Electronic Theses and Dissertations (Masters)

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Browsing Electronic Theses and Dissertations (Masters) by Department "Department of Mathematics Education"

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    Exploring learner errors and misconceptions in algebraic expressions with Grade 9 learners
    (University of the Witwatersrand, Johannesburg, 2023-09) Stemele, Bulelwa Penelope; Makonye, Judah; Asvat, Zaheera Jina
    Mathematics is a crucial skill for the acquisition of relevant skills in society and is required for admission to South African universities and other higher education institutions. However, South African learners’ performance in mathematics on local and international educational achievement tests has been a major source of concern. Algebra is one area of mathematics that learners struggle with. Algebra is challenging because it is a more abstract form of mathematics and learners are unable to relate it to their daily lives. Algebra is essential because it serves as the foundation for further study in mathematics and other disciplines. Learners in Grade 9 struggle with the variables, equations, and abstract concepts found in algebra. Most errors and misconceptions that learners commit in mathematics stem from a lack of algebra background knowledge. Therefore, the purpose of this study was to explore algebraic expression errors and misconceptions in Grade 9. The study was based on the Vygotskian sociocultural theory of learning. According to the Vygotskian sociocultural theory, teachers and mathematics manipulative plays an essential role in facilitating learning in their learners Zone of Proximal Development (ZPD). A mixed-methods study was used to explore the errors and misconceptions committed by Grade 9 learners when solving algebraic expressions. The data was collected through tests and learner interviews from a class of 22 Grade9s. After analysing the pre-test data and identifying common errors and misconceptions, an intervention involving the use of algebra tiles to teach algebraic expressions was implemented. Firstly, my study supports the error types identified in the literature. Secondly, my study demonstrates an improvement in performance on the post-test following an intervention using algebra tiles. According to research, the use of manipulatives helps learner construct a conceptual understanding by consolidating abstract ideas. This study adds to previous research indicating the usefulness of manipulatives in mathematics classrooms.
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    Grade 10 Learners errors when operating Integers
    (University of the Witwatersrand, Johannesburg, 2023-10) Naidoo, Sheldon Samuel; Pournara, Craig
    This study focuses on learners’ errors in integers and explores the changes in their errors during their grade 10 year. The data utilised in this study was collected by the WMCS project in 2018. The data was collected from learners of 15 low-performing schools in Gauteng, South Africa. Part of this study consisted of a comparison of two groups of learner responses. The first group comprised of learners of teachers who participated in a professional development course offered by the project in 2016/2017 (TM group) and the second group are learners whose teachers did not attend the course (CNT group). These schools had no prior relationships with the Wits Maths Connect Secondary (WMCS) project. I looked at the responses that grade10 learners made when ordering and operating on integers at two different points of a school year. The tests were written in February and September of the same year and were analysed from a random sample of 196 grade 10 learners from 40 low-performing secondary schools in Gauteng, South Africa. Test items dealt with ordering of integers and operating on integers. Working from a Vygotskian perspective, a framework dealing with concept formation of negative numbers was developed to analyse learners’ test responses. In this study, I focused solely on the responses given by the learners of the two groups and explored the persistency of errors within each group as well as the type of errors found across the groups. Having this data point per learner allowed for further investigations regarding persistent errors and errors which were remediated and waned during the year. Furthermore, it provided an opportunity to detect new errors arising which would impact the learning of other topics. This framework made it possible to identify seven types of errors. The findings show that while learners’ performance improved from pre-test to post-test, many grade 10 leaners still have difficulty with the concept of negative numbers.
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    The Effects of Mathematical Modelling and its Application in Algebraic Functions on Grade 11 Learners’ Performance
    (University of the Witwatersrand, Johannesburg, 2023-07) Ngubane, Sibongiseni; Ekol, George
    To explore the effects of mathematical modelling on Grade 11 learners’ academic performance in algebraic functions, teachers’ self-efficacy and their overall perceptions, is the purpose of this research study. For the achievement of this goal, the research study followed a mixed method for both collecting and analyzing data. However, a pre-test and a post-test, interviews, and a questionnaire were used to collect data. The study content was limited to mathematical modelling in algebraic functions, learners doing pure mathematics in Grade 11, and mathematics teachers in the FET phase only. Eighty-seven (87) Grade 11 learners doing mathematics from one (1) selected school under the ILembe district in KwaZulu Natal participated in the research study, where 44 (51%) formed an experimental group and the other 43 (49%) learners formed a control group. Findings revealed that the experimental group taught through modelling with a guided discovery approach outperformed the control group that was taught through a direct instruction approach to learning. Hence, the difference between the modelling and direct instruction teaching approaches is statistically significant. Six (6) learners from the experimental group were purposively sampled to participate in the semi-structured interviews for the researcher's purposes of exploring learners’ perceptions about mathematical modelling. Learners reported that modelling could improve their level of cognition. Thirty-three (33) mathematics teachers in the FET phase from fourteen (14) high schools in KwaZulu Natal participated in the study by completing a questionnaire about modelling. Findings revealed that teachers have positive attitudes, beliefs, and perceptions about modelling in mathematics education even though there are no teachers’ professional development workshops provided to encourage them based on modelling. This study recommended that the department of education put more efforts into supporting and motivating teachers to implement modelling in mathematics classrooms, provide teachers with professional development workshops based on modelling, design and distribute teaching and learning support documents to all schools providing mathematics, and do follow-up to check the progress in teachers’ developments.