Document = Resources + Scheme of Utilization” (Gueudet & Trouche, 2009, p. 205)

“We use the term resources to emphasize the variety of artifacts we consider: a textbook, a piece of software, a student’s sheet, a discussion with a colleague, etc. A resource is never isolated; it belongs to a set of resources. The subjects we study are teachers. A teacher draws on resource sets for her documentation work. A process of genesis takes place, producing what we call a document. The teacher builds schemes of utilization of a set of resources for the same class of situations across a variety of contexts.” (Gueudet & Trouche, 2009, p. 205).

A scheme of utilization “[…] is an invariant organization of activity for a given class of situations. It comprises goals and subgoals, anticipations, rules of action, of gathering information and exercising control, and possibilities of inferences. It is structured by operational invariants, which consist of implicit knowledge built through various contexts […]”(Gueudet & Trouche, 2009, p. 204) 

“These operational invariants can be inferred from the observation of invariant behaviors of the teacher for the same class of situations across different contexts. They are teacher beliefs, and are both driving forces and outcomes of the teacher’s activity, instrumented by a set of resources.” (Gueudet & Trouche, 2009, p. 205)


Gueudet, G., & Trouche, L. (2009). Towards new documentation systems for mathematics teachers? Educational Studies in Mathematics, 71(3), 199–218.