This paper is part of a broader study which explores South African pre-service teachers' use of the jump strategy on the empty number line for enhancing their confidence to do and teach mental mathematics computation strategies. The focus of this paper is the use of micro-teaching in the form of video recordings by pre-service teachers. Forty…

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'…

In this paper, we share details of a South African early grades' number intervention informed by aspects of Davydov's writing on early number teaching and learning. A key part of Davydov's approach to early number teaching involves starting with attention to relationships between quantities rather than with counting. The Structuring Number…

Concerns have been expressed that although learners may solve linear equations correctly they cannot draw on mathematically valid resources to explain their solutions or use their strategies in unfamiliar situations. This article provides a detailed qualitative analysis of the thinking of 15 Grade 8 and Grade 9 learners as they talk about their…

This article reflects critically on the guidance offered to South African teachers in two canonical texts: the Curriculum and Assessment Policy Statements (CAPS) and Mathematics teaching and learning framework for South Africa: Teaching mathematics for understanding (TMU). I make explicit my philosophical orientation, and how 'teaching mathematics…

Background: The co-establishment of social and sociomathematical norms in the microculture of South African classrooms and its possible effects on early number learning has largely been unexplored. Social norms are considered to be general classroom norms that are relevant in any teaching and learning space, whilst sociomathematical norms are…

Learners intending to enter some higher education (HE) institutions in South Africa write the National Benchmark Tests (NBTs) that are expected to provide a measure of their readiness for HE. A large gap exists between the quantitative literacy competencies of many of these learners and expectations at HE level. In this article I explore the…

It is commonly accepted that the knowledge and learning of rational numbers is more complex than that of the whole number field. This complexity includes the broader range of application of rational numbers, the increased level of technical complexity in the mathematical structure and symbol systems of this field and the more complex nature of…

This paper is centred around a framework for studying teaching--Mediating Primary Mathematics (MPM)--developed in the context of the teaching of Whole Number Arithmetic (WNA) in South Africa. Findings from the analysis of four WNA lessons are used to illustrate how the application of the MPM framework can measure nuanced differences in the…

Background: The concept of rational numbers is one of the learner's first experiences with a Mathematics concept beyond the basic skills operations on whole numbers. The personal knowledge of fractions that teachers bring to the teaching context is important because teachers mediate the conceptions that their learners construct. Aim: This study…

The study focused on the errors and misconceptions that learners manifest in the addition and subtraction of directed numbers. Skemp's notions of relational and instrumental understanding of mathematics and Sfard's participation and acquisition metaphors of learning mathematics informed the study. Data were collected from 35 Grade 8 learners'…

In this paper, illustrative excerpts from mathematics lessons are analysed to examine mathematical and multilingual moves between representations within Sepedi and English medium classrooms. Duval's theory of representational registers and the literature on multilingual practices help foreground similarities within and differences between the…

This paper reports on the development of a Learning Pathway for Number (LPN) with the aim of facilitating the teaching and learning of whole number in the early primary grades (Grades R-4) within the South African educational context. The development of the LPN was based on the Dutch Learning/Teaching Trajectory for Whole Number (Van den…

The purpose of this paper is to explore how master mathematics teachers use the concrete-representational-abstract (CRA) sequence of instruction in mathematics classrooms. Data was collected from a convenience sample of six master teachers by observations, video recordings of their teaching, and semi-structured interviews. Data collection also…

There is a general perception that the South African curriculum statements for mathematics create polarity between the 'old' and the 'new', which does not benefit both the teachers and the learners. The new curricula demand a radical shift from the traditional teacher-led approaches that teachers are familiar with, yet does not provide a model of…