In this article we investigate the transparency of language in learning place value in either a Southern African indigenous language (isiXhosa, Setswana, Oshiwambo or Emakhuwa) or a European-based language (Afrikaans, English, German or Portuguese). Since language is a key mediator in developing place value understanding, it is important to…

Developing structure sense is an important part of learning algebra. We investigated learners' structure sense of algebraic expressions involving brackets. This led us to propose the constructs "surface structure" sense and "systemic structure" sense. Using a random sample of 58 Grade 10 learners scoring above 40% in a test, we…

This article revisits and expands upon a previous phenomenographic study characterising the qualitatively different ways in which South African undergraduate physics students may experience the use of +/- signs in one-dimensional kinematics (1DK). We find the original categorisation as applicable for interpreting Swedish university-level students'…

Research on mathematical equivalence, and to some extent, on number structure in early grade mathematics, has shown that most students at primary and secondary levels understand these concepts instrumentally rather than relationally. The study reported in this paper uses a design research approach to explore both mathematical equivalence and…

The low performance of Grade 4 learners in the mathematical concept of word problems involving multiplication remains a concern for many researchers in mathematics education. Several studies conducted have largely focused on improving learners' performance on bare problems involving multiplication, with little focus on contextual problems. The…

This article reports on using open-response questions to reveal the level of, and change in, conceptual understanding of a small sample of Grade 11 learners of trigonometry in a South African high school. The investigation used learner response sheets in a regular classroom with the teacher as researcher. Combining the idea of concept image and…

This article reports on a study that investigated the extent to which 57 Grade 6 students at a particular school have misconceptions regarding equality, with the equal sign as focus. It also investigated this school's three Grade 5 and 6 teachers' mathematical knowledge for teaching regarding equality, again focusing on the equal sign. The…

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…

This paper describes the use of diagrams as self-explanatory tools. It considers the use of diagrams, in general, and more specifically, examines research that is currently being undertaken in the broad field of visualisation. The research participants referred to in this article were Advanced Certificate of Education students and the paper…

This study investigated how a teacher in a multilingual classroom attempted to support learners who are struggling to translate written/verbal mathematics into a symbolic form. Thirty-six Grade ten learners in one multilingual classroom in South Africa were given a written test involving one algebraic question and then a discussion on the solution…