Revisiting the Efficacy of Constructivism in Mathematics Education

The purpose of this paper is to critically analyse and discuss the views of constructivism, on the teaching and learning of mathematics. I provide a background to the learning of mathematics as constructing and reconstructing knowledge in the form of new conceptual networks; the nature, role and possibilities of constructivism as a learning theoretical framework in Mathematics Education. I look at the major criticisms and conclude that it passes the test of a learning theoretical framework but there is still a gap between theory and mathematics classroom practice

An analysis of teacher competences in a problem-centred approach to dynamic geometry teaching

The subject of teacher competences or knowledge has been a key issue in mathematics education reform. This study attempts to identify and analyze teacher competences necessary in the orchestration of a problem-centred approach to dynamic geometry teaching and learning. The advent of dynamic geometry environments into classrooms has placed new demands and expectations on mathematics teachers. In this study the Teacher Development Experiment was used as the main method of investigation. Twenty third-year mathematics major teachers participated in workshop and microteaching sessions involving the use of the Geometer’s Sketchpad dynamic geometry software in the teaching and learning of the geometry of triangles and quadrilaterals. Five intersecting categories of teacher competences were identified: mathematical/geometrical competences, pedagogical competences, computer and software competences, language and assessment competencies.Mathematics EducationM. Ed. (Mathematics Education

Alignment between South African mathematics assessment standards and the TIMSS assessment frameworks

Please cite as follows:Ndlovu, M., & Mji, A. 2012. Alignment between South African mathematics assessment standards and the TIMSS assessment frameworks. Pythagoras, 33(3):1-9, (Art. #182), doi:10.4102/pythagoras.v33i3.182.The original publication is available at http://www.pythagoras.org.zaSouth 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.http://www.pythagoras.org.za/index.php/pythagoras/article/view/182Publisher's versio

Simulated computer adaptive testing method choices for ability estimation with empirical evidence

Computer adaptive testing (CAT) is a technological advancement for educational assessments that requires thorough feasibility studies through computer simulations to ensure strong testing foundations. This advancement is especially germane in Africa being adopters of technology, and this should not be done blindly without empirical evidence. A quasi-experimental design was adopted for this study to establish methodological choices for CAT ability estimation. Five thousand candidates were simulated with 100 items simulate through the three-parameter logistic model. The simulation design stipulated a fixed-length test of 30 items, while examinee characteristics were drawn from a normal distribution with a mean of 0 and a standard deviation of 1. Also, controls for the simulation were set not to control item exposure or to use the progressive restricted method. Data gathered were analyzed using descriptive statistics (mean and standard deviation) and inferential statistics (Two-way multivariate analysis of variance: MANOVA) for testing the generated hypotheses. This study provided empirical evidence for choosing ability estimation methods for CAT as part of the efforts geared towards designing accurate testing programs for use in higher education

Ensuring Scalability of a Cognitive Multiple-Choice Test through the Mokken Package in R Programming Language

Abstract: This study investigated the scalability of a cognitive multiple-choice test through the Mokken package in the R programming language for statistical computing. A 2019 mathematics West African Examinations Council (WAEC) instrument was used to gather data from randomly drawn K-12 participants (N = 2866; Male = 1232; Female = 1634; Mean age = 16.5 years) in Education District I, Lagos State, Nigeria. The results showed that the monotone homogeneity model (MHM) was consistent with the empirical dataset. However, it was observed that the test could not be scaled unidimensionally due to the low scalability of some items. In addition, the test discriminated well and had low accuracy for item-invariant ordering (IIO). Thus, items seriously violated the IIO property and scalability criteria when the HT coefficient was estimated. Consequently, the test requires modification in order to provide monotonic characteristics. This has implications for public examining bodies when endeavouring to assess the IIO assumption of their items in order to boost the validity of testing

The effectiveness of a teacher professional learning programme : the perceptions and performance of mathematics teachers

Please cite as follows:Ndlovu, M. 2014. The effectiveness of a teacher professional learning programme: the perceptions and performance of mathematics teachers. Pythagoras, 35(2):1-10 (Art #237), doi: 10.4102/pythagoras. v35i2.237.The original publication is available at http://www.pythagoras.org.zaThe 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.http://www.pythagoras.org.za/index.php/pythagoras/article/view/237Publisher's versio

University-school partnerships for social justice in mathematics and science education: the case of the SMILES project at IMSTUS

My purpose in this paper is to situate a university-school mathematics and science education partnership within a social justice perspective in education. The focus of the systemic intervention endeavour was school-based teacher professional development in which university-based facilitators embarked on class visits with the aim of identifying teacher needs, co-teaching and offering professional support over a three-year period. This was in contrast to evaluation (inspection visits) often undertaken by the subject advisors under the auspices of the Department of Education which, for historical reasons, tend to be viewed with suspicion by teachers and teacher unions. Five historically disadvantaged secondary schools and their 10 feeder primary schools were involved in this study with a view to providing equal opportunities to learners from marginalized communities in the Cape Winelands district of the Western Cape. Initial results suggest that an intervention programme that is responsive to local needs can go a long way in bringing about collaborative teacher professional development that leads to reflective practice in professional learning communities and can add value to the quality of student achievement in the gateway subjects of mathematics and science

Modeling with Sketchpad to enrich students' concept image of the derivative in introductory calculus : developing domain specific understanding

It was the purpose of this design study to explore the Geometer’s Sketchpad dynamic mathematics software as a tool to model the derivative in introductory calculus in a manner that would foster a deeper conceptual understanding of the concept – developing domain specific understanding. Sketchpad’s transformation capabilities have been proved useful in the exploration of mathematical concepts by younger learners, college students and professors. The prospect of an open-ended exploration of mathematical concepts motivated the author to pursue the possibility of representing the concept of derivative in dynamic forms. Contemporary CAS studies have predominantly dwelt on static algebraic, graphical and numeric representations and the connections that students are expected to make between them. The dynamic features of Sketchpad and such like software, have not been elaborately examined in so far as they have the potential to bridge the gap between actions, processes and concepts on the one hand and between representations on the other. In this study Sketchpad model-eliciting activities were designed, piloted and revised before a final implementation phase with undergraduate non-math major science students enrolled for an introductory calculus course. Although most of these students had some pre-calculus and calculus background, their performance in the introductory course remained dismal and their grasp of the derivative slippery. The dual meaning of the derivative as the instantaneous rate of change and as the rate of change function was modeled in Sketchpad’s multiple representational capabilities. Six forms of representation were identified: static symbolic, static graphic, static numeric, dynamic graphic, dynamic numeric and occasionally dynamic symbolic. The activities enabled students to establish conceptual links between these representations. Students were able to switch systematically from one form of (foreground or background) representation to another leading to a unique qualitative understanding of the derivative as the invariant concept across the representations. Experimental students scored significantly higher in the posttest than in the pretest. However, in comparison with control group students the experimental students performed significantly better than control students in non-routine problems. A cyclical model of developing a deeper concept image of the derivative is therefore proposed in this study.Educational StudiesD. Ed. (Education

Quality elements of after-school programmes: A case study of two programmesin the Western Cape province of South Africa

The qualitative case study reported on here was commissioned and funded by the Western Cape Government (WCG) in partnership with the Cape Higher Education Consortium (CHEC) to inquire into attributes of well performing after-school programmes (ASPs) within the Western Cape provincei of South Africa. The research question of the study was: What quality elements of ASPs can be identified in 2 purposefully selected ASPs in the Western Cape province? In the multiple (double) case study we used interviews and archival data from the 2 ASPs. Using Mott’s Theory of Change (ToC) framework and Socio-Cultural Learning (SCL) theory as analytical lenses, we found that adaptability, strong management, staff commitment, involvement of current and former learners, family involvement, multi-stakeholder partnerships, continuous programme funding, and monitoring and evaluation were central to the success of the ASPs. Upscaling and replication efforts in the province and similar contexts should seriously consider embedding these quality elements in their logic models