https://ir.unisa.ac.za/handle/10500/6424 2026-10-22T19:23:47Z 2026-10-22T19:23:47Z Kumlachew, Tadesse Derseh (Derseh K T) https://ir.unisa.ac.za/handle/10500/33092 2026-09-22T16:10:15Z 2026-01-01T00:00:00Z

The effect of working memory-context-based problem-solving instruction on calculus problem-solving skills of first year students at an Ethiopian university Kumlachew, Tadesse Derseh (Derseh K T) Mathematics problem-solving, particularly in calculus, continues to pose significant challenges for university students, especially when tasks require conceptual understanding and multi-step reasoning. This study, conducted within a pragmatic research paradigm, examined the effect of Working Memory–Context-Based Problem-Solving Instruction (WMCBPSI), grounded in Cognitive Load Theory (CLT), on the calculus problem-solving performance of first-year students at an Ethiopian university. The instructional approach was designed to reduce extraneous cognitive load by integrating worked examples, structured self-explanation prompts, and strategies aimed at minimizing split-attention effects. A two-month intervention involving 79 students was implemented using a static group, post-test-only quasi-experimental design, with 41 students in the experimental group and 38 students in the comparison group. The experimental group received calculus instruction through WMCBPSI while the comparison group followed conventional problem-solving instruction. Data were collected using a standardized functional mathematics achievement test, classroom observations, and semi-structured interviews. The results indicated that students exposed to WMCBPSI significantly outperformed their peers in solving calculus problems, particularly those requiring conceptual reasoning and multi-step solution processes. Qualitative findings further revealed that students perceived the structured nature of WMCBPSI as supportive of deeper engagement with complex problem-solving tasks. The study concludes that WMCBPSI is an effective instructional approach for enhancing calculus problem-solving skills, and that aligning instructional practices with principles of human cognitive architecture offers a practical and theoretically grounded model for improving mathematics instruction in higher education, with implications for adaptation across other mathematical domains and diverse learning contexts

2026-01-01T00:00:00Z Nzuza, Philasande Zamokuhle https://ir.unisa.ac.za/handle/10500/33044 2026-09-23T14:32:39Z 2025-02-01T00:00:00Z

Using visualisation to teach grade 12 heights and distances: A study in one secondary school in Zululand district of KwaZulu-Natal province Nzuza, Philasande Zamokuhle Visualisation has been widely used to enhance learners’ conceptual understanding of problem solving in mathematics. The purpose of this study was to explore the effectiveness of visualisation in teaching and learning heights and distances in Grade 12 learners and to determine how visualisation may influence learners’ understanding and performance when solving height and distance problems. This study adopted a mixed-methods approach, utilising both quantitative and qualitative methods. A pre-test-intervention-post-test design was employed to assess the effectiveness of visualisation in teaching heights and distances in trigonometry. A pre-test and post-test were administered to 60 Grade 12 learners, divided into experimental and control groups. Semi-structured interviews were conducted with the two teachers from the experimental and control groups, along with lesson observations before, during, and after the intervention. Thematic analysis was applied to analyse the semi-structured interviews and the lesson observation data. The researcher utilised Excel and SPSS tools for statistical data analysis. Microsoft Excel was used to record pre- and post-test scores for the experimental and control group results. This study proposed potential methods for using visualisation to teach and learn about heights and distances in trigonometry. The findings revealed that, prior to the intervention, the control group outperformed the experimental group in most questions on the pre-test. Following the intervention, learners' performance in the experimental group improved, resulting in better outcomes than the control group in the post-test. This indicates that the implementation of visualisation positively impacted the performance of the experimental group. Abstract and text in English

2025-02-01T00:00:00Z Chokoe, Phuti Yvens https://ir.unisa.ac.za/handle/10500/32965 2026-08-18T13:52:20Z 2026-01-01T00:00:00Z

Effective formative assessment practices in grade 11 analytical geometry: perspectives of mathematics educators Chokoe, Phuti Yvens The purpose of this study was to explore formative assessment practices used by Grade 11 mathematics educators in teaching Analytical Geometry in secondary schools in the Kgakotlou Circuit, Capricorn South District, Limpopo Province, South Africa. Analytical Geometry presents substantial conceptual challenges for Grade 11 learners, including interpreting gradient relationships, distinguishing between perpendicular and parallel lines, and accurately applying midpoint and distance formulas. Common learner errors include reversing values during gradient substitution, misinterpreting conditions for perpendicularity, and applying coordinate formulas procedurally without conceptual understanding. These persistent misconceptions highlight the importance of using Analytical Geometry as a context for examining how formative assessment can support conceptual development through the identification and remediation of learner errors. These challenges underscore the need to investigate formative assessment practices in mathematics classrooms to enhance learner understanding and engagement. The study addressed three research questions: (a) How do educators conceptualise formative assessment in the teaching of Analytical Geometry? (b) What formative assessment practices are implemented by Grade 11 mathematics educators in Analytical Geometry? and (c) What barriers do educators encounter when implementing effective formative assessment practices? The study was theoretically grounded in Lev Vygotsky’s sociocultural theory and the Learning-Oriented Assessment framework, which served as analytical lenses to understand formative assessment as a socially mediated process linking dialogue, scaffolding, feedback, and instructional responsiveness. A qualitative exploratory phenomenological design was employed. Data were collected through semi-structured interviews, classroom observations, and lesson plan analysis. Twelve Grade 11 mathematics educators were purposively selected from secondary schools within the circuit. Interviews provided insights into educators’ perceptions and experiences of formative assessment, classroom observations captured the enactment of formative assessment practices during lessons, and lesson plan analysis revealed how formative assessment was incorporated into instructional planning. Thematic analysis was used to identify recurring patterns and themes across the datasets. Trustworthiness was ensured through methodological triangulation, member checking, prolonged engagement, and the maintenance of an audit trail, thereby enhancing credibility, dependability, and confirmability. The findings revealed that educators employed formative assessment practices such as questioning, classroom discussion, peer interaction, exercises, and oral feedback to monitor learner understanding, identify misconceptions, and adjust instruction. Learner participation and classroom dialogue were found to enhance reasoning, engagement, and conceptual understanding. However, the effectiveness of these practices was often constrained by contextual factors, including limited instructional time, large class sizes, and an examination-oriented curriculum, which restricted opportunities for individualised feedback and sustained interaction. This study contributes to mathematics education research by providing context-specific insights into the enactment of formative assessment in Grade 11 Analytical Geometry classrooms in rural South African schools. It further illustrates how structural constraints influence instructional responsiveness and learner participation. The study recommends increased support for educators in developing student-centred formative assessment strategies that promote active participation and deeper conceptual understanding in Analytical Geometry. Abstract and text in English

2026-01-01T00:00:00Z Kwankye, Emmanuel https://ir.unisa.ac.za/handle/10500/32744 2026-08-28T08:42:10Z 2025-07-30T00:00:00Z

Grade 9 learners’ understanding of algebraic expressions: A case of a selected high school in Frances Baard District in the Northern Cape Kwankye, Emmanuel Mathematics underachievement is a global challenge, with South Africa also experiencing a decline in skills consistent with international trends. This study aimed to explore the understanding of algebraic expressions amongst Grade 9 learners. The study was inspired by the fact that learners in the Northern Cape usually demonstrate dismal performance in algebraic expressions. When learners lack strong algebraic skills, it can reduce their confidence and achievement in further education and training, restricting access to careers in Science and Engineering. This study draws on Skemp’s theory of understanding to help explain and make sense of the phenomenon of poor performance in algebraic expression. The study adopted a qualitative case study research approach in which 40 learners from a selected school in the Frances Baard District, Northern Cape in South Africa, participated. Test and semi-structured interviews were used to collect data. The findings of the study revealed that learners lack the fundamental concepts or pre-requisite knowledge in algebraic expression. They also lack relational understanding in algebraic expressions and moreover, their mathematical connection abilities were very low. The implications of this study include but are not restricted to, the need for teachers to pay special attention, monitor, document and carefully examine learners’ misconceptions and conceptual gaps when teaching algebraic expression. There is also a need for learners to be exposed to appropriate, practical and real life-scenarios during the teaching and learning of algebraic expressions to make the content more simple, realistic, engaging and understandable. These stated implications should be regarded in view of some of the limitations of this research, including the small sample size, limited time and resources.

2025-07-30T00:00:00Z