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In the UK, teachers' use of dynamic geometry software (DGS) has remained limited. The importance of the teacher's role is often stated in dynamic geometry research but has been seldom elaborated. This study aims to address the apparent deficiency in research. The author conducted the research in the role of a practitioner-researcher with a high ability year 8 class. By analysing teacher/pupil interactions in a DGS context, elements of instrumental genesis are distinguished in pupils' dialogue and written work which suggest strategies that teachers can employ to facilitate this process. Whilst these strategies are specific to a DGS context, they highlight general principles of mathematics teaching. This paper argues that the focus of research needs to shift away from the context, towards teachers and the strategies they employ.

Online education is widely heralded as cost-effective and convenient, but there is a recognised need to research appropriate pedagogies for synchronous online (SOL) teaching. Prior research suggests that course design, including formative assessment, is critical in achieving accessible and flexible learning episodes. We harness a well-tested theoretical framework to analyse the development of pedagogies for synchronous online mathematics teacher education in a course designed to induct early career teachers into pre-university teaching. The lenses of 'teaching-', 'social-', 'learner-', and 'cognitivepresence' reveal opportunities for improving provision. We show participants' learning of mathematics content knowledge can then appear comparable to that achieved face-to-face, but it is more challenging to design for the growth of mathematics pedagogical knowledge in a synchronous online environment. Many digital tools work well in this medium, but the use of physical tools requires significant development before teacher engagement compares with that achieved face-to-face. However, some approaches developed to address challenges within a synchronous online course appear to have benefits also for face-to-face learning.

Challenging assumptions about relationships between mathematics pedagogy and ICT integration: surveying teachers in English secondary schoolsThis 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 'studentcentred' 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.