The production and use of explicit models of mathematics are important elements of research in Didactics of Mathematics. In this paper, we present and compare two different European approaches to didactical modelling. The first, centred around the notion of basic idea (Grundvorstellung), arose in German-speaking countries as a development within…

This study explored the perspectives of mathematics teacher educator-researchers (MTE-Rs) on the use of theory in facilitating teacher growth. We adopted the framework of the theory-centered scholarship triangle (Silver & Herbst, 2007) to probe the underlying meanings of perspectives on theory use expressed by MTE-Rs. Qualitative analysis…

This article explores some of the intellectual bases of the apparent cultural divide between the fields of mathematics and mathematics education research. The chasm is in part attributable to epistemologies or theoretical "paradigms", fashionable in education, that dismiss or deny the integrity of fundamental aspects of mathematical and scientific…

Research in mathematics education usually attempts to look into students' learning and other mental processes. It could therefore be expected to build on knowledge acquired within the academic discipline of cognitive psychology. Our aim in this paper is to show how some recent developments in cognitive psychology can help interpret empirical…

Makes a concrete proposal for bridging the gap between theory and practice in mathematics education and establishing a systemic relationship between researchers and teachers. Explains the background and implications of this proposal. Discusses four characteristics of the definition of Substantial Learning Environments (SLE). (Author/LM)

These seem to be very special times for mathematics education. The public interest in the topic has never been greater. Probably the most prominent among the occurrences that occasioned this recent leap in popularity are international comparative studies such as TIMSS and PISA. The fact that, in spite of the ongoing efforts toward reform in…