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.

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.

The development of an on-line module for students on “Working in Inter-cultural Teams”

Since 2005 QUT through a number of large Teaching and Learning Grants has sponsored a range of teamwork learning initiatives to assist students to develop the teamwork skills demanded by industry. After a suite of six online team learning modules was developed, first year unit coordinators requested an additional module to address the challenges of working with the diverse range of social, cultural and personal values that students from different backgrounds bring to student teams. The Intercultural Teams module asks students to map themselves against a Cultural Orientations Framework so they can understand their own cultural beliefs. By learning about other cultural orientations and comparing and analysing their effects, team members can develop communication and team process management strategies to leverage their differences to realise effective and creative outcomes. The interactive session will demonstrate the elements of the Intercultural Teams module and ask participants to consider ways the module can be integrated into classroom learning to support the development of students’ intercultural competencies.

Who's at risk: Answerability and the critical possibilities of classroom discourse

Our aim in this article is twofold. First, we challenge the essentialized notion of adolescents and young people as perpetually driven to resist the authority of adults. At the same time, we disrupt linguistic conceptions of adolescent discourse, along with the discourse of youth at risk, by analyzing a transcript of classroom discourse that reflects an exchange between a highly regarded and well liked preservice teacher and his students. This representative transcript highlights the preservice teacher's ability to query, without a concomitant ability to listen, respond, and build a classroom dialogue with his students; what we call here a Socratic monologue. Second, we link the notions of dialogue and responsiveness to Bakhtin's concept of answerability, emphasizing the joint construction of classroom discourse as an ethically answerable relation between teacher and students.

Inquiry-based science in a primary classroom : professional development impacting practice

The critical factor in determining students' interest and motivation to learn science is the quality of the teaching. However, science typically receives very little time in primary classrooms, with teachers often lacking the confidence to engage in inquiry-based learning because they do not have a sound understanding of science or its associated pedagogical approaches. Developing teacher knowledge in this area is a major challenge. Addressing these concerns with didactic "stand and deliver" modes of Professional Development (PD) has been shown to have little relevance or effectiveness, yet is still the predominant approach used by schools and education authorities. In response to that issue, the constructivist-inspired Primary Connections professional learning program applies contemporary theory relating to the characteristics of effective primary science teaching, the changes required for teachers to use those pedagogies, and professional learning strategies that facilitate such change. This study investigated the nature of teachers' engagement with the various elements of the program. Summative assessments of such PD programs have been undertaken previously, however there was an identified need for a detailed view of the changes in teachers' beliefs and practices during the intervention. This research was a case study of a Primary Connections implementation. PD workshops were presented to a primary school staff, then two teachers were observed as they worked in tandem to implement related curriculum units with their Year 4/5 classes over a six-month period. Data including interviews, classroom observations and written artefacts were analysed to identify common themes and develop a set of assertions related to how teachers changed their beliefs and practices for teaching science. When teachers implement Primary Connections, their students "are more frequently curious in science and more frequently learn interesting things in science" (Hackling & Prain, 2008). This study has found that teachers who observe such changes in their students consequently change their beliefs and practices about teaching science. They enhance science learning by promoting student autonomy through open-ended inquiries, and they and their students enhance their scientific literacy by jointly constructing investigations and explaining their findings. The findings have implications for teachers and for designers of PD programs. Assertions related to teaching science within a pedagogical framework consistent with the Primary Connections model are that: (1) promoting student autonomy enhances science learning; (2) student autonomy presents perceived threats to teachers but these are counteracted by enhanced student engagement and learning; (3) the structured constructivism of Primary Connections resources provides appropriate scaffolding for teachers and students to transition from didactic to inquiry-based learning modes; and (4) authentic science investigations promote understanding of scientific literacy and the "nature of science". The key messages for designers of PD programs are that: (1) effective programs model the pedagogies being promoted; (2) teachers benefit from taking the role of student and engaging in the proposed learning experiences; (3) related curriculum resources foster long-term engagement with new concepts and strategies; (4) change in beliefs and practices occurs after teachers implement the program or strategy and see positive outcomes in their students; and (5) implementing this study's PD model is efficient in terms of resources. Identified topics for further investigation relate to the role of assessment in providing evidence to support change in teachers' beliefs and practices, and of teacher reflection in making such change more sustainable.

Parents as coteachers of science and technology in a middle-school classroom

This study explores coteaching/cogenerative dialoguing with parents to investigate how it may be employed to engage parents more meaningfully in schools. The cogens provided a space where participants became aware of resources available for coteaching, made decisions about planning and enacting coteaching, as well as interstitial culture that facilitated positive parent-teacher relationships.