Mathematics Teachers’ Teaching Practices in Relation to Textbooks: Exploring Praxeologies

In this article, we explore affordances of adopting the framework of praxeology by Chevallard in the analysis of mathematics classroom communication in relation to the communication in a textbook. While adopting praxeology, we carried out detailed analysis of communication in both classroom data and textbooks. The construed praxeologies describe the organisation of knowledge expressed for the same type of task in both classroom and textbook. The praxeologies were compared, with specific attention to the teacher’s practice. This analysis illuminates how teachers’ practices, realised in classroom communication, may be compared to other texts describing the same topics, with a focus on procedures, explanations, theoretical aspects, et cetera. Hence, praxeology as a framework enabled an analytical structuring of classroom and textbook communication, and consequently a systematic comparison. In other studies about the use of mathematics textbooks the teaching frequently is categorised as regulated by the textbook, and in this article, we problematize this. The teaching practice was, in fact, closely related to the textbook when comparing exercises and procedures, but when specifically examining the explanations of concepts, it became possible to discern how the teaching practice differed from the textbook