Books by Michela Maschietto
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Che cosa sono le macchine matematiche? Una macchina matematica (in un contesto geometrico) è uno ... more Che cosa sono le macchine matematiche? Una macchina matematica (in un contesto geometrico) è uno strumento che ha uno scopo fondamentale: obbligare un punto, o un segmento, o una figura qualsiasi a muoversi nello spazio o a subire trasformazioni seguendo con esattezza una legge astrattamente, matematicamente determinata. Le macchine matematiche sono tra gli strumenti suggeriti per l'attività di laboratorio, nella proposta di nuovi curricoli avanzata dall'Unione Matematica Italiana. Una ampia collezione di macchine (oltre 200), di interesse storico e didattico, è stata ricostruita a Modena, dove è collocato, presso il Dipartimento di Matematica, un laboratorio di ricerca per la didattica della geometria con lâuso di strumenti (il Laboratorio delle Macchine Matematiche). Sono stati ricostruiti curvigrafi, pantografi, prospettografi, modelli tridimensionali di solidi e di curve sezione, strumenti per la soluzione di problemi. Quasi tutti i modelli, realizzati in legno naturale ed effettivamente funzionanti, sono ripresi da fonti storiche dall'antichità classica all'Ottocento. Il Laboratorio è aperto alle scuole su prenotazione e realizza mostre, allestimenti espositivi, laboratori interattivi. L'attività del Laboratorio è coordinata dalle due autrici, con la collaborazione dei membri dell'Associazione di promozione sociale Macchine matematiche. In questo libro sono raccolti i risultati di oltre vent'anni di ricerche didattiche sul tema, realizzate in Italia e all'estero, in tutti gli ordini scolastici.
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Papers by Michela Maschietto
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Science & Education, 2024
We introduce a geometric-mechanical artefact designed for laboratory activities related to Calcul... more We introduce a geometric-mechanical artefact designed for laboratory activities related to Calculus topics (3D models and construction instructions are freely available online). With new capabilities and a new design, this instrument adopts some mechanisms historically introduced to solve inverse tangent problems (that analytically correspond to solving differential equations). By such an instrument, besides materially revealing the tangent to a curve (tangent mode), it is possible to trace the graph of exponential functions and parabolas starting from the geometrical properties of their tangent (curvigraph mode). Furthermore, one can perform transformations as derivatives and integrals (transformation mode). Our research project aims to study the use of this artefact mainly for secondary school students. In this paper, we present the analysis of its semiotic potential, referring to the instrumental approach and the Theory of Semiotic Mediation. We also focus on a secondary school teacher manipulating the artefact to identify exploration processes and gestures of usage. The analysis supports the choice of starting the exploration in the tangent mode and suggests that the artefact fosters the emergence of the idea of the tangent line.
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European Research in Mathematics Education II 542 THE TRANSITION FROM ALGEBRA TO ANALYSIS: THE US... more European Research in Mathematics Education II 542 THE TRANSITION FROM ALGEBRA TO ANALYSIS: THE USE OF METAPHORS IN A GRAPHIC CALCULATOR ENVIRONMENT Michela Maschietto Dipartimento di Matematica, Università di Torino, Italy maschietto@ dm. unito. ...
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In questo articolo si presentano elementi del progetto di ricerca sul duo di artefatti costituito... more In questo articolo si presentano elementi del progetto di ricerca sul duo di artefatti costituito dalla macchina aritmetica pascalina Zero+1 e dalla sua controparte digitale, la e-pascalina. Tale progetto, condotto in collaborazione tra ricercatori e insegnanti italiani e francesi, riguarda sia la progettazione della e-pascalina e di quaderni informatici che la includono, sia le sperimentazioni di un percorso didattico. L\u2019analisi di queste ultime permettono di discutere potenzialit\ue0 e criticit\ue0 del duo e della sua implementazione didattica.This article presents elements of the research project on the duo artefacts consisting of the arithmetical machine pascaline Zero + 1 and its digital counterpart, the e- pascaline. This project is carried out in collaboration between Italian and French researchers teachers. It concerns the design of the e- pascaline and e-books including the e-pascaline as component and associated teaching experiments. The analysis of the latter makes it possible to discuss potentiality and critical points of the duo and its teaching implementation
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International Group for the Psychology of Mathematics Education, Jul 1, 2004
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Iris Unimore (University of Modena and Reggio Emilia), 2017
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Questo contributo presenta una sperimentazione didattica sul Teorema di Pitagora nell\u2019ambito... more Questo contributo presenta una sperimentazione didattica sul Teorema di Pitagora nell\u2019ambito del laboratorio di matematica con artefatti fisici, quali le macchine matematiche (Bartolini Bussi & Maschietto, 2006), nella scuola secondaria di I grado. Il Teorema di Pitagora \ue8 un argomento classico che di solito viene introdotto durante il secondo quadrimestre della classe seconda, dopo aver presentato agli alunni le radici quadrate in aritmetica e l\u2019area delle figure piane in geometria. La scelta di proporre il percorso che sar\ue0 qui descritto \ue8 nata da un lato dalla constatazione che, anche nei risultati della prove di valutazione nazionali, la geometria rappresenta lo scoglio maggiore per gli alunni, dall\u2019altro dall\u2019interesse dell\u2019insegnante di proporre un diverso modo di affrontarla
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Educational Studies in Mathematics, Oct 28, 2008
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International Journal of Computers for Mathematical Learning, Nov 25, 2008
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In this overview of CERME10 Working Group 4, on Geometry Education, the three main issues address... more In this overview of CERME10 Working Group 4, on Geometry Education, the three main issues addressed during the working group were the role of material activity in the construction of geometrical concepts (including the use of instruments, manipulation, investigation, modelling, and so on), the nature of visualization and spatial skills, and the issues of language, proof and argumentation. In terms of the role of material activity, the group noted that there is a true need for improving the ‘networking’ between the didactical approach and the psychological approach concerning the use of tools. In terms of the nature of visualization and spatial skills, the group noted the interconnections. In addressing language, proof and argumentation, the group noted the focus on ways of motivating proofs or argumentation.
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The paper will summarize the work of the Modena team on gestures. Such studies draw on the classi... more The paper will summarize the work of the Modena team on gestures. Such studies draw on the classical analysis of the shift from grasping to pointing in the social interaction of the pair baby-mother. We have studied the essential function of gesturing in classroom situations for the construction of scientific meanings and processes. In particular, in our previous papers concerning experiments in grades 4 and 5, we have focused the generalising potential of gesturing (in contrast with other iconic representation media, which, rather, risk to fix the particular emergences of phenomena). In the former we have studied the genesis of a germ theory of the functioning of gears, from gestures to arrows and to general, abstract and conditional statements. In the latter we have studied the construction of the meaning of painting as the intersection between a plane (the picture plane) and the visual pyramid as meant by the early theoreticians of perspective drawing, by means of \u2018cutting\u2019 gestures that mime in the space the intersection of an ideal solid, in situations of social interaction. Our results are consistent with the findings of Roth & Lawless who claim that \u201cin terms of conceptual development, gestures express features of scientific concepts and relations prior to the equivalent representation in verbal discourse. That is, gestures appear to scaffold the emergence of students\u2019 observational and theoretical language about the phenomena they study"
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EMS magazine, Sep 13, 2022
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Books by Michela Maschietto
Papers by Michela Maschietto