Research Publications (Applied Sciences)
Permanent URI for this collectionhttp://ir-dev.dut.ac.za/handle/10321/213
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Item Exploring strategies in mathematical proficiency in social sciences research(Global Academy of Training and Research (GATR) Enterprise, 2022-12-31) Brijlall, Deonarain; Jimmy Ivasen, SelvamObjective - This paper explores the mathematical proficiency espoused by Kilpatrick et al. to improve teacher and learner mathematics performance in South Africa. A mixed-method approach involving interviews and questionnaires was used. Methodology/Technique - The sample included 7 principals or deputy principals, 7 departmental heads who supervised mathematics, 1 mathematics teacher who taught mathematics in grades 10 to 12, 1 mathematics teacher who taught Mathematics, and 1 learner from each grade 8 to 12 was included in the sample. Each participant was interviewed and had to complete a questionnaire. Finding - Kilpatrick et al. (Kilpatrick, Swafford, & Findell, 2001), who viewed Mathematical Proficiency as a five-stranded process involving conceptual understanding, productive disposition, procedural fluency, strategic competence, and adaptive reasoning, were used as a lens through which this study was conducted. We discovered several systemic, societal, and pedagogical challenges that teachers and students faced, all of which had an impact on their Mathematics teaching and learning. Our findings were in line with what was found in the literature review. The researchers concluded that there were always intervention strategies that could help to reduce or eliminate the challenges that Mathematics teachers and students face. Novelty - The researchers concluded there were always intervention strategies that could assist in minimizing or eradicating the challenges faced by the teachers and learners of mathematics, thus improving their socio-economic standing. Type of Paper - Review Keywords: Conceptual Development, Mathematical Proficiency, Code-switching. JEL Classification: Z10 A14, 19. to this paper should be referred to as follows: Brijlall, D; Ivasen, S.J. (2022). Exploring strategies in mathematical proficiency in social sciences research, GATR-Global J. Bus. Soc. Sci. Review, 10(4), 249–266. https://doi.org/10.35609/gjbssr.2022.10.4(4)Item High school learners’ challenges in solving circle geometry problems(PONTE, 2022-12-19) Brijlall, Deonarain; Abakah, Fitzgerald; BoschiThis paper reports on a study that investigated high school learners’ difficulties when solving circle geometry problems. This study was conducted on the premise that, if these difficulties are well-known, then the teacher will be guided, to implement appropriate instructional strategies to address them. High school mathematics learners’ poor performances in examinations (formal/informal), nationally, necessitated this study. A high school in the Northern Cape Province was purposefully sampled to serve as the research field for the study and circle geometry lessons were conducted, with the study participants. Thereafter, activities, investigation tasks, class work, home-work and standardized tests were administered to collect data. Data was also collected through classroom observations, video recordings and field notes. This was qualitative research hence, qualitative procedures were followed for data collection, analysis and interpretations. Content analysis was carried out on participants’ written responses to the standardized tests, utilising Newman’s Error Analysis model to inductively, identify participants challenges, which also served as the theoretical framework for the study. The analysed data revealed that learners do not understand circle geometry concepts, hence, their inability to make connections across geometry concepts to solve geometric problems. The researchers concluded this lack of fundamental background prevents learners from applying appropriate techniques in solving circle geometry problems.Item Conjecturing an effective problem-solving heuristic instructional approach for circle geometry(ASR Research, 2022-04-21) Abakah, Fitzgerald; Brijlall, DeonarainAbstract- This paper reports on an investigation into finding an effective contemporary problem- solving instructional approach for circle geometry. The participants were high school learners in a South African school. This proposed instructional approach-the IPAC model, adopted four elements of this new approach, namely, the infusion approach, Polya’s approach, and APOS theory in a collaborative learning classroom. This study followed a mixed-method research design. The quantitative data was analysed by implementing descriptive statistics and inferential statistics, while content analysis was performed on data extracted from qualitative questionnaires. The research findings that emanated from this study were the following: the validity, practicality and effectiveness of the designed model were established. Based on these research findings, the researcher recommended among others: (1) the designed model, should be implemented for teaching and learning of mathematics in general and circle geometry in particular, in South African schools; (2) teaching of thinking skills and teaching effective problem-solving instructional approaches should be prioritized in mathematics classrooms in South Africa.Item Impact of challenges experienced by teachers and learners on mathematics performance in relation to their socio-economic standing(Global Academy of Training and Research (GATR) Enterprise, 2022-09-25) Brijlall, Deonarain; Ivasen, Selvam JimmyObjective – This paper explores the challenges experienced by mathematics teachers and learners of seven high schools in South Africa. A mixed method approach involving interviews and questionnaires was used. Methodology – The sample included 7 principals or deputy principals, 7 departmental heads who supervised mathematics, 1 mathematics teacher who taught mathematics in grades 10 to 12, and 1 mathematics teacher who taught Mathematics in grades 8 and 9. In addition, 1 learner from each grade 8 to 12 was included in the sample. Each participant was interviewed using a structured interview schedule, followed by participants completing a questionnaire. Findings – Vygotsky's socio-cultural and conceptual development theories in mathematics education formed the basis of this study. The 'Inputs, Processes and Output" model of Howie and Kilpatrick's model of the five strands of achieving 'mathematics proficiency was adopted. We identified many systemic, societal, and pedagogical challenges that teachers and learners experienced, which affected their mathematics teaching and learning. Our findings correlated with research in the literature review. Novelty – The researchers concluded there were always intervention strategies that could assist in minimizing or eradicating the challenges faced by the teachers and learners of mathematics, thus improving their socio-economic standing. Type of Paper: Review JEL Classification: A14, 19. Keywords: Challenges, Strategies, Blended Learning, Scaffolding, Conceptual Development, Collaborative Learning. Reference to this paper should be made as follows: Brijlall, D; Ivasen, S.J. (2022). The impact of challenges experienced by teachers and learners on Mathematics performance, in relation to their socio-economic standing, J. Bus. Econ. Review, 7(2), 112–126. https://doi.org/10.35609/jber.2022.7.2(1)Item What are the strategies for teaching and learning mathematics that can be used effectively in a multilingual classroom(Kansai University, 2021) Kahiya, Antoinette; Brijlall, DeonarainThis paper reports on a study which explores the mathematics teaching strategies used in a multilingual classroom at technical and vocational education and training colleges in South Africa. Effective teaching and learning strategies are required that will motivate students to study and understand mathematical concepts, as well as engage in both procedural and conceptual discourses. Brijlall showed that in mathematics classes collaborative learning has a higher rate of success than does individual learning. He recommends further study on this teaching strategy. This study seeks to draw up some strategies which lecturers can use to teach mathematics effectively in a multilingual classroom. Effective strategies should lead to better understanding of mathematical concepts with subsequently improved performance in mathematics examinations. Hence, this study is important in addressing the call for greater research in this area.Item Mathematics lecturers and students views on the role of language in a multilingual classroom at TVET college level(Ponte Academic Journal, 2021) Kahiya, Antoinette; Brijlall, DeonarainThis paper reports on a study exploring the teaching and learning of mathematics in a multilingual classroom at a Technical Vocational Education and Training College (TVET). A case study research method was used. Three N5 mathematics lecturers and 20 N5 students were purposefully selected from two campuses of a TVET college in South Africa. Data were collected using semi-structured interviews and through classroom observations. Lecturers were interviewed individually to find out the effects of the language of teaching and learning on student understanding, and to find out the teaching strategies they use to teach mathematics. Findings reveal that students know what they should do in order to understand mathematical concepts, although they do not always adhere to them, and they also know what they expect from lecturers. Lecturers also know the teaching strategies that could give them good results, but the students seem to not do their part. Findings also reveal that a common language between lecturers and students helps a lot in explaining some important mathematical facts and it also helps in improving participation during lessons.Item Digital instructional and pedagogical gaps in mathematics education during COVID-19 : APOS theory based laboratory methodology in higher education(Horizon Research Publishing Co., Ltd., 2021) Mukavhi, Leckson; Brijlall, Deonarain; Abraham, JoseItem Designing an APOS Theory : technoscience framework to understand mathematical thinking(2021) Mukavhi, Leckson; Brijlall, Deonarain; Abraham, JoseThe understanding of mathematical thinking is fundamental cognitive and neuroscience phenomenon in mathematics education that can enhance both instructional and pedagogical practice for improved learning outcomes in mathematics. Several studies for the past decades have been thriving to bring out both operational and structural nature of mathematical thinking. This paper presents the novel theoretical framework as a build on to the APOS theory. The APOS theory has managed to successfully explain the mathematics thinking processes involved in the construction of a mathematics concept based on the premises of limited technology integration into mathematics education. Technology and science artefacts are now ubiquitous and constantly advancing and affecting our philosophical assumptions in mathematics education. We carried out a quasi-experiment in a mathematics laboratory involving two groups of 80 students apiece per study year taking Calculus course with differentiated teaching and learning at the University of Zimbabwe. This novel framework, APOS Theory-Technoscience, factored in technological and scientific oriented actions and processes led us to suggest an APOS-T framework as a didactic model for teaching Mathematics in Higher Education. The model could be an emerging digital pedagogy for face to face and remote mathematics instruction.Item Exploring the stages of Polya’s problem-solving model during collaborative learning : a case of fractions(KRE Publishers, 2015) Brijlall, DeonarainThis paper reports on a small-scale action research, which investigated the processes involved in problem-solving in a mathematics class. Grade ten learners (n = 47) at a South African middle school were involved in the study. The participants from two classes attempted the solution of tasks involving the fraction concept. In one class, the learners worked in groups and in the other class, the learners worked individually. A qualitative method was adopted for data capture and analysis. Social constructivism was adopted as a theoretical framework and the stages advocated by Polya were interrogated when analyzing the learner responses on their problem solutions. The results revealed that those learners working in groups demonstrated most of the stages of the Polya linear problem-solving model. The findings helped identify which stages of the model promote effective problem-solving and some recommendations are made for classroom practitioners engaging their learners in problem-solving.Item An exploration of the common content knowledge of high school mathematics teachers(University of the Free State, 2014) Bansilal, Sarah; Brijlall, Deonarain; Mkhwanazi, ThokozaniMany studies point to the problem of poor mathematics content knowledge of mathematics teachers in South Africa. The purpose of this study was to investigate teachers’ knowledge of the mathematics they are themselves teaching. Data was generated from the teachers (n = 253) written responses to test that was a shortened form of a previous Grade 12 Mathematics Paper One examination. The sample of teachers were studying towards an Advanced Certificate in Education (an upgrading high school mathematics qualification) at the University of KwaZulu-Natal in South Africa. The findings revealed that the teachers in this sample obtained an average of 57% in the test. Using an APOS theory analysis it was found that many teachers who were working at an action level of a concept would require help and scaffolding to move to process or object levels of understanding of that concept. Furthermore it was found that on average teachers obtained 29% on questions which were at the problem solving level, raising concerns about how these teachers would mediate tasks that are set at high cognitive levels, with their Grade 12 learners.