The Young ERME Summer School (YESS) organised by the European Society for Research in Mathematics Education (ERME), was held online in 2020 due to the pandemic. Two out of seven thematic working groups (TWG) run in a virtual environment. Planning jointly these TWGs led the leading experts to decide on using the research pentagon (Bikner-Ahsbahs, 2017) as a tool for reflecting on research. We explore the extent to which activities proposed during TWG sessions constituted an opportunity to learn (Elliott & Bartlett, 2016) about research for the participants by focusing on the role of the pentagon. Considering the pentagon as a tool that participants need to appropriate in order to use it efficiently, instrumental approach (Vérillon & Rabardel, 1995; Rabardel, 2002) is our theoretical framework. The key idea is the distinction between an artefact – material or symbolic object available to a subject, – and an instrument – a psychological construct resulting from the use of the artefact by the subject in a given context. The development of an instrument, coined instrumental genesis (Vérillon & Rabardel, 1995), is the result of two interrelated processes: instrumentation leading to the constitution and evolution of the subject’s utilisation schemes related to the artefact, and instrumentalisation during which the subject adapts the artefact according to her knowledge and beliefs. The development of utilisation schemes manifests itself in a subject’s invariant behaviour in a class of situations. Trouche (2020) suggests seeing instrumentation both as “an action (by which someone acquires an instrument)” and as “the influence of this action on a subject’s activity and knowledge” (p. 307). Thus using an artefact yields both pragmatic and epistemic outcomes. Adopting such perspective, we consider the research pentagon as an artefact offered to participants. The purpose of this second paper is to address the question: which instruments are developed from the research pentagon by the participants and how this instrumental genesis contributes to the evolution of their knowledge about research? Our data comprise design and evaluation materials, field notes and video recorded interviews with eleven volunteers. Despite the short duration of the summer school, the analysis shows evidence suggesting the emergence of various instruments: the research pentagon is instrumented as a tool to organise own research, to analyse others’ research, and to provide feedback. Processes of instrumentalisation are much rarer. Repeated observation of expert’s and peers’ ways of using the pentagon appears as the most relevant activity for developing personal schemes.

Bikner-Ahsbahs, A. (2019). The Research Pentagon: A Diagram with which to Think about Research. In G. Kaiser and N. Presmeg (Eds.), Compendium for Early Career Researchers in Mathematics Education (pp. 153-180). Cham (Switzerland): Springer. Elliott, S. N., & Bartlett, B. J. (2016). Opportunity to learn. In P. Nathan (Ed.), Oxford handbook of education online. New York: Oxford University Press. Rabardel, P. (2002). People and technology — a cognitive approach to contemporary instruments. Université Paris 8. Trouche, L. (2020, 2nd ed). Instrumentation in Mathematics Education. In S. Lerman (Ed.), Encyclopedia in Mathematics Education (pp. 392-403). Cham (Switzerland): Springer. Verillon P., & Rabardel, P. (1995). Cognition and artifact: a contribution to the study of thought in relation to instrument activity. European Journal of Psychology of Education 9(3), 77–101.