teori pembelajaran dienes
TRANSCRIPT
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CONTENT
INTRODUCTION
PART 1 :
THEORY OF MATHEMATICS LEARNING-ZOLTAN PAUL DIENES
THE FOUR PRINCIPLE
THE SIX STAGES
PART 2 :
LESSON PLAN APPLYING DIENES SIX STAGES OF
MATHEMATICS LEARNING
BEFORE THE LESSON
DURING THE LESSON AFTER THE LESSON
PART 3 :
FINDINGS AND IMPLICATIONS OF THE DIENES THEORY
REFERENCES
APPENDIX
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INTRODUCTION
Matheat!"# !# a$ a%#t&a"t!'$ !$ e(!#te$"e) *hethe& !t +a# ,!#"'e&e, %. '&
ha# %ee$ "&eate, %. a$/!$, !# #t!00 a #%e"t ' ,e%ate#) Yet '$e th!$4 !# "e&ta!$)
Matheat!"# !# !$,!#5e$#a%0e !$ 5&e,!"t!$46 ,e#"&!%!$46 a$, $,eta$,!$4 ee$t# !$
the +'&0, a&'$, #) It ha# a0#' 5ae, the +a. '& the 5&'0!e&at!'$ ' $e&'#
te"h$'0'4!"a0 a$, #"!e$t!!" %&ea/th&'4h# a$, a,a$"ee$t#)
The $ae ' Z'0ta$ Pa0 D!e$e# #ta$,# +!th the 0e4e$,a&. !4&e# +h'#e
+'&/# 0eae a$ !$,e0!%0e !5&e##!'$ a$, "'$t&!%t!'$ !$ the !e0, ' atheat!"#
e,"at!'$) H!# $ae !# a##'"!ate, +!th a$!50at!e ate&!a0# !$ tea"h!$4
atheat!"# #"h a# the 0'4!" %0'"/# a$, the 0t! 7 %a#e %0'"/# #e, '& the
tea"h!$4 ' 50a"e a0e) He a0#' the'&!8e, that 4ae#6 #t'&!e#6 a$, ,a$"e
9e)4)6D!e$e#6 1;36 1 the "'$#t&"t!!t.
5&!$"!50e> the atheat!"a0 a&!a%!0!t. 5&!$"!50e> a$, the 5e&"e5ta0 a&!a%!0!t.?
/$'+0e,4e e%',!e$t 5&!$"!50e) A0'$4 +!th that he a0#' #44e#te, @ #ta4e# '
atheat!"# 0ea&$!$4 that he05 %!0, #t&'$4 "'$"e5ta0 !$ #t,e$t# $,eta$,!$4)
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The "h&'$'0'4!"a0 ' "'4$!t!e ,ee0'5e$t '& !$,!!,a0 "a$$'t a%!,e the
a"t' ' a4e) The "h!0, a$, the a,0t 5ha#e ' th!$/!$4 !# $'t the #ae) The a%!0!t.
' th!$/!$4 4&e+ 5 +!th a4e) H'+ee&6 the "'4$!t!e ,ee0'5e$t a0#' &e0e"t# '$
the #&&'$,!$4 a$, the #'"!a0 !$te&a"t!'$) The&e'&e ea"h 5e'$ a"h!ee ,!e&e$t
5ha#e ' "'4$!t!e ,ee0'5e$t) The&e'&e6 a$ a55&'a"h 0!/e D!e$e# The'&. '
atheat!"a0 0ea&$!$4 4!e# the "ha$"e '& a "h!0, t' a(!!8e the!& "'4$!t!e #/!00#)
Th!# 5&'e"t %e4a$ +!th the 4&'5 e%e& t&. t' /$'+ a$, $,eta$, the
!e+# ' the the'&!#t6 Z'0ta$ Pa0 D!e$e# a$, h!# "'$t&!%t!'$# t'+a&,# the !e0, '
atheat!"# a$, e,"at!'$#) Ate& that +e a550. '& $,eta$,!$4 ' the the'&. '$
a 0e##'$ that +e 50a$$e, #!$4 the #!( #ta4e# ' D!e$e# the'&. ' atheat!"#
0ea&$!$4 a$, h!# '& 5&!$"!50e#) The 't"'e ' the $,eta$,!$4 ' the the'&.6 the
!50ee$tat!'$ ' the the'&. !$ "0a## a$, the !50!"at!'$ ' the the'&. a&e #ha&e, %.
5&e#e$tat!'$ a$, ,'"e$tat!'$ ' th!# 5&'e"t !$ PLG @1 "0a##)
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THEORY OF MATHEMATICS LEARNING-ZOLTAN
PAUL DIENES
THE FOUR PRINCIPLE
THE SIX STAGES
PART
1
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LESSON PLAN APPLYING DIENES SIX STAGES OF
MATHEMATICS
LEARNING AND THE FOUR PRINCIPLES
BEFORE THE LESSON
DURING THE LESSON
AFTER THE LESSON
PART
2
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BEFORE THE LESSON
STEP 1 : The !t #te5 +a# t' ,ete&!$e, +h!"h t.5e ' #t,e$t# t' %e "h'#e !$
the 5&'e"t) It +a# e!the& 5&!a&. '& #e"'$,a&. #"h''0 #t,e$t#) Ate&
4' th&'4h the D!e$e# The'&.6 !t a55ea that D!e$e# The'&. '&e
a550!"a%0e '$ "h!0,&e$ a$, %e"a#e the 4&'5 +a$t t' ,e#!4$ 4ae#
a"t!!t!e# that 4et the .'$4 #t,e$t# !$te&e#te, !$) The&e'&e the
5&!a&. #"h''0 #t,e$t# ' #ta$,a&, #!( !$ Pe$a$4 +e&e "h'#e$)
STEP 2 : The #e"'$, #te5 +a# t' !,e$t!. the '#t #!ta%0e t'5!" t' a550. the
D!e$e# The'&. !$ Matheat!"# Lea&$!$4 ) Th&ee t'5!"# +e&e #44e#te,6
+h!"h +e&e &a"t!'$6 a"t'&!8at!'$ a$, !$te4e& $%e&) Ate& #'e
,!#"##!'$#6 the 4&'5 a4&ee, 5'$ #e0e"t!$4 the t'5!" ' !$te4e&
$%e& %. the #%t'5!" ' 0t!50!"at!'$ ' 5'#!t!e a$, $e4at!e
$%e) The ,e"!#!'$ +a# %a#e, '$ the #t,e$t# 5&e&e!#!te
/$'+0e,4e a$, the a$!50at!e# '& "'$"&ete ate&!a0# that +e "a$
5&'!,e !$ the 0e##'$)
STEP 3 : The th!&, #te5 +a# t' 5&e5a&e the a"t!!t!e#6 the #0!,e#6 the
a$!50at!e# a$, the 0e##'$ 50a$ a550.!$4 the #!( #ta4e# ' the
D!e$e# The'&.) D!e&e$t t.5e# ' a"t!!t!e# +a# 50a$$e, t' !50. the
D!e$e# 5&!$"!50e ' atheat!"a0 a&!a%!0!t. a$, the #e ' the #0!,e#
'the& tha$ +&!tte$ '$ +h!te %'a&, a$, ha$,# '$ a"t!!t!e# ' the
a$!50at!e# +a# t' !50. the D!e$e# 5&!$"!50e ' 5e&"e5ta0
a&!a%!0!t.)
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STEP : The '&th #te5 +a# t' 5&e5a&e the "0a##&'' '& the 0e##'$) The 0a%
+a# "h'#e$ %e"a#e the #5a"e +a# a50e e$'4h '& the #t,e$t# t'
+a0/ a%'t a$, 4et !$t' 4ae# a"t!!t!e#) The a&&a$4ee$t ' ta%0e a$,
"ha! '& 4&'5 a"t!!t!e# +e&e ,'$e %e'&e the #t,e$t# "ae !$t' the
"0a##) The 0a% a0#' "'$#!,e&e, t' %e a "'$,"!e 50a"e t' tea"h a$, t'
!0 the 0e##'$)
STEP : The&e +a# $' #t&ate4!" 5'!$t t' 50a"e the "ae&a %e"a#e the
#t,e$t# a"t!!t!e# +!00 %e '$ 4'!$4 th&'4h't the 0e##'$6 the&e'&e the
4&'5 a4&ee '& a e%e& t' %e the "'$,"t!$4 tea"he& a$, the 'the&
t+' t' !0 the 0e##'$ !$ 't!'$ 9 'e, a&'$, the "0a## =) A e%e&
'"#e, '$ the #t,e$t# a$, a$'the& '$e '"#e, '$ the tea"he&) The
!0!$4 +a# #!$4 a ta%0et "ae&a a$, a #a&t5h'$e "ae&a)
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The F0'+ Cha&t Beforethe Le##'$:
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U$,eta$, the the'&. Ch''#e #t,e$t#
STEP 1
Dete&!$e the t'5!" Dete&!$e the #%t'5!"
STEP 2
P&e5a&e 0e##'$ 50a$ '& 2 5e&!',# De#!4$ a"t!!t!e# P&e5a&e a$!50at!e#
STEP 3
Dete&!$e the e$e A&&a$4ee$t ' ta%0e# a$, "ha!
STEP
De0e4at!'$ ' ta#/# 9 t' tea"h ? t' !0 = P&e5a&e LCD 5&'e"t'&6 "ae&a#
9 ta%0et #a&t5h'$e =STEP
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DURING THE LESSON
STEP 1: Tea"he& a&'#e the #t,e$t# !$te&e#t '$ 5'#!t!e a$, $e4at!e $%e
%. !$t&',"!$4 the 5'#!t!e a$, $e4at!e ' the #&&'$,!$4 '%e"t a$,
$at&e)
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Suggested by the professor that we shoud g!"e e#a$pes that
reay reated to the $ea%!%g of pos!t!"e a%d %egat!"e %u$bers
su&h as the fu&tuat!o%s of the te$perature' It !s so the
stude%ts w! %ot ha"e $!s&o%&ept!o%'
Late& '$6 tea"he& te#te, the #t,e$t# 5&e&e!#!te /$'+0e,4e '$ the
a,,!t!'$ ' 5'#!t!e a$, $e4at!e $%e)
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STEP 2: A550.!$4 #ta4e 16 the &ee 50a. ' D!e$e# the'&. ' atheat!"#
0ea&$!$4) At th!# #ta4e the ,.$a!" 5&!$"!50e +a# !50!e, %. 0ett!$4 the
#t,e$t# 50a. +!th the "a&,#)
St,e$t# +e&e 4!e$ a #et ' 50a.e& "a&,# "'$#!#t ' &e, a$, %0a"/)
Let the #t,e$t# #e the "a&,# t' !$, the &e0at!'$ that "a$ a,e 2
%0a"/ "a&,# a$, 3 %0a"/ "a&,# %e"'e @ %0a"/ "a&,#)
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STEP 3: A550.!$4 #ta4e 26 50a.!$4 %. the &0e# ' D!e$e# the'&. ' atheat!"#
0ea&$!$4) Tea"he& !$t&',"e, the 4ae# a$, the &0e# t' %e 50a. %. the
#t,e$t#)
The &0e# a&e : 1) I %0a"/ "a&,# eet %0a"/ "a&,# the &e0at!'$ a,e
#t a0#' %e !$ %0a"/)
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2) I &e, "a&,# eet &e, "a&,# the &e0at!'$ a,e
#t a0#' %e !$ %0a"/
3) I &e, "a&,# eet %0a"/ "a&,# '& !"e ea the
&e0at!'$ a,e #t %e !$ &e,)
Tea"he& !$te&e$t!'$ +a# $e"e##a&. t' 4!,e a$, a/e #&e the
#t,e$t# 4et the #t&"t&e ' the a"t!!t.)
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STEP : A550.!$4 #ta4e 36 the "'5a&!#'$ #ta4e '& #ea&"h '& "'$a0!t!e# '
D!e$e# the'&. ' atheat!"# 0ea&$!$4)
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Tea"he& 4ae a e+ e#t!'$# a$, 0et the #t,e$t# !4&e, 't the
a$#+e& #!$4 the "a&,#) It +a# #' the #t,e$t# a%0e t' &e"'4$!#e the
5atte&$ ? #t&"t&e ' the a"t!!t!e#)
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STEP : A550.!$4 #ta4e 6 the &e5&e#e$tat!'$ #ta4e ' D!e$e# the'&. '
atheat!"# 0ea&$!$4)
St,e$t# !a4!$e, that the %0a"/ "a&,# a# the &e5&e#e$tat!'$ '5'#!t!e $%e a$, the &e, "a&,# a# the &e5&e#e$tat!'$ ' $e4at!e
$%e)
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STEP @: A550.!$4 #ta4e 6 the #.%'0!8at!'$ #ta4e ' D!e$e# the'&. '
atheat!"# 0ea&$!$4)
At th!# #ta4e #t,e$t# %e4a$ t' "ha$4e the &e5&e#e$tat!'$ "'0'& ' the"a&,# !$t' atheat!"a0 '&)
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STEP ;: E$&!"he$t ' a"t!!t!e# !$ '& ' 4ae# t' #t&e$4th 5 the #t,e$t#
"'$"e5ta0 $,eta$,!$4)
Gae# $ae : I$te4e& M0t!50!"at!'$ N%e& Batt0e
P0a.e : G&'5# ' t+' t' !e
Mate&!a0# : De"/ ' "a&,#6 A"e +'&th 116 a"/ +'&th 126 ee$ +'&th 136!$4 +'&th 16 #"&at"h 5a5e&
S/!00 : N%e& &e"'4$!t!'$6 5'#!t!e !$te4e $e4at!e !$te4e a$,0t!50!"at!'$
H'+ t' P0a. : B0a"/ "a&,# a&e 5'#!t!e $%e> &e, "a&,# a&e $e4at!e
$%e) P0a.e #50!t a ,e"/ ' "a&,# t' "a&,# ea"h) Ea"h50a.e& ha# t' "'%!$e t+' ' the!& %e#t "a&,# t' 4et the%!44e#t $%e&) Ree%e& that t+' $e4at!e$%e a/e a 5'#!t!e 5&',"t a$, -2 !# 4&eate& tha$ -;)
E(a50e ' &e#0t# :
P0a.e& 1: 5&',"t !# -2 90''#e= P0a.e& 2: 5&',"t !# 2< 9+!$=
The h!4he#t 5&',"t +!$# a00 "a&,# !$ the 50a.!$4 "'$te&)
I the "a&,# 5&',"t# hae the #ae a0e6 the "a&,# a&e 50a"e, !$ a "e$te& 5!0e)
The $e(t ha$, !# 50a.e, $'&a00. a$, the +!$$e& ' the $e(t 0t!50!"at!'$
$%e& %att0e ta/e# the "e$te& 5!0e a# +e00)
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STEP
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R(NC(NG(N )E*BEL(+(R(N
,EL(S - @ SIDDI
SESI - 2J1
SUB+E,- MATEMATI
BIL )EL(+(R - 2J *INGGU -
*(S(- 1 AM 2J MINIT TE*)(T :
GURU - AZMER ASRAF BIN MOHD HUSSAIN
TO)I, - NOMBOR BULAT
SUB.TO)I, - PENDARABAN MELIBATAN NOMBOR POSITIF DAN
NEGATIF
H(SIL
)E*BEL(+(R(N-
Pa,a a/h!& #e#! 5e%e0aa&a$6 5e0aa& a5 $t/:
1= e$4e$a05a#t! !$te4e& 5'#!t! ,a$ $e4at!)
2= e$.e0e#a!/a$ 5e$a%aha$ ,a$ 5e$'0a/a$ e0!%at/a$$'%'& 5'#!t! ,a$ $e4at!)
3= e$.e0e#a!/a$ 5e$,a&a%a$ e0!%at/a$ $'%'& 5'#!t! ,a$$e4at!)
,E)ERLU(N
)ENG(+(R(NB(H(N ,U(NTITI
B(H(N )ENG(+(R(N P'+e& P'!$t S0!,e1
B(H(N (UDIO /ISU(L P&'e/t'& 1
(L(T(N
a, Pe&a!$a$
Pe$ Ma&/e&
Pa5a$ Pt!h
1
2
1
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)ERING,(T0
*(S((,TI/ITI GURU (,TI/ITI *URID C(T(T(N
)ENGEN(L(N
9 !$#=
Set I$,/#!
Ra#!'$a0 :
Me&a$4#a$4
5e$4etaha$
5e0aa& te$ta$4
#!at %e&0a+a$a$
#e#at
'%e/?#!at?5e&/ataa$ ,a$
$'%'&)
Me$.a5a &!,
Me$a$,a/a$ /eha,!&a$
&!,
Me$$//a$ "!&!-"!&! #!at
.a$4 %e&0a+a$a$ ,a0a/eh!,5a$)
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e%e&!/a$ #!at%e&0a+a$a$ %a4! #e#at'%e/)
Re#5'$
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%e&0a+a$a$ .a$4,!%!$"a$4/a$)
eah!&a$Be&!/!&:
e%e&/e#a$a$
e$4e0a&/a$
!,ea
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)ERING,(T0
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)E*B(NGUN(N
)er!%g1at 2-
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Bebas
91 !$!t=
Ra#!'$a0:
Me&a$4#a$4 !,ea
/&eat! &!,
,e$4a$ %e&a!$
#e"a&a %e%a#
ta$5a at&a$
5e&a!$a$)
Me$e&a$4/a$ te$ta$4
'%e/t! 5e$4aa&a$ ha&! !$!)
Me$4a#!$4/a$ &!,
e$4!/t /50a$)
Set!a5 /50a$
e5e&'0eh #at #et /a,5e&a!$a$ .a$4 te&,!&!,a&!5a,a /a, %e&+a&$ae&ah ,a$ h!ta)
Me%e&!/a$ a/t!!t!
5e&a!$a$ /a, .a$45e&taa !a!t e$$//a$h%$4a$ a$ta&a 3 /a,
h!ta ,a$ 2 /a, h!ta %a4!e$4ha#!0/a$ @ /a, h!ta)9ta$5a at&a$?a&aha$=
Me%at "atata$)
Me%e&! 5e&hat!a$
#ea#a 4&e$a0a$/a$ #e#!5e%e0aa&a$)
Pe0aa& e$.e0e#a!/a$
a/t!!t! 5e&taa #e"a&a%e&/50a$)
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/a, 5e&a!$a$ %a4!e+a/!0! h%$4a$
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P'+e& P'!$t
S0!,e
N!0a! M'&a0 :
'$#e$t&a#!
,a$5e$40!%ata$
&!,)
Me&a$4#a$4
#!/a5 !$4!$
tah &!,)
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)ERING,(T0
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)er!%g1at 3-
)er$a!%a%Berstru1tur
91J !$!t=
Ra#!'$a0:
M&!,
e$,a5at/a$
/'$#e5
5e&a!$a$ /a,
e0a0!
5e$4a0aa$
%e&a!$ /a, ,a$
t$/ aa& 4&)
Me%e&!/a$ #e,!/!t t$/
aa& /e5a,a &!, $t/e$.e0e#a!/a$ 5e&a!$a$/a,)
Me$$//a$ /'$#e5 La&
/a,93= ,a&a% Ba&!# /a, 92=a/a$ e$4ha#!0/a$ @)
Me$,a5at/a$ #at"'&a/?#t&/t&5e&a!$a$ /a, .a$4e0!%at/a$ h%$4a$,a $'%'&)
Me$,e$4a& /e5a,a
%a$ta$?&/a$ .a$4,!%e&!/a$ 4&)
N!0a! '&a0 :
Pe&hat!a$ ,a$
'/#)
)er!%g1at 4-
Lat!ha%0)ra1t!s
91J !$!t=
Ra#!'$a0:
Lat!ha$ %e&0a!$a$
ea$ta5/a$
5e$4etaha$
&!, $t/
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"!&!-"!&!
5e&a!$a$)
Me%e&!/a$ #'a0a$ 0a!$
$t/ a/t!!t! /e,a %a4!&!, e$.e0e#a!a$a#a0ah e$44$a/a$/ae,ah .a$4 5e&a!$a$.a$4 #aa)
Me$44$a/a$ /a,
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1J)91 X 3= 9; X < = K
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Tha$/# a$, &e+a&, the #t,e$t# +h'+!00!$4 t' 5a&t!"!5ate !$ the 5&'e"t
STEP 1
D!#t&!%te e(e!"e #heet#
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IMPLICATION OF THE THEORY
THE STRENGTH
THE WEAKNESS
PART
3
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Co%&us!o% Of The D!e%es Theory !% Ge%era
1) The +h'0e-"0a## 9'& 0a&4e-4&'5= 0e##'$ +'0, %e 4&eat0. ,ee5ha#!8e, !$
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3) The &'0e ' the tea"he& +'0, !$"0,e e(5'#!t!'$ a# +e00 a# %e!$4 a a"!0!tat'&)
) The &'0e ' #t,e$t# +'0, %e e(5a$,e,) The. +'0, a##e a 4&eate&
,e4&ee ' &e#5'$#!%!0!t. '& the!& '+$ 0ea&$!$4)
) The $e+0. ,e!$e, 0ea&$!$4 e$!&'$e$t +'0, "&eate $e+ ,ea$,# '&
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