A survey in mathematics for industry: Two-timing and matched asymptotic expansions for singular perturbation problems

Following the derivation of amplitude equations through a new two-time-scale method [O'Malley, R. E., Jr. & Kirkinis, E (2010) A combined renormalization group-multiple scale method for singularly perturbed problems. Stud. Appl. Math. 124, 383-410], we show that a multi-scale method may often be preferable for solving singularly perturbed problems than the method of matched asymptotic expansions. We illustrate this approach with 10 singularly perturbed ordinary and partial differential equations. © 2011 Cambridge University Press.

Cultural economy planning in creative cities : discourse and practice

While a growing body of research analyses the functional mechanisms of the cultural or creative economy, there has been little attention devoted to understanding how local governments translate this work into policy. Moreover, research in this vein focuses predominately on Richard Florida's creative class thesis rather than considering the wider body of work that may influence policy. This article seeks to develop a deeper understanding of how municipalities conceptualize and plan for the cultural economy through the lens of two cities held up as model ‘creative cities’ — Austin, Texas and Toronto, Ontario. The work pays particular attention to how the cities adopt and adapt leading theories, strategies and discourses of the cultural economy. While policy documents indicate that the cities embrace the creative city model, in practice agencies tend to adapt conventional economic development strategies for cultural economy activity and appropriate the language of the creative city for multiple purposes.

Helpline Discourse

Helplines are services where callers can request help, advice, information, or support. While such help is usually offered through telephone helplines, web chat and email helplines are becoming increasingly available to members of the public. Helplines tend to offer specialized services, such as responding to computer software queries, or medical and health issues, or seeking information about natural disasters. Further, they may be aimed at particular populations such as children and young people. The earliest research investigating discourse in calls to helplines in social interactional research began in the 1960s with Sacks’ early work on calls to a suicide prevention center. Since then interactional research has produced a wealth of understandings into the mundane and institutional interactional practices through which help is sought and delivered. In addition to discussing the breadth of research into helplines, this entry explores the relationship between philosophies and interactional practices of helpline services.

An intentional class design model to engage first year students with threshold concepts using the academic discourse theories of Vygotsky and Laurillard

In the context of the first-year university classroom, this paper develops Vygotsky’s claim that ‘the relations between the higher mental functions were at one time real relations between people’. By taking the main horizontal and hierarchical levels of classroom discourse and dialogue (student-student, student-teacher, teacher-teacher) and marrying these with the possibilities opened up by Laurillard’s conversational framework, we argue that the learning challenge of a ‘troublesome’ threshold concept might be met by a carefully designed sequence of teaching events and experiences for first year students, and we provide a number of strategies that exploit each level of these ‘hierarchies of discourse’. We suggest that an analytical approach to classroom design that embodies these levels of discourse in sequenced dialogic methods could be used by teachers as a strategy to interrogate and adjust teaching-in-practice especially in the first year of university study.

Making meaning in mathematics problem solving using the Reciprocal Teaching approach

This paper examines the application of the Reciprocal Teaching instructional approach to Mathematical word problems in the middle years. The Reciprocal Teaching process is extended from the four traditional strategies of predicting, clarifying, questioning and summarising, to include further cognitive reading comprehension strategies applied to the context of solving Mathematical word problems.

A discourse analysis on how the sustainability agenda is defined within the mining industry

The mining industry has positioned itself within the sustainability agenda, particularly since the establishment of the International Council of Mining and Minerals (ICMM). However, some critics have questioned this position, since mining requires the extraction of non-renewable finite resources and commercial mining companies have the specific responsibility to produce profit. Complicating matters is that terms that represent the sustainability such as ‘sustainability’ and ‘sustainable development’ have multiple definitions with varying degrees of sophistication. This work identifies eleven sustainability agenda definitions that are applicable to the mining industry and organises them into three tiers: first, Perpetual Sustainability, that focuses on mining continuing indefinitely with its benefits limited to immediate shareholders; second, Transferable Sustainability, that focuses on how mining can benefit society and the environment and third, Transitional Sustainability, that focuses on the intergenerational benefits to society and the environment even after mining ceases. Using these definitions, a discourse analysis was performed on sustainability reports from member companies of the ICMM and the academic journal Resources Policy. The discourse analysis showed that in both media the definition of the sustainability agenda was focussed on Transferable Sustainability, with the sustainability reports focused on how it can be applied within a business context while the academic journal took a broader view of mining’s social and environmental impacts.

Marx as a Critical Discourse Analyst : The Genesis of a Critical Method and its Relevance to the Critique of Global Capital (with Phil Graham)

In this paper we identify elements in Marx’s economic and political writings that are relevant to contemporary critical discourse analysis (CDA). We argue that Marx can be seen to be engaging in a form of discourse analysis. We identify the elements in Marx’s historical materialist method that support such a perspective, and exemplify these in longitudinal comparison of Marx’s texts.

Taking up the discourse : theory or praxis

This article responds to the invitation extended by Carney to engage in a dialogue on the topic of graduate legal research units. In his paper, Carney stated the approach of the Sydney course as being to teach theory rather than skills, to "pursue academic goals over skill competencies... ". The Faculty of Law at Queensland University of Technology introduced a postgraduate legal research unit in 1993 with different perspectives and purposes to the Sydney course, and given this experience, the opportunity for a discussion on aspects of such units including the theoretical versus practical approach to teaching cannot be ignored.

Indigenous students transitioning to school : responses to pre-foundational mathematics

Australian Indigenous students' mathematics performance continues to be below that of non-Indigenous students. This occurs from the early years of school, due largely to knowledge and social differences on entry to formal schooling. This paper reports on a mathematics research project conducted in one Aboriginal community school in New South Wales, Australia. The project aimed to identify and explain the ways that young Australian Indigenous students (age 2-4 years) learn number language and processes, specifically attribute language, sorting, 1-1 correspondence and, counting. The project adopted a mixed methods approach. That is, the methodology was decolonising (Smith 1999) in that it collaborated with and gave benefit back to the Indigenous community and school being researched. It was qualitative and interpretative (Burns 2000) and incorporated an action-research teaching-experiment approach where and teachers collaborated with the researchers to try new teaching methods. This paper draws on data pertaining to students' response to diagnostic interview questions, the pre- and post-test results of the interview and photographic evidence as observations during mathematics learning time. Participants referred to in this paper include one female principal (N = 1), and the transition class of students' pre- (N = 6) and post-test (N = 3) results of the pre-foundational processes (also referred to as attributes). The results were encouraging with improvements in colour (34%), patterns (33%); capacity (38%). As a result of this project, our epistemology regarding the importance of finding out about students' pre-foundational knowledge and understandings and providing a culturally appropriate learning environment with resources has been built upon.

A prostitute's progress : male prostitution in scientific discourse

This paper examines discourses of male prostitution through an analysis of scientific texts. A contrast is drawn between nineteenth-century understandings of male prostitution and twentieth-century accounts of male prostitution. In contrast to female prostitution, male prostitution was not regarded as a significant social problem throughout the nineteenth century, despite its close association with gender deviation and social disorder. Changing conceptions of sexuality, linked with the emergence of the ‘adolescent’, drew scientific attention to male prostitution during the 1940s and 1950s. Research suggested that male prostitution was a problem associated with the development of sexual identity. Through the application of scientific techniques, which tagged and differentiated male prostitute populations, a language developed about male prostitution that allowed for normative assessments and judgements to be made concerning particular classes of male prostitute. The paper highlights how a broad distinction emerged between public prostitutes, regarded as heterosexual/masculine, and private prostitutes, regarded as homosexual/effeminate. This distinction altered the way in which male prostitution was understood and governed, allowing for male prostitution to be constituted as a public health concern.

Language and literacy in mathematics: stepping stones or stumbling blocks in accelerating junior-secondary students

The authors have collaborated in the development and initial evaluation of a curriculum for mathematics acceleration. This paper reports upon the difficulties encountered with documenting student understanding using pen-and-paper assessment tasks. This leads to a discussion of the impact of students’ language and literacy on mathematical performance and the consequences for motivation and engagement as a result of simplifying the language in the tests, and extending student work to algebraic representations. In turn, implications are drawn for revisions to assessment used within the project and the language and literacy focus included within student learning experiences.

Use of genetic decompositions to scaffold the development of a structurally sequenced curriculum for mathematics acceleration

The authors have collaboratively used a graphical language to describe their shared knowledge of a small domain of mathematics, which has in turn scaffolded their re-development of a related curriculum for mathematics acceleration. This collaborative use of the graphical language is reported as a simple descriptive case study. This leads to an evaluation of the graphical language’s usefulness as a tool to support the articulation of the structure of mathematics knowledge. In turn, implications are drawn for how the graphical language may be utilised as the detail of the curriculum is further elaborated and communicated to teachers.

Furthering the discourse in postcolonial education

This editorial provides a rationale for launching the new journal 'Postcolonial Directions in Education'. It discusses the term 'postcolonialism', applying it to the study of processes of domination that have their origin in European colonialism, extending beyond the period of direct colonisation to take on new forms, notably those of neo-colonialism, dependency and the intensification of globalisation. Postcolonial theory probes identity, knowledge, and social, cultural and economic structures in historical context, and challenges structures rooted in colonialism and imperialism.The editors invite the submission of manuscripts applying such perspectives to many aspects of education.

Developing young students’ meta-representational competence through integrated mathematics and science investigations

This paper describes students’ developing meta-representational competence, drawn from the second phase of a longitudinal study, Transforming Children’s Mathematical and Scientific Development. A group of 21 highly able Grade 1 students was engaged in mathematics/science investigations as part of a data modelling program. A pedagogical approach focused on students’ interpretation of categorical and continuous data was implemented through researcher-directed weekly sessions over a 2-year period. Fine-grained analysis of the developmental features and explanations of their graphs showed that explicit pedagogical attention to conceptual differences between categorical and continuous data was critical to development of inferential reasoning.