This article describes a sequence of design research projects, some exploratory others more formal, on the teaching of modelling and the analysis of modelling skills. The initial motivation was the author's observation that the teaching of applied mathematics in UK high schools and universities involved no active modelling by students, but was…

Much remains under-researched in how learners make use of domain-specific feedback. In this paper, we report on how learners' can be supported to overcome logical circularity during their proof construction processes, and how feedback supports the processes. We present an analysis of three selected episodes from five learners who were using a…

Different conceptualizations exist about the components of the knowledge teachers need to teach mathematics with professional consciousness, and a researcher needs to describe and assess that knowledge. The fact, however, is that different conceptualizations respond to different needs, and thus, the variety is even a chance to develop the field…

As a component of the ongoing development of the mathematics curriculum in China, we compare the country's high school mathematics textbooks with those of several other countries. We base our analysis on the assumption that textbooks, as primary printed teaching resources, are key tools for interpreting educational policy. In this paper, we…

Lesson Study is rapidly becoming one of the most adopted models of teacher professional development worldwide. In this paper, we examine the teachers' discussions that are an integral part of the Lesson Study research cycle. In particular, we investigate the "dialogic mechanisms" that enable teachers' pedagogical intentions to be…