Ghislaine Gueudet

University of Paris-Saclay · Etudes sur les Sciences et les Techniques

This text reports on a workshop of the DEMIMES thematic school, the aim of which was to discuss how didactic theories can equip teachers in higher education to analyse exercises and problems texts and anticipate student difficulties. We present an analysis of a first-year university physics problem using theoretical tools from mathematics didactics...

Utiliser le numérique en classe pour soutenir le développement de l’autonomie des élèves fait partie des recommandations institutionnelles, mais constitue un objectif complexe pour les professeurs. Nous étudions dans cet article dans quelle mesure une formation initiale fondée sur un travail documentaire collectif de conception de scénarios de clas...

Supporting the choice of resources for digital uses promoting students’ autonomy: comparison of an analysis grid in two disciplines — This paper focuses on what would be the autonomy of students in mathematics and physics and how digital technology can support it. We distinguish here between transversal and disciplinary autonomy on the one hand and...

In this chapter we investigate the evolution of research in mathematics education related to digital resources as an essential element of the external context for mathematics teachers’ professional activity. In the relevant research literature, we identified different themes and different kinds of evolution. We investigate the evolution of research...

Translation is a critical issue in international mathematics education studies but has seldom been carefully investigated. How can a theoretical approach be translated and subsequently used in different languages, and to what extent could the translation processes deepen the approach itself? This paper addresses such issues in the case of the Docum...

In this concluding commentary, I embed the articles of the special issue “Transition from school into university mathematics: experiences across educational contexts” into the current landscape of research on secondary–tertiary transition, and discuss the advancement they made related to the synthesis published in 2008 by Gueudet. My aim is to elab...

This chapter concerns the use of digital resources by kindergarten teachers. It presents a three-year study, using the theoretical perspective and the methods of the documentational approach. We focus on the case of an experienced kindergarten teacher, Mia, and on her teaching of numbers. At a micro-level, we investigate the evolutions of a documen...

This chapter focuses on teaching the use of programming technology for pure or applied mathematics investigation projects to university mathematics students and future mathematics teachers. We investigate how the theoretical frame of instrumental orchestration contributes to our understanding of this teaching. Our case study is situated within the...

The edited book contains 34 chapters about practice-oriented research in tertiary mathematics education, organised in five sections: Section 1: Research on the secondary-tertiary transition Section 2: Research on university students’ mathematical practices Section 3: Research on teaching and curriculum design Section 4: Research on university stude...

This article presents a synthesis of international research in mathematics education about the secondarytertiary transition, with a specific interest in the most recent works. These studies may concern students' difficulties, and investigate different factors causing these difficulties: notions become more abstract, expected practices refer to thos...

Dans cette communication, nous nous posons la question de ce que signifie l'autonomie des élèves, et de la manière dont le numérique peut la soutenir dans trois disciplines : les mathématiques, la physique-chimie et l'anglais. Dans le cadre du projet de recherche e-FRAN IDEE, nous avons conçu dans chaque discipline et de manière coordonnée une gril...

We are interested in understanding how university students learn to use programming as a tool for “authentic” mathematical investigations (i.e., similar to how some mathematicians use programming in their research work). The theoretical perspective of the instrumental approach offers a way of interpreting this learning in terms of development of sc...

The instrumental approach, and in particular the concept of scheme, can contribute to our understanding of how students learn programming for mathematical inquiry at university. While most studies consider only individual schemes, in this paper we propose to investigate schemes' social aspects, focusing on the scheme of "Validating the programmed m...

The study presented in this paper concerns the design and evaluation of curriculum material that supports mathematics teachers’ understanding and enactment of reform curricula and innovative teaching practices. Our focus is on curriculum material supporting mathematics teachers’ practices combining the use of digital technology and the development...

How can future mathematics teachers be trained to combine the use of digital technologies with student autonomy? Referring to the documentational approach to didactics, we have designed and implemented an initial training course based on collective documentation work. Here we analyze the work of a team of trainees who designed a session on programm...

The aim of the special issue is to bring together important current international research on innovative teaching and learning practices in mathematics in engineering education, and to develop deeper understandings of the characteristics of current teaching and learning practices that can inform the design and implementation of future innovative pr...

The ‘Documentation Approach to Didactics’ is an entry of the Encyclopedia of Mathematics Education (Trouche, Gueudet & Pepin 2018). This entry has been updated in 2020 (Trouche, Gueudet & Pepin 2020). This article is a Ukrainian adaptation of this updated version. It is part of a collection, gathering such adaptations in 14 languages (https://hal.a...

In this paper we aim to contribute to a better understanding of the impact of digital resources on mathematics teachers’ work and professional development. For this purpose we focus on the emblematic case of an experienced mathematics teacher at secondary level, Anna, who has also worked as a teacher educator in a university department. Using the l...

This article is an updated version of an entry of the Encyclopedia of Mathematics Education (2018). In the same time, it is the seed of the HAL collection DAD-MULTILINGUAL, constituted by the translation of this entry in various languages.The documentational approach to didactics is a theory in mathematics education. Its first aim is to understand...

The documentational approach to didactics is a young theory – it was less than 10 years old in 2018. In this chapter I look back at the process of development of this approach. I recall the initial context, motivating the elaboration of a specific frame for studying teachers’ documentation work. Several kinds of evolutions are emphasized: theoretic...

The instrumental approach is a useful theoretical lens for understanding students' learning processes with a main focus on the transformation of an artefact (a human design for a goal-directed activity) into a meaningful instrument (i.e. an artefact and schemes developed by the student). In this paper, we articulate the instrumental approach for co...

En este trabajo estudiamos las interacciones entre dos profesoras de matemáticas de secundaria y los recursos utilizando el marco teórico de la aproximación documental. Este marco propone que estas interacciones producen documentos asociados a los recursos y a los esquemas de uso. Los esquemas comprenden el conocimiento profesional en términos de i...

This edited volume will help educators better analyze methodological and practical tools designed to aid classroom instruction. It features papers that explore the need to create a system in order to fully meet the uncertainties and developments of modern educational phenomena. These have emerged due to the abundance of digital resources and new fo...

Notre étude concerne la tension entre stabilité et évolution des pratiques des professeurs, abordée dans une perspective d’approche documentaire. Nous avons suivi une professeure expérimentée mettant en œuvre avec des élèves de 1ère S un parcours d’étude et de recherche (PER) décrit dans une brochure IREM, intitulé « comment fonctionne une antenne...

The abundant digital resources on the Internet are leading to profound changes in teachers’ activity. We refer to the theoretical framework and methodology of the documentational approach to didactics to investigate these changes. We compare two case studies: an English teacher, and a mathematics teacher, both working in the same upper secondary sc...

In this paper we discuss a particular perspective on the design and use of curriculum resources brought through applying the documentational approach to didactics. We present this theoretical approach and the associated “reflective investigation” method. We consider that teachers and teacher educators develop documents, associating resources and a...

In this paper we introduce a link between the Theory of Didactical Situations and the Documentational Approach to Didactics, in order to study teaching/learning phenomena at the beginning of university mathematics studies. Specifically, we investigate the didactic contract at three levels: institutional, mathematical subject, and specific mathemati...

This chapter proposes a theoretical frame, the documentational approach to didactics (DAD), as a tool for analyzing the changes brought about by digitalization in the design and uses of mathematics teaching resources. One of the major changes appears to be initiated by the profusion of Open Educational Resources (OER), which provide new opportuniti...

The goal of this conceptual paper is to develop enhanced understandings of mathematics teacher design and design capacity when interacting with digital curriculum resources. We argue that digital resources in particular offer incentives and increasing opportunities for mathematics teachers’ design, both individually and in collectives. Indeed they...

Mathematics teachers interact with resources of various kinds in their work in and out of class. The documentational approach of didactics is a theoretical approach that has been elaborated to investigate these interactions and their consequences in terms of teachers’ practice and teachers’ beliefs in particular. According to this approach, using r...

This paper is concerned with the development of e-textbooks. We claim that analysis (and design) of e-textbooks requires the development of a specific frame. Digital affordances provide particular opportunities (e.g. in terms of interactions between users) that require specific considerations for their analysis, as teachers and students use them fo...

In this introductory chapter our aim is to set the scene for the following four chapters and situate them within the broad picture of mathematics education research concerning transitions. What kinds of transitions have been considered by mathematics education research? What research questions were studied and which theoretical approaches and assoc...

Resumo Em numerosos países os livros didáticos são, em Matemática, recursos centrais para os professores; todavia esses têm sofrido importantes evoluções ligadas ao digital. Nós estudamos estas evoluções e suas consequências em relação ao processo de designer de livros didáticos, pautados em um perspectiva de abordagem documental. Nós propomos de...

In this study, we investigated design processes in teacher collectives, which have been made possible by new ‘‘digital’’ opportunities: platforms, discussion lists, etc. The object of our study is the French Se´samath teacher association and its design of a grade 10 e-textbook, more precisely the design of the ‘‘functions’’ chapter. We analysed it...

Nous présentons dans cet article une étude des critères et méthodes de choix utilisés actuellement par les professeurs de mathématiques pour retenir un manuel pour la classe, parmi l’offre dont ils disposent. Nous avons étudié plus particulièrement le choix d’un manuel de niveau seconde, édition 2014, en suivant d’une part une équipe d’enseignants...

This book examines the kinds of transitions that have been studied in mathematics education research. It defines transition as a process of change, and describes learning in an educational context as a transition process. The book focuses on research in the area of mathematics education, and starts out with a literature review, describing the epist...

Many different kinds of transitions are studied in the research literature. In our survey we mainly address two kinds of change: (a) conceptual change and learning as a transition process and (b) transitions as people move between social groups or contexts with different mathematical practices.Some researchers have studied changes happening within...

This book examines the kinds of transitions that have been studied in mathematics education research. It defines transition as a process of change, and describes learning in an educational context as a transition process. The book focuses on research in the area of mathematics education, and starts out with a literature review, describing the epist...

Mathematics teachers work with resources in class and out of class. Textbooks, in particular, hold a central place in this material. Nevertheless, the available resources evolve, with an increasing amount of online resources: software, lesson plans, classroom videos etc. This important change led us to propose a study of mathematics teachers docume...

Notre recherche porte sur le travail conjoint entre un médiateur scientifique, un professeur et ses élèves de l'école primaire lors d'un événement de culture scientifique en dehors de la classe. À partir du cadre de la théorie de l'action conjointe en didactique, nous étudions l'articulation des actions du professeur et celles de l'intervenant scie...

In twenty-first century science classrooms, teachers and students are frequently engaged with Internet resources: lesson plans, digital textbooks, various kinds of software, videos, and much more. There is, in particular, a profusion of online resources for the teaching and learning of science. This raises important questions about the design of on...

Mathematics didactics invites to consider inquiry-based teaching as a particular form of didactic contract, leaving an important responsibility to the students, regarding the knowledge at stake and its evolution in class. Does the use of technology support the development of such a contract? Under which conditions, concerning the mathematical situa...

In this chapter we study the use of software by kindergarten teachers in mathematics, with 5 or 6-year-old students. In most countries (our study takes place in France), technology is not much used in the teaching of mathematics at kindergarten and primary school levels. Analysing the conditions, and factors, influencing its use in class is likely...

Nous nous intéressons aux ressources destinées aux professeurs des écoles et à leurs formateurs. Nous abordons des questions du type :- Quelles évolutions dans les ressources disponibles pour les professeurs ? Pour les formateurs ? On s'intéresse en particulier aux ressources numériques et à l'articulation entre ressources numériques et ressources...

In this article we present an instrumental approach in mathematics education, which focuses on the interactions between students, teachers, and artefacts. This approach analyses mediations attached to the use of a given artefact and instruments developed by the subjects from this artefact along instrumental geneses. We draw on three Research Cases...

This article deals with teaching mathematics in Breton at primary school. We mainly refer to Adler’s research inviting to consider linguistic plurality not only as a difficulty, but also as a possible resource for mathematics teaching. Her work invites to focus on available material resources and on the way teachers use them. We study the character...

In this article a review of the literature on the theme of mathematics teachers’ work and interactions with resources is provided, taking a particular perspective, the so-called ‘collective perspective’ on resources, their use and transformation. The review is presented under three headings: (1) theoretical frameworks commonly used in this area of...

In this paper we study the collective dimensions of teachers’ work in their ordinary daily practice. We argue that teachers’ ordinary work comprises many collaborative aspects, and that the interactions with colleagues, often through resources, are crucial for teacher professional development. Using a theoretical framework based on teacher document...

This article reports on an investigation of mathematic curriculum documents, commonly used textbooks, and teacher ‘curricular practice’ with respect to educational traditions in France and Norway. The study has helped to develop a deeper understanding of (1) educational traditions in France and Norway; (2) the ways the educational traditions permea...