Investigating functional thinking in the elementary classroom : foundations of early algebraic reasoning

This paper examines the development of student functional thinking during a teaching experiment that was conducted in two classrooms with a total of 45 children whose average age was nine years and six months. The teaching comprised four lessons taught by a researcher, with a second researcher and classroom teacher acting as participant observers. These lessons were designed to enable students to build mental representations in order to explore the use of function tables by focusing on the relationship between input and output numbers with the intention of extracting the algebraic nature of the arithmetic involved. All lessons were videotaped. The results indicate that elementary students are not only capable of developing functional thinking but also of communicating their thinking both verbally and symbolically.

Place value, multiplicativity, reunitizing and effective classroom teaching of decimal numeration

Student understanding of decimal number is poor (e.g., Baturo, 1998; Behr, Harel, Post & Lesh, 1992). This paper reports on a study which set out to determine the cognitive complexities inherent in decimal-number numeration and what teaching experiences need to be provided in order to facilitate an understanding of decimal-number numeration. The study gave rise to a theoretical model which incorporated three levels of knowledge. Interview tasks were developed from the model to probe 45 students’ understanding of these levels, and intervention episodes undertaken to help students construct the baseline knowledge of position and order (Level 1 knowledge) and an understanding of multiplicative structure (Level 3 knowledge). This paper describes the two interventions and reports on the results which suggest that helping students construct appropriate mental models is an efficient and effective teaching strategy.

Thai students' engagement with cooperative learning in mathematics classrooms

Over the past decade, Thai schools have been encouraged by the Thai Ministry of Education to introduce more student-centred pedagogies such as cooperative learning into their classrooms (Carter, 2006). However, prior research has indicated that the implementation of cooperative learning into Thai schools has been confounded by cultural traditions endemic within Thai schools (Deveney, 2005). The purpose of the study was to investigate how 32 Grade 3 and 32 Grade 4 students enrolled in a Thai school engaged with cooperative learning in mathematics classrooms after they had been taught cooperative learning strategies and skills. These strategies and skills were derived from a conceptual framework that was the outcome of an analysis and synthesis of social learning, behaviourist and socio-cognitive theories found in the research literature. The intervention began with a two week program during which the students were introduced to and engaged in practicing a set of cooperative learning strategies and skills (3 times a week). Then during the next four weeks (3 times a week), these cooperative learning strategies and skills were applied in the contexts of two units of mathematics lessons. A survey of student attitudes with respect to their engagement in cooperative learning was conducted at the conclusion of the six-week intervention. The results from the analysis of the survey data were triangulated with the results derived from the analysis of data from classroom observations and teacher interviews. The analysis of data identified four complementary processes that need to be considered by Thai teachers attempting to implement cooperative learning into their mathematics classrooms. The paper concludes with a set of criteria derived from the results of the study to guide Thai teachers intending to implement cooperative learning strategies and skills in their classrooms.

Teachers and the emotional dimensions of class in resource-affected rural Australia

In recent years, a 'cultural turn' in the study of class has resulted in a rich body of work detailing the ways in which class advantage and disadvantage are emotionally inscribed and embodied in educational settings. To date, however, much of this literature has focused on the urban sphere. In order to address this gap in the literature, this paper focuses on the affective evaluations made by teachers employed in rural and remote Australian schools of students' families, bodies, expectations and practices. The central argument is that moral ascriptions of class by the teachers are powerfully shaped by dominant socio-cultural constructions of rurality that equate 'the rural' with agriculture.

Implementing change within a school science department: progressive and dissonant voices

The purpose of this study was to describe the teaching and leadership experiences of a science teacher who, as head of department, was preparing to introduce changes in the science department of an independent school in response to the requirements of the new junior science syllabus in Queensland, Australia. This teacher consented to classroom observations and interviews with the researchers where his beliefs about teaching practice and change were explored. Other science teachers at the school also were interviewed about their reactions to the planned changes. Interpretive analysis of the data provides an account of the complex interactions, negotiations, compromises, concessions, and trade-offs faced by the teacher during a period of education reform. Perceived barriers existing within the school that impeded proposed change are identified

If teams are so good.. : science teachers' conceptions of teams and teamwork

The focus of this study is the phenomenon of teams and teamwork. Currently the Professional Standards of Queensland’s teachers state that teams are critical to teachers’ work. This study uses a phenomenographic approach to investigate science teachers’ conceptions of teams and teamwork in the science departments of fifteen Queensland State secondary schools. The research identifies eight conceptions of teams and teamwork. The research findings suggest that the team represents a collective of science teachers bounded by the Science Department and their current timetabled subject. Collaboration was found in the study to be an activity that occurred between teachers in the same social space. The research recognises a new category of relationship between teachers, designated as ‘ask-and-receive’. The research identifies a lack of teamwork within the science department and the school. There appears to be no teaming with other subject departments. The research findings highlight the non-supportive team and teamwork policies, procedures and structures in the schools and identify the lack of recognition of the specialised skills of science teachers. The implications for the schools and science teachers are considerable, as the current Professional Standards of Education Queensland and the Queensland College of Teachers provide benchmarks of knowledge and practice of teams and teamwork for teachers. The research suggests that the professional standards relating to teams and teamwork cannot be achieved in the present school environment.

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.

Researching Teachers for the Middle Years

The educational landscape around middle schooling reform is a contemporary focus of the Australian school education agenda. The University of Queensland Middle Years of Schooling pre-service teacher education program develops specialist teachers for this crucial phase of schooling. This program has become a national leader for middle school teacher education. This paper reports on aspects of a longitudinal study that began with the first cohort of students in the program in 2003. To date 234 students have been involved as participants in the study. The findings demonstrate that students: can articulate what is meant by the term middle years and can identify with a need for a philosophy of middle schooling; are aware that they are part of a reform movement which has swept the nation and which has implications for teaching in schools in the twenty first century; are confident the program is producing highly skilled professional teachers willing to take on the challenges of teaching in the middle years; can say how their training has helped them understand and account for the educational experiences of students in a time of transition; and hold quiet, yet firm beliefs about teaching in the middle years. Furthermore, using a measure of lexical density to analyze the verbs used by respondents, it seems that this quiet confidence has grown in the period from 2003 – 2006.

Inventing future schools

A group of Australian researchers and designers have been working on ways to imagine, demonstrate and accelerate the use of ICT that extend learning relationships and environments to include the classroom, home and local community. These learning projects aim to transform how students identify and interact with learning, subject areas, teachers, other students, family, organisations and more broadly how learning tools can create connections that permeate students' life worlds now and in the future.---------- It is our intention that such demonstrators must - Be simple, flexible, scalable and adaptive - Result in increased confidence in the use of ICT for both students and teachers - Offer opportunities for personalized learning - Promote new and effective learning partnerships between students, teachers and families. - Extend the learning experience to include other environments both local and virtual. - Inspire further innovation - Provide solutions to current limitations---------- Presenting Innovation in Practice - Innovative ICT projects currently being used by students in schools, at home and in the community - Stories of use from teacher, student, and other stakeholder perspectives - Lessons learnt so far: a design perspective - Surprising and inspiring opportunities

Potency in professional development for teachers

There has been significant research into the impact of professional development (PD) on professional organisation and behaviour. PD has emerged in a diversity of forms in schools. Programs range form one hit seminars provided by an external consultant, through to a broad range of programmed development plans that integrate seminars; school based planning groups, action research, collaborative projects across schools, clusters and with critical friends, and mentoring. PD has been delivered to prompt school and teacher professional transformation or to support an ongoing development plan. PD is not uni-lateral and exists to support a very wide range of school and teacher development needs. The relevance and effectiveness of PD design and delivery is tied to the nature of the PD need and the context of provision. This paper reports an investigation into efficacy of various approaches to PD in Queensland schools. The research drew on responses to an online survey tool, focus groups and semi-structured interviews with PD coordinators, teachers, and school and district administrators to develop a model for effective PD planning that considers strategies for addressing current and future PD need and amelioration of barriers to PD effectiveness.

Critical social theory and transformative learning : evidence in pre-service teachers' service-learning reflection logs

This paper reports on the opportunities for transformational learning experienced by a group of pre-service teachers who were engaged in service-learning as a pedagogical process with a focus on reflection. Critical social theory informed the design of the reflection process as it enabled a move away from knowledge transmission toward knowledge transformation. The structured reflection log was designed to illustrate the critical social theory expectations of quality learning that teach students to think critically: ideology critique and utopian critique. Butin's lenses and a reflection framework informed by the work of Bain, Ballantyne, Mills and Lester were used in the design of the service-learning reflection log. Reported data provide evidence of transformational learning and highlight how the students critique their world and imagine how they could contribute to a better world in their work as a beginning teacher.