Marthie van der Walt

International comparisons of foundation phase number domain mathematics knowledge and practice standards

Poor mathematics performance in schools is both a national and an international concern. Teachers ought to be equipped with relevant subject matter knowledge and pedagogical content knowledge as one way to address this problem. However, no mathematics knowledge and practice standards have as yet been defined for the preparation of Foundation Phase student teachers in South Africa. To make recommendations for the drafting of such standards for final year Foundation Phase teachers, we compared different policy documents. We performed a document analysis on policy documents from South Africa, The Netherlands, Australia and North Carolina (United States of America), all of which addressed the number domain in mathematics. Our findings indicate that knowledge standards ought to include subject matter knowledge, while practice standards require pedagogical content knowledge, noting that neither of these are fulfilled in the education system in South Africa at present.

Enabling Metacognitive Skills for Mathematics Problem Solving: A Collective Case Study of Metacognitive Reflection and Awareness.

Metacognition encompasses knowledge and regulation that, through reflection, sustain problem solving behaviour. How metacognitive awareness is constructed from reflection on metacognitive knowledge and regulation and how these reflections enable metacognitive skills for Mathematics problem solving remain unclear. Three secondary schools representing instrumental case studies are collectively reported here. In the quantitative part, a Mathematics word problem and a reflection questionnaire were administered to all Grade 8 and 9 learners (n = 609). From each school, a top achiever in Mathematics was invited to an individual interview in the qualitative part (n = 3) and was video recorded while solving a Mathematics word problem. The findings suggest that metacognitive reflection is embedded in the regulatory process and fosters metacognitive awareness. Metacognitive reflection constructs person, task and strategy awareness, particularly through planning and monitoring as it assembles the metacognitive skills necessary for Mathematics problem solving.

Systems Engineering Training in Engineering Education

The Engineering Council of South Africa (ECSA) emphasizes the role of project management, interdisciplinary projects, and other non-engineering skills that engineers inevitably will use in their careers. An excellent mechanism with which to achieve this goal is to use systems engineering and project management as teaching modules and in metacognitive fashion. This can be done in different ways, but a common thread is required over the period of the engineering course. As a result, students are exposed to engineering skills such as requirements analysis and management, specification practices, behavioral analysis, and project management. Systems engineering, when applied properly, draws together all aspects of engineering, including human, legal, economic, environmental, and other requirements, while project management draws together interpersonal skills. Ethics, entrepreneurship and other soft skills are taught under the same umbrella modules in order to show relevance that has previously been lacking.

Addressing Multi-language Diversity in Mathematics Teacher Education Programs

In this chapter, mathematics teacher educators (MTEs) from two different environments, namely South Africa (RSA) and the United States (US), join together to share our insights on the role that MTEs might play in the preparation mathematics teachers need in order to address language diversity in their mathematics classrooms. Although from two different contexts, we believe there are more similarities than differences in the issues and challenges MTEs face who must prepare and support teachers. Hence, we begin by raising awareness of some issues involved in helping students learn to read, write, speak, and listen to mathematics—a foreign language for most students, regardless of their English language proficiency. We then discuss issues related to orchestrating classroom discourse, with special attention to multilingual mathematics classrooms. We end by sharing strategies MTEs might use in preparing teachers to teach students from linguistically diverse backgrounds.