Theories of Mathematics Education : Seeking New Frontiers

This inaugural book in the new series Advances in Mathematics Education is the most up to date, comprehensive and avant garde treatment of Theories of Mathematics Education which use two highly acclaimed ZDM special issues on theories of mathematics education (issue 6/2005 and issue 1/2006), as a point of departure. Historically grounded in the Theories of Mathematics Education (TME group) revived by the book editors at the 29th Annual PME meeting in Melbourne and using the unique style of preface-chapter-commentary, this volume consist of contributions from leading thinkers in mathematics education who have worked on theory building. This book is as much summative and synthetic as well as forward-looking by highlighting theories from psychology, philosophy and social sciences that continue to influence theory building. In addition a significant portion of the book includes newer developments in areas within mathematics education such as complexity theory, neurosciences, modeling, critical theory, feminist theory, social justice theory and networking theories. The 19 parts, 17 prefaces and 23 commentaries synergize the efforts of over 50 contributing authors scattered across the globe that are active in the ongoing work on theory development in mathematics education.

Surveying theories and philosophies of mathematics education

Any theory of thinking or teaching or learning rests on an underlying philosophy of knowledge. Mathematics education is situated at the nexus of two fields of inquiry, namely mathematics and education. However, numerous other disciplines interact with these two fields which compound the complexity of developing theories that define mathematics education. We first address the issue of clarifying a philosophy of mathematics education before attempting to answer whether theories of mathematics education are constructible? In doing so we draw on the foundational writings of Lincoln and Guba (1994), in which they clearly posit that any discipline within education, in our case mathematics education, needs to clarify for itself the following questions: (1) What is reality? Or what is the nature of the world around us? (2) How do we go about knowing the world around us? [the methodological question, which presents possibilities to various disciplines to develop methodological paradigms] and, (3) How can we be certain in the “truth” of what we know? [the epistemological question]

Literacy education in the context of globalisation

This review chapter provides an overview of English language literacy education in the contexts of cultural and economic globalisation. Drawing case study examples of India and China, the authors outline three complementary models: the development paradigm, the hegemony paradigm and the new literacies paradigm. The analysis focuses on effects of the spread of English on vernacular languages and the non-synchronous issues raised by digital production cultures. Noting the difficulties of education systems in contending with new literacies - it argues for the reframing of transnational relations, global material conditions and new communications technologies as the objects of critical literacy education.

A tale of two cities: Education responds to globalisation in Hong Kong and Singapore in the aftermath of the Asian Economic Crisis

It has been suggested that although the most theorisation about globalisation has emerged from “western” contexts, the material implications of globalisation have been felt most strongly in non-western regions. With this in mind, we are undertaking a situated analysis of how two states, Singapore and Hong Kong, are interacting with the broader processes of globalisation through their educational policies. We apply Foucault's conceptual tool of governmentality to understand (i) the conduct of governing in the contemporary nation-state, and (ii) how the “right” rationalities are being inculcated by government to create “desiring subjects” who will play their part in ensuring national prosperity. We use the Asian Economic Crisis as a point of departure to show how global-local tensions are being managed by Singapore and Hong Kong. We conclude that both these global cities have adroitly managed the Asian economic crisis to steer their citizens away from pursuits of greater political freedom and towards concerns of material well being. They have done so through a selective interpretation of globalisation, by simultaneously resisting and embracing the contradictory strands of globalisation. Education has emerged as a critical space for this selective absorption of globalising trends.

Repositioning an ethic of sustainability in early childhood education, with Reconciliation as central

In this chapter I raise questions about the current scope and purpose of early childhood education for sustainability (ECEfS) and the ways ECEfS is enacted in practice. This is to highlight why social, political and economic areas of concern should be central in ECEfS alongside an environmental focus. Specifically, this chapter establishes the place of Reconciliation in ECEfS because it is one of the most pressing ethical, social, political and economic issues on the Australian landscape. To reposition an ethic of sustainability is to broaden the scope and purpose of sustainability work so that particular regard is given to the place of Reconciliation in ECEfS. An ethic of sustainability is also concerned with the responsibility of non-Indigenous educators to take ownership of Reconciliation work in education curricula and contexts.

From the cathedral to the classroom : the emergence of new discourses on religious education

In 2009, Religious Education is a designated key learning area in Catholic schools in the Archdiocese of Brisbane and, indeed, across Australia. Over the years, though, different conceptualisations of the nature and purpose of religious education have led to the construction of different approaches to the classroom teaching of religion. By investigating the development of religious education policy in the Archdiocese of Brisbane from 1984 to 2003, the study seeks to trace the emergence of new discourses on religious education. The study understands religious education to refer to a lifelong process that occurs through a variety of forms (Moran, 1989). In Catholic schools, it refers both to co-curricula activities, such as retreats and school liturgies, and the classroom teaching of religion. It is the policy framework for the classroom teaching of religion that this study explores. The research was undertaken using a policy case study approach to gain a detailed understanding of how new conceptualisations of religious education emerged at a particular site of policy production, in this case, the Archdiocese of Brisbane. The study draws upon Yeatman’s (1998) description of policy as occurring “when social actors think about what they are doing and why in relation to different and alternative possible futures” (p. 19) and views policy as consisting of more than texts themselves. Policy texts result from struggles over meaning (Taylor, 2004) in which specific discourses are mobilised to support particular views. The study has a particular interest in the analysis of Brisbane religious education policy texts, the discursive practices that surrounded them, and the contexts in which they arose. Policy texts are conceptualised in the study as representing “temporary settlements” (Gale, 1999). Such settlements are asymmetrical, temporary and dependent on context: asymmetrical in that dominant actors are favoured; temporary because dominant actors are always under challenge by other actors in the policy arena; and context - dependent because new situations require new settlements. To investigate the official policy documents, the study used Critical Discourse Analysis (hereafter referred to as CDA) as a research tool that affords the opportunity for researchers to map and chart the emergence of new discourses within the policy arena. As developed by Fairclough (2001), CDA is a three-dimensional application of critical analysis to language. In the Brisbane religious education arena, policy texts formed a genre chain (Fairclough, 2004; Taylor, 2004) which was a focus of the study. There are two features of texts that form genre chains: texts are systematically linked to one another; and, systematic relations of recontextualisation exist between the texts. Fairclough’s (2005) concepts of “imaginary space” and “frameworks for action” (p. 65) within the policy arena were applied to the Brisbane policy arena to investigate the relationship between policy statements and subsequent guidelines documents. Five key findings emerged from the study. First, application of CDA to policy documents revealed that a fundamental reconceptualisation of the nature and purpose of classroom religious education in Catholic schools occurred in the Brisbane policy arena over the last twenty-five years. Second, a disjuncture existed between catechetical discourses that continued to shape religious education policy statements, and educational discourses that increasingly shaped guidelines documents. Third, recontextualisation between policy documents was evident and dependent on the particular context in which religious education occurred. Fourth, at subsequent links in the chain, actors created their own “imaginary space”, thereby altering orders of discourse within the policy arena, with different actors being either foregrounded or marginalised. Fifth, intertextuality was more evident in the later links in the genre chain (i.e. 1994 policy statement and 1997 guidelines document) than in earlier documents. On the basis of the findings of the study, six recommendations are made. First, the institutional Church should carefully consider the contribution that the Catholic school can make to the overall pastoral mission of the diocese in twenty-first century Australia. Second, policymakers should articulate a nuanced understanding of the relationship between catechesis and education with regard to the religion classroom. Third, there should be greater awareness of the connections among policies relating to Catholic schools – especially the connection between enrolment policy and religious education policy. Fourth, there should be greater consistency between policy documents. Fifth, policy documents should be helpful for those to whom they are directed (i.e. Catholic schools, teachers). Sixth, “imaginary space” (Fairclough, 2005) in policy documents needs to be constructed in a way that allows for multiple “frameworks for action” (Fairclough, 2005) through recontextualisation. The findings of this study are significant in a number of ways. For religious educators, the study highlights the need to develop a shared understanding of the nature and purpose of classroom religious education. It argues that this understanding must take into account the multifaith nature of Australian society and the changing social composition of Catholic schools themselves. Greater recognition should be given to the contribution that religious studies courses such as Study of Religion make to the overall religious development of a person. In view of the social composition of Catholic schools, there is also an issue of ecclesiological significance concerning the conceptualisation of the relationship between the institutional Catholic Church and Catholic schools. Finally, the study is of significance because of its application of CDA to religious education policy documents. Use of CDA reveals the foregrounding, marginalising, or excluding of various actors in the policy arena.

Theory-of-Mind Continuum Model: Why Mind Matters in Philosophy, Psychology and Education

Theory-of-Mind has been defined as the ability to explain and predict human behaviour by imputing mental states, such as attention, intention, desire, emotion, perception and belief, to the self and others (Astington & Barriault, 2001). Theory-of-Mind study began with Piaget and continued through a tradition of meta-cognitive research projects (Flavell, 2004). A study by Baron-Cohen, Leslie and Frith (1985) of Theory-of-Mind abilities in atypically developing children reported major difficulties experienced by children with autism spectrum disorder (ASD) in imputing mental states to others. Since then, a wide range of follow-up research has been conducted to confirm these results. Traditional Theory-of-Mind research on ASD has been based on an either-or assumption that Theory-of-Mind is something one either possesses or does not. However, this approach fails to take account of how the ASD population themselves experience Theory-of-Mind. This paper suggests an alternative approach, Theory-of-Mind continuum model, to understand the Theory-of-Mind experience of people with ASD. The Theory-of-Mind continuum model will be developed through a comparison of subjective and objective aspects of mind, and phenomenal and psychological concepts of mind. This paper will demonstrate the importance of balancing qualitative and quantitative research methods in investigating the minds of people with ASD. It will enrich our theoretical understanding of Theory-of-Mind, as well as contain methodological implications for further studies in Theory-of-Mind

Teachers’ conceptions of essential knowledge for integrated social education : a middle years of schooling perspective from Australia

Integrated social education in Australia is a divisive educational issue. The last decade has been marked by a controversial integrated social studies curriculum called Studies of Society and Environment (SOSE) where history, geography and environmental studies were integrated with civics and citizenship. The introduction of a compulsory K-10 Australian Curriculum from 2011, however, marks the return to history and geography and the abandonment of SOSE. Curriculum reform aside, what do teachers think is essential knowledge for middle years social education? The paper reports on a phenomenographical exploration of thirty-one middle school teachers’ conceptions of essential knowledge for SOSE. Framed by Shulman’s (1986, 1987) theoretical framework of the knowledge base for teaching, the research identified seven qualitatively different ways of understanding essential knowledge for integrated social education. The study indicates a practice-based theorization of integrated social education that justifies attention to disciplinary process and teacher identity in middle school social education.

Pre-service teacher education and the development of middle school teacher identity : an exploratory study

This research study investigated the factors that influenced the development of teacher identity in a small cohort of mature-aged graduate pre-service teachers over the course of a one-year Graduate Diploma program (Middle Years). It sought to illuminate the social and relational dynamics of these pre-service teachers’ experiences as they began new ways of being and learning during a newly introduced one-year Graduate Diploma program. A relational-ontological perspective underpinned the relational-cultural framework that was applied in a workshop program as an integral part of this research. A relational-ontological perspective suggests that the development of teacher identity is to be construed more as an ontological process than an epistemological one. Its focus is more on questions surrounding the person and their ‘becoming’ a teacher than about the knowledge they have or will come to have. Hence, drawing on work by researchers such as Alsup (2006), Gilligan, (1982), Isaacs, (2007), Miller (1976), Noddings, (2005), Stout (2001), and Taylor, (1989), teacher identity was defined as an individual pre-service teacher’s unique sense of self as a teacher that included his or her beliefs about teaching and learning (Alsup, 2006; Stout, 2001; Walkington, 2005). Case-study was the preferred methodology within which this research project was framed, and narrative research was used as a method to document the way teacher identity was shaped and negotiated in discursive environments such as teacher education programs, prior experiences, classroom settings and the practicum. The data that was collected included student narratives, student email written reflections, and focus group dialogue. The narrative approach applied in this research context provided the depth of data needed to understand the nature of the mature-aged pre-service teachers’ emerging teacher identities and experiences in the graduate diploma program. Findings indicated that most of the mature-aged graduate pre-service teachers came in to the one-year graduate diploma program with a strong sense of personal and professional selves and well-established reasons why they had chosen to teach Middle Years. Their choice of program involved an expectation of support and welcome to a middle-school community and culture. Two critical issues that emerged from the pre-service teachers’ narratives were the importance they placed on the human support including the affirmation of themselves and their emerging teacher identities. Evidence from this study suggests that the lack of recognition of preservice teachers’ personal and professional selves during the graduate diploma program inhibited the development of a positive middle-school teacher identity. However, a workshop program developed for the participants in this research and addressing a range of practical concerns to beginning teachers offered them a space where they felt both a sense of belonging to a community and where their thoughts and beliefs were recognized and valued. Thus, the workshops provided participants with the positive social and relational dynamics necessary to support them in their developing teacher identities. The overall findings of this research study strongly indicate a need for a relational support structure based on a relational-ontological perspective to be built into the overall course structure of Graduate Pre-service Diplomas in Education to support the development of teacher identity. Such a support structure acknowledges that the pre-service teacher’s learning and formation is socially embedded, relational, and a continual, lifelong process.

Developing new alliances in higher education leadership and governance : autopoietic application of the “arts” creative capacities

This paper, underpinned by a framework of autopoietic principles of creativity/innovation and leadership/governance, argues that open forms of creativity in ‘arts’ provide opportunity for impact upon concepts of development, leadership and governance. The alliance of creativity and governance suggests that by examining various understandings of artistic experiences, readers may perceive new understandings of alliance, application and assessment of such experiences. This critical understanding would include assessing whether such experience supports people changing their aspirations as they become what they want to be. Such understanding may also suggest that different applications of the creative capacity of the ‘arts’ offers relevance in alleged ‘non-creative’ areas of academe, particularly in areas of management, leadership and governance. This alliance also offers the possibility of new staff development programs that facilitate learning and building of individual capacity, as well as facilitate congruent development process and policy, particularly within academic organisational structures.