https://pythagoras.org.za/index.php/pythagoras/issue/feedPythagoras2024-03-08T18:13:33+01:00AOSIS Publishingsubmissions@pythagoras.org.zaOpen Journal Systems<a id="readmorebanner" href="/index.php/pythagoras/pages/view/journal-information" target="_self">Read more</a> <img style="padding-top: 2px;" src="/public/web_banner.svg" alt="" />https://pythagoras.org.za/index.php/pythagoras/article/view/781Relating motivation and learning strategies to algebra course results in a foundation programme2024-03-08T18:13:33+01:00Wendy L. Baumgartnerwendybaumgartner@gmail.comErica D. Spangenbergericas@uj.ac.zaGeoffrey V. Lautenbachgeoffl@uj.ac.za<p>Foundation programmes provide an alternate access route for prospective students whose prior academic results exclude direct entry to undergraduate studies. Bridging courses within foundation programmes address gaps in prior knowledge while developing content knowledge and requisite skills to equip students for the rigour of undergraduate degree study. This study looks for relationships between motivation and learning strategies at course commencement and the final course results of 796 purposively chosen participants across four iterative cycles (cohorts) enrolled in an algebra course within a foundation programme at a private higher education institution in South Africa. Data were collected with the <em>motivated strategies for learning</em> questionnaire, and cohort responses were analysed using correlational statistics. Statistically significant differences mainly were detected in the motivation subscales, and the academic performance was largely related to gender and prior mathematics syllabus. Where cohorts are similar, generic interventions designed to equip one cohort may equip others. Specific intervention strategies that target the needs of students based on the needs identified in this study may equip future students to improve their algebraic knowledge.</p><p><strong>Contribution:</strong> The research contributes by augmenting the exiguous literature of studies of students in algebra courses in foundation programmes who aim to progress to undergraduate degree studies. Investigating relationships between motivation and learning strategies at course commencement and final course results within multiple cohorts promotes the development of flexible, relevant intervention strategies that can be implemented timeously. A study of multiple cohorts further allows for improved validity and reliability in conclusions relating to scalability.</p>2024-03-08T08:00:00+01:00Copyright (c) 2024 Wendy L. Baumgartner, Erica D. Spangenberg, Geoffrey V. Lautenbachhttps://pythagoras.org.za/index.php/pythagoras/article/view/763Developing undergraduate engineering mathematics students’ conceptual and procedural knowledge of complex numbers using GeoGebra2024-01-10T13:26:54+01:00Philemon M. Seloanepseloane@uj.ac.zaSam Ramailasamr@uj.ac.zaMdutshekelwa Ndlovumndlovu@uj.ac.za<p>This study explored the utilisation of GeoGebra as a modelling tool to develop undergraduate engineering mathematics students’ conceptual and procedural knowledge of complex numbers. This mission was accomplished by implementing GeoGebra-enriched activities, which provided carefully designed representational support to mediate between students’ initially developed conceptual and procedural knowledge gains. The rectangular and polar forms of the complex number were connected and merged using GeoGebra’s computer algebra systems and dynamic geometric systems platforms. Despite the centrality of complex numbers to the undergraduate mathematics curriculum, students tend to experience conceptual and procedural obstacles in mathematics-dependent physics engineering topics such as mechanical vector analysis and electric-circuit theory. The study adopted an exploratory sequential mixed methods design and involved purposively selected first-year engineering mathematics students at a South African university. The constructivist approach and Realistic Mathematical Education underpinned the empirical investigation. Data were collected from students’ scripts. Implementing GeoGebra-enriched activities and providing carefully designed representational support sought to enhance students’ conceptual and procedural knowledge of complex numbers and problem representational competence. The intervention additionally helped students to conceptualise and visualise a complex rectangular number. Implications for technology-enhanced pedagogy are discussed.</p><p><strong>Contribution:</strong> The article provides exploratory insights into the development of undergraduate engineering mathematics students’ conceptual and procedural knowledge of complex numbers using GeoGebra as a dynamic digital tool. Key findings from the study demonstrated that GeoGebra appears to be an effective modelling tool that can be harnessed to demystify the complexity of mathematics students’ conceptual and procedural knowledge of complex numbers.</p>2023-12-21T06:05:00+01:00Copyright (c) 2023 Philemon M. Seloane, Sam Ramaila, Mdutshekelwa Ndlovuhttps://pythagoras.org.za/index.php/pythagoras/article/view/728Ascertaining Grade 10 learners’ levels of mathematical modelling competency through solving simultaneous equations word problems2023-12-19T08:54:09+01:00Rajendran Govendereditor@pythagoras.org.zaDzivaidzo Machingura3054880@myuwc.ac.za<p>Possessing mathematical competence is a pre requisite for independently comprehending, understanding and applying all features of mathematical modelling in a particular setting. This research study thus explores the mathematical modelling competencies that Grade 10 learners exhibit while solving contextual problems in a mathematics learning and teaching context, with specific reference to using mathematical modelling. Since mathematical modelling is a fairly new teaching strategy used in mathematics teaching some teachers may be ignorant of the skills and competencies required for learners to solve problems efficiently. A mixed-methods approach to this study was decided upon and a case study design used within an interpretative paradigm in an effort to ascertain the levels of mathematical modelling competencies of a non-random sample of 20 Grade 10 learners. Participant learners who attended a Western Cape school were requested to solve a set of word problems involving the use of simultaneous equations. Task based activities and observations were used as a means to collect data, as well as semi-structured interviews to gauge participating learners’ views and experiences. Qualitative content analysis methods were employed together with basic descriptive statistical methods.</p><p><strong>Contribution:</strong> Research findings reveal the limited competence and abilities of the participating Grade 10 learners to make sense of, understand or constructively progress in solving contextual problems, and the challenges they experience to progress through particular stages of the modelling process, such as building and solving models and interpreting the solutions thereof.</p>2023-12-08T06:00:00+01:00Copyright (c) 2023 Rajendran Govender, Dzivaidzo Machingurahttps://pythagoras.org.za/index.php/pythagoras/article/view/742Solving quadratic equations by completing the square: Applying Newman’s Error Analysis Model to analyse Grade 11 errors2023-12-19T08:54:09+01:00Tšhegofatšo P. Makgakgamakgatp@unisa.ac.za<p>Error analysis is an instructional strategy that can assist teachers to identify learners’ areas of weakness in mathematics and that can point to remediation of those errors. This article explores the errors learners exhibit when solving quadratic equations by completing the square using Newman’s Error Analysis Model. A research study explored the errors learners exhibit when solving quadratic equations by completing the square. Newman’s Error Analysis Model provided the analytic framework for the qualitative approach that was used to explore those errors. A diagnostic test with five test items was administered to 35 learners in one secondary school in Limpopo province of South Africa. Subsequently, 12 learners whose scripts featured common mistakes were identified; these learners participated in a semi-structured interview to diagnose the errors. The findings revealed that learners commit comprehension, transformation and process errors. The findings suggest that if the errors that learners make are exposed and made explicit, the errors can be remediated and thereby enhance understanding and learning. The findings of this study indicate that for teachers to understand the types of errors learners commit when solving quadratic equations by completing the square it is vital for them (errors) to be addressed. Mathematics teachers should also consider diagnosing why learners commit those errors, as they would know the strategies to be employed to teach this topic and subsequent topics.</p><p><strong>Contribution:</strong> The findings of this article add value to the current literature by providing empirical knowledge on learner challenges when solving quadratic equations by completing the square. This study provides opportunities for mathematics teachers to focus more on the strategies that would assist learners to understand this topic.</p>2023-12-07T06:10:00+01:00Copyright (c) 2023 Tšhegofatšo P. Makgakgahttps://pythagoras.org.za/index.php/pythagoras/article/view/787The impact of artificial intelligence and the future of ChatGPT for mathematics teaching and learning in schools and higher education2023-12-05T16:49:29+01:00Rajendran Govendereditor@pythagoras.org.zaNo abstract available.2023-12-04T07:10:00+01:00Copyright (c) 2023 Rajendran Govenderhttps://pythagoras.org.za/index.php/pythagoras/article/view/756Conversations reflecting boundary-objects-related details of a teacher’s local practices with spreadsheet algebra programs on variables2023-12-04T08:36:55+01:00M. Faaiz Gierdienfaaiz@sun.ac.zaWajeeh Daherwajeehdaher@gmail.comAwni M. Abu-Samanawni_saman@yahoo.com<p>The ways teachers converse about their work in relation to information and communications technologies (ICTs) are worth studying. We analyse how a teacher converses about her local practices in relation to two spreadsheet algebra programs (SAPs) on variables. During the conversations we noticed that the teacher keeps different policy documents – boundary objects – firmly in view, in relation to the design of the two other boundary objects, namely the two SAPs. The policy documents provide details on the operative curricula which entail the intended, implemented and examined curricula. Of these curricula, the teacher regarded the examined curriculum and associated examinations as most important. Also, she conversed about how she intends to align the design features of the two SAPs with particular policy documents, especially in the context of the South African high-stakes National Senior Certificate examinations and the attendant examination pressure. Our results confirm current professional development (PD) literature suggestions that emphasise fostering coherence, for example between policy boundary objects details and what university-based PD providers do when they interact with school teachers.</p><p><strong>Contribution:</strong> The results provide guidelines for university-based PD providers to integrate SAPs or other ICTs related to algebra and variables by keeping teachers’ local practices in view. These providers should note that different policy-related boundary objects shape the ways teachers understand and converse about their local practices, namely their work at the classroom level.</p>2023-11-30T06:31:00+01:00Copyright (c) 2023 M. Faaiz Gierdien, Wajeeh Daher, Awni M. Abu-Samanhttps://pythagoras.org.za/index.php/pythagoras/article/view/711Talk that supports learners’ folding back for growth in understanding geometry2023-12-04T08:36:55+01:00Kabelo Chuenekabelo.chuene@ul.ac.zaKoena Mabotjakoena.mabotja@spu.ac.zaSatsope MaotoSatsope.Maoto@ul.ac.za<p>In this article, we argue that folding back is successful when the learners engage in exploratory talk. To support our argument, we sourced data from a Grade 10 mathematics classroom of 54 learners who participated in a four-week teaching experiment conducted by the second author. We mainly focused on talks in two groups of learners to address the silence of literature on folding back that alludes to the kind of talk that learners engage in. Data were captured through video recording of learners’ interactions as they worked on the tasks in different sessions. We present these data as transcribed extracts of talks that the learners held and synthesise them into stories through Polkinghorne’s narrative mode of data analysis, also using a process that Kim referred to as narrative smoothing. Pirie and Kieren’s conception of folding back and Wegerif and Mercer’s three ways of talking and thinking among learners were used as a heuristic device for synthesising the stories. The narratives illustrate that exploratory talk promotes folding back, where learners build on each other’s ideas to develop geometry understanding. Therefore, the significance of this article is that for classrooms that wish to promote growth in understanding through folding back, the type of talk that should be normative is exploratory talk.</p><p><strong>Contribution:</strong> Our search of the literature databases has yet to reveal an empirical study that draws attention to exploratory talk’s role in developing learners’ understanding of geometry in South Africa. However, this study is one of those that allude to the support of exploratory talk on folding back in developing geometry understanding. Our findings imply that mathematics classrooms should consider incorporating exploratory talk as part of teaching and learning geometry. Furthermore, studies on engendering exploratory talk in teaching mathematics are recommended.</p>2023-11-30T06:00:00+01:00Copyright (c) 2023 Kabelo Chuene, Koena Mabotja, Satsope Maotohttps://pythagoras.org.za/index.php/pythagoras/article/view/708Mathematics teachers’ use of assessment for learning to promote classroom diversity of learners2023-12-04T08:36:55+01:00Sizwe B. Mahlambiemahlasb@unisa.ac.za<p>Learner diversity should be understood beyond the aspects of race, culture and gender. Learner-centred practices have been highly acclaimed as practical tools to meet learner needs in diverse classrooms. The purpose of this research is to determine whether mathematics teachers can employ assessment to monitor and encourage learner diversity in their classes. Assessment for learning techniques, as per research evidence, has the ability to assist teachers to improve their teaching practices. The article does this by referencing research in which Grade 6 mathematics teachers employ assessment for learning to improve the quality of mathematics teaching and learning. For this purpose, interviews, non-participant observations and document analysis were used from selected teachers to understand teachers’ beliefs about assessment for learning and actual classroom practices. The non-participant observation was conducted in classrooms of different primary schools. Nine mathematics teachers were conveniently sampled from township primary schools in Gauteng as the study participants. The study’s findings revealed that teacher-centred assessment approaches still dominate mathematics classrooms. Furthermore, it could be deduced that mathematics teachers have classroom assessment challenges that hinder the promotion of learner diversity as it relates to assessment practices. Therefore, the study provides an understanding of the role of a teacher in responding to learner needs and academic development in mathematics through assessment for learning.</p><p><strong>Contribution:</strong> The research contributes to primary school mathematics teaching by focusing on the practical undertaking of assessment for learning and its relevance in meeting the diverse needs of learners.</p>2023-11-23T08:00:00+01:00Copyright (c) 2023 Sizwe B. Mahlambihttps://pythagoras.org.za/index.php/pythagoras/article/view/788Acknowledgement to reviewers2023-12-04T08:36:55+01:00Editoial Office10ts.srsupport@pythagoras.org.za<span>No abstract available.</span>2023-11-20T06:30:00+01:00Copyright (c) 2023 Editoial Officehttps://pythagoras.org.za/index.php/pythagoras/article/view/767Mathematics education for relevance, responsiveness, and viability in Africa within the Fourth Industrial Revolution era2023-12-04T08:36:55+01:00Rose S. Maotosatsope.maoto@ul.ac.zaNo abstract available.2023-11-06T06:00:00+01:00Copyright (c) 2023 Rose Maoto