Tools and technologies in mathematical didactics

This short paper provides an overview of recent European research about the use and impact of tools and technologies in mathematical didactics. Such research is categorised as focusing on theoretical ideas, on algebraic knowledge when using spreadsheet and computer algebra (CAS), and on dynamic geometry software (DGS). The paper reveals the variety of software technologies, education levels, and methodologies utitised in European research

The bag-of-frames approach: a not so sufficient model for urban soundscapes

The "bag-of-frames" approach (BOF), which encodes audio signals as the long-term statistical distribution of short-term spectral features, is commonly regarded as an effective and sufficient way to represent environmental sound recordings (soundscapes) since its introduction in an influential 2007 article. The present paper describes a concep-tual replication of this seminal article using several new soundscape datasets, with results strongly questioning the adequacy of the BOF approach for the task. We show that the good accuracy originally re-ported with BOF likely result from a particularly thankful dataset with low within-class variability, and that for more realistic datasets, BOF in fact does not perform significantly better than a mere one-point av-erage of the signal's features. Soundscape modeling, therefore, may not be the closed case it was once thought to be. Progress, we ar-gue, could lie in reconsidering the problem of considering individual acoustical events within each soundscape

Students working on models; an on-going experimentation in mathematics and chemistry

This paper focuses on modelling at upper secondary level. The objective is to give students an understanding of mathematical concepts and methods in close relationship to a domain of reality, as well as to give them insight into the contribution of models of different kinds. This has led to the development of a framework for modeling activities based on the Mathematical Working Spaces theory. The questions at stake concern the operationality of this framework. To what teaching situations can it lead? How do students work in these situations? We examine these questions through an on-going experimentation on models of acid-base transformations

Using Symbolic Calculators to Study Mathematics.: The case of tasks and techniques

International audienceKey words: This chapter will consider in more depth the possible contribution of technology-especially CAS-to the study of mathematical domains. Using a theoretical approach to treat examples of classroom activities, we will show how a didactical reflection can help to understand this contribution. A variety of new techniques will be presented and related to paper-and-pencil techniques. Examining the pragmatic and epistemic value of both types of technique will help to make sense of classroom situations. It will also help to clarify the situation of teachers wanting to integrate new tools. Consideration of other approaches will show that educators emphasize the use of computer algebra to promote 'conceptual' mathematics. Nevertheless, they cannot ignore instrumented techniques when considering the real potentialities of new tools and the conditions for their integration

Study of the Non-negative Matrix Factorization behavior to estimate the urban traffic sound levels

ICSV'26 ; 26ème International Congress on Sound and Vibration , MONTREAL, CANADA, 11-/07/2019 - 17/07/2019The advent of low-cost acoustic sensor networks in cities raises new interesting approaches for improving the monitoring of the acoustic quality of cities. Many innovative approaches are developed to improve knowledge on sound environments: sound environment recognition, sound source detection, etc. In order to improve the road traffic noise mapping, the use of a specific version of the Non-negative Matrix Factorization (NMF), named thresholded initialized NMF, as a source separation method to estimate the sound level of road traffic from measurements, has proved to be a successful approach. This paper proposes to further detail the functioning of the thresholded initialized NMF on a corpus composed of urban sound scenes mixing traffic and specific interfering components with calibrated sound levels in order to better understand its behavior according to the different sources encountered. The study reveals the different performances of this approach depending on the noise levels of the interfering sources and their proximity to the urban traffic spectrum

Diagnosing Latent Tuberculosis Infection in the HIV Era

Tuberculin skin testing (TST) and Interferon-gamma (IFNγ)release assays (IGRAs) are presently the only available assays for the detection of Mycobacterium tuberculosis infected individuals. IGRAs might progressively replace TST, as numerous published reports establish their higher specificity and similar sensitivity when tested in BCG vaccinated, immunocompetent individuals or in populations who may have been in contact with atypical mycobacteria. However, few published reports have commented on their role in TB diagnosis in immunocompromised individuals (HIV, immunosuppressive therapy, cancer…). It is the purpose of this report to review IGRAs published studies in HIV individuals in endemic and non endemic area for tuberculosis (TB). IGRAs were tested in the presence or absence of active TB but correlated to duration of exposure. In newly diagnosed active TB, IGRAs demonstrated a similar sensitivity to TST. In TB non infected individuals, TST and IGRAs also gave similar values when categorization of individuals was correlated to the risk of infection. A higher number of positive IGRAs was observed in individuals from TB endemic areas, in similar proportions to immunocompetent individuals. Comparison between the two IGRAs: QuantiFERON-TB Gold® (QF-TB, Cellestis, Australia) and T-SPOT-TB® (Oxford Immunotec, UK), and against TST, in the same HIV population demonstrates a higher sensitivity of T-SPOT-TB and TST than QF-TB. Indeterminate results, which correspond to the absence of a positive T-cell IFNγ response towards phytohemaglutinin (PHA), is a key point when comparing both IGRAs. This PHA control is indicative of the level of immunosuppression observed in the tested individual. QF-TB seems to present, in HIV populations, more indeterminate results than T-SPOT-TB. The calibration and/or concentration of PBMC on nitrocellulose membrane for the T-SPOT-TB, as compared to a whole blood assay, might explain this difference, with less indeterminate results with the T-SPOT-TB assay. Neither assay is able to differentiate active TB from latent TB infection (LTBI). Several laboratories have tried new antigenic epitopes to solve this issue. It is of importance that these studies need to be repeated on a larger scale by others to validate their results. Two blood assays might add information characterising the evolution from LTBI to active TB: either by losing protective immunity, as demonstrated by the whole blood killing assay, or by evaluating the kinetics of the antibodies synthesized against M. tuberculosis specific antigens. In conclusion, longitudinal studies are still needed to validate IGRAs and other assays and to define their respective predictive values

Exocomets in the circumstellar gas disk of HD 172555

The source HD172555 is a young A7V star surrounded by a debris disk with a gaseous component. Here, we present the detection of variable absorption features detected simultaneously in the Ca II K and H doublet lines (at 3,933 and 3,968 Angstrom). We identified the presence of these absorption signatures at four different epochs in the 129 HARPS high-resolution spectra gathered between 2004 and 2011. These transient absorption features are most likely due to Falling Evaporating Bodies (FEBs, or exocomets) that produce absorbing gas observed transiting in front of the central star. We also detect a stable Ca II absorption component at the star's radial velocity. With no corresponding detection in the Na I line, the resulting very low upper limit for the NaI/CaII ratio suggests that this absorption is due to circumstellar gas.Comment: Accepted for publication in Astronomy&Astrophysics Letter

Innovations technologiques dans l'enseignement des mathématiques: paradigmes et changement de la professionnalité de l'enseignant

International audienceTaking Mathematics as an exemplar, this paper addresses the processes of dissemination, regression and resurgence in the development of technological innovations for teaching/learning. Starting from the notion of technological revolution, the concepts of paradigm, instrumented action schemes and professionality are used to analyse these processes, and particularly the position of a key actor: the teacher. The example of the blackboard helps to specify how the paper looks to evolutions resulting from the use of artefacts for teaching/learning. It shows how the above concepts are relevant to analyse a century long process.Then the paper considers technological revolutions that proposed their paradigms in the last thirty years. These new paradigms demand deep changes in teachers’ professionality as well as instrumental genesis particular to the associated tools. These changes and new genesis can only develop on the long run.Mathematics teaching/learning was particularly affected by two overlapping revolutions: programming and symbolic computation on one side, and visualisation and interactivity on the other side. The underlying paradigms did not really permeate teaching practices. Didactical research worked to reconstruct these paradigms especially by taking the teacher into account. But, meanwhile, some of them lost their topicality. The Internet revolution deeply impinges on the teachers’ professionality. The paper offers two potential models of evolution and points out entries for research studies

Des situations connues aux traitements sur des données codifiées. Représentations mentales et processus d'acquisition dans les premiers apprentissages en informatiques

no abstract in englishLe travail présenté dans cette thèse concerne l'apprentissage de la programmation par des débutants dans le cadre d'un enseignement de l'informatique ouvert à tout public. Dix années d'existence d'une "Option Informatique" s'adressant, en classe de Seconde des Lycées, à un très vaste public, ont montré l'intérêt d'un enseignement de l'informatique, conçu comme une contribution au développement d'aptitudes intellectuelles et répondant aux enjeux culturels posés par l'intervention de l'informatique dans les différents champs du savoir. Elles ont mis en évidence également les difficultés rencontrées par une majorité d'élèves au cours de cet apprentissage, ainsi que l'insuffisance du cadre didactique permettant l'analyse de ces difficultés et la mise en place de moyens pour y remédier. Mon but est de contribuer à la construction de ce cadre didactique

Approches didactique et cognitive d'un instrument technologique dans l'enseignement. Le cas du calcul formel en lycée.

This document is based largely on work conducted jointly by the DIDIREM laboratory and the Commission Inter-Irem Mathématiques et Informatique with support from the Ministry. It presents a synthesis of research about the introduction of computer algebra systems (CAS) in school Mathematics, a very pressing and timely issue. It is part of the research of conditions for the viability of technological tools in education. The first issue addressed is that of the technical / conceptual relationship: I show that the potential of CAS is not in the reduction of the technical dimension of the mathematical work that would be thought of as independent of or competing with a conceptual dimension, but in the availability of new techniques, interacting with the usual techniques and potentially supporting an approach to concepts. After that, I study the impact of CAS by considering new objects it introduces into teaching and learning situations, recognizing the sensitivity of mathematical activity to ostensives highlighted by a recent trend in mathematics education research. The complexity of the relationships between these objects and other objects of the mathematical work raises the question of their appropriation by students. I show how, to address this issue, recent studies have developed a cognitive approach to computer algebra instruments and how this approach reflects the variety of computer algebra uses by students, as well as the essential role that the teacher has to play for a successful integration.A statistical annex shows how implicative analysis has been used to determine, in an inferential perspective, students’ positioning with regard to symbolic calculation, showing how complex are the changes introduced by CAS.Cette habilitation est basée en grande partie sur des travaux menés en commun par le laboratoire DIDIREM et la commission Inter-Irem Mathématiques et Informatique avec le soutien du Ministère. Elle présente une synthèse des recherches sur l'introduction du calcul formel dans l'enseignement scolaire des mathématiques, question dont l'actualité est très forte. Elle s'inscrit dans la recherche des conditions de viabilité d'un moyen technologique dans l'enseignement. La première question abordée est celle des rapports technique/conceptuel : je montre que les potentialités du calcul formel ne sont pas dans la diminution d'une dimension technique du travail mathématique, qui serait pensée comme indépendante ou concurrente d'une dimension conceptuelle, mais dans la disponibilité de nouvelles techniques, interagissant avec les techniques habituelles et susceptibles de servir de point d'appui pour aborder les concepts. J'étudie ensuite l'impact du calcul formel en m'intéressant aux objets nouveaux qu'il introduit dans les situations d'enseignement et d'apprentissage, retrouvant en cela la sensibilité de l'activité mathématique aux ostensifs, que souligne un courant récent de la didactique des mathématiques. La complexité des rapports entre ces objets et les autres objets du travail mathématique pose la question de la façon dont les élèves peuvent se les approprier. Je montre comment, pour aborder cette question, des travaux récents ont développé une approche cognitive des instruments de calcul formel et comment cette approche rend compte de la diversité des utilisations du calcul formel par les élèves, ainsi que du rôle essentiel que l'enseignant a à jouer pour une intégration réussie. Une annexe statistique présente la façon dont l'analyse implicative a pu être utilisée pour déterminer, dans une perspective inférentielle, des positionnements d'élèves utilisateurs du calcul formel, révélateurs de la complexité des modifications introduites par le calcul formel