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This study presents a quantitative approach based on Differential Item Functioning analysis within the Item Response Theory framework, to quantify gender differences in tackling specific mathematical items. We use this approach to explore two crucial topics in mathematics education (misconceptions in decimal numbers, and estimation) by analysing answers given by Italian students to specific mathematical items taken from a sample of 1400 items administered in INVALSI tests since 2008. For each item, we have a sample of 30,000 students per year, statistically representative of the entire Italian student population. The results section presents a didactic interpretation of the statistical evidence and shows how interdisciplinarity between statistics and mathematics education, with a mixed-method approach (Johnson & Onwuegbuzie, 2004), represents a good approach to exploring the gender gap in relation to specific constructs of math education. This approach, common in many disciplines, can also make an interesting contribution to mathematics education research.

Mathematics can help analyze the arts and inspire new artwork. Mathematics can also help make transformations from one artistic medium to another, considering exceptions and choices, as well as artists' individual and unique contributions. We propose a method based on diagrammatic thinking and quantum formalism. We exploit decompositions of complex forms into a set of simple shapes, discretization of complex images, and Dirac notation, imagining a world of "prototypes" that can be connected to obtain a fine or coarse-graining approximation of a given visual image. Visual prototypes are exchanged with auditory ones, and the information (position, size) characterizing visual prototypes is connected with the information (onset, duration, loudness, pitch range) characterizing auditory prototypes. The topic is contextualized within a philosophical debate (discreteness and comparison of apparently unrelated objects), it develops through mathematical formalism, and it leads to programming, to spark interdisciplinary thinking and ignite creativity within STEAM., Comment: Accepted for publication, Journal of Mathematics and Music. New references added in this version

Can we use mathematics, and in particular the abstract branch of category theory, to describe some basics of dance, and to highlight structural similarities between music and dance? We first summarize recent studies between mathematics and dance, and between music and categories. Then, we extend this formalism and diagrammatic thinking style to dance., preprint

In computer science, the notion of service is a broad term that incorporates any IT service delivered and accessible globally from the Internet. With the arrival of social networks and the pervasive entry of IT into business infrastructures, the population of (web-based) Internet service has grown large enough to turn the need, acquisition, delivery, maintenance and upgrade of computing resources into real strategic challenges. Along with the technology evolution and the growth experienced on the available information, the resource demand has been increasing in both science and engineering marketplaces. To satisfying the growth in resource demand, there have been attempting to enhance the resource-efficiency of delivered service to users, i.e., the effective utility from the available resources, before investing in additional compute resources, in an attempt to maximize their business competitiveness and return on investment of their infrastructures. Accordingly, one of the significant features that make cloud computing an attractive service-oriented architecture for competitive business is: elasticity, i.e., the ability to scale up/down the resources on-demand together with pay-per-use pricing model which eliminates the need for massive up- fronts investment in local infrastructure, a model that was not economically feasible in the era of traditional enterprise infrastructures.Therefore, the work in this thesis had the focus on improving performance and resource utilization of service in Cloud environment.

Durante i tre anni di dottorato di ricerca in Formazione della persona e mercato del lavoro ho lavorato alla progettazione di un curricolo scolastico per matematica, poi realizzato all'interno dell'indirizzo di Operatore della ristorazione e Servizi di Sala e Bar, nell? IeFP Oliver Twist presso Cometa Formazione a Como. All? interno della collaborazione con la scuola ho rivestito il ruolo di docente di matematica per gli studenti delle classi dalla prima alla quinta. Ho progettato un curricolo di matematica basato sulla metodologia dal fare al sapere, per le classi del triennio, realizzando anche una dispensa per gli studenti. Lo scopo del mio lavoro di ricerca � stato quello di ripensare al curricolo di matematica per stimolare l?interesse e la motivazione degli studenti verso questa disciplina. � risaputo infatti che la maggior parte degli studenti frequentanti gli IeFP non sono interessati alla matematica perch� la percepiscono spesso inutile in relazione alla professione che hanno scelto. Per fare ci�, ho tentato di rivisitare l?attuale curricolo di matematica ripensando alla modalit� di trattazione dei temi proposti e facendo in modo che fosse in stretta sinergia con gli aspetti professionali pi� rilevanti. Al fine di rendere il pi� realistica possibile la progettazione di questo curricolo, senza tralasciare le competenze espresse negli OSA, � stato necessario confrontarmi continuamente con i colleghi docenti professionisti nei settori di sala, bar, cucina e pasticceria. Per agevolare la comprensione della sfera professionale esaminata, quella ristorativa, ho simulato con i colleghi la realizzazione di un evento, generalmente realizzato dagli studenti, cos� da poter cogliere tutti gli aspetti di questa professione che richiedono una competenza matematica e poterla poi trasmettere correttamente e in modo funzionale agli studenti stessi. Oltre alla realizzazione della dispensa studenti e alla rivisitazione del curricolo in matematica, l'attivit� di ricerca si � anche occupata di monitorare e analizzare l'andamento delle valutazioni degli studenti che hanno potuto vivere in prima persona un percorso d'apprendimento cos� costruito. Si � inoltre indagata attraverso un questionario la percezione che hanno avuto gli studenti.

International audience; Levering on the influence and use of social media in students' perception of learning mathematics, this project has a twofold purpose: the research aim is to contribute in breaking away from the idea that digital culture can be considered as opposed to school culture, investigating the epistemic and didactical affordances of mathematical Internet memes, combined with Augmented Reality technology. The coupled educational aim is to cultivate classroom discourse and maximize linguistic and cognitive meta-awareness in high school students. The project is a work in progress of which this paper presents the theoretical background used to frame the study, the results of a first exploratory teaching experiment - conducted with a group of 24 students attending the 12th grade of Liceo Scientifico in Milan - and the methodology and the next steps of the study.

This study is aimed at exploring how different formulations of the same mathematical item may influence students’ answers, and whether or not boys and girls are equally affected by differences in presentation. An experimental design was employed: the same stem-items (i.e., items with the same mathematical content and question intent) were formulated differently and administered to a probability sample of 1647 students (grade 8). All the achievement tests were anchored via a set of common items. Students’ answers, equated and then analysed using the Rasch model, confirmed that different formulations affect students’ performances and thus the psychometric functionality of items, with discernible differences according to gender. In particular, we explored students’ sensitivity to the effect of a typical misconception about multiplication with decimal numbers (often called “multiplication makes bigger”) and tested the hypothesis that girls are more prone than boys to be negatively affected by misconception.

If abstraction makes mathematics strong, it often makes it also hard to learn, if not discouraging. If math pedagogy suffers from the lack of engaging strategies, the pedagogy of mathematical music theory must deal with the additional difficulty of double fields and double vocabulary. However, games and interdisciplinary references in a STEAM framework can help the learner break down complex concepts into essential ideas, and gain interest and motivation to approach advanced topics. Here we present some general considerations, followed by two examples which may be applied in a high-school or early college level course. The first is a musical application of a Rubik’s cube, the CubeHarmonic, to approach group theory and combinatorics jointly with musical chords; the second is an application of category theory to investigate simple musical variations together with transformations on a visual shape.

Nel presente lavoro si illustrerà un percorso didattico che usa la metodologia della storia della matematica nell’insegnamento. Si tratteranno, in particolare, i vari metodi risolutivi delle equazioni di primo e di secondo grado nella storia, dal metodo di falsa posizione degli egizi, ai metodi del completamento a quadrato o delle applicazioni delle aree nei greci, fino ai metodi risolutivi di René Descartes (Cartesio). I metodi geometrici dei greci e di Cartesio sono svolti con il software di geometria dinamica Geogebra. Il percorso si conclude con i riferimenti storici al rinascimento e alle formule risolutive delle equazioni di terzo e quarto grado e a Evariste Galois.

Mathematics, and more generally computational sciences, intervene in several aspects of music. Mathematics describes the acoustics of the sounds giving formal tools to physics, and the matter of music itself in terms of compositional structures and strategies. Mathematics can also be applied to the entire making of music, from the score to the performance, connecting compositional structures to acoustical reality of sounds. Moreover, the precise concept of gesture has a decisive role in understanding musical performance. In this paper, we apply some concepts of category theory to compare gestures of orchestral musicians, and to investigate the relationship between orchestra and conductor, as well as between listeners and conductor/orchestra. To this aim, we will introduce the concept of gestural similarity. The mathematical tools used can be applied to gesture classification, and to interdisciplinary comparisons between music and visual arts., Comment: The final version of this paper has been published by the Journal of Mathematics and Music

The mathematical formalism of category theory allows to investigate musical structures at both low and high levels, performance practice (with musical gestures) and music analysis. Mathematical formalism can also be used to connect music with other disciplines such as visual arts. In our analysis, we extend former studies on category theory applied to musical gestures, including musical instruments and playing techniques. Some basic concepts of categories may help navigate within the complexity of several branches of contemporary music research, giving it a unitarian character. Such a 'unification dream,' that we can call 'cARTegory theory,' also includes metaphorical references to topos theory.

Il presente contributo nasce da una ricerca/azione attualmente in corso relativa alla motivazione degli studenti coinvolti nell’iniziativa fiorente dei ‘Licei Matematici’ (‘LM’) in Italia. L’argomento che qui si vuole trattare riguarda una pratica d’insegnamento che rientra tra le forme del Collaborative Teaching. Nello specifico, si discute un esempio di co-planning tra docenti di matematica ed altre discipline di un Liceo Classico di Palermo, all’interno di un percorso interdisciplinare di una classe prima del LM. Sarà descritta tale forma di collaborazione in riferimento al modulo di “Matematica e Storia”, esplicitando come questa sia stata una sfida di insegnamento/apprendimento per i docenti coinvolti ma soprattutto per gli studenti.

Mathematics can help investigate hidden patterns and structures in music and visual arts. Also, math in and of itself possesses an intrinsic beauty. We can explore such a specific beauty through the comparison of objects and processes in math with objects and processes in the arts. Recent experimental studies investigate the aesthetics of mathematical proofs compared to those of music. We can contextualize these studies within the framework of category theory applied to the arts (cARTegory theory), thanks to the helpfulness of categories for the analysis of transformations and transformations of transformations. This approach can be effective for the pedagogy of mathematics, mathematical music theory, and STEAM.

The genesis of mathematical concepts in the evolutionary line of human thought in the long story and the genesis in individual optics possess evident analogies. Starting from this assumption, we describe an activity presented to 15-year-old students; the aim was to consolidate fundamental concepts of Euclidean geometry related to regular polygons. The experimentation has used a didactic approach based on the historical evolution of the formal definition of regular star polygon through the centuries. The activity and the results obtained in terms of internalization of the concepts in the students are showed.

This paper examines an annotation in Newton’s hand found by H. W. Turnbull in David Gregory’s papers in the Library of the Royal Society (London). It will be shown that Gregory asked Newton to explain to him how the trajectories of a body accelerated by an inverse-cube force are determined in a corollary in the Principia: an important topic for gravitation theory, since tidal forces are inverse cube. This annotation opens a window on the more hidden mathematical methods which Newton deployed in his magnum opus. The received view according to which the Principia are written in a geometric style with no help from calculus techniques must be revised.

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The dualism between continuous and discrete is relevant in music theory as well as in performance practice of musical instruments. Geometry has been used since longtime to represent relationships between notes and chords in tonal system. Moreover, in the field of mathematics itself, it has been shown that the continuity of real numbers can arise from geometrical observations and reasoning. Here, we consider a geometrical approach to generalize representations used in music theory introducing continuous pitch. Such a theoretical framework can be applied to instrument playing where continuous pitch can be naturally performed. Geometry and visual representations of concepts of music theory and performance strengthen the relationship between music and images: in this way, we can connect a theremin or violin performance with a study on perspective, always through mathematical ideas and paradigms. So can math explain musical concepts, and, on the contrary, can music explain mathematical concepts? Can music and math together give rise to visual arts in ever more innovative ways? In this paper, we try to connect different topics such as musical performance on instruments with continuous pitch, and the paradigm of geometry and continuity.

(EN) Gender equality in scientific research is a problematic issue and has been much debated in the last years. As a consequence, some countries have implemented policies to address the problem. In this paper we collected and analysed the last data regarding the academic careers on women mathematician in Italy, as a step for further discussion on possible positive actions. (IT) La scarsa presenza di donne nella ricerca scientifica ed in particolare nelle posizioni apicali è un problema riconosciuto e una questione molto dibattuta negli ultimi anni, con conseguente attuazione in vari stati di alcune politiche di pari opportunità. In questo articolo abbiamo raccolto ed analizzato i dati più recenti sulle carriere universitarie delle donne matematiche in Italia, con l'intenzione di proporre una discussione sulle misure da attuare.

La consapevolezza dell’importanza di guardare, attraverso una lente di tipo matematico, i disegni prodotti dai bambini, considerandoli come strumento diagnostico per quello che D’Amore et al. (2004) chiamano come il “Campo di Esperienza” Spazio, Ordine e Misura, ha dato spunto a questo contributo che discute una sperimentazione didattica condotta in una sezione di scuola dell’infanzia (5 anni). All’interno della stessa è stato chiesto ai bambini di rappresen- tare dei mattoncini Lego con un disegno, e di descrivere successivamente i propri elaborati rintracciando e argomen- tando in essi eventuali segni di scarto numerico-spaziali rispetto al mattoncino osservato/manipolato, attraverso visio- ni prospettiche di erenti. L’analisi qui discussa ci sembra interessante sia per i ricerca- tori in Didattica della Matematica sia per gli insegnanti di scuola dall’infanzia e primaria, che vogliono indagare il ruolo del disegno come forma espressiva e diagnostica per ap- profondire conoscenze, abilità e competenze matematiche dei loro studenti.

This paper presents an overview of the Italian situation in teaching discrete mathematics in primary and middle school, taking into account the national teaching guidelines and their connection with the subject. We describe research conducted with about 150 teachers, interviewed in a preliminary questionnaire. The data collected shows, for all teaching grades, interest in having more discrete mathematics in the school curriculum even if there are some difficulties in teaching it and in inserting it in the usual mathematical activities at school, mostly related to teachers’ knowledge and self-confidence about the subject. We also discuss results and future plans for a continuing research project in the field. We describe in the conclusion a design research project involving teachers in the activity-designing process, aimed at bringing new mathematical knowledge and competences to students.

We describe the historical framework and the main issues (biographical, scientific, political, etc.) of the correspondences of Placido Tardy and Luigi Cremona in the libraries of Genoa, which constitute an important contribution to the reconstruction of the History of Mathematics in the Italian “Risorgimento”. In particular, we mainly deal with the Cremona-Tardy, Betti-Tardy and Cremona-Guccia correspondences. Tardy’s letters are preserved at the Genoa University Library and Cremona’s letters at the Mazzini Institute of Genoa.

Parametric equations can also be used to draw fruits, shells, and a cornucopia of a mathematical still life. Simple mathematics allows the creation of a variety of shapes and visual artworks, and it can also constitute a pedagogical tool for students.

L'articolo mostra come la storia della matematica può diventare strumento didattico.

Powerful abstraction of mathematical category theory can be used to describe musical procedures and structures. The same mathematical theory can be applied to visual shapes and their transformations, including computational applications. Since we can connect music and images through mappings, we can also connect their networks step by step, describing progressive shape modifications. We propose a new approach to music composition based on these ideas, composing music from a network of images “sonifying” each step, as well as creating a parallel sequence of visual and musical variations. Reti di musica e immagini Il potere di astrazione della teoria delle categorie può essere utilizzato per descrivere procedure e strutture musicali. La stessa teoria matematica può essere applicata alle forme visuali e alle loro trasformazioni, comprese le applicazioni computazionali. Poiché è possibile associare musica e immagini attraverso apposite mappature (mappings), è anche possibile connettere reti (networks) di frammenti musicali e di immagini descrivendo progressivamente le modifiche apportate alle forme musicali e visuali. In questo articolo si intende proporre un nuovo approccio alla scrittura musicale secondo questi principi, ovvero componendo musica a partire da una rete di immagini in grado di “sonorizzare” ogni passaggio e creando una sequenza parallela di variazioni musicali e visuali.

This contribution, examining the increasing presence at school of East-Asian students (Chinese in particular) and the related didactical complexity rising from the contemporary presence of Western and non Western cultural heritages, discusses some historical, epistemological and linguistic aspects of Chinese culture and the related Shuxue (Mathematics) education. These were presented to Italian teachers and educators during a training course organized by the authors with the aim of answering teachers’ needs (K-12) for training about the didactical problematic of teaching in multicultural milieu (in particular with Chinese students). The laboratory activities designed and implemented in an ad hoc way by the authors, gave trainers the opportunity to construct a general epistemological framework about Chinese culture and to “compare” it with their own cultural reference. This chance offered them some key lens useful to critically reread and better understand the different cognitive styles of their Chinese and Italian students in mathematics. Thanks to the training course they learned how to refer to cultural diversity as a resource for their teaching activities and not as an obstacle.

This contribution examines the circumstances of composition of the annotated edition of Newton's Principia that was printed in Geneva in 1739-1742, which ran to several editions and was still in print in Britain in the mid-nineteenth century. This edition was the work of the Genevan Professor of Mathematics, Jean Louis Calandrini, and of two Minim friars based in Rome, Thomas Le Seur and François Jacquier. The study of the context in which this edition was conceived sheds light on the early reception of Newtonianism in Geneva and Rome. By taking into consideration the careers of Calandrini, Le Seur and Jacquier, as authors, lecturers and leading characters of Genevan and Roman cultural life, I will show that their involvement in the enterprise of annotating Newton's Principia answered specific needs of Genevan and Roman culture. The publication and reception of the Genevan annotated edition has also a broader European dimension. Both Calandrini and Jacquier were in touch with the French république des lettres, most notably with Clairaut and Du Châtelet, and with the Bernoulli family in Basel. Therefore, this study is also relevant for the understanding of the dissemination of Newton's ideas in Europe.