The aim of this study is to explore the possibility of introducing the general notions of function and inverse function through a mathematical activity on linear functions, focusing on the quantitative meaning associated to the connection between a relation and its inverse. We present a genetic decomposition, that is, a viable cognitive path for…

In this article, we analyse a script of an imagined classroom interaction from the perspectives of politeness and positioning. The script was written by a prospective teacher, Cara, as part of her Lesson Play. The Lesson Play was prompted by her reflection on how the needs of students who are disaffected with mathematics might be met, an issue…

In this article, a case is made that affect is central in determining students' experience of learning or not learning mathematics. I show how reversal theory (Apter, 2001), and particularly its taxonomy of motivations and emotions, provides a basis for a thick description of students' experiences of learning in a mathematics classroom. Using data…

Presents a study aimed at exploring (a) developmental pedagogy perspectives in early childhood conceptions of shape in space, and (b) evaluating the teacher's work in terms of what is of benefit to children from being involved in this approach to learning. (MM)

Outlines the approach of a study that aimed to observe young children as they constructed meanings for randomness in computer-based setting. Provides a snapshot of two children working with the tools made available in that setting. Uses this picture to begin the formulation of a theoretical framework for the construction of meaning in one…

Described is research which sought to prove the hypothesis that mental models tend to preserve their autonomy with regard to the originals they are meant to represent. The results of this investigation involving 200 Israeli students are presented. (CW)