From resource to document: Scaffolding content and organising student learning in teachers’ documentation work on the teaching of series

We examine teachers’ use of resources as they prepare to teach the topic of numerical series of real numbers in order to identify how their personal relationship with mathematical content—and its teaching—interacts with their use of a commonly used textbook. We describe this interplay between textbook and personal relationship, a term coined in the Anthropological Theory of the Didactic (ATD, Chevallard, 2003), in the terms of documentation work (resources, aims, rules of action, operational invariants), a key construct from the documentational approach (DA, Gueudet & Trouche, 2009). We do so in the case of five post-secondary teachers who use the same textbook as a main resource to teach the topic. Documentational analysis of interviews with the teachers led to the identification of their aims and rules of action (the what and how of their resource use as they organise their teaching of the topic) as well as the operational invariants (the why for this organisation of their teaching). We describe the teachers’ documentation work in two sets of aims/rules of action: scaffolding mathematical content (series as a stepping stone to learning about Taylor polynomials and Maclaurin series) and organising student learning about series through drill exercises, visualisation, examples, and applications. Our bridging (networking) of theoretical constructs originating in one theoretical framework (personal relationship, ATD) with the constructs of a different, yet compatible, framework (documentation work, DA) aims to enrich the latter (teachers’ documentation work) with the individual agency (teachers’ personal relationship with the topic) provided by the former

The French Didactic Tradition in Mathematics

This chapter presents the French didactic tradition. It first describes theemergence and development of this tradition according to four key features (role ofmathematics and mathematicians, role of theories, role of design of teaching andlearning environments, and role of empirical research), and illustrates it through two case studies respectively devoted to research carried out within this traditionon algebra and on line symmetry-reflection. It then questions the influence of thistradition through the contributions of four researchers from Germany, Italy, Mexicoand Tunisia, before ending with a short epilogue

Research on Teaching and Learning Mathematics at the Tertiary Level:State-of-the-art and Looking Ahead

This topical survey focuses on research in tertiary mathematics education, a field that has experienced considerable growth over the last 10 years. Drawing on the most recent journal publication as well as the latest advances from recent high quality conference proceedings, our review culls out the following five emergent areas of interest: mathematics teaching at the tertiary level; the role of mathematics in other disciplines; textbooks, assessment and students’ studying practices; transition to the tertiary level; and theoretical-methodological advances. We conclude the survey with a discussion of some potential ways forward for future research in this new and rapidly developing domain of inquiry

Studying Teachers’ Documentation Work: Emergence of a Theoretical Approach

International audienceThe documentational approach to didactics is a young theory – it was less than 10 years old in 2018. In this chapter I look back at the process of development of this approach. I recall the initial context, motivating the elaboration of a specific frame for studying teachers’ documentation work. Several kinds of evolutions are emphasized: theoretical, methodological, but also evolutions of the questions studied in the research works referring to the documentational approach. I conclude by evidencing the main evolutions so far and evoking some perspectives

Reflecting on a Theoretical Approach from a Networking Perspective: The Case of the Documentational Approach to Didactics

International audienceThis chapter analyses the emergence and development of the documentational approach to didactics (DAD), paying specific attention to the theoretical sources and connections having inspired its progressive elaboration. After introducing the two main conceptual tools used for this analysis, the scale of networking strategies between theories (Bikner-Ahsbahs, A., & Prediger, S. (2008). Networking of theories – An approach for exploiting the diversity of theoretical approaches. In B. Sriraman & L. English (Eds.), Theories in mathematics education (pp. 483–506). New York: Springer) and the idea of research praxeology (Artigue M, Bosch M, Gascón J, Bosch M et al. Centre de Recerca Matemàtica, Barcelona, 2011), the chapter proposes a chronological analysis with two main sections, respectively, devoted to the emergence and development of this approach. This analysis, based on the main publications associated with DAD, shows the respective roles played in the dynamics of this approach by the rapid emergence and stabilization of a full research praxeology and, at the same time, the impressive number of connections established with a diversity of theories in no more than one decade. These characteristics give DAD a specific identity. The chapter ends by establishing a connection with the international Lexicon project