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All Journal Journal on Mathematics Education (JME) Journal on Mathematics Education
Mukuka, Angel
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Education Mathematics Social Sciences Other

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MEDIATING EFFECT OF SELF-EFFICACY ON THE RELATIONSHIP BETWEEN INSTRUCTION AND STUDENTS’ MATHEMATICAL REASONING Mukuka, Angel; Mutarutinya, Védaste; Balimuttajjo, Sudi
Journal on Mathematics Education Vol 12, No 1 (2021)
Publisher : Department of Doctoral Program on Mathematics Education, Sriwijaya University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jme.12.1.12508.73-92

Abstract

Literature is well-stocked with studies confirming that an instructional approach, self-efficacy, and mathematical reasoning skills are critical for enhancing students’ conceptual understanding and achievement in mathematics. However, there has been little emphasis on establishing whether being able to reason mathematically depends only on the instructional approach or students’ self-efficacy beliefs about mathematics also play a hidden role. A quasi-experimental study involving 301 grade 11 students from six public secondary schools in one district was carried out to investigate the mediating effect of self-efficacy on the relationship between instruction and students’ mathematical reasoning. Participants of the study were selected using the cluster random sampling method. Data were collected before and after the intervention via a mathematical reasoning test and a mathematics self-efficacy beliefs questionnaire. A Parallel Multiple Mediator Model in SPSS using the PROCESS custom dialogue version 3.4 was employed for data analysis. Findings suggest that mathematics self-efficacy and task-specific self-efficacy beliefs collectively and significantly mediate the effect of the instructional approach on students’ mathematical reasoning. The Student Teams-Achievement Division (STAD) was found to be an effective approach for enhancing students’ mathematical reasoning alongside self-efficacy beliefs. These findings provide evidence on the need to select an instructional approach that does not only focus on developing students’ cognitive abilities such as mathematical reasoning but also fosters students’ affective attributes such as maths self-efficacy beliefs.
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.
Mediating effect of self-efficacy on the relationship between instruction and students’ mathematical reasoning Mukuka, Angel; Mutarutinya, Védaste; Balimuttajjo, Sudi
Journal on Mathematics Education Vol. 12 No. 1 (2021): Journal on Mathematics Education
Publisher : Universitas Sriwijaya in collaboration with Indonesian Mathematical Society (IndoMS)

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Literature is well-stocked with studies confirming that an instructional approach, self-efficacy, and mathematical reasoning skills are critical for enhancing students’ conceptual understanding and achievement in mathematics. However, there has been little emphasis on establishing whether being able to reason mathematically depends only on the instructional approach or students’ self-efficacy beliefs about mathematics also play a hidden role. A quasi-experimental study involving 301 grade 11 students from six public secondary schools in one district was carried out to investigate the mediating effect of self-efficacy on the relationship between instruction and students’ mathematical reasoning. Participants of the study were selected using the cluster random sampling method. Data were collected before and after the intervention via a mathematical reasoning test and a mathematics self-efficacy beliefs questionnaire. A Parallel Multiple Mediator Model in SPSS using the PROCESS custom dialogue version 3.4 was employed for data analysis. Findings suggest that mathematics self-efficacy and task-specific self-efficacy beliefs collectively and significantly mediate the effect of the instructional approach on students’ mathematical reasoning. The Student Teams-Achievement Division (STAD) was found to be an effective approach for enhancing students’ mathematical reasoning alongside self-efficacy beliefs. These findings provide evidence on the need to select an instructional approach that does not only focus on developing students’ cognitive abilities such as mathematical reasoning but also fosters students’ affective attributes such as maths self-efficacy beliefs.
Co-Authors Balimuttajjo, Sudi Mutarutinya, Védaste Mutarutinya, Vedaste Tatira, Benjamin