Mariam Haspekian

Université de Paris Cité · Sciences Humaines et Sociales

This article reports on research focused on the integration of a specific computer tool, the spreadsheet, into mathematics teaching. After presenting some important results obtained by research in this area, we revisit these in the light of an instrumental approach, which we perceive as essential to analyse the construction of mathematical meanings...

Spreadsheet is not given as didactical tool to serve mathematics education. It may progressively become such an instrument along a professional genesis of use on teachers' side. Using both the notions of distance and double genesis, the case study described in this paper illustrates the beginning of such a genesis and the complexity that comes alon...

This paper presents the methodology developed within TELMA for connecting and integrating the theoretical frames used by the different teams for studying the design and use of interactive learning environments in mathematics education. Two case studies are then analysed and compared in order to illustrate the methodology and the results it can lead...

The spreadsheet is not a priori a didactical tool for mathematics education. It may progressively become such an instrument through the process of professional geneses on the part of teachers. This chapter describes the beginning of such a genesis, and presents some results concerning teachers’ professional development with ICT by examining the out...

A case of networking two didactic phenomena - the Topaze effect and the Funnel communications pattern - through analyses of the same episode from two theoretical perspectives is presented. It shows how this networked analysis deepens insight into the kind of learning of the same episode through complementary views, how it strengthens the theoretica...

In this chapter, we offer an overview of some of the major trends in theory development and use in relation to teaching mathematics with digital technology. We showcase some of the developments that have occurred since the first edition of this book (2014). We also provide a deep review of the multiple ways in which the instrumental approach has ev...

Les programmes de mathématiques incluent algorithmique et informatique désormais dès le primaire. Comprendre l'évolution des pratiques enseignantes est alors un enjeu pour la recherche et la formation. L'article analyse les pratiques de cinq enseignants qui intègrent pour la première fois Scratch ou des robots. Nos cadres en didactique des mathémat...

MEDA2020_Haspekian plenary : Annexes and References of the plenary at MEDA 2 conference.

Plenary talk at the 10 th ERME Topic Conference MEDA 2020

Line of thought of the previous working groups in CERME5 to CERME9 Since CERME4 in 2005, theoretical approaches and perspectives have been the topic of an ongoing CERME working group. The idea of the networking of theories emerged at CERME 4 and was explored in the subsequent conferences. At CERME 5 (Arzarello et al., 2007), the diversity of theori...

Based on the observation of a teacher incorporating a programming language for the first time in his teaching, and on previous research centred on the development of teaching practices in mathematics, we highlight here the importance of didactic "landmarks", functioning as references in the dynamics involved along the development of teaching practi...

This paper presents a small case of junction of two research fields that remained, until recently, relatively cut off from each other. Using concepts of the Assessment field, specified in a didactic approach, we develop and test a methodological tool on the analysis of students-teacher interactions in mathematics classroom. We discuss then its pote...

We are interested in the perception that mathematics teachers has of the introduction of algorithmic in the mathematics curricula at the high school in France: what are their representations of these new contents? Which difficulties do they declare they meet in implementing these programs? Our research reveals the existence of a tension in the inte...

The mentoring of doctoral students towards research in mathematics education is seldom considered in scientific debates. The Artigue Colloquium provided an opportunity both for paying tribute to Michèle Artigue’s work as a supervisor of young researchers, and for engaging in a debate about this specific, complex, but crucial, mission of researchers...

This Research Forum highlights the most recent research on the development of the role of the teacher of mathematics within mathematics classrooms that involve the use of technological tools, with an emphasis on teachers’ experiences within both formal and informal professional development programmes. We foreground the theoretical ideas and methodo...

Abstract : The spreadsheet is not a priori a didactical tool for mathematics education. It may progressively become such an instrument through the process of professional geneses on the part of teachers. This chapter describes the beginning of such a genesis, and presents some results concerning teachers’ professional development with ICT by examin...

The chapter briefly introduces the Theory of Didactical Situations (TDS) by referring to the data from Chap. 2. TDS provides a systemic framework for investigating teaching and learning processes in mathematics, and for supporting didactical design. The theory is structured around the notions of a-didactical and didactical situations and includes a...

The case study of Topaze effect shows a networking practice of connecting two theoretical approaches, TSD and IDS. It investigates empirically two phenomena, Topaze effect and funnel pattern, of the two theories and networks the theories by comparing and contrasting these phenomena including also the semiotic game phenomenon. This process leads to...

This chapter presents the main ideas and constructs of the book and uses the triplet (system of principles, methodologies, set of paradigmatic questions) for describing the theories involved. In Part II (Chaps. 3, 4, 5, 6, and 7), the diversity of five theoretical approaches is presented; these approaches are compared and systematically put into a...

The case study of context, milieu, and media-milieu dialectic is a networking case that links TDS, AiC, and ATD. It compares and contrasts three concepts and their status within each theory, in order to learn how concepts which at a first glance seem to have a similar role in the understanding of teaching and learning in each theory differ.

This Research Forum highlights the most recent research on the development of the role of the teacher of mathematics within mathematics classrooms that involve the use of technological tools, with an emphasis on teachers’ experiences within both formal and informal professional development programmes. We foreground the theoretical ideas and methodo...

Actes du séminaire national de didactique des mathématiques de l'année 2013. Le séminaire national de didactique des mathématiques est organisé par l'ARDM. Il a pour but de permettre la diffusion régulière des recherches nouvelles ou en cours, des présentations de thèses ou d'habilitation à diriger des recherche et de favoriser les échanges et déb...

Le texte qui suit vise la construction des savoirs informatiques chez les débutants et s'inscrit dans le cadre d'une thèse de doctorat en cours à l'université Paris Descartes. Il s'intéresse à un aspect particulier de l'apprentissage de l'informatique - la programmation des robots - chez les étudiants de licence en début d'une spécialisation inform...

Actes du séminaire national de didactique des mathématiques de l'année 2012. Le séminaire national de didactique des mathématiques est organisé par l'ARDM. Il a pour but de permettre la diffusion régulière des recherches nouvelles ou en cours, et de favoriser les échanges et débats au sein de la communauté francophone de didactique des mathématique...

Ce chapitre poursuit l’étude de la contribution de l’approche instrumentale à l’analyse des usages des TICE par l’enseignant initiée dans le chapitre précédent à travers le cas des BEL. Il considère les usages du tableur, un logiciel dont l’emploi est fortement encouragé par les discours officiels qui, à la différence des BEL, n’est pas donné a pri...

A partir d'un panorama sur l'usage du tableur et l'apprentissage de l'algèbre dans les travaux de recherche en didactique des mathématiques, nous introduisons quelques réflexions qui peuvent aller au-delà du seul cas du tableur et de l'algèbre, à partir de deux cadres théoriques. L'approche instrumentale insiste sur l'importance des genèses instrum...

This paper shares some research reports and presents some results concerning teachers' professionnal genesis with spreadsheets by bringing closer the results abtained in different research. It aims at gaining insight into the teachers practices with technology and how these practices evolve in time. Comparing the evolution of an ordinary teacher in...

La première contribution (A. Robert) introduit le thème en balayant les premières questions, les premières recherches, et leurs cadres théoriques et problématiques, en posant, entre autres, la question cruciale, pour le chercheur, des « modalités » des formations.M. Charles-Pézard complète cette introduction avec un point sur les recherches sur le...

Research on the use of spreadsheets in mathematics education usually points out its potentialities in the learning of algebra. The link between spreadsheets and algebra is thus often seen in the direction “spreadsheet for algebra”. This paper follows the opposite direction by questioning the role of algebra in students’ spreadsheet competencies. It...

Le symposium dont ce livre est issu visait la mutualisation des modèles et ingénieries des différentes disciplines, ainsi qu'une réflexion entre ingénierie des dispositifs et analyse des pratiques, en vue de leur enrichissement mutuel, en s'appuyant notamment sur les notions d'instrumentation et de communauté de pratique. La réflexion que nous déve...

This document contains the guidelines developed by members of TELMA as a means for planning, conducting, and analysing a cross experiment aimed at contributing to the construction of a shared research perspective among TELMA teams . This is the product of the PhD students and young researchers that brought forward the whole activity. The actual exp...

This deliverable summarizes the collaborative work developed by TELMA teams on theoretical frames, and presents a methodological tool for systematic exploration of the role played by theories in technology enhanced learning in mathematics.

Cet atelier, d’une durée de quatre plages d’1h30 chacune, s’appuie sur un travail de thèse dont le sujet porte sur l’usage du tableur en collège (Haspekian, 2005). Il fournit une façon de « visiter » la thèse sous une forme alternant travail des participants et exposés brefs. Il s’est inscrit dans le Thème 1 de cette école d’été « Les nombres dans...

Il s'agit, ici, de porter un regard didactique sur l'intégration d' un outil informatique dans l'enseignement des mathématiques : le tableur. Les recherches sur le tableur y sont analysées dans une perspective instrumentale, perçue comme incontournable pour approcher les questions d'intégration technologique. Nous décrivons principalement cette ana...

In this research work, we have a didactical look on the integration of a computer tool into mathematics teaching: the spreadsheet. We have related research about spreadsheet to an instrumental approach perceived as essential to analyze the questions of technological integration. This approach allowed us to extend to this technology the theoretical...