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.

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.

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.

Associations among body size dissatisfaction, perceived dietary control, and diet history in African American and European American women

European American (EA) women report greater body dissatisfaction and less dietary control than do African American (AA) women. This study investigated whether ethnic differences in dieting history contributed to differences in body dissatisfaction and dietary control, or to differential changes that may occur during weight loss and regain. Eighty-nine EA and AA women underwent dual-energy X-ray absorptiometry to measure body composition and completed questionnaires to assess body dissatisfaction and dietary control before, after, and one year following, a controlled weight-loss intervention. While EA women reported a more extensive dieting history than AA women, this difference did not contribute to ethnic differences in body dissatisfaction and perceived dietary control. During weight loss, body satisfaction improved more for AA women, and during weight regain, dietary self-efficacy worsened to a greater degree for EA women. Ethnic differences in dieting history did not contribute significantly to these differential changes. Although ethnic differences in body image and dietary control are evident prior to weight loss, and some change differentially by ethnic group during weight loss and regain, differences in dieting history do not contribute significantly to ethnic differences in body image and dietary control.

Truth, obligation and ethics in the propagation of democracy

In this paper I present an analysis of the language used by the National Endowment for Democracy (NED) on its website (NED, 2008). The specific focus of the analysis is on the NED's high usage of the word “should” revealed in computer assisted corpus analysis using Leximancer. Typically we use the word “should” as a term to propose specific courses of action for ourselves and others. It is a marker of obligation and “oughtness”. In other words, its systematic institutional use can be read as a statement of ethics, of how the NED thinks the world ought to behave. As an ostensibly democracy-promoting institution, and one with a clear agenda of implementing American foreign policy, the ethics of NED are worth understanding. Analysis reveals a pattern of grammatical metaphor in which “should” is often deployed counter intuitively, and sometimes ambiguously, as a truth-making tool rather than one for proposing action. The effect is to present NED's imperatives for action as matters of fact rather than ethical or obligatory claims.

The 2010 Native American and Indigenous Studies Association Conference

The 2010 Native American Indigenous Studies Conference was held at The Westin La Paloma Resort, Tucson, Arizona, USA from 20-22 May. The conference was scholarly and interdisciplinary and intended for Indigenous and non-Indigenous scholars who work in American Indian/ Native American/ First Nations/ Aboriginal/ Indigenous Studies. The 2010 gathering attracted 768 registrations from the USA, Canada, Hawaii, Mexico, New Zealand and Australia and other countries. This paper is a personal reflection and overview of the 2010 Conference.

Theory-of-Mind Continuum Model: Why Mind Matters in Philosophy, Psychology and Education

Theory-of-Mind has been defined as the ability to explain and predict human behaviour by imputing mental states, such as attention, intention, desire, emotion, perception and belief, to the self and others (Astington & Barriault, 2001). Theory-of-Mind study began with Piaget and continued through a tradition of meta-cognitive research projects (Flavell, 2004). A study by Baron-Cohen, Leslie and Frith (1985) of Theory-of-Mind abilities in atypically developing children reported major difficulties experienced by children with autism spectrum disorder (ASD) in imputing mental states to others. Since then, a wide range of follow-up research has been conducted to confirm these results. Traditional Theory-of-Mind research on ASD has been based on an either-or assumption that Theory-of-Mind is something one either possesses or does not. However, this approach fails to take account of how the ASD population themselves experience Theory-of-Mind. This paper suggests an alternative approach, Theory-of-Mind continuum model, to understand the Theory-of-Mind experience of people with ASD. The Theory-of-Mind continuum model will be developed through a comparison of subjective and objective aspects of mind, and phenomenal and psychological concepts of mind. This paper will demonstrate the importance of balancing qualitative and quantitative research methods in investigating the minds of people with ASD. It will enrich our theoretical understanding of Theory-of-Mind, as well as contain methodological implications for further studies in Theory-of-Mind

Embedding 'philosophy in the classroom' in pre-service teacher education

The holistic conception of the troika, as described in the first chapter, centres on the relationship between the implicit and explicit teaching of values the nurturing of the specific dimensions of quality teaching and the opportunity to ‘walk the talk’ of the values education program through aspects such as practical citizenship (Lovat, Toomey, Clement, Crotty & Nielsen, 2009). It is proposed in this chapter that the conception can be realized through the embedding of Philosophy in the Classroom within pre-service teaching programs. The troika, a Russian sleigh with three horses, only function well when there is complete synergy and balance between all Classroom is a scaffold for ensuring that all three elements of the troika, namely, quality teaching, values education and service learning in the form of education for citizenship, exist within the classroom to achieve an optimal learning, growth and wellbeing for all students. For this to be more widely accomplished Philosophy in the Classroom and discusses how it constitutes a successful synergy and balance of the troika for effective teaching. It then proposes how it might be embedded into pre-service teacher education.

Imagination

Imagination is a capacity of internal visualization, concept creation and manipulation not directly dependent upon sensation. Imagination is associated with a range of phenomena: mental imagery, fancy, inventiveness, insight, counterfactual reasoning, pretence, simulation and conceivability.

Embracing Philosophy and Raising the Standard of Pre-service Teacher Education Programs

In this chapter, a rationale is developed for incorporating philosophy into teacher training programs as a means of both preparing quality teachers for the 21st century and meeting the expectations detailed in the professional standards established by the statutory authority that regulates the profession in Queensland, the Queensland College of Teaching is presented. Furthermore, in-service teachers from Buranda State School, a Brisbane primary school that has been successfully teaching philosophy to its students for over 10 years, shares their experiences of teaching philosophy and how it has enhanced student learning and the quality of teaching and professionalism of the teachers. Finally, the implications of embedding philosophy into teacher training programs are explored in terms of developing the personal integrity of beginning teachers.

Generalising across borders : policy and the limits of educational science.

AERA Distinguished Lecture, Annual Meetings of the American Educational Research Association, New Orleans, 8 April 2011. How well does educational policy, innovation and science cross borders? What are the parameters of a generalisable cultural science of education? What constitutes a principled policy 'borrowing'?

Linking the American Time Use Survey (ATUS) and the Compendium of Physical Activities : methods and rationale

Background: The 2003 Bureau of Labor Statistics American Time Use Survey (ATUS) contains 438 distinct primary activity variables that can be analyzed with regard to how time is spent by Americans. The Compendium of Physical Activities is used to code physical activities derived from various surveys, logs, diaries, etc to facilitate comparison of coded intensity levels across studies. ------ ----- Methods: This paper describes the methods, challenges, and rationale for linking Compendium estimates of physical activity intensity (METs, metabolic equivalents) with all activities reported in the 2003 ATUS. ----- ----- Results: The assigned ATUS intensity levels are not intended to compute the energy costs of physical activity in individuals. Instead, they are intended to be used to identify time spent in activities broadly classified by type and intensity. This function will complement public health surveillance systems and aid in policy and health-promotion activities. For example, at least one of the future projects of this process is the descriptive epidemiology of time spent in common physical activity intensity categories. ----- ----- Conclusions: The process of metabolic coding of the ATUS by linking it with the Compendium of Physical Activities can make important contributions to our understanding of Americans’ time spent in health-related physical activity.

Me and my body : the relevance of the difference for the distinction between withdrawing life support and euthanasia

In this paper I discuss David Shaw’s claim that the body of a terminally ill person can be conceived as a kind of life-support, akin to an artificial ventilator. I claim that this position rests upon an untenable dualism between the mind and the body. Given that dualism continues to be attractive to some thinkers, I attempt to diagnose the reasons why it continues to be attractive, as well as to demonstrate its incoherence, drawing on some recent work in the philosophy of psychology. I conclude that, if my criticisms are sound, Shaw’s attempt to deny the distinction between withdrawal and euthanasia fails.

Philosophy, behaviour disorders, and the school

The recent exponential rise in the number of behaviour disorders has been the focus of a wide range of commentaries, ranging from the pedagogic and the administrative, to the sociological, and even the legal. This book will be the first to apply, in a systematic and thorough manner, the ideas of the foundational discipline of philosophy. A number of philosophical tools are applied here, tools arising through the medium of the traditional philosophical debates, such as those concerning governance, truth, logic, ethics, free-will, law and language. Each forms a separate chapter, but together they constitute a comprehensive, rigorous and original insight into what is now an important set of concerns for all those interested in the governance of children. The intention is threefold: first, to demonstrate the utility, accessibility and effectiveness of philosophical ideas within this important academic area. Philosophy does not have to be regarded an arcane and esoteric discipline, with only limited contemporary application, far from it. Second, the book offers a new set of approaches and ideas for both researchers and practitioners within education, a field is in danger of continually using the same ideas, to endlessly repeat the same conclusions. Third, the book offers a viable alternative to the dominant psychological model which increasingly employs pathology as its central rationale for conduct. The book would not only be of interest to mainstream educators, and to those students and academics interested in philosophy, and more specifically, the application of philosophical ideas to educational issues, it would also be an appropriate text for courses on education and difference, and due to the breadth of the philosophical issues addressed, courses on applied philosophy.