Improving QED-Tutrix by Automating the Generation of Proofs

The idea of assisting teachers with technological tools is not new. Mathematics in general, and geometry in particular, provide interesting challenges when developing educative softwares, both in the education and computer science aspects. QED-Tutrix is an intelligent tutor for geometry offering an interface to help high school students in the resolution of demonstration problems. It focuses on specific goals: 1) to allow the student to freely explore the problem and its figure, 2) to accept proofs elements in any order, 3) to handle a variety of proofs, which can be customized by the teacher, and 4) to be able to help the student at any step of the resolution of the problem, if the need arises. The software is also independent from the intervention of the teacher. QED-Tutrix offers an interesting approach to geometry education, but is currently crippled by the lengthiness of the process of implementing new problems, a task that must still be done manually. Therefore, one of the main focuses of the QED-Tutrix' research team is to ease the implementation of new problems, by automating the tedious step of finding all possible proofs for a given problem. This automation must follow fundamental constraints in order to create problems compatible with QED-Tutrix: 1) readability of the proofs, 2) accessibility at a high school level, and 3) possibility for the teacher to modify the parameters defining the "acceptability" of a proof. We present in this paper the result of our preliminary exploration of possible avenues for this task. Automated theorem proving in geometry is a widely studied subject, and various provers exist. However, our constraints are quite specific and some adaptation would be required to use an existing prover. We have therefore implemented a prototype of automated prover to suit our needs. The future goal is to compare performances and usability in our specific use-case between the existing provers and our implementation.Comment: In Proceedings ThEdu'17, arXiv:1803.0072

Une perspective fonctionnelle pour la formation professionnelle technique assistée par ordinateur

Dans cet article, les environnements de formation assistés par ordinateur sont considérés comme une réponse partielle à la problématique contemporaine de la formation professionnelle technique. Dans cette perspective, le développement par l'élève technicien d'une connaissance fonctionnelle y est préconisé et sa signification définie. La nature de l'expertise y est étudiée en distinguant le sujet sur lequel elle porte, ses degrés de formalisation et de généralité, de même que ses origines diversifiées. Pour former les élèves, on y propose une organisation des connaissances du domaine en réseaux conceptuels technoscientifiques. On y justifie la nécessité d'incorporer à l'environnement de formation des stratégies de « gestion de l'ignorance » en raison d'une connaissance fragmentaire des savoirs véritables des élèves. À cette fin, on examine le contrôle des connaissances mobilisées dans l'acte d'apprendre et le contrôle des processus d'apprentissage.In this paper, computer assisted training environments are examined as a partial response to the problem of contemporary technical training. With this objective, the author calls for the development of students' functional knowledge and provides a definition of this concept. The nature of expertise is analysed in terms of subject, degree of formalization and generality, and origin. The author proposes an organization of technical knowledge into techno-scientific conceptual structures as a basis for training students. In response to the difficulties presented by the incomplete or partial knowledge which students have of this field, the author oudines the importance of incorporating within the training environment those strategies which can "manage ignorance". Two proposals in response to this include the control of learner's knowledge and of learning processes during a learning task.En este articulo, los entornos de formaciôn asistidos por computador son considerados como una respuesta parcial a la problemâtica contemporanea de la formacion profesional técnica. El autor preconiza y define la significacion del desarrollo de un conocimiento funcional por parte del alumno técnico. El articulo estudia la naturaleza del conocimiento, distinguiendo el sujeto sobre el cual trata, su grado de formalizacion y de generalizacion asf como los origenes diversificados del mismo. Por la formacion, se propone una organization de los conocimientos del sector en redes conceptuales técnicocientificas. Se justifica también la necesidad de incorporar al medio de formacion estratégias de "gestion de la ignorancia" en razon del conocimiento fragmentario que los alumnos poseen del verdadero saber. A taies efectos, se examinan el control de los conocimientos mobilizados en el acto de aprender y el control de los procesos de aprendizaje.In diesem Artikel wird die computergestutzte Wissensvermittlung als Teilantwort auf die gegenwàrtige Problematik der technischen Ausbildung verstanden. Die Aneignung eines funktionellen Wissens durch den Technikstudenten wird empfohlen und als signifikant herausgestellt. Die Art und Weise des wissenschaftlichen Vorgehens wird erôrtert, indem deutlich unterschieden wird zwischen dem Untersuchungsobjekt, dem Grad der Formalisierung bzw. Generalisierung und den verschiedenen Urspriingen. Um Lerner auszubilden, wird eine Gruppierung der Fachkenntnisse in technisch-wissenschaftliche konzeptuelle Organigramme vorgeschlagen. Die Notwendigkeit, in das Lernenvironment Strategien der "Ignoranzverwaltung" einzubauen, wird dadurch gerechtfertigt, dass der tatsâchliche Wissensstand der Lerner als fragmentarisch angesehen wird. In diesem Zusammenhang wird auch die Kontrolle der im Lernvorgang mobilisierten Kenntnisse sowie die Kontrolle der Lernprozesse erôrtert

A Rare Case of Hemophagocytic Lymphohistiocytosis of Unknown Etiology

Hemophagocytic lymphohistiocytosis (HLH) is an uncommon cytokine storm syndrome marked which can cause high mortality. In adults, acquired HLH usually has an underlying infectious, autoimmune or malignant process that triggers the syndrome. In this case report, we present a 64-year old Caucasian male presenting with productive cough, fevers, weight loss and altered mental status who was ultimately found to have HLH of unknown etiology

International Banking Secrecy: Developments in Europe Prompt New Approaches

The frequent connection between banking secrecy and various corrupt political and business practices has drawn considerable attention from non-secrecy states. In Europe, the issue presently is ripe because of the European Community\u27s plans for a unified economy in 1992. This Note begins with a moral and historical examination of banking secrecy. Then, the author reveals the banking practices and legal structures through which banking secrecy is exploited. The author next sets forth the substantive banking secrecy laws of four European states and attempts to surmise the direction of their policies regarding banking secrecy. Next, the author describes past attempts, both unilateral and bilateral, to resolve the issue. Finally, the author proposes that, although a worldwide solution hardly is imminent, the increasing economic interdependence of small groups of states, such as the European Community, mandates serious consideration of multilateral approaches to resolve the international banking secrecy issue

Thirteen Conversations About Art and Cultural Race Politics

Gagnon notes that the extended conversations between her and Fung, as well as with the 11other contributing artists, writers and cultural workers, represent the complexity of Canadian cultural race politics and its evolution over the years. While engaging with the history and the formative concepts of cultural race politics, this book also speculates on its future, particularly in light of the forces of globalisation. Biographical notes. Bibliography 11 p. Videography/filmography/discography 4 p

First record of the European Giant File Clam, Acesta excavata (Bivalvia: Pectinoidea: Limidae), in the Northwest Atlantic

Two large bivalve specimens collected in Bay d’Espoir, a deep fjord situated on the south coast of Newfoundland, are described and identified as belonging to the species Acesta excavata (Fabricius 1779). In situ observations onboard the manned submersible PISCES IV and color videos have provided information on the vertical distribution, density and habitat of the species. Maximum abundances of about 15 large individuals/m2 occurred on sheltered rock outcrops at depth ranging from 550 to 775 m, where warm (6°C) continental slope water is found. Differences in shape and thickness between the valves of the two specimens appear to be related to the degree of exposure to rock falls (i.e., sheltered versus exposed habitat). Prior to this account, the European Giant File Clam had never been encountered west of the Azores Islands in the North Atlantic

Sensitivity analysis of energy performance and thermal comfort throughout building design process

In a traditional building design process (TDP), design variables are fixed sequentially, as opposed to integrated design process (IDP) which tends to avoid sequential design phases to create more sustainable buildings. First, a reference building is introduced and an energy model based on TRNSYS is presented to determine the energy consumption and comfort in the building. The model is validated based on energy bills, certified simulations and literature. Then, the paper performs an extended sensitivity analysis (SA) of 30 design variables with respect to different performance criteria related to energy consumption and comfort, based on a TRNSYS model. Three SA techniques were used, namely standard regression coefficients (SRC), partial rank correlation coefficients (PRCC) and Sobol indices. Results show that all three techniques yielded a similar ranking of the importance of the variables for most model outputs. Interactions between variables were identified with second-order Sobol indices. In the second part of this paper, a traditional design framework was adopted in which sets of variables were fixed sequentially. A SA was performed at each phase of the process, assuming fixed values for parameters chosen in previous design phases. Results show that fixing variables during the phases of a traditional design process tends to reduce the probabilities of finding low-energy consumption designs. Moreover, the influence of some variables was found to change during the design phases

Performance of a sequential versus holistic building design approach using multi-objective optimization

Integrated design processes are currently pushed forward in order to achieve net-zero energy building designs at affordable cost. Through a case study of a residential building, this paper compares a sequential versus a holistic design approach based on multi-objective optimization. In the holistic approach, 39 design variables related to the architecture and HVAC systems are simultaneously optimized. In the sequential approach, the architecture variables are first optimized; several optimal solutions are then selected for the second phase optimization of the heating system parameters. Carbon footprint, life cycle cost and thermal comfort are optimized by the algorithm NSGA-II. With only 100 computational hours, the holistic approach found 59% of the optimal solutions, whereas it took 765 h to find 41% of the optimal solutions with the sequential approach. This comparison shows the negative effects of making irreversible variable selections in the early phase of a design process, as it reduces the ability to find optimal solutions in the end