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.

在本文中，我们探索了日本教师课程设计的理论方法，其中包括将数学教科书改编为教学内容。在日本，尽管大多数教师使用教科书作为课程计划的主要资源，称为kyouzai kenkyuu，但他们使用教科书的方式可能有所不同。在kyouzai kenkyuu中在实践中，日语教师有时会尝试设计超出教科书和课程指南或与之平行的创新性任务和/或学习轨迹。这种做法对国际研究人员来说通常是看不见的，因为它在文化上位于当地背景下。为了使它更清晰可见，在本研究中，我们使用为数学教育研究而建立的两个框架来解决和推进理论方法，这两个框架是教学法的人类学理论（ATD）和教学法的文献学方法（DAD）。以日本小学三年级学生使用同一教科书章节的分数为例的两个课程设计案例，以举例说明每个框架的关键要素以及组合和协调这两个框架的方式。结果，我们将教师的概念化kyouzai kenkyuu的练习使用两种方法：从基于ATD的人种学分析出发，强调了教师的数学和教学知识上的差异，而在DAD中，则强调了工具化过程上的差异。该分析表明，这两种理论方法可以兼容，并可以用来更深入地了解使用教科书和教师知识进行课程设计之间的关系。