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.

"Are there any right or wrong answers in teaching philosophy": ethics, epistemology, and philosophy in the classroom

This article assesses undergraduate teaching students’ assertion that there are no right and wrong answers in teaching philosophy. When asked questions about their experiences of philosophy in the classroom for primary children, their unanimous declaration that teaching philosophy has ‘no right and wrong answers’ is critically examined across the three sub-disciplinary areas to which they were generally referring, namely, pedagogy, ethics, and epistemology. From a pedagogical point of view, it is argued that some teaching approaches may indeed be more effective than others, and some pupils’ opinions less defensible, but pedagogically, in terms of managing the power relations in the classroom, it is counter-productive to continually insist on notions of truth and falsity at every point. From an ethical point of view, it is contended that anti-realist approaches to meta-ethics may represent a viable intellectual position, but from the point of view of normative ethics, notions of right and wrong still retain significant currency. From an epistemological point of view, it is argued using Karl Poppers’ work that while it may be difficult to determine what constitutes a right answer, determining a wrong one is far more straightforward. In conclusion, it is clear that prospective teachers engaging in philosophy in the classroom, and also future teachers in general, require a far more nuanced philosophical understanding of the notions of right and wrong and truth and falsity. In view of this situation, it we wish to promote the effective teaching of philosophical thinking to children, or produce educators who can understand the conceptual limits of the claims they make and their very real and often serious practical and social consequences, it is recommended that philosophy be reinstated to a fundamental, foundational place within the pre-service teaching curriculum.

Accounts of the visual art classroom : catering for artistically talented students

Inclusive education practices call for the diverse and individual needs of all students to be met satisfactorily. The needs and experiences of artistically talented students in Australian visual art classrooms are currently unknown. This study addresses this gap in research through an inquiry into the experiences of artistically talented students and their teachers in visual art classrooms, by examining the accounts of a group of students and teachers at one high school in South East Queensland. This study is significant as it provides teachers, parents and others involved in the education of artistically talented students with additional means to plan and cater for the educational needs of artistically talented students. Teacher and student accounts of the visual art classroom in this study indicated that identification processes for artistically talented students are unclear and contradictory. Furthermore, teacher and student accounts of their experiences presented a wide variety of conceptions of the visual art classroom and point towards an individualised approach to learning for artistically talented students. This study also discovered a mismatch between assessment practices in the subject visual art and assessment of art in the ‘real world’. Specifically, this study proposes a renewal of programs for artistically talented students, and recommends a revision of current procedures for the identification of artistically talented students in visual art classrooms.

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.

From the cathedral to the classroom : the emergence of new discourses on religious education

In 2009, Religious Education is a designated key learning area in Catholic schools in the Archdiocese of Brisbane and, indeed, across Australia. Over the years, though, different conceptualisations of the nature and purpose of religious education have led to the construction of different approaches to the classroom teaching of religion. By investigating the development of religious education policy in the Archdiocese of Brisbane from 1984 to 2003, the study seeks to trace the emergence of new discourses on religious education. The study understands religious education to refer to a lifelong process that occurs through a variety of forms (Moran, 1989). In Catholic schools, it refers both to co-curricula activities, such as retreats and school liturgies, and the classroom teaching of religion. It is the policy framework for the classroom teaching of religion that this study explores. The research was undertaken using a policy case study approach to gain a detailed understanding of how new conceptualisations of religious education emerged at a particular site of policy production, in this case, the Archdiocese of Brisbane. The study draws upon Yeatman’s (1998) description of policy as occurring “when social actors think about what they are doing and why in relation to different and alternative possible futures” (p. 19) and views policy as consisting of more than texts themselves. Policy texts result from struggles over meaning (Taylor, 2004) in which specific discourses are mobilised to support particular views. The study has a particular interest in the analysis of Brisbane religious education policy texts, the discursive practices that surrounded them, and the contexts in which they arose. Policy texts are conceptualised in the study as representing “temporary settlements” (Gale, 1999). Such settlements are asymmetrical, temporary and dependent on context: asymmetrical in that dominant actors are favoured; temporary because dominant actors are always under challenge by other actors in the policy arena; and context - dependent because new situations require new settlements. To investigate the official policy documents, the study used Critical Discourse Analysis (hereafter referred to as CDA) as a research tool that affords the opportunity for researchers to map and chart the emergence of new discourses within the policy arena. As developed by Fairclough (2001), CDA is a three-dimensional application of critical analysis to language. In the Brisbane religious education arena, policy texts formed a genre chain (Fairclough, 2004; Taylor, 2004) which was a focus of the study. There are two features of texts that form genre chains: texts are systematically linked to one another; and, systematic relations of recontextualisation exist between the texts. Fairclough’s (2005) concepts of “imaginary space” and “frameworks for action” (p. 65) within the policy arena were applied to the Brisbane policy arena to investigate the relationship between policy statements and subsequent guidelines documents. Five key findings emerged from the study. First, application of CDA to policy documents revealed that a fundamental reconceptualisation of the nature and purpose of classroom religious education in Catholic schools occurred in the Brisbane policy arena over the last twenty-five years. Second, a disjuncture existed between catechetical discourses that continued to shape religious education policy statements, and educational discourses that increasingly shaped guidelines documents. Third, recontextualisation between policy documents was evident and dependent on the particular context in which religious education occurred. Fourth, at subsequent links in the chain, actors created their own “imaginary space”, thereby altering orders of discourse within the policy arena, with different actors being either foregrounded or marginalised. Fifth, intertextuality was more evident in the later links in the genre chain (i.e. 1994 policy statement and 1997 guidelines document) than in earlier documents. On the basis of the findings of the study, six recommendations are made. First, the institutional Church should carefully consider the contribution that the Catholic school can make to the overall pastoral mission of the diocese in twenty-first century Australia. Second, policymakers should articulate a nuanced understanding of the relationship between catechesis and education with regard to the religion classroom. Third, there should be greater awareness of the connections among policies relating to Catholic schools – especially the connection between enrolment policy and religious education policy. Fourth, there should be greater consistency between policy documents. Fifth, policy documents should be helpful for those to whom they are directed (i.e. Catholic schools, teachers). Sixth, “imaginary space” (Fairclough, 2005) in policy documents needs to be constructed in a way that allows for multiple “frameworks for action” (Fairclough, 2005) through recontextualisation. The findings of this study are significant in a number of ways. For religious educators, the study highlights the need to develop a shared understanding of the nature and purpose of classroom religious education. It argues that this understanding must take into account the multifaith nature of Australian society and the changing social composition of Catholic schools themselves. Greater recognition should be given to the contribution that religious studies courses such as Study of Religion make to the overall religious development of a person. In view of the social composition of Catholic schools, there is also an issue of ecclesiological significance concerning the conceptualisation of the relationship between the institutional Catholic Church and Catholic schools. Finally, the study is of significance because of its application of CDA to religious education policy documents. Use of CDA reveals the foregrounding, marginalising, or excluding of various actors in the policy arena.

Teaching in Inclusive School Communities

"Teaching in Inclusive School Communities, 1st Edition is the essential resource to provide pre-service teachers with the most contemporary, ethical and useful framework for incorporating diversity and inclusive practices in today’s classroom. Fourteen concise chapters compose a focused picture of the values and beliefs that inform the inclusive education approach, with the most up-to-date connections to curriculum and pedagogy throughout. Complemented by the latest research in the field, this text provides the practical knowledge and skills needed for inclusive classroom teaching in Australia and New Zealand, as well as a thorough analysis of exactly what is required to build respectful relationships in modern school communities."--publisher website

Connecting Indigenous stories with geology : inquiry-based learning in a middle years classroom

One way to integrate indigenous perspectives in junior science is through links between indigenous stories of the local area and science concepts. Using local indigenous stories about landforms, a teacher of year 8 students designed a unit on geology that catered for the diverse student population in his class. This paper reports on the inquiry-based approach structured around the requirements of the Australian Curriculum highlighting the learning and engagement of students during the unit.

Embedding information and communication technologies in the early childhood classroom

New technologies and the pace of change in modern society mean changes for classroom teaching and learning. Information and communication technologies (ICTs) feature in everyday life and provide ample opportunities for enhancing classroom programs. This article outlines how ICTs complement curriculum implementation in one year two classroom. It suggests practical strategies demonstrating how teachers can make ICTs work for them and progressively teach children how to make ICTs work for them.

Learning and teaching reflection : developing capacities for lifelong learning

Reflection is an essential part of being an effective learner and working as a productive teacher. It enables the learner or teacher to deliberate about the factors that lead to successful learning and teaching for them and/or their students, in a particular place and for a specific purpose, so they can make reasoned and effective choices. This chapter introduces important frameworks that cover a century of thinking around reflection in education, and illustrates how preservice teachers can use these ideas across three phases. First, becoming a reflective learner as a university student to enhance learning and assessment outcomes; second, becoming a reflective teacher to improve classroom teaching and learning outcomes; and third, developing the reflective capacities of primary students so they can enhance their skills for lifelong learning.

Technological tools for science classrooms : choosing and using for productive and sustainable teaching and learning experiences

In this age of rapidly evolving technology, teachers are encouraged to adopt ICTs by government, syllabus, school management, and parents. Indeed, it is an expectation that teachers will incorporate technologies into their classroom teaching practices to enhance the learning experiences and outcomes of their students. In particular, regarding the science classroom, a subject that traditionally incorporates hands-on experiments and practicals, the integration of modern technologies should be a major feature. Although myriad studies report on technologies that enhance students’ learning outcomes in science, there is a dearth of literature on how teachers go about selecting technologies for use in the science classroom. Teachers can feel ill prepared to assess the range of available choices and might feel pressured and somewhat overwhelmed by the avalanche of new developments thrust before them in marketing literature and teaching journals. The consequences of making bad decisions are costly in terms of money, time and teacher confidence. Additionally, no research to date has identified what technologies science teachers use on a regular basis, and whether some purchased technologies have proven to be too problematic, preventing their sustained use and possible wider adoption. The primary aim of this study was to provide research-based guidance to teachers to aid their decision-making in choosing technologies for the science classroom. The study unfolded in several phases. The first phase of the project involved survey and interview data from teachers in relation to the technologies they currently use in their science classrooms and the frequency of their use. These data were coded and analysed using Grounded Theory of Corbin and Strauss, and resulted in the development of a PETTaL model that captured the salient factors of the data. This model incorporated usability theory from the Human Computer Interaction literature, and education theory and models such as Mishra and Koehler’s (2006) TPACK model, where the grounded data indicated these issues. The PETTaL model identifies Power (school management, syllabus etc.), Environment (classroom / learning setting), Teacher (personal characteristics, experience, epistemology), Technology (usability, versatility etc.,) and Learners (academic ability, diversity, behaviour etc.,) as fields that can impact the use of technology in science classrooms. The PETTaL model was used to create a Predictive Evaluation Tool (PET): a tool designed to assist teachers in choosing technologies, particularly for science teaching and learning. The evolution of the PET was cyclical (employing agile development methodology), involving repeated testing with in-service and pre-service teachers at each iteration, and incorporating their comments i ii in subsequent versions. Once no new suggestions were forthcoming, the PET was tested with eight in-service teachers, and the results showed that the PET outcomes obtained by (experienced) teachers concurred with their instinctive evaluations. They felt the PET would be a valuable tool when considering new technology, and it would be particularly useful as a means of communicating perceived value between colleagues and between budget holders and requestors during the acquisition process. It is hoped that the PET could make the tacit knowledge acquired by experienced teachers about technology use in classrooms explicit to novice teachers. Additionally, the PET could be used as a research tool to discover a teachers’ professional development needs. Therefore, the outcomes of this study can aid a teacher in the process of selecting educationally productive and sustainable new technology for their science classrooms. This study has produced an instrument for assisting teachers in the decision-making process associated with the use of new technologies for the science classroom. The instrument is generic in that it can be applied to all subject areas. Further, this study has produced a powerful model that extends the TPACK model, which is currently extensively employed to assess teachers’ use of technology in the classroom. The PETTaL model grounded in data from this study, responds to the calls in the literature for TPACK’s further development. As a theoretical model, PETTaL has the potential to serve as a framework for the development of a teacher’s reflective practice (either self evaluation or critical evaluation of observed teaching practices). Additionally, PETTaL has the potential for aiding the formulation of a teacher’s personal professional development plan. It will be the basis for further studies in this field.

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.

Making use of pedagogic models as reflective catalysts for investigating pedagogic practice

The notion of pedagogy for anyone in the teaching profession is innocuous. The term itself, is steeped in history but the details of the practice can be elusive. What does it mean for an academic to be embracing pedagogy? The problem is not limited to academics; most teachers baulk at the introduction of a pedagogic agenda and resist attempts to have them reflect on their classroom teaching practice, where ever that classroom might be constituted. This paper explores the application of a pedagogic model (Education Queensland, 2001) which was developed in the context of primary and secondary teaching and was part of a schooling agenda to improve pedagogy. As a teacher educator I introduced the model to classroom teachers (Hill, 2002) using an Appreciative Inquiry (Cooperrider and Srivastva 1987) model and at the same time applied the model to my own pedagogy as an academic. Despite being instigated as a model for classroom teachers, I found through my own practitioner investigation that the model was useful for exploring my own pedagogy as a university academic (Hill, 2007, 2008). Cooperrider, D.L. and Srivastva, S. (1987) Appreciative inquiry in organisational life, in Passmore, W. and Woodman, R. (Eds) Research in Organisational Changes and Development (Vol 1) Greenwich, CT: JAI Press. Pp 129-69 Education Queensland (2001) School Reform Longitudinal Study (QSRLS), Brisbane, Queensland Government. Hill, G. (2002, December ) Reflecting on professional practice with a cracked mirror: Productive Pedagogy experiences. Australian Association for Research in Education Conference. Brisbane, Australia. Hill, G. (2007) Making the assessment criteria explicit through writing feedback: A pedagogical approach to developing academic writing. International Journal of Pedagogies and Learning 3(1), 59-66. Hill, G. (2008) Supervising Practice Based Research. Studies in Learning, Evaluation, Innovation and Development, 5(4), 78-87

Investigating pre-service teachers’ perceptions of their preparedness to teach

The experiences of transition to the teaching profession have a significant impact on a teachers’ potential length of career, feelings of professional efficacy and the quality of performance in the classroom (Gore & Thomas, 2003). While the transition to practice is characterized by much expectation and excitement, it also a time of stress and uncertainty for many beginning teachers. As such, it is important to investigate this period of transition for beginning teachers. This paper explores graduate teachers perceptions of their personal ‘preparedness to teach’. The group is graduating from one Australian university, and the data is captured at the end of their teacher preparation programs,before they take up positions in schools. These graduating pre-service teachers are from one year graduate entry programs that include individual programs of early years, middle years and senior years. The key findings indicate that this group of graduating pre-service teachers are already engaged in some level of reflective practice and are actively seeking further professional learning to improve the practical aspects of their classroom teaching.

School Leadership, Literacy and Social Justice : The Place of Local School Curriculum Planning and Reform

School reform is a matter of both redistributive social justice and recognitive social justice. Following Fraser (Justice interruptus: critical reflections on the “postsocialist” condition. Routledge, New York, 1997), we begin from a philosophical and political commitment to the more equitable redistribution of knowledge, credentials, competence, and capacity to children of low socioeconomic, cultural, and linguistic minority and Indigenous communities whose access, achievement, and participation historically have “lagged” behind system norms and benchmarks set by middle class and dominant culture communities. At the same time, we argue that the recognition of these students and their communities’ lifeworlds, knowledges, and experiences in the curriculum, in classroom teaching, and learning is both a means and an end: a means toward improved achievement measured conventionally and a goal for reform and alteration of mainstream curriculum knowledge and what is made to count in the school as valued cultural knowledge and practice. The work that we report here was based on an ongoing 4-year project where a team of university teacher educators/researchers have partnered with school leadership and staff to build relationships within community. The purpose has been to study whether and how engagement with new digital arts and multimodal literacies could have effects on students “conventional” print literacy achievement and, secondly, to study whether and how the overall performance of a school could be generated through a focus on professional conversations and partnerships in curriculum and instruction – rather than the top-down implementation of a predetermined pedagogical scheme, package, or approach.

Low SES primary school students engaging in an after-school robotics program

Recent attention in education within many western contexts has focused on improved outcomes for students, with a particular focus on closing the gap between those who come from disadvantaged backgrounds and the rest of the student population. Much of this attention has supported a set of simplistic solutions to improving scores on high stakes standardized tests. The collateral damage (Nichols & Berliner, 2007) of such responses includes a narrowing of the curriculum, plateaus in gain scores on the tests, and unproductive blame games aimed by the media and politicians at teachers and communities (Nichols & Berliner, 2007; Synder, 2008). Alternative approaches to improving the quality and equity of schooling remain as viable alternatives to these measures. As an example in a recent study of school literacy reform in low SES schools, Luke, Woods and Dooley (2011) argued for the increase of substantive content and intellectual quality of the curriculum as a necessary means to re-engaging middle school students, improving outcomes of schooling and achieving a high quality, high equity system. The MediaClub is an afterschool program for students in years 4 to 7 (9-12 year old) at a primary school in a low SES area of a large Australian city. It is run as part of an Australian Research Council funded research project. The aim of the program has been to provide an opportunity for students to gain expertise in digital technologies and media literacies in an afterschool setting. It was hypothesized that this expertise might then be used to shift the ways of being literate that these students had to call on within classroom teaching and learning events. Each term, there is a different focus on digital media, and information and communication technology (ICT) activities in the MediaClub. The work detailed in this chapter relates to a robotics program presented as one of the modules within this afterschool setting. As part of the program, the participants were challenged to find creative solutions to problems in a constructivist-learning environment.