Isabelle Bloch

Isabelle Bloch
University of Bordeaux · INSPE: Institut national supérieur du professorat et de l'éducation

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56
Publications
16,733
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Introduction
Isabelle Bloch is an Emeritus Profesor at the University of Bordeaux and ESPE: Ecole supérieure du professorat et de l'éducation,. Isabelle does research in Didactics of mathematics and Teaching Methods. Her current project is developed In the context of the Groupe de Recherche - Didactique des Mathématiques et de la physique dans l'enseignement supérieur (DEMIPS); she is investigating difficulties students encounter at the transition between High School and University, especially in Analysis.
Additional affiliations
September 2001 - September 2011
University of Bordeaux
Position
  • Professor (Full)
Description
  • Research into the teaching and learning of mathematics: Tertiary level (Calculus), Students with special needs
September 2000 - December 2016
University of Bordeaux
Position
  • Professor
Description
  • Master course, Direction of PhD
Education
September 1969 - June 1975
Paris Descartes University
Field of study
  • Mathematics

Publications

Publications (56)
Chapter
Full-text available
Dans ce texte, nous reprenons certains éléments-déjà étudiés dans notre travail-de l'analyse des signes en mathématiques, et proposons en parallèle une étude des signes en physique. Ces travaux doivent nous amener à réfléchir sur l'articulation de l'usage de ces signes dans l'enseignement des sciences au secondaire et supérieur, et sur les difficul...
Conference Paper
Full-text available
Les tentatives pour relier 'Mathematics Education' et sémiotique existent depuis plusieurs années. Les auteurs concernés s'appuient généralement sur un théorie dyadique du signe, du type signifiant/signifié. Ces théories peinent à rendre compte de la spécificité de l'interprétation en mathématiques : les objets mathématiques étant imaginaires, les...
Preprint
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The purpose of this paper is to investigate learning and teaching conditions of mathematics in English or Spanish as second languages by closely examining different forms of significance of mathematical abstract objects. We start by considering some representative features of lexical significance involved in a multilingual mathematics environment....
Article
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Résumé : En mathématiques, des énoncés formels ne peuvent, à eux seuls, donner accès au sens des objets mathématiques en jeu. De fait, les cours donnés à l'université comme au secondaire sont en général bien structurés, mais ils manquent d'exemples, de situations de recherche et de questions sur le savoir ; les étudiants n'étant pas en mesure de po...
Article
Full-text available
Our research focuses on the difficulties students encounter with the learning of calculus, considering that they have to cope with many more mathematical objects but also with new ways of reasoning – not only algebraic calculation, but also the practice of approximation, and a scaffolding way of using functions, limits, derivative, integrals, etc....
Article
Full-text available
Abstract: Our research focuses on the difficulties students encounter with the learning of calculus, considering that they have to cope with many more mathematical objects but also with new ways of reasoning – not only algebraic calculation, but also the practice of approximation, and a scaffolding way of using functions, limits, derivative, integr...
Technical Report
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Various studies about the convergence of functions and sequences in first year of university
Conference Paper
Full-text available
Our research focuses on the difficulties students encounter with the learning of calculus, considering that they have to cope with much more mathematical objects but also with new ways of reasoning – not only algebraic calculation, but also the practice of approximation, and a scaffolding way of using functions, limits, derivative, integrals, etc....
Conference Paper
Full-text available
University of Bordeaux, patrick.gibel@u-bordeaux.fr Our research focuses on the difficulties students encounter with the learning of calculus, considering that they have to cope with much more mathematical objects but also with new ways of reasoning – not only algebraic calculation, but also the practice of approximation, and a scaffolding way of u...
Article
Full-text available
What are mathematical objects and concepts? Are they only abstractions or coming from the real world? Since the 50ties, mathematicians and philosophers have elaborated new answers to these very old questions. The 20 th century has also been the one where these epistemological positions had an impact on the decisions concerning the teaching of mathe...
Research
Full-text available
This text is a translation of an article published in the Cahiers rationalistes, n°631. See also union-rationaliste.org. Thanks to Alain Billecoq, Michel Henry and Jean-Pierre Kahane who have read this text and helped me to finalize it.
Article
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This paper discusses the use of the Theory of Didactic Situations (TDS) at university level, paying special attention to the constraints and specificities of its use at this level. We begin by presenting the origins and main tenets of this approach, and discuss how these tenets are used towards the design of Didactical Engineering (DE), particularl...
Conference Paper
Full-text available
We present here a research about the teaching of mathematics in English or Spanish in French secondary schools. In such classes, the teacher is led to focus on the mathematical subject and the language, but the learning of both matters takes benefit from this process, in a way we try to elucidate. We analyze the way situations are built and managed...
Conference Paper
Full-text available
Résumé – Au début de l'enseignement supérieur, le curriculum prévoit l'étude d'objets déjà explorés auparavant, comme les fonctions et les limites. Cependant, derrière ce qui paraît de simples modifications techniques, le statut des objets et les outils de validation se trouvent profondément bouleversés. Nous analysons ce basculement épistémologiqu...
Conference Paper
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Jeu sur les symboles et construction des objets de savoir en mathématiques : enseignement en anglais en classe européenne
Article
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Après un bref historique de l'enseignement de la notion de fonction depuis les années soixante-dix, j'analyse les contraintes qui conduisent à privilégier un milieu graphique pour travailler les fonctions comme objets mathématiques, et valider leurs propriétés. Cette opérationnalisation du graphique vise à récupérer son aspect procédural, et au-del...
Article
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Ambition and success, teahcing proportionality in an Ambition Success Class: didactic variables, teaching practices, visible relationship to knowledge In the framework of a planned survey of the teaching of mathematics and sciences in ASH (adapted education for disabled pupils) or in difficult classes, we observed a teacher in a secondary school (c...
Conference Paper
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When they enter the University, students have a weak conception of real numbers; they do not assign the right meaning to a writing as 2 , or π, but neither x or parameters. This prevents them to have a control about formal proofs in the field of calculus. We present some situations to improve students' real numbers understanding; these situations m...
Chapter
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It is often said that student teachers’ underlying beliefs of what mathematics consists of and how it should be taught are restricted in two ways. On the one hand, future elementary teachers in general use only weak mathematical conceptions, which often do not help them to realise their educational ambitions. On a general educational level, many of...
Chapter
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Initial mathematics teacher education is primarily concerned with knowledge–the acquisition of knowledge required for the teaching of mathematics. Opinions as to what exactly comprises this knowledge and how it is best delivered and best learned varies widely across different contexts. In what follows, we will look more closely at this concept of t...
Article
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Au début de leur cursus professionnel, les futurs professeurs manifestent souvent des conceptions très formelles des mathématiques, d'où l'impossibilité d'envisager des "mises en scène" du savoir mathématique sous forme de problèmes et l'impossibilité d'anticiper les erreurs des élèves. Or le professeur novice doit devenir capable d'instaurer dans...
Article
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Résumé : Dans les classes d'enseignement spécialisé, un diagnostic des difficultés d’apprentissage met en lumière des malentendus dans l'interprétation des signes mathématiques. L'institution ne propose habituellement que la répétition des apprentissages ayant échoué, ce qui contribue à bloquer les élèves dans un contrat ancien. Nous utilisons la p...
Conference Paper
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Étude d’une question vive : expériences spatiales, représentations et signes graphiques et figuraux, géométrie. Les travaux portant sur la géométrie sont nombreux et variés. On peut dégager au moins trois sources de problématiques :  la géométrie vue comme modélisation de l’espace ;  les problèmes que posent la transition entre des connaissances...
Conference Paper
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Abstract: This paper addresses the use and signification of mathematical signs in the teaching/learning situations we build for students with special needs. We observe that students experience great difficulties within the dynamics of interpretation: their interpretation of signs – as a zero – cannot evolve from the first signification they meet in...
Article
Full-text available
Students often get a very formal conception of mathematics during their mathematics studies. When they become teachers, this formal conception makes them both confident in a direct transmission of the knowledge and unable to tolerate approximate formulations from their own students. How can we make teachers aware of the way mathematical knowledge a...
Conference Paper
Full-text available
Les élèves qui sont l'objet d'un constat d'inaptitude à suivre l'enseignement dans une classe 'ordinaire' de collège français sont envoyés dans des classes de SEGPA – Sections d'Enseignement Général et Professionnel Adapté. Un diagnostic des difficultés d’apprentissage met en lumière des malentendus dans l'interprétation des signes mathématiques, m...
Article
Full-text available
Our investigations have been developed in two directions that could seem quite opposite: first, the teaching of calculus at the transition between Upper Secondary School and University, and second, the teaching of mathematics for children with special needs, more precisely 14-15 years-old students in secondary school. The link between these two res...
Article
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La transition entre le lycée et l'Université est un point crucial pour l'orientation des bacheliers et pour le recrutement des étudiants poursuivant des études scientifiques. Nous nous sommes posé la question de l'adéquation du programme et des pratiques de l'enseignement secondaire pour préparer les élèves aux études supérieures, et tout particuli...
Conference Paper
Full-text available
Les tentatives pour relier 'Mathematics Education' et sémiotique existent depuis plusieurs années. Les auteurs concernés s'appuient généralement sur un théorie dyadique du signe, du type signifiant/signifié. Ces théories peinent à rendre compte de la spécificité de l'interprétation en mathématiques : les objets mathématiques étant imaginaires, les...
Conference Paper
Full-text available
The aim of this work is to analyse situations that can be given to novice secondary teachers to help them understand the articulation between advanced mathematical notions and the contents that they will be teaching themselves. This leads us to: 1) Identify the conceptions of novice teachers about teaching, and the way they succeed in mathematical...
Conference Paper
Full-text available
Relations between didactics of mathematics and mathematics teachers' education have been problematic for about twenty years; they became even more crucial those last ten years in France, since research on mathematics education tried to import the main concepts of didactics into teachers' training. And although didactic tools are an efficient way to...
Chapter
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Les pratiques actuelles de travail sur les nombres dans l'enseignement secondaire permettent-elles une structuration convenable des concepts numériques, afin que les élèves puissent s'engager dans l'apprentissage de l'analyse tel qu'il leur est proposé au début de l'enseignement universitaire ?
Article
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In many countries, the first concepts of calculus (such as functions)are taught by looking at examples, noticing their properties and generalizing from them in some implicit ways. Students have no means to discuss the general truth of a statement, or to examine the validity of a theorem, relative to the mathematical field. This knowledge is nonethe...
Chapter
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Thème n° titre ou autre EDITEURS (ed.),Actes de la 11° Ecole d'Ete de Didactique des Mathématiques, 1-13. 21 au 30 Août 2001, Corps. ISABELLE BLOCH DIFFERENTS NIVEAUX DE MODELES DE MILIEU DANS LA THEORIE DES SITUATIONS Recherche d'une dialectique scientifique entre analyses théoriques et contingence. Abstract : In the theory of situations we use th...
Conference Paper
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Recherche d'une dialectique scientifique entre analyses théoriques et contingence. Abstract : In the theory of situations we use the concept of "milieux" to built different kinds of situations : fundamental situations related to the mathematical knowledge, and situations with didactical purpose. I will point out the structures, aims and functions o...
Conference Paper
Full-text available
The mathematical work in the field of Calculus is usually very difficult for even good students when they are entering the University; we have studied the transition between the secondary mathematical organisation in teaching (pre)calculus – actually the notion of limit, and the University one. Our study leads us to identify numbers of ruptures in...
Conference Paper
Full-text available
La théorie des situations a permis de construire des situations a-didactiques pour les concepts fondamentaux des mathématiques du primaire. Elle modélise ces situations par des successions de jeux ; dans l'un des niveaux de jeu, la connaissance visée est nécessaire. Il s'agit d'étudier, sur un exemple, l'articulation des niveaux de jeu, et de déter...
Article
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The study of maths curriculum in the last grades of secondary schools in France along 30 years brings to light important variations that took place since 1962 in the contents of calculus at this level. These evolutions concern the objects of calculus that are taught as well as the procedures used by students and teachers. The suggested methods affe...
Article
Full-text available
The study of maths curriculum in the last grades of secondary schools in France along 30years brings to light important variations that took place since 1962 in the contents of calculusat this level. These evolutions concern the objects of calculus that are taught as well as theprocedures used by students and teachers. The suggested methods affect...
Article
Full-text available
A partir des difficultés posées par l'enseignement de l'analyse dans les années qui précèdent l'université, cet article entreprend de questionner un problème qui préoccupe, depuis quelques années, la recherche en didactique : le rôle du professeur dans une situation didactique, et les outils dont il dispose pour piloter la situation. Les travaux de...
Article
Full-text available
From the difficulties of teaching analysis (or calculus) during the two years before the university, this paper points a other problem which is questionning, since a couple of years, research on didactics : the place of the teacher in didactical situations, and the tools at her/his disposal to drive the situation. Works of Brousseau, Margolinas, Co...
Article
Full-text available
The mathematical work in the field of Calculus is usually very difficult for even good students when they are entering the University; one reason is that students never get the opportunity of an explicit preliminary phase of experimental character during which mental objects and related intuitions would be an explicit reference to the future formal...
Article
Full-text available
The objects that the didactics of mathematics want to study are not exactly the same as a naïve or only vocational approach could identify as pertinent; didactic tools are an efficient way to analyse teaching situations, and anticipate new ways of learning, but are not always easy to communicate to future teachers, knowing that these students often...

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Projects (3)
Project
To elaborate and analyze of online educational curriculum materials (OECM) for the use of teachers in their lessons and within classroom.
Project
Our research focuses on the difficulties students encounter with the learning of calculus, considering that they have to cope with much more mathematical objects but also with new ways of reasoning – not only algebraic calculation, but also the practice of approximation, and a scaffolding way of using functions, limits, derivative, integrals, etc. for proving. The semiotic facet of new objects, and the way to manage it, is also a source of great difficulties. We use a model (Bloch & Gibel, 2011) to describe students' work when they have to deal with the resolution of exercises about parametric curves and differential equations.