Lesson study is highly regarded as a model for professional learning, yet remains under-theorised. This article examines the professional learning experiences of teachers and numeracy coaches from ...three schools in a local network of schools, participating in a lesson study project over two research cycles in 2012. It maps the interconnections between their experiences and their beliefs and practices, using Clarke and Hollingsworth's (2002) Interconnected Model of Professional Growth. Analysis of interview data and video-recordings of planning meetings, research lessons, and post-lesson discussions reveals the development of teachers' collaborative planning skills, increased attention to students' mathematical thinking, use of orchestrated whole-class discussion based on anticipated student solutions and focused questioning, and the enhancement of collaborative practices for teacher inquiry. Our findings illuminate the interplay between the External Domain, the Personal Domain, the Domain of Practice, and the Domain of Consequence, in the teaching and learning change environment, and the mediating processes of enactment and reflection. Changes in the domains across the period of the lesson study provide evidence of teachers' professional growth, with the iterative processes of enactment and reflection being critical in mediating this professional growth. Author abstract, ed
Little is known about primary school mathematics middle leaders' aspirations for mathematics learning. We sought to give mathematics middle leaders a voice to articulate their desires for mathematics ...learning based on what was most
salient to them. Statements collected from 149 primary school mathematics middle leaders through an online survey were categorised using an ecological approach to determine the system level (i.e., mathematics middle leader, classroom,
school, education system, or cultural norm) in which their aspirations for mathematics learning mostly presided. The mathematics middle leaders' aspirations were situated across the full range of ecological systems. However, more
mathematics middle leaders focused their aspirations within the classroom level, compared with any other level, and around 15% focused on their own knowledge and capacity to lead. Author abstract
Out-of-field teaching of mathematics is a reality in many secondary schools in the world. The incidence of out-of-field teaching generally occurs in low socio-economic communities and, in Australia, ...in schools located in rural and remote locations. The theory of boundary crossing enables positive perspectives of teaching out-of-field to be explored. In this paper, we explore changes in out-of-field mathematics teachers' beliefs and practices about teaching mathematics over 3 years and the way in which their in-field teaching influenced and was influenced by their out-of-field mathematics teaching. Out-of-field teachers from schools in three Australian states participated in the study. The findings show that initially the majority of these teachers held instrumentalist beliefs about the mathematics discipline and its teaching and learning. Those who continued to teach mathematics out-of-field beyond the first year of the study presented evidence of some shifts in their beliefs about the teaching and learning of mathematics by including more student-centred or problem-solving approaches. Exploring the factors that enable continuity of discourse across subject boundaries is important not only for supporting and retaining teachers of mathematics in schools with a high incidence of out-of-field teaching but also for fostering interdisciplinary approaches to teaching and learning. Author abstract
Worldwide interest in Japanese Lesson Study as a vehicle to improve mathematics teaching practice through professional learning has left largely unanswered questions about the extent to which it can ...be replicated elsewhere. This paper reports on a small-scale research project, Implementing structured problem-solving mathematics lessons through lesson study, carried out in three Australian schools during 2012, and continued in a modified form during 2013 and 2014. Two major aims of the project were to investigate critical factors in the adaptation and effective implementation of (1) structured problem-solving mathematics lessons, and (2) Japanese Lesson Study as a model for teacher professional learning in the Australian context. This paper discusses the specific affordances that contributed to both the implementation of structured problem solving and to teachers' professional learning as a result of their participation in this project, as well as the constraints encountered, and the implications of these for the sustainability of lesson study in the Australian context. Critical factors identified by the teachers as contributing to the success of the project included the opportunities for in-depth lesson planning, the presence of large numbers of observers at the research lessons and the post-lesson discussions, and the insight provided by the 'knowledgeable other'. Major constraints included the difficulty in finding suitable problem solving tasks to match the Australian curriculum, and the teaching culture that emphasises small-group rather than whole-class teaching. Author abstract
Structured problem-solving lessons are used to explore mathematical concepts such as pattern and relationships in early algebra, and regularly used in Japanese Lesson Study research lessons. However, ...enactment of structured problem-solving lessons which involves detailed planning, anticipation of student solutions and orchestration of whole-class discussion of solutions is an ongoing challenge for many teachers. Moreover, primary teachers have limited experience in teaching early algebra or mathematical reasoning actions such as generalising. In this study, the critical factors of enacting the structured problem-solving lessons used in Japanese Lesson Study to elicit and develop primary students' capacity to generalise are explored. Teachers from three primary schools participated in two Japanese Lesson Study teams for this study. The lesson plans and video recordings of teaching and post-lesson discussion of the two research lessons along with students' responses and learning are compared to identify critical factors. The anticipation of students' reasoning together with preparation of supporting and challenging prompts was critical for scaffolding students' capacity to grasp and communicate generality. Author abstract
There is a consensus that we need to improve the quality of pre-service teacher education, and teachers' mathematical content knowledge is critical for teaching. Identifying opportunities and ...influences that assist pre-service teachers to extend their mathematical content knowledge throughout their teacher education programme is important. This paper reports on qualitative data, collected over 4 years from two typical pre-service teachers whose developing mathematical content knowledge was investigated during their primary and secondary programme. These data were analysed and reported using the four dimensions of the Knowledge Quartet: foundation knowledge, transformation, connection and contingency. The results highlight the consequences of programme structure in order to help pre-service teachers to establish and sustain a positive mathematics learner identity, build teacher identity and develop mathematical content knowledge. Author abstract
•Mathematical reasoning is an important feature in the learning of mathematics.•Many primary teachers unclear about the term ‘mathematical reasoning’.•Teaching mathematics to develop mathematical ...reasoning is challenging.•Phenomenographic analysis and development of outcome space (OS) is explained.•OS demonstrates range of teachers’ perceptions of mathematical reasoning.•OS provides framework for track development of mathematical reasoning.
Mathematical reasoning has been emphasised as one of the key proficiencies for mathematics in the Australian curriculum since 2011 and in the Canadian curriculum since 2007. This study explores primary teachers’ perceptions of mathematical reasoning at a time of further curriculum change. Twenty-four primary teachers from Canada and Australia were interviewed after engagement in the first stage of the Mathematical Reasoning Professional Learning Program incorporating demonstration lessons focused on reasoning conducted in their schools. Phenomenographic analysis of interview transcripts exploring variation in the perceptions of mathematical reasoning held by these teachers revealed seven categories of description based on four dimensions of variation. The categories delineate the different perceptions of mathematical reasoning expressed by the participants of this study. The resulting outcome space establishes a framework that facilitates tracking of growth in primary teachers’ awareness of aspects of mathematical reasoning.
Engaging students in comparing and contrasting, forming conjectures, generalising and justifying is critical to develop their mathematical reasoning, but there are untapped opportunities for primary ...school students to improve these reasoning processes in mathematics lessons. Through a case study of one task, this paper reports on levels of justifying and the connections to other reasoning processes of comparing and contrasting, forming conjectures and generalising observed among Year 3-4 Australian and Canadian students (9-10-year olds) using the mathematical reasoning actions and levels (MRAL) framework (Authors 2017). The findings revealed that examining commonalities and differences was critical to allow Year 3-4 students to form conjectures and generalise for themselves. Justifying by examples and seeking counter examples to evaluate the conjecture were prevalent with some students attempting to develop logical argument. The findings have implications for frameworks that assess students' levels of justifying and for teacher actions that encourage students to communicate their reasoning through oral and non-verbal as well as written communications. Author abstract
Colleen Vale makes the case for professional learning teams collaborating together to improve their teaching and hence children's achievement. In this article she describes how this may be done. ...Along the way the teachers explored the idea of equivalence and the common conceptions and misconceptions held by children in their classes. Publisher abstract
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