Theoretical approaches to teachers’ lesson designs involving the adaptation of mathematics textbooks: two cases from kyouzai kenkyuu in Japan

Abstract

In this paper, we explore theoretical approaches to Japanese teachers’ lesson designs involving the adaptation of mathematics textbooks for instructional change. In Japan, although most teachers use textbooks as the main resource for lesson planning, called kyouzai kenkyuu, the ways in which they use textbooks can differ. In a kyouzai kenkyuu practice, Japanese teachers sometimes attempt to design innovative tasks and/or learning trajectories beyond or parallel to the textbooks and curriculum guidelines. Such practice is often invisible to international researchers, since it is culturally situated in the local context. To make it more visible, in this study we address and advance theoretical approaches using two frameworks which are well-established for research in mathematics education, namely, Anthropological Theory of the Didactic (ATD) and Documentational Approach to Didactics (DAD). Two cases of lesson design regarding fractions using the same textbook chapter for 3rd graders in primary schools in Japan, are used as examples to illustrate crucial elements of each framework and ways of combining and coordinating both frameworks. As a result, we conceptualise teachers’ kyouzai kenkyuu practice using two approaches: from a praxeological analysis based on ATD, the difference in teachers’ mathematical and didactic knowledge was emphasised, while within DAD, the difference in the instrumentalisation process was emphasised. This analysis implies that the two theoretical approaches can be compatible, and used to gain deeper insight into the relationship between lesson design using the textbook and teacher knowledge.

Conditions and constraints of implementing a mathematics lesson study-based PD program for Japanese pre-service teachers

“…Mathematical organization (MO) refers to mathematical practice and knowledge (mathematical praxeology), while didactic organization (DO) refers to teachers' pedagogies of MO. Although these notions are mostly used to characterize teachers' classroom teaching, they can also be employed to understand teachers' lesson design (e.g., Shinno & Mizoguchi, 2021) and the post-lesson discussion (e.g., Rasmussen, 2016;Rasmussen et al, 2020).…”

“…Regarding the Japanese lesson study, it is especially important to consider teachers' preparation work with kyouzai kennkyuu-the study of teaching materials-which is a crucial opportunity to develop teachers' professional knowledge (e.g., Fujii, 2018;Melville & Corey, 2021;Watanabe et al, 2008). In a kyouzai kenkyuu practice during lesson study, teachers' lesson planning can be characterized considering the didactic praxeology (including both MO and DO), which explains how curricular and textbook constraints can affect this planning phase (Shinno & Mizoguchi, 2021).…”

An anthropological point of view: exploring the Chinese and Japanese issues of translation about teaching resources

“…This is also the case for the Chinese term, 教材研究 (jiào-cái yán-jiū). These can be regarded as teachers' documentation work with different resources (e.g., Shinno & Mizoguchi, 2021), while they are customarily used in teachers' communities without any theoretical underpinning as terminologies that support their practices.…”

A didactical design for introducing the concepts in algebraic forms using the theory of praxeology

“…We adopted praxeology by Chevallard (2006;, which comprises task, technique, technology, and theory to study how students build knowledge in the concepts in algebraic form through the problems given. The praxeology has been used to study mathematical tasks, referred to as the epistemological model of mathematics knowledge, both in math textbooks and didactical designs (Wijayanti & Winsløw, 2017;Shinno & Mizoguchi, 2021). Praxeology is also proven to demonstrate students' mathematical activity thoroughly, e.g., students perform diverse techniques and explain accordingly to their chosen technique (Barraza-García et al, 2020).…”