MULTI-SCALAR SURVEYS FOR COMPLEX ARCHITECTURES

Abstract. This study is part of a much wider project in which professors and researchers from the University of Naples Federico II and the University of Campania Luigi Vanvitelli are collaborating in different subject areas. The object of study is the ancient Sanctuary of Montevergine characterized by a long history of transformations and stratifications. Driven by the desire to fill a singular gap, linked to the lack of a systematic and comprehensive study of a complex whose first settlement dates back to the early 12th century, various studies have been started relating to the historical, artistic and architectural aspects.Various surveying techniques and methods had to be used due to its architectural, compositional and settlement characteristics. Integrated 3D surveying technologies were used for both the cognitive studies of the entire complex as well as for investigating and detecting the elements at different scales, ranging from the architectural to the detailed ones

Un'esperienza di utilizzo del Tangram in attività di Matematica nella Scuola Media

In this work we have tried to give an example of how one, through creative games, can find a tangible verification of studied notions, receive stimuli and motivations for the study of Mathematics and directly be begun, in a natural way, to the pleasure and the methodology of the research. In particular we have tried to make the reader discover or revisit with new eye topics such as: homotheties, graphs, convex sets, isometrics and tessellations of the plane

Logo & Problemi: Conversazione a tre "voci"

In the paper we show, through a hypothetical "conversation" among two pupils and a computer, how it is possible to use the Logo language in interactive way for solving verbal poblems with the top-down method.The interaction man-machine is very simple: it is based on the primitives OUTPUT and TRACE of the Italian version of Logo Commodore and on the particular type of its messages of error.In the paper we present, in an unusual manner, a trace of the work developed with pupils aged 11-12, for a concrete and motivated approach to the analysis of problems and to their decomposition in to subproblems.The theme has been chosen for the importance that this method assumes both in the problem solving and in the approach to the structured programming

The Interweaving of Arithmetic and Algebra: Some Questions About Syntactic, Relational and Structural Aspects and their Teaching and Learning

After a brief introduction and a few general considerations on syntactic difficulties in the interweaving of arithmetic and algebra, we analyse the conflict between additive and multiplicative notation in arithmetic-algebraic realm and present the first results of some activities carried out according to our hypothesis of research with the aim of overcoming such conflict and promoting the semantic control of complex writings. We conclude with some reflections concerning the choice and difficulties of the didactic activities in middle school on these topics

Theory and Practice: a Case of Fruitful Relationship for the Renewal of the Teaching and Learning of Algebra

The paper consists of three parts. After presenting the viewpoint of different authors on the feedback of theoretical studies onto the teaching praxis, in the first part we portray the Italian model of research for innovation and explain its genesis together with its latest evolution, particularly the role of 'teacher-researcher'. The second part is specifically devoted to one of our innovative long-term projects, about the teaching/learning of algebra, and it focuses the attention on the teachers' behaviour. We specify the theoretical frame in which this problem is located, the problems concerning its starting up with reference to the teachers' preconceptions and beliefs, what kind of interventions and how they were carried out with and for the teachers, so that they could see and get in tune with the main objectives to be pursued in such a research. We produce examples of their contribution to the development of the project and of the feedback of the activity in the pupils. The third part contains a reflection on the problems that arise on enacting researches according to this model, both from the point of view of the teachers involved and from that of the director of the research. In particular, we first concentrate on some problems that the teachers have to face when they approach the double role of teacher-and-researcher, on what influence the development of the research can undergo owing to their beliefs or to the environment in which they work. Then we analyse the more general problem of the social incidence of such a research, also with reference to the present status of the Italian system for teacher training

Un aspetto di un percorso didattico per l’aproccio al concetto di funzione

Si espongono alcuni risultati di una ricerca rivolta all'intero triennio di scuola media, finalizzata al coordinamento dei vari registri di rappresentazione per le funzioni (verbale, numerico-tabulare, grafico e algebrico), mettendone in luce aspetti problematici legati alla sua realizzazione. In particolare ci si sofferma sulle difficoltà incontrate dagli allievi ed ai problemi didattici che si pongono in riferimento a particolari attività realizzate in classi seconda e terza e rivolte rispettivamente a: i) il riconoscimento, tra una serie data, del grafico corrispondente ad un certo fenomeno fisico descritto verbalmente; ii) la trasformazione di funzioni algebriche esprimenti una stessa relazione nelle tre forme possibili (le due esplicite e quella implicita) e la costruzione contemporanea dei relativi grafici

Il numero naturale e le sue proprieta’: loro varianza e invarianza rispetto alla rappresentazione

Si espongono i risultati di un percorso didattico sperimentato in una prima media riguardante i legami tra numeri naturali, loro rappresentazioni e loro proprietà. Il percorso, complesso per la classe in cui si è attuato, prende le mosse dal riesame dell’abaco per recuperare competenze aritmetiche di base, per dare consapevolezza della generalità della rappresentazione polinomiale al variare della base ed inoltre per individuare proprietà del numero dipendenti o indipendenti dalla rappresentazione. Tra i risultati raggiunti dagli allievi si segnalano la flessibilità nell’accettare tante rappresentazioni diverse di un numero e l’individuazione di sue proprietà evidenziate da particolari rappresentazioni. Il percorso appare problematico circa i tempi di attuazione per allievi con difficoltà

Avvio ad attività di matematizzazione attraverso problemi

Si riportano le linee guida ed i primi risultati di una ricerca, avviata con allievi di 11-12 anni, finalizzata a promuovere in essi la capacità di matematizzare situazioni problematiche e di migliorare i loro atteggiamenti e prestazioni di fronte a "il problema". La ricerca si è sviluppata intorno ad alcuni problemi-chiave, che rispecchiano situazioni reali e dove occorre capire quali sono i quesiti da porsi, i dati utili, le difficoltà o il costo del loro reperimento, ed è incentrata su una particolare strategia, finalizzata ad indurre gli allievi ad "ottimizzare" i procedimenti di soluzione. I primi risultati mostrano negli allievi l'acquisizione di una concezione più ampia de "il problema" e la capacità di porsi di fronte ad esso in modo ipotetico, cosa che promuove in essi la metaconoscenza e ne migliora le capacità risolutive