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…

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…

This study investigated the extent to which the proposed Factory of Ideas (FOI) teaching approach impacted on students' understanding of energy based on their prior knowledge. The FOI is a didactic approach that, unlike the classic cognitive conflict approach, employs a variety of activities to offer students a scientific conception for comparison…

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…

The mole concept is one of the fundamental concepts in chemistry. However, a number of studies carried out in various countries have shown that teachers and learners face many difficulties in teaching and learning the concept. One of the underlying sources of teaching and learning difficulties of the mole concept identified in literature is the…

Evidence from the literature supports the idea that a hierarchical and coherently organised curriculum fosters meaningful learning. We argue that the learning can only be realised if teaching complements the curricular coherence by allowing learners to make links during the teaching and learning process. The study reported in this paper explores…

Various reasons for underperformance in physical sciences have been found, such as a lack of teachers' content knowledge and a lack of resources. This study looks into the extent of alignment between the various levels of the curriculum on circuit electricity (intended, implemented and attained levels). The research took place in Mpumalanga…

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…

As part of curriculum changes in South Africa, an introductory programming language, Scratch, must first be taught before switching to the well-established teaching of Delphi. The nature of programming in Scratch is considerably different from that in Delphi. It was assumed that the teaching of Scratch as introductory programming language could…

In this paper we focus on how South African students' ideas about the human body are constituted in their descriptions of three different scenarios involving the pathway of a sandwich, a painkiller and a glass of water through the body. In particular, we have studied the way in which the students transferred ideas between the sandwich and the…

The impact of computer simulations on the performance of 65 grade 11 learners in electromagnetism in a South African high school in the Mpumalanga province is investigated. Learners did not use the simulations individually, but teachers used them as an interactive demonstration tool. Basic concepts in electromagnetism are difficult to understand…

In this paper, we focus specifically on Vygotsky's theory of concept formation to gain initial insights into seemingly garbled and incoherent connections we observed in learners' responses to a geometry task. While acknowledging research that is supportive of the van Hiele model as being useful when analysing concept formation in geometry, in this…

Recursion is an important concept for any computer science student to master. Many first year students develop the viable "copies" mental model of recursion and can successfully trace the execution of a simple recursive function. This article discusses a study focused on determining whether the ability to successfully trace a recursive…

This paper reflects on the difficulties students have in understanding, designing and constructing electrical circuits through an analysis of errors they have made in drawing wiring and circuit diagrams. Prior to wiring a model house, a sample of 114 primary school teacher trainees were taken through a programme of instruction in current…