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.

Academic career development workshop for research students and early career academics

For research students and early career academics, universities offer resources that help develop their research skills – for example, critical theory development, literature reviews, research methods, data analysis, writing skills, etc. However, building a successful career in academia poses a wide range of new challenges in addition to the pure academic craft of research. The resources and resilience one needs in order to shape an academic career path often appear ambiguous, particularly in the innately transformative field of Internet research. In response to feedback from AoIR members, this full-day workshop seeks to address this concern by offering a supportive and constructive environment to discuss career development related issues that are of specific interest to research students and early career academics.

Women are people too : the problem of designing for gender

Cultural theory breaks with Modern analysis by rejecting traditional notions of race, gender, class and sexuality. In doing so, alternative frameworks such as Post-Feminism emerge which are useful for thinking about culture, technology and what our interactions with it mean. From a Post-Feminist perspective it can be seen how in our multi-cultural, post-industrial, digitized world, there is space to move beyond traditional ways of dividing up society such as ‘male’ and ‘female’. We are then free to re-construct our identity in light of a rich diversity of individually relevant experiences. Therefore, in order to get a better understanding of the highly nuanced cultural interactions that characterize our use of technology, this paper argues against using the inherently stereotyped lens of gender and allowing a new set of user needs to emerge.

The cultural economy moment?

This paper explores the rise of cultural economy as a key organising concept over the 2000s. While it has intellectual precursors in political economy, sociology and postmodernism, it has been work undertaken in the fields of cultural economic geography, creative industries, the culture of service industries and cultural policy where it has come to the forefront, particularly around whether we are now in a ‘creative economy’. While work undertaken in cultural studies has contributed to these developments, the development of neo-liberalism as a meta-concept in critical theory constitutes a substantive barrier to more sustained engagement between cultural studies and economics, as it rests upon a caricature of economic discourse. The paper draws upon Michel Foucault’s lectures on neo-liberalism to indicate that there are significant problems with the neo-Marxist account hat became hegemonic over the 2000s. The paper concludes by identifying areas such as the value of information, the value of networks, motivations for participation in online social networks, and the impact of business cycles on cultural sectors as areas of potentially fruitful inter-disciplinary engagement around the nature of cultural economy.

The voices of the exegesis

In a recent journal article, Luke Jaaniste and I identified an emergent model of exegesis. From a content analysis of submitted exegeses within a local archive, we identified an approach that is quite different from the traditional thesis, but is also distinct from previously identified forms of exegesis, which Milech and Schilo have described as a ‘context model’ (which assumes the voice of academic objectivity and provides an historical or theoretical context for the creative practice) and a ‘commentary’ model’ (which takes the form of a first person reflection on the challenges, insights and achievements of the practice). The model we identified combines these dichotomous forms and assumes a dual orientation–looking outwards to the established field of research, exemplars and theories, and inwards to the methodologies, processes and outcomes of the practice. We went on to argue that this ‘connective’ exegesis offers clear benefits to the researcher in connecting the practice to an established field while allowing the researcher to demonstrate how the methods have led to outcomes that advance the field in some way. And, while it helps the candidate to articulate objective claims for research innovation, it enables them to retain a voiced, personal relationship with their practice. However, it also poses considerable complexities and challenges in the writing. It requires a reconciliation of multi-perspectival subject positions: the disinterested perspective and academic objectivity of an observer/ethnographer/analyst/theorist at times and the invested perspective of the practitioner/ producer at others. The author must also contend with a range of writing styles, speech genres and voices: from the formal, polemical voice of the theorist to the personal, questioning and sometimes emotive voice of reflexivity. Moreover, the connective exegesis requires the researcher to synthesize various perspectives, subject positions, writing styles, and voices into a unified and coherent text. In this paper I consider strategies for writing a hybrid, connective exegesis. I first ground the discussion on polyvocality and alternate textual structures through reference to recent discussions in philosophy and critical theory, and point to examples of emergent approaches to texts and practices in related fields. I then return to the collection of archived exegeses to investigate the strategies that postgraduate candidates have adopted to resolve the problems that arise from a polyvocal, connective exegesis.

Without an Alibi

The project is a book collection of 65 poems, primarily with an environmental focus. This practice-led project draws on eco-critical theory (Wilson, 1992; and Bate, 2000) and Darwinian literary theory (Carroll, 2004) to explore ideas of ecology, the ‘natural’, and conservation. The poems explore a proposal of synthesis: that nature is for us both a construction of language/culture (as argued by post structuralism/ cultural studies) and also a pragmatic, empirical entity that can be experienced through the senses as well as through culture. For example, individual poems describe genres of ‘forest’ (‘Literary Forests’, ‘The Conservative Forest’, ‘The Imperial Forest’) which demonstrate how ‘nature’ can be culturally constructed, but also remain an empirical entity with which we experience a more immediate, physical connection, as posited by Bate (following Heidegger’s ‘being-in-the-world’) . The work also explores through satire the concept of evolutionary adaptation, for example the integration of machine into forest (‘The Black Forest’), animals adopting human characteristics (‘In Praise of Bears’), and ‘nature’ as a damaged or absent ‘other’. Without an Alibi makes various strands of theoretical thinking concrete and manifest by ‘showing not telling’, in creative practice. The work has been high positively reviewed in the prestigious Australian Book Review, and by Professor Peter Pierce in the Canberra Times. Several of the poems have since been reproduced in national anthologies including The Penguin Anthology of Australian Poetry (2000) and Australian Poetry Since 1988 (Uni of NSW Press).

Teacher decision making in early childhood education

The study investigated early childhood teacher decision making at the preschool level in the state of Victoria, Australia. Victorian teachers at the preschool level were in an interesting position in 2004. Unlike most other Australian states Victoria did not have a curriculum framework guiding educational content and pedagogy. Consequently, this study was able to take advantage of this situation and examine teacher decision making at a time when early childhood teachers were relatively autonomous in deciding curriculum content. The opportunity to study teacher decision making in this way has since passed, as Victorian preschool teachers are now regulated by newly introduced state and national curricula frameworks. To identify influences affecting teacher decision making three preschool teachers were interviewed and curricula related policies were analysed. The data were analysed using Fairclough’s critical discourse analysis (CDA) technique. Critical discourse analysis enabled a close analysis of influences on teacher decision making illustrating how discourse is legitimated, marginalised, and silenced in certain curricula practices. Critical theory was the underpinning framework used for the study and enabled taken-for-granted understandings to be uncovered within early childhood policies and teacher interviews. Key findings were that despite there not being a government-mandated curricula framework for Victorian preschool education in 2004, teachers were held accountable for their curricula practice. Yet as professionals, early childhood teachers were denied public acknowledgment of their expertise as they were almost invisible in policy. Subsequently, teachers’ authority as professionals with curricula knowledge was diminished. The study found that developmentally appropriate practice (DAP) was a dominant discourse influencing teacher decision making (TDM). It operated as legitimated discourse in the 2004 Victorian preschool context. Additionally, the study found that teacher directed practice was legitimated, marginalised, and silenced by teachers. The findings have implications for early childhood teacher decision making at the practice, research, and policy levels. Findings show that the dominance of the DAP discourse informing teacher decision making limits other ways of thinking and practising.

An interview with Jacques Rancière : on medium-specificity and discipline crossovers in modern art

Jacques Rancière's work on aesthetics has received a great deal of attention in recent years. Given his work has enormous range – covering art and literature, political theory, historiography, pedagogy and worker's history – Andrew McNamara and Toni Ross (UNSW) explore his wider critical ambitions in this interview, while showing how it leads to alternative insights into aesthetics. Rancière sets aside the core suppositions linking the medium to aesthetic judgment, which has informed many definitions of modernism. Rancière is emphatic in freeing aesthetic judgment from issues of medium-specificity. He argues that the idea of autonomy associated with medium-specificity – or 'truth to the medium' – was 'a very late one' in modernism, and that post-medium trends were already evident in early modernism. While not stressing a simple continuity between early modernism and contemporary art, Ranciere nonetheless emphasizes the on-going ethical and political ramifications of maintaining an a-disciplinary stance.

The Botanist at his Mother's Grave

In this poem about processing human grief, I consciously drew on eco-critical theory – (Wilson 1992, Bate 2000) – and Darwinian literary theory (Carroll 2004) to explore the tension between ideas of the ‘natural’ apprehended through the senses, and poststructuralist ideas of the construction of reality through language.

Children as change agents for sustainability : an action research case study in a kindergarten

At a time when global consumption and production levels are 25 percent higher than the Earth’s sustainable carrying capacity, there are worldwide calls to find ways to sustain the Earth for this and future generations. A central premise of this study is that education systems have an obligation to participate in this move towards sustainability and can respond by embedding education for sustainability into curricula. This study took early childhood education as its focus due to the teacherresearcher’s own concerns about the state of the planet, coupled with early childhood education’s established traditions of nature-based and child-centred pedagogy. The study explored the experiences of a class of kindergarten children as they undertook a Project Approach to learning about environmental sustainability. The Project Approach is an adaptation of Chard’s work which is situated within a constructivist theoretical framework (Chard, 2011). The Project Approach involves in-depth investigations around an identified topic of interest. It has three phases: introductory, synthesising and culminating phase. The study also investigated the learning journey of the classroom teacher/researcher who broadened her long-held co-constructivist teaching approaches to include transformative practices in order to facilitate curriculum which embedded education for sustainability. While coconstructivist approaches focus on the co-construction of knowledge, transformative practices are concerned with creating change. An action research case study was conducted. This involved twenty-two children who attended an Australian kindergarten. Data were collected and analysed over a seven week period. The study found that young children can be change agents for sustainability when a Project Approach is broadened to include transformative practices. The study also found that the child participants were able to think critically about environmental and sustainability issues, were able to create change in their local contexts, and took on the role of educators to influence others’ environmental behaviours. Another finding was that the teacher-researcher’s participation in the study caused a transformation of both her teaching philosophy and the culture at the kindergarten. An important outcome of the study was the development of a new curriculum model that integrates and has applicability for curriculum development and teacher practice.

The politics and poetics of coexistence : experiments at the intersection of art and environmental engineering

This research project explores how interdisciplinary art practices can provide ways for questioning and envisaging alternative modes of coexistence between humans and the non-humans who together, make up the environment. As a practiceled project, it combines a body of creative work (50%) and this exegesis (50%). My interdisciplinary artistic practice appropriates methods and processes from science and engineering and merges them into artistic contexts for critical and poetic ends. By blending pseudo-scientific experimentation with creative strategies like visual fiction, humour, absurd public performance and scripted audience participation, my work engages with a range of debates around ecology. This exegesis details the interplay between critical theory relating to these debates, the work of other creative practitioners and my own evolving artistic practice. Through utilising methods and processes drawn from my prior career in water engineering, I present an interdisciplinary synthesis that seeks to promote improved understandings of the causes and consequences of our ecological actions and inactions.

Socio-Spatial Approaches To Literacy Studies: Rethinking the Social Constitution and Politics of Space

Literacy studies have begun to examine the spatial dimension of literacy practices in a way that foregrounds space, and that considers space as constitutive to human relations and practices. This chapter provides an introduction to spatial literacy research, providing a guide to key theorists, themes, and studies that have shaped historical and new developments in spatial approaches to literacy practice and pedagogy. It begins by reconceptualising socio-spatial approaches to literacy research and defines terms. Intersections with related social theories are examined, with an emphasis on critical approaches and the politics of space. It clarifies the relationship between socio-spatial and socio-cultural paradigms, revisiting the spatial in seminal socio-cultural research. It covers new ground,including networks, flows, and deterritorialisation of literacy practice. The chapter concludes with challenges and recommendations for future language research and educational practice.

The influence of digital technology on the performance space

Through practice-led research, TESSA SMALLHORN examines the influence of digital technology on the performance space. From the mechanisation of modernist culture to the digitalisation of present day, technology acts as response material for scenographers investigating the stage as machine. The interactive, real-time tools of digital culture encourage a systems-orientated approach that challenges user and operator alike. This article explores the studio practice and critical theory that was combined to offer a functional model of a digital stage machine.

Not as it seems : using Deleuzian concepts of the imaginary to rethink children’s drawings

Deleuze (1990) states in Negotiations that signs are realized in ideas. Although Deleuze referred to cinema, his thinking about signs and ideas can apply to drawings. Cinema is moving imagery and drawing is static, however both are informed and constructed from realized ideas that continue to shift beyond the artifact. Theories about children’s drawings have historically pertained to establishing schematic universalities rather than acknowledging the agglomerative connections they make to the multiple things occurring around a drawing as it is created. Universal schemas however persist within early childhood art discourses despite the growth of critical theory research into other aspects of childhood. Deleuze’s assertions about the signs and classifications of cinema help to contest notions of schematic development, i.e. children should progress through particular iconic drawing stages at particular ages. Deleuze’s quotes and thoughts on the imaginary and imagination are referenced to interrogate ‘scientific’ knowledges and the gathering of evidential truths about children’s intellectual growth and development. Four examples from a dataset of drawings from a pilot study, undertaken by the author that tested the methodological potential of intergenerational collaborative drawing in early childhood settings, facilitate focused discussion on the above contestations.

‘Doing’ social justice in early childhood : the potential of leadership

Early childhood education has long been connected with objectives related to social justice. Australian Early Childhood Education and Care (ECEC) has its roots in philanthropic and educational reform movements prevalent at the turn of the 20th century. More recently, with the introduction of the National Early Childhood Reform Agenda, early childhood education has once more been linked to the achievement of aims associated with redressing inequality and disadvantage. According to Jean-Marie, Normore and Brooks (2009), educational leaders have a moral and social obligation to foster equitable practices through advocating for traditionally marginalised and poorly served students while creating a new social order “...that subverts the long standing system that has privileged certain students while oppressing or neglecting others” (p.4). Drawing on extant literature, including data from two previously reported Australian studies in which leadership emerged as having a transformational impact on service delivery, this paper examines the potential of early childhood leadership to generate ‘socially just’ educational communities. With reference to critical theory, we argue that critically informed, intentional and strategic organisational leadership can play a pivotal role in creating changed circumstances and opportunities for children and families. Such leadership includes positional and distributed elements, articulation of values and beliefs, and collective action that is mindful and informed.