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.

‘Live your liberation, don’t lobby for it’ : Australian queer student activists’ perspectives of same-sex marriage

One topic covered in Australian queer university student print media is the legalisation of same-sex marriage. The legalisation of same-sex marriage is currently generating much debate in Western queer communities. Same-sex marriage is legalised in some countries such as, Canada, Spain, the Netherlands and Belgium. It has been outlawed in Australia and most states in the US. Campaigns continue to reverse these restrictions. Other countries, such as the UK and New Zealand allow same-sex civil unions, providing couples with the rights afforded to married couples. There is a range of research documenting queer communities’ attitudes towards this issue (for example Lannutti 2005; Clarke, Burgoyne and Burns 2006; Yep, Lovaas and Elia 2003; Wolfson 1993; Egan and Sherrill 2005). These studies document broad community views as well as those of community sub-sections. For example, Yip (2004) looks at the views of gay and lesbian Christians on same-sex marriage and Lahey and Alderson (2004) document the experiences of same-sex couples who have gotten married or who are waiting to get married. Philosophical analyses consider the legalisation of same-sex marriage in relation to, for example, liberalism, equal rights, liberation, queer theory, citizenship, history, activism, religious discourse and feminism (Ferguson 2007; Jordan 2005; Josephson 2005; Lipton 2006; Sullivan and Chauncey 2005; Riggs 2007). This paper explores Australian queer university student activist media’s representation of same-sex marriage, and the debates surrounding its legalisation. It examines a selection of queer student media from four metropolitan Australian universities, and the 2003 and 2004 editions of national queer student publication, Querelle. This paper uses discourse analysis of queer student activists’ media representations of marriage to investigate this issue in one specific context – metropolitan Australian universities. This paper thus contributes to the history of queer activism, documenting what one group of young people say about the legalisation of same-sex marriage, and furthers research on queer perspectives of marriage and same-sex relationships.

Nursing students’ knowledge and practice of infection control precautions : an educational intervention

Aim. This paper is a report of the effectiveness of a purpose-designed education program in improving undergraduate nursing students’ understanding and practice of infection control precautions. Background. The severe acute respiratory syndrome outbreak in 2003 highlighted that healthcare workers were under-prepared for such an epidemic. While many in-service education sessions were arranged by institutions in response to the outbreak, preservice nursing education has overlooked preparation for handling such infectious disease epidemics. Method. A quasi-experimental design was used and a 16-hour, purpose-designed infection control education programme was implemented for preservice nursing students in southern Taiwan. Self-administered questionnaires were distributed at three time points during the period September 2005 to April 2006 to examine the sustainability and effectiveness of the intervention. Results. A total of 175 preservice nursing students participated in the study. Following the education programme, students in the intervention group showed a statistically significant improvement across time in their knowledge of these precautions [F(2, 180) = 13Æ53, P < 0Æ001] and confidence in resolving infectionrelated issues [F(1Æ79, 168Æ95) = 3Æ24] when compared with those in the control group. Conclusion. To improve nursing students’ capacity in responding to infectious epidemics, an educational programme that integrates the theme of infection precautions, learning theory and teaching strategies is recommended for all nursing institutes.

Imaginary relish and exquisite torture : the elaborated intrusion theory of desire

The authors argue that human desire involves conscious cognition that has strong affective connotation and is potentially involved in the determination of appetitive behavior rather than being epiphenomenal to it. Intrusive thoughts about appetitive targets are triggered automatically by external or physiological cues and by cognitive associates. When intrusions elicit significant pleasure or relief, cognitive elaboration usually ensues. Elaboration competes with concurrent cognitive tasks through retrieval of target related information and its retention in working memory. Sensory images are especially important products of intrusion and elaboration because they simulate the sensory and emotional qualities of target acquisition. Desire images are momentarily rewarding but amplify awareness of somatic and emotional deficits. Effects of desires on behavior are moderated by competing incentives, target availability, and skills. The theory provides a coherent account of existing data and suggests new directions for research and treatment.

Critical Systems Theory: A Political Economy of Language, Thought, and Technology

An emergent form of political economy, facilitated by information and communication technologies (ICTs), is widely propagated as the apotheosis of unmitigated social, economic, and technological progress. Meanwhile, throughout the world, social degradation and economic inequality are increasing logarithmically. Valued categories of thought are, axiomatically, the basic commodities of the “knowledge economy”. Language is its means of exchange. This paper proposes a sociolinguistic method with which to critically engage the hyperbole of the “Information Age”. The method is grounded in a systemic social theory that synthesises aspects of autopoiesis and Marxist political economy. A trade policy statement is analysed to exemplify the sociolinguistically created aberrations that are today most often construed as social and political determinants.

Designing for engagement : building IT systems

Context The School of Information Technology at QUT has recently undertaken a major restructuring of their Bachelor of Information Technology (BIT) course. Some of the aims of this restructuring include a reduction in first year attrition and to provide an attractive degree course that meets both student and industry expectations. Emphasis has been placed on the first semester in the context of retaining students by introducing a set of four units that complement one another and provide introductory material on technology, programming and related skills, and generic skills that will aid the students throughout their undergraduate course and in their careers. This discussion relates to one of these four fist semester units, namely Building IT Systems. The aim of this unit is to create small Information Technology (IT) systems that use programming or scripting, databases as either standalone applications or web applications. In the prior history of teaching introductory computer programming at QUT, programming has been taught as a stand alone subject and integration of computer applications with other systems such as databases and networks was not undertaken until students had been given a thorough grounding in those topics as well. Feedback has indicated that students do not believe that working with a database requires programming skills. In fact, the teaching of the building blocks of computer applications have been compartmentalized and taught in isolation from each other. The teaching of introductory computer programming has been an industry requirement of IT degree courses as many jobs require at least some knowledge of the topic. Yet, computer programming is not a skill that all students have equal capabilities of learning (Bruce et al., 2004) and this is clearly shown by the volume of publications dedicated to this topic in the literature over a broad period of time (Eckerdal & Berglund, 2005; Mayer, 1981; Winslow, 1996). The teaching of this introductory material has been done pretty much the same way over the past thirty years. During this period of time that introductory computer programming courses have been taught at QUT, a number of different programming languages and programming paradigms have been used and different approaches to teaching and learning have been attempted in an effort to find the golden thread that would allow students to learn this complex topic. Unfortunately, computer programming is not a skill that can be learnt in one semester. Some basics can be learnt but it can take many years to master (Norvig, 2001). Faculty data typically has shown a bimodal distribution of results for students undertaking introductory programming courses with a high proportion of students receiving a high mark and a high proportion of students receiving a low or failing mark. This indicates that there are students who understand and excel with the introductory material while there is another group who struggle to understand the concepts and practices required to be able to translate a specification or problem statement into a computer program that achieves what is being requested. The consequence of a large group of students failing the introductory programming course has been a high level of attrition amongst first year students. This attrition level does not provide good continuity in student numbers in later years of the degree program and the current approach is not seen as sustainable.

Rethinking youth cultures : the case of the 'Gothics'

This paper has argued that subcultural social formations, such as the Gothics, did not evolve as resistance to a dominant culture. Instead, they are a response to the governmental construction of youth as an object of knowledge—the by-product of particular forms of government, generated by specific power/knowledge relations. Accordingly, attempts to account for the phenomenon of ‘subcultures’ should begin, not with notions of a shared, resistant class/generational consciousness, but rather with detailed investigations of specific forms of government, such as those involving conventions and customs within the fashion and music industries, the distribution of technologies of marketing and consumption, the adoption of various techniques of self-shaping, the prevalence of different journalistic practices, routines of policing, and so on. ‘Subcultural style’ is not an expression of relationship between a given social class, its material conditions and its economic and cultural aspirations. Rather, it constitutes the construction of particular habitus, shaped by fashion and leisure activities, through which certain youthful personae are given their form.

Re-assessing streetkids : a critique of subculture theory

Focusing on the notion of street kids, the paper suggests that youth be viewed in an alternative way to the subculture theory associated with the Center for Contemporary Cultural Studies in Birmingham (CCCS). It is argued that not only is subculture theory an unsuitable mechanism for understanding homeless youth but also, and more importantly, is itself fundamentally problematic. It is suggested that the work of Michel Foucault necessitates a reevaluation of the domain assumptions underlying subculture theory and offers in its place a model that relocates street kids, and youth itself, as artifacts of a network of governmental strategies.

Alternative schooling programs for at risk youth : three case studies

This thesis develops a critical realist explanatory critique of alternative schooling programs for youth at risk taking place at three case study sites. Throughout the thesis the author pursues the question, \Are alternative provisions of schooling working academically and socially for youth at risk?. The academic lens targets literacy learning and associated pedagogies. Social outcomes are posited as positive social behaviours and continued engagement in learning. A four phased analysis, drawing on critical realism, interpretive and subject specific theories is used to elicit explanations for the research question. An overall framework is a critical realist methodology as set out by Danermark, Ekstrom, Jakobsen and Karlsson (2002, p. 129). Consequently phase one describes the phenomena of alternative schooling programs taking place at three case study sites. This is reported first as staff narratives that are resolved into imaginable historical causal components of \generative events., \prior schooling structures., \models of alternative schooling., \purpose., \individual agency., and \relations with linked community organisations.. Then transcendental questions are posed about each component using retroduction to uncover structures, underlying mechanisms and powers, and individual agency. In the second phase the researcher uses modified grounded theory methodology to theoretically redescribe causal categories related to a \needed different teaching and administrative approach. that emerged from the previous critique. A transcendental question is then applied to this redescription. The research phenomena are again theoretically redescribed in the third phase, this time using three theoretically based constructs associated with literacy and literacy pedagogies; the NRS, the 4 Resources Model, and Productive Pedagogies. This redescription is again questioned in terms of its core or \necessary. components. The fourth phase makes an explanatory critique by comparing and critiquing all previous explanations, recontextualising them in a wider macro reality of alternative schooling. Through this critical realist explanatory critiquing process, a response emerges not only to whether alternative provisions of schooling are working, but also how they are working, and how they are not working, with realistically based implications for future improvement.

Education research and youth subculture theory

Recent theoretical developments (particularly those involving the work of Michel Foucault) have challenged the foundations upon which subcultural analysis is built. It is not the intention of this paper to take issue with the underpinning neo-Marxist assumptions concerning hegemony, consciousness and culture. Rather, the intention is simply to problematise the use of subculture theory in terms of its totalising, normalising and dichotomising nature.

Southern theory and its dynamics for postcolonial education

This paper discusses how the exploration of social texts and historical contexts from the global 'South', as put forward in Raewyn Connell's study 'Southern Theory' (2007), can improve the theoretical tools used in postcolonial education analysis. Connell analyses a selection of excellent and compelling social theory texts written by scholars in Africa, India, Iran, Latin America and Australia to show how they challenge and counter the silences, distortions and plain lies of dominant Western social theory. These texts of the global South do not mince words in laying bare the role of the institutions and elites of the West in the destruction, dispossession, and bloodshed involved in creating the world in which we live, and in perpetuating its catastrophes. The texts also reveal intense debates between scholars over their conceptualisations of local, national and global society. My paper argues that this kind of work is of vital importance to postcolonial studies in education. It helps education scholars to uncover the problematic assumptions and distortions of dominant education thought, and understand different ways of seeing. Postcolonial educators could use this to help both students and teacher unlearn many of our taught perceptions of the world, whether in the global North or the global South. Developing a countervailing social theory in education would sharpen our questioning of the structures of schooling as they relate to society, and tease out new dimensions of postcolonial leadership for education.

The role of fluency in a mathematics item with an embedded graphic: Interpreting a pie chart.

The purpose of this study was to identify the pedagogical knowledge relevant to the successful completion of a pie chart item. This purpose was achieved through the identification of the essential fluencies that 12–13-year-olds required for the successful solution of a pie chart item. Fluency relates to ease of solution and is particularly important in mathematics because it impacts on performance. Although the majority of students were successful on this multiple choice item, there was considerable divergence in the strategies they employed. Approximately two-thirds of the students employed efficient multiplicative strategies, which recognised and capitalised on the pie chart as a proportional representation. In contrast, the remaining one-third of students used a less efficient additive strategy that failed to capitalise on the representation of the pie chart. The results of our investigation of students’ performance on the pie chart item during individual interviews revealed that five distinct fluencies were involved in the solution process: conceptual (understanding the question), linguistic (keywords), retrieval (strategy selection), perceptual (orientation of a segment of the pie chart) and graphical (recognising the pie chart as a proportional representation). In addition, some students exhibited mild disfluencies corresponding to the five fluencies identified above. Three major outcomes emerged from the study. First, a model of knowledge of content and students for pie charts was developed. This model can be used to inform instruction about the pie chart and guide strategic support for students. Second, perceptual and graphical fluency were identified as two aspects of the curriculum, which should receive a greater emphasis in the primary years, due to their importance in interpreting pie charts. Finally, a working definition of fluency in mathematics was derived from students’ responses to the pie chart item.

Towards a model of the institutional logics of climate change

The proliferation of innovative schemes to address climate change at international, national and local levels signals a fundamental shift in the priority and role of the natural environment to society, organizations and individuals. This shift in shared priorities invites academics and practitioners to consider the role of institutions in shaping and constraining responses to climate change at multiple levels of organisations and society. Institutional theory provides an approach to conceptualising and addressing climate change challenges by focusing on the central logics that guide society, organizations and individuals and their material and symbolic relationship to the environment. For example, framing a response to climate change in the form of an emission trading scheme evidences a practice informed by a capitalist market logic (Friedland and Alford 1991). However, not all responses need necessarily align with a market logic. Indeed, Thornton (2004) identifies six broad societal sectors each with its own logic (markets, corporations, professions, states, families, religions). Hence, understanding the logics that underpin successful –and unsuccessful– climate change initiatives contributes to revealing how institutions shape and constrain practices, and provides valuable insights for policy makers and organizations. This paper develops models and propositions to consider the construction of, and challenges to, climate change initiatives based on institutional logics (Thornton and Ocasio 2008). We propose that the challenge of understanding and explaining how climate change initiatives are successfully adopted be examined in terms of their institutional logics, and how these logics evolve over time. To achieve this, a multi-level framework of analysis that encompasses society, organizations and individuals is necessary (Friedland and Alford 1991). However, to date most extant studies of institutional logics have tended to emphasize one level over the others (Thornton and Ocasio 2008: 104). In addition, existing studies related to climate change initiatives have largely been descriptive (e.g. Braun 2008) or prescriptive (e.g. Boiral 2006) in terms of the suitability of particular practices. This paper contributes to the literature on logics by examining multiple levels: the proliferation of the climate change agenda provides a site in which to study how institutional logics are played out across multiple, yet embedded levels within society through institutional forums in which change takes place. Secondly, the paper specifically examines how institutional logics provide society with organising principles –material practices and symbolic constructions– which enable and constrain their actions and help define their motives and identity. Based on this model, we develop a series of propositions of the conditions required for the successful introduction of climate change initiatives. The paper proceeds as follows. We present a review of literature related to institutional logics and develop a generic model of the process of the operation of institutional logics. We then consider how this is applied to key initiatives related to climate change. Finally, we develop a series of propositions which might guide insights into the successful implementation of climate change practices.