GeoGebraTUTOR : développement d’un système tutoriel autonome pour l’accompagnement d’élèves en situation de résolution de problèmes de démonstration en géométrie plane et genèse d’un espace de travail géométrique idoine

Travaux d'études doctorales réalisées conjointement avec les travaux de recherches doctorales de Nicolas Leduc, étudiant au doctorat en génie informatique à l'École Polytechnique de Montréal.Cette thèse vise le développement de GeoGebraTUTOR (GGBT), un espace de travail géométrique (ETG) qui intègre un système tutoriel pour l’obtention d’un milieu respectueux du raisonnement idiosyncratique de l’élève. Le raisonnement mathématique, comme l’apprentissage, ne s’exerce pas de manière linéaire, il repose sur un remaniement conceptuel continu. Il est donc peu étonnant qu’une approche séquentielle inflexible pour l’exercice de la démonstration en géométrie soit source d’embûches. Les systèmes tutoriels existants pour l’exercice de la démonstration en géométrie offrent une variété d’outils sans pour autant soulager l’élève de cette rigidité. Le design multidisciplinaire de GGBT repose sur une conception dans l’usage qui articule plusieurs cycles de recherche et de développement successifs. Cette méthodologie itérative et anthropocentrique confère à GGBT une intelligence qui nait d’une convergence d’analyses a priori et a posteriori successives. Cette thèse concerne les deux premiers cycles du développement de GGBT. La première phase du développement implique l’élaboration a priori d’un système capable de recevoir et d’analyser les démarches singulières de démonstration des élèves en fonction de solutions expertes préalablement identifiées. Ce premier prototype de GGBT est conçu en fonction d’une analyse de la relation didactique entre un enseignant réel et l’élève, et la relation didactique simulée entre un agent tuteur virtuel et ce même élève. Cette analyse théorique a priori établit un cadre conceptuel liminaire qui vise à encadrer la création d’un ETG idoine permettant à l’apprenti géomètre de se livrer à son travail mathématique. Cette version initiale de GGBT est mise à l’essai par des élèves réels guidés par leur enseignant ordinaire. Leurs interactions sont ensuite étudiées pour modéliser et implémenter un premier système tutoriel autonome à l’image des échanges témoignant du contrat didactique observé. Le second cycle de développement s’amorce avec la modélisation et la programmation d’une structure tutorielle autonome et d’une interface renouvelée, qui contribuent conjointement au design a priori d’un espace de travail géométrique. La deuxième version ainsi obtenue est également testée en contexte de classe réel. Cette fois, l’exercice empirique vise la validation de la gestion des messages par le système tutoriel et l’exploration des raisonnements instrumentés dans une perspective de précision du travail géométrique possible à l’interface de l’ETG qu’est GGBT. Ce parcours doctoral se clôt par l’exploration d’avenues de recherche potentielles pour la poursuite du développement et du raffinement de GGBT.This thesis aims at modeling GeoGebraTUTOR, a geometrical workspace that relies on the works of a tutorial system for the definition of a milieu respectful of the student’s idiosyncratic reasoning. Mathematical reasoning, like learning, does not evolve in a linear fashion. It relies on continuous conceptual reorganizations. Therefore, it is little wonder that a linear and inflexible approach for the exercise of geometrical proof creates difficulties. Existing tutorial systems for the solving of geometrical proof problems offer a variety of tools without relieving the student of this rigidity. GGBT’s multidisciplinary design relies on a design in use approach that articulates a series of research and development cycles. This iterative anthropocentric methodology provides GGBT with an intelligence resulting from the confrontation of successive a priori and a posteriori analyses. This thesis is rooted in GGBT’s two first development cycles. The first phase of design implies the planning of a system able to take in singular student proofs and analyze their value compared to previously implemented expert answers. This first GGBT prototype is designed according to an analysis of the didactical relationship between the teacher and the student as well as the relationship that takes place between the student and the tutor agent who evolves within the didactical milieu. This a priori analysis establishes theoretical guidelines, which will steer the design of a geometrical workspace that enables the learning geometer to accomplish his mathematical work. A first GGBT prototype is put to the test with real students assisted by their regular teacher. Their interactions are then studied in order to model and implement a first self-governing tutorial system according to the dialogues reflecting the observed didactical contract. The second design cycle begins with the modeling and programming of a tutorial structure and of a renewed interface, both of which contribute to the planning of a geometrical workspace. This second prototype is also tested in a real class environment, although this time the empirical exercise aims, on the one hand, at validating the management of the tutor’s help messages, and on the other hand at exploring the student’s instrumented reasoning to specify the mathematical activity made possible by the GGBT geometrical workspace. This doctoral endeavor ends with the exploration of potential research avenues for the ongoing design and refining of GGBT

Means of Choice for Interactive Management of Dynamic Geometry Problems Based on Instrumented Behaviour

ABSTRACT: Our paper presents a project that involves two research questions: does the choice of a related problem by the tutorial system allow the problem solving process which is blocked for the student to be restarted? What information about learning do related problems returned by the system provide us? We answer the first question according to the didactic engineering, whose mode of validation is internal and based on the confrontation between an a priori analysis and an a posteriori analysis that relies on data from experiments in schools. We consider the student as a subject whose adaptation processes are conditioned by the problem and the possible interactions with the computer environment, and also by his knowledge, usually implicit, of the institutional norms that condition his relationship with geometry. Choosing a set of good problems within the system is therefore an essential element of the learning model. Since the source of a problem depends on the student’s actions with the computer tool, it is necessary to wait and see what are the related to problems that are returned to him before being able to identify patterns and assess the learning. With the simultaneity of collecting and analysing interactions in each class, we answer the second question according to a grounded theory analysis. By approaching the problems posed by the system and the designs in play at learning blockages, our analysis links the characteristics of problems to the design components in order to theorize on the decisional, epistemological, representational, didactic and instrumental aspects of the subject-milieu system in interaction

Conception et analyse de geogebratutor, un système tutoriel intelligent : genèse d'un espace de travail géométrique idoine

Cette contribution montre l’éclairage apporté par le modèle des espaces de travail géométrique (ETG) dans la conception et la validation du système tutoriel intelligent geogebraTUTOR (GGBT). Conçu pour être employé par des élèves de l’école secondaire, ce système se destine au développement de la pensée géométrique dans un contexte de résolution de problèmes de preuve en géométrie euclidienne. Le texte présente d’abord les fondements théoriques qui sous - tendent le développement de GGBT, au sein duquel les ETG agissent en tant que carrefour conceptuel. Au coeur de notre propos, la validation d’une version perfectionnée de GGBT s’effectue en vérifiant l’idonéité de l’espace de travail engendré par l’usage du système tutoriel. Cette phase de vérification, qui s’inscrit dans une suite de phases de recherche et de développement, a pour objectif l’observation et l’analyse du travail de l’élève en tant que géomètre en formation. Les résultats expérimentaux proviennent d’élèves québécois au 2e cycle de l’école secondaire (étape 14-17 ans)

QED-Tutrix: Creating and expanding a problem database towards personalized problem itineraries for proof learning

International audienceQED-Tutrix (QEDX) is an intelligent tutoring system which assists students in proof problem solving by providing hints while taking into account the student's cognitive state. QEDX stands out by the fact that it adapts to each user and class reality, not the opposite. However, this model implies recognizing, like a teacher would, proofs that do not necessarily conform to a formal logic. Hence, QEDX can't rely on an automated proof engine (Tessier-Baillargeon, 2016), raising the question of how to expand QEDX's problem database without manually implementing each valid proof. Therefore, our poster at CERME10 doesn't present a traditional research project with its research questions, it's methodology and conclusions. It rather aims at presenting the new research questions that stem from the challenges that arise with trying to broaden QEDX's problem bank while staying true to our main goal, which is to create a geometrical workspace (Kuzniak, 2006) according to witnessed student/teacher interactions through a design in use approach (Rabardel, 1995). Here we will focus our attention on the process of problem implementation, starting with how we currently generate a proof problem's solution graph. Generating a proof problem's solution graph. QEDX's HPDIC graph (Figure 1) is used to record all the valid proofs to a given problem. It includes Hypotheses, Properties, Definitions, Intermediary results and a Conclusion. This graph is unique to each problem and is built from the inferences individually identified as true according to the problem to solve and the class context. The HPDIC graph for the rectangle problem in Figure 1 is fairly simple since it counts only 13 inferences. However, in the five problems implemented in the current QEDX version, one counts 214 inferences creating a much more complex HPDIC graph

Efficacy of intensive multitherapy for patients with type 2 diabetes mellitus: a randomized controlled trial

BACKGROUND: National guidelines for managing diabetes set standards for care. We sought to determine whether a 1-year intensive multitherapy program resulted in greater goal attainment than usual care among patients with poorly controlled type 2 diabetes mellitus. METHODS: We identified patients with poorly controlled type 2 diabetes receiving outpatient care in the community or at our hospital. Patients 30–70 years of age with a hemoglobin A(1c) concentration of 8% or greater were randomly assigned to receive intensive multitherapy (n = 36) or usual care (n = 36). RESULTS: The average hemoglobin A(1c) concentration at entry was 9.1% (standard deviation [SD] 1%) in the intensive therapy group and 9.3% (SD 1%) in the usual therapy group. By 12 months, a higher proportion of patients in the intensive therapy group than in the control group had achieved Canadian Diabetes Association (CDA) goals for hemoglobin A(1c) concentrations (goal ≤ 7.0%: 35% v. 8%), diastolic blood pressure (goal < 80 mm Hg: 64% v. 37%), low-density lipoprotein cholesterol (LDL-C) levels (goal < 2.5 mmol/L: 53% v. 20%) and triglyceride levels (goal < 1.5 mmol/L: 44% v. 14%). There were no significant differences between the 2 groups in attaining the targets for fasting plasma glucose levels, systolic blood pressure or total cholesterol:high-density lipoprotein cholesterol ratio. None of the patients reached all CDA treatment goals. By 18 months, differences in goal attainment were no longer evident between the 2 groups, except for LDL-C levels. Quality of life, as measured by a specific questionnaire, increased in both groups, with a greater increase in the intensive therapy group (13% [SD 10%] v. 6% [SD 13%], p < 0.003). INTERPRETATION: Intensive multitherapy for patients with poorly controlled type 2 diabetes is successful in helping patients meet most of the goals set by a national diabetes association. However, 6 months after intensive therapy stopped and patients returned to usual care, the benefits had vanished