Theory and its role in mathematics education

The increased recognition of the theory in mathematics education is evident in numerous handbooks, journal articles, and other publications. For example, Silver and Herbst (2007) examined ―Theory in Mathematics Education Scholarship‖ in the Second Handbook of Research on Mathematics Teaching and Learning (Lester, 2007) while Cobb (2007) addressed ―Putting Philosophy to Work: Coping with Multiple Theoretical Perspectives‖ in the same handbook. And a central component of both the first and second editions of the Handbook of International Research in Mathematics Education (English, 2002; 2008) was ―advances in theory development.‖ Needless to say, the comprehensive second edition of the Handbook of Educational Psychology (Alexander & Winne, 2006) abounds with analyses of theoretical developments across a variety of disciplines and contexts. Numerous definitions of ―theory‖ appear in the literature (e.g., see Silver & Herbst, in Lester, 2007). It is not our intention to provide a ―one-size-fits-all‖ definition of theory per se as applied to our discipline; rather we consider multiple perspectives on theory and its many roles in improving the teaching and learning of mathematics in varied contexts.

Nonlinear pedagogy : implications for teaching games for understanding (TGfU)

Nonlinear Dynamics, provides a framework for understanding how teaching and learning processes function in Teaching Games for Understanding (TGfU). In Nonlinear Pedagogy, emergent movement behaviors in learners arise as a consequence of intrinsic self-adjusted processes shaped by interacting constraints in the learning environment. In a TGfU setting, representative, conditioned games provide ideal opportunities for pedagogists to manipulate key constraints so that self-adjusted processes by players lead to emergent behaviors as they explore functional movement solutions. The implication is that, during skill learning, functional movement variability is necessary as players explore different motor patterns for effective skill execution in the context of the game. Learning progressions in TGfU take into account learners’ development through learning stages and have important implications for organisation of practices, instructions and feedback. A practical application of Nonlinear Pedagogy in a national sports institute is shared to exemplify its relevance for TGfU practitioners.

Aligning school reform and teacher education reform in the middle years : an Australian case study

This paper discusses the development of a new Bachelor of Education (Middle Years of Schooling) at The University of Queensland, Australia. The middle years of schooling have increasingly been the focus of education reform initiatives in Australia, but this has not been accompanied by significant increases in the number of teacher education institutions offering specialised middle schooling-level teacher preparation programmes. Considering the rapidly changing social and economic context and the emergent state of middle schooling in Australia, the programme represented a conceptual and practical opportunity and challenge for The University of Queensland team. Working collaboratively, the team sought to design a teacher education preservice programme that was both responsive and generative: that is, responsive to local school contexts and to current education research and reform at national and international levels; and generative of cutting-edge theories and practices associated with middle schooling, teachers' work, and teacher education. This paper focuses on one component of the Middle Years of Schooling Teacher Education programme at The University of Queensland; namely, the practicum. We first present the underlying principles of the practicum programme and then examine "dilemmas" that emerged early in the practicum. These issues and tensions were associated with the ideals of "middle years" philosophy and the pragmatics of school reform associated with that approach. Within this context, we explore what it means to be both responsive and generative, and describe how we as teacher educators negotiated the extremes these terms implied.

The ADHD debate and the philosophy of truth

There is ongoing and wide-ranging dispute over the proliferation of childhood behaviour disorders. In particular, the veracity of the category Attention Deficit Hyperactivity Disorder (ADHD), has been the subject of considerable scepticism. With no end to the debate in sight, it will be argued here that the problem might effectively be approached, not by addressing the specific features of ADHD itself, but rather by a philosophical analysis of one of the terms around which this entire problem revolves: that is, the notion of truth. If we state: “It is true that ADHD is a real disorder”, what exactly do we mean? Do we mean that it is an objective fact of nature? Do we mean that it fits seamlessly with other sets of ideas and explanations? Or do we simply mean that it works as an idea in a practical sense? This paper will examine the relationship between some of the dominant models of truth, and the assertions made by those in the field of ADHD. Specifically, the paper will contrast the claim that ADHD is a real disorder, with the claim that ADHD is a product of social governance. The intention is, first, to place some significant qualifications upon the validity of the truth-claims made by ADHD advocates, and second, to re-emphasise the potential and promise of philosophical investigation in providing productive new ways of thinking about some obstinate and seemingly intractable educational problems.

Transfer of learning across the globe : pre-service teachers taking the initiative

A continuing challenge for pre-service teacher education is the learning transfer between the university based components and the practical school based components of their training. It is not clear how easily pre-service teachers can transfer university learnings into ‘in school’ practice. Similarly, it is not clear how easily knowledge learned in the school context can be disembedded from this particular context and understood more generally by the pre-service teacher. This paper examines the effect of a community of practice formed specifically to explore learning transfer via collaboration and professional enquiry, in ‘real time’, across the globe. “Activity Theory” (Engestrom, 1999) provided the theoretical framework through which the cognitive, physical and social processes involved could be understood. For the study, three activity systems formed community of practice network. The first activity system involved pre-service teachers at a large university in Queensland, Australia. The second activity system was introduced by the pre-service teachers and involved Year 12 students and teachers at a private secondary school also in Queensland, Australia. The third activity system involved university staff engineers at a large university in Pennsylvania, USA. The common object among the three activity systems was to explore the principles and applications of nanotechnology. The participants in the two Queensland activity systems, controlled laboratory equipment (a high powered Atomic Force Microscope – CPII) in Pennsylvania, USA, with the aim of investigating surface topography and the properties of nano particles. The pre-service teachers were to develop their remote ‘real time’ experience into school classroom tasks, implement these tasks, and later report their findings to other pre-service teachers in the university activity system. As an extension to the project, the pre-service teachers were invited to co-author papers relating to the project. Data were collected from (a) reflective journals; (b) participant field notes – a pre-service teacher initiative; (c) surveys – a pre-service teacher initiative; (d) lesson reflections and digital recordings – a pre-service teacher initiative; and (e) interviews with participants. The findings are reported in terms of the major themes: boundary crossing, the philosophy of teaching, and professional relationships The findings have implications for teacher education. The researchers feel that deliberate planning for networking between activity systems may well be a solution to the apparent theory/practice gap. Proximity of activity systems need not be a hindering issue.

Teaching grammar: rethinking the approach

Margaret Kettle examines grammar, its image problem and some new developments aimed at improving its teaching and learning in the TESOL classroom.

Virtual reality or virtually real : blended teaching and learning in a Master's level research methods class

This paper examines the enabling effect of using blended learning and synchronous internet mediated communication technologies to improve learning and develop a Sense of Community (SOC) in a group of post-graduate students consisting of a mix of on-campus and off-campus students. Both quantitative and qualitative data collected over a number of years supports the assertion that the blended learning environment enhanced both teaching and learning. The development of a SOC was pivotal to the success of the blended approach when working with geographically isolated groups within a single learning environment.

The studio sans frontières : the open-studio as an answer to the challenges of teaching contemporary art

Since at least the 1960s, art has assumed a breadth of form and medium as diverse as social reality itself. Where once it was marginal and transgressive for artists to work across a spectrum of media, today it is common practice. In this ‘post-medium’ age, fidelity to a specific branch of media is a matter of preference, rather than a code of practice policed by gallerists, curators and critics. Despite the openness of contemporary art practice, the teaching of art at most universities remains steadfastly discipline-based. Discipline-based art teaching, while offering the promise of focussed ‘mastery’ of a particular set of technical skills and theoretical concerns, does so at the expense of a deeper and more complex understanding of the possibilities of creative experimentation in the artist’s studio. By maintaining an hermetic approach to medium, it does not prepare students sufficiently for the reality of art making in the twenty-first century. In fact, by pretending that there is a select range of techniques fundamental to the artist’s trade, discipline-based teaching can often appear to be more engaged with the notion of skills preservation than purposeful art training. If art schools are to survive and prosper in an increasingly vocationally-oriented university environment, they need to fully synthesise the professional reality of contemporary art practice into their approach to teaching and learning. This paper discusses the way in which the ‘open’ studio approach to visual art study at QUT endeavours to incorporate the diversity and complexity of contemporary art while preserving the sense of collective purpose that discipline-based teaching fosters. By allowing students to independently develop their own art practices while also applying collaborative models of learning and assessment, the QUT studio program aims to equip students with a strong sense of self-reliance, a broad awareness and appreciation of contemporary art, and a deep understanding of studio-based experimentation unfettered by the boundaries of traditional media: all skills fundamental to the practice of contemporary art.

Teaching and learning science and mathematics through technology practice

In this chapter we review studies of the engagement of students in design projects that emphasise integration of technology practice and the enabling sciences, which include physics and mathematics. We give special attention to affective and conceptual outcomes from innovative interventions of design projects. This is important work because of growing international concern that demand for professionals with technological expertise is increasing rapidly, while the supply of students willing to undertake the rigors of study in the enabling sciences is proportionally reducing (e.g., Barringtion, 2006; Hannover & Kessels, 2004; Yurtseven, 2002). The net effect is that the shortage in qualified workers is having a detrimental effect upon economic and social potential in Westernised countries (e.g., Department of Education, Science and Training [DEST], 2003; National Numeracy Review Panel and National Numeracy Review Secretarial, 2007; Yurtseven, 2002). Interestingly, this trend is reversed in developing economies including China and India (Anderson & Gilbride, 2003).

Connecting pre-service teachers to 'real world' teaching practices through microteaching

Action research proved a useful strategy for monitoring the evolution of microteaching task as an authentic assessment for post-graduate pre-service teachers. Through four iterations of continually reflecting on the structure, purpose and outcomes of utilising microteaching as assessment, unit coordinators implemented an authentic assessment task that simulated real world experience.

Insights from ecological psychology and dynamical systems theory can underpin a philosophy of coaching

The aim of this paper is to show how principles of ecological psychology and dynamical systems theory can underpin a philosophy of coaching practice in a nonlinear pedagogy. Nonlinear pedagogy is based on a view of the human movement system as a nonlinear dynamical system. We demonstrate how this perspective of the human movement system can aid understanding of skill acquisition processes and underpin practice for sports coaches. We provide a description of nonlinear pedagogy followed by a consideration of some of the fundamental principles of ecological psychology and dynamical systems theory that underpin it as a coaching philosophy. We illustrate how each principle impacts on nonlinear pedagogical coaching practice, demonstrating how each principle can substantiate a framework for the coaching process.

Providing innovative planning education experience : teaching regional planning in an international context

Rapidly changing economic, social, and environmental conditions have created a need for urban and regional planning practitioners who are resilient, innovative, and able to cope with the increasingly complex and cosmopolitan nature of major metropolitan areas. This need should be reflected in planning education that allows students to experience a diverse range of approaches to problems and challenges, and that exposes students to the diverse array of perspectives on planning issues. This paper investigates the outcomes of a collaborative regional planning exercise organised jointly by planning academics from both Queensland University of Technology and the International Islamic University of Malaysia, and involving planning students from both universities. The regional planning exercise consisted of a regional appraisal and report topics of the area under investigation, Klang Valley – Kuala Lumpur, Malaysia. It culminated with the presentation of regional development strategies for the area, with a field trip to Malaysia being the cornerstone of the project. The collaborative exercise involved a series of workshops and seminars organised locally, in which both Australian and Malaysian planning students participated, as well as meetings with local and federal planning officials, and also a forum for Young Planners of Australian and Malaysian Planning Institutes. The experience attempted to bridge the teaching of theoretical concepts of regional planning and development and the regional, more professional knowledge of planning practice, as it relates to specific political, institutional and cultural contexts. A survey of participating students, from both Queensland University of Technology and the International Islamic University of Malaysia, highlights the benefits of such project in terms of leaning experience and exposure to different cultural contexts.

How current pedagogy methods in games teaching in the UK, Australia and the US have been shaped by historical, socio cultural, environmental and political constraints

Crucial to enhancing the status and quality of games teaching in schools is a developed understanding of the teaching strategies adopted by practitioners. In this paper, we will demonstrate that contemporary games‟ teaching is a product of individual, task and environmental constraints (Newell, 1986). More specifically, we will show that current pedagogy in the U.K., Australia and the United States is strongly influenced by historical, socio-cultural environmental and political constraints. In summary, we will aim to answer the question „why do teachers teach games the way they do.‟ In answering this question, we conclude that teacher educators, who are trying to influence pedagogical practice, must understand these potential constraints and provide appropriate pre-service experiences to give future physical education teachers the knowledge, confidence and ability to adopt a range of teaching styles when they become fully fledged teachers. Essential to this process is the need to enable future practitioners to base their pedagogical practice on a sound understanding of contemporary learning theories of skill acquisition.

Developing the descriptions of landmark teaching styles : a spectrum inventory

Mosston & Ashworth‟s Spectrum of Teaching styles was first published in 1966 and is potentially the longest surviving model of teaching within the field of physical education. Its longevity and influence is surely testament to its value and influence. Many tools have also been developed through the years based on The Spectrum of Teaching Styles. In 2005 as part of a doctoral study, this tool was developed by the author, Dr Edwards and Dr Ashworth for researchers and teachers to identify which teaching styles were being utilised from The Spectrum when teaching physical education. It could also be utilised for self-assessment of the teaching styles and individual uses, or those who work with Physical Education Teacher Education courses. The development of this tool took approximately 4 months, numerous emails and meetings. This presentation will outline this process, along with the reasons why such a tool was developed and the differences between it and others like it.

Teaching and Learning Entrepreneurship for Micro and Small Businesses in the Cultural Industries Sector

Reports on an ESRC-funded, in-depth qualitative research project into 50 micro and small enterprises (MSEs) in the cultural industries. Our evidence sheds light on the extent to which the teaching and learning strategies adopted by higher education, further education and other VET providers are effective in providing entrepreneurship education and training for this innovative, high skill sector. Our findings suggest that entrepreneurs in this sector learn best by being able to experiment with ideas, by “doing” and networking with others and by working with more experienced mentors in their sector. The article concludes by suggesting a more “naturalistic” approach to teaching and learning entrepreneurship for micro and small businesses in the cultural industries sector.