Networking theoretical frames: the ReMath enterprise

Abstract

In this article of the special issue devoted to the European project ReMath, we present and discuss the affordances of this project in terms of networking between theoretical frameworks. After clarifying the vision of theories and networking adopted in this project, we introduce the methodological constructs that have been developed and used in ReMath for performing the planned networking enterprise. We then present its outcomes, focusing on different facets of this networking activity: the identification of possible connections and complementarities between frameworks, the identification and elaboration of boundary objects between cultures, and the progressive building of a shared theoretical framework regarding semiotic representations. In the last part of this article, we review the whole networking enterprise from the perspective of research praxeology

The French Didactic Tradition in Mathematics

“…As explained by Brousseau in the same interview, the development of the theory was also fostered by the creation of the doctorate program in Bordeaux in 1975 and the resulting necessity to build a specific didactic discourse. The core concepts of the theory, 9 those of adidactical and didactical situations, of milieu and didactic contract, of devolution and institutionalisation, the three dialectics of action, formulation and validation modelling the different functionalities of mathematics knowledge, and the fundamental distinction made in the theory between "connaissance" and "savoir" with no equivalent in English, 10 were thus firmly established already in the eighties. From that time, the theory has been evolving for instance with the introduction of the hierarchy of milieus or the refinement of the concept of didactic contract, thanks to the contribution of many researchers.…”

“…For instance, the ReMATH project (Representing Mathematics with Digital Media) has focused on the analysis of the potentiality of semiotic representations offered by dynamic digital artefacts (Kynigos & Lagrange, 2014). Adopting a perspective of networking among theoretical frameworks, this project has fostered the development of specific methodologies for such networking like the idea of cross-experiment (Artigue & Mariotti, 2014). In recent times, other research teams collaborated within the FASMED project on formative assessment.…”

“…Since its founding, the Department of Educational Research (DIE for its initials in Spanish) has maintained a close relationship with Mexico's Department of Pub-lic Education that has allowed it to participate in producing textbooks, developing teaching manuals, and formulating study plans for math courses and processes of curriculum reform for basic education (students aged [6][7][8][9][10][11][12][13][14][15]. The TDS has been the principal theoretical reference guiding these activities, as we show in the following section.…”

PME and the International Community of Mathematics Education

“…Whether a "Mainstream Theory", as Lin and Rowland (2016) call it, is a realistic goal of research or merely a guiding ideal is still under debate. Ideas to compare and combine different theories have been proposed to deal with these multiple perspectives in design research (Artigue and Mariotti 2014). However, it will be very interesting to follow the development of our understandings of teacher knowledge and its effects towards increasing coherence, since this field has proven productive in generating a variety of frameworks in the past (Lin and Rowland 2016).…”

The Use of Digital Technology in Extending Mathematical Problem Solving Reasoning

“…Artigue and Mariotti [6] characterize a conceptual framework as a structured but dynamic entity that articulates research questions, methods to address those questions, data collection, and interpretation of research results. In this perspective, our research inquiry is framed around three related fields: mathematical problem solving, digital technologies, and subjects' construction of mathematical knowledge [7].…”