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.

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.

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]

Library and information science education 2.0 : guiding principles and models of best practice ALTC Fellowship Report

This ALTC Teaching Fellowship aimed to establish Guiding Principles for Library and Information Science Education 2.0. The aim was achieved by (i) identifying the current and anticipated skills and knowledge required by successful library and information science (LIS) professionals in the age of web 2.0 (and beyond), (ii) establishing the current state of LIS education in Australia in supporting the development of librarian 2.0, and in doing so, identify models of best practice. The fellowship has contributed to curriculum renewal in the LIS profession. It has helped to ensure that LIS education in Australia continues to meet the changing skills and knowledge requirements of the profession it supports. It has also provided a vehicle through which LIS professionals and LIS educators may find opportunities for greater collaboration and more open communication. This will help bridge the gap between LIS theory and practice and will foster more authentic engagement between LIS education and other parts of the LIS industry in the education of the next generation of professionals. Through this fellowship the LIS discipline has become a role model for other disciplines who will be facing similar issues in the coming years. Eighty-one members of the Australian LIS profession participated in a series of focus groups exploring the current and anticipated skills and knowledge needed by the LIS professional in the web 2.0 world and beyond. Whilst each focus group tended to draw on specific themes of interest to that particular group of people, there was a great deal of common ground. Eight key themes emerged: technology, learning and education, research or evidence-based practice, communication, collaboration and team work, user focus, business savvy and personal traits. It was acknowledged that the need for successful LIS professionals to possess transferable skills and interpersonal attributes was not new. It was noted however that the speed with which things are changing in the web 2.0 world was having a significant impact and that this faster pace is placing a new and unexpected emphasis on the transferable skills and knowledge. It was also acknowledged that all librarians need to possess these skills, knowledge and attributes and not just the one or two role models who lead the way. The most interesting finding however was that web 2.0, library 2.0 and librarian 2.0 represented a ‘watershed’ for the LIS profession. Almost all the focus groups spoke about how they are seeing and experiencing a culture change in the profession. Librarian 2.0 requires a ‘different mindset or attitude’. The Levels of Perspective model by Daniel Kim provides one lens by which to view this finding. The focus group findings suggest that we are witnessing a re-awaking of the Australian LIS profession as it begins to move towards the higher levels of Kim’s model (ie mental models, vision). Thirty-six LIS educators participated in telephone interviews aimed at exploring the current state of LIS education in supporting the development of librarian 2.0. Skills and knowledge of LIS professionals in a web 2.0 world that were identified and discussed by the LIS educators mirrored those highlighted in the focus group discussions with LIS professionals. Similarly it was noted that librarian 2.0 needed a focus less on skills and knowledge and more on attitude. However, whilst LIS professionals felt that there was a paradigm shift within the profession. LIS educators did not speak with one voice on this matter with quite a number of the educators suggesting that this might be ‘overstating it a bit’. This study provides evidence for “disparate viewpoints” (Hallam, 2007) between LIS educators and LIS professionals that can have a significant implications for the future of not just LIS professional education specifically but for the profession generally. Library and information science education 2.0: guiding principles and models of best practice 1 Inviting the LIS academics to discuss how their teaching and learning activities support the development of librarian 2.0 was a core part of the interviews conducted. The strategies used and the challenges faced by LIS educators in developing their teaching and learning approaches to support the formation of librarian 2.0 are identified and discussed. A core part of the fellowship was the identification of best practice examples on how LIS educators were developing librarian 2.0. Twelve best practice examples were identified. Each educator was recorded discussing his or her approach to teaching and learning. Videos of these interviews are available via the Fellowship blog at .The LIS educators involved in making the videos felt uncomfortable with the term ‘best practice’. Many acknowledged that there simply seeking to do the best by their students and that there was always room for improvement. For this reason these videos are offered as examples of “great practice”. The videos are a tool for other educators to use, regardless of discipline, in developing their teaching and learning approaches to supporting web 2.0 professionals. It has been argued that the main purpose of professional education is transformation (Dall’ Alba, 2009; Dall’Alba & Barnacle, 2007). As such professional education should focus not just on skills and knowledge acquisition but also on helping students to develop ways of being the professionals in question (ie LIS professionals, teachers, lawyers, engineers).The aim of this fellowship was to establish Guidelines for Library and Information Science Education 2.0 it has however become apparent that at this point in time it is not yet possible to fulfil this aim. The fellowship has clearly identified skills and knowledge needed by the LIS professional in web 2.0 world (and beyond). It has also identified examples of ‘great practice’ by LIS educators as they endeavour to develop LIS professionals who will be successful in a web 20 world. The fellowship however has also shown that the LIS profession is currently undergoing significant attitudinal and conceptual change. Consequently, before a philosophy of LIS education 2.0 can be expressed, the Australian LIS profession must first explore and articulate what it means to be an LIS professional in the 21st century (ie a world of web 2.0 and beyond). In short, the LIS profession in Australia must take stock not of “what we know and can do” but on “who we are becoming” (Dall’Alba, 2009, p 34).

School education as social and economic governance : responsibilising communities through industry-school engagement

This article examines shifts in educational and social governance taking place in Queensland, Australia, through Industry School Engagement Strategy of Education Queensland and its Gateway Schools program. This significant educational initiative is set within the context of the social investment agenda first articulated in the education policy framework, Queensland State Education-2010. The article traces the historic extension of this governmental strategy through establishment of the Gateway Schools concept that brokers industry-school partnerships with global players in the Queensland economy. Industry sectors forming the partnerships include Minerals and Energy, Aerospace, Wine Tourism, Agribusiness, Manufacturing and Engineering, Building and Construction and ICT. We argue that this ‘post-bureaucratic’ model of schooling represents a new social settlement of neoliberal governance, in which educational outcomes align with economic objectives, and frame the conditions for community self-governance.

A communitarian theory of the education rights of students with disabilities

There is a lack of writing on the issue of the education rights of people with disabilities by authors of any theoretical persuasion. While the deficiency of theory may be explained by a variety of historical, philosophical and practical considerations, it is a deficiency which must be addressed. Otherwise, any statement of rights rings out as hollow rhetoric unsupported by sound reason and moral rectitude. This paper attempts to address this deficiency in education rights theory by postulating a communitarian theory of the education rights of people with disabilities. The theory is developed from communitarian writings on the role of education in democratic society. The communitarian school, like the community within which it nests, is inclusive. Schools both reflect and model the shape of communitarian society and have primary responsibility for teaching the knowledge and virtues which will allow citizens to belong to and function within society. Communitarians emphasise responsibilities, however, as the corollary of rights and require the individual good to yield to community good when the hard cases arise. The article not only explains the basis of the right to an inclusive education, therefore, but also engages with the difficult issue of when such a right may not be enforceable.

‘It's the end of the university as we know it (and I feel fine)’: the Generation Y student in higher education discourse

This paper examines discussions of Generation Y within higher education discourse, arguing the sector’s use of the term to describe students is misguided for three reasons. First, portraying students as belonging to Generation Y homogenises people undertaking higher education as young, middle-class and technologically literate. Second, speaking of Generation Y students allows constructivism to be reinvented as a ‘new’ learning and teaching philosophy. Third, the Generation Y university student has become a central figure in concerns about technology’s role in learning and teaching. While the notion of the ‘Generation Y student’ creates the illusion that higher education institutions understand their constituents, ultimately, it is of little value in explaining young adults’ educational experiences.

Australian higher education evaluation through assurance of learning

A collaborative research project conducted by five Australian universities inquired into the philosophy and motivation for Assurance of Learning (AoL) as a process of education evaluation. Associate Deans Teaching and Learning representing Business schools from twenty-five universities across Australia participated in telephone interviews. Data was analysed using NVIVO9. Results indicated that articulated rationale for AoL was both ensuring that students had acquired the attributes and skills the universities claimed they had, and the philosophy of continuous improvement. AoL was motivated both by ritualistic objectives to satisfy accreditation requirements and virtuous agendas for quality improvement. Closing-the-loop was emphasised, but was mostly wishful thinking for next steps beyond data collection and reporting. AoL was conceptualised as one element within the larger context of quality review, but there was no evidence of comprehensive frameworks or strategic plans.

Coteaching social education : an oasis in changing times

With the introduction and continued steady roll-out of the Australian Curriculum, teaching Social Education in 21st Century Australia has become increasingly challenging. This article explores how two teacher-educators tackled the challenge when developing a new Social Education course at a Queensland university using the strategy of coteaching. During the case study, data were collated from cogenerative dialogues, pre-service teacher questionnaires, and reflective journals. The data were subsequently explored using concepts from cultural sociology such as capital (Bourdieu, 1977) and agency and structure (Sewell, 1992). This paper examines how coteaching afforded the teacher-educators a vehicle to develop innovative curriculum and model ways to create a productive learning environment that reflected the philosophy of Social Education. It therefore speaks to higher-education institutions and schools about ways for navigating the present educational milieu through the adoption of collaborative strategies based on ethical relations that promote shared decision-making and reflexive practices.