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J
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:
h
ttp
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//ij
ere.
ia
esco
r
e.
co
m
Ana
ly
sis
of t
ea
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o
rma
nc
e t
o
build stu
dent
int
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rest and
mo
tiva
tion towa
rds ma
thema
tics a
chiev
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H
a
rdi Ta
m
bu
na
n
1
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B
o
rno
k
Sin
a
g
a
2
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Wa
hy
u Wida
da
3
1
De
p
a
rtme
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t
o
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a
th
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a
ti
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s E
d
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c
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ti
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o
m
m
e
n
se
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HK
BP
Un
i
v
e
rsity
,
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n
d
o
n
e
sia
2
De
p
a
rtme
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of
M
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s E
d
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c
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ti
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tate
Un
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e
rsit
y
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f
M
e
d
a
n
,
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d
o
n
e
sia
3
De
p
a
rtme
n
t
of
M
a
th
e
m
a
ti
c
s E
d
u
c
a
ti
o
n
,
Be
n
g
k
u
l
u
Un
i
v
e
rsity
,
In
d
o
n
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sia
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
May
2
,
2
0
20
R
ev
is
ed
No
v
2
5
,
2
0
20
Acc
ep
ted
J
an
2
1
,
2
0
21
Th
e
p
u
r
p
o
se
o
f
th
is
stu
d
y
wa
s
to
d
e
term
in
e
th
e
imp
a
c
t
a
n
d
c
a
teg
o
ries
o
f
tea
c
h
e
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p
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rfo
rm
a
n
c
e
i
n
b
u
il
d
i
n
g
stu
d
e
n
t
in
tere
st
a
n
d
m
o
t
i
v
a
ti
o
n
o
n
m
a
th
e
m
a
ti
c
s
a
c
h
iev
e
m
e
n
t.
Th
e
p
o
p
u
latio
n
i
n
t
h
is
st
u
d
y
wa
s
stu
d
e
n
ts
in
th
e
e
ig
h
t
h
g
ra
d
e
o
f
ju
n
io
r
h
i
g
h
sc
h
o
o
ls
fro
m
six
p
u
b
li
c
a
n
d
two
p
riv
a
t
e
sc
h
o
o
ls,
a
n
d
a
sa
m
p
le
o
f
2
7
7
stu
d
e
n
ts
wa
s
tak
e
n
b
y
c
l
u
ste
r
sa
m
p
li
n
g
.
Da
ta
c
o
ll
e
c
ti
o
n
in
stru
m
e
n
ts
u
se
d
a
q
u
e
stio
n
n
a
ire
,
a
n
d
d
a
ta
a
n
a
ly
sis
wa
s
d
o
n
e
b
y
u
sin
g
b
y
d
e
sc
rip
ti
v
e
a
n
d
p
a
th
a
n
a
l
y
sis.
Th
e
re
su
lt
s
o
f
d
a
ta
a
n
a
ly
sis
sh
o
we
d
th
a
t
p
a
rti
a
ll
y
,
tea
c
h
e
r
p
e
rfo
rm
a
n
c
e
sig
n
ifi
c
a
n
t
ly
a
ffe
c
ted
st
u
d
e
n
t
i
n
tere
st
a
n
d
m
o
ti
v
a
ti
o
n
e
x
c
e
l
a
t
m
a
th
e
m
a
ti
c
s.
S
imu
lt
a
n
e
o
u
sly
,
tea
c
h
e
r
p
e
rfo
rm
a
n
c
e
is
v
e
ry
sig
n
ifi
c
a
n
t
in
i
n
fl
u
e
n
c
in
g
stu
d
e
n
t
in
tere
st
a
n
d
m
o
ti
v
a
ti
o
n
t
o
b
e
e
x
c
e
ll
e
n
t
in
m
a
th
e
m
a
ti
c
s.
P
a
rti
a
ll
y
,
tea
c
h
e
r
p
e
rfo
rm
a
n
c
e
b
u
i
ld
s
i
n
tere
st
a
n
d
st
u
d
e
n
t
m
o
ti
v
a
ti
o
n
f
o
r
m
a
th
e
m
a
ti
c
s
a
c
h
iev
e
m
e
n
t
is
lo
w
c
a
teg
o
r
y
.
S
imu
l
tan
e
o
u
sl
y
,
tea
c
h
e
r
p
e
rfo
rm
a
n
c
e
b
u
il
d
s
stu
d
e
n
t
i
n
tere
st
a
n
d
m
o
ti
v
a
ti
o
n
t
o
e
x
c
e
l
a
t
m
a
th
e
m
a
ti
c
s
is
lo
w
c
a
teg
o
ry
.
Bo
th
o
f
t
h
e
se
c
a
n
b
e
c
a
u
se
d
b
y
t
h
e
a
b
il
it
y
o
f
tea
c
h
e
rs
to
b
u
il
d
m
o
t
iv
a
ti
o
n
a
n
d
i
n
tere
st
is
n
o
t
g
o
o
d
,
so
stu
d
e
n
ts
a
r
e
a
lso
les
s
in
tere
ste
d
a
n
d
m
o
ti
v
a
ted
t
o
lea
rn
m
a
th
e
m
a
ti
c
s.
K
ey
w
o
r
d
s
:
B
u
ild
I
n
ter
est
Mo
tiv
atio
n
Per
f
o
r
m
an
ce
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Har
d
i T
am
b
u
n
an
Dep
ar
tm
en
t o
f
Ma
th
em
atics E
d
u
ca
tio
n
No
m
m
en
s
en
HKBP
Un
iv
er
s
ity
J
l.
Su
to
m
o
,
No
.
4
A,
Me
d
an
,
I
n
d
o
n
esia
E
m
ail:
t
am
b
u
n
h
a
r
d
i@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
Stu
d
en
t
ac
h
iev
em
e
n
t
is
a
b
en
ch
m
ar
k
o
f
s
u
cc
ess
in
m
at
h
em
atics
ed
u
ca
tio
n
.
B
ased
o
n
s
tu
d
en
t
m
ath
em
atics
ac
h
iev
em
en
t,
it
d
escr
ib
es
th
e
q
u
ality
o
f
m
ath
e
m
atics
lear
n
in
g
.
T
h
e
h
ig
h
er
s
t
u
d
en
t
ac
h
ie
v
em
en
t
s
co
r
e
in
d
icate
s
th
e
h
ig
h
er
q
u
al
ity
o
f
lear
n
in
g
.
B
ased
o
n
th
e
r
esu
lts
o
f
th
e
Pro
g
r
am
m
e
f
o
r
I
n
ter
n
atio
n
al
Stu
d
en
t
Ass
es
s
m
en
t
(
PISA
)
ass
e
s
s
m
e
n
t
in
2
0
1
9
,
it
s
h
o
ws
th
at
m
a
th
em
atics
sc
o
r
e
is
s
ti
ll
p
r
o
b
lem
atic
.
I
n
ter
m
s
o
f
r
an
k
in
g
m
ath
em
atics sco
r
e,
it
is
r
an
k
ed
7
2
o
u
t
o
f
7
8
co
u
n
tr
ie
s
[
1
]
.
Ma
n
y
f
ac
to
r
s
ca
n
i
n
f
lu
en
ce
t
h
e
ac
h
iev
em
en
t
p
r
o
b
lem
.
On
e
o
f
th
em
is
in
ter
est
a
n
d
m
o
tiv
a
tio
n
.
T
h
ey
ar
e
s
till
im
p
o
r
ta
n
t
is
s
u
es
as
f
a
cto
r
s
th
at
in
f
lu
en
ce
th
e
s
u
cc
ess
o
f
m
ath
em
atics
lear
n
in
g
.
T
h
is
is
b
ased
o
n
t
h
e
ass
u
m
p
tio
n
th
at
s
tu
d
en
t
in
ter
est
an
d
m
o
tiv
atio
n
in
m
ath
em
atics
is
s
ti
ll
lo
w.
Ma
n
y
s
tu
d
en
ts
h
ate
m
ath
an
d
th
eir
lear
n
in
g
i
n
ter
est
is
lo
w
[
2
]
.
T
h
e
im
p
ac
t
o
f
i
n
te
r
est
an
d
m
o
tiv
atio
n
o
n
s
tu
d
en
t
m
at
h
e
m
atics
ac
h
iev
em
en
t
ca
n
b
e
s
ee
n
f
r
o
m
s
ev
er
al
r
esear
ch
r
esu
lts
,
p
ar
tially
in
ter
est
an
d
m
o
tiv
atio
n
af
f
ec
t
s
tu
d
e
n
t
ac
h
iev
em
en
t
[
3
-
6
]
,
an
d
m
o
tiv
atio
n
a
f
f
ec
t
s
tu
d
en
t
ac
h
iev
em
en
t
[
7
,
8
]
.
Simu
lta
n
e
o
u
s
ly
,
in
ter
est
a
n
d
m
o
tiv
atio
n
af
f
ec
t
m
ath
em
atics
ac
h
iev
em
en
t [
9
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
A
n
a
lysi
s
o
f te
a
ch
er p
erfo
r
ma
n
ce
to
b
u
ild
s
tu
d
e
n
t in
teres
t a
n
d
mo
tiva
tio
n
to
w
a
r
d
s
…
(
Ha
r
d
i Ta
mb
u
n
a
n
)
43
On
e
of
ex
ter
n
al
f
ac
to
r
th
at
in
f
lu
en
ce
s
s
tu
d
en
t
in
ter
es
t
an
d
m
o
tiv
atio
n
to
lear
n
is
teac
h
er
f
ac
to
r
[
1
0
]
.
T
h
e
teac
h
er
h
as
im
p
o
r
tan
t
r
o
l
e
to
b
u
ild
s
tu
d
en
t
lea
r
n
in
g
in
t
er
est
an
d
m
o
tiv
atio
n
[1
1
]
.
T
h
e
r
esu
lts
s
h
o
w
th
at
th
e
teac
h
er
'
s
r
o
le
is
to
in
cr
ea
s
e
s
tu
d
en
t le
ar
n
in
g
in
ter
est an
d
m
o
tiv
atio
n
in
m
ath
em
atics [
1
2
,
13
].
R
ea
lizin
g
th
e
r
o
le
o
f
in
ter
est
a
n
d
m
o
tiv
atio
n
in
lear
n
in
g
m
ath
e
m
atics,
s
o
m
e
m
ath
em
atics
ed
u
c
atio
n
p
r
ac
titi
o
n
er
s
co
n
d
u
ct
a
s
tu
d
y
,
test
lear
n
in
g
s
ty
le
an
d
d
ev
el
o
p
t
h
e
f
o
r
m
o
f
a
p
p
r
o
ac
h
es
o
r
lear
n
in
g
m
o
d
els
s
o
th
at
s
tu
d
e
n
ts
ar
e
m
o
tiv
ated
an
d
in
ter
ested
in
lea
r
n
in
g
m
at
h
em
atics
[
1
4
-
26
].
B
ased
o
n
th
e
ex
p
lan
atio
n
a
b
o
v
e,
th
e
r
e
ar
e
p
r
o
b
lem
s
r
e
g
ar
d
in
g
s
tu
d
en
t
ac
h
iev
e
m
en
t
in
s
ch
o
o
l
m
ath
em
atics in
I
n
d
o
n
esia,
th
e
r
e
is
d
ef
in
itely
s
o
m
eth
in
g
wr
o
n
g
in
th
e
p
r
o
ce
s
s
an
d
im
p
lem
e
n
tin
g
lear
n
in
g
.
On
e
o
f
th
e
f
ac
to
r
s
th
at
ca
n
en
ab
le
th
e
p
r
o
b
lem
is
ca
u
s
ed
b
y
th
e
teac
h
er
in
ca
r
r
y
in
g
o
u
t
th
eir
d
u
ti
es.
T
h
er
ef
o
r
e
,
it
is
im
p
o
r
tan
t
to
ex
a
m
in
e
th
e
p
er
f
o
r
m
an
ce
o
f
teac
h
er
s
in
b
u
ild
i
n
g
in
t
er
est
an
d
m
o
tiv
atio
n
o
f
s
tu
d
en
ts
in
lear
n
in
g
m
ath
em
atics.
T
h
e
p
u
r
p
o
s
e
o
f
th
is
s
tu
d
y
is
to
d
eter
m
in
e
th
e
im
p
ac
t
an
d
ca
teg
o
r
ies
o
f
teac
h
er
p
er
f
o
r
m
an
ce
in
b
u
ild
in
g
s
tu
d
e
n
ts
'
in
ter
est
an
d
m
o
tiv
atio
n
f
o
r
m
ath
em
atics
ac
h
iev
em
en
t.
T
h
e
r
esu
lts
o
b
tain
ed
ca
n
b
e
u
s
ef
u
l
as
a
b
asis
f
o
r
o
v
er
co
m
in
g
p
r
o
b
le
m
s
o
f
s
tu
d
en
ts
'
in
ter
est
an
d
m
o
tiv
atio
n
to
war
d
s
m
ath
em
atic
s
ed
u
ca
tio
n
,
s
o
th
at
a
b
etter
m
ath
em
atics e
d
u
ca
tio
n
o
u
tco
m
e
is
o
b
tain
ed
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
T
h
is
ty
p
e
o
f
r
esear
ch
is
ex
p
o
s
t
f
ac
to
.
I
t
is
a
s
tu
d
y
t
h
at
r
ev
ea
ls
ev
en
ts
th
at
h
av
e
o
cc
u
r
r
ed
.
T
h
is
r
esear
ch
was
co
n
d
u
cted
in
t
h
e
eig
h
th
g
r
a
d
e
o
f
ju
n
io
r
h
ig
h
s
ch
o
o
ls
wh
ich
was
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n
s
is
ted
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f
s
ix
p
u
b
lic
s
ch
o
o
ls
an
d
two
p
r
iv
ate
s
ch
o
o
ls
.
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h
e
n
u
m
b
er
o
f
r
esp
o
n
d
en
ts
was
2
7
7
s
tu
d
en
ts
an
d
th
e
s
am
p
le
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tak
en
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clu
s
ter
s
f
r
o
m
s
ev
en
d
is
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in
No
r
th
Su
m
atr
a.
T
h
e
r
esear
ch
i
n
s
tr
u
m
en
t
was
a
q
u
esti
o
n
n
air
e
an
d
th
e
d
ata
co
llectio
n
tech
n
iq
u
es
wer
e
ca
r
r
ied
o
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t
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y
g
iv
in
g
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n
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m
b
e
r
o
f
q
u
esti
o
n
s
to
r
esp
o
n
d
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n
ts
wh
ich
in
clu
d
ed
:
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)
s
tu
d
e
n
t
ass
es
s
m
en
t
o
f
th
e
p
er
f
o
r
m
an
c
e
o
f
m
ath
em
atics
teac
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in
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u
ild
in
g
in
ter
est
(
X1
)
,
a
n
d
m
o
tiv
atio
n
(
X2
)
;
2
)
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d
en
t
r
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ab
o
u
t
in
t
er
est
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,
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d
m
o
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v
atio
n
(
X4
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to
ex
ce
l
at
m
at
h
em
atics,
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d
s
tu
d
en
ts
'
m
ath
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atics
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h
iev
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en
t
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co
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es
(
X5
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wer
e
o
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tain
e
d
f
r
o
m
t
h
e
r
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lts
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t
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d
s
em
ester
ex
am
in
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s
in
t
h
e
eig
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th
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r
a
d
e
m
ath
em
atics su
b
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m
atter
,
an
d
t
h
is
d
ata
was o
b
tain
ed
f
r
o
m
s
ch
o
o
l d
o
c
u
m
en
t
s
.
T
o
en
s
u
r
e
th
e
v
alid
it
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f
th
e
i
n
s
tr
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o
n
e
b
y
ex
p
er
t
j
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d
g
m
e
n
t,
an
d
r
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g
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s
in
g
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h
e
f
o
r
m
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la
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r
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ac
h
'
s
Alp
h
a
[
2
7
]
,
i.e
.
,
=
[
−
1
]
[
−
∑
2
=
1
2
2
]
.
I
n
s
tr
u
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t
cr
iter
ia,
r
eliab
le
if
0
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137
with
a
s
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n
if
ican
ce
lev
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=
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05
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B
ased
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n
th
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el
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SP
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th
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r
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tiv
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d
X4
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Data
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is
u
s
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g
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is
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2
8
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h
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aly
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is
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r
r
ied
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t
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th
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am
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d
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to
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m
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e
th
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ab
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o
f
teac
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p
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m
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ce
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ed
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aly
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th
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o
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g
h
in
ter
p
r
etatio
n
o
f
in
te
r
v
als
an
d
ca
teg
o
r
ies
[
2
9
]
,
as
s
tate
in
T
ab
le
1.
W
h
ile
f
o
r
th
e
in
ter
p
r
etatio
n
o
f
th
e
co
r
r
elatio
n
co
e
f
f
icien
t
with
th
e
v
alu
e
o
f
r
[
3
0
]
,
as
s
tate
in
T
ab
le
2.
T
ab
l
e
1
.
Data
in
ter
v
al
s
an
d
ca
t
eg
o
r
ies
I
n
t
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l
s
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t
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g
o
r
y
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>
̅
+
1
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8
S
b
i
V
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y
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o
o
d
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+
0
,
6
S
b
i
<
X
≤
̅
+
1
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8
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b
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l
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Le
ss
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.
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v
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RE
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L
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SCU
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ata
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with
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Ver
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s
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twar
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test
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icien
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B
ased
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al
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m
m
ar
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in
T
a
b
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3
.
B
ased
o
n
T
ab
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3
,
th
e
in
ter
v
al
an
d
m
ea
n
ar
e
p
r
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ted
to
d
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s
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ter
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d
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m
o
tiv
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m
at
h
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atics.
B
ased
o
n
T
ab
le
4
,
it
ca
n
b
e
s
tated
th
at
1
̅
̅
̅
̅
,
2
̅
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3
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4
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̅
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ter
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at
th
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a
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X2
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L
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ewise,
th
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ter
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(
X
3
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an
d
m
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n
(
X4
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o
f
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d
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m
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.
Fu
r
th
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m
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r
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to
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th
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elatio
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twee
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v
ar
iab
les,
th
en
t
h
e
s
u
m
m
ar
y
co
r
r
elatio
n
an
al
y
s
is
as in
T
ab
le
5
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
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2
2
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1
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r
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1
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2
-
47
44
T
ab
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3
.
Descr
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2
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7
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M
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5
9
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4
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I
n
ter
v
als an
d
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teg
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f
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62
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9
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7
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Le
ss
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51
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-
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o
t
g
o
o
d
̅
,
̅
̅
̅
:
M
e
a
n
T
ab
le
5
.
C
o
r
r
elatio
n
s
b
etwe
en
v
ar
iab
les
X1
X2
X3
X4
X5
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P
e
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r
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r
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e
l
a
t
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n
1
.
2
7
6
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.
2
9
2
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2
3
9
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.
1
6
7
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g
.
(
2
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i
l
e
d
)
.
0
0
0
.
0
0
0
.
0
0
0
.
0
0
5
N
2
7
7
2
7
7
2
7
7
2
7
7
2
7
7
X2
P
e
a
r
so
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2
7
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7
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d
)
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0
0
0
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0
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9
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0
0
0
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0
0
3
N
2
7
7
2
7
7
2
7
7
2
7
7
2
7
7
X3
P
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r
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7
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(
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0
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0
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0
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9
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0
0
0
.
0
0
0
N
2
7
7
2
7
7
2
7
7
2
7
7
2
7
7
X4
P
e
a
r
so
n
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l
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t
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o
n
.
2
3
9
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2
5
0
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1
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1
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2
5
9
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.
(
2
-
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e
d
)
.
0
0
0
.
0
0
0
.
0
0
0
.
0
0
0
N
2
7
7
2
7
7
2
7
7
2
7
7
2
7
7
X5
P
e
a
r
so
n
c
o
r
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l
a
t
i
o
n
.
1
6
7
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.
1
7
7
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.
3
3
7
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.
2
5
9
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1
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g
.
(
2
-
t
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l
e
d
)
.
0
0
5
.
0
0
3
.
0
0
0
.
0
0
0
N
2
7
7
2
7
7
2
7
7
2
7
7
2
7
7
*
*
.
C
o
r
r
e
l
a
t
i
o
n
i
s
si
g
n
i
f
i
c
a
n
t
a
t
t
h
e
0
.
0
1
l
e
v
e
l
(
2
-
t
a
i
l
e
d
).
T
ab
le
5
d
escr
ib
es
th
at
all
v
ar
i
ab
les
co
r
r
elate
with
ea
ch
o
th
er
v
er
y
s
ig
n
if
ican
tly
.
T
h
u
s
,
it
ca
n
b
e
s
tated
th
at
all
ex
o
g
en
o
u
s
v
ar
iab
les
h
av
e
a
v
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y
s
ig
n
if
ican
t
p
ath
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o
en
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o
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e
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o
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s
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r
iab
les.
B
ased
o
n
T
ab
le
5
,
it
ca
n
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e
s
tated
th
at
all
ex
o
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o
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s
v
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les
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e
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ig
n
if
ica
n
t
p
ath
to
en
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o
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en
o
u
s
v
ar
iab
le
s
.
T
h
e
p
ath
ca
n
b
e
s
tated
as in
Fig
u
r
e
1
.
Fig
u
r
e
1
.
Path
d
iag
r
am
a
n
d
c
o
r
r
elatio
n
Fig
u
r
e
1
s
h
o
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at
th
e
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er
'
s
p
er
f
o
r
m
an
ce
p
at
h
way
b
u
il
d
s
in
ter
est
(
X1
)
an
d
m
o
tiv
atio
n
(
X2
)
,
s
o
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tu
d
en
ts
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ter
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(
X3
)
an
d
m
o
tiv
ated
(
X4
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to
ex
ce
l
in
m
ath
em
atics
(
X5
)
.
So
th
at
th
e
p
ath
eq
u
atio
n
ca
n
b
e
s
tated
in
to
two
p
ath
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,
n
a
m
ely
th
e
d
ir
ec
t
p
ath
an
d
t
h
e
co
r
r
elate
d
p
ath
way
.
Dir
ec
t
p
ath
f
r
o
m
X1
to
X
5
,
i.e
.
,
1
:
1
5
=
5
1
+
5
2
1
3
,
an
d
th
e
p
ath
eq
u
atio
n
f
r
o
m
X2
to
X5
,
i.e
.
,
2
:
2
5
=
5
1
+
5
2
1
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
A
n
a
lysi
s
o
f te
a
ch
er p
erfo
r
ma
n
ce
to
b
u
ild
s
tu
d
e
n
t in
teres
t a
n
d
mo
tiva
tio
n
to
w
a
r
d
s
…
(
Ha
r
d
i Ta
mb
u
n
a
n
)
45
Fu
r
th
er
m
o
r
e
,
th
e
co
r
r
elatio
n
al
p
ath
way
co
n
s
is
ts
o
f
two
p
ath
s
,
th
e
p
ath
e
q
u
atio
n
f
r
o
m
X1
to
X5
,
i.e
.
,
1
:
1
5
=
5
1
+
5
2
1
2
+
5
3
1
3
+
3
2
1
2
+
4
2
1
2
+
4
3
1
4
5
4
1
4
,
an
d
th
e
p
ath
eq
u
atio
n
f
r
o
m
X
2
to
X5
,
i.e
.
2
:
2
5
=
5
2
+
5
1
1
2
+
5
4
2
4
+
4
1
1
2
+
3
1
1
2
+
3
4
2
3
+
5
3
23
.
Fu
r
th
er
m
o
r
e,
b
ased
o
n
d
ata
an
aly
s
is
with
th
e
h
elp
o
f
SP
S
S
v
er
s
io
n
1
9
,
t
h
e
p
at
h
c
o
ef
f
icien
t
is
o
b
ta
in
ed
f
r
o
m
th
e
e
x
o
g
e
n
o
u
s
v
ar
ia
b
le
to
th
e
e
n
d
o
g
en
o
u
s
v
ar
ia
b
le
as
in
t
h
e
T
a
b
le
6
.
T
ab
le
6
d
escr
ib
es
th
e
m
ag
n
itu
d
e
o
f
th
e
p
ath
co
e
f
f
icien
t
f
r
o
m
ex
o
g
en
o
u
s
v
ar
iab
les
to
en
d
o
g
en
o
u
s
v
ar
iab
les.
Af
ter
s
o
lv
in
g
t
h
e
p
ath
eq
u
atio
n
u
s
in
g
th
e
d
ata
in
T
a
b
le
6
,
th
e
co
ef
f
icien
ts
an
d
p
ath
ca
teg
o
r
ies
a
r
e
s
u
m
m
ar
ize
d
in
T
ab
le
7
.
T
ab
le
6
.
Ma
tr
ix
p
ath
c
o
e
f
f
icie
n
t
s
f
o
r
all
v
ar
ia
b
le
V
a
r
i
a
b
l
e
X1
X2
X3
X4
X5
X1
1
0
.
2
7
6
0
.
2
7
0
0
.
1
8
4
0
.
0
3
3
X2
0
.
2
7
6
1
0
.
0
8
3
0
.
1
9
9
0
.
0
9
5
X3
0
.
2
7
0
0
.
0
8
3
1
0
.
3
8
1
0
.
2
6
4
X4
0
.
1
8
4
0
.
1
9
9
0
.
3
8
1
1
0
.
1
2
7
T
ab
le
7
.
C
o
ef
f
icien
ts
an
d
p
ath
ca
teg
o
r
ies
P
a
t
h
P
a
t
h
c
o
e
f
f
i
c
i
e
n
t
C
a
t
e
g
o
r
y
P1
0
.
2
9
Lo
w
P2
0
.
2
4
Lo
w
P3
0
.
3
0
Lo
w
P4
0
.
3
1
Lo
w
B
ased
o
n
T
ab
le
7
,
it
c
an
b
e
s
tated
in
two
way
s
.
Firstl
y
,
Dir
ec
t
p
ath
o
r
p
ar
tially
,
p
ath
co
ef
f
icien
t
v
alu
e
P1
,
i.e
.
1
5
=
0
.
293
>
r
(
=
0.
01)
=
0
.
1
3
7
.
I
n
o
th
er
wo
r
d
s
,
teac
h
er
p
er
f
o
r
m
an
ce
b
u
ild
s
s
tu
d
en
t
in
ter
e
s
t.
I
t
s
ig
n
if
ican
tly
in
f
lu
e
n
ce
s
s
tu
d
en
t
in
ter
est
to
e
x
ce
l
at
m
at
h
em
at
ics.
T
h
is
is
co
n
s
is
ten
t
with
th
e
r
es
u
lts
o
f
r
esear
ch
th
at
s
h
o
w
th
at
in
ter
est
in
f
lu
en
ce
s
s
tu
d
en
t
ac
h
iev
em
e
n
t
[
3
1
]
.
Path
c
o
ef
f
icien
t
v
alu
e
P2
,
i.e
.
2
5
=
0
.
239
>r
(
=
0.
01)
=0
.
1
3
7
.
I
t
m
ea
n
s
th
at
teac
h
er
p
er
f
o
r
m
a
n
ce
b
u
ild
m
o
tiv
atio
n
.
I
t
s
ig
n
if
ican
tly
in
f
lu
e
n
ce
s
s
tu
d
en
t
m
o
tiv
atio
n
to
ex
ce
l
at
m
a
th
e
m
atics.
T
h
is
i
s
co
n
s
is
ten
t
w
it
h
th
e
r
esu
lts
o
f
r
esear
ch
s
h
o
win
g
th
at
m
o
tiv
atio
n
in
f
lu
en
ce
s
th
e
v
al
u
e
o
f
lea
r
n
in
g
in
m
ath
em
atics
[
3
2
,
3
3
]
.
T
h
er
e
is
a
v
er
y
s
tr
o
n
g
r
elatio
n
s
h
i
p
b
etwe
en
lear
n
in
g
m
o
tiv
atio
n
an
d
teac
h
er
ac
tio
n
s
to
war
d
lear
n
i
n
g
ac
h
ie
v
em
en
t
[
3
4
].
C
o
r
r
elatio
n
al
p
ath
o
r
s
im
u
lta
n
eo
u
s
ly
,
th
e
p
ath
c
o
ef
f
icien
t
v
alu
e
P3
,
i.e
.
1
5
=
0
.
302
>
r
(
=
0.
01)
=
0
.
1
3
7
.
I
t
m
ea
n
s
th
at
teac
h
er
p
er
f
o
r
m
an
ce
b
u
ild
s
in
ter
est
an
d
m
o
tiv
atio
n
.
I
t
si
g
n
if
ica
n
tly
in
f
lu
en
ce
s
s
tu
d
e
n
t
in
ter
est
in
m
at
h
em
atics
ac
h
ie
v
em
en
t
.
T
h
e
p
ath
co
ef
f
icien
t
v
alu
e
P4
,
i.e
.
2
5
=
0
.
308
>
r
(
=
0.
01)
=
0
.
1
3
7
.
T
ea
ch
er
p
e
r
f
o
r
m
an
ce
b
u
ild
s
m
o
tiv
atio
n
a
n
d
in
ter
est
.
I
t
s
ig
n
if
ican
tly
in
f
l
u
en
ce
s
s
tu
d
en
t’
s
m
o
tiv
atio
n
t
o
ex
ce
l
at
m
ath
em
atics.
T
h
is
is
r
elate
d
to
th
e
r
esu
lts
o
f
r
esear
ch
s
h
o
win
g
th
at
in
ter
est
an
d
m
o
tiv
atio
n
af
f
ec
t
s
tu
d
en
t
lear
n
in
g
o
u
tco
m
es
[
9
]
.
T
h
er
ef
o
r
e,
to
b
u
ild
i
n
ter
est
an
d
m
o
ti
v
atio
n
to
lear
n
,
t
h
e
teac
h
er
'
s
cr
ea
tiv
ity
is
n
ee
d
ed
.
T
h
e
teac
h
er
p
lay
s
an
im
p
o
r
ta
n
t r
o
le
in
in
f
lu
en
cin
g
s
tu
d
e
n
t in
ter
ests
an
d
m
o
tiv
atio
n
to
teac
h
m
ath
em
atics [
3
5
]
.
T
h
er
e
is
a
p
o
s
itiv
e
r
elatio
n
s
h
i
p
b
etwe
en
teac
h
er
cr
ea
tiv
ity
a
n
d
s
tu
d
en
t m
at
h
em
atics lea
r
n
i
n
g
o
u
tc
o
m
es [
3
6
]
.
Seco
n
d
ly
,
p
ar
tially
P1
p
ath
way
s
h
o
ws
th
at
teac
h
er
p
er
f
o
r
m
an
ce
b
u
ild
s
in
ter
est.
I
t
in
f
lu
en
ce
s
s
tu
d
en
ts
'
in
ter
est
to
ex
ce
l
at
m
ath
e
m
atics
is
lo
w
ca
teg
o
r
y
.
T
h
is
ca
n
b
e
ca
u
s
ed
b
y
th
e
ab
ilit
y
o
f
teac
h
er
s
to
b
u
ild
in
ter
est is
n
o
t g
o
o
d
,
s
o
s
tu
d
en
ts
ar
e
also
less
i
n
t
e
r
e
s
t
e
d
i
n
l
e
a
r
n
i
n
g
m
a
t
h
e
m
a
t
i
c
s
.
P
a
t
h
P
2
s
h
o
w
s
t
h
a
t
t
e
a
c
h
e
r
p
e
r
f
o
r
m
a
n
c
e
b
u
i
l
d
s
m
o
t
i
v
a
t
i
o
n
.
I
t
i
n
f
l
u
e
n
c
e
s
s
t
u
d
e
n
t
m
o
t
i
v
a
t
i
o
n
i
n
m
a
t
h
e
m
a
t
i
c
s
a
c
h
i
e
v
e
m
e
n
t
i
s
l
o
w
ca
teg
o
r
y
.
I
t
ca
n
b
e
ca
u
s
ed
b
y
th
e
a
b
ilit
y
o
f
th
e
teac
h
er
to
b
u
ild
is
n
o
t
g
o
o
d
,
s
o
s
tu
d
en
ts
ar
e
less
m
o
tiv
ated
to
lear
n
m
ath
em
atics.
Simu
ltan
eo
u
s
ly
,
p
ath
P3
s
h
o
ws
th
at
teac
h
er
p
er
f
o
r
m
a
n
ce
b
u
ild
s
s
tu
d
en
t
in
ter
est
an
d
m
o
tiv
atio
n
.
I
t
in
f
l
u
en
ce
s
ac
h
iev
em
en
t
in
ter
est
in
m
ath
em
atics
is
lo
w.
I
t
ca
n
b
e
ca
u
s
ed
b
y
th
e
ab
ilit
y
o
f
teac
h
er
s
to
b
u
ild
in
ter
est
an
d
m
o
tiv
atio
n
is
n
o
t
g
o
o
d
,
s
o
s
tu
d
en
ts
ar
e
also
less
in
te
r
ested
in
lear
n
in
g
m
ath
em
atics.
Path
P4
s
h
o
ws
th
at
teac
h
er
p
er
f
o
r
m
an
ce
b
u
il
d
s
s
tu
d
en
t
m
o
tiv
atio
n
an
d
in
t
er
est.
I
t
in
f
lu
en
ce
s
ac
h
iev
em
en
t
m
o
tiv
atio
n
in
m
ath
em
atics
is
lo
w
.
I
t
ca
n
b
e
ca
u
s
ed
b
y
th
e
ab
ilit
y
o
f
teac
h
er
s
to
b
u
ild
m
o
tiv
atio
n
an
d
in
te
r
est
is
n
o
t
g
o
o
d
,
s
o
s
tu
d
en
ts
ar
e
also
less
in
ter
este
d
an
d
m
o
tiv
ated
to
lear
n
m
at
h
em
atics.
T
h
e
lo
w
ca
teg
o
r
y
o
f
teac
h
e
r
p
er
f
o
r
m
a
n
ce
ca
n
b
e
in
f
lu
e
n
ce
d
b
y
s
ev
er
al
f
ac
to
r
s
,
s
u
ch
as
teac
h
e
r
co
m
p
eten
c
y
.
T
h
e
r
esu
lts
o
f
th
e
s
tu
d
y
s
h
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.
[2
]
A.
C.
F
re
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z
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l,
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t
a
l.
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De
v
e
l
o
p
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a
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s
In
tere
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d
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flu
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2
,
p
p
.
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0
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.
[3
]
P.
Kp
o
lo
v
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e
t
a
l.
,
“
A
c
a
d
e
m
ic
A
c
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m
e
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P
re
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:
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le
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I
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tere
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Lea
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Att
it
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to
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S
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,”
In
ter
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]
P
.
M
u
t
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d
H.
Ng
iran
d
e
,
“
Th
e
In
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tu
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p
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a
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.
A
Ca
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Hig
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o
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Af
rica
,
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e
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it
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o
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.
3
,
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p
.
4
3
1
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5
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2
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.
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]
E.
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“
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[6
]
S.
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,
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Th
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Eff
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M
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s,”
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ter
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rn
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(IJ
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,
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l.
6
,
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.
4
,
p
p
.
2
7
7
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2
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2
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.
[7
]
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A.
G
u
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n
d
ir,
“
S
t
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n
ts’
E
x
tri
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tri
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o
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m
a
ti
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s
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m
e
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t,
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ter
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s T
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[8
]
M.
S
.
S
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a
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tri
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n
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P
.
A.
W
h
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a
n
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lati
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twe
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,
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p
.
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8
-
125
,
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0
1
7
.
[9
]
K.
S
u
k
a
d
a
,
e
t
a
l.
,
“
C
o
n
tri
b
u
ti
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o
f
In
tere
st
in
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rn
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n
g
,
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h
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v
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m
e
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t
M
o
ti
v
a
ti
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n
,
a
n
d
M
a
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m
a
ti
c
a
l
Lo
g
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In
telli
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e
n
c
e
Ag
a
in
st S
tu
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t
M
a
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m
a
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s
Lea
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in
g
O
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tco
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a
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S
tate
Hig
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h
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1
i
n
Ki
n
tam
a
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i
(
i
n
Ba
h
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sa
),
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-
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rn
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Pro
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it
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s P
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,
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.
4
,
p
p
.
1
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1
1
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2
0
1
3
.
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0
]
H.
O.
Yu
s
u
f
a
n
d
A.
A.
Da
d
a
,
“
In
fa
c
t
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f
Tea
c
h
e
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Qu
a
li
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e
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u
c
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ti
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n
Ka
d
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n
a
S
tate
,
Nig
e
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,”
T
h
e
On
li
n
e
J
o
u
rn
a
l
o
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Qu
a
li
ty
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n
Hig
h
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r
Ed
u
c
a
t
io
n
,
v
o
l.
3
,
n
o
.
2
,
pp.
52
-
6
1
,
2
0
1
6
[1
1
]
A.
M
.
S
a
rd
ima
n
,
In
ter
a
c
ti
o
n
a
n
d
M
o
ti
v
a
ti
o
n
f
o
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L
e
a
rn
in
g
a
n
d
T
e
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h
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n
g
(in
Ba
h
a
sa
)
.
Ja
k
a
rta:
P
e
n
e
rb
it
Ra
ja
G
ra
fin
d
o
P
e
rsa
d
a
, p
.
2
1
4
,
2
0
1
1
.
[1
2
]
R.
A.
F
e
d
e
rici,
e
t
a
l.
,
“
S
t
u
d
e
n
t
s’
P
e
rc
e
p
ti
o
n
s
o
f
Tea
c
h
e
r
S
u
p
p
o
rt,
Nu
m
e
ra
c
y
,
a
n
d
As
se
ss
m
e
n
t
fo
r
Lea
rn
i
n
g
:
Re
latio
n
s
wit
h
M
o
ti
v
a
ti
o
n
a
l
Re
sp
o
n
se
s
a
n
d
M
a
ste
ry
Ex
p
e
rien
c
e
s
,”
In
ter
n
a
ti
o
n
a
l
E
d
u
c
a
ti
o
n
S
tu
d
ies
,
v
o
l.
9
,
n
o
.
1
0
,
p
p
.
1
-
1
5
,
2
0
1
6
.
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3
]
H.
Tam
b
u
n
a
n
a
n
d
T.
Na
ib
a
h
o
,
“
P
e
rfo
rm
a
n
c
e
o
f
M
a
th
e
m
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s
Te
a
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to
B
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ts'
Hi
g
h
Ord
e
r
Th
in
k
in
g
S
k
il
ls
(HO
TS
),
”
J
o
u
r
n
a
l
o
f
Ed
u
c
a
ti
o
n
a
n
d
L
e
a
r
n
in
g
(E
d
u
L
e
a
rn
)
,
v
o
l.
1
3
,
n
o
.
1
,
p
p
.
1
1
1
-
1
1
7
,
2
0
1
9
.
[1
4
]
Tri
sn
a
a
n
d
D.
U.
Wu
tsq
a
,
“
Co
m
p
a
riso
n
o
f
th
e
Ef
fe
c
ti
v
e
n
e
ss
o
f
Qu
a
n
t
u
m
Tea
c
h
in
g
a
n
d
TG
T
in
M
a
t
h
e
m
a
ti
c
s’
In
stru
c
ti
o
n
Vie
we
d
f
ro
m
Ac
h
ie
v
e
m
e
n
t
a
n
d
M
o
ti
v
a
ti
o
n
,
”
J
u
rn
a
l
Ri
se
t
Pen
d
i
d
ika
n
M
a
tem
a
ti
k
a
,
v
o
l.
2
,
n
o
.
2
,
p
p
.
2
9
6
-
3
0
7
,
2
0
1
5
[1
5
]
M.
L.
C
h
rissa
n
ti
a
n
d
D.
B.
Wi
d
jaja
n
ti
,
“
T
h
e
e
ffe
c
ti
v
e
n
e
ss
o
f
M
e
tac
o
g
n
it
iv
e
Ap
p
ro
a
c
h
a
c
c
o
r
d
i
n
g
t
o
Lea
rn
i
n
g
Ac
h
iev
e
m
e
n
t,
Crit
ica
l
Th
i
n
k
in
g
S
k
il
l,
a
n
d
I
n
tere
st
in
Lea
rn
i
n
g
M
a
th
e
m
a
ti
c
s
,”
J
u
rn
a
l
Ri
se
t
P
e
n
d
id
ik
a
n
M
a
tem
a
t
ika
,
v
o
l.
2
,
n
o
.
1
,
p
p
.
5
1
-
5
2
,
2
0
1
5
.
[1
6
]
R.
Am
il
u
d
d
i
n
a
n
d
S
.
S
u
g
ima
n
,
“
Th
e
Eff
e
c
t
P
r
o
b
lem
P
o
si
n
g
a
n
d
P
BL
o
n
Lea
rn
in
g
Ac
h
ie
v
e
m
e
n
t,
a
n
d
Lea
rn
i
n
g
M
o
ti
v
a
ti
o
n
S
t
u
d
e
n
t
s
M
a
t
h
e
m
a
t
i
c
s
E
d
u
c
a
t
i
o
n
,
”
J
u
r
n
a
l
R
i
s
e
t
P
e
n
d
i
d
i
k
a
n
M
a
t
e
m
a
t
i
k
a
,
v
o
l
.
3
,
n
o
.
1
,
p
p
.
1
0
0
-
108
,
2
0
1
6
.
[1
7
]
A.
Ab
d
u
ra
h
im,
“
Th
e
Eff
e
c
ti
v
e
n
e
ss
o
f
th
e
Re
a
li
stic
M
o
d
e
l
i
n
Co
o
p
e
ra
ti
v
e
S
e
tt
i
n
g
in
Term
s
o
f
th
e
Att
it
u
d
e
,
M
o
ti
v
a
ti
o
n
,
a
n
d
M
a
th
e
m
a
ti
c
a
l
Crit
ica
l
Th
in
k
i
n
g
S
k
il
l
o
f
Ju
n
io
r
Hig
h
S
c
h
o
o
l
S
t
u
d
e
n
ts
,
”
J
u
rn
a
l
R
ise
t
Pen
d
id
ika
n
M
a
tem
a
t
ika
,
v
o
l
.
3
,
n
o
.
2
,
p
p
.
1
3
7
-
1
4
9
,
2
0
1
6
.
[1
8
]
R.
S
.
Ah
m
a
d
,
“
Th
e
Eff
e
c
t
o
f
M
a
th
P
h
o
b
ia,
S
e
lf
-
Eff
ica
c
y
,
Ad
v
e
r
sity
Qu
o
ti
e
n
t
a
n
d
Ac
h
ie
v
e
m
e
n
t
M
o
ti
v
a
ti
o
n
o
n
M
a
th
e
m
a
ti
c
s
Lea
rn
in
g
Ac
h
iev
e
m
e
n
t
o
f
Ju
n
io
r
Hig
h
S
c
h
o
o
l
S
tu
d
e
n
ts,”
J
u
rn
a
l
R
ise
t
Pen
d
i
d
ika
n
M
a
t
e
ma
ti
k
a
,
v
o
l.
3
,
n
o
.
2
,
p
p
.
2
5
9
-
2
7
2
,
2
0
1
6
.
[1
9
]
A.
H.
As
tu
ti
k
,
“
Th
e
Eff
e
c
ti
v
e
n
e
s
s
o
f
th
e
P
r
o
b
lem
-
Ba
se
d
Lea
rn
in
g
o
n
P
lan
e
S
o
l
id
F
ig
u
re
in
Term
s
o
f
M
a
ste
ry
o
f
Co
m
p
e
ten
c
y
S
tan
d
a
r
d
,
Lea
rn
i
n
g
M
o
ti
v
a
ti
o
n
a
n
d
Lea
rn
i
n
g
I
n
tere
st
o
f
Ju
n
i
o
r
Hig
h
S
c
h
o
o
l
S
t
u
d
e
n
ts,
”
J
u
rn
a
l
Ri
se
t
Pen
d
i
d
ika
n
M
a
tem
a
ti
k
a
,
v
o
l.
4
,
n
o
.
1
,
p
p
.
5
6
-
6
6
,
2
0
1
7
.
[2
0
]
R.
S
a
striaw
a
n
,
“
Th
e
Eff
e
c
ti
v
e
n
e
ss
o
f
th
e
M
o
d
e
l
o
f
S
e
a
rc
h
,
S
o
l
v
e
,
Cre
a
te,
a
n
d
S
h
a
re
Term
s
o
f
Ac
h
iev
e
m
e
n
t,
M
a
th
e
m
a
ti
c
a
l
Re
a
s
o
n
in
g
,
a
n
d
M
o
ti
v
a
ti
o
n
t
o
Lea
rn
,
”
J
u
rn
a
l
Ri
se
t
Pen
d
i
d
ika
n
M
a
tem
a
ti
k
a
,
v
o
l.
4
,
n
o
.
1
,
p
p
.
8
7
-
9
9
,
2
0
1
7
.
[2
1
]
A.
W
ib
o
wo
,
“
Th
e
Eff
e
c
t
o
f
Tea
c
h
in
g
Re
a
li
stic
a
n
d
S
c
ien
ti
fic
M
a
th
e
m
a
ti
c
s
Ap
p
ro
a
c
h
o
n
S
tu
d
e
n
ts
Lea
rn
in
g
Ac
h
iev
e
m
e
n
t,
M
a
th
e
m
a
ti
c
a
l
R
e
a
so
n
in
g
A
b
il
it
y
,
a
n
d
I
n
tere
st,”
J
u
rn
a
l
Ri
se
t
Pen
d
id
ik
a
n
M
a
tem
a
ti
k
a
,
v
o
l.
4
,
n
o
.
1
,
p
p
.
1
-
1
0
,
2
0
1
7
.
[2
2
]
H.
Tam
b
u
n
a
n
,
“
Im
p
a
c
t
o
f
He
u
risti
c
S
trate
g
y
o
n
S
tu
d
e
n
ts’
M
a
th
e
m
a
ti
c
s
Ab
il
it
y
in
Hig
h
Ord
e
r
Th
in
k
i
n
g
,
”
In
ter
n
a
t
io
n
a
l
El
e
c
tro
n
ic Jo
u
rn
a
l
o
f
M
a
t
h
e
ma
ti
c
s E
d
u
c
a
ti
o
n
,
v
o
l.
1
3
,
n
o
.
3
,
p
p
.
3
2
1
-
3
2
8
,
2
0
1
8
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
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al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
A
n
a
lysi
s
o
f te
a
ch
er p
erfo
r
ma
n
ce
to
b
u
ild
s
tu
d
e
n
t in
teres
t a
n
d
mo
tiva
tio
n
to
w
a
r
d
s
…
(
Ha
r
d
i Ta
mb
u
n
a
n
)
47
[2
3
]
H.
Tam
b
u
n
a
n
,
“
T
h
e
Eff
e
c
ti
v
e
n
e
ss
o
f
th
e
P
ro
b
lem
-
S
o
l
v
in
g
S
trat
e
g
y
a
n
d
t
h
e
S
c
i
e
n
ti
f
ic
Ap
p
ro
a
c
h
to
S
t
u
d
e
n
ts’
M
a
th
e
m
a
ti
c
a
l
Ca
p
a
b
il
it
ies
in
Hig
h
Ord
e
r
T
h
i
n
k
i
n
g
S
k
il
ls
,”
I
n
t
e
rn
a
ti
o
n
a
l
El
e
c
tro
n
ic
J
o
u
rn
a
l
o
f
M
a
th
e
ma
ti
c
s
Ed
u
c
a
ti
o
n
,
v
o
l
.
1
4
,
n
o
.
2
,
p
p
.
2
9
3
-
3
0
2
,
2
0
1
9
.
[2
4
]
B.
D.
P
e
rm
a
tas
a
ri,
G
u
n
a
rh
a
d
i
a
n
d
Riy
a
d
i,
“
T
h
e
I
n
flu
e
n
c
e
o
f
P
r
o
b
lem
Ba
se
d
L
e
a
rn
in
g
To
wa
rd
s
S
o
c
ial
S
c
ien
c
e
Lea
rn
in
g
O
u
tco
m
e
s
Vie
we
d
fro
m
Lea
rn
in
g
I
n
tere
st,”
In
ter
n
a
t
io
n
a
l
J
o
u
r
n
a
l
o
f
Eva
lu
a
ti
o
n
a
n
d
Res
e
a
rc
h
in
Ed
u
c
a
ti
o
n
(IJ
ER
E
)
,
v
o
l.
8
,
n
o
.
1
,
p
p
.
3
9
-
4
6
,
2
0
1
9
.
[2
5
]
G
.
S
a
w,
e
t
a
l.
,
“
Ou
t
-
of
-
S
c
h
o
o
l
Ti
m
e
S
TE
M
P
ro
g
ra
m
:
S
t
u
d
e
n
ts’
Atti
tu
d
e
s
To
wa
rd
a
n
d
Ca
re
e
r
In
tere
sts
in
M
a
th
e
m
a
ti
c
s
a
n
d
S
c
ien
c
e
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Eva
l
u
a
ti
o
n
a
n
d
Res
e
a
rc
h
i
n
E
d
u
c
a
t
io
n
(IJ
ER
E)
,
v
o
l.
8
,
n
o
.
2
,
p
p
.
3
5
6
-
3
6
2
,
2
0
1
9
.
[2
6
]
H.
Tam
b
u
n
a
n
,
B.
S
in
a
g
a
a
n
d
T.
Y.
E.
S
iswo
n
o
,
“
S
t
u
d
e
n
ts'
Ab
il
it
y
i
n
S
o
lv
i
n
g
M
a
t
h
e
m
a
ti
c
a
l
P
ro
b
lem
s
with
He
u
risti
c
S
trate
g
ies
(in
Ba
h
a
sa
)
,
”
J
o
u
rn
a
l
o
f
M
a
th
e
m
a
ti
c
s E
d
u
c
a
ti
o
n
a
n
d
Ap
p
li
e
d
,
v
o
l.
0
1
,
n
o
.
0
2
,
p
p
.
28
-
3
3
,
2
0
2
0
.
[2
7
]
M
.
J.
Al
len
a
n
d
W
.
M
.
Ye
n
,
In
t
ro
d
u
c
ti
o
n
to
M
e
a
s
u
re
me
n
t
T
h
e
o
r
y
.
M
o
n
tere
y
:
Br
o
o
k
s
Co
le
P
u
b
li
s
h
in
g
c
o
m
p
a
n
y
,
p
.
2
7
4
,
1
9
7
9
.
[2
8
]
S
u
g
i
y
o
n
o
,
S
ta
ti
st
ics
fo
r R
e
se
a
rc
h
(
i
n
Ba
h
a
sa
).
Ba
n
d
u
n
g
:
Alfa
b
e
ta
,
p
p
.
3
0
4
,
2
0
1
1
.
[2
9
]
S
u
d
i
jo
n
o
,
A.,
I
n
t
r
o
d
u
c
t
i
o
n
t
o
E
d
u
c
a
t
i
o
n
a
l
E
v
a
l
u
a
t
i
o
n
(
i
n
B
a
h
a
s
a
)
.
J
a
k
a
r
t
a
:
P
T
R
a
j
a
G
r
a
f
i
n
d
o
P
e
r
s
a
d
a
,
p
p
.
3
2
9
,
2
0
1
1
.
[3
0
]
S
.
Arik
u
n
t
o
,
Res
e
a
rc
h
Pro
c
e
d
u
re
(
i
n
Ba
h
a
sa
).
Ja
k
a
rta:
Ri
n
e
k
a
Cip
t
a
,
p
.
3
1
9
,
2
0
1
0
.
[3
1
]
R.
E.
F
.
S
iag
ian
,
“
Eff
e
c
ts
o
f
S
tu
d
e
n
t
I
n
tere
st
a
n
d
S
tu
d
y
Ha
b
i
t
s
o
n
M
a
th
e
m
a
ti
c
s
Lea
rn
in
g
Ac
h
iev
e
m
e
n
t
(
in
Ba
h
a
sa
)
,”
J
u
rn
a
l
F
o
rm
a
ti
f
,
v
o
l.
2
,
n
o
.
2
,
p
p
.
1
2
2
-
1
3
1
,
2
0
1
5
.
[3
2
]
W.
Les
tari,
“
Th
e
Eff
e
c
ti
v
e
n
e
ss
o
f
Lea
rn
i
n
g
S
trate
g
ies
a
n
d
Lea
rn
in
g
M
o
ti
v
a
ti
o
n
Ag
a
in
st
M
a
th
e
m
a
ti
c
s
Lea
rn
in
g
Ou
tco
m
e
s
(in
Ba
h
a
sa
)
,”
J
u
rn
a
l
F
o
rm
a
ti
f
,
v
o
l.
2
,
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3
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Ju
frid
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t
a
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,
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At
ti
tu
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[3
4
]
As
tri
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a
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Tr
iy
o
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d
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p
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w.
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,
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e
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lati
o
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sh
ip
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twe
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c
h
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s
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ti
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with
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t
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s
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with
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p
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1
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.
[3
5
]
H.
Tam
b
u
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a
n
,
“
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in
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s Ac
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ter
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a
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d
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ies
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p
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.
[3
6
]
Wah
d
a
n
ia
,
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h
m
a
n
,
U
.
a
n
d
S
u
l
a
ste
ri,
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.
,
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e
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e
lf
-
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tate
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in
jai
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n
Ba
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a
sa
)
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u
rn
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l
M
a
tem
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n
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b
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ra
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o
.
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p
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0
1
7
.
[3
7
]
M
a
u
li
n
a
r,
“
Tea
c
h
e
r
Co
m
p
e
ten
c
e
in
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o
ti
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ti
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g
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tu
d
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ts
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th
e
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e
a
rn
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r
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ss
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t
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tate
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n
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r
Hig
h
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c
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1
,
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y
a
m
talira Bay
u
,
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o
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h
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i
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t
(
i
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B
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)
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d
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.
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.
1
,
p
p
.
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-
157
,
2
0
1
5
.
[3
8
]
D.
Isk
a
n
d
a
r,
“
Im
p
lem
e
n
tatio
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o
f
Tea
c
h
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r
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ro
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ss
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m
p
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in
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p
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tu
d
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a
rn
in
g
M
o
ti
v
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ti
o
n
(i
n
Ba
h
a
sa
)
,”
J
o
u
rn
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me
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t
Rev
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,
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l.
2
,
n
o.
3
,
p
p
.
2
6
1
-
2
7
0
,
2
0
1
8
.
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