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Transcrição

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3 :\9*+,%_T9%&&*1.*9%;*+,%#'9%I1*#'(0*0%&ET%;I1%2#2%(''%.1.*#*'19%D* 9%;*'($*jS1#%&z?9t*#'E566ZkW:;A.0(&&EA1.2#2%('.1;'(\*2%'*0W<.%\%('E2. &1N;(#O*=*.#j566^E9%\%9(#0a(%9%#kA(.T9'*#'%I1%&*;1#&'%#O*.1.*%_T%9(h#2(* *0%I1*0*2.*&.f;'(T;*&(#'%9T9%'*+b%&0%\9*+,E1#*&&1*&T*;*$9*&ErT%9&#*;(0*0%& 0&#f.%9&9*2(#*(&sjTWZ]5kxT*9'%G'0E9*D,ET%9*09EI12(%#'%%.%0(0*x%I1% #,*&2#&(0%9%.2..%9&Nd%'&0%24;21;WS*&1*T%9&T%'($*E*2.T9%%#&,0 2#2%('0%\9*+,$*(G&%2#&'91(#0*T*9'(90%#'%#0(.%#'0%&'*&$49(*&rT%9&#*;(0*0%&s 1&()#(\(2*0&W /&'% 2*94'%9.1;'(\*2%'*0 0 2#2%(' 0% \9*+, 2.T;%_(\(2* '9*N*;O 0 T9\%&&9 (.T;(2*#01.*$(&,O;C&'(2*0*2#&'91+,0%#f.%99*2(#*;WB2#d1#'0*&0($%9&*& rt%9&#*;(0*0%&se I1% &% (#'%9G9%;*2(#*.E '9#*. 1. 2#2%(' &(.T;%& #1. 2#2%(' 2.T;%_E'9*#&\9.*#0'0%.*;).*(&I1%*&.*0*&&1*&T*9'%&W<O*9*;*.N1&% 8(''*G8*#'*D(j566Zk%#\*'(D*.I1%0%&%#$;$(.%#'02#2%('0%\9*+,*T*9'(90%1. 0& &%1& &()#(\(2*0& #, )*9*#'% * 2.T9%%#&, 0& 9%&'*#'%& 2.T9.%'%#0 * 2.T9%%#&,);N*;02#2%('W:T(*#0G&%#1..0%;0%?%O9E&*1'9%&T9219*9*. 9%;*2(#*9&0(\%9%#'%&&()#(\(2*0&0*\9*+,2.&2#2%('&2O*$%#'9*N*;O2.* \9*+,i * #+, 0% %I1($*;h#2(* 0% \9*+b%&E *& T%9*+b%& 2. \9*+b%& % * 9%&;1+, 0% T9N;%.*&jP()W7kW B& *1'9%& 2#2;1C9*. I1% &()#(\(2*0 rt*9'%g'0se A 2#&(0%9*0E d1#'*.%#'% 2. T92%&&0%T*9'(+,jT*9'(;O*%I1('*'($*kE%&&%#2(*;T*9*0%&%#$;$(.%#'0*2.T9%%#&, 0&9%&'*#'%&I1*'91'9&&()#(\(2*0& 5 *&&(.2..*(&9%;*2(#*02.*9%&;1+,0% T9N;%.*& % * *0(+, 0% \9*+b%& jp()w 7kW B &()#(\(2*0 r9*d,s A.*(& r#*'19*;s T*9* T9.$%9 * 2.T9%%#&, 0* %I1($*;h#2(* 0% \9*+b%& % & &()#(\(2*0& rt%9*09s % ri12(%#'%s&,&i1%.*(&2#'9(n1%.t*9*%#'%#0(.%#'0*.1;'(t;(2*+,0%\9*+b%&w /.&1.*E%#&(#0&#f.%9&9*2(#*(&%E%.T*9'(21;*90*&\9*+b%&E'9*D0%&*\(&*29%&2(0& * I1% '%9 %. 2#'* & $49(& &()#(\(2*0& 0% \9*+,E *& 0(\%9%#'%& 9%T9%&%#'*+b%&0&#f.%9&9*2(#*(&%*\9.*2.%&'%'9*N*;OT0%&%90%&%#$;$(0WB 0(;%.*ET*9**;1#&%T9\%&&9%&EA0%2.%&'*N%;%2%9*&2#%_b%&*T9T9(*0*&T*9*1.*.*019*%\;%_C$%;2.T9%%#&,0%&'%&#f.%9&W O'0)92,.,2)94&$92,.>n$r,$.1n&'p)2$&)0,0,2,"2$'&,0$p9)*+, 8$92,99$91.2).'"m,>)%%)"0,>,9>,"&,%0$9$p$9w"2') /.N9**&0(\%9%#+*&%#'9%&#f.%9&(#'%(9&%&#f.%9&9*2(#*(&&%d*.\#'%&0% 0(\(21;0*0%&T*9*&*;1#&E3&&%<*&%j7[[[k0%\%#0%.I1%%&'%&&*T9%#0%.'*.NA. 0%&0%(#C2(0*&1*%&2;*9(0*0%i 5 M*D,ET%9*09EI12(%#'%%.%0(0* 3*9)*9(0*S1#%&>(;$*E:#*3*9(*?*$(0*%@A;(*B;($%(9* 56H

4 /. I1*;I1%9 0& 2*&&E 2#&'9%. %&I1%.*& #1.A9(2& I1*#'('*'($& );N*(& &%T*9*0*.%#'% %E o.%0(0* I1% $, 0%&%#$;$%#0 1. #C$%;.*(& %;%$*0 0% T%#&*.%#'E $, 290%#*#0 )9*01*;.%#'% %&'%& r%&i1%.*&s T*9* N'%9%. 1.* 2.T9%%#&,0#f2;%E'*#'#I1%&%9%\%9%o\9.*2.&#f.%9&%.I1%&', %&',%&'91'19*0&E2.o#'*+,1&*0*T*9*&9%T9%&%#'*9WjTW75]k Este entendimento nuclear é estendido a números mais complexos e às formas de representação desses números até que a estrutura global de todo o campo é compreendida. Este processo de domínio progressivo de dois universos numéricos tem semelhanças com o que acontece quando as crianças aprendem duas línguas. V*.NA.S1#%&%?9t*#'j566Zk&1N;(#O*.I1%&*;1#&'h.1.*2.T9%%#&,(#'1('($*0* #*'19%D*9%;*'($*0*\9*+,*T*9'(90*&%_T%9(h#2(*&2.*0($(&,EI1%(#0(2(*I1%& T9)9*.*&2199(21;*9%&I1%'%#O*.2.T#'0%T*9'(0**&(#'1(+b%&0&*;1#&*2%92*0% &('1*+b%&0%T*9'(;O*%I1('*'($*%%&'*N%;%2%#02#%_b%&2.*&r\9*+b%&2.#f.%9&s H E T0%.'%91.(.T*2'T&('($#**T9%#0(D*)%.W /&'*&(0%(*&T*9%2%.&%9N*&'*#'%2#$%9)%#'%&2.*&T%9&T%'($*&0%Q*#y*;;%%=$(# j566zki1%t9%2#(d*.1.2*.(#o0%*t9%#0(d*)%.*#29*0#*2#&'91+,0+"),.#,# g0'.#6'$ef.jr\9*2'(##1.n%9&%#&%setw5z5ki1%t%9.('%(90%1.**n90*)%..*(& (#'1('($* * 1.* \9.*;(0*0% T9)9%&&($*.%#'%.*(9E 1&*#0 0($%9&&.0%;& 2. \%99*.%#'*&T*9**T(*9T%#&*.%#'0&*;1#&WV*.NA.P&#'%K;`j5665k&%9%\%9%.o 2#&'91+,02#2%('0%\9*+,2.1.*r$(*)%.sI1%&*;1#&\*D%.*'9*$A&0%1.* <$)+$30#,#$<',)L$30jr%$,+*$<#.6#%$')3 ETW57k%.I1%T*&&*.%$;'*.*T*&&*9 T9 rt#'& 0% 9%\%9h#2(*s I1% &% $, '9#*#0.*92& # &%1 T9JT9( T%9219& 0% *T9%#0(D*)%.W >%)1#0 %&'%& *1'9%&E T*9* I1% 2*.(#O%. %. 0(9%+, * O9(D#'% 0* 2.T9%%#&,0*&\9*+b%&EA(.T9'*#'%I1%T9\%&&9&%;%2(#%%&%I1%#2(%29('%9(&*.%#'% T9N;%.*&%I1%T9.$**0(&21&&,2;%'($*0*&&1*&9%&;1+b%&0%.0*I1%&*;1#& $,2#&'91(#0E#.%*0*.%#'%*&&%)1(#'%&3'$,+#),)$+#r 8)3#),$+ :#<B#[[fi *&\9*+b%&&,9%;*+b%&%&,9%;*+b%&T*9'%G'0v '0(.T9'*T9I1%*&\9*+b%&&,9%;*+b%&v *&T*9'%&\9*2(#49(*&#,'h.0%&%92#)91%#'%&.*&%I1($*;%#'%&v *\9*+,A1.*0($(&,%ET9'*#'E%&'49%;*2(#*0*2.*.1;'(T;(2*+,v *0($(&,%*.1;'(T;(2*+,0%\9*+b%&&,9%;*+b%&0%9%;*+b%&v &#f.%9&0%2(.*(&t0%.9%t9%&%#'*9g&%t9\9*+b%&21d0%#.(#*09a1.* T'h#2(*0%76%*&T%92%#'*)%#&T9\9*+b%&21d0%#.(#*09A1.*T'h#2(*0% 766%ET9(&&E&,9%;*+b%&\9*2(#49(*&%&T%2C\(2*&v I1%r1#(\(2*s#f.%9&(#'%(9&%0%2(.*(&A*2.T9%%#&,0$*;90%T&(+,W :&&(.E A (.T9'*#'% I1% %&'*& 3'$,+# ),)$+ 2#&'('1*. ;(#O*& #9'%*09*& 0* *+, 0 T9\%&&9EI1%#%.&%.T9%A'*9%\*&(.T;%&W:#'%&0%.*(&T9I1%.1('&#,'h.1.* 2.T9%%#&,T9\1#0*02#2%('0%\9*+,#%.'($%9*.1.*\9.*+,*0%I1*0*T*9* %#&(#*9N%.%&'%2#2%('j<;*9`%EM2O%z3('2O%;E566FkW:;A.0(&&ET9I1%'9*N*;O0% %#&(# %#$;$% 1.* )%&', 2.T;%_* 0% 9%;*+b%& 2. & *;1#&E & r.1#0&s 0% #0% T9$h.E*&&1*&%_T%9(h#2(*&.*'%.4'(2*&*#'%9(9%&%2.2#'%f0.*'%.4'(2*%#&(#*9 j=*.t%9'e5667kw31('*&$%d%&e%#'9%*&(#'%#+b%&0t9\%&&9%*&&1*&*+b%&o40(&'c#2(*& 2#&(0%94$%(&%*.(f0%&19)%.(#2.T*'(N(;(0*0%&(#2#'9#4$%(&WB&T;*#&\%('&T*9** &('1*+,0%%#&(#E9%;*2(#*.*&*+b%&2.*&(#'%#+b%&E.*&%&&%&T;*#&#,0%'%9.(#*. I1%1.T9\%&&90%$%E1#,E\*D%9#0%219&0**1;*WP9%I1%#'%.%#'%E0%&2N9(9I1% H P9*+,%#I1*#'9%T9%&%#'*+,0%1.#f.%99*2(#*; 56] 3*9)*9(0*S1#%&>(;$*E:#*3*9(*?*$(0*%@A;(*B;($%(9*

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