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Resumen basado en el de la publicación Resumen en inglés Monográfico con el título: "El aprendizaje y la enseñanza de las matemáticas en la Universidad" Investigación centrada en la implementación de propuestas de enseñanza a nivel universitario que promuevan un cambio del paradigma pedagógico. Se parte del paradigma dominante en estas instituciones, principalmente basado en la visita de los saberes como si fueran monumentos, para avanzar hacia un paradigma más centrado en el estudio de cuestiones. En el marco de teoría antropológica de lo didáctico, se trabaja en el diseño de los recorridos de estudio e investigación (REI) como dispositivos de enseñanza en la transición entre paradigmas, los cuales se han desarrollado en distintas modalidades. El estudio se centra en la formación universitaria del profesorado como agente crucial en este cambio, principalmente en la adaptación de los REI al caso de la formación del profesorado (REI-FP). Se observa en qué sentido los REI-FP permiten avanzar en el estudio de las condiciones y restricciones que emergen en la difusión de los REI ESP

Resumen Este trabajo empieza con la discusion de las nociones de indagacion y de modelizacion y en que sentido estos constructos son cuestionados e integrados en el paradigma de cuestionamiento del mundo y, en particular, a traves de la propuesta de los recorridos de estudio e investigacion (REI). Discutiremos los modelos epistemologicos y pedagogicos subyacentes que las propuestas de modelizacion e indagacion ofrecen, y como estos pueden ser reformulados en el ambito de investigacion de la teoria antropologica de lo didactico. Nos centraremos entonces en analizar el caso de un REI codisciplinar de matematicas e historia, que ha sido experimentado a nivel de Secundaria, para mostrar como indagacion y modelizacion aparecen como dos actividades indisociables en la construccion del conocimiento codisciplinar matematico-historico. Palabras-Clave : Modelizacion Matematica; Indagacion; Codisciplinar Abstract This paper starts with the discussion of the notions of inquiry and modelling and how these constructs are questioned and integrated into the paradigm of questioning the world, in particular, through the proposal of the study and research paths (SRP). We focus on underlying the epistemological and pedagogical models that inquiry-based and modelling approaches offer and how they can be understood in the framework of the anthropological theory of didactics. Then, we present the case of a codisciplinary SRP that links mathematics and history, which has been implemented at Secondary school level, to show how inquiry and modelling appear as two inseparable processes in the construction of mathematical-historical codisciplinary knowledge. Keywords : Mathematical Modeling, Inquiry, Codisciplinary.

Resumen La profesionalizacion docente en la modalidad online se ha venido conformando como una oportunidad de formacion para los profesores de matematicas en servicio. El Programa de Matematica Educativa del Instituto Politecnico Nacional de Mexico se fundo en el ano 2000 y desde entonces ha ofrecido un dispositivo de formacion a los profesores de diversas regiones de Mexico y de toda Latinoamerica. Uno de los objetivos principales de este programa es poner a disposicion de los profesores herramientas teoricas y metodologicas producidas en la disciplina de la Educacion Matematica para regular e innovar su practica docente. Es asi como desde el ano 2013 hasta la fecha hemos venido disenando e impartiendo cursos basados en la metodologia REI-FP (Sierra 2013 y Ruiz-Olarria 2015). En esta comunicacion se analizan elementos de ultima edicion con el objetivo de mostrar “aciertos” y desafios, reconociendo las particularidades de la modalidad online y de los dispositivos multimedia. Palabras-clave : profesionalizacion docente, modalidad online, Recorridos de Estudios y de Investigacion. Abstract Teaching professionalization in online mode has become a training opportunity for in-service mathematics teachers. The Educational Mathematics Program of the National Polytechnic Institute of Mexico was founded in 2000 and since then has offered a training device to teachers from various regions of Mexico and Latin America. One of the main objectives of this program is to make available to teachers theoretical and methodological tools produced in the discipline of Mathematics Education to regulate and innovate their teaching practice. Since 2013 we have been designing and delivering courses based on the REI-FP methodology (Sierra 2013 and Ruiz-Olarria 2015). This communication analyses elements of latest edition with the aim of showing "successes" and challenges, recognizing the particularities of online mode and multimedia devices. Keywords : Teacher professionalization, Online modality, Study and Research Tours.

Taking the example of teaching mathematical modelling in university degrees, this paper focuses on how the unit of analysis adopted by different research frameworks in mathematics education transfo...

We present the first implementation of a finalised study and research path (SRP) related to basic enumerative combinatorics. The SRP starts with a generating question about “How long would it take to open different kinds of padlocks?”. This paper describes the main steps of the SRP as implemented with secondary school students of grade 10. We want to stress some specific features of the SRP: the role of the empirical milieu and its enrichment through the collective construction of specific terminology; the students’ use of question-answer maps to organise and describe their inquiry; the experimental validation of the final answers; and the use of padlocks as models to solve combinatorics problems. We implemented the SRP in a secondary school with a long tradition in “active methodologies”. It is interesting to study these particular institutional conditions and their effects in the evolution of the SRP.

Considering the general problem of integrating mathematical modelling into current educational systems, this paper focuses on the ecological dimension of this problem—the institutional constraints that hinder the development of mathematical modelling as a normalised teaching activity—and the inevitable step of the professional development of teachers. Within the framework of the Anthropological Theory of the Didactic, this step is approached using the study and research paths for teacher education (SRP-TE), an inquiry-based process combining practical and theoretical questioning of school mathematical activities. We present a research study focusing on the design and analysis of an online and distance-learning course for in-service mathematics teachers based on the SRP-TE methodology. This course starts from the initial question of how to analyse, adapt and integrate a learning process related to mathematical modelling and how to sustain its long-term development. Our analysis is based on a case study consisting in four successive editions of a course for Latin American in-service mathematics teachers held at the Centre for Applied Research in Advanced Science and Technology in Mexico. The starting point is a modelling activity about forecasting the number of Facebook users, which includes functional modelling and regression. The results show how the course represents a valuable instrument to help teachers progress in the critical issue of identifying institutional constraints—most of them beyond the scope of action of teachers and students and not approached by previous research—hindering the integration of mathematical modelling in current secondary schools.

This paper focuses on how to link and combine activities of posing and answering questions with the ones of studying pre-existing answers at university level. Our research, developed within the framework of the Anthropological Theory of the Didactic, presents the design and use of an instructional device – study and research paths (SRP) – aimed at encouraging the interaction between inquiry and study activities. In this paper, we focus on an SRP about the evolution of the number of Facebook users, which was designed and implemented with first-year university students. We discuss the SRP analysis paying special attention to: (a) how to enhance the internal dynamics of the SRP to engage students in self-sustained study and research activities, and (b) how the integration of the SRP in the regular mathematics course helped to combine inquiry with more ‘transmissive’ instructional devices and why this interaction was essential to enrich the students’ milieu.

espanolEl desarrollo profesional online del profesorado permite articular la difusion de nuevas propuestas basadas en la investigacion didactica con la experiencia del docente y sus dificultades para integrarlas en el aula. Presentamos una investigacion sobre el diseno e implementacion de Unidades de Aprendizaje online y a distancia para profesores de matematicas en activo basada en una adaptacion de la metodologia de los Recorridos de Estudio e Investigacion para la Formacion del Profesorado (REI-FP) propuesta por Ruiz-Olarria (2015). De acuerdo con esta metodologia, la Unidad de Aprendizaje (en adelante, UA) pretende abordar, junto con los profesores participantes, los obstaculos institucionales que plantea la ensenanza de la modelizacion matematica en relacion con la ensenanza por transmision de conocimientos preestablecidos: rigidez del curriculo, gestion del tiempo, escasez de dispositivos de evaluacion adaptados, control del uso de las TIC, multidisciplinariedad, entre otros.La investigacion se basa en un estudio de caso formado por cuatro ediciones sucesivas de una UA para profesores de matematicas latinoamericanos en activo que se realizo en el Centro de Investigacion en Ciencia Aplicada y Tecnologia Avanzada de Mexico. La UA se centra en una actividad de modelizacion sobre previsiones de ventas que adapta la metodologia de los REI-FP al caso online y a distancia. Despues de describir el contenido de la UA, se realiza un analisis clinico exploratorio del proceso de formacion implementado, usando como material empirico las producciones de un grupo de profesores. Los resultados muestran la viabilidad de la adaptacion metodologica, poniendose de manifiesto que los dispositivos de formacion implementados facilitan la emergencia e identificacion de restricciones institucionales generalmente ocultas a los docentes en su quehacer cotidiano. Tambien muestran limitaciones del proceso de formacion que requieren mayor explotacion de las herramientas multimedia, asi como la necesidad de extender el proceso de formacion impartido mas alla de la estricta temporalidad de la UA. EnglishOnline professional development of teachers enables to connect the dissemination of new proposals based on educational research to teachers’ experience and their difficulties when they are trying to integrate those proposals into the classroom. We present a research focused on the design and implementation of online and distance learning courses for in-service mathematics teachers based on an adaptation of the methodology of “Study and Research Paths for Teacher Education” (SRP-TE) by Ruiz-Olarria (2015). According to this methodology, the course aims at addressing, together with the participating teachers, the institutional obstacles that appear when mathematical modelling is taught. These obstacles are related to traditional pedagogical practices based on the transmission of pre-established knowledge: curricular rigidity, time management, lack of adapted assessment devices, use of ICT, multidisciplinary aspects, etc.The research is based on a case study consisting of four successive editions of a course for Latin American mathematics teachers held by the Centro de Investigacion en Ciencia Aplicada y Tecnologia Avanzada in Mexico. The course focuses on a modelling activity about sales forecasts and it adapts the SRP-TE methodology to online and distance learning education. After describing the course organization, we carry out an exploratory clinical analysis of the implemented educational process considering the evidence provided by the productions of a group of teachers. The results show the viability of the methodological adaptation, showing how the educational devices facilitate the emergence and identification of institutional constraints that generally remain hidden in the teacher’s daily work. The results also highlight limitations of the course that require greater exploitation of multimedia tools, as well as the need to extend the educational process beyond its strict length.

We present the main elements of an online and in-distance study and research path for teacher education (SRP-TE) that we have designed, implemented and evaluated using the herbartian scheme as a main tool for the analysis. We show its potentiality, especially to emancipate researchers from the more traditional teacher education programmes and ensure (or at least try to) the development of some of the main study dialectics: question-answer, media-milieu and individual-collective. In particular, we focus on a posteriori analysis on the main weakness of some of the implemented educational devices as well as the strength of many others. Resumen Presentamos los principales elementos de un REI para la formacion del profesorado (REI-FP) online y a distancia que hemos disenado, experimentado y evaluado utilizando el esquema herbartiano como herramienta principal de analisis. Mostramos la potencia de esta nueva herramienta de analisis, especialmente para emanciparse de las formas tradicionales de formacion y asegurar (o por lo menos intentar) el desarrollo de las principales dialecticas del estudio: cuestion-respuesta, media-medio e individuo-colectivo. Veremos en particular muchas de las debilidades de los dispositivos experimentados, asi como las potencialidades de muchos otros.

En la Teoría Antropológica de lo Didáctico (TAD), el diseño de tareas se integra dentro de su metodología experimental planteada en términos de ingeniería didáctica. La implementación de nuevas organizaciones de enseñanza y aprendizaje, basadas en nuevas formas de concebir las actividades matemáticas escolares, se inscribe en una problemática epistemológica e institucional. En este artículo, presentamos una reflexión sobre los objetivos, los principios, la metodología y el alcance que atribuimos a este trabajo experimental. La reflexión se complementa con la descripción de tres casos, que sirven para ejemplificar cómo estos objetivos, principios y metodología han sido implementados en procesos didácticos concretos. Concluimos con una reflexión sobre la necesaria dialéctica y articulación entre investigación, diseño y prácticas de aula a fin de profundizar en el análisis de la ecología de estas propuestas, es decir, de las condiciones que permiten que ciertas tareas puedan vivir en las instituciones docentes, así como las restricciones que impiden su desarrollo como actividades normalizadas en el aula, desde una visión no normativa de la investigación didáctica In the Anthropological Theory of the Didactic (ATD), task design is integrated into its experimental methodology in terms of didactic engineering. The implementation of new teaching and learning organizations, based on new ways of conceiving school mathematical activities, is an integral component of the ATD epistemological and institutional analyses. In this article, we reflect on the objectives, principles, methodology and scope that we attribute to this experimental work. Three cases complement this reflection, to exemplify how these objectives, principles and methodology have been implemented in concrete didactic processes. We conclude with a reflection about the necessary dialectic between research, design and teaching practices, with the aim of deepening into the analysis of the ecology of our proposals, that is, the conditions that enable certain activities to exist in school institutions, as well as the constraints that hinder their development as normalised classroom activities, from a non-normative perspective of didactic research Na Teoria Antropológica do Didático (TAD), o desenho de tarefas integra-se dentro da sua metodologia experimental formulada em termos de engenharia didática. A implementação de novas organizações de ensino e aprendizagem, baseadas em novas formas de conceber as atividades matemáticas escolares, faz parte de uma problemática epistemológica e institucional. Neste artigo, apresentamos uma reflexão sobre os objetivos, os princípios, a metodologia e o alcance que atribuímos a este trabalho experimental. Esta reflexão é complementada com a descrição de três casos, que servem para exemplificar como estes objetivos, princípios e metodologia foram implementados em processos didáticos concretos. Concluímos com uma reflexão sobre a necessária dialética e articulação entre investigação, desenho e práticas de aula, a fim de aprofundar a análise da ecologia destas propostas, ou seja, as condições que permitem que certas tarefas possam viver nas instituições de ensino, assim como as restrições que impedem o seu desenvolvimento como atividades normalizadas em sala de aula, a partir de uma visão não normativa da investigação didática Dans la Théorie Anthropologique du Didactique (TAD), la conception de tâches d'enseignement est intégrée dans sa méthodologie expérimentale en termes d'ingénierie didactique. La mise en place de nouvelles organisations didactiques, basées sur de nouvelles façons de concevoir les activités mathématiques scolaires, s'inscrit dans une problématique épistémologique et institutionnelle. Dans cet article, nous présentons une réflexion sur les objectifs, principes, méthodologie et portée que nous attribuons à ce travail expérimental. Cette réflexion est complétée par la description de trois cas qui illustrent comment ces objectifs, principes et méthodes ont été mis en oeuvre dans des processus didactiques concrets. Nous concluons par une réflexion sur la dialectique et l'articulation nécessaires entre la recherche, le design et les pratiques en classe pour approfondir l'analyse de l'écologie des nouvelles organisations didactiques, c'est-à-dire des conditions qui permettent à certaines activités de vivre dans les institutions scolaires, ainsi que des contraintes qui empêchent leur développement comme activités normalisées en classe, dans une perspective non-normative de la recherche en didactique

This article describes the design process and the first implementation of an interdisciplinary teaching sequence within a context that links Mathematics with History based on the war of the Spanish Succession in 1714. Its design and experimentation with a group at Secondary school students lead us to show up some conditions that facilitate and restrictions that hinder the development competences on mathematical modelling and inquiry. From these first results, we will then move to its redesign in the case of teacher training programmes.

International audience; In order to identify mechanisms that can support mediation, this paper analyses the decision making process in a collaborative design of a digital learning resource by two different Communities of Interest (CoI). It focuses especially on the influence of both the CoI contexts and the socio-technical environment. This research was carried out within the framework of the "M C Squared" European project aiming at studying social creativity in the resource design. Specific conceptual and technical tools were used in this project to ease and document social interactions in the design of innovative learning resources promoting Creative Mathematical Thinking in the users. We focus on two main forces: tools and culture, which supported the collaborative design work between two CoIs.

This chapter focuses on studying the potentialities of interdisciplinary approaches for mathematical modelling. The research presents the design of a teaching sequence based on an archaeological context—the ruins of a Roman theatre discovered in Badalona (Catalonia)—implemented with 12–14-year-old students in their 2015 course. The aim was to promote inquiry and student modelling competences and to investigate how making multiple disciplines interact could enhance modelling and inquiry processes. An initial historical situation involving the students was presented to deal with a problem integrating an interdisciplinary approach. Mathematical modelling appeared as a central tool in the teaching and learning processes. Furthermore, a constant dialectic between mathematics and history was required to facilitate evolution of the modelling process.

University mathematics education (UME) is considered, in this paper, as a kind of didactic practice - characterised by institutional settings and by the purpose of inducting students into mathematical practices. We present a research programme - the anthropological theory of the didactic (ATD) - in which this rough definition can be made much more precise; we also outline some cases of ATD-based research on UME. Three cases are presented in more detail. The first is a theoretical and empirical study of the topic of dual vector spaces, as it appears in undergraduate courses on linear algebra. The second case concerns a similar study of the practices and theories on limits of functions which students may develop in calculus courses. Finally, a third study illustrates the use of ATD to design and experiment innovative approaches to mathematical modelling in the setting of a first mathematics course for engineering students.

We assume that task design-based research refers to any research that is experimentally based on an educational context and pays special attention to the description, analysis, and organization of the content to be taught (the “task” in the expression “task design”). This chapter focuses on the field of didactics of mathematics as it emerged in the middle of the 1970s with the works of the French researcher Guy Brousseau (1997). The notion of didactic engineering was used early in this field to define the relationships between the theoretical developments of didactics and the empirical reality of the classrooms. It can be presented as a research methodology structured in distinct intertwined phases with the double aim of studying didactic phenomena and developing new educational proposals (Artigue, 1990, 2008). We are illustrating this methodology by means of two examples: the measure of quantities at primary school and the modeling of a population growth at university level. The first one is taken from the theory of didactic situations which is at the origin of didactics as a scientific discipline; the second one corresponds to an evolved conception of didactic engineering within the anthropological theory of the didactic.

In this course, I articulate two previous results: the changes in reference knowledge of arithmetic in the 1970s and of numeration in the 1980s. I first show why the disappearance of quantities leads to the disappearance of related units (an object introduced on occasion), and then a consequence of this result: the units of numeration being relative units, even though they survive the change of reference knowledge in 1970, their disappearance from the reference knowledge of numeration in 1980 makes their disappearance from arithmetic inevitable. The quantities thus appear as “raisons d'être” for units. This result is important. It also makes it possible to grasp the multiplicity of the roles of units in school mathematics up to the 1940s and to shed light on certain current problems. The methodology is original in that it compares three areas: China today, France until the 1940s, and France today. Two examples make it possible to envisage the scope of the results, three others are presented in the text of the workshop. A possibility of links with work on unitizing in cognitive psychology emerges., Dans ce cours, j’articule deux résultats anciens : les changements de savoirs de référence au socle de l’arithmétique dans les années 1970 et au socle de la numération dans les années 1980. Je montre d’abord pourquoi la disparition des grandeurs conduit à la disparition des unités relatives (objet introduit à l’occasion), puis une conséquence de ce résultat : les unités de la numération étant des unités relatives, même si elles survivent au changement de savoir de référence en 1970, leur suppression du savoir de référence de la numération en 1980 rend leur vie dans l’arithmétique scolaire très improbable ensuite. Les unités apparaissent donc comme des raisons d’être des grandeurs. Ce résultat est important. Il permet aussi de saisir la multiplicité des rôles des unités dans les mathématiques scolaires jusqu’aux années 1940 et d’éclairer certains problèmes actuels. La méthodologie est originale car elle compare trois terrains : la Chine aujourd’hui, la France jusqu’aux années 1940, la France aujourd’hui. Deux exemples permettent d’envisager la portée des résultats, trois autres sont présentés dans le texte du TD. Une possibilité de liens avec les travaux sur le unitizing en psychologie cognitive émerge.

In close articulation with Christine Chambris' course, this text presents three complementary studies in the field of the teaching-learning of numbers and arithmetic at school. The first deals with the difficulties encountered in the implementation of a project to teach a technique of subtractive calculation by truncation and the reasons for these difficulties, in relation to the technology of this technique concerning the numeration and the units of this domain. The second is an analysis of the implementation of a teaching project that aims to articulate numeration and the metric system by introducing a mixed table of numeration and conversion. The third study, which is more prospective in nature, deals with poorly highlighted knowledge involved in the teaching or learning of multiplication. These three studies reveal the importance of a common object: relative units. In each of the studies, the potentialities of these units are studied, from both praxeological and ecological points of view, as well as the conditions in which these relative units actually live in the institution., En articulation étroite avec le cours de Christine Chambris, ce texte présente trois études complémentaires dans le champ de l’enseignement-apprentissage des nombres et du calcul à l’école. La première porte sur les difficultés rencontrées dans la mise en œuvre d’un projet d’enseignement d’une technique de calcul soustractif par troncature et sur les raisons de ces difficultés, en relation avec la technologie de cette technique concernant la numération et les unités de ce domaine. La deuxième porte sur l’analyse de la mise en œuvre d’un projet d’enseignement qui se propose d’articuler numération et système métrique en introduisant un tableau mixte de numération et de conversion. La troisième étude, qui a un caractère plus prospectif, porte sur des savoirs qui interviennent dans l’enseignement ou l’apprentissage de la multiplication et qui sont mal mis en évidence. Ces trois études révèlent l’importance d’un objet commun : les unités relatives. Dans chacune des études, on étudie des potentialités de ces unités, du double point de vue praxéologique et écologique, ainsi que les conditions dans lesquelles ces unités relatives vivent effectivement dans l’institution.

The notion of a polynomial, as one of the most fundamental concepts in all areas of mathematics, has a prominent role in pre-tertiary and tertiary education. Due to the repeated encounter of students with this notion, it makes sense to study its role in the transition to university mathematics. In this paper, the secondary-tertiary transition of mathematics students at the University of Split concerning the notion of a polynomial is analysed using tools of the Anthropological Theory of the Didactic.

International audience; This workshop was dedicated to a discussion of epistemological and didactic aspects of mathematical structuralism with a focus on Abstract Algebra, in particular Group Theory. The participants worked on a corpus of documents comprising excerpts of the Bourbaki Manifesto “the architecture of mathematics” and the transcript of a discussion thread from a mathematical forum online. To what extent does mathematical structuralism rely on didactic principles? How is this reflected in a teaching-learning environment? The key construct within the Anthropological Theory of the Didactic was the theoretical notion of “structuralist praxeology”, introduced by the author. The analyses of the corpus led to the discussion of the rationale of such praxeologies, their historical development, how they may be reconstructed by learners, and the role played by the “dialectic of objects and structures” that should be added to Chevallard’s model for study and research processes in order to account for the development of structuralist praxeologies.

International audience; Issu des travaux dirigés directement associés au cours de Michèle Artaud, cet article traite des besoins praxéologiques de la position de professeur selon la position de chercheur en didactique, dans le cas des grandeurs et de leur mesure. Il poursuit deux objectifs, celui de l'identification de ces besoins et celui de leur satisfaction. La première partie illustre, à partir d'un exemple, les praxéologies mises en œuvre pour identifier les besoins. La deuxième partie propose une exploration des besoins relatifs à certaines grandeurs, essentiellement au niveau du collège ; des éléments visant la satisfaction de ces besoins praxéologiques sont alors explicités, en allant du niveau technique au niveau théorique. La troisième partie est consacrée à une grandeur particulière, la température, et le territoire de l'enquête sur les besoins s'élargit aux disciplines scientifiques concernées et aux mathématisations récentes des grandeurs. En conclusion, les besoins praxéologiques sont resitués dans une perspective plus large, mettant en valeur le rôle d'interface que les grandeurs jouent entre les besoins sociétaux et l'école, et leur rôle en mathématiques, comme instrument de modélisation de situations du monde et du travail mathématique lui-même.

I will present some results from my doctoral work which concerns the study of the conditions and constraints determining teaching practices when imple- menting mathematics’ study and research paths in French secondary schools during the 2013–2015 period (Bernad 2017). In the framework of this inquiry, I highlight elements of a teacher’s praxeological equipment that are useful for the achievement of the project to implement such a study and research path (SRP). I will focus on under- lining how the study of didactic praxeologies activated by a teacher has led me to make the hypothesis that he achieves to extract the collective class from the paradigm of visiting works in order to fall within a paradigm of study through research. It will also show these analyses have led me to think that the praxologies’ model and the individual-collective dialectics, media-milieu dialectics, questions-answers dialec- tics are relevant tools for thinking about the teacher’s role, and the anticipation of his decisions in the setting up of closed SRP.

This paper aims to present the results of the mathematical activity of students measured in a the context of a school exhibition in a priority educational network. On this occasion, we present the system as well as the adopted methodology based on a multilevel analysis in categories of actions. The results of this analysis allowed us to identify a first category of invariants – artifactual, cognitive and social – giving favorable conditions for the emergence of mathematical activity in a school exhibition (Da Ronch, 2019a, 2019b). In a vision of democratization of mathematics and access to its practices, the objective of this second part is to show the preliminary study of the conditions and constraints of the mathematical activity and more generally the scientific approach at the level of our society and its non-formal education institutes., Cette contribution vise à présenter les résultats de l’activité mathématique d’élèves mesurée dans le cadre d’une exposition scolaire en réseau d’éducation prioritaire. A cette occasion, nous présentons le dispositif ainsi que la méthodologie adoptée basée sur une analyse multiniveau en catégories d’actions. Le résultat de cette analyse nous a permis d’élaborer une première caractérisation d’invariants – artefactuel, cognitif et social – donnant des conditions favorables à l’émergence d’une activité mathématique en contexte d’exposition scolaire (Da Ronch, 2019a, 2019b). Dans une vision de démocratisation des mathématiques et d’accès à ses pratiques, la deuxième partie de ce texte a pour but de présenter un premier travail sur l’étude des conditions et contraintes de viabilité de l’activité mathématique, et plus généralement de la démarche scientifique à l’échelle de notre société et de ses institutions de l’éducation non formelle.