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Content uploaded by Emine gaye Contay
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PROOF UNDERSTANDINGS OF PRESERVICE MATHEMATICS TEACHERS
Introducon:
!"
" #$$%& '
()
!"#$$%&
*+ +
) * * + * +
!" " #$$,& *
+ *
- *
" !#$$% #$$,& *
+ + '
"* .( !/001&
* *
*
23
Method: 2
( " 4 2 !#$/0-"$/,&
*+5
6 * 78 !1 91 *&
: * ;+
<<+=<+
5*+!
;+&
' 6 3 *
'
+ *
> ? + 4
@*<'A!4'&*?+
'<'A!''&*
( +
*
?@*;<'A!@;'&*
B *
5 ?C DA ?'
*DA * '' 4' >+
*!-'&
<6
>( *
+5) *
References
EFGH4!#$/#&FIJJEJ + JKEL@I
#$!/&#/0M#98
.!#$$/& 6<;4>+'" +4NG!&O
+64! /1%M#/#&<+)+
.H"*O!/001&" 64) -="'=,#97M#19
"<P"PH ;!#$$%& Q6C'"R "'-
+D' =7#7/M#71
"P"<PH ;!#$$,&Q* +P=/$
/7%M/88
4' >*/& *
#&) *
5 9&) *
7&**
**%&
+ & !*S
&
'' * ( +
!* & : 6 >
* * "
6*
! + !" #$$%
#$$,&
@;' +*
/# >5!*S&
-' <B 9
* 5 ?C
DA?'*DA* '4'4'
! &
+/3
Findings: > ( *
+ 5 )
*5
:4'6
4' * *
* 5'5
+
+'+
3 +
+ +
! &
:'4'6
True/
Paral/
False
Explanaon/Proof
Scheme
Deducon
Direct proof
Proof by trial
Proof by inducon
Reduco ad
absurdum
Counterexample
Contradicon
Reasoning
All possible
situaons
No response
1/0/43 ; T
, /9 8 % # 9 / / $ %
18/6/20 ; * +
T # /9 /$ 8 # $ / $ / ,
0/3/39 ; T
# 8 0 8 # 7 % $ / 0
0/0/39 ; T
9 , 1 / 9 % / / $ 1
0/0/42 ; T
/ / /9 , # 0 9 $ $ 8
+#:4'
''U**
*+ >* +
V * ! &U
+ *
? !& !W/&A ! &
* * R
*!& +
'
+
!5&5
'
++)+ * +
!"#$$%U#$$,&(
!E#$/#U.#$$/U"#$$,&
:@;'6= !%%X&*
?* AU * *6 ?
!& !W/&A?A?GA?
A ? A < *
= *
?YA
Conclusion6 =2 +
+ ( *
Y
' *
U S * *
* " +
*)
*
:4:"! & Z/ Z#
! & 7!X0& 8!X/9&
! & /9!9$X& //!#%X&
" ! & /1!7/X& /,!90X&
<+ * 0!#$X& /$!#9X&
+9:'4'