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]

Politicizing mathematics education : has politics gone too far? Or not far enough?

In this chapter we tackle increasingly sensitive questions in mathematics education, those that have polarized the community into distinct schools of thought as well as impacted reform efforts.

The educational affordances of generative media in arts education

Network Jamming systems provide real-time collaborative media performance experiences for novice or inexperienced users. In this paper we will outline the theoretical and developmental drivers for our Network Jamming software, called jam2jam. jam2jam employs generative algorithmic techniques with particular implications for accessibility and learning. We will describe how theories of engagement have directed the design and development of jam2jam and show how iterative testing cycles in numerous international sites have informed the evolution of the system and its educational potential. Generative media systems present an opportunity for users to leverage computational systems to make sense of complex media forms through interactive and collaborative experiences. Generative music and art are a relatively new phenomenon that use procedural invention as a creative technique to produce music and visual media. These kinds of systems present a range of affordances that can facilitate new kinds of relationships with music and media performance and production. Early systems have demonstrated the potential to provide access to collaborative ensemble experiences to users with little formal musical or artistic expertise.This presentation examines the educational affordances of these systems evidenced by field data drawn from the Network Jamming Project. These generative performance systems enable access to a unique kind of music/media’ ensemble performance with very little musical/ media knowledge or skill and they further offer the possibility of unique interactive relationships with artists and creative knowledge through collaborative performance. Through the process of observing, documenting and analysing young people interacting with the generative media software jam2jam a theory of meaningful engagement has emerged from the need to describe and codify how users experience creative engagement with music/media performance and the locations of meaning. In this research we observed that the musical metaphors and practices of ‘ensemble’ or collaborative performance and improvisation as a creative process for experienced musicians can be made available to novice users. The relational meanings of these musical practices afford access to high level personal, social and cultural experiences. Within the creative process of collaborative improvisation lie a series of modes of creative engagement that move from appreciation through exploration, selection, direction toward embodiment. The expressive sounds and visions made in real-time by improvisers collaborating are immediate and compelling. Generative media systems let novices access these experiences with simple interfaces that allow them to make highly professional and expressive sonic and visual content simply by using gestures and being attentive and perceptive to their collaborators. These kinds of experiences present the potential for highly complex expressive interactions with sound and media as a performance. Evidence that has emerged from this research suggest that collaborative performance with generative media is transformative and meaningful. In this presentation we draw out these ideas around an emerging theory of meaningful engagement that has evolved from the development of network jamming software. Primarily we focus on demonstrating how these experiences might lead to understandings that may be of educational and social benefit.

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.

From Sydney and Shanghai : Australian and Chinese women writing modernism

In the 1930s and 1940s, Australian women writers published novels, poems, and short stories that pushed the boundaries of their national literary culture. From their position in the Pacific, they entered into a dialogue with a European modernism that they reworked to invigorate their own writing and to make cross-continental connections. My interest in the work of Australian women prose writers of this period stems from an appreciation of the extent of their engagement with interwar modernism (an engagement that is generally under-acknowledged) and the realization that there are commonalities of approach with the ways in which contemporaneous Chinese authors negotiated this transnational cultural traffic. China and Australia, it has been argued, share an imaginative and literal association of many centuries, and this psychic history produces a situation in which ‘Australians feel drawn towards China: they cannot leave it alone.’1 Equally, Chinese exploration of the great southern land began in the fifteenth century, prior to European contact. In recent times, the intensity of Australia’s cultural and commercial connections with Asia has led to a repositioning of the Australian sense of regionalism in general and, in particular, has activated yet another stage in the history of its relationship with China. In this context, the association of Australian and Chinese writing is instructive because the commonalities of approach and areas of interest between certain authors indicate that Australian writers were not alone in either the content or style of their response to European modernism. This recognition, in turn, advances discussions of modernism in Australia and reveals an alternative way of looking at the world from the Pacific Rim through literature. The intent is to examine selective Australian and Chinese authors who are part of this continuous history and whose writing demonstrates common thematic and stylistic features via the vector of modernism. I focus on the 1930s and 1940s because these are the decades in which Australia and China experienced wideranging conflict in the Pacific, and it is significant that war, both forthcoming and actual, features as an ominous soundtrack in the writing of Chinese and Australian women. I argue that, given the immensity of cultural difference between Australia and China, there is an especially interesting juncture in the ways in which the authors interrogate modernist practices and the challenge of modernism. The process in which writing from the Pacific Rim jointly negotiates the twin desires of engaging with European literary form and representing one’s own culture may be seen as what Jessica Berman identifies as a geomodernism, one of the ‘new possible geographies’ of modernism.2 My discussion centres on the work of the Australian women, to which the Chinese material serves as a point of reference, albeit a critical one. The Chinese writing examined here is restricted to authors who wrote at least some material in English and whose work is available in translation.

Psychometric evaluation of the Chinese version of the diabetes coping measure scale

Purpose: To evaluate the psychometric properties of a Chinese version of the Diabetes Coping Measure (DCM-C) scale.----- Methods: A self-administered questionnaire was completed by 205 people with type 2 diabetes from the endocrine outpatient departments of three hospitals in Taiwan. Confirmatory factor analysis, criterion validity, and internal consistency reliability were conducted to evaluate the psychometric properties of the DCM-C.----- Findings: Confirmatory factor analysis confirmed a four-factor structure (χ2 /df ratio=1.351, GFI=.904, CFI=.902, RMSEA=.041). The DCM-C was significantly associated with HbA1c and diabetes self-care behaviors. Internal consistency reliability of the total DCM-C scale was .74. Cronbach’s alpha coefficients for each subscale of the DCM-C ranged from .37 (tackling spirit) to .66 (diabetes integration).----- Conclusions: The DCM-C demonstrated satisfactory reliability and validity to determine the use of diabetes coping strategies. The tackling spirit dimension needs further refinement when applies this scale to Chinese populations with diabetes.----- Clinical Relevance: Healthcare providers who deal with Chinese people with diabetes can use the DCM-C to implement an early determination of diabetes coping strategies.

Alternate reality games and education innovation

An Alternate Reality Game (ARG) is a unique experience that blurs the edges between our everyday lives and imagined game worlds. Players are invited to interact with each other and fictional characters using familiar tools such as emails, websites, telephones, and sometimes newspapers, radio and television. ARGs come in all shapes and sizes, tell a variety of different stories and inspire all kinds of interactions between people, their networks and the very streets in which they live. Some ARGs simply immerse you in fictional scenarios and indulge you in quirky challenges. While others reveal hidden histories of a city and teach us about important political causes. But the most exciting thing about ARGs is that they have the potential to inspire participants to imagine their everyday tools and places as resources for their own creative endeavors. Deb Polson will be presenting some of the most inspiring ARGs of recent years and revealing some of the design techniques that were used to create them. Most significantly Deb will discuss ways in which educators can imagine using ARGs as rich teaching tools that inspire collaborative learning and motivate students to engage in all kinds of subject matter.

A constraints-led perspective to understanding skill acquisition and game play: A basis for integration of motor learning theory and physical education praxis?

Background: In order to design appropriate environments for performance and learning of movement skills, physical educators need a sound theoretical model of the learner and of processes of learning. In physical education, this type of modelling informs the organization of learning environments and effective and efficient use of practice time. An emerging theoretical framework in motor learning, relevant to physical education, advocates a constraints-led perspective for acquisition of movement skills and game play knowledge. This framework shows how physical educators could use task, performer and environmental constraints to channel acquisition of movement skills and decision making behaviours in learners. From this viewpoint, learners generate specific movement solutions to satisfy the unique combination of constraints imposed on them, a process which can be harnessed during physical education lessons. Purpose: In this paper the aim is to provide an overview of the motor learning approach emanating from the constraints-led perspective, and examine how it can substantiate a platform for a new pedagogical framework in physical education: nonlinear pedagogy. We aim to demonstrate that it is only through theoretically valid and objective empirical work of an applied nature that a conceptually sound nonlinear pedagogy model can continue to evolve and support research in physical education. We present some important implications for designing practices in games lessons, showing how a constraints-led perspective on motor learning could assist physical educators in understanding how to structure learning experiences for learners at different stages, with specific focus on understanding the design of games teaching programmes in physical education, using exemplars from Rugby Union and Cricket. Findings: Research evidence from recent studies examining movement models demonstrates that physical education teachers need a strong understanding of sport performance so that task constraints can be manipulated so that information-movement couplings are maintained in a learning environment that is representative of real performance situations. Physical educators should also understand that movement variability may not necessarily be detrimental to learning and could be an important phenomenon prior to the acquisition of a stable and functional movement pattern. We highlight how the nonlinear pedagogical approach is student-centred and empowers individuals to become active learners via a more hands-off approach to learning. Summary: A constraints-based perspective has the potential to provide physical educators with a framework for understanding how performer, task and environmental constraints shape each individual‟s physical education. Understanding the underlying neurobiological processes present in a constraints-led perspective to skill acquisition and game play can raise awareness of physical educators that teaching is a dynamic 'art' interwoven with the 'science' of motor learning theories.