Investigating the transition between educational levels is one of the main themes for the
future of mathematics education. In particular, the transition from secondary school to STEM …

This conceptual research framework addresses the problem of rote learning by
characterising key aspects of the dominating imitative reasoning and the lack of creative …

What sorts of mathematics competencies must teachers have in order to teach the discipline
well? This book offers a novel take on the question. Most research is focused on explicit …

Over the last three years, in our Early Algebra Thinking Project, we have been studying
Years 3 to 5 students' ability to generalise in a variety of situations, namely, compensation …

How do students think about algebra? Here we consider a theoretical framework which
builds from natural human functioning in terms of embodiment–perceiving the world, acting …

In this chapter our aim is to seek how individuals develop ideas of proof appropriate for their
level of maturity at the time, and how these ideas change in sophistication over the long …

In this paper, the development of mathematical concepts over time is considered. Particular
reference is given to the shifting of attention from step-by-step procedures that are performed …

This article offers a reflection on the findings of three PhD studies, in the domains of,
respectively, subtraction under 100, fractions, and algebra, which independently of each …

In this paper, research on some problematic aspects high school students have in learning
trigonometry is presented. It is based on making sense of mathematics through perception …

The research in geometry and spatial thinking has evolved from studies in psychology.
Initially problem solving was a focus of these studies and it has continued as an area of …