Although the field lacks a theoretically grounded, well-defined, and shared conception of
mathematical knowledge required for teaching, there appears to be broad agreement that a …

The variation theory of learning emphasizes variation as a necessary condition for learners
to be able to discern new aspects of an object of learning. In a substantial number of studies …

We describe and use an analytical framework to document mathematics discourse in
instruction (MDI), and interpret differences in mathematics teaching. MDI is characterised by …

Though written accounts of collegiate mathematics teaching exist (eg, mathematicians'
reflections and analyses of learning and teaching in innovative courses), research on …

Lesson study, a powerful teacher professional development approach, originating in Asia,
has spread globally. Although the positive effects of lesson study on teacher learning and …

This paper aims to offer a new perspective on role modelling by examining adolescents' own
efforts to lead a morally virtuous life. While traditional approaches to moral education …

Despite its centrality in teaching, what it takes to identify the goals of instruction and use
those goals to manage the work has yet to be articulated in ways that it can be adequately …

This article deals with the roles of variation problems (“one problem multiple solution” and
“one problem multiple changes”) as used in Chinese textbooks. It is argued that variation …

Examples can play a critical role in the exploration of conjectures and in the subsequent
development of proofs. Although proof has been an object of extensive study, there is more …

Studying teaching behavior in controlled conditions is difficult. It seems intuitive that a
human learner might have trouble reliably recreating response patterns over and over in …