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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.

Despite extensive research on attainment grouping, the impact of attainment grouping on pupil attainment remains poorly understood and contested. This paper presents evidence from a study conducted with 2944 12-13 year olds, from 76 schools in England, who were allocated to between-class attainment groups ('setting') in English and mathematics over the first 2 years of secondary schooling. After controlling for prior attainment, pupils in the top set performed significantly better than pupils in the middle and bottom sets in both English and mathematics. The findings indicate a widening gap in attainment, especially in the case of English. Findings, especially in the case of mathematics, provide more evidence of a relative benefit for pupils placed in top sets than a relative detriment for those in bottom sets.

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.

This paper examines nursing students' experiences of the teaching and assessment of numeracy for nursing. Data from interviews with eight student nurses at a large school of nursing in the United Kingdom are analysed using a constructivist grounded theory approach to explore their perceptions of any disjunctures between the ways in which numeracy is taught and assessed in universities and the broader context in which calculations are carried out by nurses in practice. This paper makes an original contribution through providing an in-depth qualitative exploration of how these disjunctures may arise and hence proposes a change to the focus of numeracy courses and assessments which may begin to resolve some of these tensions.

Despite extensive research on attainment grouping, the impact of attainment grouping on pupil attainment remains poorly understood and contested. This paper presents evidence from a study conducted with 2944 12–13 year olds, from 76 schools in England, who were allocated to between‐class attainment groups ('setting') in English and mathematics over the first 2 years of secondary schooling. After controlling for prior attainment, pupils in the top set performed significantly better than pupils in the middle and bottom sets in both English and mathematics. The findings indicate a widening gap in attainment, especially in the case of English. Findings, especially in the case of mathematics, provide more evidence of a relative benefit for pupils placed in top sets than a relative detriment for those in bottom sets. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

According to Alan Slonsom, "Mathematics without proof is like brandy without alcohol: the spirit of the subject is missing." This author relates how she became motivated to pick proof as an exciting topic to teach. It is important to distinguish between the usage of the word "proof" in everyday life and its meaning in a mathematical context. Proof in everyday life tends to take the form of evidence used to back up a statement. Mathematical proof is something quite distinct: evidence alone might support a conjecture but would not be sufficient to be called a proof. Popular literature defines mathematical proof as "a reasoned argument from accepted truths" (French and Stripp). This article is an overview of the author's research into approaches for teaching proof and focuses on four areas: what people mean by proof, pupil's common misconceptions, levels of proof, and teaching strategies.

Reviews of mathematics teacher development point to a problematic and under-theorized relationship between learning mathematics and learning about mathematics pedagogy. We adopt a Bernsteinian perspective to the design and delivery of a course preparing early career teachers to teach pre-university mathematics. The iterative development and underlying rationale of five ‘key pedagogic messages’ is outlined as a process of tactical design. Ongoing evaluation showed the pedagogic messages provided a critical pivot in managing transitions between thinking about the mathematical content and thinking about how to teach that content. In particular, they provided a means for us, as teacher educators, to make explicit our own thinking on mathematics pedagogy and its operationalization, and hence render it available for reflection and critique. We argue for a design principle of articulating how teacher educators operationalize a few, explicit pedagogic messages; that pre-university mathematics presents a critical site for mathematics teacher education because it facilitates this principle, and that Bernsteinian notions of framing and knowledge structures are useful in designing as well as characterizing pedagogic settings. [ABSTRACT FROM AUTHOR]

Online education is widely heralded as cost-effective and convenient, but there is a recognized 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 SOL mathematics teacher education in a course designed to induct English early career teachers into pre-university teaching. The lenses of ‘teaching-’, ‘social-’, ‘learner-’ and ‘cognitive-presence’ 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 an SOL 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 an SOL course appear to have benefits also for face-to-face learning. [ABSTRACT FROM AUTHOR]

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.