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This article investigates the knowledge arising in mathematics teachers' planning of how to manage transitions within and beyond dynamic geometry environments in the topic of circle theorems. The notion of situated abstraction is used to elaborate the central TPACK construct within mathematics education and address previous criticisms of the framework, specifically to clarify the distinction between the central construct and the dyadic constructs. Four case-study teachers each participated in a semi-structured interview based upon a pre-configured GeoGebra file. The teachers were asked to demonstrate how they would use the GeoGebra file to introduce students to the circle theorem that the angle at the centre of the circle, subtended by an arc, is double the angle at the circumference subtended by the same arc. The visual and audio aspects of the GeoGebra interviews were recorded and the TPACK framework used to analyse teachers' knowledge arising in the four interviews. The central TPACK construct is illustrated with examples of teachers' strategies for capitalising on transitions within and beyond dynamic geometry environments for the purposes of teaching circle theorems and contrasted with the dyadic construct of TCK. The utility of the theoretical elaboration of the TPACK construct within mathematics education is demonstrated and implications discussed.

This study investigates associations between mathematics pedagogy and teachers' integration of Information Communication Technologies (ICT). As an early adopter of presentation-oriented hardware and software in mathematics classrooms, England represents a critical case for investigating associations between mathematics pedagogy and teachers' integration of ICT into classroom practice. This paper reports the results of a survey of English secondary mathematics teachers' use of ICT (n = 183). Using Rasch analysis to construct a measure of mathematics pedagogy, a consistent trend is found between frequent use of "teacher-centred" software and a more "student-centred" orientation. The analysis also suggests that some "teacher-centred" practices involving ICT may instead be construed as "dominant" practices. Taken together with case-study evidence of teachers' ICT integration from research on technology in education, these findings challenge assumptions about relationships between mathematics pedagogy and ICT integration prevalent in the mathematics education literature.

The article focuses on a study conducted to investigate the role of teachers in promoting the classroom use and integration of dynamic geometry software (DGS) in mathematics education. It reports study's use of instrumental approach to explore the teaching strategies that facilitate instrumental genesis. It explains the concept of instrumental genesis, and discusses the data collection and analysis process of the study. It also states study's findings on the strategies that can be used by the teachers for DGS implementation which include explaining geometric invariance through dynamic variation and resolving functional dependency of the software. Also discussed is the need for further research on the impact of National Curriculum 2007 in England, on teaching and learning of mathematics.