Teacher actions to maximize mathematics learning opportunities in heterogeneous classrooms

The basic unit of school based mathematics teaching is the lesson. This article is a contribution to understanding teacher actions that facilitate successful lessons, defined as those that engage all students, especially those who may sometimes feel alienated from mathematics and schooling, in productive and successful mathematical thinking and learning. An underlying assumption is that lessons can seek to build a sense in the students that their experience has elements in common with the rest of the class and that this can be done through attention to particular aspects of the mathematical and socio-mathematical goals. We examine three teacher actions that address the mathematical goals: using open-ended tasks, preparing prompts to support students experiencing difficulty, and posing extension tasks to students who finish the set tasks quickly; as well as actions that address the socio-mathematical goals by making classroom processes explicit. To illustrate and elaborate these actions, we describe a particular lesson taught to a heterogeneous upper primary (age 11–12) class.

The graphic calculator as a thinking tool : perspectives from the classroom

For over a decade, the graphic calculator has been promoted not only as a computational tool, but also as a thinking tool - for example, as an aid to enhance conceptual understanding, as a problem-solving tool and as a means of enabling students to engage in meaningful investigations. However, research studies focusing on these aspects have shown mixed results and have mostly focused on graphs and functions.

This paper reports on one aspect of a case study in a year 10 mathematics classroom - the role of the graphic calculator as a thinking tool. Data from observations of nine statistics lessons and interviews with the teacher and five students, are analysed from three perspective's: the teacher's intentions with respect to the use of the graphic calculator as a tool to promote conceptual understanding as opposed to procedural competence; the opportunities afforded during the lessons for student investigation; and students' views of how the graphic calculator enhanced conceptual understanding.

The results provide insights into ways in which students perceive the graphic calculator as promoting conceptual understanding, as well as some of the difficulties encountered in practice in a classroom where the teacher clearly intends to use the graphic calculator as a thinking tool.

The use of Web 2.0 Technologies to promote higher order thinking skills

During 2007 several independent Victorian secondary schools participated in a study exploring the ways in which the use of learning technologies can support the development of higher order thinking skills for students. This paper focuses on the use of Information and Communications Technologies (ICT) including Web 2.0 technologies for promoting effective teaching and learning in science. A case study methodology was used to describe how individual teachers used ICT and Web 2.0 in their settings. Data included interviews (focus group and individual), questionnaires, monitoring of teacher and student use of smart tools, analysis of curriculum documents and delivery methods and of student work samples. The evaluation used an interpretive methodology to investigate five research areas: Higher-order thinking, Metacognitive awareness, Team work/collaboration, Affect towards school/learning and Ownership of learning. Three cases are reported on in this paper. Each describes how student engagement and learning increased and how teachers’ attitudes and skills developed. Examples of student and teacher blogs are provided to illustrate how such technologies encourage students and teachers to look beyond text science.

Critical analysis of action research-based inservice teacher education : four case histories

Changing the nature of institutionalised education is the central theme of the thesis. The potential for radical changes to classroom teaching and to inservice teacher education is considered through four curriculum and teaching reform projects structured by action -research. The problems explored through the thesis are at the levels of teaching, institutional and research practices. It is argued that the professional activity of teachers, administrators, consultants, teacher educators and researchers can be understood to be tightly bound and determined by rules for acceptable professional ways of acting which are often unquestioned and unexamined by educators themselves. It is further argued that institutionalised education is dominated by ways of thinking and acting that are inherently individualistic. The thesis analyses the ideological character of this 'individualistic1 structuring of educational practice, identifying belief systems that hold the lived reality of educators and students in place. The thesis endeavours to show that the bureaucratic character of institutionalised education primarily serves and maintains the interests of dominant groups. The thesis examines the possibilities for radical reform in classroom teaching, the support teachers need when embarking on curriculum and teaching change processes, and the possible outcomes of such reform. The thesis also examines the interaction between the institutional practices of schools, universities and regional offices in the Ministry of Education in Victoria, Australia on these reform processes in classrooms. Finally, the thesis examines the potential of action research as a research and educative process in the professional development of educators who are both critically aware of the ideological nature of institutionalised education and committed to collective social action. From the analyses of the four action research projects the thesis concludes that action research has the potential to transform institutionalised education when its own practice is firstly, developed as a liberating pedagogy and not as research projects structured by individualistic and paternalistic interests; secondly, is driven by a commitment to the political struggle for equity and social justice; and thirdly, is itself an expression of communitarian work. The thesis concludes that the transformative processes associated with action research under these conditions hold the promise of democratising the 'individualistic' character of institutional education.

On strangers, ‘moral panics’ and the neo-liberalization of teacher education

This paper explores the convergence of neo-liberal managerialism with the neo-conservative technologies of creating ‘moral panics’ about teacher education, English language and literacy curriculum and traditional values that allegedly fail to address the issues of public safety and cultural integration in the post- September 11th world. It problematises the neo-conservative vision of managing ‘strangers’ and public risks through dominant cultural literacy. The paper counters the neo-conservative backlash with a framework that emphasizes dialogical ethics in teaching for difference and conceptualizes transcultural literacy as an alternative model of education in multicultural conditions. This model is presented both as a way of resisting the subliminal infiltration of neo-conservative thinking in teacher education today and as a way of imagining a ‘cosmopolitan’ professional.

Examining how teachers use web 2.0 technologies in Science lessons to promote higher order thinking in teaching science

During 2007 several independent Victorian secondary schools participated in a study exploring the ways in which the use of learning technologies can support the development of higher order thinking skills for students. This paper focuses on the use of Information and Communications Technologies (ICT) including Web 2.0 technologies for promoting effective teaching and learning in science. A case study methodology was used to describe how individual teachers used ICT and Web 2.0 in their settings. Data included interviews (focus group and individual), questionnaires, monitoring of teacher and student use of smart tools, analysis of curriculum documents and delivery methods and of student work samples. The evaluation used an interpretive methodology to investigate five research areas'. Higher-order thinking, Metacognitive awareness, Team work/collaboration, Affect towards school/learning and Ownership of learning. Three cases are reported on in this paper. Each describes how student engagement and learning increased and how teachers' attitudes and skills developed. Examples of student and teacher blogs are provided to illustrate how such technologies encourage  students and teachers to look beyond text science.

The national mapping of teacher professional learning project : a multi-dimensional space?

This essay focuses on the National Mapping of Teacher Professional Learning (2008), a report that we co-authored along with a number of other researchers on the basis of extensive surveys and interviews relating to the policies and practices of teacher professional learning in Australia. The report is an update of an earlier survey conducted by David McRae and others, entitled PD 2000, and it registers significant changes in attitudes and practices relating to professional learning across Australia in the intervening period. Perhaps the most significant development is the way professional learning is now recognized as an important vehicle for education reform by systems, schools and by teachers themselves, most notably the standards-based reforms that have such a decisive effect on the policy landscape here in Australia and in other countries. The work of the AATE in developing the Standards for Teachers of English Language and Literacy (STELLA) is mentioned in the report. It was acknowledged that STELLA provides a generative framework for professional learning, sometimes in contradiction to more managerial approaches. The question remains, however, of how English teachers as a professional community might locate themselves within the policy landscape described in this report. This essay is an attempt to promote this kind of discussion and to argue the distinctive nature of the standpoint that English teachers might bring to thinking about and planning for professional learning and practitioner inquiry.

A study of rural preschool practitioners’ views on young children’s mathematical thinking

The project Mathematical Thinking of Preschool Children in Rural and Regional Australia: Research and Practice aimed to investigate views of preschool practitioners about young children’s mathematical thinking and development. Structured individual interviews were conducted with 64 preschool practitioners from rural areas of three Australian states. The questions focused on five broad themes: children’s mathematics learning, support for mathematics teaching, technology and computers, attitudes and feelings, and assessment and record keeping. We review results from the interview data for each of these themes, discuss their importance, and outline recommendations related to teacher education as well as resource development and research.

The use of video recording in professional development of teachers and teacher educators in Indonesia

Design-based research has gained currency in educational research over the past decade due to its strength to bridge the divide between theoretical research and educational practice in naturalistic settings. Design based approaches involve a process of designing mathematical tasks, observing the enacted design in classrooms and reflecting on the process from analysing the classroom artifacts. Video plays a central role in supporting teachers and teacher educators to study and reflect on students’ mathematical thinking and in capturing the dynamic of classroom teaching and learning process.

This chapter will examine and analyse practitioner’s lenses in capturing the dynamic and complexity of classroom mathematical learning using video segments, and classroom artifacts including digital photos of classroom moments and students’ work. Practitioners’ lenses are taken as a window to capture key teaching and learning moments from the lessons. Analysis of this selection of these video segments along with other classroom artifacts based on practitioners’ lenses provide insights into practitioners’ views on key teaching and learning moments in mathematics lessons.

Equivalence and relational thinking: opportunities for professional learning

In this article an argument for the use of collaborative professional learning teams to improve teaching and children's achievement is presented together with an explanation of how this can be done. The case provided in this article concerns children's understanding of equivalence and the way in which teachers together can explore children's conceptions and misconceptions held by children in their classroom. An effective teaching strategy using a number talk about a true/false number sentence is also described.

Shifts in thinking and practice: reflecting on an applied learning programme

The implementation of the first iteration of a curriculum for an applied learning programme for police trainers received a hostile response from participants. It was perceived as irrelevant and supplanting, rather than augmenting, trainers’ fixed and untested training practices. This paper presents the reflections on my journey as a nonpolice person straddling an outsider-insider position while challenging that which is taken-for-granted and introducing an educative intent, as opposed to a doctrinal, technical intent, to police training. On a daily basis I simultaneously work within and against the prevailing D/discourses and dominant subcultures, while establishing and nurturing relationships with police trainers: being teacher, coach and ‘critical friend’. The response to the second and now third iterations of the learning programme has been increasingly positive, revealing shifts in trainers’ thinking and practice.

Australian pre-service secondary teacher education courses : challenges and Dilemmas

Mathematical thinking of preschool children in rural and regional Australia : research and practice

At what age do young children begin thinking mathematically? Can young children work on mathematical problems? How do early childhood educators ensure young children feel good about mathematics? Where do early childhood educators learn about suitable mathematics activities?

A good early childhood start in mathematics is critical for later mathematics success. Parents, carers and early childhood educators are teaching mathematics, either consciously or unconsciously, in any social interaction with a child.

Mathematical Thinking of Preschool Children in Rural and Regional Australia is an extension of a conference of Australian and New Zealand researchers that identified a number of important problems related to the mathematical learning of children prior to formal schooling. A project team of 11 researchers from top Australian universities sought to investigate how early childhood education can best have a positive influence on early mathematics learning.

The investigation complements and extends the work of Project Good Start by focusing attention on critical aspects of parents, carers and early childhood educators who care for young children. Early childhood educators from regional and rural New South Wales, Queensland and Victoria were interviewed, following a set of structured questions. The questions focused on: children’s mathematics learning; support for mathematics teaching; use of technology; attitudes to mathematics; and assessment and record keeping.

The researchers also reviewed research focusing on the mathematical capacities and potential foundations for further mathematical development in young children (0–5 years) published in the last decade and produced an annotated bibliography. This should provide a good basis for further research and reading.

Based upon the results of this investigation, the researchers make 11 recommendations for improving the practices of early childhood education centres in relation to young children’s mathematical thinking and development. The implications for policy and decision makers are outlined for teacher education, the provision of resources and further research.

Using video to promote pre-service teachers’ thinking about their transition to teaching

This paper reports on research investigating the use of video representations of first-year teachers’ experiences in undergraduate teacher education workshops that focus on the transition to teaching. The use of the video is a responsive act that draws on the notion of looking back, where graduates in their first year of teaching ‘speak to’ current students. Scenes from video footage of the theatre-based research performance The First Time shaped workshop activities and discussions in the unit. Themes ranged from pedagogical to practical, covering topics such as teacher identity discourses; epiphanic and revelatory moments of transition to becoming a teacher; and preparing for job applications and interviews. Data from the researcher’s journal, Student Evaluation of Teaching and Units (SETU) comments, and semi-structured interviews with undergraduate students upon completion of the workshops are framed within a phenomenographic paradigm. The aim in phenomenography is to describe variations of conception that people have of a particular phenomenon (Sin, 2010), in this case the video as a tool to promote critical thinking about the transition to teaching. The researcher explored her own, and participants’ experiences, and identified a range of conceptual meanings of the phenomenon. These were classified into categories according to their similarities and differences concerning the effectiveness of this specific video in assisting undergraduates in their transition to teaching. Early results reveal some similarities and many variations among participants as to the effectiveness of the video as a tool. Their conceptions of the phenomenon are individual and relational, and as such are quite varied. Emergent varied themes include: ‘I know what it is that I need to learn’; ‘Is this theory or practice?’; and ‘I don’t do drama’. Emergent similarities include: ‘Preparing for the unexpected’.