https://ir.unisa.ac.za/handle/10500/6440 2026-06-27T07:43:07Z 2026-06-27T07:43:07Z Palayandi, Marcus Anthony https://ir.unisa.ac.za/handle/10500/32469 2026-05-13T10:57:09Z 2025-08-01T00:00:00Z

An exploration of the use of virtual manipulatives in enhancing understanding of circle geometry : a case of level 4 national vocational students Palayandi, Marcus Anthony This study explored the impact of virtual manipulatives (VMs), specifically GeoGebra, on enhancing National Certificate Vocational (NC(V)) Level 4 students’ understanding of circle geometry. It investigated how technology-integrated instruction can address learning challenges in Euclidean Geometry. The research was guided by three key objectives: (i) to identify the challenges students face in understanding circle geometry (ii) to examine the nature of VM-based activities that promote comprehension, and (iii) to determine how virtual tools help minimise learning barriers. The study was framed within the Pirie-Kieren theory of the growth of mathematical understanding, which views learning as a dynamic and recursive process. A spiral action research methodology was employed, progressing through three instructional phases: conventional teaching, practical hands-on activities and VM-based learning using GeoGebra. Thirty Level 4 students from Molapo Campus, located in the South West Gauteng TVET College, participated in the study. Qualitative data was collected through semi-structured interviews, questionnaires, as well as pre- and post-tests structured in line with the Pirie-Kieren theory of the growth of mathematical understanding. The final results showed that the baseline assessment revealed significant gaps in students’ foundational understanding of circle geometry. In particular, many students struggled to recognise and apply key properties of circles, especially when these properties needed to be used in combination with triangles and straight lines. Although the introduction of practical instruction improved student engagement—most notably during lessons involving cyclic theorems—its impact was limited by time constraints and students’ difficulties in accurately using measurement instruments. Furthermore, several students reported that they had minimal exposure to mathematics outside the classroom, which restricted opportunities for revision, practice, and consolidation of newly learned concepts. The introduction of GeoGebra significantly improved conceptual clarity, visualisation and interactive learning. Students demonstrated enhanced confidence, better problem-solving skills and a deeper grasp of geometric relationships. VM-based learning allowed learners to explore, test theories and connect geometric ideas more effectively than through traditional methods. This study highlights the transformative potential of digital tools in mathematics education, especially in bridging conceptual gaps in challenging topics like circle geometry. It advocates for the integration of VMs into NC(V) instructional strategies to promote deeper understanding, active engagement and improved academic performance in mathematics.

2025-08-01T00:00:00Z Mahlangu-Olorunfemi, Catherine Lindiwe https://ir.unisa.ac.za/handle/10500/32362 2026-04-14T10:49:29Z 2023-11-01T00:00:00Z

Learner’s problem solving abilities in Grade 11 Euclidean geometry tasks Mahlangu-Olorunfemi, Catherine Lindiwe The aim of this study was to explore Grade 11 learners’ problem-solving abilities that are manifest when they solve Euclidean geometry tasks. Additionally, this study evaluated the levels of problem-solving ability they operated within. The investigation was underpinned by the Polya problem-solving model. Through this model, the learners’ problem-solving abilities that guided them to solve the related problem-solving task were analysed and interpreted. The study used a qualitative method of enquiry and followed a case study research approach. Participants consisted of 63 Grade 11 mathematics learners from two different schools which were selected through convenience sampling. This study used two instruments to collect data, namely, the Euclidean geometry task and semi-structured interviews. The study revealed that 69.8% of participants had low problem-solving abilities, while 28.6% of participants had average problem-solving abilities. Only 1.6% of participants had high problem-solving abilities. In addition, the researcher was able to identify participants’ misconceptions and errors. It is anticipated that this study will make a valuable contribution to the enhancement of learners' proficiency in problem-solving skills, specifically in the domain of Euclidean geometry, as well as their overall performance in mathematics.

2023-11-01T00:00:00Z Ndebele, Jane https://ir.unisa.ac.za/handle/10500/32352 2026-04-09T12:21:14Z 2024-06-01T00:00:00Z

The effect of problem-centred teaching approach on learners’ mathematical performance in Grade 7 algebraic expressions Ndebele, Jane The poor performance of South African grade 7 learners in mathematics motivated this study. The mathematical domain of algebraic expressions in grade 7 has been identified as one of the challenging topics contributing to learners’ high failure rate. The teaching strategies that teachers use during mathematics lessons influence the level of understanding of their learners. Traditional teaching methods (TTM) employed by mathematics teachers have been identified as one of the reasons for the observed instances of failure rate. This study investigated the comparative effect of a problem-centred teaching approach (PCTA) on the performance of grade 7 learners in algebraic expressions, in relation to TTM. Six primary schools participated in the study, with two schools in the pilot study and four schools in the main study. A total of n=311 learners participated in the main study, with n=154 learners from two schools forming the control group, and n=157 learners from the other two schools forming the experimental group. Four teachers from the four schools took part in the study. The study employed a mixed methods research approach, consisting of a quasi-experimental approach with a non-equivalent control group using pre- and post-test design. The study employed both qualitative and quantitative methods in collecting and analysing data, using a performance test at pre- and post-testing stages, teacher questionnaires, semi-structured interviews with teachers, and a lesson observation schedule. The quantitative data were analysed using Statistical Package for Social Sciences (SPSS). Data from the lesson observations and the semi-structured interviews were analysed qualitatively and were used in answering some of the research questions. The information gathered through the questionnaires was coded and run on SPSS for analysis. The output was used in answering the first two research questions. The constructivist learning theory framed this study together with Pólya’s problem-solving model used when implementing the PCTA. Analysis of results using the analysis of covariance (ANCOVA) revealed that there was a statistically significant difference between the performance of the learners taught using PCTA and those taught using TTM. Learners taught using the PCTA performed better than those in the control group at the post-testing stage. The PCTA was deemed to be superior to TTM in teaching algebraic expressions in grade 7.

2024-06-01T00:00:00Z Hagoramagara, Franco https://ir.unisa.ac.za/handle/10500/32350 2026-04-08T07:35:52Z 2021-07-08T00:00:00Z

Using a smart noise regulator to mitigate learners’ poor performance in Grade 10 mathematics classrooms Hagoramagara, Franco This study was both a development and an evaluation study whose aim was to design a Smart Noise Regulator (SNR) technological device and assess its potential in monitoring extraneous noise in mathematics classrooms, with a view of increasing efficiency of teacher control of classroom learning environments. Learners’ classroom noise has been identified to impact on their mathematical performance. Using a technological device, named the Smart Noise Regulator (SNR), this study aimed to mitigate learners’ poor performance in Grade 10 mathematics. The SNR device, which was developed in this study, was designed to generate a signal to learners when their noise level exceeded an appropriate level in each phase of a mathematics lesson. The study explored five main variables associated with learners’ poor performance in mathematics, namely, classroom noise level, inappropriate classroom behaviour, extraneous cognitive load (ECL), learners’ motivation to engage in the lesson, and teaching and learning time. The SNR device was largely infused into a series of single experimental research designs using a multiple-baseline and A-B-A-B designs for three successive years. Study participants consisted of 205 learners and their six mathematics teachers. Six Grade 10 mathematics classes were sampled from a population of 30 schools and two stages of cluster sampling were used. The participating group was drawn from three clusters, each of which had a different environmental noise sources identified as follows: ten schools were closest to the railway line, ten schools were within the inner-city proximity, and ten schools had the oldest school buildings assumed to be possibly subjected to noise from loose decaying building structures. Data related to the noise level were captured using the sound level meter with a computer software and the lesson observation instruction guideline. Data sought to determine numbers and types of mathematics errors that the learners made in three type of tests administered to them in the classroom that was controlled by SNR device, with the noise level range of 50 to 60 dBA and the classroom without the SNR device with the noise level ranging from 70 to 80 dBA. The analysis of the combined data from six schools revealed that the use of SNR device in a mathematics lesson had resulted in an average of 4,8% reduction of classroom noise. Learners’ accuracy in responding to algebraic tasks, Euclidean geometry and basic and mental calculations increased by 23% when the SNR device was used. Incorrect answers decreased by 16% when the SNR device was used. About 22.3% of learners’ responses indicated that a noise-infested environment of 70 to 80 dBA seemed to imposed relatively undesirable constraints to effective learning when compared with a noise environment of 50 to 60 dBA when the SNR device was used.

2021-07-08T00:00:00Z