Recognising and respecting Torres Strait Islander mathematics knowledges and home languages through mainstream mathematics education [Abstract]

This abstract provides a preliminary discussion of the importance of recognising Torres Strait Islander knowledges and home languages of mathematics education. It stems from a project involving Torres Strait Islander Teachers and Teacher Aides and university based researchers who are working together to enhance the mathematics learning of students from Years 4-9. A key focus of the project is that mathematics is relevant and provides students with opportunities for further education, training and employment. Veronica Arbon (2008) questions the assumptions underpinning Western mainstream education as beneficial for Aboriginal and Torres Strait Islander people which assumes that it enables them to better participate in Australian society. She asks “how de we best achieve outcomes for and with Indigenous people conducive to our cultural, physical and economic sustainability as defined by us from Indigenous knowledge positions?” (p. 118). How does a mainstream education written to English conventions provide students with the knowledge and skills to participate in daily life, if it does not recognise the cultural identity of Indigenous students as it should (Priest, 2005; cf. Schnukal, 2003)? Arbon (2008) states that this view is now brought into question with calls for both ways education where mainstream knowledge and practices is blended with Indigenous cultural knowledges of learning. This project considers as crucial that cultural knowledges and experiences of Indigenous people to be valued and respected and given the currency in the same way that non Indigenous knowledge is (Taylor, 2003) for both ways education to work.

High quality/high equity systems of education: Curriculum, teachers and reform in the search for equitable outcomes for all students

The issue of what an effective high quality / high equity education system might look like remains contested. Indeed there is more educational commentary on those systems that do not achieve this goal (see for example Luke & Woods, 2009 for a detailed review of the No Child Left Behind policy initiatives put forward in the United States under the Bush Administration) than there is detailed consideration of what such a system might enact and represent. A long held critique of socio cultural and critical perspectives in education has been their focus on deconstruction to the supposed detriment of reconstructive work. This critique is less warranted in recent times based on work in the field, especially the plethora of qualitative research focusing on case studies of ‘best practice’. However it certainly remains the case that there is more work to be done in investigating the characteristics of a socially just system. This issue of Point and Counterpoint aims to progress such a discussion. Several of the authors call for a reconfiguration of the use of large scale comparative assessment measures and all suggest new ways of thinking about quality and equity for school systems. Each of the papers tackles different aspects of the problematic of how to achieve high equity without compromising quality within a large education system. They each take a reconstructive focus, highlighting ways forward for education systems in Australia and beyond. While each paper investigates different aspects of the issue, the clearly stated objective of seeking to delineate and articulate characteristics of socially just education is consistent throughout the issue.

Using information criteria to select the correct variance–covariance structure for longitudinal data in ecology

1. Ecological data sets often use clustered measurements or use repeated sampling in a longitudinal design. Choosing the correct covariance structure is an important step in the analysis of such data, as the covariance describes the degree of similarity among the repeated observations. 2. Three methods for choosing the covariance are: the Akaike information criterion (AIC), the quasi-information criterion (QIC), and the deviance information criterion (DIC). We compared the methods using a simulation study and using a data set that explored effects of forest fragmentation on avian species richness over 15 years. 3. The overall success was 80.6% for the AIC, 29.4% for the QIC and 81.6% for the DIC. For the forest fragmentation study the AIC and DIC selected the unstructured covariance, whereas the QIC selected the simpler autoregressive covariance. Graphical diagnostics suggested that the unstructured covariance was probably correct. 4. We recommend using DIC for selecting the correct covariance structure.

Learning to be literate : issues of pedagogy for recently arrived refugee youth in Australia

This paper focuses on issues of access to productive literacy learning as part of socially just schooling for recently arrived refugee youth within Australia. It argues that a sole reliance on traditional ESL pedagogy is failing this vulnerable group of students, who differ significantly from past refugees who have settled in Australia. Many have been ‘placeless’ for some time, are likely to have received at best an interrupted education before arriving in Australia, and may have experienced signification trauma (Christie & Sidhu, 2006; Cottone, 2004; Miller, Mitchell, & Brown, 2005). Australian Government policy has resulted in spacialized settlement, leaving particular schools dealing with a large influx of refugee students who may be attending school for the first time (Centre for Multicultural Youth Issues, 2004; Sidhu & Christie, 2002). While this has implications generally, it has particular consequences for secondary school students attempting to learn English literacy in short periods of time, without basic foundations in either English or print-based literacy in any first language (Centre for Multicultural Youth Issues, 2006). Many of these students leave schools without the most basic early literacy practices, having endured several years of pedagogy pitched well beyond their needs. This paper suggests that schools must take up three key roles: to educate, to provide a site for the development of civic responsibility, and to act as a site for welfare with responsibility. As a system, our department needs to work out what can we do for 17-18 year olds that are coming into our school system in year 10 without more than 1-2 years of education. I don't think there is a policy about what to do. – (T2-ESL teacher)

Undressing Kellerman, Uncovering Broadhurst : the modern woman and "un-Australia"

This article explores the contributions of two unique Australian women, Annette Kellerman and Florence Broadhurst, to global fashion and aesthetics through subverting and challenging female gender roles of the early twentieth century. These two women are brought together here as a means of highlighting their markedly contrasting social tactics: undressing versus layering. Kellerman's body became an instrument in her quest for global fame, engaging in daring public "undress" in swimming and diving performances around the world that served to show case her innovative swimwear design. In contrast, Broadhurst, through repeated reconstructions of her persona and constant relayering of identities, concocted versions of herself in order to pass through Shanghai, London, and Sydney societies. Their lives exist as binaristic parallels, expressing contrasting values of un-Australianness - the disavowal of national identity; and Australianness - the promotion of national identity. Both Kellerman and Broadhurst tested the limits of body, dress and national identity as vehicles for global recognition. The recent interest in their historical roles is evidenced in the films "The original Mermaid"( 2004) and "Unfolding Florence" (2005) in addition to numerous books and journal articles. Despite this resurgent public recognition of their lives and achievements, scholarly analysis of their legacies in the fields of fashion and design are still relatively neglected. This article explores their contributions to celebrity and modernity, fashion and gender as modern un-Australian women.

Young Australians reading in a digital world

The realities of new technological and social conditions since the 1990s demand a new approach to literacy teaching. Looking onward from the original statement of aims of the multiliteracies movement in 1996, this volume brings together top-quality scholarship and research that has embraced the notion and features new contributions by many of the originators of this approach to literacy. Drawing on large research projects and empirical evidence, the authors explore practical and educational issues that relate to multiliteracies, such as assessment, pedagogy and curriculum. The viewpoint taken is that multiliteracies is a complementary socio-cultural approach to the new literacies that includes pedagogy and learning. The differences are addressed from a multiliteracies perspective – one that does not discount or undermine the new literacies, but shows new ways in which they are complementary. Computers and the Internet are transforming the way we work and communicate and the very notion of literacy itself. This volume offers frontline information and a vital update for those wishing to understand the evolution of multiliteracies and the current state of literacy theory in relation to it.

Reading fictions

Each of the six chapters, which offer a cumulative course of study, begins with a concise overview of the concepts to be explored through the students’ reading of selected stories. The first chapter, 'Texts and readings', tries to make reading seem 'strange' through a series of de-familiarising activities that ask students to consider not only what particular stories might mean, but also how they are made to mean in different, and often quite contradictory, ways. This is explored further in the second chapter which introduces the idea of 'reading positions' and investigates the idea that in some senses, stories are always 'already read'. The next two chapters, called 'Intertextuality' and 'Re-readings?', invite students to consider how they produce particular readings and how they might choose among quite different readings or interpretations of the same story. The fifth chapter explores ideas about texts and their relationship to 'reality' through readings of racism, while the final chapter, 'Real people?' asks students to consider how they produce often rich and detailed readings of characters from minimal textual information. Terms and concepts which may be new to some students are highlighted in the text and indexed for easy reference. The short stories in this collection are by writers from different parts of the world and will appeal to students. They range from 'expressive realist' texts to less conventional narrative forms. Those teachers who have enjoyed using Reading Stories with their students will have a lot to look forward to in this collection of surefire 'winners' - by writers as varied as Bessie Head, Kristin Hunter, Tim Winton, Joyce Carol Oates, John Wain and Patricia Grace - each of which is accompanied by imaginative, enjoyable and thought-provoking activities.

Reading stories

What expectations do readers have of stories? Where do readers’ expectations come from? Do certain kinds of readings serve to support particular beliefs and assumptions? These and other questions are raised in Reading Stories, a collection of eleven short stories that have been very popular with Year 10 classes and above, accompanied by activities for talk and writing that encourage students to reflect on stories and their reading of them. Reading Stories aims to make recent literary theory accessible to students through a range of practical activities that work well in the classroom. Each story’s accompanying activities are designed to give students not only the opportunity but also the support they might need to construct and analyse possible readings of the text. There are five chapters - offering a cumulative learning experience - that consider such areas as readers’ expectations, how and why readings change, what is at stake in the disagreements between readings, and reading for gender, race and class. The approaches used begin with students’ familiarity with stories and then work to make available for analysis aspects of reading and ‘interpretation’ that are often taken for granted. While the concepts addressed are complex, the book aims to encourage participation from all students.

Questions of English : ethics, aesthetics, rhetoric, and the formation of the subject in England, Australia and the United States

The impact and content of English as a subject on the curriculum is once more the subject of lively debate. Questions of English sets out to map the development of English as a subject and how it has come to encompass the diversity of ideas that currently characterise it. Drawing on a combination of historical analysis and recent research findings Robin Peel, Annette Patterson and Jeanne Gerlach bring together and compare important new insights on curriculum development and teaching practice from England, Australia and the United States. They also discuss the development of teacher training, highlighting the variety of ways in which teachers build their own beliefs and knowledge about English.

Investigating Texts

The first chapter called 'Investigating texts' asks students to investigate the concept of text and what it might mean to 'behave like a reader'. After reading and comparing two short stories, the question, 'what is a story?' is posed. Students are then asked to distinguish a fiction text from a number of non-fiction texts and to identify the sources of the latter. It is suggested that although it is quite easy to perform these tasks, it is not so easy to describe texts in terms only of their features or ingredients; that it is necessary to talk about how texts are read, and what is more, how they are read on particular occasions. 'Making texts', the second chapter, asks students via a series of activities to consider what they expect of texts, and to investigate the conventions of fiction and non-fiction. They are given the opportunity to manipulate the 'ingredients' of texts, to read in terms of commonalities and to speculate about the rules by which both the composition and consumption of texts are organised. The ways in which particular kinds of reading and writing activities assume the text as a certain kind of object - as a model, for example, or as an object of criticism or as an occasion for self-questioning - is made explicit, and students are encouraged to investigate a range of uses of texts and the implications of these for reading and writing. Chapter three, 'Changing texts' asks students to consider, through a number of fascinating examples, how both fiction and non-fiction texts have changed over time, and how the ways in which readers read texts can change too. The 'retelling' of texts in terms of changing norms is considered via an 'updated' version of 'Scheherazade'; a student's feminist adaptation of her own text (initially written using a romance as a model), and an encyclopedia entry. 'Reading practices', the fourth chapter, poses further questions about different ways of reading. Through reading a number of didactic texts alongside three stories from a genre that is not usually read for morally improving lessons, students are asked to consider how different their reading practices can be.

Strategies for comparing decimal numbers with the same whole-number part

The strategies employed by 130 Grade 5 Brisbane students in comparing decimal numbers which have the same whole-number part were compared with those identified in similar studies conducted in the USA, France and Israel. Three new strategies were identified. Similar to USA results, the most common comparison errors stemmed from the incorrect whole-number strategy in which length is confused with size. The findings of this present study tend to support Resnick et al.’s (1989) hypothesis that the introduction of decimal-fraction recording before common-fraction recording seems to promote better comparison of decimal numbers.

Year 8, 9 and 10 students’ understanding and access of percent knowledge

This paper reports on Years 8, 9 and 10 students’ knowledge of percent problem types, use of diagrams, and type of solution strategy. Non- and semi-proficient students displayed the expected inflexible formula approach to solution but proficient students used a flexible mixture of estimation, number sense and trial and error instead of expected schema based methods.

Construction of multiplicative abstract schema for decimal-number numeration

This paper reports on an intervention study planned to help Year 6 students construct the multiplicative structure underlying decimal-number numeration. Three types of intervention were designed from a numeration model developed from a large study of 173 Year 6 students’ decimal-number knowledge. The study found that students could acquire multiplicative structure as an abstract schema if instruction took account of prior knowledge as informed by the model.

Reunitising hundredths: prototypic and nonprototypic representations

This paper reports on a study in which 29 Year 6 students (selected from the top 30% of 176 Year 6 students) were individually interviewed to explore their ability to reunitise hundredths as tenths (Behr, Harel, Post & Lesh, 1992) when represented by prototypic (PRO) and nonprototypic (NPRO) models. The results showed that 55.2% of the students were able to unitise both models and that reunitising was more successful with the PRO model. The interviews revealed that many of these students had incomplete, fragmented or non-existent structural knowledge of the reunitising process and often relied on syntactic clues to complete the tasks. The implication for teaching is that instruction should not be limited to PRO representations of the part/whole notion of fraction and that the basic structures (equal parts, link between name and number of equal parts) of the part/whole notion needs to be revisited often.

Fractions, reunitisation and the number-line representation

Centre for Mathematics and Science Education, QUT, Brisbane, Australia This paper reports on a study in which Years 6 and 10 students were individually interviewed to determine their ability to unitise and reunitise number lines used to represent mixed numbers and improper fractions. Only 16.7% of the students (all Year 6) were successful on all three tasks and, in general, Year 6 students outperformed Year 8 students. The interviews revealed that the remaining students had incomplete, fragmented or non-existent structural knowledge of mixed numbers and improper fractions, and were unable to unitise or reunitise number lines. The implication for teaching is that instruction should focus on providing students with a variety of fraction representations in order to develop rich and flexible schema for all fraction types (mixed numbers, and proper and improper fractions).