Developing mathematics understanding and abstraction : the case of equivalence in the elementary years

Generalising arithmetic structures is seen as a key to developing algebraic understanding. Many adolescent students begin secondary school with a poor understanding of the structure of arithmetic. This paper presents a theory for a teaching/learning trajectory designed to build mathematical understanding and abstraction in the elementary school context. The particular focus is on the use of models and representations to construct an understanding of equivalence. The results of a longitudinal intervention study with five elementary schools, following 220 students as they progressed from Year 2 to Year 6, informed the development of this theory. Data were gathered from multiple sources including interviews, videos of classroom teaching, and pre-and post-tests. Data reduction resulted in the development of nine conjectures representing a growth in integration of models and representations. These conjectures formed the basis of the theory.

Humanistic science education : moves from within and challenges from without

For a number of years now it has been evident that the major issue facing science educators in the more developed countries of the world is the quantitative decline in enrolments in the senior secondary sciences, particularly the physical sciences, and in the number of higher achieving students applying for places in universities to undertake further studies in science. The deep malaise in school science to which these quantitative measures point has been elucidated by more qualitative studies of the students’ experience of studying science in secondary school in several of these countries (Sweden, Lindahl (2003); England, Simon and Osborne (2002); and Australia, Lyons (2005)). Remarkably concordant descriptions of these experiences can be summarized as: School science is: • transmission of knowledge from the teacher or the textbook to the students. • about content that is irrelevant and boring to our lives. • difficult to learn in comparison with other subjects Incidentally, the Australian study only involved consistently high achieving students; but even so, most of them found science more difficult than other more interesting subjects, and concluded that further science studies should be avoided unless they were needed for some career purpose. Other more representative confirmations of negative evaluations of the science curricula across Australia (and in particular states) are now available in Australia, from the large scale reviews of Goodrum, Hackling and Rennie (2001) and from the TIMSS (2002). The former reported that well under half of secondary students find the science at school relevant to my future, useful ion everyday life, deals with things I am concerned with and helps me make decisions about my health.. TIMSS found that 62 and 65 % of females and males in Year 4 agree with I like learning science, but by Year 8 only 26 and 33 % still agree. Students in Japan have been doubly notably because of (a) their high performance in international measures of science achievement like TIMSS and PISA and (b) their very low response to items in these studies which relate to interest in science. Ogura (2003) reported an intra-national study of students across Years 6-9 (upper primary through Junior High); interest in a range of their subjects (including science) that make up that country’s national curriculum. There was a steady decline in interest in all these subjects which might have indicated an adolescent reaction against schooling generally. However, this study went on to ask the students a further question that is very meaningful in the Japanese context, If you discount the importance of this subject for university entrance, is it worth studying? Science and mathematics remained in decline while all the other subjects were seen more positively. It is thus ironic, at a time when some innovations in curriculum and other research-based findings are suggesting ways that these failures of school science might be corrected, to find school science under a new demands that come from quite outside science education, and which certainly do not have the correction of this malaise as a priority. The positive curricular and research findings can be characterized as moves from within science education, whereas the new demands are moves that come from without science education. In this paper I set out these two rather contrary challenges to the teaching of science as it is currently practised, and go on to suggest a way forward that could fruitfully combine the two.

Biotechnology learnings using ‘Claymation’ and ‘Slowmation’

This ‘Claymation’ and ‘Slowmation’ project incorporated content as well as skill development. The participants – 4 pre-service teachers and 4 secondary school students explored chromosome mapping and DNA replication. Through research, the writing, revising and editing of storyboards, two short videos were produced. Two of the pre-service teachers had prior experience with Claymation, however none of the participants had prior knowledge of chromosome mapping or DNA replication. This paper describes the learnings of the participants in terms of their self generated questions, the need for attention to detail, and argumentation / negotiation skills.

Transfer of learning across the globe : pre-service teachers taking the initiative

A continuing challenge for pre-service teacher education is the learning transfer between the university based components and the practical school based components of their training. It is not clear how easily pre-service teachers can transfer university learnings into ‘in school’ practice. Similarly, it is not clear how easily knowledge learned in the school context can be disembedded from this particular context and understood more generally by the pre-service teacher. This paper examines the effect of a community of practice formed specifically to explore learning transfer via collaboration and professional enquiry, in ‘real time’, across the globe. “Activity Theory” (Engestrom, 1999) provided the theoretical framework through which the cognitive, physical and social processes involved could be understood. For the study, three activity systems formed community of practice network. The first activity system involved pre-service teachers at a large university in Queensland, Australia. The second activity system was introduced by the pre-service teachers and involved Year 12 students and teachers at a private secondary school also in Queensland, Australia. The third activity system involved university staff engineers at a large university in Pennsylvania, USA. The common object among the three activity systems was to explore the principles and applications of nanotechnology. The participants in the two Queensland activity systems, controlled laboratory equipment (a high powered Atomic Force Microscope – CPII) in Pennsylvania, USA, with the aim of investigating surface topography and the properties of nano particles. The pre-service teachers were to develop their remote ‘real time’ experience into school classroom tasks, implement these tasks, and later report their findings to other pre-service teachers in the university activity system. As an extension to the project, the pre-service teachers were invited to co-author papers relating to the project. Data were collected from (a) reflective journals; (b) participant field notes – a pre-service teacher initiative; (c) surveys – a pre-service teacher initiative; (d) lesson reflections and digital recordings – a pre-service teacher initiative; and (e) interviews with participants. The findings are reported in terms of the major themes: boundary crossing, the philosophy of teaching, and professional relationships The findings have implications for teacher education. The researchers feel that deliberate planning for networking between activity systems may well be a solution to the apparent theory/practice gap. Proximity of activity systems need not be a hindering issue.

Boys 'doing' and 'undoing' media education : new possibilities for theory and practice

The purpose of this study is to investigate how secondary school media educators might best meet the needs of students who prefer practical production work to ‘theory’ work in media studies classrooms. This is a significant problem for a curriculum area that claims to develop students’ media literacies by providing them with critical frameworks and a metalanguage for thinking about the media. It is a problem that seems to have become more urgent with the availability of new media technologies and forms like video games. The study is located in the field of media education, which tends to draw on structuralist understandings of the relationships between young people and media and suggests that students can be empowered to resist media’s persuasive discourses. Recent theoretical developments suggest too little emphasis has been placed on the participatory aspects of young people playing with, creating and gaining pleasure from media. This study contributes to this ‘participatory’ approach by bringing post structuralist perspectives to the field, which have been absent from studies of secondary school media education. I suggest theories of media learning must take account of the ongoing formation of students’ subjectivities as they negotiate social, cultural and educational norms. Michel Foucault’s theory of ‘technologies of the self’ and Judith Butler’s theories of performativity and recognition are used to develop an argument that media learning occurs in the context of students negotiating various ‘ethical systems’ as they establish their social viability through achieving recognition within communities of practice. The concept of ‘ethical systems’ has been developed for this study by drawing on Foucault’s theories of discourse and ‘truth regimes’ and Butler’s updating of Althusser’s theory of interpellation. This post structuralist approach makes it possible to investigate the ways in which students productively repeat and vary norms to creatively ‘do’ and ‘undo’ the various media learning activities with which they are required to engage. The study focuses on a group of year ten students in an all boys’ Catholic urban school in Australia who undertook learning about video games in a three-week intensive ‘immersion’ program. The analysis examines the ethical systems operating in the classroom, including formal systems of schooling, informal systems of popular cultural practice and systems of masculinity. It also examines the students’ use of semiotic resources to repeat and/or vary norms while reflecting on, discussing, designing and producing video games. The key findings of the study are that students are motivated to learn technology skills and production processes rather than ‘theory’ work. This motivation stems from the students’ desire to become recognisable in communities of technological and masculine practice. However, student agency is not only possible through critical responses to media, but through performative variation of norms through creative ethical practices as students participate with new media technologies. Therefore, the opportunities exist for media educators to create the conditions for variation of norms through production activities. The study offers several implications for media education theory and practice including: the productive possibilities of post structuralism for informing ways of doing media education; the importance of media teachers having the autonomy to creatively plan curriculum; the advantages of media and technology teachers collaborating to draw on a broad range of resources to develop curriculum; the benefits of placing more emphasis on students’ creative uses of media; and the advantages of blending formal classroom approaches to media education with less formal out of school experiences.

An extended CDIO syllabus framework with preparatory engineering proficiencies

The CDIO Initiative has been globally recognised as an enabler for engineering education reform. With the CDIO process, the CDIO Standards and the CDIO Syllabus, many scholarly contributions have been made around cultural change, curriculum reform and learning environments. In the Australasian region, reform is gaining significant momentum within the engineering education community, the profession, and higher education institutions. This paper presents the CDIO Syllabus cast into the Australian context by mapping it to the Engineers Australia Graduate Attributes, the Washington Accord Graduate Attributes and the Queensland University of Technology Graduate Capabilities. Furthermore, in recognition that many secondary schools and technical training institutions offer introductory engineering technology subjects, this paper presents an extended self-rating framework suited for recognising developing levels of proficiency at a preparatory level. The framework is consistent with conventional application to undergraduate programs and professional practice, but adapted for the preparatory context. As with the original CDIO framework with proficiency levels, this extended framework is informed by Bloom’s Educational Objectives. A proficiency evaluation of Queensland Study Authority’s Engineering Technology senior syllabus is demonstrated indicating proficiency levels embedded within this secondary school subject within a preparatory scope. Through this extended CDIO framework, students and faculty have greater awareness and access to tools to promote (i) student engagement in their own graduate capability development, (ii) faculty engagement in course and program design, through greater transparency and utility of the continuum of graduate capability development with associate levels of proficiency, and the context in which they exist in terms of pre-tertiary engineering studies; and (iii) course maintenance and quality audit methodology for the purpose of continuous improvement processes and program accreditation.

Re-thinking pedagogy for middle school students with little, no or severely interrupted schooling

The arrival of substantial cohorts of English language learners from Africa with little, no or severely interrupted schooling is requiring new pedagogic responses from teachers in Australia and other Western countries of refugee re-settlement. If the students are to have optimal educational and life chances, it is crucial for them to acquire resources for conceptually deep and critical literacy tasks while still learning basic reading and writing skills. This requires teachers to extend their pedagogic repertoires: subject area teachers must teach language and literacy alongside content; high school teachers must teach what has been thought of as primary school curriculum. The aim of this article is to describe some teacher responses to these challenges. Data are drawn from a study involving an intensive language school and three high schools, and also from the author’s experience as a homework tutor for refugees. Stand-alone basic skills programs are described, as are modifications of long-established ESL programs. It is also argued that teachers need to find ways of linking with the conceptual knowledge of students who arrive with content area backgrounds different from others in their class. Everyday life experiences prior to, and after re-settlement in the West, are rich with potential in this regard.

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)

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.

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.

Comprehension as social and intellectual practice : rebuilding curriculum in low socioeconomic and cultural minority schools

This article reframes the concept of comprehension as a social and intellectual practice. It reviews current approaches to reading instruction for linguistically and culturally diverse and low socioeconomic students, noting an emphasis on comprehension as autonomous skills. The Four Resources model (Freebody & Luke, 1990) is used to make the case for the integration of comprehension instruction with an emphasis on student cultural and community knowledge, and substantive intellectual and sociocultural content in elementary school curricula. Illustrations are drawn from research underway on the teaching of literacy in primary schools in low SES communities.

The awareness and explication of disciplinarity across four senior-secondary subject areas

This paper issues a challenge to the notion of domain-general teaching and learning, positing that different subject areas require distinct approaches to developing student knowledge and understanding. The aim has been to observe and compare awareness and explication of disciplinarity in four senior secondary school subjects: Biology, History, Music and Physics. Specifically, we were interested in: (1) teachers’ concepts of what it means to ‘know the discipline’, to ‘think like a disciplinary expert’ and to ‘teach and learn the discipline’; and (2) how teachers draw these concepts together to build student knowledge in the classroom. The research informs educational practice and policy, in particular curricular initiatives involving interdisciplinary curricula.

Student perceptions of the impact of online discussion forum participation on learning outcomes

Choosing the “right” type of technology, either synchronous or asynchronous, to facilitate learning outcomes is a new challenge as the pace of emerging technologies increases and diversifies. Teachers are encouraged to design courses that require collaboration in online learning communities to facilitate the development of higher order thinking skills for life long learning. It is therefore important to gather evidence of the kinds of opportunities afforded to students and whether the students themselves endorse collaborative online tools as a legitimate method of assisting in their learning. This paper outlines the way in which one secondary school has used an online discussion forum to support students in the International Baccalaureate (IB) Diploma Program in enhancing research skills and skills for lifelong learning. The paper considers whether online collaborative tools are perceived by students as a positive way to improve learning outcomes.

Curriculum and religion

Across continents and cultures and periods of history, religious beliefs have underpinned curriculum in institutions of education. More recently, the so-called culture wars and terrorism have moved religion to center stage. In both state and independent education sectors, deep-seated assumptions about the nature of reality, spirituality, ethics and knowledge converge and clash in the curriculum documents of science, history, literacy education, and the like. With a focus on textual genres of power, starting with antiquity, this chapter argues that little has changed through millennia as the secular mysticism of price has replaced theology today in constraining the potentials of education.

Teachers’ conceptions of essential knowledge for integrated social education : a middle years of schooling perspective from Australia

Integrated social education in Australia is a divisive educational issue. The last decade has been marked by a controversial integrated social studies curriculum called Studies of Society and Environment (SOSE) where history, geography and environmental studies were integrated with civics and citizenship. The introduction of a compulsory K-10 Australian Curriculum from 2011, however, marks the return to history and geography and the abandonment of SOSE. Curriculum reform aside, what do teachers think is essential knowledge for middle years social education? The paper reports on a phenomenographical exploration of thirty-one middle school teachers’ conceptions of essential knowledge for SOSE. Framed by Shulman’s (1986, 1987) theoretical framework of the knowledge base for teaching, the research identified seven qualitatively different ways of understanding essential knowledge for integrated social education. The study indicates a practice-based theorization of integrated social education that justifies attention to disciplinary process and teacher identity in middle school social education.