Peter Grootenboer

Affect and mathematics education

Not only has interest in the affective domain in mathematics educat ion been long standing, but it is an area to which considerable research at tention continues to be directed. Even a casual perusal of MERGA publications, and in particular of the Mathematics Education Research Journal [MER]], of Mathematics Education and Development [MTED], and of the Proceedings of the Annual MERGA conferences, reveals the sustained interest by the mathematics educat ion research communi ty in Australia and elsewhere in beliefs, values, att i tudes and emotions as they relate to mathematics education. Indeed, the most recent four-year ly review of Research in Mathematics Education in Australasia 2000 2003 (Perry, Anthony, & Diezmann, 2004) included, for the first time, an entire chapter on affective issues in mathematics educat ion (Schuck & Grootenboer, 2004). Given this prolonged and persistent interest, it is t imely to publish a special issue of MERJ focused specifically on affective issues in mathematics education.

Leading practice development: voices from the middle

Leadership has long been acknowledged as a significant dimension in effective school functioning and, indeed, school leaders can play a substantial role in professional development of staff. Here we have centred on the practices of leading as opposed to the qualities or characteristics of leaders, and this is emphasised by our use of the term ‘leading’ rather than ‘leadership’. In this article we explicitly focus on the leading practices of practitioners we describe as middle leaders, those with an acknowledged position of leadership but also a significant teaching role. Here we present data from a cross-national study of middle leaders in Australian primary schools and Swedish pre-schools that investigates the leading practices of middle leaders in educational contexts. The article draws on interviews with 22 teachers who have been given the responsibility for leading the practice development of their colleagues; these interviews give voice to this distinctive group of school leaders. In particular, the article draws on the theory of practice architectures to examine the social nature of the language, activities and relationships of leading ‘in the middle’, and the particular conditions or practice architectures that enable or constrain the development of middle leading practices in education. From this analysis we conclude with a definition of middle leading that includes positional, philosophical and practice dimensions. This could then be used to inform the domains of higher education, policy development and school education globally where middle leading practices are well established.

The Affective Domain and Mathematics Education

This is the third chapter on affective issues to appear in MERGA reviews of research in mathematics education and as such reflects the ongoing importance of affective issues to the mathematics education research community. The first two chapters (Grootenboer, Lomas, & Ingram, 2008; Schuck & Grootenboer, 2004) noted a continuing move away from studies on attitudes to projects on beliefs and the consideration of a broader range of affective aspects. In the current review period, 2008-2011, there is a lessening focus on beliefs, a growing focus on identity, and an even spread of studies on other affective aspects.

Mathematics performance and the role played by affective and background factors peter grootenboer and brian hemmings

In this article, we report on a study examining those factors which contribute to the mathematics performance of a sample of children aged between 8 and 13 years. The study was designed specifically to consider the potency of a number of mathematical affective factors, as well as background characteristics (viz., gender, ethnicity, and socioeconomic status), on children’s mathematics performance. Data were collected by surveying the children and drawing on performance ratings from their teachers. A correlation analysis revealed that the relationships between the respective dispositional and background variables with mathematics performance were significant and in the direction as predicted. Moreover, the findings from a logistic regression showed that a combination of these variables was able to appropriately classify students who either were below-average or above-average mathematics performers. We pay particular attention to the influence of certain dispositions with respect to mathematics performance and conclude by detailing the implications of the study for teachers and researchers.

Challenges for teacher education: the mismatch between beliefs and practice in remote Indigenous contexts

The poor performance of Australian Indigenous students in mathematics is a complex and enduring issue that needs a range of strategies to enable success in schooling for these students. Importantly, large numbers of teachers in remote Indigenous contexts are new graduates who, although full of enthusiasm, lack experience. Similarly, many of them are unfamiliar with the demands and nuances of teaching in remote and/or Indigenous contexts. This paper explores the nexus between the beliefs and practices of teachers working in a remote, Indigenous region of Australia. In particular, it proposes that the discrepancy between beliefs and practices found in the reconnaissance phase of a design study is due to the teachers realising that they need to implement changed practices to enable students to learn but having little knowledge of what such practices may look like. This finding has implications for pre-service and in-service teacher education.

Staying alive in academia: collective praxis at work

Internationally, as the twenty‐first century unfolds, there is a burgeoning literature that documents the changing nature of academic work and workplaces. One recurring theme in this literature is the extent to which academic freedom and autonomy are being threatened in higher education settings. In this article, the nature of this ominous threat and what might be done about it are interrogated using praxis as a conceptual lens. On one meaning of praxis, we consider the actions of academics as individuals aiming for ‘right conduct’; on a second meaning, we consider praxis as collective ‘history‐making action’. An analysis of the existing practices of researchers in two international settings revealed particular kinds of practice architectures – collective research practices – that have revitalised and sustained the working lives of these academics. The notion of collective praxis is suggested as a model of intellectual engagement for building communicative connections. It provides a strategic way forward both to enable academic freedom and autonomy and to benefit the institutions in which academics work.

The praxis of mathematics teaching: developing mathematical identities

Mathematics teaching as praxis recognises that teachers are required to continually make morally dense and value-laden decisions about their work. However, mathematics teachers’ practice is constrained by the practice architectures of their field. Therefore, to facilitate effective mathematics pedagogy, it is not enough to attend only to the teachers’ practices without also working to reform the practice architectures within which they work. In this paper, data from interviews and observations with effective mathematics teachers are used to identify and explore aspects of classroom practice where students’ broader mathematical identities are engaged. A praxis lens is employed to examine these aspects and discuss the moral and ethical dimensions of the teacher’s decisions and actions, highlighting the implications for the development of students’ mathematical identities. Finally, the data are examined to identify practice architectures that enhance or constrain the teacher’s capacity for praxis and the student’s opportunities to develop robust mathematical identities.

Facilitating a Culture of Relational Trust in School-Based Action Research: Recognising the Role of Middle Leaders.

Abstract Practices such as formal focused professional dialogue groups, coaching conversations, mentoring conversations and professional learning staff meetings have been taken up in schools and pre-schools as part of long-term action research and development activities to improve the learning and teaching practices. The development of relational trust has long been described in the literature as pivotal for the ongoing ‘success’ of such research and development in sites. In this article, we attempt to re-characterise relational trust as it is accounted for by participants in action research. We present data from a cross-nation study of middle leaders from Australian primary schools and Swedish pre-schools. Middle leaders are those teachers who ‘lead across’; they have both an acknowledged position of leadership or responsibility for the practice development of colleagues and a significant teaching role. The larger study examined the practices of middle leaders; and in this article we draw on interview data from one of the case-study sites that illustrate how colleagues in schools recognise the role middle leaders have for facilitating action research and teaching development. This article specifically presents excerpts from semi-structured interviews with 25 teachers, three principals, three executive teachers and three district consultants. Interviewees described how nourishing a culture of relational trust and mutual respect are critical features in the change endeavour. For them, the practices of the middle leader who facilitated the action research were instrumental in developing trust for teacher development. Analysis of participant accounts revealed five dimensions of trust: interpersonal trust, interactional trust, intersubjective trust, intellectual trust, and pragmatic trust.

Affective development in university education

There seems to be an increasing requirement for university courses and programs to develop students’ affective qualities (beliefs, values, dispositions and attitudes). This study explored the ways academics determined what the desirable qualities were for their particular disciplines and the pedagogical strategies and approaches they used to develop them. The participants were able to articulate certain beliefs, values and attitudes that were central to their discipline, although they appeared to be assumed and somewhat tacit in nature. The teaching and assessing of affective qualities was seen as problematic by the participants in the study owing to inadequate policy structures of the University, but the data revealed some practical teaching approaches. It was clear from this initial study that there is still a great deal of research and scholarship required in this area.

Learning as being ‘stirred in’ to practices

This chapter provides a ‘societist’ (Schatzki in Philos Soc Sci 33(2):174–202, 2003) account of ‘learning’ using the theory of ‘practice architectures’ (Kemmis and Grootenboer in Situating praxis in practice: Practice architectures and the cultural, social and material conditions for practice. Enabling praxis: Challenges for education. Sense, Rotterdam, pp. 37–62, 2008; Kemmis et al. in Changing education, changing practices. Springer Education, Singapore, 2014). Drawing on observations of classrooms, schools and a school district, the authors argue, first, that people ‘learn’ practices , not only ‘knowledge ’, ‘concepts’ or ‘values’, for example. They suggest that learning a practice entails entering—joining in—the projects and the kinds of sayings , doings and relatings characteristic of different practices. The metaphor that learning involves being ‘stirred in’ to practices conveys the motion and dynamism of becoming a practitioner of a practice of one kind of another, like learning or teaching. Being stirred into practices suggests an account of ‘learning’ that elucidates the process, activity and sociality of learning as a practice.