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.

Scaffolding an EFL (English as a foreign language) ‘effective writing’ class in a hybrid learning community

This study sought to establish and develop innovative instructional procedures, in which scaffolding can be expanded and applied, in order to enhance learning of English as a Foreign Language (EFL) writing skills in an effective hybrid learning community (a combination of face-to-face and online modes of learning) at the university where the researcher is working. Many educational experts still believe that technology has not been harnessed to its potential to meet the new online characteristics and trends. There is also an urgency to reconsider the pedagogical perspectives involved in the utilisation of online learning systems in general and the social interactions within online courses in particular that have been neglected to date. An action research design, conducted in two cycles within a duration of four months, was utilised throughout this study. It was intended not only to achieve a paradigm shift from transmission-absorption to socio-constructivist teaching/learning methodologies but also to inform practice in these technology-rich environments. Five major findings emerged from the study. First, the scaffolding theory has been extended. Two new scaffolding types (i.e., quasi-transcendental scaffolding and transcendental scafolding), two scaffolding aspects (i.e., receptive and productive) and some scaffolding actions (e.g., providing a stimulus, awareness, reminder, or remedy) for EFL writing skills in an effective hybrid learning community have been identified and elaborated on. Second, the EFL ‘Effective Writing’ students used the scaffolds implemented in a hybrid environment to enhance and enrich their learning of writing of English essays. The online activities, conducted after the F2F sessions most of the time, gave students greater opportunities to both reinforce and expand the knowledge they had acquired in the F2F mode. Third, a variety of teaching techniques, different online tasks and discussion topics utilised in the two modes bolstered the students’ interests and engagement in their knowledge construction of how to compose English-language essays. Fourth, through the scaffolded activities, the students learned how to scaffold themselves and thus became independent learners in their future endeavours of constructing knowledge. Fifth, the scaffolding-to-scaffold activities provided the students with knowledge on how to effectively engage in transcendental scaffolding actions and facilitate the learning of English writing skills by less able peers within the learning community. Thus, the findings of this current study extended earlier understandings of scaffolding in an EFL hybrid learning environment and will contribute to the advancement of future ICT-mediated courses in terms of their scaffolding pedagogical aspects.

Crossing the language and cultural divide : the challenges of educating Asian law students in a globalising world

In 2004, there were sweeping, radical changes made to the underlying legal framework regulating life in China. This reflected such things as the incorporation of basic international human rights standards into domestic law - not only in China but in countries worldwide which highlights the increasingly global nature of many important legal issues. China is not immune from this development of cross pollination of legal processes. This has led to an increase in the internationalisation of legal education and the rapid rise in the number of overseas students who undertake at least part of their university studies in a foreign country. Academics need to develop cross-cultural sensitivity in teaching these overseas students; there are important reasons why the educative process needs to meet the different set of needs presented by international students who come to study in Australia. This teaching note sets out the experiences of two particular situations, the teaching of Business Law to Asian students and an innovative Australian postgraduate program taught in Mandarin.

Validation of an Australian sign language instrument of outcome measurement for adults in mental health settings

Objective: There are currently no adult mental health outcome measures that have been translated into Australian sign language (Auslan). Without a valid and reliable Auslan outcome measure, empirical research into the efficacy of mental health interventions for sign language users is unattainable. To address this research problem the Outcome Rating Scale (ORS), a measure of general functioning, was translated into Auslan and recorded on to digital video disk for use in clinical settings. The purpose of the present study was therefore to examine the reliability, validity and acceptability of an Auslan version of the ORS (ORS-Auslan). Method: The ORS-Auslan was administered to 44 deaf people who use Auslan as their first language and who identify as members of a deaf community (termed ‘Deaf’ people) on their first presentation to a mental health or counselling facility and to 55 Deaf people in the general community. The community sample also completed an Auslan version of the Depression Anxiety Stress Scale-21 (DASS-21). Results: t-Tests indicated significant differences between the mean scores for the clinical and community sample. Internal consistency was acceptable given the low number of items in the ORS-Auslan. Construct validity was established by significant correlations between total scores on the DASS-21-Auslan and ORS-Auslan. Acceptability of ORS-Auslan was evident in the completion rate of 93% compared with 63% for DASS-21-Auslan. Conclusions: This is the only Auslan outcome measure available that can be used across a wide variety of mental health and clinical settings. The ORS-Auslan provides mental health clinicians with a reliable and valid, brief measure of general functioning that can significantly distinguish between clinical and non-clinical presentations for members of the Deaf community.

Gifted young adolescents and email : developing a personal language of self

This paper reports on the use of email as a means to access the self-constructions of gifted young adolescents. Australian research shows that gifted young adolescents may feel more lonely and misunderstood than their same-age counterparts, yet they are seldom asked about their lives. Emerging use of online methods as a means of access to individual lives and perceptions has demonstrated the potential offered by the creation of digital texts as narrative data. Details are given of a qualitative study that engaged twelve children aged between 10 and 14 years, who were screened for giftedness, in a project involving the generation of emailed journal entries sent over a period of 6 months. With emphasis on participatory principles, individual young adolescents produced self-managed journal entries that were written and sent to the researcher from personal computers outside the school setting. Drawing from a theoretical understanding of self as constructed within dialogic relationships, the digital setting of email is proposed as a narrative space that fosters healthy self-disclosure. This paper outlines the benefits of using email as a means to explore emotions, promote reflective accounts of self and support the development of a personal language for self-expression. Individual excerpts will be presented to show that the harnessing of personal narratives within an email context has potential to yield valuable insights into the emotions, personal realities and experiences of gifted young adolescents. Findings will be presented to show that the co-construction of self-expressive and explanatory narratives supported by a facilitative adult listener promoted healthy self-awareness amongst participants. This paper contributes to appreciative conversations about using online methods as a flexible and practical avenue for conducting educational research. Furthermore, digital writing in email form will be presented as having distinct advantages over face-to-face methods when utilised with gifted young adolescents who may be unwilling to disclose information within school-based settings.

Traveller’s Tales : The Expatriate English Language Teacher in the New Global Culture

Most of the research into ELT has focused on its linguistic and methodological aspects, which are based on Western scientific traditions. The contributions and experiences of English language teachers themselves, especially their work in overseas contexts, have frequently been overlooked. This volume aims to document the complexity of ELT as ‘work’ in new global economic and cultural conditions, and to explore how this complexity is realised in the everyday experiences of ELT teachers. The development of ELT from the colonial experience to its current status as a global commodity is explored; ELT is then situated in the discourses of globalisation, specifically within Appadurai’s theorisation of global flows of people, images, ideas, technology and money, or scapes. Within this framework, narratives are constructed from the experiences of Native-speaking English teachers. These reveal much about the personal, pedagogical and cultural dimensions of ELT work in non-Centre countries, and will contribute to a greater understanding of the intercultural dimensions of ELT for all those who work in it, and in related educational fields.

What is language and how is it learnt?

This chapter describes the nature of human language and introduces theories of language acquisition.

Teaching English as an additional language in senior high school : critical discourses in critical times

This paper presents a Critical Discourse Analysis (CDA) of four policy documents currently offering ‘sets of possibilities’ for the teaching of English as an additional or second language (hereafter EAL/ESL) in senior classrooms in Queensland, Australia. The aim is to identify the ways in which each document re-presents the notion of critical literacy. Leximancer software, and Fairclough’s textually-oriented discourse analysis method (2001, 2003) are used to interrogate the relevant sections of the documents for the ways in which they re-present (sic) and construct the discourses around critical language study. This paper presents the description, interpretation and explanation of the discourses in these documents which constitute part of a larger project in which teacher interviews and classroom teaching are also investigated for the ways in which ‘the critical’ is constructed and contested in knowledge and practice.