This module develops the praxeology analysis previously introduced on the case of proportionality already used in the previous modules. Praxeologies of different “sizes” (pinpoint, local, regional and global) help consider this school mathematical content from a broad perspective and elaborate a research reference model about proportionality. The didactic transposition phenomena affecting the teaching and learning of proportionality can then be related to different mathematical domains, like the old theory of “ratios and proportions”, algebra, functions and, especially, the neglection of quantities and units in school mathematical work.
An article in the ICMI bulletin to celebrate the 25 years of the first publication of the book on didactic transposition. It presents praxeological analysis as an extension of analysis in terms of didactic transposition and introduces the notion of reference epistemological (or praxeological) model:
• Bosch, M., & Gascón, J. (2006). Twenty-five years of the didactic transposition. ICMI Bulletin, 58, 51–65.
A chapter introducing the ATD as a research methodology in a book about networking theories. The praxeological analysis is particularly developed about both mathematical and didactic (teaching and learning) activities:
• Bosch, M., & Gascón, J. (2014). Introduction to the Anthropological Theory of the Didactic (ATD). In A. Bikner-Ahsbahs, S. Prediger (Eds.), Networking of Theories as a Research Practice in Mathematics Education (pp. 67-83). Dordrecht: Springer.
A book including contributions from several researchers from France, Spain, Denmark, Japan, Belgium, Portugal and Mexico working within the ATD (Chapters 3, 4, 5, 6):
• Bosch, M., Chevallard, Y., Garcia, F. J., & Monhagan, J. (2020). Working with the anthropological theory of the didactic. A comprehensive casebook. Routledge.