Capitalizing on cognitive load theory and learning by analogy, we propose two instructional methods to learn a complex linear equation (e.g. two-step equation) by building on prior knowledge of a simpler linear equation (e.g. one-step equation). We will examine the proposal theoretically in this paper. In line with the design principles of…

I investigate how and whether a heterogeneous group of first-year university mathematics students in South Africa harness the potential power of a computer algebra system (CAS) when doing a specific mathematics task. In order to do this, I develop a framework for deconstructing a mathematics task requiring the use of CAS, into its primary…

The paper provides a college mathematics student's concept maps, definitions, and essays to support the thesis that language-based prior knowledge can influence students' cognitive processes of mathematical concepts. A group of intermediate algebra students who displayed terms mainly from the spoken language on the first and the second concept…

In the present article, we argue that the conceptual change approach to learning can apply in the case of mathematics, taking into consideration the particular nature of mathematical knowledge and the neurobiological bases of mathematical cognition. In the empirical study that is reported in this article, we investigated ninth graders'…

As children make the transition to school, many things may change for them. Among these are the ways they interact with curriculum areas such as mathematics. This paper explores some of these changes by considering examples of children's mathematical experiences in prior-to-school and school settings and analysing them in terms of the mathematical…