Secondary students' proof schemes during the first encounters with formal mathematical reasoning: appreciation, fluency and readiness.

The topic of the thesis is proof. At Year 9 Greek students encounter proof for the first time in Algebra and Geometry. Thus the principal research question of the thesis is: How do students’ perceive proof when they first encounter it? The analysis tool in order to obtain an image of students’ perception of proof, the Harel and Sowder’s taxonomy, is itself a research question in what concerns its applicability under Greek conditions. Its applicability, of which there is strong evidence, provides the space to shape an image of students’ proof fluency, proof appreciation, proof readiness etc. In order to collect data with regard to answering the research questions in collaboration principally with the class teacher I constructed the two tests on proof that are presented in this thesis. The first test was administered to the students of Year 9 at the beginning of the school year 2010-2011 before the teaching of proof. The second was administered after the teaching of proof of the same school year. Students’ answers were analyzed and provided strong evidence that the Harel and Sowder’s taxonomy is applicable on them. Thus every answer was characterized in terms of the taxonomy. As a result every individual student but also the whole sample is depicted by proof schemes. The major findings of the analysis are the two following: • Students’ proof fluency is higher in simple proof issues. Although they face difficulties when the issues are more demanding, they show high proof appreciation. • There is strong evidence of the applicability of the Harel and Sowder’s taxonomy in a completely different socio-cultural and educational environment in comparison to that of its original invention and application. In the same vein the research proposes the mixture of proof schemes within one proof as theoretical and methodological contribution. Finally from the findings emerge new research questions as e.g. • How teaching and curriculum affect students’ proof schemes? • What is the origin of mixed proof schemes

De la vie sociale du texte. L’intertexte comme facteur de la coopération interprétative

Cet article cherche à explorer, sous un mode dialectique, les rapports interprétatifs entre texte et intertexte. Dans un premier temps on cherche le chemin qui conduit de la problématique du texte à celle de l’intertexte. On réfute ensuite trois thèses : l’intertexte ne s’identifierait ni au contexte, ni à l’encyclopédie, ni au corpus. La troisième partie s’occupe à montrer que le concept d’intertexte doit être compris comme qualité interprétative. Enfin, on montre dans quelle mesure l’intertexte engage un auteur et un lecteur dans un commerce de modèles de compréhension. On conclut par une discussion concernant les rapports de l’intertexte avec la théorie linguistique.In this paper we aim to explore the interpretative relevance between text and intertext dialectically. Firstly, we investigate the epistemic path leading from text to intertext. Secondly, we attempt to refute three theses: that the intertext is neither the context, nor the encyclopaedia, nor the corpus. Thirdly, we attempt to justify why the intertext has to be understood as an interpretative quality. Finally, we show how the intertext engages an author and a reader in an interchange of comprehension models. We conclude with a discussion concerning the possible impact of the notion of intertext in linguistic theory

Présentation

Une idée simple, mais de mémoire célèbre, proclame que l’on ne peut comprendre une chose en dehors d’un cadre. Enfin, d’un certain cadre. Et qu’entre la chose et son cadre, il existe un lien de mutuelle détermination, voire de formation, peut-être même de mutuelle conformation : le cadre, qui n’existe ni pour la chose ni par la chose, se démontre toujours essentiel pour le dévoilement d’une possibilité de manifestation de cette dernière, qui, rétrospectivement, devient nécessaire pour le pose..

Initial Classifier Weights Replay for Memoryless Class Incremental Learning

Incremental Learning (IL) is useful when artificial systems need to deal with streams of data and do not have access to all data at all times. The most challenging setting requires a constant complexity of the deep model and an incremental model update without access to a bounded memory of past data. Then, the representations of past classes are strongly affected by catastrophic forgetting. To mitigate its negative effect, an adapted fine tuning which includes knowledge distillation is usually deployed. We propose a different approach based on a vanilla fine tuning backbone. It leverages initial classifier weights which provide a strong representation of past classes because they are trained with all class data. However, the magnitude of classifiers learned in different states varies and normalization is needed for a fair handling of all classes. Normalization is performed by standardizing the initial classifier weights, which are assumed to be normally distributed. In addition, a calibration of prediction scores is done by using state level statistics to further improve classification fairness. We conduct a thorough evaluation with four public datasets in a memoryless incremental learning setting. Results show that our method outperforms existing techniques by a large margin for large-scale datasets.Comment: Accepted in BMVC202

Proof schemes combined: mapping secondary students’ multi-faceted and evolving first encounters with mathematical proof

In this paper, we propose an enriched and extended application of Harel and Sowder’s proof schemes taxonomy that can be used as a diagnostic tool for characterizing secondary students’ emergent learning of proof and proving. We illustrate this application in the analysis of data collected from 85 Year 9 (age 14–15) secondary students. We capture these students’ first encounters with proof and proving in an educational context (mixed ability, state schools in Greece) where mathematical proof is explicitly present in algebra and geometry lessons and where proving skills are typically expected, and rewarded, in key national examinations. We analyze student written responses to six questions, soon after the students had been introduced to proof and we identify evidence of six of the seven proof schemes proposed by Harel and Sowder as well as a further eight combinations of the six. We observed these combinations often within the response of the same student and to the same item. Here, we illustrate the eight combinations and we claim that a dynamic use of the proof schemes taxonomy that encompasses sole and combined proof schemes is a potent theoretical and pedagogical tool for mapping students’ multi-faceted and evolving competence in, and appreciation for, proof and proving

Considering the subjectivity to rationalise evaluation approaches : the example of "Spoken Dialogue Systems"

International audienceWe present in this paper a reading grid aiming at helping the evaluator take into account the subjectivity factor when designing evaluation protocols. Actually, however most contributions to Spoken Dialogue Systems evaluation tend to objectify their approach for rationalising purpose, we believe subjectivity is to be considered to enforce valuable evaluations. The first section shows how closely evaluation processes are dependant on their contexts and on the evaluators’ perspectives. We then present an anthropocentric framework that establishes the evaluator as a mediator between the consideration of contextual elements and a rationalising corpus of evaluation procedures. We finally anticipate the benefits brought by our framework at both individual and community levels

Assistance informatique à l'interprétation des données en cartographie linguistique. Informatisation anthropocentrée du Nouvel Atlas Linguistique de la Basse-Bretagne

International audienceNous discutons les motivations et les caractéristiques fondamentales d'un projet de recherche qui vise à mettre sur pied un système informatique d'assistance à l'interprétation pour les besoins de la recherche en cartographie linguistique. Dans la première partie nous exposons rapidement les traits fondateurs de la démarche de la cartographie linguistique sur la trace d'un morceau de son histoire récente. Notre objectif est de montrer combien ses aspirations tissent, dès le début, avec le traitement des données, et, par voie de conséquence, combien elle est tributaire des moyens de ces traitements. Dans la seconde, nous discutons le thème de l'introduction de l'informatique à son secours. Cependant, nous cherchons à défendre parallèlement l'idée suivant laquelle l'appel à l'informatique peut être plus qu'un simple service de calcul, et qu'il peut être pensé comme facteur de jonction intersémiotique, entre les différents niveaux de données qui intéressent la cartographie linguistique. L'objectif de notre argument est coordonné par une vision interprétative de la discipline. Enfin, dans la troisième partie, nous montrons les premières réalisations informatiques issues d'une telle vision. Mots clés : Cartographie linguistique, systèmes anthropocentrés, traitement de données, assistance informatique à l'interprétation, atlas linguistique

Interpretative e-Learning Personalization: Methodology, Formal Aspects and generic Scenarios of Individual/Group Dynamics. A case of a course in art history.

International audienceMost of today’s e-learning development focus on knowledge formats and production, supposing perhaps that reception can be seen as the symmetric case of production in a courseware. In other words, that the point of view of the teacher may be transposed towards the learner. Nevertheless, understanding is an interpretation-dependent process, lying mainly on reading Strategies adopted by the learner. We may thus wonder whether it is yet possible to conceive systems whose architecture is driven by hermeneutical principles (i.e. where the interpretational activity is considered as a priority, and the role of the receptor of the course in the very constitution of the course is at least as important as this of the teacher) inherited from [3]. A reading strategy may be represented as a knowledge path built up from information put at disposal in the framework of a course. The aim of our work is to furnish some modeling issues in such a direction, using as case study academic course in art history. In collaboration with the Art Diagnosis Centre of Ormylia (Greece), some of us contributed, in the framework of various projects, to the setting up of a fine art ontology (over 30 000 concepts) able to cover the knowledge of large range iconographic corpora (see, for instance, [1])