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Le difficoltà degli studenti in Teoria degli Spazi Vettoriali viste da due prospettive teorche diverse
No full textSTRAITGH ON THE SPHERE: MEANINGS AND ARTEFACTS
No full textThis report is drawn from a teaching intervention which aims at introducing spherical geometry in a primary school. Assuming a perspective according to which learning should involve students in processes leading to the explicit formulation and elaboration of meanings, this report is meant to explore the dynamics between students’ elaboration of meanings emerging from an activity with artefacts and students’ explicit reflection on the use of the artefacts themselves
Il problema del raccordo Scuola Superiore - Università
No full textIn a moment when few students enrol in courses within the Faculty of Science, the problem of first year undergraduates’ difficulties in mathematics has become a social issue. The main consequences for students are a delay in graduating and, sometimes, the feeling that they made the wrong choice. Lately, a number of initiatives have been undertaken by both the Ministry and the Universities in order to stem this phenomenon.
In this paper, we look at students’ difficulties in mathematics from a perspective that is opposed to that viewing the only origin of these difficulties in students’ lack of preparation. Our “alternative” interpretation guided us in the design and planning of preliminary courses that have been organised over the past five years by the University of Pisa’s Faculty of Science and set up by a working group including both the authors. We will try to account for the specific nature of these courses through a description of objectives, part of the original materials produced and used during the sessions and methodology underlying the actual development of the session
Le difficoltà in matematica nel passaggio Scuola Superiore - Università: dalla teoria alla pratica
No full textUn artefact comme outils de médiation sémiotique : une ressource pour l’enseignant
No full textRésumé
Ce chapitre considère les questions de médiation sémiotique posées par le développement du numérique. Il examine comment le professeur peut exploiter dans la classe le potentiel sémiotique d’un artefact, et comment un tel artefact peut se constituer en instrument de médiation sémiotique pour le professeur.
Le potentiel de médiation de chaque artefact réside dans le double lien sémiotique qu’il réalise, d’une part avec les significations qui émergent de son utilisation pour la réalisation d’une tâche, d’autre part avec les significations potentielles qui pourraient émerger de cette utilisation, telles qu’un expert peut les identifier. De ce point de vue, chaque artefact peut être considéré à la fois d’un point de vue individuel – par exemple l’élève mobilisant un outil pour réaliser une tâche – et d’un point de vue social – par exemple le corpus de significations partagées d’une communauté d’experts, mathématiciens ou enseignants de mathématiques. Dans une perspective socio-culturelle, la tension entre ces deux points de vue est le moteur d’un processus d’apprentissage-enseignement centré sur l’utilisation d’un artefact. Cette double relation sémiotique suscitée par un artefact peut devenir l’objet d’une analyse a priori, impliquant simultanément deux perspectives entrelacées, cognitive et épistémologique. La coordination de ces deux directions d’analyse conduit à l’identification du potentiel sémiotique d’un artefact, qui peut être mis en relation avec des buts éducatifs particuliers. Au-delà, mais de façon non contradictoire, avec l’objectif de rendre l’artefact transparent, ou de “transformer les outils en instruments mathématiques” (Guin & Trouche 1999), cette approche se focalise sur les processus d’apprentissage impliquant un artefact, en utilisant un regard sémiotique. Le modèle théorique proposé décrit l’apprentissage comme une interaction sociale, où l’évolution des signes est intentionnellement organisée et dirigée par l’enseignant. En résumé, d’une part nous reconnaissons les potentialités sémiotiques d’un artefact et son usage dans la réalisation d’une tâche, par rapport à une connaissance mathématique spécifique, d’autre part nous assignons un rôle crucial à l’enseignant qui est supposé agir comme médiateur culturel. La structure d’une séquence d’enseignement peut être décrite comme une itération de ce que nous avons appelé un cycle didactique où différentes typologies d’activités prennent place, visant à développer un processus sémiotique complexe.
Cette perspective prend en compte le rôle du professeur, et fournit la base pour un modèle explicite de ce qui est attendu de celui-ci. Nous voulons préciser ce modèle, avec l’objectif d’éclairer la manière dont le professeur peut utiliser l’artefact pour accomplir ses tâches didactiques. Il s’agit donc d’analyser le rôle spécifique joué par l’artefact comme ressource pour le professeur. Dans le fil de l’approche instrumentale (Rabardel 1995), en exploitant la notion de schème d’utilisation, nous analysons le développement, par le professeur, de cet artefact en instrument de médiation sémiotique. Plus particulièrement, nous nous centrons sur les actions du professeur médiées par l’artefact, concernant l’orchestration de la discussion de classe
Dai precorsi al progetto P.O.R.T.A.: lavori in corso sul problema del raccordo Scuola Superiore - Università"
No full textIl passaggio dalla Scuola Superiore all’Università è, sicuramente, uno dei momenti più importanti e di conseguenza delicati nel percorso educativo degli studenti che proseguono gli studi dopo la scuola superiore. La scelta del Corso di Laurea può incidere sul futuro dello studente sia in termini di successo/insuccesso negli studi che di prospettive lavorative eppure spesso tale scelta è fatta senza la necessaria consapevolezza. D’altra parte per molto tempo Scuola e Università sono stati due mondi quasi separati con pochi rapporti e pochi scambi di informazioni e solo negli ultimi anni sono nati progetti strutturati di orientamento alla scelta universitaria.
Ma le difficoltà legate al passaggio Scuola Superiore – Università non sono limitate solo alla scelta del Corso di Laurea: ci sono sicuramente difficoltà di carattere socio-ambientale (lo studente si trova a dover ricostruire una serie di rapporti in un contesto molto diverso da quello a cui era abituato, basti pensare al rapporto con il docente) e più specifiche su alcuni insegnamenti universitari. A questo proposito i corsi di matematica la fanno tristemente da padrone: le statistiche ufficiali (poche e un po’ datate per la verità) registrano come soltanto una percentuale piuttosto bassa delle matricole della Facoltà di Scienze (escludendo quelle di Matematica e Fisica) superino durante il primo anno gli esami previsti per gli insegnamenti di matematic
Semiotic mediation within an AT frame
No full textThis article is meant to present a specific elaboration of the notion of mediation in relation to the use of artefacts to enhance mathematics teaching and learning: the elaboration offered by the Theory of Semiotic Mediation. In particular, it provides an explicit model – consistent with the activity-actions-operations framework – of the actions which are expected from the teacher in order to make mathematics learning occur through the mediation of an artefact. The teacher’s actions are identified by their goals and are related to the motive of the teaching-learning activity
Resources for the teacher from a semiotic mediation perspective
No full textAbstract
The potential of ICT tools for learning have been extensively studied, with a main focus on their possible use by students and the subsequent benefits for them. However, there has been the tendency to underestimate the complexity of the teacher’s role in exploiting this potential. In this chapter, we assume a semiotic mediation perspective and discuss different kinds of resources which are offered to teachers to enhance the teaching–learning activity centred on the use of an ICT tool: by resource for the teacher we mean any artefact which may help the teacher accomplish her educational objectives. Taking a semiotic mediation perspective means to acknowledge the central role of signs in teaching–learning activity: the focus is on semiotic processes, specifically production of signs and their transformation. Fostering or guiding these processes is a crucial issue and a demanding task for the teacher. Consequently, from such a perspective, a resource for the teacher is any artefact that can help her promoting and sustaining the development of those semiotic processes. In this chapter, we discuss the teacher’s use of specific resources – namely written texts – with respect to the semiotic processes which she is expected to orchestrate in the different moments of the teaching sequence
The secondary-tertiary transition: beyond the purely cognitive
No full textTransition from secondary to tertiary level is an important issue in mathematics education, indeed this transition is often problematic for many students. University spontaneously reacts through running bridging courses, lowering the level of the mathematics taught, or reducing the examination standards in order to avoid massive failure. For different reasons these reactions rarely proved to be effective. Instead, research in mathematics education highlights that students’ difficulties are related to a multiplicity of factors – cognitive, meta-cognitive, affective and linguistic – the incidence of which is amplified when accessing tertiary education. Starting from these findings, the authors designed and developed two parallel mathematical “university preparatory” courses for grade 12-13 students
Synergies between theoretical approaches to mathematics education with technology: A case study through a cross-analysis methodology
No full textMathematics education as a research domain is characterized by a plurality of theoretical approaches. Acknowledging the existence of such diversity and the risks of an excessive theoretical fragmentation does not mean to search for a unifying theory but to urge the community to develop strategies for coping with this diversity. This article is meant to show the potential of a “cross-analysis” methodology for establishing connections between different theoretical approaches to mathematics education with technology. Within the frame of the ReMath European Project, two Teaching Experiments were realized, centred on the use of a same ICT tool—Casyopée. Two distinct theoretical approaches shaped both the Teaching Experiments design and their enactments: the Theory of Didactical Situations and the Theory of Semiotic Mediation. The two Teaching Experiments have then been analysed from both theoretical points of view. In this article we will provide some examples drawn from this cross-analysis that show the synergy which can be established between the aforementioned theoretical approaches. Beyond contributing to a deeper understanding of the observed “didactical phenomena”, that synergy allows establishing connections between the two approaches that lead to their reciprocal enrichment
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