I like Merrilyn and Vince's phrase" practical wisdom" to denote something of what is needed
to bridge university and school domains of discourse. Wiliam problematised the issue of how …

What types of things do you typically notice as you watch your students in class each day?
For instance, when the bell rings at the start of class, what do you look for as you scan the …

This paper reports on the development of an analytical instrument which identifies
mathematical affordances in the public tasks, questions and prompts of mathematics …

Awareness is a complex concept comprising both conscious and unconscious powers and
sensitivities which enable people to act freshly and creatively in the moment. In the case of …

This article reports on research into primary student teachers' understanding of mathematics
and its teaching undertaken at the Manchester Metropolitan University and funded by the …

The question of how to teach mathematics has become increasingly problematic in recent
years as critics from diverse perspectives have offered wide-ranging, and often seemingly …

BACKGROUND There is evidence from earliest historical records that examples play a
central role in both the development of mathematics as a discipline and in the teaching of …

Many tests were seen as focusing too narrowly on routine procedures and factual
knowledge, whilst paying far too little attention to conceptual understanding, problem …

This paper deals with an idea that plays an increasing role in teaching and in teacher
education-investigating as a powerful paradigm of knowledge construction. Investigations …

This paper seeks to identify actions that can be regarded as building elements of teachers'
classroom practice in mathematical discussion and how these actions may be combined to …