435 research outputs found
Strategie di conteggio del numero delle facce, dei vertici e degli spigoli di un poliedro
No full textAbstract. Si discutono i risultati di un'indagine, svolta a diversi livelli di età e riguardante i processi mentali coinvolti nel ragionamento geometrico. Il quadro di riferimento è quello dei concetti figurali (Fischbein, 1993, Mariotti, 1992). Il ragionamento geometrico è descritto come dialettica tra aspetto figurale e aspetto concettuale, tale dialettica è descritta con esempi tratti dalle interviste con allievi
La dimostrazione e la sua pratica nell'insegnamento della matematica
No full textL'articolo è una traduzione e adattamento del capitolo :
Mariotti M.A. (2006) Proof and proving in mathematics education. A. Gutiérrez & P. Boero (eds) Handbook of Research on the Psychology of Mathematics Education, (pp. 173-204) Sense Publishers, Rotterdam, The Netherlands. ISBN: 9077874194 , pp. 173-204
From using artefacts to mathematical meanings: the teacher’s role in the semiotic mediation process
No full textThe didactic potential of artefacts 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 exploiting this potential, and specifically the
complexity of the teacher’s role orchestrating the teaching
and learning process. Following Vygotskij’s seminal idea of
semiotic mediation, the theoretical framework of Theory
of Semiotic Mediation (TSM) has been developed (Bartolini
Bussi & Mariotti, 2008) with the aim of providing a teaching
and learning model, where attention is focused on the
semiotic processes related to the use of cultural artefacts.
Through the semiotic lens it is possible to analyse the classroom
discourse and highlight specific patterns in the teacher’s
action that make students’ personal meanings evolve towards
the mathematical meanings that are the objective
of the didactic intervention. The paper presents a first model
of the teacher’s action and provides some examples drawn
from long term teaching experiments carried out at the primary
school level
Geometrical proof: the mediation of a microworld
No full textAbstract. From a didactic point of view, the introduction of a deductive approach presents two interwoven aspects to be developed: on the one hand the need of justification and on the other hand the idea of a theoretical system within which that justification may becomes a proof. Proof makes sense in respect to a theory and vice versa; thus, the introduction of a deductive approach presents two problems of sense, which are interrelated: the sense of proof and the sense of theory.
Thus, the first difficulty the teacher has to overcome, is related to developing the need of a justification, and this contrasts with the intuitive approach to which pupils are used, the second difficulty is related to the possible cognitive rupture between argumentation, i.e. a set of arguments supporting the acceptance of a statement, and mathematical proof, validating a statement within a theory.
After analysing the nature of these difficulties, the author discusses how it is possible to face these crucial educational issues presenting the choice of a specific "field of experience" (Boero et al., 1995): geometrical constructions within a particular Dynamic Geometry Environment (Cabri- géomètre
Reasoning By Contradiction in Dynamic Geometry
No full textThis paper addresses contributions that dynamic geometry systems (DGSs) may give in reasoning by contradiction in geometry. We present analyses of three excerpts of students’ work and use the notion of pseudo object, elaborated from previous research, to show some specificities of DGS in constructing proof by contradiction. In particular, we support the claim that a DGS can offer “guidance” in the solver’s development of an indirect argument thanks to the potential it offers of both constructing certain properties robustly, and of helping the solver perceive pseudo objects
From action to symbols: giving meaning to the symbolic representation of the distributive law in primary school
No full textThe use of artifacts to introduce the distributive law of multiplication over addition in primary school is a diffused approach: it is possible to find pre-constructed learning trajectories in instructional materials. However, it is still unclear how the teacher might support his/her students in transitioning from concrete to symbolic representations of the distributive law. In the theoretical frame of the Theory of Semiotic Mediation, we report on a study where Laisant’s table, an artifact embodying the rectangular model of multiplication, is used to introduce distributive law in second grade. Taking a microanalytical approach, we show how a group of students connects the representation provided by the artifact with the symbolic representation of the arithmetic property (as equivalence of numerical sentences). Two different semiotic chains are identified and presented, showing the continuity between the activity with the artifact and the mathematical signs emerging in following activities and promoted by tasks specifically designed. The role of the teacher in triggering and scaffolding this process is highlighted
Introduzione alla dimostrazione all'inizio della scuola secondaria superiore
No full textAbstract A research project was carried out with the main objective of studying the possibility of introducing a deductive approach to geometry. The experiment concerns the activities at 9th and 10th grade level (14 - 16 year old pupils).
The main point we were interested in concerned the change of the status of justification in geometrical problems. This modification is strictly related to the passage from an 'intuitive' geometry as a collection of facts submitted to empirical verification, to a 'theoretical' geometry, as a system of relations among statements, validated by proof. The experience is centred on the activity of construction, in particular in the Cabri environment; and aims to introduce pupils to the theoretical meaning of justification.
The main ideas which constitute the theoretical reference frame are the following.
* The theory of figural concepts.
* The Cabri-géomètre environment as a "context" for the construction of the meaning of proof.
* The collective discussion as a basic element in the social construction of knowledge
L'approccio psicologico nella didattica della matematica
No full textAbstract. Si analizzano i rapporti tra teorie psicologiche nel campo dell'apprendimento e le problematiche specifiche della didattica della matematica. In particolare si discute alcuni esempi tratti dall aletteratura corrente
Artefacts and instruments for mediating mathematical meanings
No full textSpecial Issue Joint Meeting of UMI-SIMAI/SMAI-SMF "Mathematics and its Applications" , Torino, July 6th 200
Lo zero è un problema?
No full textAbstract. Analisi delle intuzioni legate al concetto di zero. i dati raccolti tramite un questionario mettono in evidenza un problema generale riguardante il calcolo delle espressioni algebriche legato all'instaurarsi di un contratto didattico specifico relativo al calcolo. In particolare, lo zero si presenta come elemento distruttore di controlli e pertanto genera occasioni di errore
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