Theses and Dissertations (Mathematics Education)
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Item Grade 12 rural mathematics teachers 'discourses during calculus lessons: a case of effective teachers in Qwa-Qwa, Free State Province, South Africa(2024-10) Sempe, Matobako; Mbhiza, HlamuloThis study investigates the mathematical discourses of Grade 12 mathematics teachers in rural classrooms during Calculus lessons in Qwa-Qwa, Free State Province, South Africa. The selection of five teachers was based on their consistent achievement of an 80% pass rate in the National Senior Certificate mathematics assessment over a period of three years or more. Employing a qualitative research approach, the study utilised three primary data sources: unstructured classroom observations, semi-structured interviews, and Video-Stimulated Recall Interviews (VSRI). Framed as a multiple case study within the interpretivist paradigm, the research focused on the discourse practices of these teachers during their teaching of Calculus. Critical Discourse Analysis (CDA) served as the analytical framework, complemented by the Mathematics Discourse in Instruction (MDI) conceptual framework. The study reveals how the components of MDI—namely exemplification, explanatory talk, and learner participation—were effectively integrated into the teachers’ lessons to convey Calculus concepts. The findings indicate that these elements were not only present but were also skilfully utilised by the teachers. They initiated Calculus instruction by linking it to students' prior knowledge and potential career paths, employing visual aids to facilitate comprehension. However, some teachers did not sufficiently connect graphical and algebraic representations. The discourses observed included scaffolding of new knowledge and structured questioning, though these practices sometimes restricted more profound mathematical discussions. While visual aids, gestures, and exemplification were employed to clarify concepts, certain methods inadvertently led to misconceptions. Furthermore, although teachers promoted learner participation, their reliance on structured questioning often limited opportunities for independent reasoning. The findings highlight both effective instructional strategies and areas for improvement, particularly in promoting deeper conceptual understanding and addressing potential misunderstandings in Calculus.Item Exploring South African high school learners problem-solving skills in Euclidean Geometry(2024-07) Matsho, Stephens Kgalushi; Faleye, SundayThis study investigated the effects of South African mathematics learners’ problem-solving errors in Euclidean geometry on their performance in matric mathematics paper 2 of the National Senior Certificate (NSC) examination. The study also proposed Euclidean geometry teaching-learning continuum approach that may reduce the problem-solving errors and ultimately improve performance in the matric mathematics paper 2 examination. The study was underpinned by Newman problem-solving error analysis (Newman, 1977). To this end, the study was conducted in two phases: Phase I and Phase II. In Phase I, type of errors committed in the matric mathematics paper 2 and their effect on performance was investigated, while the Phase II of the study explored the efficacy of the teaching-learning continuum (EGPSLM-EGPSIA) approach proposed. Mixed method research approach was used in the study. This involved quasi-experimental and descriptive research designs. Quasi-experimental design used ex-post facto and pre-test post-test matching control research approach to collect data, while the descriptive research design adopted solution appraisal and classroom observation to collect data. In Phase I, 244 scripts from the 2020 mathematics paper 2 exam from three provinces and 432 scripts from the 2021 mathematics paper 2 exam from five provinces were used to collect data. In Phase II, random and convenient sampling were used to select three schools from the study population. Two of the selected schools were experimental schools and the remaining one was a control school. A total of 95 Grade 12 mathematics learners formed the study participants for the study in Phase II. There were nine itemised findings but they are summarised as but not limited to (1) problem-solving errors in Euclidean geometry significantly affected the learners’ matric mathematics paper 2 performance, (2) South African mathematics learners commit similar pattern of errors in Euclidean geometry yearly, (3) reading error was the leading error that were commonly committed in Euclidean geometry problem-solving, (4) EGPSLM-EGPSIA continuum intervention facilitate the learning of Euclidean geometry concepts, and (5) EGPSLM-EGPSIA continuum intervention has the potential to improve the learners’ performance in Euclidean geometry.Item Using erroneous examples for teaching Grade 9 Algebraic Linear Equations at a School in Johannesburg Central District(2024-05-23) Gwenzi, Julius; Makgakga, Tšhegofatšo PhutiThe importance of mathematics is well known the world over, and its applications in commerce, science, technology and everyday life situations cannot be emphasised. Algebra is an abstract and challenging branch of mathematics to teach and learn. Teachers struggle to teach it, and learners struggle to understand it, hence they develop a plethora of misconceptions and associated errors. Passing mathematics at FET is a prerequisite for admission into tertiary institutions to study science, engineering, technology and mathematics. To pass mathematics, one has to have a comprehensive understanding of algebra at an early stage of learning. This study’s purpose was to explore the impact and effectiveness of erroneous examples for teaching Grade 9 algebraic linear equations. Learners’ performance in mathematics in Grade 9 is crucial because, in South Africa, learners use their results to choose the subject combination they will take at FET. This study was underpinned by constructivism, which recognises the role of the individual in making knowledge. This study followed an explanatory embedded mixed-methods research design. Qualitative data for this study was collected through lesson observations and semi-structured interviews with two Grade 9 mathematics teachers. A pre-test was used to collect quantitative data from both the experimental and control groups (N=31) and (N=28) respectively. A post-test was also administered to both the experimental group (N=12) and the control group (N=24). Excel was used for data management. Statistical data analysis was done using IBM SPSS version 28. The experimental and control groups were compared using a t-test at the 95% confidence limit (2-sided). The results were declared statistically and significantly different for all p-values of 0.05 or less. The post-test results after the intervention showed an improvement in performance for the two study groups, with the experimental group improving from 𝑥𝑥̅=1.12903 in the pre-test to 𝑥𝑥̅=18.83333 in the post-test, an increase of 𝑥𝑥̅=17.7043. In contrast, the control group improved from 𝑥𝑥̅=12.82143 in the pre-test to 𝑥𝑥̅=23.00000 in the post-test an increase of 𝑥𝑥̅=10.17857. The greater increase in the mean differences by the experimental group suggests that the intervention positively impacted learners’ performance. Qualitative data obtained from semi-structured interviews and lesson observations were coded and identified according to different themes. Erroneous examples positively impacted the TEG’s teaching practice and improved the learners’ performance.Item The effect of problem-solving teaching approach on learning fractions in Grade 8(2024) Agadagba, Oghenerukewe Emmanuel; Masilo, M. M.Problem-solving teaching approach is critical in improving learners’ cognition and problem-solving skills in different content areas in mathematics. Therefore, this quantitative study evaluated the effect of the problem-solving teaching approach on learning Fractions in Grade 8. This study draws from Polya’s Problem-Solving framework that consists of sequential learning phases applied by the facilitator for intervention in guiding learners during their learning process. This study’s null hypothesis, which was rejected, stated that there is no difference between the problem-solving teaching approach and traditional teaching approach on learning addition and subtraction of fractions (H0): μproblem-solving approach =μtraditional approach. The positivist view in this study emphasised that the complexity of teaching and learning is understood through a scientific approach and numerical measurement. Participants were educators and learners in Mopani East and West District of Limpopo, categorised into experimental and comparison groups. The quasi-non-equivalent pre and post-test design, and questionnaire were used to engage the participants to access the empirical evidence. The 363 learners’ who took part were 175 experimental group learners’ and 188 comparison group learners. Participants were conveniently sampled, and no random assignment of participants was done. Data analysis combined both descriptive analysis and inferential Kruskal-Wallis and Sample Wilcoxon Signed Rank measurements. Learners were exposed to problem-solving learning in the experimental group and to traditional teaching and learning in the comparison group. In response to problem-solving teaching and learning, learners engaged in understanding the problem phase, devising the plan phase, carrying out the plan phase, and evaluating the solution phase through self-centred, group and self-regulated learning to build knowledge and skills. Findings revealed that learners who learned through problem-solving gained problem-solving skills and improved their performance. The results generated from SPSS, Kruskal-Wallis, Wilcoxon Signed Rank through paired t-test data analysis according to learners’ performance in experimental group indicates significant p-value of p=0.000 with large effect size H= 0.163, p<0.05. The large effect size implies problem-solving contributed significantly towards the improvement of learners’ problem-solving learning, skills, and achievement of moderate and advanced scores on learning addition and subtraction of fractions.Item The challenges faced by Grade 7 Mathematics teachers in integrating digital technologies to teach data handling(2023-12) Paulus, Johannes Natangwe; Masilo, M. M.This study explored the challenges faced by mathematics teachers in integrating digital technologies in teaching Data handling in Grade 7 in Ohangwena Region, Namibia. In this digital era, it is crucial for teachers to realise the significant role that technologies play in learners’ performance. A qualitative case study approach was adopted for this study. The sample includes two (2) Grade 7 Mathematics teachers and twenty-six (26) Grade 7 Mathematics learners. Semi-structured interviews and observations were used to collect data. Data from interviews and observations were analysed using deductive thematic analysis and the TPACK theory guided this study. The results of this study show that teachers are faced with several challenges in integrating technology in teaching. The challenges include the inadequate technological skills in teachers on integrating technology in teaching, insufficient technological tools in schools, negative perspectives among teachers towards the utilisation of technology to teach and limited scope on the integration of technology in the curriculum. This study thus recommends the provision of sufficient digital tools in schools. The study also recommends that in-service teachers be provided with continuous professional development to improve the technical skills and sufficient training of pre-service teachers on technology integration in teaching Mathematics. It is further recommended that curriculum developers need to revise the curriculum and improve it to accommodate technological integration in teaching.