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All Journal Journal of Education and Learning (EduLearn) Journal on Mathematics Education (JME)

Zakaria Ndemo

Bindura University of Science Education

Author-ID : 2468609

Humanities Education Library & Information Science Mathematics Social Sciences Other

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What should be the object of research with respect to the notion of mathematical proof? Zakaria Ndemo; David J Mtetwa; Fred Zindi
Journal of Education and Learning (EduLearn) Vol 13, No 1: February 2019
Publisher : Intelektual Pustaka Media Utama

Despite its central place in the mathematics curriculum the notion mathematical proof has failed to permeate the curriculum at all scholastic levels. While the concept of mathematical proof can serve as a vehicle for mathematical thinking, studies have revealed that students experience serious difficulties with proving that include: not knowing how to begin the proving process, the proclivity to use empirical verifications for tasks that call for axiomatic methods of proving, resorting to rote memorization of uncoordinated fragments of proof facts. While several studies have been conducted with the aim of addressing students’ fragile grasp of mathematical proof the majority of such studies have been based on activities that involve students reflecting and expressing their level of convincement in arguments supplied by the researchers thereby compromising the voice of the informants. Further, research focus has been on the front instead of the back of mathematics. Hence, there is a dearth in research studies into students’ thinking processes around mathematical proof that are grounded in students’ own proof attempts. Therefore current research strides should aim at identifying critical elements of students’ knowledge of the notion of proof that should be informed by students’ actual individual proof construction attempts.

Secondary school students’ errors and misconceptions in learning algebra Zakaria Ndemo; Osten Ndemo
Journal of Education and Learning (EduLearn) Vol 12, No 4: November 2018
Publisher : Intelektual Pustaka Media Utama

The aim of the study is to develop an understanding of the kinds and sources errors and misconceptions that characterise students’ learning of school algebra. Systematic random sampling was used to draw sixty-five participants from a population of two hundred and twenty-three form three students. A cross sectional survey design was employed to collect data using written tests, a structured questionnaire and interviewing of the students from one high school in Zimbabwe. Content analysis technique was applied to textual data from three sources in order to determine the types of errors and misconceptions. The main findings are that both procedural and conceptual errors were prevalent that errors and misconceptions can be explained in terms of the students’ limited understanding of the nature of algebra; in particular their fragile grasp of the notion of a variable. Sources of misconceptions could be explained in terms of the abstract nature of algebra Mathematics educators should embrace errors and misconceptions in their teaching and should not regard them as obstacles to learning but rather engage with them for better understanding of algebraic concepts by students. Future studies can be carried on systematic errors as one of the ways of improving students’ understanding school mathematics.

Towards a Comprehensive Conception of Mathematical Proof Zakaria Ndemo; David. J. Mtetwa; Fred Zindi
Journal of Education and Learning (EduLearn) Vol 12, No 4: November 2018
Publisher : Intelektual Pustaka Media Utama

There is overwhelming evidence that students face serious challenges in learning mathematical proof. Studies have found that students possess a superficial understanding of mathematical proof. With the aim of contributing to efforts intended to develop a comprehensive conception of mathematical proof, literature search was conducted to identify areas where research could be directed in order to increase proof understanding among students. To accomplish this goal, literature on modes of reasoning involved in proof construction, ideas on the classification of activities that constitute a proof path, and categories of proof understanding are exemplified using mathematical content drawn from Real Analysis. These exemplifications were used to illustrate the connections between modes of reasoning and levels of proof understanding. With regard to students’ fragile grasp of mathematical proof this critique of literature has revealed that many previous studies have given prominence to proof validations while there is lack of crucial interplay between structural and inductive modes of reasoning during proving by students. Hence, it is suggested in this paper that current research could also focus on mechanisms that promote an analytic conceptions of mathematical proof that are comprehensive enough to allow students to engage in more robust proof constructions.

FLAWS IN PROOF CONSTRUCTIONS OF POSTGRADUATE MATHEMATICS EDUCATION STUDENT TEACHERS Zakaria Ndemo
Journal on Mathematics Education Vol 10, No 3 (2019)
Publisher : Department of Doctoral Program on Mathematics Education, Sriwijaya University

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.

Secondary mathematics teachers’ use of learners’ responses to foster justification skills Hilda Pfende; Zakaria Ndemo; Osten Ndemo
Journal of Education and Learning (EduLearn) Vol 16, No 3: August 2022
Publisher : Intelektual Pustaka Media Utama

This study aimed to understand how secondary mathematics teachers engage with learners during the teaching and learning process. A sample of six participants was purposively selected from a population of ordinary level mathematics teachers in one urban setting in Zimbabwe. Field notes from lesson observations and audio-taped teachers’ narrations from interviews constituted data for the study to which thematic analysis technique was then applied to determine levels of mathematical intimacy and integrity displayed by the teachers as they interacted with the students. The study revealed some inadequacies in the manner in which the teachers handled students’ responses as they strive to promote justification skills during problem solving, in particular teachers did not ask students to explain wrong answers. The teachers indicated that they did not have sufficient time to engage learners in authentic problem-solving activities since they would be rushing to complete syllabus for examination purposes. On the basis of these findings, we suggest teachers to appreciate the need to pay special attention to the kinds of responses given by learners during problem-solving in order to promote justification skills among learners.

Co-Authors David J Mtetwa David. J. Mtetwa Fred Zindi Hilda Pfende Osten Ndemo

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