Browsing by Author "Ndlovu, Mdutshekelwa"
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- ItemAlignment between South African mathematics assessment standards and the TIMSS assessment frameworks(AOSIS Publishing, 2012-12) Ndlovu, Mdutshekelwa; Mji, AndileSouth Africa’s performance in international benchmark tests is a major cause for concern amongst educators and policymakers, raising questions about the effectiveness of the curriculum reform efforts of the democratic era. The purpose of the study reported in this article was to investigate the degree of alignment between the TIMSS 2003 Grade 8 Mathematics assessment frameworks and the Revised National Curriculum Statements (RNCS) assessment standards for Grade 8 Mathematics, later revised to become the Curriculum and Assessment Policy Statements (CAPS). Such an investigation could help to partly shed light on why South African learners do not perform well and point out discrepancies that need to be attended to. The methodology of document analysis was adopted for the study, with the RNCS and the TIMSS 2003 Grade 8 Mathematics frameworks forming the principal documents. Porter’s moderately complex index of alignment was adopted for its simplicity. The computed index of 0.751 for the alignment between the RNCS assessment standards and the TIMSS assessment objectives was found to be significantly statistically low, at the alpha level of 0.05, according to Fulmer’s critical values for 20 cells and 90 or 120 standard points. The study suggests that inadequate attention has been paid to the alignment of the South African mathematics curriculum to the successive TIMSS assessment frameworks in terms of the cognitive level descriptions. The study recommends that participation in TIMSS should rigorously and critically inform ongoing curriculum reform efforts.
- ItemThe effectiveness of a teacher professional learning programme : the perceptions and performance of mathematics teachers(AOSIS Publishing, 2014-12-12) Ndlovu, MdutshekelwaThe purpose of this article is to report on an investigation of the perceptions and performance of mathematics teachers in a teacher professional learning (TPL) programme based on realistic mathematics education (RME) principles, which included a topic on transformations, undertaken by the researcher. Forty-seven Senior Phase (Grade 7–9) teachers took part in the mixed-methods study in which they answered a questionnaire with both closed and openended items. Fifty teachers took an achievement test at the end of the programme. The TPL programme used the RME approach in the design and delivery of mathematical tasks intended to enhance teachers’ mathematical knowledge for teaching. The sessions were conducted in a manner that modelled one way in which RME principles can be adopted as a teacher professional development strategy. The significance of the study is that continuing TPL is acknowledged to contribute to improvement in teaching and learning to address the concern about unsatisfactory learner achievement in mathematics. The responses suggested that the majority of teachers experienced the sessions positively in relation to all but one of the six RME principles. The teachers reported that they took an active part both as individuals and in small groups and expressed their willingness to adopt the type of activities and materials for their classrooms, which is an essential first step in Guskey’s first level of evaluation of a teacher TPL programme. The teachers’ average performance in an achievement test at the end of the topic was 72% which was indicative of modest learning gains at Guskey’s second level of TPL effectiveness.
- ItemAn instrumental approach to modelling the derivative in Sketchpad(AOSIS Publishing, 2011-11) Ndlovu, Mdutshekelwa; Wessels, Dirk; De Villiers, MichaelEncouragement to integrate information and communication technologies into mathematics education curricula is an increasingly universal phenomenon. As a contribution to the discourse, this article discusses the potential use in the classroom of The Geometer’s Sketchpad® (Key Curriculum Press, Emeryville, CA, United States) mathematics software in modelling the derivative and related concepts in introductory calculus. In an empirical study involving first-year non-mathematics major undergraduate science students, a hypothetical learning trajectory (HLT) was conjectured and implemented for students to experience the visualisation and multiple representations of calculus concepts on the Cartesian plane with a computer graphic interface. The utilisation scheme is interpreted through the lens of the instrumental1 approach proposed by Trouche. The HLT was partly informed by the historical development of the derivative as synthesised from the literature on the history of calculus and partly by the affordances, enablements, constraints and potentialities of Sketchpad itself. The findings of the study suggest that when exposed to the capabilities of this software, learners can experience Geometer’s Sketchpad® as an effective visualisation tool or instrument for the representation and learning of the derivative and related concepts in introductory calculus. However, the effectiveness of this tool is not a given or a foregone conclusion − it is a product of the teacher’s instrumental orchestration, gradual learner mastery of the software syntax and careful resolution of theoretical-computational conflicts that can arise during early use of the instrument.
- ItemIntroducing problem-based learning (PBL) into a foundation programme to develop self-directed learning skills(Education Association of South Africa, 2014) Malan, Sharon B.; Ndlovu, Mdutshekelwa; Engelbrecht, PetraThis article reports on the qualitative aspects of a study that examined whether introducing a Problem-based Learning (PBL) approach in a one-year foundation programme can create conditions for learners to develop and sustain self-directed learning skills. This interpretiveconstructivist case study was located in evaluation research. Data were collected by means of classroom observations and interviews with 35 students and 14 former students. Findings indicated that introducing students to a PBL approach did promote more meaningful learning patterns, typified by processing the subject matter critically and self-regulating learning processes. The sustainability of the meaning-directed learning skills was questionable if student beliefs in the approach did not support the activities employed. Introducing PBL into a foundation programme can develop self-directed learning skills in students and set in motion a process of growth towards lifelong learning.
- ItemPedagogical implications of students' misconceptions about deductive geometric proof(SUN MeDIA Bloemfontein, 2012) Ndlovu, Mdutshekelwa; Mji, AndileThe role of proof in school geometry has been a subject of intense debate throughout the twentieth century and that debate persists even today. This study aims to identify and analyse deductive geometric proof difficulties encountered by Bachelor of Education (BEd) in-service student teachers and to propose possible ways of remediating them. The authors conducted a content analysis of responses to a circle geometry item in an achievement test taken by 170 students. Although 78% of the students performed well in the deductive proof item, 22% evidenced misunderstandings or misconceptions which varied in complexity. The misconceptions were analysed into four categories and implications for pedagogy proffered to turn the misconceptions into critical teaching and learning opportunities.