Educational Studies in Mathematics

, Volume 98, Issue 3, pp 231–252 | Cite as

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

  • Alejandro S. González-Martín
  • Elena Nardi
  • Irene Biza


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 terms of documentation work (resources, aims, rules of action, operational invariants), a key construct from the documentational approach (DA, Gueudet & Trouche, in Educational Studies in Mathematics, 71, 199–218, 2009). We do so in the case of five post-secondary teachers who use the same textbook as a main resource for teaching 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 relationships with the topic) provided by the former.


Documentational approach Documentation work ATD Personal relationship Series Textbook use 

Supplementary material

10649_2018_9813_MOESM1_ESM.doc (74 kb)
ESM 1 (DOC 74 kb)
10649_2018_9813_MOESM2_ESM.pdf (31 kb)
ESM 2 (PDF 31.4 kb)


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Département de Didactique, Bureau D-522, Faculté des Sciences de l’ÉducationUniversité de MontréalMontréalCanada
  2. 2.School of EducationUniversity of East AngliaNorwichUK

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