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All Journal Research in Social Sciences and Technology Journal of Advanced Sciences and Mathematics Education
Machaba, Masilo France
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Chemistry Education Mathematics Physics Social Sciences

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An Exploration of Grade 12 Learners’ Misconceptions on Solving Calculus Problem: A Case of Limits Jameson, Goredema; Machaba, Masilo France; Matabane, Mogalatjane Edward
Research in Social Sciences and Technology Vol 8 No 4 (2023): Research in Social Sciences and Technology
Publisher : Research in Social Sciences and Technology- OpenED Network

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46303/ressat.2023.34

Abstract

This case study explored Grade 12 learners’ misconceptions in limits of functions. The study aimed at understanding problems that learners face in learning the concepts of limit by analyzing misconceptions that learners have and identifying the possible sources of these misconceptions to take remedial action. An exploratory research design was adopted, and purposive sampling employed to select 35 Grade 12 learners (21 females and 14 males) who wrote a test on limits. From the 35 learners who wrote the test, five learners were interviewed guided by their written responses. Theoretically, the study was guided by the constructivism theory and used a systematic error conceptual framework to categories the learners` misconceptions according to extrinsic and intrinsic calculus misconceptions. The study sought to answer the questions: (a) What type of misconceptions do Grade 12 learners exhibit in responding to limit questions? (b) What are the possible sources of these misconceptions? The study found that Learners exhibited misconceptions on the limit concept and related symbolism. Learners who had a flawed understanding of algebraic concepts struggled to apply limits correctly. The weak foundation on algebraic skills impacted negatively on their learning of new concepts on limits. The study recommends that, educators should always check and make sure that learners have appropriate prior knowledge before the teaching of new concepts in calculus. It is recommended that that teaching and learning approaches need to be adjusted to give equal weight to both the procedural and the conceptual understanding of mathematical knowledge in learners.
Addressing misconceptions in ratio and proportion: A constructivist approach for enhancing grade 9 learners' understanding Machaba, Masilo France; Madzingira, Daniel Madzingrra
Journal of Advanced Sciences and Mathematics Education Vol 5, No 1 (2025): Journal of Advanced Sciences and Mathematics Education
Publisher : CV. FOUNDAE

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58524/jasme.v5i1.569

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Backgorund: Proportionality, deeply rooted in the fundamental principles of ratio and proportion, is a core component of mathematics education that supports cognitive processes such as problem-solving and reasoning. Despite its inclusion in global curricula, empirical research suggests that students often face significant challenges in applying ratio and proportion in problem-solving scenarios. These challenges are largely attributed to the use of flawed cognitive strategies, resulting in persistent misconceptions.Aim: This study examines the misconceptions regarding ratio and proportion among Grade 9 learners in the Lebowakgomo District, Limpopo Province, and aims to explore how these learners conceptualize and solve related mathematical problems through the lens of constructivist learning theory.Method: Employing a qualitative case study approach, this research utilized tests and semi-structured interviews to gather data from 30 Grade 9 learners. A representative subset was selected for qualitative analysis, with five learners chosen for follow-up interviews to ensure diverse perspectives.Results: The study revealed that learners struggled primarily with problems requiring proportional reasoning, resorting to incorrect strategies such as intuitive thinking, additive methods, incomplete problem-solving approaches, and erroneous use of cross-multiplication.Conclusion: These misconceptions are primarily due to a lack of foundational mathematical skills and conceptual understanding, which impede learners' ability to engage in proportional reasoning. Based on these findings, the study advocates for enhancing teachers' pedagogical content knowledge in ratio and proportion to improve the instructional support provided to learners.
Mathematics student teachers external supervisors beliefs about mathematics: ODeL environment in focus Machaba, Masilo France; Age, Terungwa James; Rankweteke, Puleng Edwin
Journal of Advanced Sciences and Mathematics Education Vol 4, No 2 (2024): Journal of Advanced Sciences and Mathematics Education
Publisher : CV. FOUNDAE

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58524/jasme.v4i2.411

Abstract

Background: There are diverse beliefs regarding the nature of mathematics, which directly influence the teaching and learning approaches adopted in mathematics education. These beliefs range from mathematics being a collection of facts, rules, and skills, to viewing it as a dynamic and ever-evolving discipline.Aim: This study investigates the beliefs of mathematics student teachers external supervisors regarding the nature of mathematics, learning mathematics, mathematics achievement, and their preparedness for teaching mathematics within an Open Distance e-Learning (ODeL) environment to address challenges and improve the effectiveness of Teaching Practice (TP) supervision.Method: A quantitative survey design was employed, utilizing a structured questionnaire adapted from the Firstmath Project. Data were collected from 43 respondents out of a population of 76 mathematics student teachers external supervisors, selected through random sampling across six provinces in South Africa. The analysis framework was guided by Ernest, three conceptions of mathematics: problem-solving, Platonist, and Instrumental views. Descriptive statistics were used to analyze the data.Results: The findings revealed a significant gap in external supervisors understanding of the mathematics classroom as a dynamic environment for teaching and learning. Many supervisors lacked exposure to contemporary pedagogical strategies tailored for the ODeL context.Conclusion: The study recommends the implementation of developmental programs aimed at equipping mathematics external supervisors with innovative approaches to teaching and learning mathematics. Such initiatives would enhance their readiness to support student teachers effectively in an ODeL environment.
Co-Authors Age, Terungwa James Jameson, Goredema Madzingira, Daniel Madzingrra Matabane, Mogalatjane Edward Rankweteke, Puleng Edwin