This study investigated children's knowledge of the addition of fractions with unlike denominators. It focussed on the strategies used by children to add fractions with unlike denominators. A cross-sectional survey of Grade 8 children in schools in two districts in Ghana was used. A test on the addition of fractions with unlike denominators was…

This article discusses the findings of a case study that explored the use of explanatory talk in mathematics teacher education lessons on how to teach the concept of place value. The Mathematics Discourse in Instruction framework guided the study, in particular the element of naming in explanatory talk. Three teacher educators' lessons on the…

The literature describes different stances concerning the focus on how mathematics should be taught, with some preferring a conceptual knowledge approach and others a procedural knowledge approach. The current study investigated the relationship between students' conceptual and procedural knowledge in a calculus context. To better understand the…

The derivative is a central concept in calculus and has applications in many disciplines. This study explored students' understanding of derivatives with a particular focus on the graphical (geometric) representation. The participants were four Mathematics Honours students from a university in Lesotho. Data were generated from the written…

In this paper we focused on university mathematics students' mental constructions on the concept limit of a sequence. The aim was to explore the nature of the mental constructions and to contribute to Action-Process-Object-Schema (APOS) theory in terms of instructional strategy for teaching limit of sequences. The belief that understanding…

One of the biggest challenges for primary school children is moving beyond the use of counting in calculation. The purpose of this study was to investigate how Zambian Grade 1 to Grade 4 children at primary school see a group of 10 as an effective pattern and structure with the given concrete material. The study consisted of three phases…

The aim of the study was to determine the effects of a dialogical argumentation instructional model (DAIM) on pre-service teachers' ability to solve conceptual maths-in-physics (MIP) problems. Using a quasi-experimental design the study included two equal groups of pre-service teachers (N = 40) to follow two instructional methods in which the…

This exploratory study investigated 10 pre-service mathematics students' understanding of vector subspaces at a university in Zimbabwe. The study involved an in-depth document analysis of the students' written responses to five items based on the vector subspace concept. An APOS (Action--Process--Object--Schema) approach was used to identify the…

Ratio and proportion have many daily life applications and hence form an important part of the Mathematical Literacy (ML) curriculum in South African schools. The purpose of this study was to explore ML teachers' application of ratio in an assessment task with multiple measure spaces set within the real-life context of the need to establish the…

The concept of pattern recognition lies at the heart of numerous deliberations concerned with new mathematics curricula, because it is strongly linked to improved generalised thinking. However none of these discussions has made the deceptive nature of patterns an object of exploration and understanding. Yet there is evidence showing that pattern…

This paper reports on the findings from individual interviews and focus group discussions involving six teachers implementing the Singapore Mathematics Curriculum (SMC) in the Foundation Phase (Grade R to Grade 3) in a school in South Africa. The interviews presented an opportunity to explore teachers' experiences with their attempts to use the…

This study is part of ongoing research in undergraduate mathematics education. The study was guided by the belief that understanding the mental constructions the pre-service teachers make when learning matrix algebra concepts leads to improved instructional methods. In this preliminary study the data was collected from 85 pre-service teachers…

This paper reports a study on the effect of using the Lakatosian heuristic method to teach the surface area of a cone (SAC) on students' achievement according to Bloom's taxonomy levels. Two groups of students (experimental and control) participated in the study. The experimental group (n = 20) was taught using the Lakatosian heuristic method…

The purpose of this study was to explore and compare the proficiency of Grade 11 Mathematics and Mathematical Literacy (ML) learners in solving two problems based on the temperature conversion formula. The first was a result-unknown problem that asks for the result of a formula for a given input. The second was a start-unknown problem in which the…

Within the South African school curriculum, the section on graphical functional relationships consists of signs which include symbols, notation and imagery. In a previous article we explored the role visualisation played in the way learners understood mathematical concepts. That paper reported on the learners' fixation with the physical features…