This paper addresses the continuing need for mathematics teachers to enrich their mathematical knowledge beyond the school curriculum, in order to effectively engage students in creative and imaginative thinking, particularly, but not exclusively, students who show exceptional promise. The author, a retired university professor, works staff and…

This article reports the investigation of change in preservice teachers' conceptions of effective history teaching across a secondary history methods course in a postgraduate diploma of education program. Using concept mapping to plot shifts in their expressed reflections, data were obtained that indicate personal constructs of effective history…

This article presents data from a group of secondary pre-service teachers who used vee diagrams to illustrate their conceptual and methodological analyses of a problem, as part of a required mathematics methods course assignment. The individually constructed vee diagrams were analysed in terms of the extent to which they displayed principles and…

Studies such as the Effective Teachers of Numeracy Study (Askew, Brown, Rhodes, Johnson, & Wiliam (1997) have contributed much to our understanding of what constitutes effective teaching of numeracy. This paper aims to build on these findings and to contribute a model that could be used to understand teachers' numeracy practices and the…

This paper reports an analysis of qualitatively different ways in which teachers experience change in their understanding of subject matter they have recently taught. In this exploratory study, interviews with 31 'typical' teachers from a range of first and second-year university subjects revealed that 20 reported no experience of change in their…

This paper addresses the evidence that secondary school students use to imply that they understand something in mathematics. As part of a larger study, an open-ended questionnaire probing several aspects of metacognitive self-knowledge, was administered to students (N=72) in four schools. Two previously identified types of understanding were…

This paper describes the actions of one secondary school mathematics teacher in establishing a community of mathematical practice within which students acquire not only knowledge and skills, but also the epistemological values of mathematics. Classroom observations over a period of 18 months, together with interview and questionnaire data, are…

This study compares the results of Australian and Taiwanese Grade 10 students (N=2959) on the Students' Perceptions of Teacher Knowledge (SPOTK) questionnaire. The purposes of this paper are to quantitatively compare the mean scores of each item in the two countries and to use qualitative research methods involving classroom observations and…