Verso una didattica inclusiva in matematica

8/10/2019 Verso una didattica inclusiva in matematica

http://slidepdf.com/reader/full/verso-una-didattica-inclusiva-in-matematica 1/179

!""# %#&&#'()")*+,#"-

.")/0,1)23 4) 5640"# 0 70'')6 89)()#

:%#&&#'()")*+,#"- 585; <=:>

?0,16 @"# 4)4#A&# )"&(@1)/#)" 9#209#B&#



C,090116 &D0EEE

%#&&#'()")*+,#"- 585; <=:>

)" 9#209#B&# F.FFG D#""64)H&6(23I 9#

16(6 #(&@") (0 1@J0,#"6EEE

&) 46KK)#96 &D)040,0 !"#$%&

<



+6"B J,)"&)J#() 4) 6,)')"0

40((0 4)H&6(23•

+#L6,) 0J)12096(6')&)

•

+#L6,) #M0A/)• +#L6,) &6'")B/)

• +#L6,) 4)4#A&)

%#&&#'()")*+,#"- 585; <=:> N



+6"B J,)"&)J#() 4) 6,)')"0

40((0 4)H&6(23•

+#L6,) 0J)12096(6')&)

•

+#L6,) #M0A/)• +#L6,) &6'")B/)

• +#L6,) 4)4#A&)

%#&&#'()")*+,#"- 585; <=:> >



O690 P@"Q)6"# )( "612,6 &0,/0((6,)1J0L6 #) "@90,)R

?04,096 ,)1@(2#B 0 )J6201) J,6J6120 4#

%@L0,S6,2D 0 4# T0D#0"0&0,&#"46 4) 2,#,"0 )J6201) J0, J611)K)()2,#1J61)Q)6") 4)4#A&D0 &D0 "0 20"'#"6 &6"26EEE

@" &69J)26 2@LU#(2,6 &D0 P#&)(0VV

%#&&#'()")*+,#"- 585; <=:> W



!"#$% ' ()*('"' +,' -.#$' *%/'0 #."1)".

O6" /#,) 01J0,)90"B X 12#26 9612,#26 &D0 @"K#9K)"6 4) J6&D) 901)

! J0,&0J)1&0 (0 Y@#"B23 0 4@"Y@0 J611)040 @"#)"20,"#I #12,#L# 0 #964#(0 ,#JJ,010"2#Q)6"040((0 Y@#"B23I

!

D# (# &#J#&)23 4) #12,#Q)6"0I

! J@Z &#(&6(#,0 ) ,)1@(2#B 4) 109J()&) 6J0,#Q)6")E

T@"Y@0I '() 0110,) @9#")I )" 9#")0,# )""#2#IJ6110''6"6 (# &#J#&)23 4) 010'@),0 109J()&) &#(&6()#,)290B&)E

%#&&#'()")*+,#"- 585; <=:> [



!"#$% ' ()*('"' +,' -.#$' *%/'0 #."1)".

O6" /#,) 01J0,)90"B X 12#26 9612,#26 &D0 @"K#9K)"6 4) J6&D) 901)

•

J0,&0J)1&0 (0 Y@#"B23 0 4@"Y@0 J611)040 @"#)"20,"#I #12,#L# 0 #964#(0 ,#JJ,010"2#Q)6"040((0 Y@#"B23I

• D# (# &#J#&)23 4) #12,#Q)6"0I

• J@Z &#(&6(#,0 ) ,)1@(2#B 4) 109J()&) 6J0,#Q)6")E

T@"Y@0I '() 0110,) @9#")I )" 9#")0,# )""#2#IJ6110''6"6 (# &#J#&)23 4) 010'@),0 109J()&)&#(&6() #,)290B&)E

%#&&#'()")*+,#"- 585; <=:>

<< Alla nascita un bimbo è

un essere umano in

potenza;

ma non può diventarlo

nell'isolamento.>>

Henri Pieron

7



Lo spazio dei numeri

I numeri non fanno venire alla mente soltantouna nozione di quantità, ma anche un irresistibile

senso di estensione nello spazio.

(!

)L'associazione tra numeri e spazio è all'origine

dell'immaginazione con cui le quantità numerichesono rappresentate nel nostro cervello,

ossia quella di una retta numerica.

%#&&#'()")*+,#"- 585; <=:>

Dehaene, 2010

8



Nel 1880 studi di Galton hanno indicato che molte personeoccidentali si rappresentano i numeri in un modo stabile suuno spazio interno bidimensionale, organizzati lungo lineedei numeri idiosincratiche.

Alcuni individui vi associano ancheuna serie di caratteristiche visuo-spaziali associate alle informazioninumeriche, come il colore o la

brillantezza che variano a secondadelle configurazioni della sequenza dinumeri.

\

2. 3-)4'. % ' 56*%7'

%#&&#'()")*+,#"- 585; <=:>



G "@90,) 0 (6 ]J#Q)6

L’idea di Galton ha trovato conferma in studi successivi incui venivano messi in relazione il processamento di numerie quello dello spazio (per esempio, Piazza, Pinel, &Dehaene, 2006; Seron, Pesenti, Noël, Deloche, & Cornet,1992).

Effetto SNARC(Spatial Numerical Association of Response Codes): uneffetto del comportamento in esperimenti classici perdocumentare “l’effetto dello spazio” nella rappresentazione

dei numeri (Dehaene, Bossini, & Giraux,1993).

:=%#&&#'()")*+,#"- 585; <=:>



G "@90,) 0 (6 ]J#Q)6Effetto SNARCIl soggetto deve decidere se il numero è pari o dispariusando la mano destra in un caso e sinistra nell’altro.Nel diagramma sono riportate le differenze dei tempi dirisposta tra la mano destra e sinistra (i valori maggiori di 0indicano un vantaggio della mano sinistra).

::%#&&#'()")*+,#"- 585; <=:>



G "@90,) 0 (6 ]J#Q)6Effetto SNARCIn generale si ha un vantaggio nel tempo di risposta dellamano destra per numeri grandi e nella sinistra per numeripiccoli. L’effetto si ha in compiti di confronto di numeri,giudizio di parità/disparità, e ordinamento (de Hevia, et al.,2008; Dehaene, et al., 1993; Hubbard, et al., 2005).

:<%#&&#'()")*+,#"- 585; <=:>



G "@90,) 0 (6 ]J#Q)6Compiti di BisezioneQuando si chiede al soggetto di indicare il punto medio siun segmento costituito di numeri piccoli, il soggetto sceglieun punto a sinistra del vero punto medio se i numeri sonopiccoli e a destra del reale punto medio se i numeri sonograndi (Calabria & Rossetti, 2005; Fischer, 2001).

:N%#&&#'()")*+,#"- 585; <=:>



G "@90,) 0 (6 ]J#Q)6Bias attentivoQuando si presenta al soggetto un numero mentre fissauno schermo, automaticamente avviene uno shift diattenzione verso la destra o la sinistra del numero (sulloschermo) che porta a risposte più rapide a stimolipresentati in queste zone.

:>%#&&#'()")*+,#"- 585; <=:>



G "@90,) 0 (6 ]J#Q)6

:W

2 3 41 5 6 87 9

%#&&#'()")*+,#"- 585; <=:>



G "@90,) 0 (6 ]J#Q)6

:[%#&&#'()")*+,#"- 585; <=:>



G "@90,) 0 (6 ]J#Q)6

Questa è la forma a cui miriamo culturalmente (ematematico), con la possibilità di estenderla ai numerinegativi, ai razionali e agli irrazionali...

:^%#&&#'()")*+,#"- 585; <=:>



G "@90,) 0 (6 ]J#Q)6

Questa è la forma a cui miriamo culturalmente (ematematico), con la possibilità di estenderla ai numerinegativi, ai razionali e agli irrazionali...

3

2_

*:

:`%#&&#'()")*+,#"- 585; <=:>



...ma attenzione!!La Linea (mentale) dei Numeri

Punto di vista culturale o innatista? Alcuni riferimenti

Nuñez R. (2011), No Innate Number Line in the

Human Brain, Journal of Cross-Cultural Psychology,42(4) 651-668.

e altri articoli nello stesso numero (Maggio 2011)della rivista.

Journal of Cross-Cultural Psychology

%#&&#'()")*+,#"- 585; <=:> 19



]26,)# 40((# 9#209#B&#

a# ()"0# 40) "@90,) X,0(#B/#90"20 ,0&0"20

b&690 ,#JJ,010"2#Q)6"0 0

#"&D0 &690 1@JJ6,264)4#A&6c

d6D" e#(()1 b:[`Wc

f6" &) 16"6 2,#&&0 "0((#9#209#B&# #"B&# 0 "6";&&)40"2#(0E

%#&&#'()")*+,#"- 585; <=:> <=



]2@4) 1@ g,@JJ) G"4)'0") 7096B

5@"4@,@-h b%,#Q)(cE

C#J@# f0S g@)"0#

a# 9#JJ#2@,# 40) "@90,) bJ#,6(0iJ@"Bi26")c"6" ,)1J0L# (# 16()2# &6"/0"Q)6"01@((U'#()*+,"*-'E

a# 1)2@#Q)6"0 J0,Z &#9K)# 46J6 16(2#"26 J6&D0

10A9#"0 4) 1&@6(#ET)K#A26 )" .$)"*$" b<==`c 2,# T0D#0"0 02 #(E 0f@"0QE

%#&&#'()")*+,#"- 585; <=:> <:



K0DEEE

a#1&)#96 #'() 1&)0"Q)#B b"0@,6c&6'")B/) )(4)K#A26 1@((U)""#B196 ,)1J0L6 #((# &@(2@,#E

j@0((6 &D0 &) )9J6,2# Xk

l2D0 "@9K0,*26*()"0 9#JJ)"'I #(2D6@'D@K)Y@)26@1 )" 2D0 9640," S6,(4I )1 "62@")/0,1#((m 1J6"2#"06@1 K@2 ,#2D0, 10091 26 K0

(0#,"04 2D,6@'D n #"4 &6"B"@#((m ,0)"P6,&04 Km n 1J0&)o& &@(2@,#( J,#&B&01p

bf@"0QI <=::I JE [[:cE

%#&&#'()")*+,#"- 585; <=:> <<



f0( "612,6 &0,/0((6 /) X @" 6,'#"6 J,0J6126#((# J0,&0Q)6"0 0 #((# ,#JJ,010"2#Q)6"0 40((0 Y@#"B23"@90,)&D0q (0 1@0 &#,#L0,)1B&D0 (6 &6((0'#"6 10"Q#

4@KK)6 #((0 P#&6(23 J,626*#,)290B&D0 J,010"B"0((r#")9#(0 0 "0) K#9K)") 96(26 J)&&6()kJ@Z &64)o&#,0 &6" J,0&)1)6"0 16(6 '() )"1)09)

)( &@) "@90,6 &#,4)"#(0 "6" 1@J0,) )( N 0I

J)s ) "@90,) 16"6 ',#"4) 0 /)&)")I 9#'')6,0 X(# P#&)()23 &6" &@) () &6"P6"40E

%#&&#'()")*+,#"- 585; <=:>

T0D#0"0I <=:=

<N



8.*% /6-%7)7% 9:)--7.//'*)4'."%;

aU@696 D# 1@J0,#26 (# &6"&0Q)6"0#JJ,611)9#B/# 40) "@90,) ',#Q)0#((r)"/0"Q)6"0 40((# ,#JJ,010"2#Q)6"0

1)9K6()&#V

%#&&#'()")*+,#"- 585; <=:> <>



< -6"= >.7= ,%99) "./17) 7)--7%/%"1)4'."%

/'*(.9'#) ,%' "6*%7'

G( J,)"&)J)6 4) J61)Q)6"0t# J0,90116 (r)"/0"Q)6"0 4) 109J()&) #('6,)29) J0, 010'@),0 )

&#(&6()E

G( 1)9K6(6 Q0,6t# J0,90116I #4 0109J)6I 4) "6" &6"P6"40,0 )( W: &6" )( W=: 6&6" )( W:=E

a# 1&0(2# 4) := &)P,0 4) #1J0L6 #,K)2,#,)6

O) J0,90L0 4) ,)&6"61&0,0 )12#"2#"0#90"20 6'") "@90,6 4# =# \E

b?0 /' /-./) ) *%7)@'A9') #." ' -6"= >.7=

,%9 "./17. #%7@%99.B

%#&&#'()")*+,#"- 585; <=:> <W



@'/'@.

)7)('#.

C

D%7()9%

6,'=@.

E/%F%G

!")9.A'#.

(0L@,# 4) "@90,) )"&64)&0 #,#K)&6

]&,)L@,# 4) "@90,) )"

&64)&0 #,#K)&6

!1&6(26 4) J#,E "@9

?0, K# ( ) Q Q# Q )6"

0 J#,E f@9E

H

!

88I

JJI

KLJM22L JM2 NO<P2L 8LJ<8M

+J%$)%"%Q RSST0

Baccaglini-Frank MEMO 2014 <[



G( (011)&6 0 (# 1)"2#11) 40) "@90,) )"u@)1&6"6 1@((6,6 #JJ,0"4)90"26

%#&&#'()")*+,#"- 585; <=:> <^



La memoria gioca un ruolo fondamentalenel calcolo mentale!

%#12# 90"6 4) @"10&6"46 J0, 2,6/#,0

)( ,)1@(2#26 4) <vN 6 <wNI

9# &) /@6(0 &),&# @"10&6"46 0 2,0 40&)9)

J0, ,)16(/0,0 `v^ 6 `w^

%#&&#'()")*+,#"- 585; <=:> <`



M/%*-'. ,%99:)61.*)=#'1U ,%99) *%*.7')

)7'1*%=#)

Perché il gioco riesca bene rispondete il piùvelocemente possibile, alle seguenti domande:

Quanto fa 2 più 2?

4 più 4?

8 più 8?

16 più 16?

Adesso scegliete un numero compreso tra 12 e 5.Fatto?

%#&&#'()")*+,#"- 585; <=:> <\



Il numero che avete scelto è 7?

a# 109J()&0 (0L@,# 40) "@90,) :< 0 W X 1@H&)0"20# 90L0,0 )"&61&)0"2090"20 )" #Q)6"0 )" /6)

@"# 16L,#Q)6"0 :<*WEY@0126 0M0L6 X 10"Q# 4@KK)6 #9J()o&#264#((r#44012,#90"26 )")Q)#(0 #((0 #44)Q)6")I

4#((r6,4)"0 4) J,010"2#Q)6"0 )"/0,1# 40) "@90,) :< 0 W

0 4#((# P6,9@(#Q)6"0 #9K)'@# 40((0 J#,6(0l2,# :< 0 Wp

&D0 )"/)2# # &#(&6(#,0 (# 4)12#"Q# 2,# ) 4@0 "@90,)E

%#&&#'()")*+,#"- 585; <=:> N=



Dunque...

Ci risulta facile:contare perché sibasa su capacità che

noi abbiamo innate.

Ci risultano difficili:! imparare le tavole di

addizione e

moltiplicazione! gli algoritmi di addizione

e sottrazione in colonnaPerché sono operazioni

formali alle quali ilnostro cervello non èpredisposto.

%#&&#'()")*+,#"- 585; <=:>

T0D#0"0I <=:=

N:



O690 16"6 6,'#")QQ#B "0((#5096,)# # a@"'6 F0,9)"0R

f0( 209J6 1) 16"6 1@110'@)B /#,) 9640(() J0,1J)0'#,0 )( 9646 )" &@) ) P#A #,)290B&) 16"66,'#")QQ#B "0((# 5aFE

G J#,#902,) @B()QQ#B J0, &,0#,0 Y@01B 9640(() 16"6) 209J) 4) ,)1J612# 0 (0 BJ6(6')0 4) 0,,6,)E

G" J#,B&6(#,0 '() 0,,6,) P,0Y@0"2090"20 &699011)4#) K#9K)") b0 "6" 16(6c P6,")1&6"6 40((0)"4)&#Q)6") )" 90,)26 #((# K6"23 40) 9640(()E

%#&&#'()")*+,#"- 585; <=:> N<



5640((6 # F#K0((#b!1D&,#x c

CVW

%#&&#'()")*+,#"- 585; <=:> NN



2% 1)@.9% ,%99:),,'4'."% % ,%99)

*.9=-9'#)4'."%

C,6/#20 # 9096,)QQ#,0EEEE

!

OD#,(01 T#/)4 #K)2# )" /)# g@)((#@90

!

OD#,(01 g@)((#@90 #K)2# )" /)# !(K0,2 y60

!

g@)((#@90 8B0""0 #K)2# )" /)# !(K0,2 %0,2,#"40 #"&6,#EEE

! OD#,(01 T#/)4 (#/6,# )" /)# !(K0,2 %0,2,#"4

! OD#(01 g@)((#@90 (#/6,# )" /)# %0,2,#"4 !(K0,2

! g@)((#@90 8B0""0 (#/6,# )" /)# OD#,(01 8B0""0

Questo tipo di elenco risulta per noi difficilissimoperché siamo dotati di una memoria associativa!

3+4=73+7=10

7+5=12

3x4=12

3x7=217x5=35

%#&&#'()")*+,#"- 585; <=:> N>



F)J6(6')0 4) 0,,6,) 4)M@10

/##'#) () '!"#+*('k 16"6 '() 0,,6,) &699011) #@90"2#"46 64)9)"@0"46 @" 6J0,#"46 b16()2#90"20 )( 10&6"46c 4) : 6 <I4)H&)(90"20 4) J)sE 81k ` w ^ z >`

/##'#) () -+1"22+k "6" &UX @" 6J0,#"46 )" &69@"0 P,#(U6J0,#Q)6"0 ,)&D)#9#2# 0 Y@0((# &D0 0M0A/#90"20#/,0KK0 )( ,)1@(2#26 P6,")26I 9# Y@0( ,)1@(2#26 &69J#,0 "0((#2#/6(# J)2#'6,)&# bJ0, 1699# J)s 4)H&)(0 4# /#(@2#,0cE81k ` w ^ z W>

/##'#) () '!"#+3)'*"k (# ,)1J612# P6,")2# X &6,,0L# J0, @"U#(2,#6J0,#Q)6"0E 81k W w < z ^

%#&&#'()")*+,#"- 585; <=:> NW



G"6(2,0k 8M0A/4"5' () (),"*6)'*" ("227'!"#+*('k 1) J@Z 6110,/#,0 "0'() 0109J)

P6,")B J,)9#I Y@#"46 /)0"0 P6,")26 @" ,)1@(2#26 1&6,,0L6I Y@0126 X1J0116 /)&)"6 b)" 20,9)") 4) 6,4)"0 4) ',#"40QQ#c # Y@0((6 &6,,0L6E

/4"5' () (),"*6)'*" ("2 !#'12",+k 1) "62# &D0 (# 9#'')6, J#,20 40'()0,,6,) 1) J,010"2#"6 "0((0 6J0,#Q)6") b16J,#L@L6 96(BJ()&#Q)6")c&D0 D#""6 6J0,#26,) /)&)"6 #( := b&6" (U0&&0Q)6"0 40( :=cE

/4"5' )**"6$'k Y@#"46 @" ,)1@(2#26 X ')3 12#26 ,)&D)#9#26 #((6,# X J)s

P#&)(0 &D0 /0"'# ,)&D)#9#26 )" 10'@)26E aU0M0L6 X J#,B&6(#,90"20P6,20 Y@#"46 4@0 J,646A 6 16990 J6116"6 ,)&#40,0 )" @" 0,,6,J#L0," 4) Y@0(() /)1B 16J,#E

8.*% /'/-'%A);

%#&&#'()")*+,#"- 585; <=:> N[



5640((6 # 7020bO#9JK0((c

XVY

Y

X

W

XVY

XVW

TY

Z[

ZX

Y[

YW

K%,'

\7)",'

%#&&#'()")*+,#"- 585; <=:> N^



O61# 1@''0,)1&6"6R

g() "##'#) () '!"#+*(' &6"1)126"6 "0( 4#,0 @" ,)1@(2#26 &D01) 2,6/# #((U)"20,"6 40((# 12011# l2#K0(()"#p Y@01261@''0,)1&0 &D0 (0 96(BJ()&#Q)6") &D0 D#""6 )" &69@"0

)( J,)96 P#L6,0 1)#"6 &6((0'#20 #((U)"20,"6 40((#9096,)# 4#26 &D0 @"# P# )*-"#8"#"*3+ &6" (U#(2,#E

C62,0KK0 4)J0"40,0 4#( 9646 )" &@) ) K#9K)")9096,)QQ#"6 (0 2#K0(()"0R

%#&&#'()")*+,#"- 585; <=:> N`



g() "##'#) () -+1"22+ 1@''0,)1&6"6 &D0 )( 9646 )" &@) )P#A #,)290B&) /0"'6"6 6,'#")QQ#B "0((# P#10 4)#JJ,0"4)90"26 bY@)"4) (# 1)@.9) -'1)A.7'#)c/0"'6"6 )"20,)6,)QQ#BE

a# &6"P@1)6"0 J62,0KK0 "#1&0,0 4#( P#L6 &D0 (04)/0,10 2#K0(()"0 bY@0((# 40( WI 40( [I 40( Î 02&Ec/0"'6"6 9096,)QQ#20 @"# 46J6 (U#(2,# )" 209J),0(#B/#90"20 K,0/)R

%#&&#'()")*+,#"- 585; <=:> N\



g() "##'#) () '!"#+3)'*" 1@''0,)1&6"6 &D0 (0 4)/0,10

6J0,#Q)6") "6" 16"6 "0L#90"20 10J#,#20 #((U)"20,"640((# 9096,)#E j@0126 "6" 12@J)1&0 4#26 &D0 (#96(BJ()&#Q)6"0 l"#1&0p &690 1699# ,)J02@2#E

%#&&#'()")*+,#"- 585; <=:> >=



." 9640((6 ,0&0"20f6"612#"20 ) J#L0," 4) 0,,6,) /)1B o"6,# "6" 1) 40/0 J0"1#,0 &D0

(U6,'#")QQ#Q)6"0 )" 9096,)# 1)# 12#B&#E

8/)40"Q0 1J0,)90"2#() 9612,#"6 &690I "0( 209J6I (U6,'#")QQ#Q)6"0 40)P#A )" 9096,)# J611# @)7')7% #"&D0 )" K#10 #'() #JJ,0"4)90"BE

." 0109J)6k %@L0,S6,2D 02 #(E b<==Nc 9612,#"6 &D0 (# J,6J,)023&699@2#B/# )"20,/)0"0 "0((U6,'#")QQ#Q)6"0 40) P#A )" 9096,)#E]J0116I Y@#"46 1) 40/0 ,)&D)#9#,0 @" P#L6I 1) ,)6,4)"#"6 ) 20,9)"))" 9646 &D0 )( 9#'')6,0 1)# )( J,)96 b1)# "0((U#44)Q)6"0 &D0 "0((#96(BJ()&#Q)6"0c

G"6(2,0 P#""6 "62#,0 &D0 "6" 1) 9096,)QQ#"6 16(6 1)"'6() P#A 9##"&D0 l)"1)09)p 4) P#A &690 f w = z = w f z =E

%#&&#'()")*+,#"- 585; <=:> >:



<""6*%7)=/*.

É l'equivalente dell'analfabeta nella matematica.L'innumerato è capace di fare conclusioni azzardatefrutto di un ragionamento che solo in apparenza è

matematico.

:iWv<iWzNi:=J0,&D{

:v<zN 0 WvWz:=

=I<v>z=I[

J0,&D{ >v<z[

."# /#1&# 4) #&Y@# &#(4# # NW|IJ)s @"r#(2,# /#1&#I #"&Dr011# # NW|I

P# @"# /#1&# 4r#&Y@#96(26 &#(4# # ^=|

]0 &rX )( W=} 4) J,6K#K)()23 &D0 1#K#26

J)6/#I 0 )( W=} &D0 J)6/# 4690")&#I&rX #((6,# )( :==} 4) J,6K#K)()23&D0 Y@0126 o"0 10A9#"# J)6/#E

%#&&#'()")*+,#"- 585; <=:>

=I:: ~ =I`

J0,&D{ :: ~ `

><



8.*% '"1%7-7%1)7% 9:'""6*%7)=/*.

%#&&#'()")*+,#"- 585; <=:>

a0 &6"61&0"Q0 9#209#B&D0 "6" 90L6"6 )" P@"Q)6"0 @"&),&@)26 &0,0K,#(0 1J0&)#()QQ#26I 9# "@90,610 ,0B 4)M@10IJ#,Q)#(90"20 )"4)J0"40"B 0 #@269#BQQ#20E ?0")#96 #(96"46 &6" @" &),&@)26 #&&@9@(#26,0 &D0 &) &6"P0,)1&0

@"r)"2@)Q)6"0 40((0 Y@#"B23 "@90,)&D0E O6" (r#&Y@)1)Q)6"040( ()"'@#'')6 40) "@90,) 0"2,#"6 )" P@"Q)6"0 96(B #(2,)

&),&@)B 4) 9#")J6(#Q)6"0 40) 1)9K6() "@90,)&) 0 4) &6"20'')6

/0,K#(0E b•c <9 -7.(9%*) /1) "%9 >)F. #$% ]6%/= #'7#6'=/' )61.*)=44)". #')/#6". -%7 #."1. -7.-7'.Q "." /%*-7%

#..7,'")",./' '" *.,. -%7>%F.B G( (6,6 &66,4)"#90"26I 16L6(r0')4# 40((# &6,20&&)# &0,0K,#(0I X @"# &#J#&)23 )"20,#90"20

# J#,20I 1J0116 (0"2# # 0"2,#,0 )" P@"Q)6"0E

>N



5%67."' % "6*%7'

Attraverso lo studio e l'osservazione di persone chehanno subito lesioni cerebrali è stato scoperto che ilcervello è suddiviso in aree altamente specializzate,connesse tra di loro da numerose vie di trasferimento.

%#&&#'()")*+,#"- 585; <=:> >>



G"4)J0"40"Q# 40) &),&@)B 4)0(#K6,#Q)6"0 40) "@90,)

G"4)J0"40"Q# P,# "@90,6 0 ()"'@#'')6

G"4)J0"40"Q# P,# "@90,6 0 9096,)#

G"4)J0"40"Q# P,# "@90,6 0 ,#')6"#90"26

%#&&#'()")*+,#"- 585; <=:> >W



G"4)J0"40"Q# 40) &),&@)B 4)0(#K6,#Q)6"0 40) "@90,)

G"4)J0"40"Q# P,# "@90,6 0 ()"'@#'')6

G"4)J0"40"Q# P,# "@90,6 0 9096,)#

G"4)J0"40"Q# P,# "@90,6 0 ,#')6"#90"26

%#&&#'()")*+,#"- 585; <=:> >[





G &),&@)B 1J0&)#()QQ#B "0((0 /#,)0 &#J#&)23 &6"61&)B/0I &690(0L@,#I 1&,)L@,#I &#(&6(6I 0&&EEE 16"6 )""#B 6 "6R

a# (0L@,# 0 )( &#(&6(6 01)126"6 16(2#"26 4# Y@#(&D0 9)'()#)6 4) #"")I@" J0,)646 2,6JJ6 K,0/0 J0,&D{ (r0/6(@Q)6"0 /) #KK)#

'0"0B&#90"20 J,04)1J6126 #(&@") &),&@)B "0@,#()Ej@0120 &#J#&)23 &6"61&)B/0 #JJ#,10 4) ,0&0"20 40/6"6 4@"Y@0#/0,0 )"/#16 &),&@)B )")Q)#(90"20 401B"#B #4 #(2,6 @16E

]0 "0 #JJ,6J,)#"6 2#(/6(2# )" 9646 &61€J0,/#1)/6 4# 4)/0"),"0 (r@")&# P@"Q)6"0E

b•car#JJ,0"4)90"26 "6" &,0# 9#) &),&@)B ,#4)&#(90"20 "@6/)I

9# 10(0Q)6"#I ,#H"# 0 1J0&)#()QQ# &),&@)B J,001)120"BIo"6 # &6"P0,), (6,6 @" 1)'")o&#26 0 @"# P@"Q)6"0 96(26 4)/0,1#

4# Y@0((0 #((0 Y@#() (# "#2@,# () #/0/# 401B"#BE

%#&&#'()")*+,#"- 585; <=:> >`



G( ,@6(6 P6"4#90"2#(0 40((# O@(2@,#

C0, Y@#"26 &) J611#"6 0110,0 40((0 J,04)1J61)Q)6") &6"&@) 1) "#1&#I "6" X J0"1#K)(0 &D0 4# 16(6 @" K#9K)"6J611# 1&6J,),0 4# 16(6 2@L# (# 9#209#B&# "0((U#,&640((# 1@# /)2#E

%#&&#'()")*+,#"- 585; <=:> >\





G( ,@6(6 P6"4#90"2#(0 40((# O@(2@,#

C0, Y@#"26 &) J611#"6 0110,0 40((0 J,04)1J61)Q)6") &6"&@) 1) "#1&#I "6" X J0"1#K)(0 &D0 4# 16(6 @" K#9K)"6J611# 1&6J,),0 4# 16(6 2@L# (# 9#209#B&# "0((U#,&640((# 1@# /)2#E

!"&D0 J0, Y@0126 @"# K@6"#

4)4#A&# n &690 )99)11)6"0 "0((#O@(2@,# 5#209#B&# n X

P6"4#90"2#(0V%#&&#'()")*+,#"- 585; <=:> W:



M i b i d f ti i D l li



Left hemisphere Right hemisphere

Mapping brain dysfunction in Dyscalculia^_-.1$%/'/

E8.7% J%`#'1G a

J%`#'1 '" 1$% !--7.V'*)1%

K)A"'16,% /_/1%*b%@L0,S6,2DI :\\\q g0,120" OD#,4I:\\\q e)(16" T0D#0"0I <==^c

^_-.1$%/'/

E!##%//G a

Deficit Exact Number Representationand the link between Arabic –Magnitude Representationb76@10((0 f6‚(I <==Î <=::c

%#&&#'()")*+,#"- 585; <=:> WN



5# )( 9640((6 P6,10 X 1@J0,#26V

]Q@&1I T0/)"0I ]6(201QI f6K01 0 g#K,)0( bO6,20wI <=:Nc)J6BQQ#"6 &D0 (# T8 1)# )" ,0(#Q)6"0 &6" (U#K)()23 4))")K)Q)6"0 0 (# 9096,)# 4) (#/6,6 /)1@6*1J#Q)#(0E

aU)J6201) 1J)0'D0,0KK0 (0 J,012#Q)6") K#110 )" 20121 4)1@K)BQ)"' 0 4) &6"P,6"26 4) "@90,61)23 1)9K6()&# &6"4)12,#L6,0

%#&&#'()")*+,#"- 585; <=:>

&690 "0( &#16 4) EEEb4),0 Y@#() 40) 10'@0"B "@90,) X 9#'')6,0c

W>



%#&&#'()")*+,#"- 585; <=:> WW



%#&&#'()")*+,#"- 585; <=:> W[



%#&&#'()")*+,#"- 585; <=:> W^



%#&&#'()")*+,#"- 585; <=:> W`



%#&&#'()")*+,#"- 585; <=:> W\



%#&&#'()")*+,#"- 585; <=:> [=



%#&&#'()")*+,#"- 585; <=:> [:





%#&&#'()")*+,#"- 585; <=:> [N

Una prestazione rapida edaccurata si basa

principalmente sul

l’abilità di inibizione



G( 5 4 (( 4 (( 5 ) 4) a



G( 5640((6 40((# 5096,)# 4) a#/6,6b%#440(0m t)2&DI :\^>q %#440(0mI <===c

%#&&#'()")*+,#"- 585; <=:> [W

T]! 4)H (23 4) 4) 2



T]!EEE0 4)H&6(23 4) #JJ,0"4)90"26." &,)20,)6 J0, ,)&6"61&0,0 @" 16''0L6 &6" @" /0,6

T]! &6"1)120 "0( /#(@2#,0 &690 ,)1J6"40#((U)"20,/0"26 b701J6"10 26 G"20,/0"B6"I 7FGc 04)#'"61B&#,(6 &6" T]! 16(2#"26 10 X ,01)120"20 #(J620"Q)#90"26E

]0&6"46 2#(0 &,)20,)6 ,)1@(2#"6 0110,0 P#(1) J61)B/)2@A ) 16''0A &D0 4#) 2012 4)#'"61B&) )")Q)#(),)1@(20,0KK0,6 J61)B/)I 9# &D0 46J6 @" J0,)646 4)

J620"Q)#90"26 40) J,6&011) J)s 40K6() ,0&@J0,#"6#(90"6 4) 4@0 40/)#Q)6") 12#"4#,4 Y@#"4616L6J61B #'() 12011) 2012E

%#&&#'()")*+,#"- 585; <=:> [[

a0 "0@,61&)0"Q0 &) 4)&6"6 &D0



a0 "0@,61&)0"Q0 &) 4)&6"6 &D0

)( &0,/0((6 X J(#1B&6

%#&&#'()")*+,#"- 585; <=:> [^

a# "0@,6J(#1B&)23 1) ,)P0,)1&0 #((# &#J#&)23 40(&0,/0((6 4) &#9K)#,0 0 4) &,0#,0 "@6/0 &6""011)6")E

a0 "0@,61&)0"Q0 &) 4)&6"6 &D0



a0 "0@,61&)0"Q0 &) 4)&6"6 &D0

)( &0,/0((6 X J(#1B&6

%#&&#'()")*+,#"- 585; <=:> [`

j@#"46 1) )9J#,#I @"# 1)"#J1) l1) #&&0"40pI &)6XJ#11# &6,,0"20 0(0L,)&# 0 @"# "@6/# &6""011)6"01) P6,9# 2,# &0((@(0 "0,/610E

a0 "0@,61&)0"Q0 &) 4)&6"6 &D0



a0 "0@,61&)0"Q0 &) 4)&6"6 &D0

)( &0,/0((6 X J(#1B&6

%#&&#'()")*+,#"- 585; <=:> [\

G J0,&6,1) 1)"#JB&) 16"6 &690 6,90 "0((# 1#KK)#kJ6116"6 4)/0"2#,0 J0,&6,1) 12#K)() 10 16"6 @1#B 4)P,0Y@0"20I 6JJ@,0 J6116"6 1K)#4),0 04 0110,0

1J#QQ#B /)# 10 @1#B J6&6E

f@6/0 &6""011)6") 1) &,0#"6 04 #(2,0 1J#,)1&6"6

6'") 10&6"46E

a0 "0@,61&)0"Q0 &) 4)&6"6 &D0



a0 "0@,61&)0"Q0 &) 4)&6"6 &D0

)( &0,/0((6 X J(#1B&6

%#&&#'()")*+,#"- 585; <=:> ^=

;'") 01J0,)0"Q# 4U#JJ,0"4)90"26 964)o&# (#12,@L@,# 40( &0,/0((6EG( J620"Q)#(0 4) 6'") K#9K)"6 X 8f;758E

f6" 1#JJ)#96 #"&6,# Y@#() &6"10'@0"Q0 "0((61/)(@JJ6 9#209#B&6 4) @" K#9K)"6 J611#"6 #/0,0

/0,) 40o&)2 (0'#BI #4 0109J)6 #((# 5a?] 6 #4 #K)()23)")K)26,)0E

OD ) Z



OD0 &61# 1) J@Z "62#,0b#"&D0 J,0&6&090"20c )" 12@40"B # ,)1&D)6R

• 40K6(0 l10"16 40( "@90,6p

•

40K6(0 lJ0,&0Q)6"0 4) 12,@L@,#p

%#&&#'()")*+,#"- 585; <=:> ^:





G( 10"16 40( "@90,6 X

4)1&,)9)"#"20316,%"= /.-7) 9) *%,') 316,%"= /.F. 9) *%,')

N=} @1# P#A &6"61&)@B [} P#A &6"61&)@B

[:} 10"16 40( "@90,6 =} 10"16 40( "@90,6\} &6@"B"' 6" ^<} &6@"B"' 6"

<<} &6"20'')6 262#(0

%#&&#'()")*+,#"- 585; <=:>

v

^N



G( 10"16 40( "@90,6 X

4)1&,)9)"#"20316,%"= /.-7) 9) *%,') 316,%"= /.F. 9) *%,')

N=} @1# P#A &6"61&)@B [} P#A &6"61&)@B

[:} 10"16 40( "@90,6 =} 10"16 40( "@90,6\} &6@"B"' 6" ^<} &6@"B"' 6"

<<} &6"20'')6 262#(0

%#&&#'()")*+,#"- 585; <=:>

v

OD) X )" 4)H&6(23

)9J#,# @" BJ6 4)/0,164) 9#209#B&#VVV

^>



G( 10"16 40( "@90,6 X

4)1&,)9)"#"20OD) X )" 4)H&6(23 "6" 1/)(@JJ# bD# 1/)(@JJ#26c )( 10"1640( "@90,6I 9# 26,"# 1@ 12,#20')0 4) &6"20'')6 0 K#12#E

T3 1)&@,0QQ# 0 ,#M6,Q# (# 9)1&6"&0Q)6"0 &D0 (#9#209#B&# 1)# l&6"2#,0 )" 9646 96(26 J,0&)16Ep

]J0116 1) 1&0'()0 4) )"10'"#,0 (6,6 J,6&04@,0 )"/0&0 &D0@" @16 u011)K)(0 40) "@90,)I J0,&D{ &61€ 1) D# (U)((@1)6"0

&D0 l#KK)#"6 &#J)26pE5# &61€ () 1) 4)1J0"1# 4#( P#,0 9#209#B&#E

%#&&#'()")*+,#"- 585; <=:> ^W

OD0 &61U#(2,6 X &6,,0(#26 &6" @" K@6"6 1/)(@JJ6 40(



OD0 &61 #(2,6 X &6,,0(#26 &6" @" K@6"6 1/)(@JJ6 40(l10"16 40( "@90,6pR

%#&&#'()")*+,#"- 585; <=:> ^[

%@6"0 J,012#Q)6") )" &69J)B#,)290B&) 109K,#"6 &6,,0(#B&6" @"# K@6"# J0,&0Q)6"0 4)12,@L@,#E

b5@(()'#" 5)2&D0(96,0I <=:Nc



%#&&#'()")*+,#"- 585; <=:> ^^



%#&&#'()")*+,#"- 585; <=:> ^`



%#&&#'()")*+,#"- 585; <=:> ^\



%#&&#'()")*+,#"- 585; <=:> `=

Guarda queste palline



%#&&#'()")*+,#"- 585; <=:> `:

Guarda queste palline7)J,64@&)(0



%#&&#'()")*+,#"- 585; <=:> `<

Mulligan & Mitchelmore

(2013). Early Awarenessof Mathematical Patternand Structure. In L.English & J. Mulligan(Eds.),Reconceptualizing EarlyMathematics Learning .Springer

O69J6"0"20 /)1@6*1J#Q)#(0i12,@L@,#(0



40( J0"1)0,6 #('0K,)&6G" #(&@") ,0&0"B (#/6,) 4) 7#4P6,4 b<=::c 0 4) 7)/0,#

b<=:=c /)0"0 16L6()"0#26 &690 J0, 0120"40,0 @"#10Y@0"Q# 4) o'@,0 '() 12@40"B D#""6 K)16'"6 4),)&6"61&0,0 @"# ,0'6(#,)23 0 Y@0126I 4# @" J@"26 4)/)12# &6'")B/6I ,)&D)040 (# &#J#&)23 4) &66,4)"#,0 (012,@L@,0 "@90,)&D0 # Y@0((0 1J#Q)#()E

lFD0 #S#,0"011 6P 2D010 12,@&2@,01 #"4 2D0),&66,4)"#B6" 0"2#)( # &69J(0w ,0(#B6"1D)J K02S00"

b)""0, 6, 6@20,c 1J00&DI P6,91 6P /)1@#()Q#B6" #"4)9#')"#B6"I '012@,0I #"4 #&B/)2m 6" 1)'"1 b0E'EI"@9K0,1 #"4 J,626*#('0K,#)& "62#B6"1cp b7#4P6,4I<=::I JE <NcE

%#&&#'()")*+,#"- 585; <=:> `N



C,6/)#96 # l9#")J6(#,0p ) "@90,)



C,6/)#96 # 9#")J6(#,0 ) "@90,)

O690 401&,)/0,0120 Y@012# 4)1J61)Q)6"0 4)120(()"0R

%#&&#'()")*+,#"- 585; <=:> `W

j@#"B 16"6 ) Y@#4,#B ,611)R



j@# B 16 6 Y@#4 #B 611 R

%#&&#'()")*+,#"- 585; <=:> `[

j@#"B 16"6 ) Y@#4,#B ,611)R



j Y

%#&&#'()")*+,#"- 585; <=:> `^

()



J#,()#96"0EEE

:= w >

:= v := v ` v `

:= w > n >

:= v \ v \ v `

\ v \ v \ v \EEE

%#&&#'()")*+,#"- 585; <=:> ``



j@#"B 9#L6"&)") "0( &#16 >R

&#16 : &#16 < &#16 N &#16 >

%#&&#'()")*+,#"- 585; <=:> `\





;,# J,6/)#96 # J0"1#,0 #

:< w :W

ƒ10"Q# 1&,)/0,0 0 10"Q# @1#,0 #('6,)29696(BJ()&#Q)6"0 )" &6(6""#„

%#&&#'()")*+,#"- 585; <=:> \:

C,6/)#96 # l9#")J6(#,0p ) "@90,)



C,6/)#96 # 9#")J6(#,0 ) "@90,)

N w b> w :Wc

> w :W

%#&&#'()")*+,#"- 585; <=:> \<

C,6/)#96 # l9#")J6(#,0p ) "@90,)



C,6/)#96 # 9#")J6(#,0 ) "@90,)

b:< w Wc w N

:< w W

%#&&#'()")*+,#"- 585; <=:> \N

C,6/)#96 # l9#")J6(#,0p ) "@90,)



C,6/)#96 # 9#")J6(#,0 ) "@90,)

%#&&#'()")*+,#"- 585; <=:> \>

C,6/)#96 # l9#")J6(#,0p ) "@90,)



C,6/)#96 # 9#")J6(#,0 ) "@90,)

b:= v <c w :W

:= v<%#&&#'()")*+,#"- 585; <=:> \W

C,6/)#96 # l9#")J6(#,0p ) "@90,)



C,6/)#96 # 9#")J6(#,0 ) "@90,)

b:= v <c w :W

:= v<%#&&#'()")*+,#"- 585; <=:> \[

C,6/)#96 # l9#")J6(#,0p ) "@90,)



C,6/)#96 # 9#")J6(#,0 ) "@90,)

%#&&#'()")*+,#"- 585; <=:> \^

b:= v <c w :W

:= v<

C,6/)#96 # l9#")J6(#,0p ) "@90,)



C,6/)#96 # 9#")J6(#,0 ) "@90,)

%#&&#'()")*+,#"- 585; <=:>

:= w :W < w

: W

\`

b:= v <c w :W

:= v<

C,6/)#96 # l9#")J6(#,0p ) "@90,)



C,6/)#96 # 9#")J6(#,0 ) "@90,)

;,# J,6/)#96 # J0"1#,0 #

:< w :WbJ,6J612# 4) 12@40"B &6" 4)#'"61) 4) T]!c

:Ww:=z:W=

:Ww<zN=b:=v<cw:Wz:=w:Wv<w:Wz:W=vN=z:`=

%#&&#'()")*+,#"- 585; <=:> \\

C,6/)#96 # l9#")J6(#,0p ) "@90,)



C,6/)#96 # 9#")J6(#,0 ) "@90,)

C0"1)#96 #40116 #

<W w <\

)" 2#"B 964) 4)/0,1)E

%#&&#'()")*+,#"- 585; <=:> :==



%#&&#'()")*+,#"- 585; <=:> :=:





%#&&#'()")*+,#"- 585; <=:> :=N

! #$% #./) -6e /%7@'7% 6")



Un’adeguata stimolazione attraverso una buonadidattica può• favorire i processi della plasticità cerebrale;• alleviare alcune difficoltà causate dai DSA;•

prevenire il fenomeno degli studenti “falsipositivi” alle prove per la diagnosi di DE aiutandopiù del 20% della popolazione scolastica

(percentuale di studenti che manifestanodifficoltà in matematica entro la fine della scuolaelementare).

fH6.") J',)d#)g;

:=>%#&&#'()")*+,#"- 585; <=:>

36 ]6)9' ()/' 1%.7'#$% >.",)7% 6") f(6.")



•

Su trasposizioni didattiche “intelligenti” (!) discoperte e modelli neuroscientifici rilevanti;

• su buone pratiche individuate perpotenziamenti individuali;

•

su appropriate teorie dal campo delladidattica della matematica che consentano diadattare il lavoro uno-a-uno ad unasituazione di classe

, con un’attenzioneverso le caratteristiche cognitive di tutti glistudenti.

,',)d#)g ,%99) *)1%*)=#);

:=W%#&&#'()")*+,#"- 585; <=:>

j@#() K#1) 1&)0"Bo&D0R



bf0@,61&)0"Q0 0 J1)&6(6')# &6'")B/#c

•

5640((6 40( F,)J(6 O64)&0 4) T0D#0"0• 5640((6 1@((6 1/)(@JJ6 40((# ()"0# 40) "@90,)

90"2#(0

•

7@6(6 40((# 9096,)# – # (@"'6 20,9)"0

– # K,0/0 20,9)"0 b)" J#,B&E 5a?]c

• #(2,0 P@"Q)6") &6'")B/0 &6,,0(#20 &6" K#110

J,012#Q)6") )" J#,B&6(#,) #9K)B 40((# 9#209#"B&#

• 1B() 4U#JJ,0"4)90"26 0 &#"#() J,0P0,0"Q)#() J0, )(u@116 4) )"P6,9#Q)6")

%#&&#'()")*+,#"- 585; <=:> :=[

j@#() K#1) 1&)0"Bo&D0R



bT)4#A&# 40((# 5#209#B&#c

•

,@6(6 40((# J0,&0Q)6"0 4) l12,@L@,#p "0((61/)(@JJ6 40( l10"16 40( "@90,6p

• &6*&612,@Q)6"0 4) 1)'")o&#B 9#209#B&)

•

F06,)# 40((# 504)#Q)6"0 ]09)6B&# –

@16 4) l#,20P#A )"20(()'0"Bp bo1)&) 0 4)')2#()c "0((#4)4#A&# J0, 904)#,0 ) &6"20"@B 9#209#B&) 4)

,)P0,)90"26• O6"&0A +)'@,#()

• 70')12,) 4) ,#JJ,010"2#Q)6"0 109)6B&#%#&&#'()")*+,#"- 585; <=:> :=^

]B(0 l(69K,)&6p 0 l',)((6p



]B(0 (69K,)&6 0 ',)((6

]B(0 (69K,)&6k #L#&&#26 #((0 P6,9@(0IJ,6&04@,#(0I 10Y@0"Q)#(0I K)16'"6 4)46&@90"2#,0 2@L6

]B(0 ',)((6k 6()1B&6I )"2@)B/6I 6JJ6"'6"6,01)120"Q# #((# ,)&D)012# 4) 46&@90"2#,0 )((6,6 J0"1)0,6E

b5#,6(4# T#/)416"I <===q OD)""I <=:<c%#&&#'()")*+,#"- 585; <=:> :=`



… 4)J0"40"20 4# #K)()23

/0,K#()E

C,0P0,)1&0 1B96() J0,&0A/) 0

,0)"20,J,02# 1)2@#Q)6") #12,#L0 )"9#")0,# /)1)/#E

50L0 # P@6&6 40L#'()1J0&)o&) 6 #1J0A 1)"'6() 4)

@"# 1)2@#Q)6"0E

g() J)#&&)6"6 ) "@90,) ',#"4) 0"6" /@6(0 0110,0 4)12@,K#26 #

'01B,0 ) 40L#'()E?040 '() †#(K0,)U 9# "6"J0,&0J)1&0 (# †P6,012#UEC,0P0,)1&0 O;58 # C87Ot‡

C,0P0,)1&0 C87Ot‡ # O;58

T)J0"40 4# @"# 10Y@0"Q#J,04)(0L# 4) J#11) J0,,#'')@"'0,0 @"# 902#E

C,0P0,)1&0 #JJ,6&&) "6"10Y@0"Q)#() &D0 &6)"/6('6"6lJ#L0,"1p 0 ,0(#Q)6") 2,# 4)/0,1)0(090"B

%#&&#'()")*+,#"- 585; <=:> :=\



G( K@6" 9#209#B&6 ,#'')@"'0 @" 0Y@)()K,)6A ( B )



6A9#(0 2,# Y@01B 012,09)

:::%#&&#'()")*+,#"- 585; <=:>

8109J) 4) J,6J6120 4)4#A&D0



f0( J,6'0L6 C0,O6"2#,0 b2,# )( <=:: 0 )( <=:>cI',#Q)0 #4 @" (#/6,6 &6"')@"26 2,# 4)4#A&) 40((#9#209#B&# 0 J1)&6(6') &6'")B/)I #KK)#96

1/)(@JJ#26 /#,)0 #A/)23 J0, @" K@6" #//)6#((U#,)290B&#I # J#,B,0 4#((# 2,#"1)Q)6"0 4#((#1&@6(# 40((U)"P#"Q)# #((# 1&@6(# J,)9#,)#E

b#(2,0 )"P6,9#Q)6") # J0,&6"2#,0E#1JD)E)2c

%#&&#'()")*+,#"- 585; <=:> ::<

C,6J6120 J0, @" K@6" #//)6 #( &#(&6(6b4#((# J,)9# &(#110 6 J,)9#c



::N%#&&#'()")*+,#"- 585; <=:>

b4#((# J,)9# &(#110EEE6 J,)9#cFate usare le mani.

]0"Q# (# &#J#&)23 4) #116&)#,0 (#,#JJ,010"2#Q)6"0 40) "@90,) #((#,#JJ,010"2#Q)6"0 "0@,#(0 40((0

4)2# 0 40((0 9#") "0((0 (6,6J61)Q)6") "6,9#()I '() 12011) "@90,)

"6" J6116"6 #/0,0 @"#,#JJ,010"2#Q)6"0 "6,9#(0 "0(

&0,/0((6E

(Butterworth, 1999 )

J)99% "%67./#'%"4%

h , 99 K '



GJ6201)k F,0 #K)()23 4) K#10 1@ &@) J6'')#"6(0 J)s &69J(0110 #K)()23 "@90,)&D0 16"6• ]#J0, ,)&6"61&0,0 J)&&6(0 "@90,61)23

10"Q# &6"2#,0 b1@K)BQ)"'c• a0 #K)()23 9626,)0 o") bo"'0, 2#JJ)"'c• a# ,#JJ,010"2#Q)6"0 &D0 )( 16''0L6 D#

40((0 J,6J,)0 4)2# b'"61)# 4)')2#(0c

(Butterworth, 2000, 2005 )

h/. ,%99% K)"'

%#&&#'()")*+,#"- 585; <=:> ::>

7)1@(2#B 1J0,)90"2#() 1@((#“ 4 ( ”



“'"61)# 4)')2#(0”

•

G( J620"Q)#90"26 40((# '"61)#4)')2#(0 D# J6,2#26 @" ',@JJ61J0,)90"2#(0 4) K#9K)") &6"1&#,1# #K)()23 # 1@J0,#,0 @"',@JJ6 lP6,20p "6" 16L6J6126# J620"Q)#90"26E b%#P#((@m f6‚(I <==`c

•

la# &6"1#J0/6(0QQ# 40((0 4)2#p X @" K@6"J,04)L6,0 40((0 #K)()23 "@90,)&D0 40(K#9K)"6E bf6‚(I <==Wc

%#&&#'()")*+,#"- 585; <=:> ::W



C611)#96 1/)(@JJ#,0

40((0 K@6"0 J,#B&D0J0, 1/)(@JJ#,0&6"1#J0/6(0QQ# 40((0

4)2#I 90"2,01/)(@JJ)#96 (0 #K)()23

"@90,)&D0E

%#&&#'()")*+,#"- 585; <=:> ::[



EEE0 l(0''0,0p 4#) 964))" &@) '() 12@40"B @1#"6(0 9#") '() 1&D09) &D0

D#""6 #JJ,6J,)#26b6JJ@,0 "6cE

%#&&#'()")*+,#"- 585; <=:> ::^



%#&&#'()")*+,#"- 585; <=:> ::`



%#&&#'()")*+,#"- 585; <=:> ::\

?#,)!,20P#A

G"20(()'0"B

j@0126 /#(0 )" '0"0,#(0Y@#"46 P#&&)#96 @16 4)

l#,20P#A )"20(()'0"Bp "0((0J,#B&D0 4)4#A&D0

f%k(# ,)&0,&# 1@''0,)1&0 4)

1P,@L#,0 ,#JJ,010"2#Q)6")

4) BJ6 #"#(6')&6 40("@90,6 &D0 J@"2#"6 1@(

&#"#(0 /)1)/6 "6" /0,K#(0 0&)"0120B&6E



3 dieci

30

6 (sparse)

63 dieci 6 - trentasei

36%#&&#'()")*+,#"- 585; <=:> :<=

C0,&D{ ) P#1&0A 4) &#""@&&0 16"6 @"K@6"6 12,@90"26R



K@6"6 12,@90"26R

%#&&#'()")*+,#"- 585; <=:>

•

J0,90L6"6 #((U)"10'"#"20 4) 90L0,1) )",0(#Q)6"0 &6" )9J6,2#"B 1)'")o&#B 9#209#B&)IJ0, 01Ek – (# 40&)"#

–

"62#Q)6"0 40&)9#(0 – &69J6,,0i1&69J6,,0

• &6"10"26"6 4) 9#"20"0,0 @"# ,0(#Q)6"0 &6"&,02#&6" (U#1J0L6 109#"B&6 40( "@90,6 10"Q#J#11#,0 J0, )( &64)&0 /0,K#(0 6 Y@0((6 /)1)/6*#,#K6

• (U#A/)23 &6" (0 &#""@&&0 #A/# )( &#"#(0&)"0120B&6

:<:salta cannucce

5640((6 40((0 1&#26(0 2,#1J#,0"B



J

%#&&#'()")*+,#"- 585; <=:>

Ho tre decine e quattordici unità.Che numero è?

:<<

5640((6 40((0 1&#26(0 2,#1J#,0"B



J

%#&&#'()")*+,#"- 585; <=:>

Ho tre decine e quattordici unità.Che numero è?

:<N

5640((6 40((0 1&#26(0 2,#1J#,0"B



J

%#&&#'()")*+,#"- 585; <=:>

3 decine e 14 unità

:<>

5640((6 40((0 1&#26(0 2,#1J#,0"B



%#&&#'()")*+,#"- 585; <=:>

a0'6 ) P#1&0A &D0J6116 0 () 90L6

"0((# (6,6 1&#26(#

:<W

5640((6 40((0 1&#26(0 2,#1J#,0"B



%#&&#'()")*+,#"- 585; <=:> :<[



O#""@&&0# C#1&#()"## !K#&6



f62#Q)6"0 J61)Q)6"#(0 40&)9#(0G "@90,) 1) J6116"6 40&69J6,,0 )" DI 4#I @k

":w:== v "<w:= v "N

D 4# @ %#&&#'()")*+,#"- 585; <=:> :<`

O6,,)1J6"40"Q# &#""@&&0 * ,620((0



":w:== v "<w:= v "N

%#&&#'()")*+,#"- 585; <=:> :<\

8 o"#(90"20 (U#K#&6•



%#&&#'()")*+,#"- 585; <=:>

4 decine e 4 unità

:N=

C#11#"46 #( &#(&6(6•b#"&D0 Y@0((6 )" &6(6""#c



%#&&#'()")*+,#"- 585; <=:>

4 decine e 4 unità

:N:

salta calcolo in colonna



%#&&#'()")*+,#"- 585; <=:> :N<



%#&&#'()")*+,#"- 585; <=:> :NN

Questa strategia rispecchia procedure “tradizionali” che perònon dovrebbero essere insegnate a memoria, maconquistate attraverso una “scoperta” da parte dei bambini.

Analogamente si possono far esplicitare similitudini traprocedure eseguite con la pascalina e procedure di calcolo in



%#&&#'()")*+,#"- 585; <=:> :N>

procedure eseguite con la pascalina e procedure di calcolo incolonna, costruendo così il significato di questi ultimi a partire

dai primi.

7)#11@90"46•



Difficoltà nella rappresentazione dei numeripossono emergere da:• passaggio codice analogico/cod simbolico• gestione passaggio unità-decine e vs

Difficoltà nell’addizione/sottrazione possonoemergere da:• passaggio cod analogico/cod simbolico•

gestione passaggio unità-decine e vs• diverse procedure per operandi a più cifre

%#&&#'()")*+,#"- 585; <=:> :NW

7)#11@90"46•



8)""6##% %

/#)1.9%

-)/#)9'") )()#. 8)71) %

-%"") '"#.9."")

7#JJ,01E"@90,)

O64 #"#(6')&6i&64 1)9K6()&6

#"#(6')&6 ])9K6()&6b&)P,0 0J61)Q)6"0c

])9K6()&6J61)Q)6"0I#"#(6')&6&)P,0

])9K6()&6&6" '01B6"0/)1@6*1J#QE

C#11#'')6@")23*40&)"0 0/1

! &#,)&6K#9K)"6

! &#,)&612,@90"26

! &#,)&6K#9K)"6

! &#,)&6K#9K)"6b#"B&)J#2#90"20c

O#(6(6b#44i16Lc

C,6&04@,#,)')4# J0,'01B6"040&)"0i@")23

f6I )"2@)B/60 ,)9#"0P6,20 (#&69J6"0"20#"#(6')&#

"6 b&690&#""@&&0cI #&#,)&6 40((612,@90"26

"6I 9# /)0"0)"10'"#2#&690 2#(0I2@L# # &#,)&640( K#9K)"6

]€ bJ0, )(K)16'"6 4)l#"B&)J#,0p)( ,)1@(2#26c

%#&&#'()")*+,#"- 585; <=:> :N[



C0,&6,1) P6"4#90"2#() J,6J61B "0(L C O 2



?#,)!,20P#A#4 #(26

J620"Q)#(0

J,6'0L6 C0,O6"2#,0

!"&6,# (# /6,6

1@ ( (# "6 2# Q )6"0

J6 1 ) Q )6"# (0

%#&&#'()")*+,#"- 585; <=:> :N`

C,6J6120 J0, (U)"10'"#90"26 40((0lF#K0(()"0p



:N\%#&&#'()")*+,#"- 585; <=:>

G ,0L#"'6() &690 9640((6 J0, (# 96(BJ()&#Q)6"0$

Fanno parte della nostra tradizioneculturale: prima i pitagorici poi ripresi

da Euclide$

Le prime ricerche (anni 2000)rivelano buoni risultati

$

In alcune nazioni sono consigliati nel

curricolo nazionale (per es. USA)$ Sono già presenti in alcuni libri ditesto

G" lG9J#,#,0 &6" )( F@KZ C)2#'6,)&6p J,6J6")#96EEE



f%k

F#/6(#J)2#'6,)&#

l,6/01&)#2#p

%#&&#'()")*+,#"- 585; <=:> :>=

:=

\



: < N > W [ ^ ` \ :=

`

^

[

W>

N

<

:

w

.1#"46 ) ,0L#"'6() &D0

')3 &6"61&) K0"0I J,6/## 401&,)/0,0 '() #(2,)E

C0, 0109J)6 >w<E

%#&&#'()")*+,#"- 585; <=:> :>:

:=

\



: < N > W [ ^ ` \ :=

`

^

[

W>

N

<

:

w %#&&#'()")*+,#"- 585; <=:> :><

O6"61&6 < w <

>

:=

\



: < N > W [ ^ ` \ :=

`

^

[

W>

N

<

:

w %#&&#'()")*+,#"- 585; <=:> :>N

!"&D0 J0,&D{ 9) ,)&6,46) Y@#4,#BEEE

>

\

:[

:





%#&&#'()")*+,#"- 585; <=:> :>W



%#&&#'()")*+,#"- 585; <=:> :>[



%#&&#'()")*+,#"- 585; <=:> :>^





T)H&6(23 4) #JJ,0"4)90"26)" '06902,)#

!(2,0 4)H&6(23 4) #JJ,0"4)90"26)" #,)290B&# b01J,011)6")c

%#&&#'()")*+,#"- 585; <=:> :>\

aU#JJ,0"4)90"26 40((# '06902,)#



]09K,# 0110,0 )( ,)1@(2#26 4) 4)M0,0"B #K)()23 k

•

a0'#20 #( ()"'@#'')6 * &6"61&0"Q# 4)&D)#,#B/# b01E 20,9)")I40o")Q)6")I 206,09)•EcI

•

a0'#20 #((U#12,#Q)6"0 0 #( ,#')6"#90"26 * 4) J,6K(09 16(/)"'b01E ,)&6"61&)90"26 4) )"/#,)#"BI 16(@Q)6"0 4) J,6K(09)•Ec

• a0'#20 #((# 9096,)# b01E 9096,)QQ#Q)6"0 4) )"P6,9#Q)6") 0J,6&04@,0I 9096,)# 4) (#/6,6 /)1@61J#Q)#(0c

–

!%GaGF!U ?G].;]C!yG!aG b1&69J61)Q)6"0 4) o'@,0I &612,@Q)6"0

4) o'@,0 16()40I &#(&6(6 40( /6(@90 n # J#,B,0 4# @")23 4) K#10I9096,)# 4) (#/6,6 * 0wk &6(6,# (# 1@J0,o&)0 46/0 2@L0 (0 o'@,01) )"20,10&#"6• c

%#&&#'()")*+,#"- 585; <=:> :W=

aU#JJ,0"4)90"26 40((# '06902,)#



]09K,# 0110,0 )( ,)1@(2#26 4) 4)M0,0"B #K)()23 k

•

a0'#20 #( ()"'@#'')6 * &6"61&0"Q# 4)&D)#,#B/# b01E 20,9)")I40o")Q)6")I 206,09)•EcI

•

a0'#20 #((U#12,#Q)6"0 0 #( ,#')6"#90"26 * 4) J,6K(09 16(/)"'b01E ,)&6"61&)90"26 4) )"/#,)#"BI 16(@Q)6"0 4) J,6K(09)•Ec

•

a0'#20 #((# 9096,)# b01E 9096,)QQ#Q)6"0 4) )"P6,9#Q)6") 0J,6&04@,0I 9096,)# 4) (#/6,6 /)1@61J#Q)#(0c

– !%GaGF!U ?G].;]C!yG!aG b1&69J61)Q)6"0 4) o'@,0I &612,@Q)6"0

4) o'@,0 16()40I &#(&6(6 40( /6(@90 n # J#,B,0 4# @")23 4) K#10I9096,)# 4) (#/6,6 * 0wk &6(6,# (# 1@J0,o&)0 46/0 2@L0 (0 o'@,01) )"20,10&#"6• c

%#&&#'()")*+,#"- 585; <=:> :W:

aU#JJ,0"4)90"26 40((# '06902,)#



• a# #)7%"4) J0,Z "6" 1#,0KK0 "0( ˆ9#'#QQ)"6 J#11)/6ÎY@#"26 J)@L6126 "%99) #)-)#'1U ,' *)"'-.9)7% ' #."1%"6=

,%99) *%*.7') )' ,'@%7/' 9'@%99' ,' )d@'1Uk J0, &6"10,/#,0 #(@"'6 (r)"P6,9#Q)6"0I J0, #"#()QQ#,(# 04 ˆ#'')@12#,(#Î J0,2,#1P6,9#,(# 0 ,0)"20,J,02#,(#E

•

]0&6"46 O6,"6(4) b:\\\c Y@0120 .-%7)4'."' #.'"@.9A.".

9:)d@'1U '**)A'")=@) @'/'@)E G"P#AI (0 )99#')") 90"2#(),)&D)046"6 &D0 &6"20"@B /)1@6*1J#Q)#()I 1)# 4) 01J0,)0"Q0)9904)#2#90"20 J,0&040"B 1)# #JJ#,20"0"B #( 96"46 40)

,)&6,4)I 1)#"6 6,'#")QQ#B 04 0(#K6,#B 4#((# 9096,)# 4)(#/6,6E

%#&&#'()")*+,#"- 585; <=:> :W<

j@0120 )J6201)I ,)40o")1&6"6 )" J#,20 (0 &#,#L0,)1B&D0 J,6J,)0 40((#])"4,690 "6" /0,K#(0 bO6,"6(4) 02 #(EI :\\^ck

• K(6&&6 4) P,6"20 # &6"10'"0 4)H&)()k J,6K#K)(90"20 Y@012# X @"# 964#()23



K(6&&6 4) P,6"20 # &6"10'"0 4)H&)()k J,6K#K)(90"20 Y@012# X @"# 964#()234)P0"1)/# J0, "6" (#1&)#,1) 16J,#M#,0 4#((r0&&011)/6 &#,)&6 4) )"P6,9#Q)6")

&D0 40/0 '01B,0 b(# &#J#&)23 4) 9096,)# /)1@6*1J#Q)#(0 X ()9)2#2#cq• #JJ,6&&)6 #( &69J)26 4) BJ6 26J*46S"k )( 16''0L6 #')1&0 16J,#L@L6 )"

K#10 #'() 1&D09) 90"2#() #A/#BI J)s &D0 #((0 )"P6,9#Q)6") 0120,"0q 20"40# o11#,1) 1@ @"r)40# 10"Q# J,012#,0 1@H&)0"20 #L0"Q)6"0 #'() 1B96()0120,")k "0 &6"10'@0 @"# &0,2# J0,10/0,#"Q# "0((r0,,6,0 6 4)H&6(23 #

&#9K)#,0 102 4) ,)1J612#q• 4)H&6(23 "0( 9#")J6(#,0I &612,@),0 0 J,6'0L#,0 (r)99#')"0 90"2#(0q

• 4)H&6(23 "0((# J)#")o&#Q)6"0 0 J,6'0L#Q)6"0 4) 96(B &69J)Bq

• )9J#&&)6 4) P,6"20 #((# "6/)23k 16''0A 26J*46S" /046"6 Y@0((6 &D0D#""6 )" 90"20 0 "6" 1) #&&6,'6"6 40((0 0&&0Q)6") 6 40) J#,B&6(#,) "@6/)q

•

4)H&6(23 40((# 9096,)# 4) (#/6,6 /)1@6*1J#Q)#(0q• @16 J,)/)(0')#26 40( &#"#(0 @4)B/6*/0,K#(0 J0, 0(#K6,#,0 (0 )"P6,9#Q)6")E

.B()QQ6 40( ()"'@#'')6 # 1@JJ6,26 0 &69J0"1#Q)6"0 40( 40o&)2 /)1@6*1J#Q)#(0E

%#&&#'()")*+,#"- 585; <=:> :WN

9* !+#:$'2+#"; 6",1#+ ),!'#-+*-"



.1#,0 @" &64)&0 &D0 &6"10"2# 4) #((0''0,),0)( &#,)&6 40((# 9096,)# /)1@6 1J#Q)#(0kJ0,90L# 4) /040,0 J)s )"P6,9#Q)6")1)9@(2#"0#90"20 0 4) 90L0,0 )" ,0(#Q)6"06''0A '06902,)&)

%#&&#'()")*+,#"- 585; <=:> :W>

<+*+2) () +$$"66' +22" )*8'#,+3)'*) "

6:2) (7+!!#"*(),"*-'



6:2) ( +!!#"*(),"*-'

)"P6,9#Q)6"0

?)1)/6*/0,K#(0

!*%*O

?)1)/6 "6"/0,K#(0 @4)B/6

&)"0120B&6

]) )9J#,# (0''0"46

]) )9J#,# 1@((# K#10 4)@"# 9096,)# /)1)/#E

]) )9J#,# #1&6(2#"46

]) )9J#,# P#&0"46

]20((#I <=:< lO690 (0''0,0 (# 4)1(011)#p

G( &#"#(0 /)1)/6 /0,K#(0

f;f … Y@0((6 !T!FF;J0, )"P6,9#Q)6") &D0

40/6"6 0110,0 0(#K6,#204#( 469)")6 /)1@6*

1J#Q)#(0

%#&&#'()")*+,#"- 585; <=:> :WW

]0,/6"6 12,@90"B &D0 &6"10"2#"6 4) &612,@),0)99#')") &D0 D#""6 &#,#L0,)1B&D0 1)9)() #((0

)99#')") 90"2#() 0 &D0 &6"10"2#"6 4)



'9#")J6(#,(0 &690 10 P6110,6 )99#')") 90"2#()

aU6''0L6 9#209#B&6 &D0 '() 12@40"B @B()QQ#"6 )" @"16xS#,0 4) '06902,)&# 4)"#9)&# J@Z 0110,0 4# (6,6 /)126 )"4@0 964) 4)/0,1)k &690 6",!2)$" =>?#+ b611)# P#&0"46 (0/#1@'() #1J0A J0,&0A/) 4) 6110,/#Q)6"0c 6JJ@,0 &690 =>?#+

2">+-+ + ?*+ -"'#)+ b&)6X P#&0"46 (0/# 1@'() #1J0A&6"&0L@#()c+)'@,#( &6"&0J2k (0 o'@,0 '06902,)&D0 16"6 0"B23 90"2#() &D0J611)046"6 &6"209J6,#"0#90"20 J,6J,)023 &6"&0L@#() bJ0,01k J,6J,)023 40((# '06902,)# 0@&()40#c 0 J,6J,)023 o'@,#()

bP6,9#I J61)Q)6"0I ',#"40QQ#c." ,#')6"#90"26 '06902,)&6 J,64@A/6 b&690 @"#4)9612,#Q)6"0c J@Z 0110,0 1J)0'#26 4#( P#L6 &D0 #1J0A&6"&0L@#() 0 o'@,#() 1) P6"46"6 )* $'*$"@ =>?#+2)

%#&&#'()")*+,#"- 585; <=:> :W[

." 0109J)6 4#((# '06902,)# 4)"#9)&#



%#&&#'()")*+,#"- 585; <=:> :W^

A+ B)6$+2$?2)+ /C'2?:C+ " 27+!!#"*(),"*-'("227+2>"1#+D

E2$?*" !#","66"



E2$?*" !#","66"

%#&&#'()")*+,#"- 585; <=:> :W`

B)6$+2$?2)+ " +!!#"*(),"*-' ("227+2>"1#+(+2 !?*-' () C)6-+ ("22" *"?#'6$)"*3"



%#&&#'()")*+,#"- 585; <=:>

(0 #K)()23 4) ,0&@J0,640) P#A #,)290B&)I&D0 16"6

&69J,690110

(0 9#")J6(#Q)6")#('0K,)&D0I &D0 16"6)"2#L0

7)&0,&# 1@ 16''0A &6" 4)1&#(&@()# bt)L9#),*T0(#Q0, 02 #(EI :\\WI T0D#0"0I :\\^c D#

90116 )" (@&0 &D0 &UX @"# 4)116&)#Q)6"0 2,#k

]6"6 )" ',#46 4) ')@4)&#,0(# "6"*0Y@)/#(0"Q# 2,#01J,011)6") #('0K,)&D0

]6"6 &#J#&) 4) 2,#1P6,9#,0 0109J()o&#,0+#""6 P#B&# # &#(&6(#,0

<%NI ^*NI \kNI W%>

:W\

B)6$+2$?2)+ " +!!#"*(),"*-' ("227+2>"1#+(+2 !?*-' () C)6-+ ("22" *"?#'6$)"*3"



1#J0,0 #('0K,)&6

()/0((6 P6,9#(0* #('0K,)&6

1#J0,0 #,)290B&6

()/0((6 #,)290B&6*"@90,)&6

!788 ?G].;*]C!yG!a8#A/#20 4@,#"20 (02,#1P6,9#Q)6") #('0K,)&D0b# 4)1&#J)26 40((0 #,00

404)&#20 #( ()"'@#'')6c

t)L9#),*T0(#Q0, 02#(EI :\\W

%#&&#'()")*+,#"- 585; <=:> :[=

B)66'$)+3)'*" -#+ 2)*>?+>>)' " +#)-,":$+



• a0 &69J020"Q0 ,0(#B/0 #( #)9#.9. )7'1*%=#. /.". 9%A)1%

-7'"#'-)9*%"1% )99i)7%) @'/6. /-)4')9% 40( &0,/0((6 bJ#,20K)(#20,#(0 P,6"2#(0c: nello svolgimento di compiti

aritmetici sono attivate le aree cerebraliassociate alla memoria visuospaziali e alleimmagini mentali

• <",'-%",%"4) >7) ' *%##)"'/*' )99) ()/% ,%9 9'"A6)AA'. %

]6%99' )99) ()/% ,%9 #)9#.9. bparietofrontale bilateralee la circonvoluzioni temporale inferiorebilaterale)

aGfg.!ggG; f!F.7!a8 8 !7GF58FGO!

t6@40 FQ6@,)6*5#Q6m0,I <==Nq

?0"-#2,#9#"I!"1#,)I OD00I<==Wq y#'6 02 #(I<==:

%@L0,S6,2DI:\\\

%#&&#'()")*+,#"- 585; <=:> :[:

G" #,)290B&# b0 )" #('0K,#c 16"6 1P,@L#B#1J0A /)1@6*1J#Q)#()



G 9#209#B&) D#""6 1P,@L#26 4# 109J,0 )( P#L6 &D0#."À67)4'."' /-)4')9' ,' /'*(.9' -.1%//%7. %//%7%

6/)1% -%7 *%F%7% '" %@',%"4) 9% /176F67% ,'

%/-7%//'."'Q /176F67% f) ".,.g b"01204 12,@&2@,01cE C0,0109J)6I 10J#,#,0 )( "@90,#26,0 0 )( 40"69)"#26,0 &6"@"# 9'"%) ,' >7)4'."% 6,)QQ6"2#(0I @1#,0 -)7%"1%/'

#J0,20 0 &D)@10 J0, ("2),)-+#" 2" 6-#?5?#" +2>"1#)$%" "

("=*)#" 2+ !#)'#)-FE

%#&&#'()")*+,#"- 585; <=:> :[<

O6"o'@,#Q)6") 1J#Q)#() 0 1)"2#11) 4) 01J,011)6")9#209#B&D0k ,)1@(2#B 40((# ,)&0,&#



!(&@"0 ,)&0,&D0 D#""6 90116 )" 0/)40"Q# &D0 (0 12,@L@,0 &0(0K,#(),01J6"1#K)() 40((U#"#()1) 4) 12,@L@,0 ")4)o&#20 * 12,@L@,0 4) 01J,011)6")"@90,)&D0 &690 :vb>‰b<vNc * "6" 16"6 &6"4)/)10 &6" Y@0((0 404)&#20 #((#1)"2#11) 40((0 01J,011)6") ()"'@)1B&D0E

]) 16"6 &6"1)40,#B :: 1)9K6() &69K)"#B

)" 9646 4)/0,16 P,# (6,6k* G" 9646 0,,#26I &690 >*vcNcbv<b:

* G" 9646 &6,,0L6 &690 bbN*<cv>cv:

T0o"0"46 > ()/0(() 4) &69J(011)23

&,01&0"20k

%#&&#'()")*+,#"- 585; <=:> :[N

Maruyama, M., Pallier, C., Jobert, A., Sigman, M., &Dehaene, S. (2012). The cortical representation ofsimple mathematical expressions. NeuroImage,61(4), 1444–1460.

;110,/)#96 &D0 "0( 469)")6"@90,)&6I



Y@#(1)#1) 01J,011)6"01)"2#A&#90"20 K0" P6,9#2# X#"&D0 109#"B&#90"20 &6,,0L#E

%#&&#'()")*+,#"- 585; <=:>

j@)"4)I "0((6 1&D09# 16J,#I (# 1)"2#11) 0 (# 109#"B&# "6" J6116"6 0110,0 &6"1)40,#20 10J#,#2#90"20I 04X J0, Y@0126 &D0 (U)"20,0110 4) Y@012# ,)&0,&# 1)

&6"&0"2,# 1@ &690 )( &0,/0((6 '01B1&0i,#JJ,010"2#01J,011)6") 9#209#B&D0 0(090"2#,) # l)"&#12,)pE

:[>

f#2@,# 40((0 4)H&6(23 4) 12@40"B &6" 4)1&#(&@()#)" #,)290B&#E

• T)H&6(23 "0( ,)&6"61&)90"26 40) 1)9K6() "@90,)&)i6J0,#26,)



%#&&#'()")*+,#"- 585; <=:>

•

T)H&6(23 "0( ,)&6"61&)90"26 40) 1)9K6() "@90,)&)i6J0,#26,)#,)290B&)q

•

T)H&6(23 "0((U#L,)K@),0 )( &6,,0L6 1)'")o&#26 #((0 6J0,#Q)6")q

•

T)H&6(23 "0((# &69J,0"1)6"0 40) 20,9)") 6 40) 10'") 9#209#B&)b01E zq~q Šq •cq

•

T)H&6(23 #4 #L@#,0 9#")J6(#Q)6") #,)290B&D0 12#"4#,4q

•

T)H&6(23 4) &6"2,6((6 109#"B&6k &69J,0"40,0 Y@#() "@90,)16"6 J0,B"0"B #( J,6K(09# #,)290B&6 &D0 1) 12# &6"1)40,#"46q

• T)H&6(23 4) "#2@,# ',#o&# 0i6 4) 6,'#")QQ#Q)6"0 1J#Q)#(0k#(()"0#,0 &6,,0L#90"20I )"10,),0 40&)9#() 6 1)9K6() 4@,#"20 )

&#(&6() b0wE z "0((0 01J,011)6") "@90,)&D0 0 "0((0 0Y@#Q)6")cq•

T)H&6(23 "0( ,0&@J0,6 4) P#A #,B90B&) *~ "0&011)23 4) ,)&6,,0,0#((# &#(&6(#2,)&0 J0, 6J0,#Q)6") 96(26 109J()&) &690 <‹<I6JJ@,0 >‹:

5)"6,0 4)H&6(23 "0((U010'@),0 &#(&6() &6" ),#4)&#() b,#Q)6"#()QQ#Q)6"0I J6,2#,0 P@6,) 640"2,6EEc J0,&D{ 1) P# @16 9#'')6,90"2040((U)99#')"0 J)@L6126 &D0 40( &#(&6(6#,)290B&6 )" 10k 4) P#L6 1) 010'@0 J,)9# @"#

9#")J6(#Q)6"0 1)9K6()&# 0 16(6 )" &6"&(@1)6"0@"# 6J0,#Q)6"0 #,)290B&#E

:[W

O690 J611)#96 9)'()6,#,0 ) J,6&011) 4))"10'"#90"26*#JJ,0"4)90"26 )"



)"10'"#90"26 #JJ,0"4)90"26 )"

90209#B&#R

%#&&#'()")*+,#"- 585; <=:> :[[

G"20,/0"B &0"2,#B J,0/#(0"2090"20 1@(1)'")o&#26



%#&&#'()")*+,#"- 585; <=:> :[^

<,%% -%7 9) ,',)d#) #." /.AA%d ,'/#)9#69'#' ,%99) /#6.9) /%#.",)7')

•

(# &612,@Q)6"0 0 )( ,0&@J0,6 40( 1)'")o&#26 40((0 "6Q)6") #('0K,)&D0 0'06902,)&D0 1) J6116"6 ,0#()QQ#,0 2,#9)20 @" ,0')12,6 4) ,#JJ,010"2#Q)6"04) BJ6 /)1@6*1J#Q)#(0 J)@L6126 &D0 4) BJ6 J,0/#(0"2090"20 /0,K#(0E

• aU#JJ,6&&)6 /)1@6*1J#Q)#(0I &D0 &#,#L0,)QQ# (U)40# 4)4#A&# J)s)""6/#B/#I 109K,# 0110,0 0H&#&0 1)# J0, #L,)K@),0 1)'")o&#26 #) &6"&0A

#('0K,)&) b/#,)#K)(0I 01J,011)6")I 0Y@#Q)6")I 0&&Ec 1)# #((0 J,6&04@,09#")J6(#B/0 b(0'#20I J0, 0109J)6I #((# 16(@Q)6"0 40((0 0Y@#Q)6") 0,0#()QQ#20 2,#9)20 (U#JJ()&#Q)6"0 4) ,0'6(0 0 J,6J,)023cE

• O)Z 1@''0,)1&0 (U)9J6,2#"Q#I 4#( J@"26 4) /)12# 4)4#A&6I 40((0 *.,)9'1UI40'() /176*%"= 0 40) #."1%/= &6" ) Y@#() ) &6"&0A 9#209#B&) /0"'6"6

J,6J61BE g() 12,@90"B b1)#"6 011) &#,2# 0 J0""#I #K#&6I 16xS#,0•cJ6116"6 904)#,0 (U)"2,64@Q)6"0 4) @"# "@6/# "6Q)6"0 9#209#B&# )" 964)4)/0,1) P6,"0"46"0I 4) P#L6I 4)/0,10 ,#JJ,010"2#Q)6") 1@((# K#10 40((0 Y@#()0(#K6,#,0 )99#')") 0 9640(() 90"2#()E

7@6(6 40((# 20&"6(6')#



%#&&#'()")*+,#"- 585; <=:> :[`

•

;&&6,,6"6 12,@90"B &D0 &6"10"2#"6 4) 904)#,0(U)"2,64@Q)6"0 4) "6Q)6") 9#209#B&D0 #L,#/0,16,#JJ,010"2#Q)6"0 4) BJ6 ',#o&6 J)@L6126 &D0 /0,K#(0E

• (# ,)&0,&# )" 4)4#A&# 9612,# &D0 &)Z X J611)K)(01P,@L#"46 (0 ,#JJ,010"2#Q)6") P6,")20 4# 4)/0,1)12,@90"B 4) 904)#Q)6"0 4)4#A&# b4)')2#() 0 "6"cE

• G" J#,B&6(#,0 &) )"20,011#"6 /176*%"= /.jk)7% &D0&6"10"26"6 #((0 ,#JJ,010"2#Q)6") 4) #//#(0,1) 40((#&#,#L0,)1B&# 4) ()*+,)$)-FI 0110"Q)#(0 J0, J620, #"*("#"

"6!2)$)-" 2" #"2+3)'*) ,+-",+:$%" 8#+ >2) '>>"@,+-",+:$) )" ')6&6 0 J0, J620,"0 &612,@),0 ) 6)>*)=$+: E

a# 20&"6(6')# J@Z



•

O69J0"1#,0 /#,) 40o&)2

• !('9'1)7%I "0( 10"16 4)4#A&6 40(20,9)"0I &)6X P6,"),0 1@JJ6,26 J0, 4#,0#&&0116 #( 1)'")o&#26 40) &6"&0A9#209#B&)

O;58R

%#&&#'()")*+,#"- 585; <=:> :[\

8./1764'."% ,%99) >7)4'."% ZlT *%,')"1% '9

*.,%99. A%.*%17'#.



A

,%99) ,'@'/'."% /699) O%F) !9A%(7'#)B

%#&&#'()")*+,#"- 585; <=:>

#'')@12# (# ,0L# )" 9646&D0 J#11) J0, N 0 J0, <

:^=

8./1764'."% ,' >7)4'."' )@%"= R #.*%

"6*%7)1.7% -%7 .//%7@)7% #$%



)99i)6*%"1)7% ,%9 ,%".*'")1.7% 9)

>7)4'."% m /%*-7% -'n -'##.9)B

%#&&#'()")*+,#"- 585; <=:> :^:

b#(&@")c ,@6() 40((# 20&"6(6')#



•

]2,@90"B 16xS#,0 &690 O#K,)*'{69X2,0 6g06g0K,# &6"10"26 4) &612,@),0 o'@,0 &D0 J6116"60110,0 #11)9)(#20 # $'*$"@ =>?#+2) I J0,&DX9#"20"'6"6 (0 J,6J,)023 '06902,)&D0 b&#,#L0,)1B&#4) 4)"#9)&)23c 0 P@"Q)6"#"6 &690 )99#')") 90"2#() 0

J6116"6 0110,0 9#")J6(#20 )" (@6'6 40((0 )99#')")90"2#()• C6116"6 1@JJ6,2#,0 (# 9096,)# 4) (#/6,6 /)1@6*

1J#Q)#(0

•

C6116"6 &6"2,)K@),0 # 4)9)"@),0 )( K(6&&6 4) P,6"20 #&6"10'"0 4)H&)()I 16120"'6"6 )( 16''0L6 "0((U#'),0 )"K#10 #((0 )"P6,9#Q)6") P6,")20E

%#&&#'()")*+,#"- 585; <=:> :^<

."# J)&&6(# ,#&&69#"4#Q)6"0



Non è tutto oro quello che luccica!

-

Non esistono strumenti che possono insegnare al postodell’insegnante

-

Non esistono tecniche didattiche o strumenti che vannobene per tutti- Non esistono metodologie didattiche per fare le cose allasvelta- Non esistono metodologie che vanno bene per qualsiasi

tema/materia/etc.

Diffidate da chiunque vi promette qualcosa del genere!

%#&&#'()")*+,#"- 585; <=:> :^N



%#&&#'()")*+,#"- 585; <=:>

!raziee

# uon Lavoro

:^>

Bibliografia



:^W%#&&#'()")*+,#"- 585; <=:>

Aritmetica in pratica

Strumenti e strategie dallatradizione cinese per l'inizio della

scuola primaria

Maria Giuseppina Bartolini

Bussi, Alessandro Ramploud, Anna Baccaglini-Frank

Bibliografia



:^[%#&&#'()")*+,#"- 585; <=:>

Imparare con il Tubò pitagorico

Esercizi e strategie per l’uso delle

tabelline nelle moltiplicazioni e divisioni

Andrea Maffia, Anna Baccaglini-Frank

Bibliografia



:^^%#&&#'()")*+,#"- 585; <=:>

Numeri in movimento Attività per apprendere l'aritmetica

con la pascalina

Michela Maschietto, Ketty Savioli

Bibliografia!]CtG b<=::cG 92 !#'>"5' H"#<'*-+#"E !((U)"4),)QQ6 J0,&6"2#,0E#1JD)E)2%#&&#'()")*+,#"-I !E b<=:N#cE !"#()1) 40((0 C620"Q)#()23 4) !JJ()&#Q)6") 5@(B*F6@&D J0, (#O612,@Q)6"0 40( ])'")o&#26 4) f@90,6 f#2@,#(0 9*6">*+,"*-' ("22+ I+-",+:$+ " ("22"



:^`%#&&#'()")*+,#"- 585; <=:>

O612,@Q)6"0 40( ])'")o&#26 4) f@90,6 f#2@,#(0G 9*6">*+,"*-' ("22+ I+-",+:$+ " ("22"

.$)"*3" 9*-">#+-"; JK E fENI <N^*<[<E%#&&#'()")*+,#"-I !E b<=:>cE F,#L#90"26 40((6 Q0,6 "0( J,6'0L6 C0,O6"2#,0EaUG"10'"#90"26 40((# 5#209#B&# 0 40((0 ]&)0"Q0 9*-">#+-"; JL E MGNI <W^*<`<E%#&&#'()")*+,#"-I !E 0 g#9K0,)")I + b<=:>#cE N?)(+ +22" +@C)-F !"# 2+ ,+-",+:$+ $2+66"

!#),+E T)1J6")K)(0 6"()"0 J,0116 (U)"4),)QQ6 J0,&6"2#,0E#1JD)E)2%#&&#'()")*+,#"-I !E 0 g#9K0,)")I+ b<=:>KcE N?)(+ +22" +@C)-F !"# 2+ ,+-",+:$+ $2+66"

6"$'*(+E T)1J6")K)(0 6"()"0 J,0116 (U)"4),)QQ6 J0,&6"2#,0E#1JD)E)2%#&&#'()")*+,#"-I !E ]&6,Q#I 5E b<=:N#cE G( C,6'0L6 C0,O6"2#,0 n J,#B&D0 J0, @"# lK@6"#4)4#A&#p 0 90264) J0, (# ,)(0/#Q)6"0 4) K#9K)") &6" 4)H&6(23 )" 9#209#B&#E !( &6"/0'"6lG"&6"2,) &6" (# 9#209#B&# ŒŒ?GGpI O#120( ]E C)02,6 F0,90I `*\*:= "6/09K,0 <=:NE%#&&#'()")*+,#"-I !E 0 ]&6,Q#I 5E b<=:NKcE g01B,0 '() 12@40"B &6" T]! )" &(#110 @16 40((09#") 0 40((# ()"0# 40) "@90,) "0( J,6'0L6 C0,O6"2#,0E G" OE O#20")I OE +#L6,)I 7E G9J0,)#(0I

%E C)6&D)I 0 CE ?)'D)I j@#40,") g7G50T "E :I :`N*:\=E%#&&#'()")*+,#"-I !E 0 76K6AI 8E b<=:NcE N"6:#" .-?("*: $'* B.E )* <2+66" O E2$?*) /2","*:

() ?* P?+(#' <',?*"I G"k †!A 40( Œ?GGG O6"/0'"6 f#Q)6"#(0 g7G50TI <N * <> 5#,Q6 <=:NUI%6(6'"#k C)2#'6,# 04E

BibliografiaO#"#()") O6,J#&&)I 7E 5#1&D)0L6E 5E b<=::cI g() #,20P#A*12,@90"B 0 # &69J,0"1)6"040((# "62#Q)6"0 J61)Q)6"#(0 "0((# 1&@6(# J,)9#,)#E a# †J#1&#()"#U y0,6v: "0((# &(#110k '0"01)12,@90"2#(0E 9*6">*+,"*-' ("22+ ,+-",+:$+ " ("22" 6$)"*3" )*-">#+-"; ?6(E N> ! fE<I:[:*:`È



:[: :`ÈT0D#0"0I ]E b<=:=cI 92 !+22)*' ("22+ ,+-",+:$+G .$'!#)#" )2 >"*)' (") *?,"#) $%" Q )* *')G

7#M#0((6 O6,B"# 84)26,0I 5)(#"6EG#"")BI !E a@&#"'0()I T b<==WcE C0,&D{ ) &#(&6() 16"6 4)H&)()R GJ6201) 0 9640(() J1)&6(6')&)40((U#K)()23 4) &#(&6(6E B)R$'2-F )* I+-",+:$+; Sb<cI :WN*:^=Ea@&#"'0()I TE b<==WcE M+:'*+2 6?#C"T '* 2"+#*)*> ()6+1)2):"6E 7690k G2#()#" G"1B2@20 6P7010#,&D 6" G"P#"&mE5#,@m#9#I 5EI C#(()0,I OEI d6K0,2I !EI ])'9#"I 5EI T0D#0"0I ]E b<=:<cE FD0 &6,B&#(

,0J,010"2#B6" 6P 1)9J(0 9#2D09#B&#( 0wJ,011)6"1E M"?#'9,+>"I KSb>cI :>>>n:>[=E5@(()'#"I dE 5)2&D0(96,0I 5E b<=:NcE 8#,(m !S#,0"011 6P 5#2D09#B&#( C#L0," #"4]2,@&2@,0E G" aE 8"'()1D dE 5@(()'#" b841EcI U"$'*$"!-?+2)3)*> /+#2T I+-%",+:$6 A"+#*)*>E]J,)"'0,E f6‚(I 5CE b<==WcE +)"'0, '"61)#k # J,04)&26, 6P "@90,)&#( #K)()B01 )" &D)(4,0"R <%)2(

M"?#'!6T$%'2'>T I ::k :n:È

C#,,)1D ] b<=:=c M?,1"# -+2V6D W"2!)*> $%)2(#"* 1?)2( ,"*-+2 ,+-% +*( $',!?-+:'*

Documents

Verso una didattica inclusiva in matematica