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a
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s a
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m
e
n
t.
K
ey
w
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s
:
E
f
f
icac
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Ma
s
ter
y
ex
p
er
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ce
Ma
th
em
atics a
ch
iev
em
en
t
s
o
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p
er
s
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asio
n
Pro
b
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-
s
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in
g
Vica
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u
s
ex
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ce
T
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s
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c
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a
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u
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d
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CC B
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.
C
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r
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s
p
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A
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r
:
J
an
u
ar
d
D.
Dag
d
ag
C
o
lleg
e
o
f
E
d
u
ca
tio
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I
s
ab
ela
State
Un
iv
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s
ity
R
o
x
as,
I
s
ab
ela,
Ph
ilip
p
in
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E
m
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jan
u
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.
d
.
d
ag
d
ag
@
is
u
.
ed
u
.
p
h
1.
I
NT
RO
D
UCT
I
O
N
On
e
o
f
th
e
m
o
s
t
im
p
o
r
tan
t
co
m
p
eten
cies
s
tu
d
en
ts
m
u
s
t
ac
q
u
ir
e
to
d
ay
to
in
cr
ea
s
e
th
eir
o
p
p
o
r
tu
n
ities
an
d
p
o
ten
tials
f
o
r
s
u
cc
ess
,
is
m
ath
em
atica
l
k
n
o
wled
g
e
an
d
s
k
ills
[
1
]
.
I
r
o
n
ically
,
th
e
ac
h
ie
v
em
en
ts
o
f
ty
p
ical
s
tu
d
en
ts
in
co
lleg
e
m
ath
em
ati
cs
ar
e
n
o
t
s
atis
f
a
cto
r
y
,
if
n
o
t
b
elo
w
th
e
s
tan
d
a
r
d
s
[
2
]
,
[
3
]
.
Se
v
er
al
in
v
esti
g
atio
n
s
h
av
e
estab
lis
h
ed
th
at
a
f
f
ec
t
iv
e
ch
ar
ac
te
r
is
tics
ar
e
im
p
o
r
tan
t
f
ac
to
r
s
th
at
af
f
ec
t
a
ch
iev
em
en
t
[
4
]
-
[
6
]
p
ar
ticu
lar
ly
,
m
ath
em
atics
ac
h
i
ev
em
en
t
[
7
]
-
[
1
2
]
.
On
e
o
f
th
e
s
e
af
f
ec
tiv
e
ch
ar
ac
ter
is
tics
i
s
s
elf
-
ef
f
icac
y
b
elief
[
5
]
,
[
7
]
,
[
9
]
,
[
1
0
]
,
[
1
3
]
,
[
1
4
]
.
Self
-
ef
f
icac
y
co
m
es
f
r
o
m
f
o
u
r
m
ain
s
o
u
r
ce
s
b
ased
o
n
li
ter
atu
r
e:
m
aster
y
ex
p
er
ien
ce
,
v
icar
io
u
s
ex
p
er
ien
ce
,
s
o
cial
p
er
s
u
asio
n
,
an
d
s
o
m
atic
r
esp
o
n
s
es.
Ma
s
ter
y
ex
p
er
ien
ce
is
th
e
r
esu
lt
o
f
o
n
e'
s
p
r
ev
io
u
s
ex
p
er
ien
ce
th
at
allo
ws
s
tu
d
en
t
s
to
ap
p
ly
co
n
ce
p
ts
th
ey
h
a
v
e
alr
ea
d
y
lear
n
ed
[
1
2
]
a
n
d
is
th
e
s
tr
o
n
g
est
s
o
u
r
ce
o
f
s
elf
-
ef
f
icac
y
[
5
]
.
Vica
r
io
u
s
ex
p
er
ie
n
ce
is
s
ee
in
g
a
r
o
le
m
o
d
el
wh
o
is
d
o
in
g
th
e
r
elat
ed
task
s
u
cc
ess
f
u
lly
an
d
wh
o
h
as
p
o
s
itiv
e
o
r
n
e
g
at
iv
e
ef
f
ec
t
o
n
o
n
e'
s
s
elf
-
ef
f
icac
y
[
1
3
]
.
So
cial
p
er
s
u
asio
n
is
m
ain
ly
th
e
f
ee
d
b
ac
k
,
n
eg
ativ
e
o
r
p
o
s
itiv
e,
to
th
e
p
e
r
f
o
r
m
a
n
ce
o
f
an
i
n
d
iv
id
u
al
f
r
o
m
th
e
p
eo
p
le
ar
o
u
n
d
[
1
2
]
;
an
d
s
o
m
atic
r
esp
o
n
s
es
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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J
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ar
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b
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5
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Acc
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to
B
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[
5
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s
elf
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n
t
o
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ef
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t
th
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ap
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ly
in
th
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d
th
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p
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s
ev
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an
ce
in
f
ac
in
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d
if
f
icu
lties
an
d
s
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ess
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Ma
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ter
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ex
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,
ac
co
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d
in
g
to
o
th
er
s
tu
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ies,
ar
e
also
s
h
o
wn
to
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s
ig
n
if
ican
tly
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elate
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to
s
o
m
e
s
elf
-
ef
f
icac
y
s
o
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r
ce
s
[
1
5
]
,
[
1
6
]
.
Mo
s
t
s
tu
d
i
es
s
h
o
w
th
e
v
ar
iatio
n
s
o
n
th
e
lev
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f
s
ig
n
i
f
ican
ce
o
f
s
elf
-
ef
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icac
y
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d
m
aster
y
ex
p
er
ien
ce
s
[
7
]
,
[
1
2
]
,
[
1
5
]
,
[
1
6
]
.
Similar
ly
,
s
ev
e
r
al
s
tu
d
ie
s
ass
er
t
d
if
f
er
en
t
lev
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o
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s
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g
n
if
ican
ce
b
etwe
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s
y
ch
o
lo
g
ical
s
tates
an
d
v
ica
r
io
u
s
ex
p
er
ie
n
ce
s
[
7
]
,
[
1
7
]
-
[
1
9
]
.
On
t
h
e
o
th
e
r
h
an
d
,
a
s
tu
d
y
af
f
ir
m
s
th
at
s
elf
-
ef
f
icac
y
an
d
v
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io
u
s
ex
p
er
ie
n
ce
s
ar
e
in
s
ig
n
if
ican
tly
r
elate
d
[
1
8
]
.
Mo
s
t
s
tu
d
ies
ass
er
t
th
at
th
e
s
tr
o
n
g
est
p
r
ed
icto
r
o
f
m
ath
em
at
ics
ac
h
iev
em
en
t
is
m
aster
y
e
x
p
er
ien
ce
s
,
f
o
llo
wed
b
y
s
o
cial
p
er
s
u
asio
n
s
,
p
h
y
s
io
lo
g
ical
s
tates,
an
d
th
e
wea
k
est
p
r
e
d
icto
r
is
v
icar
io
u
s
ex
p
er
ie
n
ce
s
[
1
2
]
,
[
1
9
]
-
[
2
1
]
.
On
th
e
o
th
er
h
an
d
,
th
er
e
ar
e
s
o
m
e
s
tu
d
ies
th
at
ar
g
u
e
s
o
cial
p
er
s
u
asio
n
h
as
g
r
ea
ter
ass
o
ciatio
n
with
m
ath
em
atics
ac
h
iev
em
en
t
th
a
n
th
e
th
r
ee
[
1
7
]
,
[
2
2
]
,
[
2
3
]
;
m
ath
em
atics
p
er
f
o
r
m
an
c
e
an
d
v
icar
io
u
s
ex
p
er
ien
ce
s
h
av
e
n
o
r
elatio
n
s
h
ip
[
1
7
]
,
[
2
2
]
;
an
d
th
e
r
elatio
n
s
h
ip
s
o
f
p
s
y
ch
o
lo
g
ical
s
tates
with
ac
ad
em
ic
ac
h
iev
em
en
t
an
d
m
ath
em
atics a
ch
iev
em
en
t v
a
r
y
i.e
.
wh
ile
s
o
m
e
s
tu
d
ies s
h
o
w
th
at
p
h
y
s
io
lo
g
ical
s
tates a
r
e
s
i
g
n
if
ican
t f
ac
to
r
s
o
f
ac
h
iev
em
en
t [
1
6
]
,
[
1
7
]
,
[
2
4
]
,
[
2
5
]
,
o
th
er
s
ass
er
t th
at
it h
as lo
w
an
d
in
s
ig
n
if
ican
t e
f
f
ec
t [
1
9
]
,
[
2
4
]
,
[
2
6
]
-
[
2
8
]
.
C
lear
ly
,
th
er
e
ar
e
in
co
n
s
is
ten
t
r
esu
lts
am
o
n
g
s
tu
d
ies
th
at
e
x
am
in
ed
t
h
e
r
elatio
n
s
b
etwe
e
n
th
e
f
o
u
r
s
elf
-
ef
f
icac
y
s
o
u
r
ce
s
a
n
d
b
etwe
en
s
elf
-
ef
f
icac
y
an
d
m
ath
em
atics
ac
h
iev
em
en
t.
T
h
e
r
esu
l
ts
v
ar
y
d
ep
e
n
d
in
g
o
n
cu
ltu
r
al
d
if
f
er
e
n
ce
s
an
d
ed
u
ca
tio
n
al
lev
el
[
1
5
]
,
[
1
6
]
.
Mo
s
t
s
tu
d
ies
o
n
th
ese
co
n
s
tr
u
cts
h
av
e
f
o
cu
s
ed
o
n
s
elf
-
ef
f
icac
y
a
n
d
ac
ad
em
ic
ac
h
iev
em
en
t
am
o
n
g
ch
ild
r
e
n
a
n
d
h
i
g
h
s
ch
o
o
l
s
tu
d
e
n
ts
ab
r
o
ad
.
L
i
ttle
is
k
n
o
wn
to
d
ay
ab
o
u
t
th
e
m
ath
em
atics
p
r
o
b
le
m
-
s
o
lv
in
g
ef
f
icac
y
an
d
th
e
m
ath
em
atics
ac
h
iev
em
en
t
o
f
Fil
ip
in
o
p
r
o
s
p
ec
tiv
e
teac
h
er
s
p
ar
ticu
lar
ly
in
Ma
th
e
m
atics in
th
e
Mo
d
er
n
W
o
r
ld
(
MM
W
)
co
u
r
s
e.
Ma
th
em
atics
p
r
o
b
lem
-
s
o
lv
in
g
ef
f
icac
y
is
a
s
p
ec
if
ic
ty
p
e
o
f
s
elf
-
ef
f
icac
y
.
I
t
p
ar
tic
u
lar
ly
r
ef
er
s
to
one
’
s
p
e
r
ce
iv
ed
ab
ilit
y
to
s
o
lv
e
a
m
at
h
em
atica
l
p
r
o
b
lem
o
r
t
ask
.
Pro
b
lem
-
s
o
lv
in
g
ef
f
icac
y
is
also
d
ete
r
m
in
e
d
b
y
s
o
cial
p
er
s
u
asio
n
,
s
o
m
atic
r
esp
o
n
s
es,
v
icar
io
u
s
ex
p
er
ie
n
ce
s
,
an
d
m
aster
y
ex
p
er
ien
ce
s
[
2
3
]
.
Hen
ce
,
th
e
p
r
o
b
lem
-
s
o
lv
in
g
ef
f
icac
y
o
f
p
r
o
s
p
ec
tiv
e
teac
h
er
s
r
ef
lects
th
eir
co
n
f
id
en
ce
in
th
eir
ab
ilit
y
t
o
ex
ec
u
te
th
e
s
k
ills
n
ec
ess
ar
y
f
o
r
lear
n
in
g
t
h
eir
cu
r
r
en
t m
ath
em
atics c
o
u
r
s
e
wh
ich
is
MM
W
.
MM
W
is
a
3
-
u
n
it
g
en
er
al
e
d
u
ca
tio
n
co
u
r
s
e
o
f
f
er
ed
am
o
n
g
f
ir
s
t
y
ea
r
s
tu
d
en
ts
in
th
e
Ph
ilip
p
in
es.
As
p
ar
t
o
f
th
e
C
HE
D
K
-
1
2
tr
an
s
itio
n
p
r
o
g
r
a
m
f
o
r
2
0
1
6
-
2
0
2
1
,
th
e
co
u
r
s
e
d
ea
ls
with
m
ath
em
atics
as
an
ex
p
lo
r
atio
n
o
f
p
atter
n
s
,
ap
p
licatio
n
o
f
in
d
u
ctiv
e
a
n
d
d
ed
u
ctiv
e
r
ea
s
o
n
in
g
,
a
n
d
a
to
o
l
i
n
d
aily
life
.
I
n
t
h
e
cu
r
r
en
t
s
tu
d
y
,
m
ath
em
atics
ac
h
iev
em
en
t
r
ef
er
s
to
th
e
test
(
p
er
ce
n
t)
s
c
o
r
es
o
f
th
e
s
tu
d
e
n
t
s
in
th
e
th
r
ee
m
ain
less
o
n
s
o
f
MM
W
;
n
am
ely
,
No
n
-
R
o
u
tin
e
Pro
b
lem
-
So
lv
in
g
an
d
Natu
r
e
an
d
Nu
m
b
er
Patter
n
s
T
r
ac
in
g
(
NR
PS
&
NNPT
)
,
Ma
th
em
atica
l L
an
g
u
ag
e
an
d
Sy
m
b
o
ls
(
ML
S),
an
d
Data
Ma
n
ag
em
en
t (
DM
)
.
Hen
ce
,
th
e
cu
r
r
en
t
s
tu
d
y
ai
m
s
to
ex
am
in
e
th
e
r
elatio
n
s
b
etwe
en
th
e
p
r
o
b
lem
-
s
o
lv
in
g
ef
f
icac
y
s
o
u
r
ce
s
an
d
th
e
m
ath
em
atics
ac
h
iev
em
en
t
o
f
Fil
ip
in
o
p
r
o
s
p
ec
tiv
e
teac
h
er
s
.
Sp
ec
if
ically
,
th
is
s
tu
d
y
s
o
u
g
h
t
an
s
wer
s
to
th
e
f
o
llo
win
g
q
u
esti
o
n
s
:
i)
W
h
at
is
th
e
m
ath
em
a
tics
ac
h
iev
em
en
t
o
f
th
e
p
r
o
s
p
ec
tiv
e
teac
h
er
s
?;
ii)
W
h
at
ar
e
th
eir
p
r
o
b
lem
-
s
o
lv
in
g
ef
f
icac
y
s
o
u
r
ce
s
?;
iii)
I
s
th
er
e
a
s
ig
n
if
ican
t
r
elatio
n
s
h
ip
b
etwe
en
an
d
am
o
n
g
th
eir
m
aster
y
ex
p
er
ien
ce
s
,
v
ic
ar
io
u
s
ex
p
e
r
ien
ce
s
,
s
o
cial
p
er
s
u
asio
n
s
,
an
d
s
o
m
atic
r
esp
o
n
s
es?;
an
d
iv
)
W
h
ic
h
o
f
th
e
p
r
o
b
lem
-
s
o
lv
in
g
e
f
f
icac
y
s
o
u
r
ce
s
ca
n
s
ig
n
if
ica
n
tly
p
r
e
d
ict
m
ath
em
atics a
ch
iev
em
en
t
?
I
t
is
h
o
p
e
d
th
at
t
h
is
s
tu
d
y
c
an
f
u
r
th
er
t
h
e
u
n
d
er
s
tan
d
in
g
o
f
t
h
e
im
p
o
r
tan
ce
o
f
s
elf
-
e
f
f
icac
y
o
n
Fil
ip
in
o
p
r
o
s
p
ec
tiv
e
teac
h
er
s
’
s
u
cc
ess
in
co
lleg
e
m
ath
em
atics,
an
d
p
r
o
v
id
e
im
p
o
r
tan
t
d
i
s
cu
s
s
io
n
s
wi
th
th
e
ab
o
v
em
e
n
tio
n
ed
co
n
t
r
ad
ictin
g
liter
atu
r
e
f
in
d
i
n
g
s
.
As
f
u
t
u
r
e
teac
h
e
r
s
,
th
eir
ac
q
u
is
itio
n
o
f
m
ath
e
m
atica
l
co
m
p
eten
cies
is
h
i
g
h
ly
im
p
o
r
tan
t
a
n
d
t
h
eir
p
r
o
b
lem
-
s
o
lv
in
g
e
f
f
icac
y
m
ig
h
t
af
f
ec
t
th
eir
m
ath
em
atics
ac
h
iev
em
en
t.
T
h
e
r
ef
o
r
e
,
th
is
s
tu
d
y
ca
n
h
elp
teac
h
er
e
d
u
ca
to
r
s
esp
ec
ially
m
ath
em
atics
teac
h
er
s
to
in
teg
r
ate
in
th
e
in
s
tr
u
ctio
n
al
p
lan
n
in
g
an
d
im
p
lem
en
tatio
n
th
e
d
eg
r
ee
o
f
im
p
o
r
tan
ce
o
f
ea
ch
p
r
o
b
le
m
-
s
o
lv
in
g
ef
f
icac
y
s
o
u
r
ce
o
n
m
ath
em
atics p
er
f
o
r
m
an
ce
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
2
.
1
.
Resea
rc
h desi
g
n
T
h
is
s
tu
d
y
u
tili
ze
d
c
o
r
r
elatio
n
al
d
esig
n
t
o
ass
ess
th
e
r
elatio
n
s
h
ip
b
etwe
en
s
tu
d
en
ts
’
m
ath
em
atics
ac
h
iev
em
en
ts
an
d
p
r
o
b
lem
-
s
o
lv
in
g
ef
f
icac
y
s
o
u
r
ce
s
.
Acc
o
r
d
in
g
t
o
C
r
eswell
[
2
9
]
,
a
co
r
r
e
latio
n
al
d
esig
n
is
a
non
-
e
x
p
er
im
e
n
tal
f
o
r
m
o
f
r
esear
ch
th
at
u
s
es
co
r
r
elatio
n
al
s
tatis
t
ics
to
d
escr
ib
e
an
d
m
ea
s
u
r
e
th
e
d
eg
r
ee
o
f
r
elatio
n
s
h
ip
b
etwe
en
two
o
r
m
o
r
e
q
u
a
n
titativ
e
v
ar
iab
les.
2
.
2
.
P
a
rt
icipa
nts
T
h
e
cu
r
r
en
t
s
tu
d
y
tar
g
ets
all
ed
u
ca
tio
n
s
tu
d
en
ts
en
r
o
lled
i
n
GE
C
0
3
:
Ma
th
em
atics
in
t
h
e
Mo
d
e
r
n
W
o
r
ld
(
MM
W
)
in
a
u
n
iv
er
s
ity
d
u
r
in
g
th
e
s
ch
o
o
l
y
ea
r
2
0
1
9
-
2
0
2
0
.
T
o
co
n
tr
o
l
th
e
ef
f
ec
t
o
f
ex
tr
an
eo
u
s
v
ar
iab
les,
a
clu
s
ter
s
am
p
lin
g
was
d
o
n
e
to
s
elec
t
o
n
e
h
ig
h
e
r
ed
u
ca
tio
n
i
n
s
titu
tio
n
wh
er
e
s
tu
d
en
ts
wer
e
tau
g
h
t
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
P
r
ed
ictive
a
b
ilit
y
o
f p
r
o
b
lem
-
s
o
lvin
g
effica
cy
s
o
u
r
ce
s
o
n
ma
t
h
ema
tics
a
ch
ieve
men
t
(
Ja
n
u
a
r
d
D.
Da
g
d
a
g
)
1187
in
th
e
s
aid
s
u
b
ject
b
y
th
e
s
am
e
teac
h
er
.
All
th
e
1
2
3
f
r
esh
m
en
co
lleg
e
o
f
e
d
u
ca
tio
n
s
tu
d
en
ts
in
th
is
h
ig
h
er
ed
u
ca
tio
n
in
s
titu
tio
n
s
er
v
ed
a
s
th
e
p
ar
ticip
an
ts
.
T
h
er
e
wer
e
3
6
m
ale
s
tu
d
en
ts
an
d
8
7
f
e
m
ale
s
tu
d
en
ts
th
at
s
ec
tio
n
ed
h
eter
o
g
e
n
eo
u
s
ly
in
t
o
4
3
,
4
4
,
an
d
3
6
s
tu
d
en
ts
.
T
h
ey
wer
e
tau
g
h
t
b
y
a
s
in
g
le
teac
h
er
in
th
e
s
aid
m
ath
em
atics su
b
ject.
2
.
3
.
Resea
rc
h ins
t
rum
ent
s
T
h
e
s
tu
d
y
ad
o
p
te
d
th
e
5
-
p
o
i
n
t
L
ik
er
t
s
ca
les
d
ev
elo
p
ed
th
r
o
u
g
h
an
ex
p
lo
r
ato
r
y
f
ac
to
r
a
n
aly
s
is
b
y
Dag
d
ag
,
e
t
a
l.
[
2
3
]
to
m
e
asu
r
e
th
e
u
n
d
er
ly
in
g
co
n
s
tr
u
ct
o
f
s
tu
d
en
ts
’
p
r
o
b
lem
-
s
o
lv
in
g
ef
f
icac
y
in
m
ath
em
atics.
T
h
is
in
s
tr
u
m
en
t
was
ch
o
s
en
as
it
is
n
o
r
m
alize
d
in
th
e
co
n
te
x
t
o
f
th
e
p
ar
ticip
an
ts
[
2
3
]
.
T
h
e
3
0
-
item
in
s
tr
u
m
en
t
h
as
f
o
u
r
co
m
p
o
n
e
n
t
f
ac
to
r
s
,
n
am
ely
:
s
o
cial
p
er
s
u
asio
n
s
(
1
0
item
s
)
,
s
o
m
atic/p
h
y
s
io
lo
g
ical
r
esp
o
n
s
es (
1
0
item
s
)
,
v
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ltip
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h
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ab
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g
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.
Stu
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t in
m
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A
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atic
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ltip
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t
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s
tu
d
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m
ath
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atics
ac
h
iev
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en
t
in
NR
PS
&
NN
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(
β
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.
3
7
8
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0
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ML
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β
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ch
iev
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en
t (
β =
.
4
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p
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0
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
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DIS
CU
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h
is
s
tu
d
y
aim
ed
to
ass
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s
th
e
u
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ly
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n
s
tr
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o
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s
tu
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ts
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p
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ce
s
s
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n
if
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ed
ict
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atics
ac
h
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e
n
t.
R
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lts
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th
at
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n
s
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d
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aster
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ativ
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ly
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with
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o
m
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g
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as
s
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s
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asio
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o
r
m
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ce
)
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cr
ea
s
es,
s
o
m
atic
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n
s
es
d
ec
r
ea
s
es.
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asio
n
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th
e
v
a
r
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in
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s
es.
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r
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s
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d
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r
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ated
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.
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h
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atter
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s
o
f
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s
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s
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th
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r
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t
with
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s
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r
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ap
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d
in
,
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n
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ak
ci,
an
d
C
ey
la
n
d
ag
[
3
4
]
ar
g
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e
th
at
m
aster
y
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er
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ce
s
h
av
e
a
m
ed
iatio
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t
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o
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d
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io
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g
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l
s
tate
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u
t
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o
m
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n
ef
f
ec
t
f
o
r
v
icar
io
u
s
ex
p
er
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ce
s
.
Ush
er
an
d
Pajar
es
[
1
8
]
ass
er
t
th
at
v
icar
io
u
s
ex
p
er
ien
ce
is
n
o
t
s
ig
n
if
ican
tly
a
s
s
o
ciate
d
with
s
elf
-
ef
f
icac
y
.
Similar
ly
,
th
e
r
esu
lt
o
f
th
e
cu
r
r
e
n
t
s
tu
d
y
r
eb
u
ts
th
e
f
in
d
in
g
o
f
s
ev
er
al
r
esear
ch
e
s
[
7
]
,
[
1
7
]
-
[
1
9
]
th
at
v
icar
io
u
s
ex
p
e
r
ien
ce
is
s
ig
n
if
i
ca
n
tly
r
elate
d
to
s
o
m
atic
r
esp
o
n
s
e.
Am
o
n
g
th
e
f
o
u
r
e
f
f
icac
y
s
o
u
r
ce
s
,
o
n
ly
s
o
cial
p
er
s
u
asio
n
s
a
ch
iev
ed
s
ig
n
if
ica
n
t
r
esu
lts
in
ex
p
lain
in
g
ac
h
iev
em
en
ts
in
m
ath
em
atics
in
th
e
ar
ea
s
o
f
s
o
lv
in
g
n
o
n
-
r
o
u
tin
e
p
r
o
b
lem
s
an
d
tr
ac
in
g
p
a
tter
n
s
in
n
atu
r
e
an
d
n
u
m
b
er
s
,
lo
g
ic,
an
d
s
tatis
tic
s
(
with
b
eta
r
an
g
in
g
f
r
o
m
.
3
7
8
to
.
4
7
)
.
I
t
ag
r
ee
s
with
s
tu
d
ies
[
1
7
]
,
[
2
2
]
th
at
th
e
s
tr
o
n
g
est
ef
f
icac
y
s
o
u
r
ce
p
r
ed
icto
r
o
f
m
ath
em
atics
ac
h
iev
e
m
en
t
is
p
r
aise
an
d
f
ee
d
b
ac
k
.
On
th
e
o
th
er
h
a
n
d
,
it
r
ef
u
tes
th
e
claim
o
f
p
r
ev
io
u
s
s
tu
d
ies
[
5
]
,
[
1
2
]
,
[
1
9
]
,
[
2
1
]
th
at
m
aster
y
e
x
p
er
ien
ce
is
th
e
b
est
p
r
e
d
icto
r
o
f
m
ath
em
atics
p
er
f
o
r
m
an
ce
.
T
h
e
r
esu
lt
o
f
th
e
cu
r
r
en
t
s
tu
d
y
also
n
eg
lects
th
e
as
s
er
tio
n
o
f
s
ev
er
al
r
esear
ch
es
[
1
6
]
,
[
1
7
]
,
[
2
4
]
,
[
2
5
]
t
h
at
s
tated
s
o
m
atic
r
esp
o
n
s
e
is
a
s
ig
n
if
ican
t
f
ac
to
r
o
f
ac
ad
e
m
ic
ac
h
iev
em
en
t.
On
t
h
e
o
th
er
h
an
d
,
it a
f
f
ir
m
s
th
e
s
tate
m
en
t o
f
s
ev
er
al
s
tu
d
ies [
1
9
]
,
[
2
4
]
,
[
2
6
]
-
[
2
8
]
th
at
s
o
m
atic
r
esp
o
n
s
e
h
as a
lo
w
an
d
in
s
ig
n
if
ican
t
ef
f
ec
t.
Mo
r
e
o
v
e
r
,
th
e
cu
r
r
e
n
t
f
in
d
i
n
g
h
ig
h
lig
h
ts
th
at
v
icar
io
u
s
ex
p
er
ien
ce
as
a
m
ath
em
atics
p
r
o
b
lem
-
s
o
lv
in
g
e
f
f
icac
y
s
o
u
r
ce
d
o
es n
o
t sig
n
if
ica
n
tly
co
n
t
r
ib
u
te
to
m
ath
em
atics a
ch
iev
e
m
en
t [
7
]
,
[
1
7
]
,
[
2
2
]
.
5.
CO
NCLU
SI
O
N
T
h
is
q
u
an
titativ
e
r
esear
c
h
f
o
u
n
d
th
at
s
o
cial
p
er
s
u
asio
n
s
an
d
m
aster
y
ex
p
er
ien
ce
s
ar
e
b
o
t
h
in
v
er
s
ely
ass
o
ciate
d
with
s
o
m
atic
r
esp
o
n
s
es,
an
d
am
o
n
g
t
h
e
f
o
u
r
ef
f
ic
ac
y
s
o
u
r
ce
s
in
d
icate
d
in
t
h
e
lit
er
atu
r
e,
o
n
ly
s
o
cial
p
er
s
u
asio
n
s
ca
n
s
ig
n
if
ican
tly
p
r
ed
ict
m
ath
em
atics
ac
h
iev
em
en
t
in
th
e
ar
ea
s
o
f
s
o
lv
in
g
n
o
n
-
r
o
u
tin
e
p
r
o
b
lem
s
an
d
tr
ac
in
g
p
atter
n
s
in
n
atu
r
e
an
d
n
u
m
b
er
s
,
lo
g
ic,
an
d
s
tatis
t
ics.
T
h
is
s
tu
d
y
c
o
n
tr
ib
u
tes
to
t
h
e
u
n
d
er
s
tan
d
i
n
g
o
f
th
e
r
o
les
o
f
th
e
f
o
u
r
m
ath
e
m
atics
p
r
o
b
le
m
-
s
o
lv
in
g
ef
f
icac
y
s
o
u
r
ce
s
o
n
m
at
h
em
at
ics
ac
h
iev
em
en
t
an
d
g
u
id
es
th
e
d
ec
is
io
n
o
f
s
ch
o
o
ls
as
to
w
h
ich
o
f
t
h
e
s
o
u
r
ce
s
s
h
o
u
ld
b
e
g
iv
e
n
m
o
r
e
atten
ti
o
n
an
d
p
r
io
r
ity
t
o
b
etter
en
h
an
ce
s
tu
d
en
ts
’
p
er
f
o
r
m
an
ce
i
n
m
ath
em
atics.
T
h
e
s
tu
d
y
s
u
g
g
ests
th
at
m
ain
tain
in
g
an
e
n
co
u
r
ag
in
g
lear
n
in
g
en
v
ir
o
n
m
en
t
a
n
d
e
x
p
an
d
in
g
s
tu
d
en
ts
’
m
aster
y
lear
n
in
g
o
p
p
o
r
tu
n
ities
co
u
ld
r
ed
u
ce
s
tu
d
en
ts
’
an
x
iety
in
s
o
lv
in
g
m
ath
em
atics
p
r
o
b
le
m
s
o
r
task
s
.
T
h
e
s
ig
n
if
ican
ce
o
f
th
e
p
r
ed
ictiv
e
ab
ilit
y
o
f
s
o
cial
p
er
s
u
asio
n
o
n
m
at
h
em
atics
ac
h
iev
e
m
en
t
s
u
p
p
o
r
ts
th
at
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
10
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
1
1
8
5
-
1
1
9
1
1190
b
ec
o
m
in
g
a
tr
u
s
ted
v
o
ice
o
f
en
co
u
r
a
g
em
en
t
an
d
d
esig
n
in
g
a
p
er
s
u
asiv
e
lear
n
in
g
e
n
v
ir
o
n
m
en
t
ar
e
h
ig
h
l
y
r
ec
o
m
m
en
d
ed
r
o
les
o
f
s
ch
o
o
l
s
in
f
ac
ilit
atin
g
th
e
s
tu
d
en
ts
to
attain
th
e
n
ec
ess
ar
y
co
m
p
eten
cies
o
f
th
e
co
u
r
s
e.
Ma
th
em
atics
teac
h
er
s
s
h
o
u
ld
g
iv
e
s
in
ce
r
e
an
d
tim
ely
f
ee
d
b
ac
k
to
s
tu
d
en
ts
’
p
r
o
g
r
ess
to
war
d
a
lear
n
i
n
g
g
o
al
an
d
en
co
u
r
ag
e
t
h
em
to
attr
ib
u
te
s
u
cc
ess
an
d
f
ailu
r
e
in
m
a
th
em
atics
to
th
e
am
o
u
n
t
o
f
ef
f
o
r
t
th
ey
e
x
er
ted
in
lear
n
in
g
.
Nev
er
t
h
eless
,
th
e
s
t
u
d
en
ts
s
h
o
u
ld
b
e
en
a
b
led
to
ev
alu
ate
th
eir
o
wn
lear
n
in
g
p
r
o
g
r
ess
ag
ain
s
t
th
e
d
esire
d
m
ath
em
atica
l
co
m
p
et
en
cies
an
d
o
u
tco
m
es
r
ath
e
r
th
an
ag
ain
s
t
th
e
lear
n
in
g
p
er
f
o
r
m
an
ce
o
f
o
th
er
s
tu
d
en
ts
.
Ho
wev
er
,
th
e
v
ar
iatio
n
s
o
f
th
e
f
in
d
in
g
s
with
ex
is
tin
g
s
tu
d
ies
m
ig
h
t
b
e
d
u
e
to
th
e
d
is
tin
ct
n
atu
r
e
o
f
th
e
test
s
a
d
m
in
is
ter
ed
to
th
e
s
tu
d
en
ts
an
d
th
e
ar
ea
s
o
f
m
at
h
em
atics
in
v
o
lv
ed
.
B
o
th
th
e
N
R
PS
&
NNPT
an
d
th
e
DM
test
s
co
n
tain
e
d
m
u
ltip
le
-
ch
o
ice
t
y
p
e
wh
ile
th
e
ML
S
test
f
o
cu
s
ed
o
n
m
ath
e
m
atica
l
lo
g
ic
(
wh
ich
ca
n
n
o
t
b
e
m
ea
s
u
r
ed
v
alid
ly
b
y
m
u
ltip
le
-
ch
o
ice)
.
T
h
e
r
eliab
ilit
y
in
d
ex
o
f
th
ese
test
s
was
n
o
t
estab
lis
h
ed
.
T
h
e
s
tu
d
y
was
also
lim
ited
to
a
li
n
ea
r
r
e
g
r
ess
io
n
m
o
d
el
b
etwe
e
n
m
ath
em
atics
p
r
o
b
lem
-
s
o
lv
i
n
g
ef
f
icac
y
s
o
u
r
ce
s
an
d
m
ath
em
atics a
ch
iev
e
m
en
t
.
Fu
tu
r
e
r
esear
ch
m
ay
wis
h
to
r
ep
licate
th
e
cu
r
r
en
t
s
tu
d
y
u
s
in
g
s
tan
d
ar
d
ized
m
ea
s
u
r
in
g
in
s
tr
u
m
en
ts
.
Oth
er
af
f
ec
tiv
e
v
ar
iab
les
s
u
ch
as
attitu
d
e
to
war
d
m
ath
em
ati
cs,
m
ath
em
atics
an
x
iety
,
an
d
m
o
tiv
atio
n
m
ay
b
e
in
clu
d
ed
th
r
o
u
g
h
a
s
tr
u
ctu
r
al
eq
u
atio
n
m
o
d
el
to
g
et
a
m
o
r
e
h
o
lis
tic
an
d
r
ea
lis
tic
m
ea
s
u
r
e
o
f
th
e
r
elatio
n
s
h
ip
o
f
th
ese
v
ar
iab
le
s
o
n
m
ath
em
atics
ac
h
iev
em
en
t.
A
q
u
alitativ
e
r
esear
ch
m
a
y
b
e
c
o
n
d
u
cted
to
u
n
d
e
r
s
tan
d
h
o
w
s
o
cial
p
er
s
u
asio
n
en
h
an
ce
s
t
h
e
lear
n
in
g
o
f
m
ath
em
atics
an
d
to
ex
p
lo
r
e
th
e
p
h
e
n
o
m
e
n
o
lo
g
y
o
f
teac
h
er
s
’
en
g
ag
em
e
n
t in
g
iv
i
n
g
f
ee
d
b
ac
k
an
d
p
r
aise in
th
eir
class
r
o
o
m
.
ACK
N
O
WL
E
DG
E
M
E
NT
S
T
h
e
au
th
o
r
s
wo
u
ld
lik
e
t
o
ac
k
n
o
wled
g
e
th
e
I
s
ab
ela
State
Un
iv
er
s
ity
f
o
r
f
u
n
d
i
n
g
th
e
s
tu
d
y
.
RE
F
E
R
E
NC
E
S
[1
]
Na
ti
o
n
a
l
Co
u
n
c
il
o
f
Tea
c
h
e
rs
o
f
M
a
th
e
m
a
ti
c
s
(
NCTM
),
Prin
c
ip
les
a
n
d
S
t
a
n
d
a
rd
s
f
o
r
S
c
h
o
o
l
M
a
th
e
ma
ti
c
s
.
Re
sto
n
,
VA
,
2
0
0
0
.
[2
]
A.
G
.
Ro
m
a
n
,
“
Cu
rricu
l
u
m
im
p
lem
e
n
tatio
n
a
n
d
p
e
rfo
rm
a
n
c
e
o
f
m
a
th
e
m
a
ti
c
s
e
d
u
c
a
ti
o
n
stu
d
e
n
ts
i
n
o
n
e
sta
te
u
n
i
v
e
rsity
i
n
t
h
e
P
h
il
i
p
p
i
n
e
s
,
”
Asi
a
n
J
o
u
rn
a
l
o
f
M
u
lt
id
isc
ip
li
n
a
ry
S
t
u
d
ies
,
v
o
l
.
2
n
o
.
2
,
p
p
1
-
8
,
2
0
1
9
.
[3
]
A.
D.
P
a
ten
a
a
n
d
B
.
L
.
H.
Din
g
la
sa
n
,
“
S
t
u
d
e
n
ts’
p
e
rf
o
rm
a
n
c
e
o
n
m
a
th
e
m
a
ti
c
s
d
e
p
a
rtme
n
tal
e
x
a
m
in
a
ti
o
n
:
Ba
sis
f
o
r
m
a
th
in
terv
e
n
ti
o
n
p
r
o
g
ra
m
,
”
Asi
a
n
Aca
d
e
mic
Res
e
a
rc
h
J
o
u
r
n
a
l
o
f
S
o
c
ia
l
S
c
ien
c
e
&
Hu
ma
n
it
ies
,
v
o
l
.
1
,
n
o
.
1
4
,
p
p
.
2
5
5
-
268
,
2
0
1
3
.
[4
]
B.
S
.
Bl
o
o
m
,
İn
sa
n
n
it
e
li
k
ler
i
v
e
o
k
u
ld
a
ö
ğ
re
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me
(ç
e
v
.
D.
A.
Öz
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e
li
k
)
(
3
.
Ba
sk
ı
)
.
İsta
n
b
u
l:
M
EB
Ya
y
ın
ları
,
1
9
9
8
.
[5
]
A.
Ba
n
d
u
ra
,
S
e
lf
-
e
ff
ic
a
c
y
:
T
h
e
e
x
e
rc
ise
o
f
c
o
n
tro
l
.
Ne
w Yo
rk
:
F
re
e
m
a
n
,
1
9
9
7
.
[6
]
D.
H.
S
c
h
u
n
k
a
n
d
B
.
J.
Zi
m
m
e
rm
a
n
,
S
e
lf
-
re
g
u
la
ted
lea
rn
i
n
g
:
Fr
o
m
tea
c
h
in
g
t
o
se
lf
-
re
fl
e
c
ti
v
e
p
ra
c
ti
c
e
.
G
u
il
fo
r
d
P
re
ss
,
1
9
9
8
.
[7
]
E.
Yu
rt,
“
Th
e
p
re
d
ictiv
e
p
o
we
r
o
f
se
lf
-
e
ffica
c
y
so
u
rc
e
s
fo
r
m
a
th
e
m
a
ti
c
s
a
c
h
iev
e
m
e
n
t,
”
Ed
u
c
a
ti
o
n
a
n
d
S
c
ien
c
e
,
v
o
l.
3
9
,
n
o
.
1
7
6
,
p
p
.
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5
9
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6
9
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0
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4
,
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i
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0
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1
5
3
9
0
/
EB.
2
0
1
4
.
3
4
4
3
[8
]
M
.
L.
P
e
ters
,
“
E
x
a
m
in
in
g
t
h
e
re
latio
n
sh
i
p
s
a
m
o
n
g
c
las
sro
o
m
c
li
m
a
te,
se
lf
-
e
ffic
a
c
y
,
a
n
d
a
c
h
iev
e
m
e
n
t
in
u
n
d
e
r
g
ra
d
u
a
te
m
a
th
e
m
a
ti
c
s:
A
m
u
lt
i
-
lev
e
l
a
n
a
ly
sis,”
I
n
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
S
c
ien
c
e
a
n
d
M
a
th
e
m
a
ti
c
s
Ed
u
c
a
ti
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n
,
v
o
l.
1
1
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o
.
2
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.
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3
,
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o
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0
7
6
3
-
0
1
2
-
9
3
4
7
-
y
.
[9
]
P
.
Ch
e
n
a
n
d
B.
Zi
m
m
e
rm
a
n
,
“
A
c
ro
ss
-
n
a
ti
o
n
a
l
c
o
m
p
a
riso
n
stu
d
y
o
n
t
h
e
a
c
c
u
ra
c
y
o
f
se
lf
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e
ffica
c
y
b
e
li
e
fs
o
f
m
id
d
le
-
sc
h
o
o
l
m
a
th
e
m
a
ti
c
s
stu
d
e
n
ts,”
T
h
e
J
o
u
r
n
a
l
o
f
Exp
e
rime
n
t
a
l
Ed
u
c
a
ti
o
n
,
v
o
l
.
7
5
,
n
o
.
3
,
p
p
.
2
2
1
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4
4
,
2
0
0
7
,
d
o
i:
1
0
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3
2
0
0
/JEXE
.
7
5
.
3
.
2
2
1
-
2
4
4
.
[1
0
]
E.
Yu
rt
a
n
d
A.
M
.
S
ü
n
b
ü
l,
“
A str
u
c
tu
ra
l
e
q
u
a
ti
o
n
m
o
d
e
l
e
x
p
lain
i
n
g
8
t
h
g
ra
d
e
stu
d
e
n
ts’
m
a
th
e
m
a
ti
c
s a
c
h
iev
e
m
e
n
ts,”
Ed
u
c
a
ti
o
n
a
l
S
c
ien
c
e
s: T
h
e
o
ry
&
Pra
c
ti
c
e
,
v
o
l.
1
4
,
n
o
.
4
,
p
p
.
1
6
4
2
-
1
6
5
2
,
2
0
1
4
.
[1
1
]
C.
W.
Lo
o
a
n
d
J.
L.
F
.
Ch
o
y
,
“
S
o
u
rc
e
s
o
f
se
lf
-
e
ffica
c
y
in
flu
e
n
c
i
n
g
a
c
a
d
e
m
ic
p
e
rfo
rm
a
n
c
e
o
f
e
n
g
in
e
e
rin
g
st
u
d
e
n
ts,”
Ame
ric
a
n
J
o
u
r
n
a
l
o
f
Ed
u
c
a
ti
o
n
a
l
Res
e
a
rc
h
,
v
o
l.
1
,
n
o
.
3
,
p
p
.
8
6
-
92
,
2
0
1
3
,
d
o
i:
1
0
.
1
2
6
9
1
/e
d
u
c
a
ti
o
n
-
1
-
3
-
4
.
[1
2
]
E.
L.
Us
h
e
r
a
n
d
F
.
P
a
jare
s,
“
S
o
u
rc
e
s
o
f
se
lf
-
e
ffica
c
y
in
m
a
th
e
m
a
ti
c
s:
A
v
a
li
d
a
ti
o
n
st
u
d
y
,
”
Co
n
tem
p
o
ra
ry
Ed
u
c
a
ti
o
n
a
l
Psy
c
h
o
l
o
g
y
,
v
o
l.
3
4
,
n
o
.
1
,
p
p
.
8
9
-
1
0
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,
2
0
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9
,
d
o
i:
1
0
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1
0
1
6
/j
.
c
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d
p
s
y
c
h
.
2
0
0
8
.
0
9
.
0
0
2
.
[1
3
]
D.
H
.
S
c
h
u
n
k
,
L
e
a
rn
i
n
g
th
e
o
rie
s:
An
e
d
u
c
a
ti
o
n
a
l
p
e
rs
p
e
c
ti
v
e
.
P
e
a
rso
n
E
d
u
c
a
ti
o
n
,
I
n
c
.
,
2
0
1
1
.
[1
4
]
E.
L
.
Us
h
e
r,
“
S
o
u
rc
e
s o
f
m
i
d
d
le
s
c
h
o
o
l
st
u
d
e
n
t'
s
se
lf
-
e
ffica
c
y
in
m
a
th
e
m
a
ti
c
s
a
q
u
a
li
tativ
e
in
v
e
stig
a
t
io
n
,
”
Ame
ric
a
n
Ed
u
c
a
ti
o
n
a
l
Res
e
a
rc
h
J
o
u
r
n
a
l
,
v
o
l.
4
6
,
n
o
.
1
,
p
p
.
2
7
5
–
3
1
4
,
2
0
0
9
,
d
o
i:
1
0
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3
1
0
2
/0
0
0
2
8
3
1
2
0
8
3
2
4
5
1
7
.
[1
5
]
Y.
C.
C
h
e
n
,
“
S
o
u
rc
e
s
o
f
m
a
th
e
m
a
ti
c
s
se
lf
-
e
ffica
c
y
a
n
d
p
re
d
ict
o
rs
o
f
m
a
th
e
m
a
ti
c
s
a
c
h
iev
e
m
e
n
t
a
m
o
n
g
se
v
e
n
th
-
a
n
d
e
ig
h
t
h
-
g
ra
d
e
Taiwa
n
e
se
stu
d
e
n
t
s,”
Un
p
u
b
li
s
h
e
d
D
o
c
to
ra
l
Diss
e
rtatio
n
,
Un
i
v
e
rsity
o
f
Ke
n
tu
c
k
y
,
Lex
i
n
g
t
o
n
,
Ke
n
tu
c
k
y
,
UMI
N
o
.
3
4
9
2
8
0
7
,
2
0
1
0
.
[1
6
]
A.
Ars
lan
,
“
P
re
d
ictiv
e
p
o
we
r
o
f
t
h
e
so
u
rc
e
s
o
f
p
rima
ry
sc
h
o
o
l
stu
d
e
n
ts’
se
lf
-
e
ffica
c
y
b
e
li
e
fs
o
n
th
e
ir
se
lf
-
e
ffica
c
y
b
e
li
e
fs
fo
r
lea
rn
i
n
g
a
n
d
p
e
rfo
rm
a
n
c
e
,
”
Ed
u
c
a
ti
o
n
a
l
S
c
ien
c
e
s:
T
h
e
o
ry
&
Pra
c
ti
c
e
,
v
o
l.
1
2
,
n
o
.
3
,
p
p
.
1
9
1
5
-
1
9
2
0
,
2
0
1
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
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N:
2252
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8
8
2
2
P
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ed
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a
b
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o
f p
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b
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a
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men
t
(
Ja
n
u
a
r
d
D.
Da
g
d
a
g
)
1191
[1
7
]
T.
S
tev
e
n
s,
A.
Oli
v
á
re
z
,
a
n
d
D.
Ha
m
m
a
n
,
“
Th
e
r
o
le
o
f
c
o
g
n
it
i
o
n
,
m
o
ti
v
a
ti
o
n
,
a
n
d
e
m
o
ti
o
n
i
n
e
x
p
lain
i
n
g
t
h
e
m
a
th
e
m
a
ti
c
s
a
c
h
iev
e
m
e
n
t
g
a
p
b
e
twe
e
n
Hisp
a
n
ic
a
n
d
Wh
i
te
stu
d
e
n
ts,”
Hisp
a
n
ic
J
o
u
r
n
a
l
o
f
Beh
a
v
io
ra
l
S
c
ien
c
e
s
,
v
o
l.
2
8
,
n
o
.
2
,
p
p
.
1
6
1
-
1
8
6
,
2
0
0
6
.
[1
8
]
E.
L.
Us
h
e
r
a
n
d
F
.
P
a
jare
s,
“
S
o
u
rc
e
s
o
f
a
c
a
d
e
m
ic
a
n
d
se
lf
-
re
g
u
l
a
to
ry
e
ffica
c
y
b
e
li
e
fs
o
f
e
n
terin
g
m
id
d
le
sc
h
o
o
l
stu
d
e
n
ts,”
C
o
n
tem
p
o
ra
ry
Ed
u
c
a
ti
o
n
a
l
Psy
c
h
o
l
o
g
y
,
v
o
l.
3
1
,
n
o
.
2
,
p
p
.
1
2
5
–
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4
1
,
2
0
0
6
,
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o
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:
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0
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1
0
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6
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c
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d
p
s
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c
h
.
2
0
0
5
.
0
3
.
0
0
2
.
[1
9
]
G
.
Jo
ë
t,
E.
L.
Us
h
e
r,
a
n
d
P
.
Bre
ss
o
u
x
,
“
S
o
u
rc
e
s
o
f
se
lf
-
e
ff
ica
c
y
:
An
in
v
e
sti
g
a
ti
o
n
o
f
e
lem
e
n
tary
sc
h
o
o
l
st
u
d
e
n
ts
in
F
ra
n
c
e
,
”
J
o
u
rn
a
l
o
f
E
d
u
c
a
ti
o
n
a
l
Psy
c
h
o
lo
g
y
,
v
o
l.
1
0
3
,
n
o
.
3
,
p
p
.
6
4
9
–
6
6
3
,
2
0
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1
,
d
o
i:
1
0
.
1
0
3
7
/a0
0
2
4
0
4
8
.
[2
0
]
R.
W.
Le
n
t,
F
.
G
.
Lo
p
e
z
,
a
n
d
K
.
J.
Bies
c
h
k
e
,
“
M
a
t
h
e
m
a
ti
c
s
se
lf
-
e
ffica
c
y
:
S
o
u
rc
e
s
a
n
d
re
latio
n
t
o
sc
ien
c
e
-
b
a
se
d
c
a
re
e
r
c
h
o
ice
,
”
J
o
u
rn
a
l
o
f
C
o
u
n
se
li
n
g
Psy
c
h
o
l
o
g
y
,
v
o
l
.
3
8
,
n
o
.
4
,
p
p
.
4
2
4
–
4
3
0
.
1
9
9
1
.
[2
1
]
F
.
G
.
L
o
p
e
z
,
R.
W.
Len
t
,
S
.
D.
Bro
wn
,
a
n
d
P
.
A.
G
o
re
,
“
Ro
le
o
f
so
c
ial
–
c
o
g
n
it
i
v
e
e
x
p
e
c
tatio
n
s
in
h
i
g
h
sc
h
o
o
l
stu
d
e
n
ts'
m
a
th
e
m
a
ti
c
s
-
re
late
d
in
tere
st
a
n
d
p
e
rfo
rm
a
n
c
e
,
”
J
o
u
rn
a
l
o
f
C
o
u
n
se
li
n
g
Psy
c
h
o
l
o
g
y
,
v
o
l.
4
4
,
n
o
.
1
,
p
p
.
44
-
52
,
1
9
9
7
.
[2
2
]
T.
S
te
v
e
n
s,
K.
Wa
n
g
,
A.
Oliv
á
re
z
Jr,
a
n
d
D.
Ha
m
m
a
n
,
“
Us
e
o
f
se
lf
-
p
e
rsp
e
c
ti
v
e
s
a
n
d
t
h
e
ir
s
o
u
rc
e
s
to
p
re
d
ict
t
h
e
m
a
th
e
m
a
ti
c
s
e
n
ro
ll
m
e
n
t
i
n
ten
ti
o
n
s
o
f
g
irl
s
a
n
d
b
o
y
s,”
S
e
x
Ro
l
e
s
,
vol
.
5
6
,
n
o
.
5
-
6
,
p
p
.
3
5
1
-
3
6
3
,
2
0
0
7
,
d
o
i:
1
0
.
1
0
0
7
/s
1
1
1
9
9
-
0
0
6
-
9
1
8
0
-
2
.
[2
3
]
J.
D.
Da
g
d
a
g
,
O.
C
.
An
o
li
n
g
,
Jr.,
R.
P
.
S
a
lv
iejo
,
a
n
d
J.
F
.
P
a
sc
u
a
l,
“
De
v
e
lo
p
m
e
n
t
o
f
p
ro
b
lem
-
so
lv
i
n
g
e
ffica
c
y
sc
a
les
in
m
a
th
e
m
a
ti
c
s,”
Un
ive
rs
a
l
J
o
u
rn
a
l
o
f
E
d
u
c
a
t
io
n
a
l
Res
e
a
rc
h
,
v
o
l
.
8
,
n
o
.
6
,
p
p
.
2
3
9
7
-
2
4
0
5
,
2
0
2
0
,
d
o
i:
1
0
.
1
3
1
8
9
/u
jer.2
0
2
0
.
0
8
0
6
2
4
.
[2
4
]
R.
M
.
Kla
ss
e
n
,
“
A
Cro
ss
-
Cu
lt
u
r
a
l
In
v
e
stig
a
ti
o
n
o
f
th
e
Eff
ica
c
y
Be
li
e
fs
o
f
S
o
u
t
h
As
ian
Im
m
ig
r
a
n
t
a
n
d
An
g
l
o
Ca
n
a
d
ian
No
n
imm
ig
ra
n
t
Early
Ad
o
les
c
e
n
ts,”
J
o
u
r
n
a
l
o
f
Ed
u
c
a
t
io
n
a
l
Psy
c
h
o
lo
g
y
,
v
o
l.
9
6
,
n
o
.
4
,
p
p.
7
3
1
–
7
4
2
,
2
0
0
4
.
[2
5
]
K.
A.
G
a
in
o
r
a
n
d
R.
W.
Le
n
t,
“
S
o
c
ial
c
o
g
n
it
i
v
e
e
x
p
e
c
tati
o
n
s
a
n
d
ra
c
ial
id
e
n
ti
ty
a
tt
it
u
d
e
s
in
p
re
d
ictin
g
th
e
m
a
th
c
h
o
ice
in
ten
ti
o
n
s
o
f
Blac
k
c
o
l
leg
e
stu
d
e
n
ts,”
J
o
u
rn
a
l
o
f
C
o
u
n
se
li
n
g
Psy
c
h
o
lo
g
y
,
v
o
l.
4
5
,
n
o
.
4
,
p
p
.
403
–
4
1
3
,
1
9
9
8
,
d
o
i:
1
0
.
1
0
3
7
/0
0
2
2
-
0
1
6
7
.
4
5
.
4
.
4
0
3
.
[2
6
]
R.
Öz
y
ü
re
k
,
“
In
fo
rm
a
ti
v
e
so
u
rc
e
s
o
f
m
a
th
-
re
late
d
se
lf
e
ffica
c
y
e
x
p
e
c
tatio
n
s
a
n
d
th
e
ir
re
latio
n
sh
i
p
wi
th
m
a
th
-
re
late
d
se
lf
-
e
ffica
c
y
,
in
tere
st,
a
n
d
p
re
fe
re
n
c
e
,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Ps
y
c
h
o
lo
g
y
,
v
o
l
.
4
0
,
n
o
.
3
,
p
p
.
1
4
5
–
1
5
6
,
2
0
0
5
,
d
o
i:
1
0
.
1
0
8
0
/
0
0
2
0
7
5
9
0
4
4
4
0
0
0
2
4
9
.
[2
7
]
N.
Z.
Ha
m
p
t
o
n
a
n
d
E.
M
a
so
n
,
“
Lea
rn
in
g
d
isa
b
il
it
ies
,
g
e
n
d
e
r,
so
u
rc
e
s
o
f
e
ffica
c
y
,
se
lf
-
e
ffica
c
y
b
e
li
e
fs,
a
n
d
a
c
a
d
e
m
ic
a
c
h
iev
e
m
e
n
t
in
h
i
g
h
sc
h
o
o
l
st
u
d
e
n
ts
,”
J
o
u
rn
a
l
o
f
S
c
h
o
o
l
Psy
c
h
o
l
o
g
y
,
v
o
l.
4
1
,
n
o
.
2
,
p
p
.
1
0
1
-
1
1
2
,
2
0
0
3
,
d
o
i:
1
0
.
1
0
1
6
/S
0
0
2
2
-
4
4
0
5
(
0
3
)
0
0
0
2
8
-
1
.
[2
8
]
A.
Ars
lan
,
“
In
v
e
stig
a
ti
o
n
o
f
re
lat
io
n
sh
ip
b
e
twe
e
n
so
u
rc
e
s
o
f
se
lf
-
e
ffica
c
y
b
e
li
e
fs
o
f
se
c
o
n
d
a
ry
sc
h
o
o
l
stu
d
e
n
ts
a
n
d
so
m
e
v
a
riab
les
,
”
Ku
ra
m ve
Uy
g
u
l
a
ma
d
a
E
ğ
it
im
B
il
imler
i
,
v
o
l
.
1
3
,
n
o
.
4
,
p
p
.
1
9
8
3
-
1
9
9
3
,
2
0
1
3
.
[2
9
]
J.
W.
Cre
sw
e
ll
a
n
d
J.
D.
Cre
sw
e
ll
,
Res
e
a
rc
h
De
sig
n
:
Qu
a
l
it
a
t
ive
,
Qu
a
n
ti
ta
ti
v
e
,
a
n
d
M
ixe
d
M
e
t
h
o
d
s
Ap
p
r
o
a
c
h
e
s
,
5
th
Ed
.
S
AG
E,
2
0
1
8
.
[3
0
]
M
.
Ra
h
n
,
“
F
a
c
to
r
a
n
a
l
y
sis:
A
sh
o
rt
in
tr
o
d
u
c
ti
o
n
,
P
a
rt
5
–
Dro
p
p
i
n
g
u
n
imp
o
rtan
t
v
a
riab
les
fr
o
m
y
o
u
r
a
n
a
ly
sis,”
Th
e
An
a
ly
sis F
a
c
to
r,
2
0
0
8
.
[On
li
n
e
].
Av
a
il
a
b
le:
h
tt
p
s://
ww
w.t
h
e
a
n
a
ly
s
isfa
c
to
r.
c
o
m
/fac
to
r
-
a
n
a
ly
sis
-
5
.
[3
1
]
J.
P
a
ll
a
n
t,
S
PS
S
S
u
rv
iva
l
M
a
n
u
a
l:
A
S
tep
b
y
S
tep
to
Da
ta
A
n
a
lys
is
Us
in
g
S
PS
S
.
Ne
w
S
o
u
th
Wale
s: Al
len
&
Un
win
,
2
0
1
1
.
[3
2
]
G
.
F
.
Tem
p
leto
n
,
“
A
two
-
ste
p
a
p
p
r
o
a
c
h
f
o
r
tra
n
sfo
rm
in
g
c
o
n
ti
n
u
o
u
s
v
a
riab
les
t
o
n
o
rm
a
l:
I
m
p
li
c
a
ti
o
n
s
a
n
d
re
c
o
m
m
e
n
d
a
ti
o
n
s
f
o
r
IS
re
se
a
rc
h
,
”
Co
mm
u
n
ica
t
io
n
s
o
f
th
e
Asso
c
ia
ti
o
n
f
o
r
In
fo
rm
a
t
io
n
S
y
ste
ms
,
v
o
l.
2
8
,
n
o
.
4
,
p
p
.
4
2
-
58
,
2
0
1
1
,
d
o
i:
1
0
.
1
7
7
0
5
/1
CAIS.
0
2
8
0
4
.
[3
3
]
J.
P
a
ll
a
n
t,
S
PS
S
su
rv
iva
l
ma
n
u
a
l:
A
ste
p
b
y
ste
p
g
u
i
d
e
to
d
a
ta
a
n
a
lys
is
u
sin
g
S
PS
S
f
o
r
wi
n
d
o
ws
,
3
r
d
e
d
.
M
c
G
ra
w
-
Hill
,
Ne
w Yo
rk
,
USA,
2
0
0
7
.
[3
4
]
Y.
Ca
p
a
-
Ay
d
i
n
,
E.
Uz
u
n
ti
ry
a
k
i
-
Ko
n
d
a
k
c
i,
a
n
d
R.
Ce
y
lan
d
a
g
,
“
Th
e
re
latio
n
sh
i
p
b
e
twe
e
n
v
ica
ri
o
u
s
e
x
p
e
rien
c
e
,
so
c
ial
p
e
rsu
a
sio
n
,
p
h
y
si
o
l
o
g
ica
l
s
tate
,
a
n
d
c
h
e
m
istry
se
lf
-
e
ffica
c
y
:
Th
e
ro
le
o
f
m
a
ste
ry
e
x
p
e
rien
c
e
a
s
a
m
e
d
iato
r
,
”
Psy
c
h
o
lo
g
y
in
th
e
S
c
h
o
o
ls
,
v
o
l
.
5
5
,
n
o
.
1
0
,
p
p
.
1
2
2
4
-
1
2
3
8
,
2
0
1
8
,
d
o
i
:1
0
.
1
0
0
2
/
p
it
s.
2
2
2
0
1
.
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