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Ingenious and Fun Games of Maths Strategies for an Effective Teaching of Maths

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Ingenious and Fun Games of Maths Strategies for an Effective Teaching of Maths Ingenious and Fun Games of Maths Strategies for an Effective Teaching of Maths Final product of Ingenious and fun games of Maths Summary 1. Italy Project presentation Countries and schools presentation Project LOGO Maths convention 2. Turkey Survey results (about parents-students-teachers) 3. Romania Countries curriculum Good practices 4. Reunion Island Test for 3th - 4th-5th grade first (version by Poland) Special needs games 5. Spain Games Test results first version 6. Poland Guide lines Tests for 3th -4th-5th grade (second version by Turkey) International competition 1 Ingenious and fun games of Maths 1. ITALY MEETING Project presentation Progetto E.Te.Mat. “Effective Teaching of Mathematics”, programma UE Erasmus+, Key Action 2 - Partenariati Strategici- V A S T O Prof. Paolo ROTONDO L’ORGANIZZAZIONE DEL CURRICOLO TRA COMPETENZE E OBIETTIVI DI APPRENDIMENTO IL CASO DELLA MATEMATICA 18 FEBBRAIO 2015 1. LE < INDICAZIONI PER IL CURRICOLO > D. M. 254 / 16 NOV. 2012 2. LA SCUOLA DEL PRIMO CICLO 3. L‟ORGANIZZAZIONE DEL CURRICOLO 4. LE COMPETENZE 5. LE INDICAZIONI INVALSI 6. LA MATEMATICA NEL PRIMO CICLO ALCUNI SPUNTI DI RIFLESSIONE a) PER LE SUE SUGGESTIONI FORMATIVE E CULTURALI (ANCHE SE A VOLTE SANA- MENTE UTOPISTICHE), LA PREMESSA (CULTURA – SCUOLA – PERSONA + FINALITA’ GENERALI) APPARE LA PARTE PIU‟ IMPORTANTE DEL DOCUMENTO DEL 4 / 09 / 2012, ANCHE SE LA GENERALITA‟ DEGLI ENUNCIATI VA POI CONCRETIZZATA IN PARTICO- LARI PERCORSI DIDATTICI. b) LA SUCCESSIVA PANORAMICA DELLE DISCIPLINE, ARTICOLATE IN OBIETTIVI DI APPRENDIMENTO (PER LA 3.a E LA 5.a PRIMARIA E PER LA 3.a MEDIA) E TRAGUARDI 2 Ingenious and fun games of Maths b) LA SUCCESSIVA PANORAMICA DELLE DISCIPLINE, ARTICOLATE IN OBIETTIVI DI APPRENDIMENTO (PER LA 3.a E LA 5.a PRIMARIA E PER LA 3.a MEDIA) E TRAGUARDI PER LO SVILUPPO DELLE COMPETENZE, AL TERMINE DEI DUE CICLI, E`RICCA DI SPUNTI CHE VANNO INTERPRETATI E CONDIVISI SIA A LIVELLO DI CURRICOLO COMPLESSIVO (L‟INSIEME DEGLI INSEGNANTI CHE OPERANO CON I MEDESIMI ALUNNI), SIA TRA DOCENTI DI UNA MEDESIMA DISCILINA IN UN ISTITUTO (GRUPPO DISCIPLINARE), AFFINCHE‟ SI POSSA IN- QUADRARE L‟OPERATO DIDATTICO NEL CONTESTO VOLUTO DALLE INDICA- ZIONI, CHE COMUNQUE NON APPAIONO UNA RIVOLUZIONE RISPETTO ALLA PRECEDENTE “RIFORMA MORATTI” ( D. 59 / 2004) O ALLE PRECEDENTI “INDICAZIONI 2007”, E NEMMENO RISPETTO AI PRECEDENTI “PROGRAMMI” DELLA SCUOLA ELEMENTARE (1985) E DELLA SCUOLA MEDIA (1979). LA SCUOLA DEL PRIMO CICLO L’alfabetizzazione culturale di base La scuola primaria mira all‟acquisizione degli apprendimenti di base, come primo eser- cizio dei diritti costituzionali. Ai bambini e alle bambine che la frequentano va offerta l‟opportunità di sviluppare le dimensioni cognitive, emotive, affettive, sociali, corporee, etiche e religiose, e di acquisire i saperi irrinunciabili. Si pone come scuola formativa che, attraverso gli alfabeti delle discipline, permette di esercitare differenti potenzialità di pensi- ero, ponendo così le premesse per lo sviluppo del pensiero riflessivo e critico. Per questa via si formano cittadini consapevoli e responsabili a tutti i livelli, da quello locale a quello europeo. La scuola secondaria di primo grado rappresenta la fase in cui si realizza l‟accesso alle discipline come punti di vista sulla realtà e come modalità di interpretazione, sim- bolizzazione e rappresentazione del mondo. La valorizzazione delle discipline avviene pienamente quando si evitano due rischi: sul piano culturale, quello della frammentazione dei saperi; sul piano didattico, quello della im- postazione trasmissiva. Rispetto al primo, le discipline non vanno presentate come territori da proteggere definendo confini rigidi, ma come chiavi interpretative. I problemi complessi richiedono, per essere esplorati, che i diversi punti di vista disciplinari interessati dialoghino e che si presti attenzione alle zone di confine e di cerniera fra discipline. L’ambiente di apprendimento Il primo ciclo, nella sua articolazione di scuola primaria e secondaria di primo grado, persegue efficacemente le finalità che le sono assegnate nella misura in cui si costituisce come un contesto idoneo a promuovere apprendimenti significativi e a garantire successo formativo per tutti gli alunni. 3 Ingenious and fun games of Maths come un contesto idoneo a promuovere apprendimenti significativi e a garantire successo formativo per tutti gli alunni. A tal fine è possibile individuare, nel rispetto della libertà di insegnamento, alcune imposta- zioni metodologiche di fondo. - Valorizzare l’esperienza e le conoscenze degli alunni - Attuare interventi adeguati nei riguardi delle diversità - Favorire l’esplorazione e la scoperta - Incoraggiare l’apprendimento collaborativo - Promuovere la consapevolezza del proprio modo di apprendere Realizzare percorsi in forma di laboratorio PROPOSTA: GLI INVARIANTI DELLA DIDATTICA 1. LA CONTINUITA 2. LA COMPRENSIONE DI UN TESTO SCRITTO 3. ORGANIZZARE E RAPPRESENTARE LE INFORMAZIONI 4. LE MAPPE CONCETTUALI 5. LE CONCEZIONI DELLA MATEMATICA E DEL SUO APPRENDIMENTO L‟O R G A N I Z Z A Z I O N E D E L C U R R I C O L O < Ogni scuola predispone il curricolo all’interno del Piano dell’offerta formativa con riferimento al profilo dello studente al termine del primo ciclo di istruzione, ai traguardi per lo sviluppo delle competenze, agli obiettivi di apprendimento specifici per ogni disci- plina. > FINALITA‟ EDUCATIVE (Profilo dello studente) TRAGUARDI PER LE COMPETENZE OBIETTIVI DI APPRENDIMENTO 4 Ingenious and fun games of Maths F I N A L I T A` E D U C A T I V E LA FINALITA‟ DEL PRIMO CICLO E‟ LA PROMOZIONE DEL PIENO SVILUPPO DELLA PERSONA Elaborare il senso della propria esperienza Promuovere la pratica consapevole della cittadinanza LA SCUOLA PRIMARIA MIRA ALL‟ACQUISIZIONE DEGLI APPRENDIMENTI DI BASE, COME PRIMO ESERCIZIO DEI DIRITTI COSTITUZION- ALI. LA SCUOLA SECONDARIA DI PRIMO GRADO RAPPRESENTA LA FASE IN CUI SI REALIZZA L‟ACCESSO ALLE DISCIPLINE COME PUNTI DI VISTA SULLA REALTÀ E COME MODALITÀ DI INTERPRETA- ZIONE, SIMBOLIZZAZIONE E RAPPRESENTAZIONE DEL MONDO. I TRAGUARDI PER LE COMPETENZE SONO INDICATI AL TERMINE DI CIASCUN CICLO: FINE QUINTA ELEMENTARE FINE TERZA MEDIA RAPPRESENTANO “RIFERIMENTI PER GLI INSEGNANTI” INDICANO “PISTE CULTURALI E DIDATTICHE DA PERCORRERE” AIUTANO A “FINALIZZARE L‟AZIONE EDUCATIVA ALLO SVILUPPO INTEGRALE DELL‟ALLIEVO” COSTITUISCONO CRITERI PER LA VALUTAZIONE DELLE COMPETENZE AT- TESE 5 Ingenious and fun games of Maths O B I E T T I V I D I A P P R E N D I M E N T O ACQUISIZIONE DEGLI ALFABETI DI BASE DELLA CULTURA VENGONO POSTI COME SAPERE / SAPER FARE ED INDICATI: Per la SCUOLA PRIMARIA AL TERMINE DELLA TERZA E DELLA QUINTA CLASSE Per la SCUOLA SECONDARIA DI I GRADO AL TERMINE DELLA TERZA CLASSE ACQUISIZIONE DEGLI ALFABETI DI BASE DELLA CULTURA VENGONO POSTI COME SAPERE / SAPER FARE ED INDICATI: Per la SCUOLA PRIMARIA AL TERMINE DELLA TERZA E DELLA QUINTA CLASSE Per la SCUOLA SECONDARIA DI I GRADO AL TERMINE DELLA TERZA CLASSE I TRAGUARDI PER LE COMPETENZE RAPPRESENTANO – PROBABILMENTE – A META‟ STRADA TRA FINALITA’ E OBIETTIVI, UNA SORTA DI COLLEGAMENTO TRA L’EDUCAZIONE (PRODOTTA DALLE FINALITA‟) E L’ ISTRUZIONE (PRODOTTA DAGLI OBIETTIVI DI APPRENDIMENTO) EDUCARE ISTRUENDO POTREBBE PERTANTO VOLER DIRE: 6 Ingenious and fun games of Maths 1) PERSEGUIRE LE FINALITA’ EDUCATIVE Elaborare il senso della propria esperienza Promuovere la cittadinanza attiva a t t r a v e r s o 2) L` ACQUISIZIONE DEGLI ALFABETI DI BASE DELLA CULTURA sapere (conoscenze) saper fare (abilità) a v e n d o c u r a d i 3) MIRARE AL PIENO POSSESSO DELLE COMPETENZE LE COMPETENZE INDICATE NELLA < INDICAZIONI > SONO STRETTAMENTE DISCIPLINARI; MANCANO SUGGERIMENTI PER COMPETENZE COMPIUTAMEN- TE `TRASVERSALI` L A M A T E M A T I C A D A I 6 A N N I I N P O I .dalle INDICAZIONI PER IL CURRICOLO SUGGERIMENTI GENERALI PER LA MATEMATICA In Matematica è elemento fondamentale il laboratorio . Caratteristica della pratica matematica è la risoluzione di problemi . Nella scuola secondaria di primo grado si svilupperà un’attività più propriamente di tematizzazione, formalizzazione, generalizzazione. Un’attenzione particolare andrà dedicata allo sviluppo della capacità di esporre e di discutere con i compagni le soluzioni e i procedimenti seguiti. L’uso consapevole e motivato di calcolatrici e del computer deve essere incorag- giato opportunamente fin dai primi anni della scuola primaria . Di estrema importanza è lo sviluppo di un’adeguata visione della matematica . riconosciuta e apprezzata come contesto per affrontare e porsi problemi signifi- cativi . 7 Ingenious and fun games of Maths I N V A L S I QUADRO DI RIFERIMENTO PRIMO CICLO DI ISTRUZIONE / PROVA DI MATEMATICA Le due dimensioni della valutazione Le prove INVALSI di matematica per il primo ciclo scolastico sono volte a valutare le cono- scenze e le abilità matematiche acquisite dagli studenti in entrata e in uscita del ciclo d‟istruzione (classe II della scuola primaria; classe V della scuola primaria; classe I della scuola secondaria di primo grado; classe III della scuola secondaria di primo grado). Le domande di matematica sono costruite in relazione a due dimensioni: - i contenuti matematici coinvolti, organizzati nei quattro ambiti (Numeri, Spazio e figure, Dati e previsioni, Relazioni e funzioni); - i processi coinvolti nella risoluzione. Questa bi-dimensionalità della valutazione è utilizzata in quasi tutte le indagini internazionali ed è indispensabile per fotografare correttamente gli apprendimenti dello studente, individ- uandone le componenti strutturali. È importante sottolineare il fatto che (in matematica) non è possibile in generale stabilire una corrispondenza univoca tra il singolo quesito e un unico contenuto (conoscenza o abilità) il cui possesso venga verificato in esclusiva mediante quello stesso quesito. Infatti, in generale, la risposta a ciascuna domanda coinvolge diversi livelli di conoscenze di vario tipo e richiede contemporaneamente il possesso di diverse abilità. È questa una conseguenza della natura stessa del pensiero matematico, che non consiste solo in convenzioni o procedure di calcolo, ma in ragionamenti complessi, fatti di rappresentazio- ni, congetture, argomentazioni, deduzioni.
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