In this article, we examine secondary mathematics teachers’ work with resources using the Documentational Approach to Didactics lens. Specifically, we look at the resources and a teacher’s scheme of use (aims, rules of actions, operational invariants, and inferences) of these resources across a set of lessons (macro-level analysis) that aim towards students’ preparation for the examinations and how this use emerges in a set of three lessons on the same topic (micro-level analysis) as a response to contingent moments. We propose the terms scheming—a teacher’s emerging scheme of use related to the same set of resources used for the same aim—and re-scheming, namely, shifts in such scheming. Our analysis of lesson observations and the teacher’s reflections on his actions from a post-observation interview demonstrate the interplay between the stable characteristics of the scheme of use and the scheming and re-scheming in individual lessons. We conclude this article with a discussion on the methodological potential of using both macro- and micro-level analyses in the investigation of teachers’ use of resources.
Translation is a critical issue in international mathematics education studies but has seldom been carefully investigated. How can a theoretical approach be translated and subsequently used in different languages, and to what extent could the translation processes deepen the approach itself? This paper addresses such issues in the case of the Documentational Approach to Didactics (DAD). We explore possibilities of translating selected critical notions expressed in English terms into French, Arabic, and Chinese, and of developing insights from these. We further deal with the translation issues 'in situ', i.e., in an English mathematics teacher's lesson where we can identify the embodiments of the DAD concepts. The most challenging part in the translation is the embedding of the English terms in the English cultural sphere, and 're-bedding' them into another cultural sphere. It is claimed that examining the nuances between the different possibilities of translation for the same concept in connection with their use 'in situ', and drawing inspiration from the educational, cultural, and theoretical traditions in other cultural spheres, can help to deepen the theoretical constructs.
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