Percorsi CLIL di matematica in inglese per un apprendimento di successo

1. Percorsi CLIL di matematica in inglese per un apprendimento di successo Esperienze CLIL di matematica in inglese Laura Nanna Pisa 7/5/2012

2. Perché matematica in inglese? • ‘è una ‘scienza esatta’ priva di ambiguità terminologiche • Simboli/grafici forte elemento visivo • Strutture grammaticali e lessicali ben precise • Aspetti operativi • Problem-solving

3. Tuttavia…pone alcune criticità… • Lettura e pronuncia dei simboli/operazioni • Definizioni esatte e precise • Carico cognitivo elevato • Livello contenutistico(disciplinare) collima con livello linguistico (frasi ipotetiche, imperativi)

4. Esperienze di Maths in English • Linear inequalities in two unknowns II Liceo Scientifico • Probability IV Liceo Scientifico • Cartesian Plane III ITI • Ellipse III Liceo Scientifico

5. Modalità di codocenza • Esporre gli studenti a modalità di lavoro diverse • Alternare ruoli di spettatori e di attori • Realizzare un ‘triangolo’ di apprendimento • Scambio e confronto continuo • Stimolare la motivazione e la metacognizione degli studenti e degli insegnanti

6. Tipologie di co-docenze adattato da Carmel M. Coonan,Planning for CLIL. A general outline and thoughts on two micro features

7. Fondamenti di un percorso Clil di matematica in inglese • Identificazione di obiettivi, tempi e attività/compiti • Ricerca di materiali e didattizzazione • Assegnazione ruoli dei docenti nelle lezioni • Monitoraggio • Verifica e valutazione

8. Identificazione di obiettivi,tempi, attività/compiti • Identificazione della classe, livello linguistico in LS degli studenti, prerequisiti linguistici e disciplinari, livello motivazionale-condizioni socio-affettive. • gestione delle ore a disposizione per le lezioni e pianificazione • Identificazione obiettivi linguistici, disciplinari, ma soprattutto trasversali • Articolazione delle attività /compiti con ruoli • Ausilii didattici e materiali

10. Ricerca di materiali e didattizzazione • Risorse su Internet (youtube, wikipedia, lezioni in LS, testi GCSE) • Operazione di selezione e didattizzazione

11. a time parenthesis  -pl. parentheses a multiplied/times by b is (/ equals / is equal to) p a divided by b is (/ equals / is equal to) q a minus b is (/ equals / is equal to) d a divided by b (as a normal division ), or a over b. The equals sign a plus b is (/ equals / is equal to) s two thirds x squared / x (raised) to the power two x is equivalent to (or identical with) y root x / square root x / square root of x MATCHING! • HOW DO YOU READ THESE SYMBOLS??? • PRONUNCIATION • = • x≡y • a+b=s (addition) • a-b=d(subtraction or difference) • a×b=p, or a·b=p, • a:b=q, or a/b=q • (fraction) • x2

12. 1° LESSON: Cartesian Plane • Gli insegnanti e gli studenti hanno utilizzato esclusivamente la lingua straniera come lingua veicolare. • PRIMA LEZIONE (compresenza inglese-matematica con FOCUS SULLA LS) • Breve introduzione per spiegare la struttura, gli obiettivi e le attività del modulo (insegnante di inglese) • Preview: ricognizione delle preconoscenze possedute dagli studenti- L’insegnante chiama alla lavagna e chiede agli studenti cosa sanno del piano cartesiano e se lo sanno disegnare con i suoi elementi costitutivi • Comprensione di lettura: testo tratto da Wikipedia con esercizi di comprensione testuale e sul lessico specifico. (matching +cloze text) • Introduzione e ripasso del glossario di alcuni simboli della matematica tramite cartelloni preparati dagli studenti Successivamente i cartelloni vengono appesi in classe in modo che ogni studente possa consultarli in ogni momento. • Homework: creazione di una mappa mentale con i termini specifici • Compresenza: • RUOLO DI PREVALENZA Insegnante di lingua RUOLO DI SUPPORTO Insegnante di disciplina • modello collaborativo con interazione dialogica

13. Reading:Cartesian coordinate system • 1)a cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the distances from the point to two fixed perpendicular directed lines, measured in the same unit of lenght. each reference line is called a coordinate axis or just axis of the system, and the point where they meet is its origin. the coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as a signed distances from the origin. • 2)the invention of cartesian coordinates in the 17th century by rené descartes revolutionized mathematics by providing the first systematic link between and euclidean geometry and algebra .using the cartesian coordinate system, geometric shapes (such as curves) can be described by cartesian equations: algebraic equations involving the coordinates of the points lying on the shape. for example, the circle of radius 2 may be described as the set of all points whose coordinates x and y satisfy the equation x2 + y2 = 22.the adjective cartesian refers to the french mathematician rené descartes.the idea of this system was developed in 1637 in two writings by descartes. in part two of his discourse on method descartes introduces the new idea of specifying the position of a point or object on a surface, using two intersecting axes as measuring guides. • 3)choosing a cartesian coordinate system for a one-dimensional space\that is, for a straight line\means choosing a point o of the line (the origin), a unit of length, and an orientation for the line. the latter means choosing which of the two half-lines determined by o is the positive, and which is negative; we then say that the line is oriented (or points) from the negative half towards the positive half. then each point p of the line can be specified by its distance from o, taken with a + or | sign depending on which half-line contains p. • 4)a line with a chosen cartesian system is called a number line. every real number, whether integer, rational, or irrational, has a unique location on the line. conversely, every point on the line can be interpreted as a number in an ordered continuum which includes the real numbers. • 5)the axes of a two-dimensional cartesian system divide the plane into four infinite regions, called quadrants, each bounded by two half-axes. these are often numbered from 1st to 4th and denoted by roman numerals: i (where the signs of the two coordinates are (+,+), ii (－,+), iii (－,－), and iv (+,－). when the axes are drawn according to the mathematical custom, the numbering goes counter-clockwise starting from the upper right ("northeast") quadrant (adapted from Wikipedia)

14. READ THE TEXT AND MATCH THE TITLES WITH THE NUMBERED PARAGRAPHS:THE NUMBER LINE________Q UADRANT________ORIGIN OF THE CARTESIAN COORDINATE SYSTEM_________DEFINITION OF THE CARTESIAN COORDINATE SYSTEM_______STRUCTURE AND ELEMENTS OF THE CARTESIAN PLANE________MATCH THE ENGLISH WORD FROM THE TEXT WITH THE ITALIAN EQUIVALENT WORD:1.axesa. senso antiorario2.coordinateb.insieme di punti3.set of pointsc.assi4.shaped.segno positivo o negativo5.counter-clockwisee.linea retta6.quadrantf.coordinata7.+ or- signg.quadrante8. straight lineh.figuraCLOZE TEXT:Fill in the blanks to complete the text with the words below:AXES; LINE; POINT; ORIGIN; PERPENDICULARA Cartesian coordinate system specifies each _______uniquely in a plane by a pair of numerical coordinates, which are the distances from the point to two fixed ___________ directed lines, measured in the same unit of lenght. Each reference _______ is called a coordinate axis or just axis of the system, and the point where they meet is its _______. The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two _____, expressed as a signed distances from the origin.axes; quadrants; numbered; divideThe axes of a two-dimensional Cartesian system _________ the plane into four infinite regions, called __________, each bounded by two half-axes. These are often__________from 1st to 4th and denoted by Roman numerals: I (where the signs of the two coordinates are (+,+), II (－,+), III (－,－), and IV (+,－). When the ______ are drawn according to the mathematical custom, the numbering goes counter-clockwise starting from the upper right ("northeast") quadrant.READ THE TEXT AND MATCH THE TITLES WITH THE NUMBERED PARAGRAPHS:THE NUMBER LINE________Q UADRANT________ORIGIN OF THE CARTESIAN COORDINATE SYSTEM_________DEFINITION OF THE CARTESIAN COORDINATE SYSTEM_______STRUCTURE AND ELEMENTS OF THE CARTESIAN PLANE________MATCH THE ENGLISH WORD FROM THE TEXT WITH THE ITALIAN EQUIVALENT WORD:1.axesa. senso antiorario2.coordinateb.insieme di punti3.set of pointsc.assi4.shaped.segno positivo o negativo5.counter-clockwisee.linea retta6.quadrantf.coordinata7.+ or- signg.quadrante8. straight lineh.figuraCLOZE TEXT:Fill in the blanks to complete the text with the words below:AXES; LINE; POINT; ORIGIN; PERPENDICULARA Cartesian coordinate system specifies each _______uniquely in a plane by a pair of numerical coordinates, which are the distances from the point to two fixed ___________ directed lines, measured in the same unit of lenght. Each reference _______ is called a coordinate axis or just axis of the system, and the point where they meet is its _______. The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two _____, expressed as a signed distances from the origin.axes; quadrants; numbered; divideThe axes of a two-dimensional Cartesian system _________ the plane into four infinite regions, called __________, each bounded by two half-axes. These are often__________from 1st to 4th and denoted by Roman numerals: I (where the signs of the two coordinates are (+,+), II (－,+), III (－,－), and IV (+,－). When the ______ are drawn according to the mathematical custom, the numbering goes counter-clockwise starting from the upper right ("northeast") quadrant.Esercizi/Attività • READ THE TEXT AND MATCH THE TITLES WITH THE NUMBERED PARAGRAPHS: • THE NUMBER LINE________ • Q UADRANT________ • ORIGIN OF THE CARTESIAN COORDINATE SYSTEM_________ • DEFINITION OF THE CARTESIAN COORDINATE SYSTEM_______ • STRUCTURE AND ELEMENTS OF THE CARTESIAN PLANE________ • MATCH THE ENGLISH WORD FROM THE TEXT WITH THE ITALIAN EQUIVALENT WORD: • 1.COORDINATE a INSIEME DI PUNTI • 2.SET OF POINTS b COORDINATA • CLOZE TEXT:Fill in the blanks to complete the text with the words below: • AXES; LINE; POINT; ORIGIN; PERPENDICULAR • A Cartesian coordinate system specifies each _______uniquely in a plane by a pair of numerical coordinates, which are the distances from the point to two fixed ___________ directed lines, measured in the same unit of lenght. Each reference _______ is called a coordinate axis or just axis of the system, and the point where they meet is its _______. The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two _____, expressed as a signed distances from the origin. • axes; quadrants; numbered; divide • The axes of a two-dimensional Cartesian system _________ the plane into four infinite regions, called __________, each bounded by two half-axes. These are often__________from 1st to 4th and denoted by Roman numerals: I (where the signs of the two coordinates are (+,+), II (－,+), III (－,－), and IV (+,－). When the ______ are drawn according to the mathematical custom, the numbering goes counter-clockwise starting from the upper right ("northeast") quadrant.

15. ELLIPSE:group activity • GROUPWORK WORKSHEET • Material: cardboard, drawing pin, string, pens (different colours) • Instructions: • Make a loop with your string so that it measures 18 cm from end-to-end when pulled taut. Place your loop around BOTH pins.. With your red pen tip also inside the loop and held vertically, pull the loop taut and trace an ellipse on your paper as shown in Figure 1 below. Label this RedEllipse • Step-by-Step procedure • first cut the string and tie a knot so a sto form a circumference of 18 cm • place the pins in the cardboard about 8 cm apart on the marked line segment on the cardboard and let the string pass under both pins. • Use the red pen and place it inside the string and draw a curve while keeping the string tight. • What can you notice?____________________________________________________ • Move the pins closer together keeping them on the line segment and measure the new distance between the two which is________ • Use the black pen: tip the pen inside the loop and held vertically, pull the loop taut and trace an ellipse on your paper. • What can you notice? ____________________________________________________ • Move the pins farther apart and place them at a greater distance than the beginning one. The distance is___________. • Use the blue pen: tip the pen inside the loop and held vertically, pull the loop taut and trace an ellipse on your paper. • What can you notice? ____________________________________________________ • Analysis • According to the definition are all the drawn curves ellipses? Test this with the red ellipse. • Mark a point on your ellipse. • Use your ruler to measure the distance from each focus to this point. • .PF1= ________ PF2=___________ • Add these distances and record your results PF1+PF2=________ • Repeat this for two other points on the ellipse. What do you notice about these sums?___________________________________________ • So, is it an ellipse?______________________ • What do you think your figure would look like if the two points were on top of each other? • _______________________________________________________________

16. Assegnazione dei ruoli docenti nelle lezioni • Tipologie di co-docenze ( tratto da Carmel M. Coonan,Planning for CLIL. A general outline and thoughts on two micro features): • Collaborativo • Supporto/monitoraggio • Parallelo TUTTA LA CLASSE o GRUPPI

17. Lezione pre-verifica: Cartesian Plane • Ripasso generale e preparazione alla verifica (divisione in due gruppi): gli studenti sono divisi in due gruppi e affidati ad uno dei due insegnanti per svolgere attività con focus sul contenuto o con focus sulla lingua. Dopo circa venti minuti gli insegnanti si scambiano i gruppi in modo tale da fare esercitare gli studenti su entrambi gli aspetti. • RUOLO PARALLELO (focus disciplina) Insegnante di disciplina • RUOLO PARALLELO (focus lingua) Insegnante di lingua

18. VERIFICA E VALUTAZIONE • Verifiche semistrutturate preparate da entrambi i docenti • Verifica per compiti??? • Voto integrato

19. VERIFICA SCRITTA (Cartesian Plane) • NAME:_______________ CLASS:____________ DATE:__________ • 2.4. TEST:CARTESIAN PLANE • 1) Draw the points A (2, 0) B (-1 , - 3) on the Cartesian plane. • a) Find the midpoint and the distance between A and B. • (Comprehension and relevance /1+ Correctness of procedure application /2+ Clarity of use of mathematical language and representation /1) /4 • b) Write the equation of the straight line passing through A and B. • (Comprehension and relevance /1+ Correctness of procedure application /2+ Clarity of use of mathematical language and representation /1) /4 • c) Find and draw the perpendicular straight line to the one requested at point b) and passing through the point C(1, 1). • (Comprehension and relevance /1+ Correctness of procedure application /2+ Clarity of use of mathematical language and representation /1) /4

20. VERIFICA SCRITTA • 2) Find the straight line which is parallel to the line y = 3x – 4 and passes through the point P(1, 6). • (Comprehension and relevance /1+ Correctness of procedure application /2+ Clarity of use of mathematical language and representation /1) /4 • 3) Draw the graph of the straight line y = - 4x + 3. • (Comprehension and relevance /1+ Correctness of procedure application /2+ Clarity of use of mathematical language and representation /1) /4 • 4) Give a definition of a quadrant and say how many quadrants there are in a Cartesian plane and how they are denoted. (max 4 lines) • (Comprehension /1+ Content relevance /2 + Grammar and vocab accuracy /1) /4 • 5) How can we find a straight line? (max 3 lines) • (Comprehension /1+ Content relevance /2 + Grammar and vocab accuracy /1) /4 • 6) Cloze text: fill in the blanks with the appropriate word: • The _________ __________ consists of two directed lines that perpendicularly intersect their respective zero points. The position of any ________ on the Cartesian plane is described by using two numbers:  (x, y). The position of a point on a Cartesian plane is represented by referring to it in terms of a _________ line and a ________ line, which are called the x-axis and y-axis respectively. The point of ________, where the axes meet, is called the _________. • /3

21. VALUTAZIONE DELLA PROVA • TOTAL SCORE: / 31 PASS: 20 /31 (2/3 test) • SCORE MARK • 11/31 3 • 14/31 4 • 17/31 5 • 20/31 6 • 23/31 7 • 26/31 8 • 29/31 9 • 31/31 10

22. Verifica ELLIPSE • TEST THE ELLIPSE – CLIL NAME_____________________________________ • Cloze text: fill in the blanks with the appropriate word: • The Cartesian plane consists of two __________ that perpendicularly cross their respective in one point called____________. The position of any point on the ______________ is described by using an ordered pair:  (x, y). The _______________ of a two-dimensional Cartesian system divide the plane into four infinite regions, called ________________. • An ellipse is usually defined as the set of points such that ________________________to two fixed_______ is constant. • The ________________ is the longest diameter of an ellipse , the ________________is the shortest diameter of an ellipse. The semi-major axis (denoted by _______in the figure) and the semi-minor axis (denoted by ________in the figure) are _____________of the major and minor axes, respectively. • The intersection of the major and minor axes is called ____________of the ___________and it is also the _____________of the line segment linking the two foci. • The foci of the ellipse are two special points (denoted by ________ in the figure) on the ellipse's ________________ and are equidistant from the center point. Each of these two points is called a ___________of the ellipse. • Pick a number to be a and b for an ellipse. • a=______ b =______ • Write the equation (standard form) of the ellipse: • Graph the ellipse • Label each of the following • major axis:_________ • minor axis:_________ • center:___________ • Find the standard equation of the ellipse such that the sum of the distances from any point of the curve to F1(-6, 0) and F2 (+6,0) is 20. • 3) A commercial artist plans to include an ellipse in a design and wants the length of the horizontal axis to equal 10 and the length of the vertical axis to equal 6. Which equation could represent this ellipse? a) b) c) • d) Why?____________________________________________________________

23. MONITORAGGIO • La codocenza consente maggiore controllo sul processo di insegnamento/apprendimento • Strumenti di monitoraggio • Si ovvia al problema dell’autoreferenzialità • Attivazione di un circolo virtuoso che ha al centro la METACOGNIZIONE • (studenti-insegnanti) i: i:

24. DIARIO DEL DOCENTE • Docenti in aula INGLESE MATEMATICA • Obiettivi • Argomenti: • Materiali/ausili didattici: • Durata / Descrizione • Focus su inglese • Focus su contenuti disciplinari • Tipo di attività richiesta • Richiede operazione meccanica • Richiede operazione complessa • Richiede creatività • Organizzazione classe • Lezione frontale dell’insegnante/relazione • Lezione partecipata (attraverso domande insegn.) • Lavoro individuale • Lavoro in coppia • Lavoro in gruppo • Difficoltà degli studenti • Strategie/attività risultate particolarmente efficaci

25. DIARIO DELLO STUDENTE • School year: 2009/2010 • Diario di bordo dello studente (da compilare uno per lezione) • MY CLIL DIARY • Lesson(date)____________________________ • Teachers ENGLISH MATHS • Activities during the lesson: • - • - • - • Difficulties: • What I learnt: • What did I like best?:

26. QUESTIONARIO AGLI STUDENTI • A conclusione della sperimentazione del percorso “CLIL Maths in English” • Ti chiediamo di compilare questo questionario per conoscere la tua opinione sull’esperienza di insegnamento della lingua veicolare realizzata quest’anno. Indica le tue risposte con una “X”. • Grazie per la collaborazione! 1.Come consideri la tua esperienza di apprendimento della lingua veicolare? • Molto importante • Importante • Importante solo in parte • Non importante

27. QUESTIONARIO AGLI STUDENTI • Quando ti esprimi in lingua veicolare (in LS su un’altra disciplina) ritieni importante: • a. la pronuncia corretta delle singole parole • f. la capacità di improvvisare • c. la conoscenza del lessico • d. la conoscenza dei contenuti • h. l’uso di espressioni facciali, gesti e movimenti del corpo • b. la correttezza grammaticale • e. la chiarezza dell’esposizione • g. la capacità di riformulare

29. ESITI DELLE ESPERIENZE • Esperienza stimolante, ‘non scolastica’ • Esiti positivi per le verifiche somministrate • gli studenti hanno considerato importanti la ripetizione dei concetti, gli esercizi, il prendere appunti, il dialogo con le insegnanti • Difficoltà lessicali e di pronuncia • vedere che la professoressa di matematica spiegasse in inglese, perché è stata una novità e uno stimolo a comunicare in lingua straniera • portfolio dove raccogliere tutto il materiale e avere un punto di riferimento: “I like the idea of the portfolio where I can study and do the exercises

30. Concludendo… • Codocenza consente: • maggiore equilibrio • Maggiore equilibrio tra Lingua e contenuti • Diverse metodologie e diversi stili di insegnamento • Confronto con diverse dinamiche relazionali (empatia) • Maggiore monitoraggio • Pronto intervento • Ampliamento del campo d’osservazione • Pluralità di prospettive • Sviluppo della capacità di adattamento e di flessibilità (insegnanti/studenti)