Escaping the Trap of too Precise Topic Queries

At the very center of digital mathematics libraries lie controlled vocabularies which qualify the {\it topic} of the documents. These topics are used when submitting a document to a digital mathematics library and to perform searches in a library. The latter are refined by the use of these topics as they allow a precise classification of the mathematics area this document addresses. However, there is a major risk that users employ too precise topics to specify their queries: they may be employing a topic that is only "close-by" but missing to match the right resource. We call this the {\it topic trap}. Indeed, since 2009, this issue has appeared frequently on the i2geo.net platform. Other mathematics portals experience the same phenomenon. An approach to solve this issue is to introduce tolerance in the way queries are understood by the user. In particular, the approach of including fuzzy matches but this introduces noise which may prevent the user of understanding the function of the search engine. In this paper, we propose a way to escape the topic trap by employing the navigation between related topics and the count of search results for each topic. This supports the user in that search for close-by topics is a click away from a previous search. This approach was realized with the i2geo search engine and is described in detail where the relation of being {\it related} is computed by employing textual analysis of the definitions of the concepts fetched from the Wikipedia encyclopedia.Comment: 12 pages, Conference on Intelligent Computer Mathematics 2013 Bath, U

Intergeo: Interoperable Interactive Geometry for Europe

10 pages http://www.icvl.eu/2008/International audienceIntergeo (http://inter2geo.eu/) is an eContent+ European project dedicated to the sharing of interactive geometry constructions. It will enable teachers and pupils all over Europe to participate from experiences made by pioneers in the field of interactive geometry as a tool for teaching, learning, and research. Educational contents that were hard to access are made available in a common interoperable format. Tagged with relevant topics and competency based metadata and categorised according to curricula, they will be searchable and easily (re­)usable by everyone. It will impact the value chain in e­Learning, by providing building blocks of quality controlled, semantically enriched interactive educational content, on all levels from K­12 to university, for classrooms, on­line courses, or integrated digital education systems. This project will help a multicultural community, built around interoperable quality controlled e­Learning standards, to emerge and sustain itself with a wider audience than the present days niche of dedicated experts, which would not happen by market forces alone

Mathematics teacher education advanced methods: an example in dynamic geometry

International audienceWe present a research work about an innovative national teacher training program in France: the Pairform@nce program, designed to sustain ICT integration. The Pairform@nce trainings are grounded in a principle of collective lesson design by teams of trainees; they associate face-to-face and distant training. We study here a training for secondary school teachers, whose objective is to foster the development of an inquiry-based approach in the teaching of mathematics, using investigative potentialities of dynamic geometry environments (DGE). We adopt the theoretical background of the documentational approach to didactics for studying how a training organizing the design of lessons by teachers teams can contribute to teacher professional development, directed in particular towards more inquiry in the classroom supported by DGE. This approach conceptualizes the interactions between teachers and resources as geneses: complex, long-term processes, associating evolutions and stability. In the frame of this approach, for studying these geneses, we develop a specific methodology: we organize a follow-up of teachers during several weeks; during this period, the teachers fill a logbook describing their activity; they answer to questionnaires and interviews; we also collect as completely as possible the material resources involved in their work. We followed in particular the work of a team of trainees; drawing on the data collected, we analyse their professional development, related with the training. We discuss on a more general level, the consequences of a training based on collective documentation work for the integration of technology by mathematics teachers

Defining and Classifying Learning Outcomes: A case study

Bologne came to globalize education in higher education, creating a unified architecture that potentiates higher education and enhances the continued interconnection of the spaces of education policy in higher education in the world, in particular in Europe. The aim of this work consists in the presentation of an identification model and skills’ classification and learning outcomes, based on the official documents of the course units (syllabus and assessment components) of a course of Higher Education. We are aware that the adoption of this model by different institutions, will contribute to interoperability learning outcomes, thus enhancing the mobility of teachers and students in the EHEA (European Higher Education Area) and third countries

Apprendre, enseigner, se former en mathématiques : quels effets des ressources: Actes des journées mathématiques de l'INRP 2010

Cette question a été mise à l'étude lors des 5e journées mathématiques de l'INRP qui se sont tenues à Lyon en juin 2010. Ces journées rassemblent les membres des groupes INRP travaillant en mathématiques, mais sont également largement ouvertes à des chercheurs intéressés par les thématiques retenues. Il s'agissait ici de se pencher sur des ressources élaborées à des fins d'enseignement et/ou de formation d'enseignants, et d'amorcer une réflexion allant dans la direction de l'efficacité des ressources et de leurs usages. Ces journées ont comporté trois conférences : - Enseignants et élèves dans le laboratoire de mathématiques, (Michela Maschietto, Università di Modena e Reggio Emilia, Italie) - Recherches sur l'enseignement des mathématiques et équipes de professeurs associés à l'INRP : genèses de ressources et de réseaux (Luc Trouche, INRP) - L'écologie des parcours d'étude et de recherche au secondaire (Marianna Bosch, Universitat Ramon Llull, Espagne) Elles ont également donné lieu à trois ateliers thématiques : - atelier 1 : Ressources, démarches d'investigation et résolution de problèmes - atelier 2 : Ressources, usage des technologies en mathématiques et en sciences et démarches d'investigation - atelier 3 : Ressources, critères de qualité pour la conception et les usages Ces actes présentent les textes de ces conférences et ateliers. http://www.inrp.fr/editions/editions-electroniques/apprendre-enseigner-se-former-en-mathematique

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

Evaluación de un programa de formación de profesores de matemáticas de secundaria y media: prácticas de planificación e implementación

Evaluar programas de formación de profesores es importante porque permite, entre otras cosas, apreciar la pertinencia del diseño y la implementación de los programas a las necesidades de formación y valorar si se han logrado los cambios previstos en las prácticas curriculares de los participantes. El foco de esta tesis doctoral es la evaluación de un programa de formación de profesores de matemáticas de secundaria y media que participó en la política pública de formación de profesores “Excelencia docente” del Ministerio de Educación (MEN): la Maestría en Educación Matemática, de la Universidad de los Andes. Para este propósito, en una primera parte, presento la relevancia del estudio, el marco conceptual y los objetivos de investigación. En la segunda parte, incluyo cinco manuscritos y artículos en los que caracterizo los profesores participantes del programa de formación desde sus prácticas de planificación e implementación del currículo de matemáticas, comparo sus prácticas curriculares de planificación, implementación y evaluación antes y después de participar en el programa, formulo un modelo de toma de decisiones del profesor y presento evidencia del funcionamiento del modelo de toma de decisiones. Finalmente, cierro con un capítulo de conclusiones en el que describo los objetivos logrados y las líneas de investigación futuras con motivo de este trabajo