematics teachers to foster reasoning and argumentation skills in their future classrooms.
First-Year Undergraduate Students’ Ways of Thinking in Combinatorics Tatira, Benjamin
Jurnal Pendidikan Matematika IKIP Veteran Semarang Vol 8 No 1 (2024): Journal of Medives : Journal of Mathematics Education IKIP Veteran Semarang
Publisher : Urogram Studi Pendidikan Matematika, Universitas Ivet

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31331/medivesveteran.v8i1.2576

Abstract

The fundamental counting principle and counting problems, jointly called combinatorics in this study, commence in the last year of secondary school and proceeds in undergraduate studies and beyond. The South African secondary school situation reflect the same worldwide scenario where counting principles is regarded as difficult and poorly performed in the final national examinations. The purpose of this study was to explore undergraduate students’ mental constructions in solving counting problems against the backdrop of Grade 12 fundamental counting principles. The Action-Process-Object-Schema theory was used to describe undergraduate students’ thinking ways in combinatorics. A single case of a first-year class of 182 students was considered in this study, whereby they all wrote a task on combinatorics and a seven were further interviewed. The findings revealed that students were skilled at solving problems involving the counting principles, which was mainly step-by-step application of the formulae. This conception is at action level according to APOS theory, but the goal of teaching is to guide students to attain the object mental conception. Object conception allows for solving of diverse real-world counting problems and promotes mathematical thinking skills.
Opportunities for curriculum improvement in secondary school mathematics education Machisi, Eric; Tatira, Benjamin
UNION : Jurnal Ilmiah Pendidikan Matematika Vol 13 No 2 (2025)
Publisher : Universitas Sarjanawiyata Tamansiswa

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30738/union.v13i2.19367

Abstract

This study investigates opportunities for enhancing the secondary school mathematics curriculum in South Africa. Employing a cross-sectional survey design, data were collected from a purposive sample of 80 postsecondary students enrolled at higher education institutions across the country. An online questionnaire was administered, and responses were analyzed using the Statistical Package for the Social Sciences (SPSS), focusing on frequency distributions and mean ranks. The findings reveal that while the current mathematics curriculum adequately prepares some students for postsecondary studies, it falls short for others. Key areas identified for improvement include better alignment with tertiary-level mathematics, reforming examination formats, enhancing pedagogical approaches, and increasing collaboration with local industries. Based on these insights, the study proposes several recommendations: offering specialized mathematics tracks, including optional exam questions, reducing exam length, introducing calculus prior to Grade 12, integrating digital tools in instruction, and connecting mathematical learning with real-world industry applications. By foregrounding students’ perspectives, this research promotes a bottom-up approach to curriculum development. The study contributes to the literature by providing empirical evidence on curriculum gaps from the learner’s viewpoint and offering context-specific recommendations to bridge secondary and tertiary mathematics education in South Africa.
Co-Authors Machisi, Eric Mukuka, Angel