APLUSIX, un EIAH de l'algèbre

Grandbastien , Monique and Labat , Jean-Marc (Eds)International audienceCe chapitre décrit la (re-)conception de l'EIAH APLUSIX, micromonde d'apprentissage de l'algèbre pour les collèges et les lycées, ainsi que les premières expérimentations effectuées et les premiers usages observés en classe avec le produit obtenu. En particulier, ce chapitre témoigne de la tension qui existe au moment de la conception d'un EIAH entre deux problématiques, la première est liée aux objectifs d'apprentissage, la seconde concerne le développement d'une interface homme-machine (IHM). À l'intersection de ces deux domaines de recherche se trouvent les notions de micromonde et d'ergonomie notions centrales de ce chapitre

An Application of CLP: Checking the Correctness of Theorems in Geometry

International audienceConstraint Logic Programming can be advantageously used to deal with quadratic constraints stemming from the verification of planar geometry theorems. A hybrid symbolic--numeric representation involving radicals and multiple precision rationals is used to denote the results of quadratic equations. A unification--like algorithm tests for the equality of two expressions using that representation. The proposed approach also utilizes geometric transformations to reduce the number of quadratic equations defining geometric constructions involving circles and straight lines. A large number (512) of geometry theorems has been verified using the proposed approach. Those theorems had been proven correct using a significantly more complex (exponential) approach in a treatise authored by Chou in 1988. Even though the proposed approach is based on verification -rather than strict correctness utilized by Chou- the efficiency attained is polynomial thus making the approach useful in classroom situations where a construction attempted by student has to be quickly validated or refuted

Verification of non-linear overconstraints in Euclidean geometry with linear programming

International audienceThis paper is about one representation of constructible numbers which allows use of solver of linear constraints. A implementation is given in PrologIII and experiments are discussed

Verification of non-linear overconstraints in Euclidean geometry with linear programming

International audienceThis paper is about one representation of constructible numbers which allows use of solver of linear constraints. A implementation is given in PrologIII and experiments are discussed

De la compréhension de programmes en génie logiciel à la reconnaissance d’algorithmes d’apprenants en EIAH

International audienceIn order to assess learners in algorithmics, we suggest a methodbased on the automatic understanding of the algorithms proposed by thestudents using comprehension methods from the domain of the softwareengineering. We use prebuilt models of student’s propositions, each onerepresenting algorithms, organized into tasks and subtasks and documentedwith information and pedagogical characteristics. The mark is based on adistance calculus between the model and the proposition. A first experimentoccurs with exam forms. It gives interesting recognition rates and marks forrecognized forms close to the marks obtained during the exam.Dans le but d’évaluer les productions d’apprenants en algorithmique,nous présentons une méthode de reconnaissance des algorithmes proposés parles apprenants basée sur les techniques de compréhension des programmes dugénie logiciel. Notre méthode repose sur une décomposition des algorithmes entâche et sous-tâche à accomplir ; à associer à chaque sous-tâche des « lignescritiques » et des propriétés spécifiques. Cette décomposition/modélisationpermet l’utilisation des techniques de compréhension de programmes de GénieLogiciel et mène à une évaluation/notation des propositions d’algorithmesbasée sur le modèle identifié d’une base de modèles étiquetés et sur la distanceentre le modèle et la proposition. Une première expérimentation à partir decopies d’examen donne des taux de reconnaissance intéressants et des notespour les copies reconnues proches des notations manuelles

An Analysis of Interactive Learning Environments for Arithmetic and Algebra Through an Integrative Perspective

International audienceThe analysis presented in this article tries to obtain a global view of the field of interactive learning environments (ILE) dedicated to arithmetic and algebra. As preliminaries, a brief overview of evaluation methods focusing on educational software is given and a short description of ten ILEs concerned by the study is provided as a kind of a state-of-the-art. Then the methodology of ILEs analysis developed in the TELMA project is explained consisting in the design and the refinement of an analysis grid and its use on the ten ILEs is mentioned. Next, a first level analysis of results leading to a compiled, analytic and synthetic view of the ILEs available and/or missing functionalities is given. A second level of the analysis is also proposed, with two concise representations of the ILEs, composed of graphical representations of the previous results, leading to a 3D map of ILEs dedicated to arithmetic and algebra. This map provides, as promised, a global view of the field and permits to define five sorts of ILEs according to two criteria: the first one is teacher-oriented and concerns usages enabled by the ILE; the second one is student-oriented and concerns control provided by the ILE to accomplish such usages

Doing mathematics with the APLUSIX-Editor

International audienceThe APLUSIX-Editor is a microworld dedicated to the learning of algebra. First it includes an advanced editor that allows the student to build easily algebraic expressions. Second it reifies the student's reasoning as a linear development of equivalent steps or as a tree. Third it verifies the equivalence between the different steps during student's calculations, and gives indications about the progression of the reasoning. The first three parts of the paper present the syntactical aspect, the semantic aspect and the strategic aspect of the APLUSIX-Editor. The last parts present experiments conducted with the APLUSIX-Editor

An Analysis of Interactive Learning Environments for Arithmetic and Algebra Through an Integrative Perspective

International audienceThe analysis presented in this article tries to obtain a global view of the field of interactive learning environments (ILE) dedicated to arithmetic and algebra. As preliminaries, a brief overview of evaluation methods focusing on educational software is given and a short description of ten ILEs concerned by the study is provided as a kind of a state-of-the-art. Then the methodology of ILEs analysis developed in the TELMA project is explained consisting in the design and the refinement of an analysis grid and its use on the ten ILEs is mentioned. Next, a first level analysis of results leading to a compiled, analytic and synthetic view of the ILEs available and/or missing functionalities is given. A second level of the analysis is also proposed, with two concise representations of the ILEs, composed of graphical representations of the previous results, leading to a 3D map of ILEs dedicated to arithmetic and algebra. This map provides, as promised, a global view of the field and permits to define five sorts of ILEs according to two criteria: the first one is teacher-oriented and concerns usages enabled by the ILE; the second one is student-oriented and concerns control provided by the ILE to accomplish such usages

Helping Teachers Generate Exercises with Random Coefficients

International audienceFirst, we propose two taxonomies concerning software designed for teaching mathematics, which we call Technology Enhanced Learning (TEL) environments, the first one concerns the teacher's place and role in TEL environments, the second one concerns the activities which are foreseen and provided by TEL environments. Second, we consider TEL environments which provide teachers with tools for building patterns of exercises used in the TEL environment to generate randomly and dynamically exercises or lists of exercises. Our approach is compared to classical approaches (based on standards like IMS-QTI or on Computer Algebra Systems)

Analyse d'EIAH en arithmétique et en algèbre : Conception, utilisation et exploitation d'un questionnaire d'analyse d'EIAH en mathématiques à la recherche d'une classification du domaine

International audienceUne méthodologie de conception, d'utilisation et d'analyse synthétique des résultats obtenus après enquête sur des EIAH en arithmétique et algèbre est exposée dans cet article. Issu d'un effort interne et disciplinaire d'un ensemble d'équipes de recherche appartenant à un même projet européen, ce travail a renouvelé les genres " état de l'art " et " analyse " en introduisant des grilles d'observation concertées et structurées permettant une collecte des informations collaborative. Suite à un travail de lecture croisée, de fusion de publication et de communication de ces documents, la base d'informations obtenue a rendu possible une action d'analyse et la mise en place d'outils de synthèse qui ont finalement abouti à la constitution d'un panorama 3D des EIAH en arithmétique et en algèbre, peuplé des EIAH étudiés, menant à une classification possible des EIAH de mathématiques potentiellement applicable aux EIAH en général