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The aim of the trial path described in this article is to highlight the possibility to develop intuition, analysis and synthesis abilities, which are typical of the logical - deductive mathematical thought, in primary school children (2nd class), through a significant approach to musical education, meant as systematic analysis of the sound parameters, which characterize and qualify its language. The Vygotskijan theoretical framework, which leads and interprets the didactic engineering proposed in class, emphasizes how the Mathematics - Music pair has promoted the changeover among different semiotic registers (Duval 2002), referred to Natural, iconographic, musical, geometric and pre - algebraic Language. The didactic strategy, masterfully lead in class by the teacher through a polyphony of voices (Bartolini Bussi et al, 1995) and a democratic climate (Skovsmose & Valero, 2002), has fostered the acquisition of good skills of analysis and production of argumentations, typical of the musical and mathematical thought.

Aim of this short contribution is to briefly discuss our experience as young researchers in Math Education and give an example of developing a research program, together with a program of preparation of young researchers.

Uno dei problemi più interessanti che si pongono oggi è certamente quello di confrontarsi con la “diversabilità” in situazioni di multicultura, realtà ormai presente nella nostra società, in continuo mutamento socio-culturale, e quindi nodo centrale per la ricerca in didattica della Matematica e non solo. Se infatti i fenomeni di insegnamento/apprendimento delle discipline hanno già sistemi complessi di indagine, la “diversabilità multiculturale” ne aumenta notevolmente la complessità. Ogni persona, appartenente ad una stessa cultura, possiede differenze cognitive rispetto ai suoi simili; in ambienti multiculturali queste si sommano a quelle riscontrabili nei diversi saperi che interagiscono. Nello specifico, la mia ricerca ha focalizzato l’attenzione sulle relazioni (analizzate anche attraverso un continuo riferimento alla storia della Matematica), tra Lingua Naturale e forme argomentative nella cultura Orientale (cinese) ed Occidentale (italiana) rilevanti per l’apprendimento della disciplina in generale e in particolare per il problem solving algebrico e pre-algebrico.

Obiettivo primario della ricerca sulla quale ho lavorato negli ultimi quattro anni è stato quello di riflettere sulle questioni riguardanti le Matematiche Elementari in una visione quanto più ampia possibile, alla luce di una scuola sempre più “diversificata”, multiculturale e globalizzata, trattando in maniera diretta non soltanto le problematiche strettamente riferite ai contenuti disciplinari relativi specificatamente al pensiero algebrico e geometrico per la scuola Primaria e Secondaria, ma anche quelli che in molti casi possono definirsi come gli aspetti storico-epistemologici della disciplina discussa in aula con gli allievi. Quale didattica disciplinare nella classe del terzo millennio? Quale formazione matematica? Quali saperi? E quindi…Quale matematica trasmettere agli allievi? Come relazionare questa alle culture presenti in classe e quindi come condividerla? Riflettendo su questo aspetto attraverso uno studio epistemologico della cultura cinese che ha tenuto in considerazione gli elementi cardine della differente tradizione culturale orientale come la filosofia, la logica, la lingua, la storia dello sviluppo del pensiero matematico etc., ho comparato, in un’ottica interculturale, schemi logico-argomentativi messi in atto da studenti italiani e cinesi inseriti nelle classi italiane evidenziandone analogie e differenze alla luce di analisi teorico/sperimentali condotte in Italia e direttamente in Cina.

Il presente contributo discute alcune delle problematiche affrontate dal G.R.I.M. di Palermo sull'insegnamento/apprendimento delle matematiche in situazione di multiculturalità ed in particolare affronta lo studio della disciplina attraverso considerazioni di carattere sociale, culturale, antropologico, geografico etc. Si focalizza l’attenzione sulle relazioni (analizzate anche attraverso un continuo riferimento alla storia della Matematica), tra lingua naturale e forme argomentative rilevanti per l’apprendimento della disciplina nella cultura orientale (cinese) ed occidentale (europea). Vengono presentati i risultati di ricerca ottenuti dalla fine degli anni ’90 sino alla pubblicazione del volume: F. Spagnolo & B. Di Paola, (2010), European and Chinese cognitive styles and their impact on teaching mathematics (Springer, Studies in Computational Intelligence, Vol. 277).

A General Framework and Theoretical References.- The Chinese Written Language as Tool for a Possible Historical and Epistemological Reflections on the Mathematics and the Impact of Teaching/Learning of Mathematics.- The Meta-rules between Natural Language and History of Mathematics.- Common Sense and Fuzzy Logic.- The Experimental Epistemology as a Tool to Observe and Preview Teaching/Learning Phenomena.- Strategy and Tactics in the Chinese and European Culture: Chess and Weich'i.- Rhythm and Natural Language in the Chinese and European Culture.- Conclusions.

In the last 20 years we witnessed a development of research on "how" our brain works, how it processes the information, how it stores, how it links these, which are the areas appointed to a certain function and how these are interconnected with this each other etc. Then how it learn. Many people are interested to these results, first of all psychologists that are interested in the problems since long time, but also the neurophysiologists and the many categories of people who have intentions of speculative nature, but also with other kind of application. We can think to problems arising from situations of disability, related to brain injury to various types and more, etc ... In the study of the processes of teaching / learning the knowledge of the results of this field is central. Not only for the study of disorders in learning mathematics or in situations of physical disability but also for those situations that are labeled with the word "normal." Do so an innate mathematical knowledge exist? Is an understanding of natural language innate? What is the relationship between natural languages and mathematics? To all these questions, the neurophysiology of the brain begins to give tentative results. They, as scientific knowledge, can not be definitive , but they could immediately help us to "better" interpret the phenomena of teaching / learning of Mathematics. We present a general outline of this work: 1. A possible consolidated overview of the neuroscience research and learning of Mathematics: The Numeric Module, the approximation, the distance effect. 2. Does the numerical module explains everything? 3. The effects on teaching / learning of Numeric Module: discrete / continuous, etc.. A new classification of obstacles? 4. Plasticity and disability: an example of injured brain. 5. The mirror neurons: the laboratory, the processes of communication in teaching / learning, etc. 6. Fractions: the open problem of the day ... What we discuss, even if in a first approximation, in this work is to be a further study on some epistemological and educational issues related to neuroscience research and consolidate learning of Mathematics. Specifically we want to discuss some of the most significant results on key aspects of mathematics learning such as the Numeric Module, the approximation, the concept of fraction and rational number and the behaviour continuous / discrete significant for same didactical activity in scientific subject. With this objective in this work, we will discuss an appropriate analysis of the case study referred to a injured brain with cognitive difficulties in learning of the order relation, a reading of the processes of teaching learning activities through the workshop mirror neurons.

This paper focusing on the complex situation of the Italian multiculturalism and trying to reply to why Asian children mathematically outperform students from other countries, discusses from the epistemological point of view, Chinese children’s skills before to start their formal education in Italian educational school context. A review of the literature, comparing pre-schoolers competences of Asian and Western students, reveals two important influenced factors: linguistic and parental stimuli. In particular many researchers showed that the structure of the Chinese language provides in children a head start in basic math skills, for example to discover, since preschool activities, a pre-algebraic structures of writing. An example with numbers is shown in the paper. Other studies also show that Asian parents, compared to the Western cultures ones, tend to promote in a strong way the development of good basic mathematics skills and a stronger epistemological discipline foundation. A general framework on these two important aspects for the education context is presented with the aim to help teacher and researchers to better understand Chinese and Italian possible different cognitive styles in mathematics learning just from Preschool.