Mathematical practice in textbooks analysis: Praxeological reference models, the case of proportion

Abstract

We present a new method in textbook analysis, based on so-called praxeological reference models focused on specific content at task level. This method implies that the mathematical contents of a textbook (or textbook part) is analyzed in terms of the tasks and techniques which are exposed to or demanded from readers; this can then be interpreted and complemented by a discussion of the discursive and theoretical level of the text. The praxeological reference model is formed by the analyst to categorize various elements of the text, in particular the tasks and techniques which it explains or requires from readers. We demonstrate the methodological features of this approach by analyzing examples and exercises in three Indonesian textbooks, focusing on the chapters dealing with arithmetic proportion (defined theoretically by the model). We also illustrate how this rigorous analysis can be used to provide a quantitative “profile” of textbooks within a topic.