Upload
anna-baccaglini-frank
View
219
Download
0
Embed Size (px)
Citation preview
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@ �BB
BH/2I+"02'9 #8 J#3+/( (/3 G+;;2# K$2*2(C L'(*9
BBM#/3#/ N/#7*+3;+ M()C L,KC H/2I+"02'9 #8 M#/3#/
8/11/2019 From Notable Occurrences to Situated Abstractions: a window for analyzing learners’ thinking-in-change in a microworld
http://slidepdf.com/reader/full/from-notable-occurrences-to-situated-abstractions-a-window-for-analyzing-learners 2/35
O=(' 20 '=+ P"#)*+$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
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 3/35
:; <5$$&25+57 =1$ ($*9! >?@
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 4/35
Level 4
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 5/35
an intelligent exploratory learning environment for
supporting the construction of mathematical
generalisations & their expression as rules
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 6/35
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
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 7/35
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 8/35
O=(' ("+ 7+ '"92/; '# *##> ('Q
!"#$%#$&'#$'(")$&*
72'=2/ ( 32;2'(*
*+("/2/; +/I2"#/$+/'
U� F E#9*+0C VWWXY
/TZ
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 9/35
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
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 10/35
Solver
TaskTool/Artefact
^##*0 U("'+8(-'0Y (/3 L/0'".$+/'0
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 11/35
Solver
TaskTool/Artefact
Scheme
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 12/35
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
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 13/35
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@
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 14/35
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� F N+/'C cddeC P@fVeY
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 15/35
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/$2-"#7#"*3 +TP*#"(5#/0@
8/11/2019 From Notable Occurrences to Situated Abstractions: a window for analyzing learners’ thinking-in-change in a microworld
http://slidepdf.com/reader/full/from-notable-occurrences-to-situated-abstractions-a-window-for-analyzing-learners 16/35
K*+$+/'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-=+$+
8/11/2019 From Notable Occurrences to Situated Abstractions: a window for analyzing learners’ thinking-in-change in a microworld
http://slidepdf.com/reader/full/from-notable-occurrences-to-situated-abstractions-a-window-for-analyzing-learners 17/35
K*+$+/'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>
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 18/35
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#$+#/+@
8/11/2019 From Notable Occurrences to Situated Abstractions: a window for analyzing learners’ thinking-in-change in a microworld
http://slidepdf.com/reader/full/from-notable-occurrences-to-situated-abstractions-a-window-for-analyzing-learners 19/35
K*+$+/'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
'=+ $2-"#7#"*3@
8/11/2019 From Notable Occurrences to Situated Abstractions: a window for analyzing learners’ thinking-in-change in a microworld
http://slidepdf.com/reader/full/from-notable-occurrences-to-situated-abstractions-a-window-for-analyzing-learners 20/35
K*+$+/'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/;
#.'-#$+0 8#" 2/32I23.(*0 #" 8#" ;"#.P0@UE#9*+0 +' (*@C cddeY
8/11/2019 From Notable Occurrences to Situated Abstractions: a window for analyzing learners’ thinking-in-change in a microworld
http://slidepdf.com/reader/full/from-notable-occurrences-to-situated-abstractions-a-window-for-analyzing-learners 21/35
K*+$+/'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@
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 22/35
^=+ 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@
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 23/35
^=+ 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'= '=+ $8 /9 ,-*1 /9 )(/-/+5 2/ '=+ )@)@
8/11/2019 From Notable Occurrences to Situated Abstractions: a window for analyzing learners’ thinking-in-change in a microworld
http://slidepdf.com/reader/full/from-notable-occurrences-to-situated-abstractions-a-window-for-analyzing-learners 24/35
1+i.+/-+ #8 0-=+$+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'= '=+ /.$)+"#8 ).2*32/; )*#->0 0=#7/ 2/ '=+ P(R+"/0 P"#P+"5+0 72/3#7U7=+'=+" 2' 20 *#->+3 #" ./*#->+3Y@ H0+ '=20 ".*+ '# (/07+"@
8/11/2019 From Notable Occurrences to Situated Abstractions: a window for analyzing learners’ thinking-in-change in a microworld
http://slidepdf.com/reader/full/from-notable-occurrences-to-situated-abstractions-a-window-for-analyzing-learners 25/35
1-=+$+ V
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 26/35
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'= '=+ /.$)+" #8).2*32/; )*#->0 0=#7/ 2/ '=+ P(R+"/0 P"#P+"5+0 72/3#7U7=+'=+" 2' 20 *#->+3 #" ./*#->+3Y@ H0+ '=20 ".*+ '# (/07+"@
8/11/2019 From Notable Occurrences to Situated Abstractions: a window for analyzing learners’ thinking-in-change in a microworld
http://slidepdf.com/reader/full/from-notable-occurrences-to-situated-abstractions-a-window-for-analyzing-learners 27/35
4""2I2/; (' 1-=+$+ f
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 28/35
1-=+$+ f
8/11/2019 From Notable Occurrences to Situated Abstractions: a window for analyzing learners’ thinking-in-change in a microworld
http://slidepdf.com/reader/full/from-notable-occurrences-to-situated-abstractions-a-window-for-analyzing-learners 29/35
1+i.+/-+ #8 0-=+$+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'= '=+ /.$)+" #8).2*32/; )*#->0 0=#7/ 2/ '=+ P(R+"/0 P"#P+"5+0 72/3#7U7=+'=+" 2' 20 *#->+3 #" ./*#->+3Y U,`Y@ H0+ '=20 ".*+ '#(/07+"@
D,j&L^L]K
GK!L&KJK&^
8/11/2019 From Notable Occurrences to Situated Abstractions: a window for analyzing learners’ thinking-in-change in a microworld
http://slidepdf.com/reader/full/from-notable-occurrences-to-situated-abstractions-a-window-for-analyzing-learners 30/35
1+i.+/-+ #8 0-=+$+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'= '=+ /.$)+" #8).2*32/; )*#->0 0=#7/ 2/ '=+ P(R+"/0 P"#P+"5+0 72/3#7U7=+'=+" 2' 20 *#->+3 #" ./*#->+3Y U,`Y@ H0+ '=20 ".*+ '#(/07+"@
8/11/2019 From Notable Occurrences to Situated Abstractions: a window for analyzing learners’ thinking-in-change in a microworld
http://slidepdf.com/reader/full/from-notable-occurrences-to-situated-abstractions-a-window-for-analyzing-learners 31/35
1+i.+/-+ #8 0-=+$+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&^
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 32/35
^(>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."+@
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 33/35
^(>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/ $9 =+(3C '=+ P(R+"/ 72** 0'(9-#*#."+3@\
8/11/2019 From Notable Occurrences to Situated Abstractions: a window for analyzing learners’ thinking-in-change in a microworld
http://slidepdf.com/reader/full/from-notable-occurrences-to-situated-abstractions-a-window-for-analyzing-learners 34/35
D#/-*.02#/0• 1@4@0 =(I+ ;.23+3 2$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'@
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 35/35
Thank you
m.+05#/0Q