Meeting La Réunion 15 novembre 2015

1. Meeting La Réunion15 novembre 2015 Dr. Rachele Giammario Psychologist - pedagogist, psychomotrist, Therapistof the neuro and psycomotricityof the childhood Teacher at L’Aquila University

2. 3rd meeting Howchildren learnmaths The analogmethod Gap between the analog and the traditionalmethod Learning the multiplicationtables: suggestionfor a game Learningdifficulties: dyscalculia

3. If we did a little statistical survey among friends, asking them which the most difficult school subject was , probably the most part would answer: maths.As a students’ bugaboo, this subject often seems to be an abstract and innatural way to represent reality.

4. When do children learntocount?

5. Recent neurological researches have shown that human brain is genetically predisposed to calculation.Besides it is possible to develop and strengthen children maths skills from an early age.   How? By playing with them to ……mathematize reality!

6. Calculatorssince birth In a particular area (so called fronto-parietal cortex) since the birth there are some present and active neuronal maths circuits, a series of “chips” superspecialized in the different kinds of number processing: Measurementofquantity and space , calculationtableslearntbyheart , abstracttheoremes, mathsoperationswritten and in mind.

7. School responsibilities By growing up, you loose these natural gifts and numbers become foreign. According some researchers, faults must be also attributed to teaching methods, that can’t use spontaneity of “natural” maths, and change it to an almost philosophical abstraction .

8. PIAGET He stated the first fundamental cognitive theories concerning the number (1941).

9. According Piaget, in order to enter the concept of number, it’s necessary that the child intelligence passes from the level of pre-operative thinking (typical of 4-5 ages) to the level of concrete thinking, that is developped in the school ages.

10. Tokenexperiment (Piaget) When a 5-6 aged child puts 12 red tokens opposite 12 blue ones to check that they are the same, it is enough to put a wider space among the blue ones to see that he considers the blue line longer than the red one. Onlyduring the concrete thinkingages, the child can learnmathsconcepts!

11. RecentresearchesPiagettheoryhasbeendiscussed • The latest researches tend to put under evidence the great skills of children since their birth. • Since ’80s many researchers have been telling actually children approach maths and calculation very early and not, as Piaget told, after having acquired some cognitive schemes.

12. Recentresearches Mandler e Shebo (1982), Fuson (1991), Haith e Benson (1998), Xu Clearfield e Mix (1999) e Spelke (2000), • The results of many researches suggest there is an EARLY NUMBER SKILL that let us represent both quantities and approximation of an easy maths operation result.

13. Recentresearches Newbornbabies can recognizesmall quantitieswithoutcounting. Some newborns (from 1 to 12 daysold) havebeenshown some cardswithtwoblackballsdrawn at variabledistances. Aftermanyrepetitions, the babiesstartedtopaylowerattentiontodrawings, becauseoftheywereusedto .

14. Werebabiesbornwith the conceptofnumber? “As soon as human beings can see, they can develop a skill called subitizing That let them understand at a glance quantities from 1 to 4.

15. Subitizing • The skill to understand the large number of a set of objects at a glance • This process works with a maximum of 4 elements

17. The growing up • Manychilden, at the ageof 18 months, can say some numbers in sequence. • After a fewmonthsthey can count concrete objects. • At the ageof 4 they can start to express opinions on numbers’ size. • Beforefinishing enfant school, due tocomparisonwithfriends and adults, they can start towrite some numbers, evenmake easy additions and subtractions.

18. “Mathematizing” reality around a child, that is making him pass from an elementary representation of the environment to a more and more structured one, in which he/she must deal with elements such as numerosity, shape, extension, quantity Is NOT “early learning”

19. You can easily get this Leaving the child free to move and analyze the surrounding space, inside and outside Learning by playing

20. Doesdyscalculiaexist? • 5 children per class Have difficulty with calculation • 5-7 children per class Have difficulty with problem solving + 20% OF POPULATION

21. Dyscalculia What it is and how to recognize it

22. Dyscalculia DifficultiesofChildrenwithnumbers and maths in general. It’s a disorderrelatedtolearningnumbers and calculation. It’s oftenassociatedtodyslexia.   The diagnosisofdyscalculia can begiven in the 3rd grade

23. Dyscalculia is a specificdisorderrelatedtonumbers and calculation system in absenceofneurologicallesions and cognitive problems There can bedyscalculiaevenwith a normaleducation, a right intelligence, a good culture and a nice family atmosphere

24. Dyscalculia Such disorder concerns the acquisition of easy skills, e.g.: • Writing numbers • Reading numbers • Calculation system (like memorising calculation tables, executing calculations etc.).

25. Dyscalculiaisdividedin primary and secondary • Primary dyscalculia is a disorder  about  numerical and arithmetic skills • Secondary dyscalculia is associated to otherlearning problems, such as dyslexia, la dysgraphia, etc. In these situations we will deal above all with the dyslexia and its rehabilitation

26. Dyscalculia Childrenwith a dyscalculiadesorderfrequentlymake the followingmistakes: • They don’t recognizenumberswhenreading or writing , in particulariftheyhavegotmanyfigures • They can’t recognize the figuresthatmake a number • They can’t recognize relations betweenfigures inside a number

27. Dyscalculia • Difficulty in grasping mathematical links • Difficulty in associating a quantity corresponding number • Difficulty in learning the meaning of signs  (plus, minus, times and divided for) - Difficulty in analysing and recognizing data that can give a problem solution • Difficulty in learning the rules of calculations (loan, reporting, queuing, etc.)

28. Dyscalculia • Difficulty in learning easy operations like calculation tables, the results of which are got automatically, without making difficult calculations • Difficulty in space-time and look-space organization • Difficulty in motor coordination, above all handy • Difficulty in  making works in sequences.

29. You must work on the origin of the problem and not just on the calculation desorder, because it would not be satisfying.

30. Mathshasgot a fundamentalrole in compulsoryschool: Ithasgot the purposeof: • arousing interest thatstimulatesstudents’ intuitive abilities; • graduallygettingtocheck the validityofinsightsbyusing more and more organizedreasonings • urgingto express and communicateby the meansof a specificlanguage, that can makethinking easy byusingsymbols and graphicalrepresentations

31. Mathshasgot a fundamentalrole in compulsoryschool: It tries to develop concepts, methods and ability to order, quantify and measure reality facts and phenomena and to give the necessary ability to critically interpret and to knowingly operate on it.

32. Useoffingers Counting by the use of fingers (so useful mechanism to learn the ability to count and automate correspondences, stable order and cardinality)

33. Useofschoolsplints At school, countingisreplacedbysplints, that are based on a geometric and chromaticrepresentation. Theyremovechildrenfrom the easiestquantityrepresentationbased on analogmechanisms due tofingers.

34. Operationswithabacus

35. Digital I must know the code to decode time

36. Analog No matterknowing the code!

37. Bycomparing DIGITAL / ANALOG itispossibleto assume forchildrentwowaysevenforasmuchas MATHS LEARNING concerns LOGIC The child needs to reason before “understanding reality” ANALOG The child examines reality to reason

38. LOGIC APPROACH (conceptual) ANALOGICAL APPROACH (non conceptual) • Abacus • Analogic tools

39. da u

40. Whatis the AnalogMethod • It’s the most natural way to learn numbers until 20, it develops the mental calculation simulating hands, a real analogical computer   given by our nature.

41. Whyit’s called“AnalogMethod” • Because the whole world is built on an analog basis

42. Logiclearning 11 children= 1 big child (thatis 10) + 1 child da u

43. 11 children= 11 keys (analogy = experience, Reality knowledge, concreteness)

47. Analog method

48. Analog method Each shelf is ten 10 shelves of the one hundred wardrobe