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All Journal Journal on Mathematics Education (JME) Journal of Research and Advances in Mathematics Education Journal of Innovation in Educational and Cultural Research JRAMathEdu (Journal of Research and Advances in Mathematics Education) Journal on Mathematics Education
Ndemo, Zakaria
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FLAWS IN PROOF CONSTRUCTIONS OF POSTGRADUATE MATHEMATICS EDUCATION STUDENT TEACHERS Ndemo, Zakaria
Journal on Mathematics Education Vol 10, No 3 (2019)
Publisher : Department of Doctoral Program on Mathematics Education, Sriwijaya University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1077.652 KB) | DOI: 10.22342/jme.10.3.7864.379-396

Abstract

Intending to improve the teaching and learning of the notion of mathematical proof this study seeks to uncover the kinds of flaws in postgraduate mathematics education student teachers. Twenty-three student teachers responded to a proof task involving the concepts of transposition and multiplication of matrices. Analytic induction strategy that drew ideas from the literature on evaluating students’ proof understanding and Yang and Lin’s model of proof comprehension applied to informants’ written responses to detect the kinds of flaws in postgraduates’ proof attempts. The study revealed that the use of empirical verifications was dominant and in situations. Whereby participants attempted to argue using arbitrary mathematical objects, the cases considered did not represent the most general case. Flawed conceptualizations uncovered by this study can contribute to efforts directed towards fostering strong subject content command among school mathematics teachers.
Mathematics education undergraduates’ personal definitions of the notion of angle of contiguity in Kinematics Ndemo, Zakaria; Mtetwa, David
JRAMathEdu (Journal of Research and Advances in Mathematics Education) Volume 6 Issue 2 April 2021
Publisher : Department of Mathematics Education, Universitas Muhammadiyah Surakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.23917/jramathedu.v6i2.11130

Abstract

The concept of a mathematical definition causes severe difficulties among students during problem solving and proving activities. Students’ difficulties with the use of mathematical definitions often arise from the fact that students are often given those definitions instead of constructing them. With the aim of developing an understanding of the kinds of student teachers evoked concept images of the notion of  angle of contiguity, a qualitative case study was conducted at one state university in Zimbabwe. Purposive sampling was used to select 28 mathematics undergraduate student teachers who responded to a test item. Qualitative data analysis was guided by ideas drawn from the theoretical framework of Abstraction in Context and idea of imperative features of a mathematical definition.  Student teachers written responses revealed that student teachers personal concept definitions consisted of ambiguous and irrelevant formulations that did not capture the essence of the idea of the angle of contiguity. In some cases their responses were not consistent with the definition of the angle of contiguity.  Although there were a few instances of adequate descriptions of the concept, (8 out of  32) these and the inadequate descriptors elicited can contribute significantly towards efforts intended to improve mathematics instruction.  Improved mathematics instruction will lead to enhanced conceptualizations of mathematics concepts.
Student teachers’ conceptualizations of mathematical problem solving and the nature of their warrants Ndemo, Zakaria; Mtetwa, David K. J.
JRAMathEdu (Journal of Research and Advances in Mathematics Education) Volume 7 Issue 4 October 2022
Publisher : Universitas Muhammadiyah Surakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.23917/jramathedu.v7i4.15303

Abstract

Absence of inquiry about meaning of mathematical objects learners deal with has permeated the school mathematics curriculum. Deep learning through questioning situations can be achieved if learners are helped to embrace the argumentation discourse in their problem solving efforts.  This paper reports on a study that investigated linkages between the kinds of mathematical arguments constructed by students and the students’ grasp of the concept of problem solving.  With the overall goal of teasing out such linkages a questionnaire that elicited likert-style and textual data was administered to 30 undergraduate and 5 postgraduate mathematics education students. The two data sources were triangulated with reflective interviews guided by students’ written responses and their validations on likert items. Descriptive statistics were applied to likert data and directed content analysis was used to analyze and interpret the qualitative data. The study concluded that students lacked appropriate conceptions of the notion of problem solving and in particular their thinking as reflected in their arguments that contradicted current understandings on the construct. The fragile grasp of the idea of mathematical problem solving uncovered by this study has the potential to inform mathematics instruction
Mathematics education undergraduates’ personal definitions of the notion of angle of contiguity in Kinematics Ndemo, Zakaria; Mtetwa, David
JRAMathEdu (Journal of Research and Advances in Mathematics Education) Volume 6 Issue 2 April 2021
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.v6i2.11130

Abstract

The concept of a mathematical definition causes severe difficulties among students during problem solving and proving activities. Students’ difficulties with the use of mathematical definitions often arise from the fact that students are often given those definitions instead of constructing them. With the aim of developing an understanding of the kinds of student teachers evoked concept images of the notion of angle of contiguity, a qualitative case study was conducted at one state university in Zimbabwe. Purposive sampling was used to select 28 mathematics undergraduate student teachers who responded to a test item. Qualitative data analysis was guided by ideas drawn from the theoretical framework of Abstraction in Context and idea of imperative features of a mathematical definition. Student teachers written responses revealed that student teachers personal concept definitions consisted of ambiguous and irrelevant formulations that did not capture the essence of the idea of the angle of contiguity. In some cases their responses were not consistent with the definition of the angle of contiguity. Although there were a few instances of adequate descriptions of the concept, (8 out of 32) these and the inadequate descriptors elicited can contribute significantly towards efforts intended to improve mathematics instruction. Improved mathematics instruction will lead to enhanced conceptualizations of mathematics concepts.
Student teachers’ conceptualizations of mathematical problem solving and the nature of their warrants Ndemo, Zakaria; Mtetwa, David K. J.
JRAMathEdu (Journal of Research and Advances in Mathematics Education) Volume 7 Issue 4 October 2022
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.v7i4.15303

Abstract

Absence of inquiry about meaning of mathematical objects learners deal with has permeated the school mathematics curriculum. Deep learning through questioning situations can be achieved if learners are helped to embrace the argumentation discourse in their problem solving efforts. This paper reports on a study that investigated linkages between the kinds of mathematical arguments constructed by students and the students’ grasp of the concept of problem solving. With the overall goal of teasing out such linkages a questionnaire that elicited likert-style and textual data was administered to 30 undergraduate and 5 postgraduate mathematics education students. The two data sources were triangulated with reflective interviews guided by students’ written responses and their validations on likert items. Descriptive statistics were applied to likert data and directed content analysis was used to analyze and interpret the qualitative data. The study concluded that students lacked appropriate conceptions of the notion of problem solving and in particular their thinking as reflected in their arguments that contradicted current understandings on the construct. The fragile grasp of the idea of mathematical problem solving uncovered by this study has the potential to inform mathematics instruction.
Flaws in proof constructions of postgraduate mathematics education student teachers Ndemo, Zakaria
Journal on Mathematics Education Vol. 10 No. 3 (2019): 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

Intending to improve the teaching and learning of the notion of mathematical proof this study seeks to uncover the kinds of flaws in postgraduate mathematics education student teachers. Twenty-three student teachers responded to a proof task involving the concepts of transposition and multiplication of matrices. Analytic induction strategy that drew ideas from the literature on evaluating students’ proof understanding and Yang and Lin’s model of proof comprehension applied to informants’ written responses to detect the kinds of flaws in postgraduates’ proof attempts. The study revealed that the use of empirical verifications was dominant and in situations. Whereby participants attempted to argue using arbitrary mathematical objects, the cases considered did not represent the most general case. Flawed conceptualizations uncovered by this study can contribute to efforts directed towards fostering strong subject content command among school mathematics teachers.
Student teachers’ conceptualizations of mathematical problem solving and the nature of their warrants Ndemo, Zakaria; Mtetwa, David K. J.
JRAMathEdu (Journal of Research and Advances in Mathematics Education) Volume 7 Issue 4 October 2022
Publisher : Universitas Muhammadiyah Surakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.23917/jramathedu.v7i4.15303

Abstract

Absence of inquiry about meaning of mathematical objects learners deal with has permeated the school mathematics curriculum. Deep learning through questioning situations can be achieved if learners are helped to embrace the argumentation discourse in their problem solving efforts.  This paper reports on a study that investigated linkages between the kinds of mathematical arguments constructed by students and the students’ grasp of the concept of problem solving.  With the overall goal of teasing out such linkages a questionnaire that elicited likert-style and textual data was administered to 30 undergraduate and 5 postgraduate mathematics education students. The two data sources were triangulated with reflective interviews guided by students’ written responses and their validations on likert items. Descriptive statistics were applied to likert data and directed content analysis was used to analyze and interpret the qualitative data. The study concluded that students lacked appropriate conceptions of the notion of problem solving and in particular their thinking as reflected in their arguments that contradicted current understandings on the construct. The fragile grasp of the idea of mathematical problem solving uncovered by this study has the potential to inform mathematics instruction
ARUNG: A Cultural Heritage-Based Application for Android Augmented Reality in Learning Geometry Munir, Nilam Permatasari; Anas, Aswar; Musa, Lisa Aditya Dwiwansyah; Ndemo, Zakaria
Journal of Innovation in Educational and Cultural Research Vol 7, No 2 (2026): Article in Press
Publisher : Yayasan Keluarga Guru Mandiri

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46843/jiecr.v7i2.2522

Abstract

Although Augmented Reality (AR) has been extensively discussed and reported in mathematics education, there is limited research on its integration with local culture. This study introduces ARUNG, an Android-based application that integrates cultural heritage into geometry education. The innovation focuses on three main aspects: the integration of local cultural heritage into ARUNG, the design of the ARUNG system for geometry learning, and the analysis of the effectiveness on geometry concept comprehension. A research and development (RD) study was conducted, involving three stages: input, output, and feedback. ARUNG was applied to 25 junior high schools in the eighth grade. Data on the conceptual understanding test results were analyzed to test the research hypothesis using a paired t-test. Cultural heritage markers integrated into ARUNG included Walasuji (cube), the walls of the Jami Tua Mosque in Palopo (rectangular prism), the Soko Guru pole (twelve-sided prism), the royal tomb of Lokko’e (square prism), and the PNIEL church (octagonal pyramid). The findings revealed that students' average comprehension of geometry concepts improved after using ARUNG compared to before. This research contributes to the field by introducing an innovative AR learning medium that incorporates cultural heritage, thereby promoting cultural awareness.
Co-Authors Anas, Aswar Mtetwa, David Mtetwa, David K. J. Munir, Nilam Permatasari Musa, Lisa Aditya Dwiwansyah