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.

Análisis Praxeológico de los Métodos de Enseñanza: un Puente entre la Investigación y la Práctica

“…Las praxeologías se utilizan, principalmente, en el análisis del material didáctico (e.g. Schivani, Brockington, & Pietrocola, 2013;Barbé, Espinoza, & Gellert, 2017;Wijayanti, & Winsløw, 2018;Wijayanti, 2019) y de la práctica en el aula (e.g. Barbé, Bosch, Espinoza, & Gascón, 2005;Corica, & Otero, 2011.…”

Linking proportionality of arithmetic, algebra and geometry domains in Indonesian lower secondary textbooks

“…A narrower research on how the notion of praxeology is used to analyse different types of tasks in textbooks was conducted by Wijayanti and Winsløw (2017) who found two themes in the arithmetical domain that were divided into seven specific types of tasks. Additionally, this research also showed that there were some dominant tasks that appeared in the textbooks.…”

“…The example of table 1 illustrates the type of tasks T 6 . Wijayanti and Winsløw (2017) found seven types of tasks that are divided into two themes: 1. ratio and scale, and 2. direct and inverse proportion (table 2).…”

A Comparative Study of Norwegian and Ethiopian Textbooks: The Case of Relations and Functions Using Anthropological Theory of Didactics (ATD)

“…That is, the knowledge block is a tuple (θ, Θ). Altogether, the theory of praxeology (fusion of "praxis" and "logos") is of a quadruple (T, , θ, Θ) and, thus, the praxeology block models an amalgam of human practice and knowledge [3,21,23,26,27].…”