Since 2009, Mathematical Working Spaces (MWSi) Symposia give a place to share studies on mathematical work in schooling. The symposia are organized into working groups based on the contributions proposed by participants under this unifying theme. The form of the Symposium allows an interesting exchange of ideas amongst participants and encourages the development of a scientific community with common interests.
The first two MWS’s meetings were initially dedicated to the study, development and possible uses of the Mathematical Working Spaces theory[1] (from French ETM, Espace de Travail Mathématique), a framework specially thought to study the mathematical work: the idea of mathematical work, as an activity practiced by the expert, serves as an epistemological and cognitive reference for mathematical activity in school, both for the student and the teacher. The epistemological and cognitive approach are linked by three geneses (semiotic, instrumental and discursive).
Thanks to this central notion of mathematical work, two essential points are highlighted in MWS theory: the purpose of the activities carried out by teachers and students in classrooms and the necessary effort to achieve this end. The work of individuals is seen as the result of a rational activity that can be based on conceptual or material tools. This activity is mediated by communication between individuals that promotes interactions. Thus, this conception of work presupposes a combination of epistemological and cognitive approaches.
Within the 3rd MWS[2] and 4th MWS[3], only one thematic group was dedicated to the development of the MWS theory as a methodological and a theoretical framework to study the mathematical work. Indeed, the focus of these symposia was on the foundational component of these meetings: the mathematical work. This evolution has deepened and diversified the approaches to the subject. In particular, the semiotic, cognitive and instrumental dimensions, as elements of the MWS, were the subject of specific contributions. Similarly, the institutional and social dimensions of mathematical work were integrated in all working topics.
Following the 4th MWS, one of the main objectives of the fifth MWS meeting was to strengthen a community of mathematics education researchers interested in the mathematical work and, for some of them, by the MWS theory.
This special issue of MENON proposes a selection of ten communications that were presented for the fifth symposia, MWS 5, at the University of West Macedonia, in Florina, Greece, from 18 to 22 July 2016 - proceedings are available at: etm5.web.uowm.gr/. These 10 papers give specific examples of the application of MWS theory to different topics and different levels of mathematics education and also some connections with other frameworks. The first five papers propose a study that considers the MWS theory with another framework. This is an essential role of the MWS meetings to give a place where theories can speak together. Then, we present 4 studies relying exclusively on MWS theory. And finally, there is a paper that does not use the MWS theory to study a modelling task that grounded the new theme of sixth MWS symposia[4]. More specifically:
Alain Kuzniak combines the MWS theory with epistemography of Drouhard and defines different tools available in mathematical work.
Gisela Camacho Espinoza and Asuman Oktaç, propose a study on a task in linear algebra solved by a Mexican teacher using APOS and MWS theory.
Vasiliki Tsiapou and Kostas Nikolantonakis, consider the MWS theory with the Theory of Semiotic Mediation to study the teaching of proof with historical texts.
Miguel Montes, José Carrillo and Luis Carlos Contreras, propose a study on geometry with preservice math teachers using an articulation of MTSK and MWS framework.
Gonzalo Espinoza-Vásquez, C. Miguel Ribeiro and Diana Zakaryan, use the same articulation between MTSK and MWS to explore teachers’ work in class.
Matthew Anastasiadis and Kostas Nikolantonakis, study the Mathematical Working Space for area and perimeter at the end of primary school in Greece.
Carolina Guerrero-Ortiz and Carolina Henríquez-Rivas, study the personal Mathematical Working Space of three Chilean teachers for the notion of parabola.
Assia Nechache, identifies the geneses of the Mathematical Working Space for different resolutions of a probabilistic task.
Soledad Estrella, Raimundo Olfos, Sergio Morales and Pedro Vidal-Szabo, identify caracteristics of a Statistical Working Space, assuming that statistic is not a mathematical domain, in studying the case of two grade 2 students resolving a task.
Minerva Martínez Ortega and Hugo Rogelio Mejía Velasco, study two modelling tasks using a motion sensor to introduce sinus function.
Six papers are in Spanish (2, 4, 5, 7, 9 and 10), two papers are in English (3 and 6) and two papers are in French (1 and 8) that reflects the three language community of MWS meetings.
This special issue is dedicated to the memory of
Jean-Philippe Drouhard that suddenly died on December, 14th, 2015.
The Editors of the 3rd Thematic Issue
Kostas Nikolantonakis
Philippe R. Richard
Laurent Vivier
[1] For a quick presentation of the theory, see the paper of Kuzniak in this issue. For more details on the MWS theory, the reader can find papers to the various special issues principally in French, in Annales de Didactique et de Sciences Cognitives (2011-14), in Spanish in Bolema (2016-18) and Relime (2014-19(4)), in English, in ZDM (2016-48(6)).
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