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]

Rethinking corporate governance and law in China : the theories, rules and practices

Economic reforms have transformed China into a modern economy - this requires greater emphasis on regulating markets and governing corporations to ensure economic growth continues. Yet, legal reforms are not as straightforward as transplanting Western models; more modification to suit Chinese political land cultural considerations needs to be incorporated. Likewise privatisation of the telecommuications sector does not mean that government influence in the new corporations cease. This is not necessarily negative as long as safeguards are in place. Plainly further reforms to the law and governance will be needed. Given that Confucian philosophy continues to play a central role in Chinese society and values, developing laws and governance practices from Confucian principles will arguably be appropriate for modern China.

Using developmental theories to inform the design of technology for children

Electronic Blocks are a new programming environment, designed specifically for children aged between three and eight years. As such, the design of the Electronic Block environment is firmly based on principles of developmentally appropriate practices in early childhood education. The Electronic Blocks are physical, stackable blocks that include sensor blocks, action blocks and logic blocks. Evaluation of the Electronic Blocks with both preschool and primary school children shows that the blocks' ease of use and power of engagement have created a compelling tool for the introduction of meaningful technology education in an early childhood setting. The key to the effectiveness of the Electronic Blocks lies in an adherence to theories of development and learning throughout the Electronic Blocks design process.

Researching the 'reception' of indigenous affairs in Australia

The Reporting and Reception of Indigenous Issues in the Australian Media was a three year project financed by the Australian government through its Australian Research Council Large Grants Scheme and run by Professor John Hartley (of Murdoch and then Edith Cowan University, Western Australia). The purpose of the research was to map the ways in which indigeneity was constructed and circulated in Australia's mediasphere. The analysis of the 'reporting' element of the project was almost straightforward: a mixture of content analysis of a large number of items in the media, and detailed textual analysis of a smaller number of key texts. The discoveries were interesting - that when analysis approaches the media as a whole, rather than focussing exclusively on news or serious drama genres, then representation of indigeneity is not nearly as homogenous as has previously been assumed. And if researchers do not explicitly set out to uncover racism in every text, it is by no means guaranteed they will find it1. The question of how to approach the 'reception' of these issues - and particularly reception by indigenous Australians - proved to be a far more challenging one. In attempting to research this area, Hartley and I (working as a research assistant on the project) often found ourselves hampered by the axioms that underlie much media research. Traditionally, the 'reception' of media by indigenous people in Australia has been researched in ethnographic ways. This research repeatedly discovers that indigenous people in Australia are powerless in the face of new forms of media. Indigenous populations are represented as victims of aggressive and powerful intrusions: ‘What happens when a remote community is suddenly inundated by broadcast TV?’; ‘Overnight they will go from having no radio and television to being bombarded by three TV channels’; ‘The influence of film in an isolated, traditionally oriented Aboriginal community’2. This language of ‘influence’, ‘bombarded’, and ‘inundated’, presents metaphors not just of war but of a war being lost. It tells of an unequal struggle, of a more powerful force impinging upon a weaker one. What else could be the relationship of an Aboriginal audience to something which is ‘bombarding’ them? Or by which they are ‘inundated’? This attitude might best be summed up by the title of an article by Elihu Katz: ‘Can authentic cultures survive new media?’3. In such writing, there is little sense that what is being addressed might be seen as a series of discursive encounters, negotiations and acts of meaning-making in which indigenous people — communities and audiences —might be productive. Certainly, the points of concern in this type of writing are important. The question of what happens when a new communication medium is summarily introduced to a culture is certainly an important one. But the language used to describe this interaction is a misleading one. And it is noticeable that such writing is fascinated with the relationship of only traditionally-oriented Aboriginal communities to the media of mass communication.

Making use of theories about literacy and justice: teachers re-searching practice

This article considers teachers’ work as they grapple with theories in practice in the everyday worlds of their classroom. It argues that Bourdieu’s theory of practice and the concept of habitus may be useful in moving past theory/practice dichotomies. After establishing the historical context for teacher research in South Australia, the work of two school-based literacy educators with an overt social justice standpoint is explored. The complexity of teachers’ intellectual work and identity formation over time is outlined and implications for teacher education are discussed.