is the second part.
OS: What do you expect a Chinese family of schools and mathematics? Can a common general education for students from cultures as diverse as Chinese, Arabic, Indian and European?
GN: In such a wide variety of languages \u200b\u200band aspirations, it is also necessary to rethink what it means "teaching." We can no longer think of fall from the top of the content and methods in the hope that someone will not put you to acquire something of his own. The teaching mathematics itself must be rebuilt as class by class of assets that particular group of individuals, mediating with the needs posed by programs and examinations. These too are part of a cultural dynamic that has to be based increasingly on the exchange and sharing of personal contributions. It is not just to enrich the curriculum with the mathematical elements from other cultural contexts of the families of our students (which is also desirable because it shows respect for them). It is necessary to stimulate the discussion and proposals boobies mathematical beliefs they bring to class from their environment. Algorithms for operations, methods of measurement and inference systems, but to do that ... it is necessary that the teacher knows how to listen and observe his students.
To be more specific, tell you a story. In a vocational high culture does not include students of Italian in Bologna, I noticed that some teachers and students in some classes the first Filipinos were strange gestures with his fingers during class assignments. We studied their gestures and then asking for an explanation, according careful not to intimidate them. These students, after some signs of astonishment to our questions, explained that this was a technique of calculation with the convenient and fast fingers. There we found the drawing and brilliant. Then we decided that this knowledge would become the patrimony of all. Philippine recruited a small group in a couple of classes and sent it to make a presentation on the computer, promising to evaluate the outcome as a question of mathematics. After the presentation was shown to the classes and the calculation technique was implemented for all students, jumped out other methods of calculation and a Bengali student wanted to make a presentation on a system of counting and calculation based sulle pieghe tra le falangi delle mani. A lui affiancammo non solo studenti bengalesi, ma anche ragazzi delle più diverse origini. Poi la cosa divenne di moda e diversi gruppetti eterogenei si misero al lavoro. Ne risultarono attività molto coinvolgenti per i ragazzi che si sentirono valorizzati e stimolati. Le presentazioni più belle furono pubblicate sul sito della scuola , dove sono consultabili ancora oggi.
Possiamo dire che abbiamo nelle classe una situazione di multiculturalità e che dobbiamo passare per una fase di elaborazione interculturale per arrivare poi alla costruzione di una transcultura. Questo è il processo delineato da D’Ambrosio, il fondatore dell’etnomatematica. A questo processo siamo sostanzialmente condannati, ma se non lo gestiamo può dare esiti deludenti, che non valorizzano quella messe di contenuti e metodi matematici che ci si presenta.
OS: Il suo approccio ci consente di accennare alla disciplina recente e particolarmente stimolante dell’etnomatematica. Ci dice in poche parole di cosa si tratta?
GN: L’etnomatematica è nata da quel movimento di riflessione su che cosa si studia e si intende per matematica, sviluppato negli anni settanta in Brasile e negli Stati Uniti d’America (non a caso Paesi di immigrazione planetaria). Può essere definita come un programma di ricerca sulla matematica propria dei sociocultural groups. The prefix "ethno" is understood in the broad sense of "human group that shares experiences and problems" and covers a small company without writing and living in remote areas, both professional groups, religious communities or other communities that are part of the particular society advanced. The basic idea is that members of a people, users of a service, the players of a certain set of card games, civil engineers, the drug dealers in a certain area of \u200b\u200ba city ... have developed in their personal history and some collective expertise, ideas, and mathematical representations of their methods and their salient mathematical aspects: questi gruppi hanno ciascuno la sua cultura matematica. L’etnomatematica si interessa dei loro metodi di calcolo, misura, stima, inferenza, decisione, sistemi di numerazione, conteggio, rappresentazioni artistiche, concezioni dello spazio e del tempo, tecniche di costruzione di edifici ed opere pubbliche, giochi e di tante altre attività mentali o pratiche che possono essere tradotte nelle forme della matematica accademica.
La matematica viene vista come una pratica legata ai bisogni materiali o simbolici e alle caratteristiche del gruppo sociale che la produce e la condivide. E, dato che le situazioni in cui si trovano i gruppi umani sono diverse, si hanno matematiche diverse con interessi e metodi particolari, che possono in parte essere translated with the unifying language of academic mathematics. This interdisciplinary course of studies, which are based on observational methods similar to those of anthropologists. But given that anthropologists study today with absolutely everything (direct observations, statistics, stories, novels, songs, works of art, scientific and technical works ...), even for Ethnomathematics there is great freedom to choose methods or means .
OS: In southern India, we study the geometry of kolam , Oceania games that children are intertwined strings. And in Italy, what could study Ethnomathematics?
GN: As is already clear, meeting the wonderful traditions of mathematics teaching and is happening today in the Italian school, thanks to immigration and globalization offers us interesting opportunities to socialize and learn things that we do not know: algorithms, representations, beliefs ...
addition, our country has perhaps the richest artistic traditions in the world, with systems of representation and optical processes varied. Also in this field there is still much to discover.
We can also turn to the many craft traditions that are disappearing. For example, to me, having the time, like to examine the precious embroideries and marched kept in different musei della provincia di Ragusa o nelle cassapanche di alcune nonne. Credo che troverei nelle testimonianze di quell’antica arte femminile delle regolarità di motivi decorativi (nella letteratura specifica più note come patterns ), dei metodi di misura e rappresentazione schematica, e insomma tanta matematica. Quella stessa che si può cercare nei kolam del Tamil Nadu o nei lusona angolani.
Analogamente, anche il mondo delle tecniche di produzione agricola tradizionale è un giacimento di conoscenze e pratiche matematiche. Altrettanto dicasi delle tradizioni religiose o simboliche, delle fiabe o degli usi sopravvissuti dall’era pre-industrial. Of the recipes or certain games.
There are many languages \u200b\u200band codes with which every day people who live around us exchanging mathematical content, often without the full knowledge that the characteristics of these languages \u200b\u200brequire representations that may impact on patterns that are formed in their heads , and therefore on their ability to analyze situations. These are all areas of study that have a wide range of educational effects.
OS: Ethnomathematics has been accused of focusing too much on the differences between cultures, a criticism also extended to the disciplines ethno- in toto, and not on the similarities. And if there was a common substrate that goes unnoticed?
The substrate and there is no doubt is the common human experience. All stomachs need food, all the bodies feel the space and time, but each in its own way. On the other hand, if someone swallows some items that are delicious food, I could die poisoned. The same applies to sexual mores and taste: some things that even with full cooperation I would find repellent, and other festive cause biological reactions. Even math can be somewhat like that. Who says that two plus two is four everywhere committing the misconduct naive to suppose that "two", "more" and "four", which in themselves are objects that do not exist in our reality of the senses and that we must "dress" of an interpretation are the same for everyone, everywhere. It is clear that if we think of the number of bottles to put in the fridge next to each other (which would be the addition), then two plus two equals four, but even if we speak of electrons, or spirits of clouds speech may also be different . There are countless spirits such as bottles, no one can do the same tasks. This is not the sand or water as the grains of sand or water droplets.
Moreover, the crisis of the foundations and the issue of non-Euclidean geometry taught mathematicians to be critical, first of all with their deepest convictions and with what seems obvious and natural.
Those who rightly points out that in the history of civilization is also distant mathematical discoveries are found surprisingly similar (the Pythagorean theorem, the zero, the representation of natural numbers in base 10, negative numbers, the triangle Tartaglia, even the concept to infinity ...), no recognition that the same can be said of the artistic and architectural production, economic activities or forms of government. Rather than resorting to a substratum of mathematical reality can be thought the similarity of problems as those in mathematics were the solution. Concrete problems or symbolic, the result of minds that, beyond the differences, were brought into the common structure of the human brain.
0 comments:
Post a Comment