La fase successiva sarà quella dell’operazione aritmetica vera e propria, che consente la comprensione della sequenza dei numeri.
Nei test d'intelligenza di Burt, così ricchi di operazioni logiche, si trova il test seguente, che un tempo ho studiato con grande interesse. Si tratta di tre ragazzine che differiscono per il colore dei capelli, si chiede di stabilire chi delle tre sia più scura di Lilli. Quale delle tre è più scura? È evidente che ci vuole un piccolo ragionamento non immediato, anche per un adulto, per trovare che la più scura è Susanna e non Lilli.
Con il bambino sarà necessario aspettare dodici anni prima che un tale problema sia risolto, poiché è posto in termini di enunciato verbale...
J.PIAGET: ricerche sullo sviluppo e l'educazione dell'intelligenza (antologia di scritti a cura di Roberto Maragliano), Loescher Editore, 1977, Torino
Anche questa fase dovrà sempre essere preceduta dal gioco manipolatorio - se aggiungo un’altra pecorella nel recinto rosso ho una pecorella di più – se la tolgo ne ho una di meno e in seguito dal disegno della situazione (i bambini si divertono a scegliere loro cosa disegnare nei recinti: alcuni preferiscono fiori o altri, altri, come la bambina qui sotto, si accontentano di rappresentare i quadratini dei regoli)
L’uso di materiale variato favorisce l’acquisizione anche dei concetti logici di “sottoinsieme” e “sottoinsieme comune” (da non dimenticare la contemporanea esecuzione di altri tipi di giochi numerici, dell’apprendimento della sequenza verbale, della classificazione di oggetti quasivoglia, ecc).
Egli elaborerà degli insiemi in sequenza “aggiungendo” o “togliendo” 1 elemento . Poi comincerà a scrivere i relativi simboli numerici nei cartellini e infine potrà annotare a parte l’operazione eseguita 3 + 1 = 4, che leggerà “tre aggiungo1 ottengo 4”
Questa attività consente a ciascun bambino di seguire un proprio percorso cognitivo: l’alunno più dotato vorrà molto presto aumentare il numero delle quantità e quello dei gruppi, quello più lento potrà esercitarsi nelle piccole quantità nelle quali si sente più sicuro, sempre annotando su di una scheda, sempre lavorando come gli altri e senza quindi sentirsi per questo “indietro”.
E’ importante che l’insegnante non abbia fretta e faccia ripetere più volte l’attività, in modo da essere sicuro della corrispondenza quantità manipolata, quantità disegnata, simbolo numerico abbinato.
Per tutto il primo anno di scuola i bambini useranno aggiungo e tolgo per indicare il + e il -, solitamente chiamati, anche in prima classe, “più” e “meno”, cioè con un significato del tutto estraneo alla loro esperienza linguistica.
Avrò quindi “1 pecorella” cui “aggiungo 1 pecorella” e così ne ottengo 2 e non già 1 più 1 è uguale a 2!
(I numeri sono aggettivi e pertanto vanno sempre abbinati a un qualche oggetto: è del tutto sbagliato pensare che i bambini possano operare con numeri astratti, tipo 1+2 fa 3. Se considerate i numeri quali sono, cioè degli aggettivi, vedrete che la cosa non ha senso di per sè e ancor meno quando si consideri l’immaturità neurologica propria dell’età, che non può utilizzarli per operare astrazioni!
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