In education systems where out-of-field secondary mathematics teachers have become more prevalent, policy responses have included funding programmes to address these teachers' professional development needs. We examine the implications of programme design for the professionality of out-of-field teacher participants by analysing and comparing three government supported professional development programmes that have been implemented over the last 20 years, two in England and one in Ireland. We review research-based reports of these programmes by analysing the explicit or implicit ways that different professionalities for teaching mathematics are supported. We do this principally through analysing the forms of knowledge, agency and sociality integral to the programmes, supported by considering the programmes' modes of professional learning, and material and systemic arrangements. The application of the theoretical frameworks provides a model for the analysis of other programmes. The analysis draws attention to how policy supported programmes offer the potential to extend teachers' existing professional identity to also embrace being a mathematics teacher or alternatively positioning them as technicians who teach mathematics.

The concept of fidelity is important to the implementation of mathematics education innovations. However, viewing fidelity as only adherence to protocols and planned activities may mean that the importance of underpinning causal mechanisms or innovation theory are not attended to fully. To expand and clarify the meaning of fidelity, I consider how the constructs of fidelity and theory are used in implementation methodology, including in mathematics education implementation studies. Alongside consideration of fidelity to implementation design as adherence to planned activity, I propose that fidelity to innovation theory is also important. The construct of fidelity to innovation theory supports assessing whether adaptations in implementation are acceptable or positive. I illustrate how these complementary constructs are applicable depending on the innovation theory, the implementation path characteristics, the fidelity focus, the generative instance, and the actor and activity. The impact sheet to this article is available online at 10.6084/m9.figshare.28722908.

Increasingly, debates about school mathematics curriculum and pedagogy refer to evidence. The Office for Standards in Education (Ofsted), the inspection service in England, published a series of research reviews, including one on mathematics. Using features of education review quality, we analyse Ofsted's departure from scholarly norms, identifying a lack of transparency, weakness of research design and search strategy, and lack of rigour in the selection of evidence. Further, cited research is frequently misinterpreted and unwarranted causal claims made due to overgeneralisation and oversimplification. A specific example of this is the misappropriation of research on problem solving leading to recommendations conflicting with both the National Curriculum in England and the findings of other, more rigorous, research reviews. From this analysis, we argue that the mathematics review is an example of "policy-based evidence" and point to alternative ways that inspection evidence can complement mathematics education research to support evidence-informed policy and practice.

Using a theoretical framework of policy assemblage, we analyse current primary mathematics teacher professional development in England, in the context of a transnational policy of mastery in mathematics influenced by East Asian practices. As well as the increased discourse of marketisation, and school and teacher autonomy, there has also been a paradoxical process of greater state influence over the content and form of professional learning. This paper maps the mathematics mastery market to show how marketisation and competition form a mirage that masks state-market assemblage. An analysis of these assemblages illuminates the state’s role in fostering a market whilst also operating as an actor in this market, in this case in mastery professional development. Within the mastery market, tensions arise between the phenomena of replication and isomorphism and differentiation of ‘offers’ that develop affinity groups and networks. Thus, we extend previous descriptions of the hierarchy, markets, and networks, and the roles of state funded actors within teacher professional development by identifying the importance of multiplicity of logics, assemblage as a process of labour, and the dynamic nature of relationships and activity. Resources to support teacher professional learning are mobilised in competitive processes with apparent choice hiding state direction.

Transformative professional learning is connected to educational and social transformation and possibilities for critical forms of teacher professionalism. Examining and fostering this connection requires greater conceptual clarity about these constructs and how they are enacted. A conceptual review, combining narrative and systematic methods, was undertaken of research on transformative professional learning that embraced educational and social change, and of accounts of professional learning associated with critical forms of professionalism: activist, transformative, and democratic. A common analytical framework was used consisting of modes of professional learning, educational purpose, knowledge, sociality, agency, and material and systemic arrangements. The conceptual framework used in this review has wider potential for analysing professional learning and its outcomes. The review indicates that transformative professional learning is under-theorised with accounts emphasising only one or two features, usually agency, collaboration, or educational purpose. We argue that transformative professional learning should be grounded, additionally, in clarity about purpose, knowledge, and the relationship to knowledge that is developed. Different possibilities for enacting professional learning are identified that can foster critical teacher professionalism, including those rooted in teacher activism connected to wider social movements.

Trauma-informed practice in education is an area of growing interest in England and internationally. Embracing trauma-informed practice in schools requires trauma and related content to be included in teacher education. Over a period of eight years, a short course was developed and incorporated into the teacher preparation programmes at a large university in England. Through methods of teacher educator self-study and autoethnography, we examine the process of the course’s development and identify mechanisms, enablers and barriers to change in the current policy context of teacher education in England. Important factors that supported change were the gradual development, external collaboration, positive outcomes as a warrant and source of motivation, the development of champions and enthusiasts for trauma-informed practice, and departmental leadership support. Barriers to the development were the constraints of prescribed content on initial teacher education courses, prevailing practices in some schools and settings, challenges in adapting material suitably for all education phases, and some beginning teachers’ responses to personally relevant course content. The successful introduction of the short course demonstrates that inclusion of trauma-informed content in initial teacher education is possible even in an unfavourable policy environment.

We describe a pathfinding collaboration in England to develop a short course for beginning teachers against the background of marketization of teacher education and schooling and pervasive accountability regimes. The aims and structure of the short course are described. We then draw on reflections by course leaders and tutors on their experiences and feedback from the short course evaluations and course participants. We consider outcomes of the course and tensions and issues in course development and delivery, in relation to: current teacher preparation policy; conflicting discourses and practices in schools; models of learning across the age phases; ethical and practice dilemmas concerning individual beginning teachers’ experiences; and to developing trauma-informed practice in our department, given competing priorities and views. We conclude by discussing future development plans to further develop the introductory course, embedding trauma-informed practice across the wider teacher preparation program, specific developments in the early years, addressing issues of teacher well-being, and attending to the relationship of trauma-informed practice and social justice.

Life on Planet Earth is changing in response to the actions of humans to a degree that can be considered a crisis. Mathematics educators have not yet responded adequately to the challenges of this crisis. We propose a relational, dialogic perspective on mathematics education through which mathematics educators can understand and enact their responsibilities. A dialogical stance leads to an ethics calling on our answerability and responsibility in relation to the living world. We use this perspective to reflect on previous research in mathematics education that seeks to respond to environmental issues. We look back to consider work that has addressed the relationship of mathematics and of mathematics education to the living world and draw out links to a dialogical stance. We conclude with questions for research and practice for mathematics education to respond to the ecological crisis.

Neoliberal policies dominate in many parts of the world, setting a frame within which education practices are frequently constrained. In mathematics, perhaps more than other subjects, these constraints seem to be more keenly felt, not least because of the economic value placed on mathematics expertise and the related effects of performativity and accountability. In this symposium we explore potential sources of support that may enable mathematics teachers to challenge orthodox practices, facilitate creative responses to and/or rejections of policy constraints as they negotiate agency over their practice and their learning.

Evaluations of professional development programmes often seek to represent definitive outcomes, with phenomena posited as discrete, bounded and independent entities, and researchers positioned as external actors. An alternative is to understand the complexity of these relationships as entanglements by applying Baradian concepts. The value of this is illustrated through the example of the evaluation of the Mathematics Teacher Exchange (MTE). The MTE is a transnational professional learning programme, part of a policy described as learning from East-Asian mathematics teaching to introduce 'teaching for mastery' in England. Four instances of entanglement are analysed. The first two of these relate to the entanglement of evaluation processes and the mastery innovation in knowledge production. The other two examples are entanglements and diffractions that are found in changes in pedagogical practice related to mathematics representations and ways learners are grouped in classrooms. Although the transnational nature of the MTE is unusual and specific to the current English context, similar entanglements may be found in more locally generated teacher change initiatives and in their evaluation. Thinking in terms of entanglements adds another conceptual tool for sociomaterial and related analysis and also draws attention to our ethical responsibility for these relationalities.

Increasingly, educational practitioners committed to social justice embrace trauma-informed practices and those who advocate for and enact trauma-informed practices are committed to social justice. However, connecting social justice to trauma-informed practice requires greater conceptual clarity than is currently found, given the malleable meanings of both 'trauma informed' and 'social justice'. Further, the complex relationship between these educational aims is under-examined. To address these issues, an analytical framework is developed that brings together a model of forms of trauma-informed practice in education with orientations to social justice. This draws on models of social justice developed in social work and teaching, and teacher education. Applying this framework to trauma-informed practice indicates that trauma- informed practice, as so far developed, generally has either a conservative or a socially liberal social justice orientation. Practices are proposed that align with a critical orientation, which attends to cultural and structural relationships implicated in trauma and adversity in childhood. A critical orientation should not only consider practice but also be informed by further theoretical, philosophical and ethical engagement as part of a project of activist professionalism across educational professions.

This chapter has two main aims. First, to examine where the current focus on mastery has come from and how the word mastery is being used. Second, to consider the evidence that what is being promoted in the mastery brand might benefit students and teachers. Policymakers in England promote East Asian informed classroom practices, but not the very different conditions of service of teachers in relation to the amount of class contact and the amount of time for paid professional development. Education seems to have fashions. Perhaps, like with clothing styles, once something has become fashionable it is easy to forget that what is currently the trend was not always the case. There is a long history of looking overseas for ideas to improve mathematics teaching in England, for example this informed the National Numeracy Strategy.

School life in England (and beyond) is temporally structured, with learning planned as a time-limited activity, both within lessons and across units of work. Discourses of performativity and measurement pervade school life in many societies and, what we call regulated time controls school-based learning. In particular, primary mathematics learning is often marked by a focus on speed and pace and on children and teachers demonstrating progress against fragmented goals. Taking this as an exemplar, and in the context of the pedagogical approaches promoted through two curriculum development projects, we consider disruptions to regulated approaches to learning as children and teachers work collaboratively on mathematical activities. We argue that the expansive timescape that emerges is generated through extended timescales and through an acceptance of unfinishedness, a key change from usual school mathematics that leaves mathematical meaning making open to revision, providing a more meaning-full experience of primary mathematics.

This guide accompanies the following article: Boylan, M., Adams, G., Willis, B., Coldwell, M. & Demack, S. (2018) Theorising variation in engagement in professional and curriculum development: Performativity, capital, systems and purpose. Review of Education, https://doi.org/10.1002/rev3.3140 Policymakers and school leaders seek to improve the quality of teaching through curriculum innovations and professional development programmes, increasingly drawing on evidence-based approaches. For innovations involving teacher professional learning, a causal connection is posited between professional development activities, teacher engagement in them, changed practices and outcomes for learners. However, implementation and teachers’ engagement in professional development activity varies. Reasons for this include the influence of both the local and wider systemic environment in which the activity takes place and actors’ relationships to these environments. Currently, both environments and actors’ relationships are often shaped by performativity discourses and pressures. Typical implementation and process evaluation methodologies are limited by a focus on the easily measurable, often using tools that do not support fine-grained understanding of how actors’ situations, purposes and systemic influences, and the interrelationships between these, mediate and shape different degrees of participation. Developing more in-depth accounts are hindered by a relative lack of theorisation of context in relation to professional development. The paper uses a set of theoretical constructs to provide a stronger account of the variation and engagement in participation in such activity, with particular attention paid to the way school and teachers’ positioning within performativity systems influences participation. Constructs employed are teachers and schools’ positioning in terms of relative degrees of systemic privilege or disadvantage—understood as economic, cultural, social and symbolic capital—figured worlds and system coupling. The paper demonstrates that two of the ways governmental education policymakers seek to improve the quality of teaching—through, first, the use of accountability measures and, second, professional development and innovation programmes—can have contradictory effects, leading to differences in the capacity of schools to engage in and lead innovations and professional development. Important here is the extent of alignment between the school and department's culture—its figured world and purposes—and the purposes of the innovation or professional development. One specific way to address this is to ensure that government-funded innovations seek to involve the commitment of school leaders to allow participating teachers to engage in professional experimentation. Another way is to build into professional development programmes support for participants to act as ‘adaptive system leaders’—in other words, teacher leaders who consciously change the situation in which they are working and so understand the dynamics of change. These implications for government policymakers are paralleled for those developing local policies for schools or clusters of schools such as multi-academy trusts. Attention needs to be paid to avoiding contradictions between pressures on teachers to perform and on effective professional development that should often promote professional experimentation. Teacher leaders need support for agency to lead change adaptively in response to local circumstances. A second important implication is that the study indicates that certain types of school are more able to engage in and take up opportunities. The paper identifies that government policy in relation to performativity and quasi-marketisation may undermine its other policy priorities for social mobility, ‘closing the gap’ and programmes such as the pupil premium. Policymakers and funders of innovations and professional development can potentially ameliorate these effects by recognising the need to offer additional resource and incentives to schools in most need. To some extent this is being addressed in England through the Teaching and Leadership Innovation Fund (TLIF) and Opportunity Areas initiatives. Even so, there can be gaps between rhetoric and even the performance of collaboration or sharing on the one hand, and a collective engagement in experimentation on the other. For policymakers, funders and school leaders, addressing ways to improve engagement and participation in professional development opportunities such as the MRP is clearly important, and if conditions are optimised for engagement then improved pupil outcomes may follow. Implicitly, optimal conditions involve a looser coupling to performativity systems or indeed a loosening of these peformativity systems. There is some evidence in England of the schools inspection service Ofsted reflecting on the negative consequences of overly focussing on examination outcomes as the main marker of school quality. The study reported in this paper supports such reflections. A further implication of this analysis is that well-positioned schools may come to dominate the professional development opportunities made available, or at least flourish from them the most - indeed they may already be doing so. At the same time, other schools that are arguably in greater need are not able to fully access such opportunities owing to other inhibiting factors. School leaders who are committed to teachers’ experimentation and professional learning can consider the examples of schools discussed in the paper such as Beech and Sycamore in which teachers are supported to engage in PD opportunities in spite of accountability pressures. This suggests the need to decouple teachers and leaders from performativity systems, at least in relation to innovations. At schools such as Hawthorn and Maple, which are high capital and entrepreneurial, leaders might consider the extent to which they are ‘walking their talk’ in terms of enacting innovation in their own schools. In all schools, it is clear that if teachers who engage in external professional development are not coupled to the department then the potential benefits will be restricted to the teachers participating. Organisations providing professional development opportunities and professional development facilitators should consider including within programmes and PD activities, content on aspects of the micro-politics of instigating and leading change in the classroom and when working with colleagues.

Background: Current policy discourses emphasise the importance of evidence in education, including evidencing the impact of teacher professional learning on student outcomes. Randomised controlled trial (RCT) designs are promoted to measure 'impact'. Recent debates about this reflect longer standing methodological disputes. Advocates of comparative approaches contend that these are uniquely capable of establishing causality. However, others dispute this and consider their application in education as often being flawed. Whilst acknowledging the importance of these debates, our concern is how RCTs and similar evaluation designs are specifically used to evaluate innovations in which professional learning is important. Purpose: Arguably, professional learning is often under-theorised within experimental and quasi-experimental designs. The purpose of this paper is to address this by encouraging developers of innovations and evaluators to consider a proposed typology of professional learning and other important relevant methodological issues. This is so that developers of innovations that involve professional learning are better able to theorise their endeavours and to support more appropriate design of RCTs and other forms of evaluation of innovations. Sources of evidence: Theoretical and methodological literature from diverse fields is drawn on, namely: descriptions of RCT implementation and process evaluation designs; research on effective professional development; and theoretical models of professional learning. Insights and theories from this literature are used to develop and illustrate the typology and to identify methodological concerns and potential ways to address these. Main argument: In trials of those innovations that involve professional learning, there is both assessment of the extent to which professional learning occurs and also of whether resulting changes in practice improve outcomes. A novel typology of three different ways that professional learning may occur in innovations is proposed. This is related to the centrality (or not) of professional learning to the innovation's success and related to the form and purpose of the professional learning involved. The three analytical categories described are pedagogical professional learning, technical professional learning and curriculum professional learning. Based on this typology, features of professional learning that are likely to lead to impact on student outcomes are discussed. Tensions are identified between the implementation of experimental and quasi-experimental designs and interpretation of resulting evidence. Further, tensions are identified between the complex and recursive nature of pedagogical professional learning systems and the models of linear pathways in some RCT designs. This is illustrated by discussing examples of innovations and trials. Conclusion: The proposed typology and greater theorisation of professional learning can support more robust evaluation design. It is important to assess rigorously teacher learning alongside changes in student outcomes.

'Mastery' is central to current policy in mathematics education in England, influenced by East Asian success in transnational assessments. We scrutinise the prospects for mastery pedagogies to improve pupil attainment in English primary schools. The Mathematics Teacher Exchange (MTE)-an element of the mastery innovation-involves teachers visiting Shanghai and then hosting Shanghai teachers in their schools. Informed by programme evaluation, core component practices are analysed, which were implemented by schools belonging to the first cohort of MTE schools. These consist of: varied and interactive teaching; meaningful and coherent mathematical activity; and full curriculum access for all. These elements are supported, optimally, by collaborative, embedded, and mathematically focused professional development. Details of the implemented pedagogy and forms of professional development are reported. Differences from prevailing practice in primary mathematics in England are highlighted. Evidence is reviewed from quasi-experimental trials, reviews and meta-analyses, and rigorous observational studies of the efficacy of practices similar to the MTE mastery pedagogy components in order to assess the prospects for increases in pupil attainment. The analysis suggests that many of the specific practices, if considered individually, have the potential to improve attainment, though overall policy ambitions may not be realised. Based on the review, component practices are identified for which existing evidence justifies immediate implementation by schools and teachers. In addition, practices that would benefit from further testing and evaluation are highlighted.

Internationally, there is increasing emphasis on teacher leadership of professional development. This provides opportunities for teachers to initiate and facilitate professional learning activities beyond their own schools. There is a need for theoretical tools to analyse their leadership activity and how to support it. Constructs from complexity leadership theory and the concept of teacher system leadership are used to develop a framework to analyse the purposes and practices of teacher professional development leaders supported by a national programme for mathematics teacher professional development in England. I argue that the teachers' activities constitute a form of adaptive leadership involving innovating and organising professional development within arenas of leadership, through the processes of mobilising, brokering and the creation of networks. This required engaging in system work' to fulfil purposes connected to both local and system-wide concerns. The teachers were supported by the enabling leadership of headteachers and by national warrants for exercising leadership. The study demonstrates the value of the analytical framework and indicates that a cadre of teacher system leaders can be developed by attending to the interplay of professional development leadership and a wider system-orientated professional identity and by specific support to develop adaptive leadership capacities and skills.