Mathematical tasks and learning goals: examples from Japanese lesson study

This paper explores how to select, or design, the best mathematical task for a given learning goal. Examples are taken from a recent project in Victorian primary schools that employed Japanese lesson study as the means to provide teachers with professional learning within their own classrooms. The discussions by participating teachers and researchers provide some insights into the difficulties and solutions facing teachers intending to improve the critical thinking skills of their pupils. Examples of tasks and goals are provided.

Lesson study - Could it work for you?

1. Introduction Japanese Lesson Study first came to world-wide attention through Makoto Yoshida’s doctoral dissertation (Yoshida, 1999; Fernandez & Yoshida, 2004) and Stigler and Hiebert’s (1999) accounts of Lesson Study based on the Third International Mathematics and Science Study (TIMSS). By 2004, Lesson Study was taking place in the USA in at least 32 states and 150 lesson study clusters.Lewis (2002) describes the Lesson Study Cycle as having four phases: goal-setting and planning – including the development of the Lesson Plan; teaching the “research lesson” – enabling the lesson observation; the post-lesson discussion; and the resulting consolidation of learning, which has many far-reaching consequences (see, for example, Lewis & Tsuchida, 1998). It could be said that research lessons make participants and observers think quite profoundly about specific and general aspects of teaching.In Japan, Lesson Study occurs across many curriculum areas, mainly at the elementary school level, and to a lesser extent junior secondary. In mathematics, the research lesson usually follows the typical lesson pattern for a Japanese “structured problem solving lesson”.Major characteristics of such lessons include: the hatsumon – the thought-provoking question or problem that students engage with and that is the key to students’ mathematical development and mathematical connections; kikan-shido – sometimes referred to as the “purposeful scanning” that takes place while students are working individually or in groups, which allows teachers not only to monitor students’ strategies but also to orchestrate their reports on their solutions in the neriage phase of the lesson; neriage – the “kneading” stage of alesson that allows students to compare, polish and refine solutions through the teacher’s orchestration and probing of student solutions; and matome — the summing up and careful review of students’ discussion in order to guide them to higher levels of mathematical sophistication (see, for example, Shimizu, 1999).

Teachers’ professional growth through engagement with lesson study

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 (Teach Educ 18(8):947–967, 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.

Primary teachers’ algebraic thinking: example from lesson study

Previous studies have reported on primary children’s algebraic thinking and generalising in a range of problem settings but there is little evidence of primary teachers’ knowledge of algebraic thinking. In this paper the development in algebraic thinking of one primary teacher who taught a research lesson in a Japanese Lesson Study project involving teachers from three primary schools is presented. The findings suggest the need for professional learning in algebra and reasoning and indicate the value of Lesson Study.

Teacher beliefs in ‘testing’ times: a lesson from Singapore

International benchmarking and national testing of students at all levels of schooling have provoked teachers to critically reflect on their place in this endeavour. Many of the curriculum and pedagogical approaches associated with this type of assessment and accountability conflict with long-held beliefs about the role of teachers and the work of schooling. Singapore is recognised for significant achievement in the international schooling arena and also has a long history of national testing. This study draws specifically on positioning theory to investigate teacher beliefs and positioning in these times. A large qualitative research project located in Singapore sought the ways experienced teachers positioned themselves and their work as they negotiated multiple and sometimes conflicting discourses of teaching. A rigorous process was used to elicit teacher beliefs and resultant teacher positions.

Critical factors in the adaptation and implementation of Japanese Lesson Study in the Australian context

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 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

Japanese lesson study : a numeracy coach's view

This paper reports findings based on interview data from a professional teacher educator who was a Numeracy Coach for a group of schools that participated in a research project, Implementing structured problem-solving mathematics lessons through Lesson Study. The Numeracy Coach was a highly-skilled professional teacher educator, whose position was such that she was both a support person to the teachers and a participant in the project. Her insights into the processes and effects of Japanese Lesson Study, on teachers, as well as herself, are extremely enlightening, and form the data for this paper. While the evidence is from a single source, the evidence is consistent with other projects into the effectiveness of the Japanese model of Lesson Study. Aspects of the project with implications for teacher professional development are detailed.