From Notable Occurrences to Situated Abstractions: a window for analyzing learners’...

8/11/2019 From Notable Occurrences to Situated Abstractions: a window for analyzing learners’ thinking-in-change in a microworld

http://slidepdf.com/reader/full/from-notable-occurrences-to-situated-abstractions-a-window-for-analyzing-learners 1/35

!"#$ &#'()*+ ,--.""+/-+0 '#12'.('+3 4)0'"(-5#/06

( 72/3#7 8#" (/(*9:2/; *+("/+"0<

'=2/>2/;?2/?-=(/;+ 2/ ( $2-"#7#"*3

4@ A(--(;*2/2?!"(/>BC D@ E#9*+0BB F G@ &#00BB

BH/2I+"02'9 #8 J#3+/( (/3 G+;;2# K$2*2(C L'(*9

BBM#/3#/ N/#7*+3;+ M()C L,KC H/2I+"02'9 #8 M#/3#/



O=(' 20 '=+ P"#)*+$Q

!"#$!%%&'( (!'!$*+&,- &% .!++/0'1.' *%* 23*++!'(&'( ,1#&24

– 0'.3+/'0 $2;=' 23+/589 P(R+"/0 ).' ("+ /#'

/+-+00("2*9 ()*+ '#

!

0++ '=+ %,$52,5$! #8 '=+ P(R+"/

! *$625+*,! '=+ ;+/+"(*2'9

!

+0P+-2(**9 (0 ( %-781+&2 ".*+ 21''!2,!9 '# '=+ 0'".-'."+

–

(*;+)"( 20 #S+/ I2+7+3 (0 (/ !'9#1&', F

9&%21''!2,!9 8"#$ #'=+" $+(/0 #8 +TP"+002/;

;+/+"(*2'9



:; <5$$&25+57 =1$ ($*9! >?@



Level 4



an intelligent exploratory learning environment for

supporting the construction of mathematical

generalisations & their expression as rules



Mi Gen System

The MiGen system comprises! a microworld (the eXpresser)

! Intelligent Support to encourage generalisation

through

!

feedback (generic & adaptive) to students!

support for teachers to monitor students’ progress

! tools to support collaboration

! group tasks for sharing & discussing constructions

and rules

!

classroom Dynamics and Student Tracking tools





O=(' ("+ 7+ '"92/; '# *##> ('Q

!"#$%#$&'#$'(")$&*

72'=2/ ( 32;2'(*

*+("/2/; +/I2"#/$+/'

U&#00 F E#9*+0C VWWXY

/TZ



1-=+$+

[4/ 2/I("2(/' #";(/2:(5#/ #8 )+=(I2#." 8#" (;2I+/ -*(00 #8 02'.(5#/0@\

U]+";/(.3C VWWXY

4 0-=+$+<0 -#$P#/+/'06

• '=+ ;#(* (/3 '=+ (/5-2P('+3 #.'-#$+0C

• '=+ ".*+0 #8 (-5#/C #8 ;('=+"2/; 2/8#"$(5#/C #8

-#/'"#* '(>2/;

•

(/3 '=+ #P+"(5I+ 2/I("2(/'0 U2$P*2-2' >/#7*+3;+Y



Solver

TaskTool/Artefact

^##*0 U("'+8(-'0Y (/3 L/0'".$+/'0



Solver

TaskTool/Artefact

Scheme



Solver

TaskTool/Artefact

Scheme

[@@@'=+ 2/0'".$+/' 3#+0 /#' +T20' 2/ 2'0+*8C 2'

)+-#$+0 (/ 2/0'".$+/' 7=+/ '=+ 0.)_+-'

=(0 )++/ ()*+ '# (PP"#P"2('+ 2' 8#" =2$0+*8

(/3 =(0 2/'+;"('+3 2' 72'= =20 (-5I2'9@\

U]+";/(.3 F G()("3+*C VWW`Y



L/0'".$+/'+3 (-5#/ 0-=+$+

G()("3+* UVWW`Y 2/'"#3.-+3 '=+ /#5#/ #8+,-#.),/$ 1("*2* #8 ( '##*C (0 ( 0-=+$+

#";(/2:2/; '=+ (-5I2'9 72'= ( '##*C 2/ #"3+" '#

"+(*2:+ ( ;2I+/ '(0>@

E+ 3205/;.20=+0

•

+1)&* 1("*2*1 U#"2+/'+3 '#7("30 '=+

$(/(;+$+/' #8 '=+ '##*Y

•

)$3 #$145+2*$4*3 )(,/$ 1("*2*1 U#"2+/'+3 '#-(""9 #.' ( 0P+-2a- '(0>Y@



4)0'"(-5#/

[@@@2' 20 '=+ P"#-+00 #8 ()0'"(-5#/ #8$('=+$(5-(* P"#P+"5+0 (/3 2/I("2(/'0 '=(' 20>+9C (/3 '=20 20 /+-+00("2*9 )#'= 02'.('+3 (/30=(P+3 )9 '=+ '##*0 )+2/; .0+3C '=+ .0+"0<

"+*(5#/0=2P '# '=+ '##*0 b 2/-*.32/; 7=+'=+" '=+.0+"0 _.3;+ '=+$ '# )+ +TP"+002I+ #8 '=+2"3+I+*#P2/; $('=+$(5-(* $+(/2/;0 b (/3.*5$('+*9 7=+'=+" '=+0+ $+(/2/;0 ("+ I(*.+3

(/3 _.3;+3 )9 '=+ -#$$./2'9 U+@;@C '=+-*(00"##$Y '# )+ $('=+$(5-(*@\

UE#9*+0C&#00 F N+/'C cddeC P@fVeY



12'.('+3 4)0'"(-5#/

^=+ 7#"3 )6145)(,/$ "+8+"0 '# )#'= (/ (-5#/ U(-#**+-5I+ (-5#/C 2/ '=+ -*(00"##$YC (/3 '# '=+

2/'+**+-'.(* 0'".-'."+ U72'=2/ 2/32I23.(*0Y '=('

"+0.*'0 8"#$ '=(' (-5#/@

4 1#4+)4*3 )6145)(,/$ 20 (/ ()0'"(-5#/ '=('

3+0-"2)+0 ( P("5-.*(" 2/'+**+-'.(* (-5I2'9

2/I#*I+3 2/ >/#7*+3;+ 3+I+*#P$+/' 7#4"#$

02'.('+3 +TP+"2+/-+0 0.-= (0 '=#0+ 2/$2-"#7#"*3 +TP*#"(5#/0@



K*+$+/'0 #8 '=+ g"#P#0+3 !"($+7#">

•

/#'()*+ #--.""+/-+0C &@,@ U2/ ^"#.-=+<0 7#"30( '9P+ #8 [;+0'."+0\Y

• U2/0'".$+/'+3 (-5#/Y 0-=+$+ ./3+" '=+ &@,@0

•

3+0-"2P5#/ #8 ( '##* 2/ (-5#/• 02'.('+3 ()0'"(-5#/C 1@4@

•

2/'+/3+3 0-=+$+

• (/(*95-(* (--#./' #8 '=+ +I#*.5#/ #8 (

0-=+$+



K*+$+/'0 #8 '=+ g"#P#0+3 !"($+7#">

•

/#'()*+ #--.""+/-+0C &@,@ U2/ ^"#.-=+<0 7#"30( '9P+ #8 [;+0'."+0\Y

• U2/0'".$+/'+3 (-5#/Y 0-=+$+ ./3+" '=+ &@,@0

•

3+0-"2P5#/ #8 ( '##* 2/ (-5#/• 02'.('+3 ()0'"(-5#/C 1@4@

•

2/'+/3+3 0-=+$+

• (/(*95-(* (--#./' #8 '=+ +I#*.5#/ #8 (

0-=+$+

^=+ 7(9 ( *+("/+" 3+-23+0 '# .0+

#/+ #" $#"+ '##*0 '# (--#$P*20=

( '(0>



K*+$+/'0 #8 '=+ g"#P#0+3 !"($+7#">

•

/#'()*+ #--.""+/-+0C &@,@ U2/ ^"#.-=+<0 7#"30( '9P+ #8 [;+0'."+0\Y

• U2/0'".$+/'+3 (-5#/Y 0-=+$+ ./3+" '=+ &@,@0

•

3+0-"2P5#/ #8 ( '##* 2/ (-5#/• 02'.('+3 ()0'"(-5#/C 1@4@

•

2/'+/3+3 0-=+$+

• (/(*95-(* (--#./' #8 '=+ +I#*.5#/ #8 (

0-=+$+

4R+$P' '# $(>+ '=+ 0-=+$+

+TP*2-2' 7=+/ -#$$./2-(5/; 2'

'# 0#$+#/+@



K*+$+/'0 #8 '=+ g"#P#0+3 !"($+7#">

•

/#'()*+ #--.""+/-+0C &@,@ U2/ ^"#.-=+<0 7#"30( '9P+ #8 [;+0'."+0\Y

• U2/0'".$+/'+3 (-5#/Y 0-=+$+ ./3+" '=+ &@,@0

•

3+0-"2P5#/ #8 ( '##* 2/ (-5#/• 02'.('+3 ()0'"(-5#/C 1@4@

•

2/'+/3+3 0-=+$+

• (/(*95-(* (--#./' #8 '=+ +I#*.5#/ #8 (

0-=+$+

4)0'"(-5#/0 '=(' (**#7 -#;/25I+

"+a/+$+/' #8 ( 0-=+$+ 7=2*+ 2' 20 05**02'.('+3 72'=2/ '=+ 0P+-2a- -#/'+T' #8

'=+ $2-"#7#"*3@



K*+$+/'0 #8 '=+ g"#P#0+3 !"($+7#">

•

/#'()*+ #--.""+/-+0C &@,@ U2/ ^"#.-=+<0 7#"30( '9P+ #8 [;+0'."+0\Y

• U2/0'".$+/'+3 (-5#/Y 0-=+$+ ./3+" '=+ &@,@0

•

3+0-"2P5#/ #8 ( '##* 2/ (-5#/• 02'.('+3 ()0'"(-5#/C 1@4@

•

2/'+/3+3 0-=+$+

• (/(*95-(* (--#./' #8 '=+ +I#*.5#/ #8 (

0-=+$+

L' 20 =+*P8.* '# '=2/> #8 '=+ P#002)2*25+0 '=('

(--".+ 2/ '=+ .0+0 )9 0'.3+/'0 #8 ("'+8(-'0C+0P+-2(**9 7=+/ '=+0+ ("'+8(-'0 ("+ 3+02;/+3

72'= '=+ 2/'+/5#/ #8 P"#$#5/; *+("/2/;

#.'-#$+0 8#" 2/32I23.(*0 #" 8#" ;"#.P0@UE#9*+0 +' (*@C cddeY



K*+$+/'0 #8 '=+ g"#P#0+3 !"($+7#">

•

/#'()*+ #--.""+/-+0C &@,@ U2/ ^"#.-=+<0 7#"30( '9P+ #8 [;+0'."+0\Y

• U2/0'".$+/'+3 (-5#/Y 0-=+$+ ./3+" '=+ &@,@0

•

3+0-"2P5#/ #8 ( '##* 2/ (-5#/• 02'.('+3 ()0'"(-5#/C 1@4@

•

2/'+/3+3 0-=+$+

• (/(*95-(* (--#./' #8 '=+ +I#*.5#/ #8 (

0-=+$+

1'.3+/'0< '=2/>2/;?2/?-=(/;+ '=(' -(/ )+

0++/ (0 '=+ -=(/;2/; #8 '=+ $20$('-=

)+'7++/ '=+ 2/'+/3+3 0-=+$+ (/3 '=+

*+("/+"0< 0-=+$+0@



^=+ D#*#."2/; ^(0>

&@,@0 2/ '=+ 2/'+/3+3 0-=+$+6•

H/*#->2/; '=+ /.$)+" #8 "+P+55#/0 #8 '=+ ).2*32/; )*#-> U)@)@Y U,`(Yh

• -#$P#02/; '=20 $.*5P*2-(5I+*9 72'= '=+ /.$)+" #8 5*+0 #8 ( -+"'(2/

-#*#." 2/ ( )@)@ U,`)Y@



^=+ D#*#."2/; ^(0>

^=+ &@,@0 8#./3 3."2/; '=+ 0'.396•

,V6 $+/'(**9 -#./' #" -(*-.*('+ '=+ 5*+0 (/3 .0+ '=+/.$)+" ;+/+"('#"

• ,c6 ./*#-> '=+ /.$)+" #8 5*+0

• ,f6 $.*5P*9 U(PP("+/'*9Y ["(/3#$\ /.$)+"0 '#

(/07+"

• ,e6 -(*-.*('+ '=+ I(*.+ #8 '=+ ).2*' ".*+ U(/3 .0+ 2' '#

"+0P#/3Y

•

,`(6 ./*#-> '=+ /@ #8 "+P+55#/0 #8 '=+ ).2*32/; )*#->

•

,`)6 ).2*3 ( ;+/+"(* ".*+ -#$P#02/; $.*5P*2-(5I+*9'=+ $8 /9 5*:*,,/$1 /9 4"* 686@ 72'= '=+ $8 /9 ,-*1 /9 )(/-/+5 2/ '=+ )@)@



1+i.+/-+ #8 0-=+$+0 8#" J#**9

•

1-=+$+ V6 -#$P.'+ '=+ /.$)+" #8 5*+0 $+/'(**9 (/3 .0+'=+ /.$)+" ;+/+"('#" '# 7"2'+ '=+ (/07+" U,VYC (/3 3"(; 2''# (/07+" '=+ i.+05#/h

• 1-=+$+ c6 3"(; #/'# '=+ -(/I(0 ( /.$)+" 8"#$ '=+).2*32/; )*#-> P"#P+"5+0 72/3#7 (/3 (/#'=+" /.$)+" (/3$.*5P*9 '=+$@ ^=+/ -(*-.*('+ '=+ I(*.+ (/3 .0+ '=20

/.$)+" '# (/07+" '=+ i.+05#/h• 1-=+$+ f6 3"(; '=+ /.$)+" #8 5*+0 #8 '=+ 3+02"+3 -#*#." 2/

( ).2*32/; )*#-> (/3 '=+ ./*#->+3 /.$)+" #8 "+P+55#/0 #8'=+ ).2*32/; )*#-> #/'# '=+ -(/I(0 (/3 $.*5P*9 '=+$@ ^=+/-(*-.*('+ '=+ I(*.+@ H0+ '=+ ".*+ '# (/07+"h

• 1-=+$+ e6 ).2*3 ( ".*+ $.*5P*92/; '=+ /.$)+" #8 5*+0 #8

'=+ -#*#." 9#. 7(/' 2/ +(-= ).2*32/; )*#-> 72'= '=+ /.$)+"#8 ).2*32/; )*#->0 0=#7/ 2/ '=+ P(R+"/0 P"#P+"5+0 72/3#7U7=+'=+" 2' 20 *#->+3 #" ./*#->+3Y@ H0+ '=20 ".*+ '# (/07+"@



1-=+$+ V



1+i.+/-+ #8 0-=+$+0 8#" J#**9

•

1-=+$+ V6 -#$P.'+ '=+ /.$)+" #8 5*+0 $+/'(**9 (/3 .0+ '=+/.$)+" ;+/+"('#" '# 7"2'+ '=+ (/07+" U,VYC (/3 3"(; 2' '#(/07+" '=+ i.+05#/h

• 1-=+$+ c6 3"(; #/'# '=+ -(/I(0 ( /.$)+" 8"#$ '=+ ).2*32/;)*#-> P"#P+"5+0 72/3#7 (/3 (/#'=+" /.$)+" (/3 $.*5P*9'=+$ U,fY@ ^=+/ -(*-.*('+ '=+ I(*.+ (/3 .0+ '=20 /.$)+" '#

(/07+" '=+ i.+05#/ U,eYh• 1-=+$+ f6 3"(; '=+ /.$)+" #8 5*+0 #8 '=+ 3+02"+3 -#*#." 2/ (

).2*32/; )*#-> (/3 '=+ ./*#->+3 /.$)+" #8 "+P+55#/0 #8 '=+).2*32/; )*#-> U,`(Y #/'# '=+ -(/I(0 (/3 $.*5P*9 '=+$U,`)Y@ ^=+/ -(*-.*('+ '=+ I(*.+ U,eY@ H0+ '=+ ".*+ '# (/07+"h

• 1-=+$+ e6 ).2*3 ( ".*+ $.*5P*92/; '=+ /.$)+" #8 5*+0 #8 '=+

-#*#." 9#. 7(/' 2/ +(-= ).2*32/; )*#-> 72'= '=+ /.$)+" #8).2*32/; )*#->0 0=#7/ 2/ '=+ P(R+"/0 P"#P+"5+0 72/3#7U7=+'=+" 2' 20 *#->+3 #" ./*#->+3Y@ H0+ '=20 ".*+ '# (/07+"@



4""2I2/; (' 1-=+$+ f



1-=+$+ f



1+i.+/-+ #8 0-=+$+0 8#" J#**9

•

1-=+$+ V6 -#$P.'+ '=+ /.$)+" #8 5*+0 $+/'(**9 (/3 .0+ '=+/.$)+" ;+/+"('#" '# 7"2'+ '=+ (/07+" U,VYC (/3 3"(; 2' '#(/07+" '=+ i.+05#/h

• 1-=+$+ c6 3"(; #/'# '=+ -(/I(0 ( /.$)+" 8"#$ '=+ ).2*32/;)*#-> P"#P+"5+0 72/3#7 (/3 (/#'=+" /.$)+" (/3 $.*5P*9'=+$ U,fY@ ^=+/ -(*-.*('+ '=+ I(*.+ (/3 .0+ '=20 /.$)+" '#

(/07+" '=+ i.+05#/ U,eYh• 1-=+$+ f6 3"(; '=+ /.$)+" #8 5*+0 #8 '=+ 3+02"+3 -#*#." 2/ (

).2*32/; )*#-> (/3 '=+ ./*#->+3 /.$)+" #8 "+P+55#/0 #8 '=+).2*32/; )*#-> U,`(Y #/'# '=+ -(/I(0 (/3 $.*5P*9 '=+$U,`)Y@ ^=+/ -(*-.*('+ '=+ I(*.+ U,eY@ H0+ '=+ ".*+ '# (/07+"h

• 1-=+$+ e6 ).2*3 ( ".*+ $.*5P*92/; '=+ /.$)+" #8 5*+0 #8 '=+

-#*#." 9#. 7(/' 2/ +(-= ).2*32/; )*#-> 72'= '=+ /.$)+" #8).2*32/; )*#->0 0=#7/ 2/ '=+ P(R+"/0 P"#P+"5+0 72/3#7U7=+'=+" 2' 20 *#->+3 #" ./*#->+3Y U,`Y@ H0+ '=20 ".*+ '#(/07+"@

D,j&L^L]K

GK!L&KJK&^



1+i.+/-+ #8 0-=+$+0 8#" J#**9

•

1-=+$+ V6 -#$P.'+ '=+ /.$)+" #8 5*+0 $+/'(**9 (/3 .0+ '=+/.$)+" ;+/+"('#" '# 7"2'+ '=+ (/07+" U,VYC (/3 3"(; 2' '#(/07+" '=+ i.+05#/h

• 1-=+$+ c6 3"(; #/'# '=+ -(/I(0 ( /.$)+" 8"#$ '=+ ).2*32/;)*#-> P"#P+"5+0 72/3#7 (/3 (/#'=+" /.$)+" (/3 $.*5P*9'=+$ U,fY@ ^=+/ -(*-.*('+ '=+ I(*.+ (/3 .0+ '=20 /.$)+" '#

(/07+" '=+ i.+05#/ U,eYh• 1-=+$+ f6 3"(; '=+ /.$)+" #8 5*+0 #8 '=+ 3+02"+3 -#*#." 2/ (

).2*32/; )*#-> (/3 '=+ ./*#->+3 /.$)+" #8 "+P+55#/0 #8 '=+).2*32/; )*#-> U,`(Y #/'# '=+ -(/I(0 (/3 $.*5P*9 '=+$U,`)Y@ ^=+/ -(*-.*('+ '=+ I(*.+ U,eY@ H0+ '=+ ".*+ '# (/07+"h

• 1-=+$+ e6 ).2*3 ( ".*+ $.*5P*92/; '=+ /.$)+" #8 5*+0 #8 '=+

-#*#." 9#. 7(/' 2/ +(-= ).2*32/; )*#-> 72'= '=+ /.$)+" #8).2*32/; )*#->0 0=#7/ 2/ '=+ P(R+"/0 P"#P+"5+0 72/3#7U7=+'=+" 2' 20 *#->+3 #" ./*#->+3Y U,`Y@ H0+ '=20 ".*+ '#(/07+"@



1+i.+/-+ #8 0-=+$+0 8#" J#**9

•

1-=+$+ V6 -#$P.'+ '=+ /.$)+" #8 5*+0 $+/'(**9 (/3 .0+ '=+/.$)+" ;+/+"('#" '# 7"2'+ '=+ (/07+" U,VYC (/3 3"(; 2' '#(/07+" '=+ i.+05#/h

• 1-=+$+ c6 3"(; #/'# '=+ -(/I(0 ( /.$)+" 8"#$ '=+ ).2*32/;)*#-> P"#P+"5+0 72/3#7 (/3 (/#'=+" /.$)+" (/3 $.*5P*9'=+$ U,fY@ ^=+/ -(*-.*('+ '=+ I(*.+ (/3 .0+ '=20 /.$)+" '#

(/07+" '=+ i.+05#/ U,eYh• 1-=+$+ f6 3"(; '=+ /.$)+" #8 5*+0 #8 '=+ 3+02"+3 -#*#." 2/ (

).2*32/; )*#-> (/3 '=+ ./*#->+3 /.$)+" #8 "+P+55#/0 #8 '=+).2*32/; )*#-> U,`(Y #/'# '=+ -(/I(0 (/3 $.*5P*9 '=+$U,`)Y@ ^=+/ -(*-.*('+ '=+ I(*.+ U,eY@ H0+ '=+ ".*+ '# (/07+"h

• 1-=+$+ e6 ).2*3 ( ".*+ $.*5P*92/; '=+ /.$)+" #8 5*+0 #8 '=+

-#*#." 9#. 7(/' 2/ +(-= ).2*32/; )*#-> 72'= '=+ /.$)+" #8).2*32/; )*#->0 0=#7/ 2/ '=+ P(R+"/0 P"#P+"5+0 72/3#7U7=+'=+" 2' 20 *#->+3 #" ./*#->+3Y U,`Y@ H0+ '=20 ".*+ '#(/07+"@

D,j&L^L]K

GK!L&KJK&^



^(>2/; 2' 8."'=+"

• J#**9 (PP+("0 '# )+ -#$8#"'()*+ ).2*32/;

[".*+0\ U+TP"+002#/0Y 8#" '=+ -#*#."2/; 0-=+$+U1-=+$+ eY (/3 8#" (/07+"2/; #'=+"i.+05#/0h

•

8#" =+"C [7"25/; ".*+0\ 20 7=(' 9#. /++3 '# 3#

'# '+** '=+ -#$P.'+" 7=(' 9#. 323 2/ 9#."=+(3@

• 1=+ *('+" =+*P0 ( -*(00$('+ -#$P*+'+ '=+ '(0>CI+")(*2:2/; '=+ 0'+P0 #8 =+" P"#-+3."+@

•

1=+ 20 ()*+ '# k+T2)*9 "+?(3(P' =+" 0-=+$+ '#=+" -*(00$('+<0 (-5#/0 7=+/ '=+0+ ("+ /#'-#$P*+'+*9 2/ *2/+ 72'= =+" P"#-+3."+@



^(>2/; 2' 8."'=+"

• J#**9 (PP+("0 '# )+ -#$8#"'()*+ ).2*32/;

[".*+0\ U+TP"+002#/0Y 8#" '=+ -#*#."2/; 0-=+$+U1-=+$+ eY (/3 8#" (/07+"2/; #'=+"i.+05#/0h

•

8#" =+"C [7"25/; ".*+0\ 20 7=(' 9#. /++3 '# 3#

'# '+** '=+ -#$P.'+" 7=(' 9#. 323 2/ 9#."=+(3@

• 1=+ *('+" =+*P0 ( -*(00$('+ -#$P*+'+ '=+ '(0>CI+")(*2:2/; '=+ 0'+P0 #8 =+" P"#-+3."+@

•

1=+ 20 ()*+ '# k+T2)*9 "+?(3(P' =+" 0-=+$+ '#=+" -*(00$('+<0 (-5#/0 7=+/ '=+0+ ("+ /#'-#$P*+'+*9 2/ *2/+ 72'= =+" P"#-+3."+@

-#/-+P'?2/?(-5#/

[".*+\ -#/0'".-'+3C (/ #)_+-'

"+P"+0+/5/; ( P"#-+00 -(""2+3

#.' $+/'(**9@ L' 20 ( 7(9 #8

'(*>2/; '# '=+ -#$P.'+"@

'=+#"+$?2/?(-5#/

2' -#.*3 )+ [28 L 7"2'+ ( ".*+ '=('

(*7(90 3#+0 '=+ -(*-.*(5#/ L 3#

2/ $9 =+(3C '=+ P(R+"/ 72** 0'(9-#*#."+3@\



D#/-*.02#/0• 1@4@0 =(I+ ;.23+3 2$P#"'(/' -#;/25I+

"+a/+$+/'0 #8 '=+ 0-=+$+C 0++/ '="#.;=+I#*I2/; 0+'0 #8 &@,@0@

• J#**9 20 ()0'"(-5/; $+(/2/;0 8#" '=+ -#/-+P'?2/?(-5#/ [".*+\C '=#.;= /+I+" ()0'"(-5/; 2')+9#/3 '=+ -#/'+T' #8 '=+ $2-"#7#"*3C(**#72/;6 – '"(/025#/0 0-=@ c" 0-=@ f (/3 0-=@f" 0-=@e

– k+T2)2*2'9 2/ ;.232/; =+" -*(00$('+C 72'=#.'2/0'".-5/; =+" '# 8#**#7 ( "2;23 0+i.+/-+ #8 0'+P0@

1# J#**9 =(0 +*()#"('+3 ( 0#$+7=(' &*$*5)- 0-=+$+C 9+' 05** 02'.('+3 72'=2/ '=+ +lP"+00+"-#/'+T'@



Thank you

m.+05#/0Q

Date post:	02-Jun-2018
Category:	Documents
Upload:	anna-baccaglini-frank
View:	218 times
Download:	0 times

From Notable Occurrences to Situated Abstractions: a window for analyzing learners’...

Documents