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Critical
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Chun
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n P
ha
m
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a
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hi
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y
Ng
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n
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r
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e
rime
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tal
re
su
lt
s
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re
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c
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m
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th
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rian
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e
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t
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a
ta.
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e
CF
A
re
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o
rts
v
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li
d
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ted
t
h
e
6
-
fa
c
to
r
m
o
d
e
l,
d
e
m
o
n
stra
ti
n
g
stro
n
g
m
o
d
e
l
fit
i
n
d
ice
s
a
n
d
e
n
su
rin
g
h
i
g
h
re
li
a
b
il
it
y
a
n
d
v
a
li
d
it
y
.
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h
e
se
fa
c
to
rs
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isc
o
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e
re
d
a
n
d
n
a
m
e
d
in
th
i
s stu
d
y
a
re
a
s:
fa
c
il
it
ies
a
n
d
tea
c
h
in
g
su
p
p
o
r
t,
c
a
p
a
c
it
y
to
o
rg
a
n
ize
p
ro
jec
t
-
b
a
se
d
lea
rn
in
g
(
P
jBL
)
,
p
e
rc
e
p
ti
o
n
o
f
P
jBL
,
re
a
d
i
n
e
ss
fo
r
P
jBL
,
tea
c
h
e
rs
’
c
o
n
fid
e
n
c
e
in
a
p
p
l
y
i
n
g
P
jBL
,
a
n
d
st
u
d
e
n
ts
’
c
h
a
ra
c
teristics
.
T
h
e
fin
d
in
g
s
v
a
li
d
a
ted
th
e
se
late
n
t
fa
c
to
rs
’
m
o
d
e
l
a
s
a
c
o
m
p
re
h
e
n
siv
e
fra
m
e
wo
rk
fo
r
u
n
d
e
rsta
n
d
i
n
g
t
h
e
e
ss
e
n
ti
a
l
a
sp
e
c
ts
o
f
o
r
g
a
n
izi
n
g
P
jBL
.
By
a
d
d
re
ss
in
g
b
o
t
h
th
e
id
e
n
t
ifi
c
a
ti
o
n
a
n
d
e
m
p
iri
c
a
l
v
a
li
d
a
ti
o
n
o
f
in
fl
u
e
n
c
in
g
fa
c
to
rs,
th
e
stu
d
y
th
o
r
o
u
g
h
l
y
re
sp
o
n
d
s
t
o
t
h
e
re
se
a
rc
h
q
u
e
stio
n
s
a
n
d
stre
n
g
t
h
e
n
s
t
h
e
o
v
e
ra
ll
c
o
n
tri
b
u
ti
o
n
to
t
h
e
field
.
T
h
is
stu
d
y
is
n
o
v
e
l
in
it
s
d
e
v
e
l
o
p
m
e
n
t
a
n
d
v
a
li
d
a
ti
o
n
o
f
a
c
o
n
tex
t
-
s
p
e
c
ifi
c
m
e
a
su
re
m
e
n
t
m
o
d
e
l
fo
r
P
jBL
i
n
m
a
th
e
m
a
ti
c
s
e
d
u
c
a
ti
o
n
,
p
a
rti
c
u
larl
y
wit
h
i
n
t
h
e
Vie
tn
a
m
e
s
e
e
d
u
c
a
ti
o
n
a
l
c
o
n
tex
t,
wh
e
re
e
m
p
iri
c
a
ll
y
g
r
o
u
n
d
e
d
m
o
d
e
ls
o
f
th
is
n
a
t
u
re
re
m
a
in
sc
a
rc
e
.
F
u
rt
h
e
rm
o
re
,
it
o
ffe
rs
v
a
l
u
a
b
le
p
ra
c
ti
c
a
l
i
n
fo
rm
a
ti
o
n
f
o
r
tea
c
h
e
rs,
e
d
u
c
a
ti
o
n
a
l
a
d
m
in
istrato
rs,
a
n
d
re
se
a
rc
h
e
rs
to
e
n
h
a
n
c
e
a
n
d
p
ro
m
o
te
th
e
e
ffe
c
ti
v
e
a
p
p
li
c
a
ti
o
n
o
f
P
jBL
in
m
a
th
e
m
a
ti
c
s e
d
u
c
a
ti
o
n
.
K
ey
w
o
r
d
s
:
C
o
n
f
ir
m
ato
r
y
f
ac
to
r
a
n
aly
s
is
E
x
p
lo
r
ato
r
y
f
ac
t
o
r
an
aly
s
is
Ma
th
em
atics
Pro
ject
-
b
ased
lear
n
in
g
Sch
o
o
l te
ac
h
er
s
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
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SA
li
c
e
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se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Han
g
T
h
i M
y
N
g
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y
e
n
C
o
lleg
e
o
f
E
d
u
ca
tio
n
,
Vin
h
Un
iv
er
s
ity
No
.
1
8
2
L
e
Du
an
,
Vin
h
C
ity
,
Ng
h
e
An
,
Vietn
am
E
m
ail: n
g
u
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e
n
m
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h
a
n
g
3
0
0
8
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
Ma
s
ter
in
g
ess
en
tial
s
k
ills
p
la
y
s
a
cr
itical
r
o
le
t
o
s
u
cc
ess
in
th
is
f
ast
-
ch
an
g
i
n
g
wo
r
ld
,
an
d
th
es
e
ab
ilit
ies
wer
e
ac
q
u
ir
ed
to
tr
i
als
an
d
er
r
o
r
s
.
I
n
th
is
r
eg
ar
d
,
p
r
o
ject
-
b
ased
lear
n
in
g
(
PjB
L
)
is
co
n
s
id
er
ed
as
p
r
ef
er
r
a
b
le
o
p
tio
n
a
m
o
n
g
o
th
e
r
s
.
P
j
BL
i
s
b
eliev
ed
to
d
ee
p
en
s
tu
d
en
ts
’
u
n
d
er
s
tan
d
i
n
g
o
f
ac
a
d
em
ic
co
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ten
t a
n
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en
h
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ce
s
k
ey
2
1
s
t
-
ce
n
tu
r
y
s
k
ills
,
in
clu
d
in
g
“…c
r
iti
ca
l
th
in
k
in
g
,
c
r
ea
tiv
ity
,
c
o
llab
o
r
atio
n
,
an
d
co
m
m
u
n
icatio
n
”
[
1
]
,
[
2
]
.
I
n
t
h
e
co
n
tex
t
o
f
Vietn
am
,
PjB
L
is
g
ain
in
g
p
o
p
u
lar
as
an
in
s
tr
u
ctio
n
al
m
et
h
o
d
d
u
e
to
th
e
ed
u
ca
tio
n
al
r
e
f
o
r
m
p
o
licy
in
s
cien
ce
,
tech
n
o
lo
g
y
,
en
g
in
ee
r
i
n
g
,
a
n
d
m
at
h
em
ati
cs
(
STE
M
)
.
B
ein
g
co
n
s
id
er
ed
as
a
co
r
e
d
is
cip
lin
e
in
STE
M,
m
ath
em
atics
g
ain
s
its
in
d
is
p
o
n
ib
le
p
o
s
itio
n
i
n
th
e
s
o
cio
-
ec
o
n
o
m
ic
d
ev
elo
p
m
e
n
t
o
f
ev
e
r
y
c
o
u
n
t
r
y
[
3
]
,
[
4
]
,
b
ec
au
s
e
o
f
its
s
tr
o
n
g
em
p
h
asis
o
n
lo
g
ical
th
i
n
k
in
g
an
d
r
ea
s
o
n
in
g
.
T
h
u
s
,
th
is
s
u
b
ject
is
wel
l
-
s
u
it
ed
f
o
r
PjB
L
[
1
]
,
[
4
]
.
Yet,
wh
en
ap
p
ly
in
g
to
th
e
r
ea
l
-
wo
r
l
d
co
n
tex
t,
th
e
PjB
L
im
p
lem
en
tatio
n
in
m
ath
e
m
atics
en
co
u
n
ter
ed
s
ev
er
al
c
h
allen
g
es,
s
u
ch
as
teac
h
er
co
m
p
eten
cy
,
s
tu
d
en
ts
’
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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J
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&
R
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d
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c
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N:
2252
-
8
8
2
2
C
r
itica
l fa
cto
r
s
s
h
a
p
in
g
p
r
o
je
ct
-
b
a
s
ed
lea
r
n
in
g
in
ma
th
ema
t
ics ed
u
ca
tio
n
(
C
h
u
n
g
X
u
a
n
P
h
a
m
)
4541
ch
ar
ac
ter
is
tics
,
s
ch
o
o
l
p
o
licies,
in
f
r
astru
ctu
r
e,
an
d
tech
n
o
lo
g
ical
s
u
p
p
o
r
t
[
1
]
,
[
2
]
.
As
s
u
ch
,
th
er
e
is
a
n
ee
d
to
ex
am
in
e
th
e
f
ac
t
o
r
s
in
f
lu
e
n
cin
g
th
e
o
r
g
an
izatio
n
o
f
PjB
L
in
m
ath
em
atics to
o
p
tim
ize
its
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f
ec
tiv
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ess
.
T
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er
e
ar
e
s
ev
er
al
s
tu
d
ies
th
at
ex
p
lo
r
e
d
an
d
h
ig
h
lig
h
ted
th
e
b
en
ef
its
o
f
PjB
L
in
m
ath
em
a
tics
in
th
e
ed
u
ca
tio
n
al
s
ettin
g
s
.
Fo
r
ex
a
m
p
le,
s
ev
er
al
s
tu
d
ies
[
5
]
,
[
6
]
d
em
o
n
s
tr
ated
h
o
w
m
ath
em
a
tical
co
n
ce
p
ts
was
ac
h
iev
ed
b
y
im
p
lem
e
n
tin
g
S
T
E
M
-
in
teg
r
ated
PjB
L
m
o
d
el.
I
n
ad
d
itio
n
,
PjB
L
was
also
s
h
o
wn
to
h
av
e
a
p
o
s
itiv
e
im
p
ac
t
o
n
s
tu
d
en
ts
’
attitu
d
es
to
war
d
tech
n
o
lo
g
y
an
d
s
cien
ce
,
th
u
s
f
o
s
ter
in
g
g
r
ea
ter
in
ter
est
an
d
m
o
tiv
atio
n
in
lea
r
n
in
g
[
2
]
,
[
7
]
.
I
n
t
h
e
s
am
e
v
ein
,
a
n
o
th
e
r
s
tu
d
ies
[
8
]
,
[
9
]
c
o
n
f
ir
m
e
d
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
PjB
L
m
o
d
el
in
:
i
)
in
cr
ea
s
in
g
ac
ad
em
ic
o
u
tc
o
m
es
an
d
co
n
c
ep
tu
al
u
n
d
er
s
tan
d
in
g
;
ii
)
m
o
ti
v
atin
g
lear
n
i
n
g
;
an
d
iii
)
f
o
s
ter
in
g
h
ig
h
er
-
o
r
d
er
th
i
n
k
in
g
s
k
ills
.
Ad
d
itio
n
ally
,
n
u
m
er
o
u
s
s
tu
d
ies
em
p
h
asize
th
e
cr
u
cial
r
o
le
o
f
teac
h
er
s
in
d
esig
n
in
g
,
g
u
id
in
g
,
an
d
ass
ess
in
g
lear
n
in
g
p
r
o
jects
to
en
s
u
r
e
th
e
s
u
cc
ess
f
u
l
im
p
lem
en
tatio
n
o
f
PjB
L
[
1
0
]
,
[
1
1
]
.
I
n
Vietn
am
,
s
ev
er
al
r
esear
ch
er
s
ex
p
lo
r
ed
t
h
e
f
ea
s
ib
ilit
y
o
f
PjB
L
in
m
at
h
em
atics;
h
o
wev
er
,
th
ese
p
r
io
r
r
esear
ch
es
d
id
n
o
t
p
r
o
v
id
e
a
co
m
p
r
eh
e
n
s
iv
e
an
aly
s
is
o
f
th
e
f
ac
to
r
s
in
f
lu
en
cin
g
its
ap
p
licatio
n
with
in
th
e
c
o
n
tex
t
o
f
Vietn
am
ese
g
en
er
al
e
d
u
ca
tio
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[
1
2
]
–
[
1
4
]
.
Fu
r
t
h
er
m
o
r
e,
th
ese
r
esear
c
h
d
id
n
o
t
y
et
f
u
lly
in
v
esti
g
ated
th
e
p
ar
ticu
lar
d
if
f
icu
lties
th
at
ed
u
ca
to
r
s
an
d
lear
n
er
s
e
n
co
u
n
ter
wh
e
n
ad
o
p
tin
g
PjB
L
in
m
ath
em
atics.
Desp
ite
ex
ten
s
iv
e
r
esear
ch
o
n
PjB
L
to
d
ate,
n
u
m
er
o
u
s
r
esear
ch
g
a
p
s
r
em
ain
t
h
at
r
eq
u
ir
e
ad
d
itio
n
al
in
v
esti
g
atio
n
.
R
esear
ch
h
as
y
et
to
co
n
d
u
ct
a
c
o
m
p
lete
s
t
u
d
y
o
f
th
e
elem
en
ts
s
h
ap
in
g
PjB
L
s
tr
u
ctu
r
e
in
m
ath
em
atics
wh
ile
m
is
s
in
g
th
o
r
o
u
g
h
ev
al
u
atio
n
s
o
f
h
o
w
r
e
g
u
latio
n
s
an
d
tec
h
n
o
l
o
g
ical
s
u
p
p
o
r
ts
im
p
ac
t
th
is
ap
p
r
o
ac
h
.
E
x
is
tin
g
s
tu
d
ies
id
e
n
tifie
d
m
u
ltip
le
c
h
allen
g
es
te
ac
h
er
s
ex
p
er
ie
n
ce
wh
e
n
th
ey
d
esig
n
,
im
p
lem
e
n
t,
an
d
ev
alu
ate
m
ath
em
atica
l
p
r
o
jects
d
u
r
in
g
in
s
tr
u
ctio
n
al
p
r
ac
tice.
T
h
is
s
tu
d
y
s
ee
k
s
to
en
h
an
ce
cu
r
r
e
n
t
u
n
d
er
s
tan
d
i
n
g
b
y
ex
a
m
in
in
g
wh
ich
f
ac
to
r
s
af
f
ec
t
th
e
im
p
lem
en
tatio
n
o
f
PjB
L
with
in
s
ec
o
n
d
ar
y
an
d
h
ig
h
s
ch
o
o
ls
m
ath
em
atics e
d
u
ca
tio
n
.
T
h
e
r
esear
ch
q
u
esti
o
n
s
r
ep
r
esen
t th
e
s
p
ec
if
ic
f
o
cu
s
o
f
th
is
s
tu
d
y
:
i)
W
h
at
ar
e
th
e
p
o
ten
tial f
ac
to
r
s
in
f
lu
en
cin
g
th
e
im
p
lem
e
n
tatio
n
o
f
PjB
L
?
(
R
Q1
)
ii)
Ar
e
th
ese
f
ac
to
r
s
s
u
f
f
icien
tly
r
eliab
le
an
d
v
alid
ated
f
o
r
u
s
e
i
n
f
u
r
th
er
r
esear
ch
?
(
R
Q2
)
T
h
is
r
esear
ch
g
ath
er
s
em
p
ir
ic
al
d
ata
b
y
s
u
r
v
ey
in
g
m
ath
e
m
atics
teac
h
er
s
f
r
o
m
s
ec
o
n
d
a
r
y
an
d
h
ig
h
s
ch
o
o
l
to
im
p
r
o
v
e
PjB
L
ap
p
licatio
n
in
m
ath
em
atics
teac
h
in
g
an
d
s
u
g
g
ests
s
u
p
p
o
r
tiv
e
s
tr
ateg
ies
f
o
r
ed
u
ca
tio
n
al
in
s
titu
tio
n
s
an
d
p
o
licy
m
a
k
er
s
.
T
h
e
liter
atu
r
e
r
ev
iew
will
o
r
g
an
ize
ex
is
tin
g
r
esear
ch
ab
o
u
t
f
ac
to
r
s
af
f
ec
tin
g
PjB
L
im
p
lem
en
tatio
n
in
s
ec
o
n
d
ar
y
s
ch
o
o
l
m
ath
em
ati
cs
th
r
o
u
g
h
e
v
alu
atio
n
an
d
s
y
n
th
esis
o
f
p
r
ev
io
u
s
s
tu
d
ies
wh
ile
p
in
p
o
in
tin
g
r
esear
ch
g
ap
s
n
ee
d
i
n
g
f
u
r
th
er
in
v
esti
g
atio
n
.
T
h
e
s
tu
d
y
will
th
en
d
escr
ib
e
th
e
m
et
h
o
d
s
u
s
e
d
f
o
r
g
ath
er
in
g
an
d
an
aly
zin
g
d
ata.
T
h
e
r
esear
ch
f
in
d
in
g
s
will
id
en
tify
th
e
m
ai
n
f
ac
to
r
s
im
p
ac
tin
g
PjB
L
in
m
ath
em
atics
b
ef
o
r
e
co
m
p
ar
in
g
th
ese
r
esu
lts
with
ex
is
tin
g
s
tu
d
ies.
T
h
e
co
n
clu
s
io
n
will
b
r
in
g
to
g
eth
e
r
th
e
p
r
im
ar
y
d
is
co
v
er
ies
an
d
r
ec
o
g
n
ize
s
tu
d
y
lim
itatio
n
s
b
e
f
o
r
e
p
r
o
v
id
in
g
g
u
id
an
ce
f
o
r
s
tak
eh
o
ld
er
s
to
b
etter
im
p
lem
en
t
PjB
L
m
eth
o
d
s
in
m
ath
em
atics tea
ch
in
g
.
2.
L
I
T
E
R
AT
U
RE
R
E
VI
E
W
T
h
is
s
ec
tio
n
p
r
o
v
id
es
an
o
v
e
r
v
iew
o
f
k
ey
co
n
ce
p
ts
,
s
y
n
th
esizes
an
d
an
aly
ze
s
p
r
ev
io
u
s
s
tu
d
ies
o
n
PjB
L
in
m
ath
em
atics,
ca
teg
o
r
izes
r
esear
ch
d
ir
ec
tio
n
s
,
an
d
id
en
tifie
s
g
ap
s
f
o
r
th
e
c
u
r
r
e
n
t
s
tu
d
y
.
PjB
L
is
a
co
n
tem
p
o
r
ar
y
teac
h
in
g
m
et
h
o
d
o
lo
g
y
wh
er
ei
n
s
tu
d
en
ts
p
r
o
ac
tiv
ely
tak
e
p
ar
t
in
ex
p
lo
r
i
n
g
,
r
esear
ch
in
g
,
an
d
s
o
lv
in
g
r
ea
l
-
w
o
r
ld
p
r
o
b
lem
s
th
r
o
u
g
h
p
r
o
ject
-
b
ased
e
x
er
c
is
es
[
1
5
]
.
T
h
is
ap
p
r
o
ac
h
eq
u
ip
es
s
tu
d
en
ts
with
k
n
o
wled
g
e
ac
cu
m
u
latio
n
an
d
en
h
an
ce
s
im
p
o
r
tan
t
s
k
ills
,
n
am
ely
co
m
m
u
n
icativ
e
s
k
ills
,
co
llab
o
r
ativ
e
s
k
ills
,
cr
ea
tiv
e
an
d
cr
itical
th
in
k
in
g
s
k
ills
[
1
]
,
[
2
]
,
[
1
6
]
.
I
n
m
ath
ed
u
ca
tio
n
,
PjB
L
h
as
g
ain
ed
atten
tio
n
o
f
r
esear
ch
e
r
s
d
u
e
to
its
ab
ilit
y
to
r
ein
f
o
r
ce
s
tu
d
en
ts
’
ac
q
u
is
itio
n
o
f
m
ath
e
m
atica
l
co
n
ce
p
ts
th
r
o
u
g
h
r
ea
l
-
wo
r
ld
in
ter
ac
tio
n
s
[
5
]
,
[
6
]
.
Ho
we
v
er
,
th
e
im
p
le
m
en
tatio
n
o
f
th
is
ap
p
r
o
ac
h
s
till
en
co
u
n
ter
e
d
m
an
y
f
ac
ets,
f
o
r
ex
am
p
le:
teac
h
er
ca
p
ac
ity
,
s
tu
d
en
t e
n
g
ag
em
e
n
t,
s
ch
o
o
l p
o
licies,
in
f
r
astru
ctu
r
e
,
an
d
tech
n
o
lo
g
y
s
u
p
p
o
r
t
[
1
]
,
[
1
0
]
.
Pro
ject
is
a
s
er
ies
o
f
task
s
th
at
r
eq
u
ir
e
s
tu
d
en
ts
to
b
e
in
v
o
l
v
ed
in
a
s
et
o
f
ac
tiv
ities
s
u
ch
as
d
esig
n
,
p
r
o
b
lem
-
s
o
lv
in
g
,
d
ec
is
io
n
-
m
a
k
in
g
.
PjB
L
p
u
r
p
o
r
ts
at
p
r
o
v
i
d
in
g
s
tu
d
en
ts
a
n
u
m
b
er
o
f
o
p
p
o
r
tu
n
ities
to
w
o
r
k
in
d
ep
en
d
en
tly
o
v
e
r
a
lo
n
g
d
u
r
atio
n
an
d
c
u
lm
in
ate
in
a
p
r
o
d
u
ct
[
1
5
]
.
As
s
u
ch
,
PjB
L
is
co
n
s
id
er
ed
as
a
d
y
n
am
ic,
s
tu
d
e
n
t
-
ce
n
ter
e
d
lea
r
n
in
g
m
o
d
el
in
wh
ich
lear
n
e
r
s
,
s
et
g
o
als,
co
llab
o
r
ate,
co
m
m
u
n
icate
,
an
d
r
ef
lect
wh
ile
s
o
lv
in
g
r
ea
l
-
wo
r
ld
p
r
o
b
lem
s
u
n
d
er
th
e
g
u
id
a
n
ce
o
f
a
teac
h
er
[
1
]
.
Stem
m
ed
f
r
o
m
th
e
“
lear
n
in
g
b
y
d
o
in
g
”
id
ea
,
PjB
L
f
o
cu
s
es
o
n
ac
h
iev
in
g
lear
n
in
g
o
u
tco
m
es
t
h
r
o
u
g
h
ac
tiv
e
en
g
ag
em
e
n
t
in
g
o
al
-
o
r
ie
n
ted
task
s
.
I
n
ad
d
itio
n
,
it
also
f
o
s
ter
s
cr
itical
th
in
k
in
g
an
d
p
r
o
m
o
tes
d
ir
e
ct,
h
an
d
s
-
o
n
p
a
r
ticip
atio
n
,
m
a
k
in
g
lear
n
in
g
m
o
r
e
ef
f
ec
tiv
e
co
m
p
ar
ed
t
o
co
n
v
en
t
io
n
al
k
n
o
wled
g
e
-
b
ased
ap
p
r
o
a
ch
es
[
9
]
.
I
n
Vietn
am
,
th
e
Min
is
tr
y
o
f
E
d
u
ca
tio
n
an
d
T
r
ain
in
g
r
ef
o
r
m
ed
th
e
n
ew
g
en
er
al
ed
u
ca
tio
n
cu
r
r
icu
lu
m
in
2
0
1
8
,
wh
ich
em
p
h
asizes
co
m
p
eten
cy
-
b
ased
lear
n
in
g
an
d
co
m
p
r
eh
e
n
s
iv
e
s
tu
d
en
t
d
ev
elo
p
m
en
t.
T
h
is
cu
r
r
icu
lu
m
r
eq
u
ir
es
s
i
g
n
if
ican
t
ch
an
g
es
in
teac
h
in
g
m
eth
o
d
s
to
ac
h
iev
e
less
o
n
o
b
jectiv
es
wh
ile
p
r
o
m
o
tin
g
s
tu
d
en
t
d
e
v
elo
p
m
e
n
t.
Acc
o
r
d
in
g
ly
,
teac
h
er
s
ar
e
n
o
lo
n
g
e
r
s
im
p
ly
k
n
o
wled
g
e
p
r
o
v
id
er
s
b
u
t
in
s
tead
p
lay
th
e
r
o
le
o
f
f
ac
ilit
ato
r
s
,
g
u
id
in
g
s
tu
d
en
ts
to
ac
q
u
ir
e
k
n
o
wled
g
e
an
d
m
aster
ess
en
tial
s
k
ills
[
1
7
]
.
C
u
r
r
en
tly
,
m
an
y
in
n
o
v
ativ
e
teac
h
in
g
m
et
h
o
d
s
ar
e
wid
ely
a
p
p
lied
in
ed
u
ca
tio
n
al
in
s
titu
tio
n
s
,
o
f
wh
ic
h
PjB
L
is
o
n
e
o
f
th
e
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
.
14
,
No
.
6
,
Dec
em
b
er
20
25
:
4
5
4
0
-
4
5
5
4
4542
m
o
s
t
p
r
o
m
in
e
n
t
m
eth
o
d
s
[
1
8
]
.
T
h
is
is
ex
p
lain
ed
b
y
th
e
f
ac
t
th
at
th
is
ap
p
r
o
ac
h
is
co
n
s
is
ten
t
with
th
e
s
tu
d
en
t
-
ce
n
ter
ed
o
r
ien
tatio
n
o
f
th
e
n
ew
g
en
e
r
al
ed
u
ca
tio
n
p
r
o
g
r
am
.
Ov
er
all,
s
tu
d
ies
o
n
Pj
B
L
in
m
ath
em
atics
ed
u
ca
tio
n
ca
n
b
e
ca
teg
o
r
ized
i
n
to
th
r
ee
p
r
im
ar
y
g
r
o
u
p
s
.
T
h
e
f
ir
s
t g
r
o
u
p
f
o
cu
s
es o
n
th
e
ef
f
ec
tiv
en
ess
o
f
PjB
L
wh
en
ap
p
lied
to
s
p
ec
if
ic
en
v
ir
o
n
m
e
n
ts
.
Ov
er
all,
em
p
ir
ical
r
esu
lts
r
ep
o
r
ted
th
a
t
th
e
PjB
L
m
o
d
el
h
as
a
p
o
s
it
iv
e
im
p
ac
t
o
n
lear
n
i
n
g
o
u
tc
o
m
es.
Fo
r
in
s
tan
ce
,
Yu
n
ita
et
a
l.
[
6
]
f
o
u
n
d
th
at
t
h
e
ap
p
licatio
n
o
f
th
e
PjB
L
m
o
d
el
s
ig
n
if
ican
tly
im
p
r
o
v
ed
s
tu
d
en
ts
’
u
n
d
er
s
tan
d
in
g
o
f
m
ath
e
m
atica
l
co
n
ce
p
ts
,
p
r
o
b
lem
-
s
o
lv
in
g
ab
ilit
y
,
cr
ea
tiv
e
th
in
k
in
g
,
c
r
itical
th
in
k
in
g
,
an
d
m
at
h
em
atica
l
co
m
m
u
n
icatio
n
s
k
ills
.
Similar
ly
,
Asmi
et
a
l.
[
9
]
s
u
p
p
lem
en
ted
th
at
PjB
L
im
p
r
o
v
es
ac
ad
em
ic
ac
h
iev
em
en
t,
h
ig
h
er
-
o
r
d
e
r
th
in
k
in
g
s
k
ills
,
lear
n
in
g
m
o
tiv
atio
n
.
Ad
d
itio
n
all
y
,
r
esear
ch
b
y
Ub
u
z
a
n
d
A
y
d
ı
n
y
er
[
7
]
co
n
f
ir
m
ed
th
at
s
tu
d
en
ts
’
k
n
o
wled
g
e
an
d
th
eir
attitu
d
es
to
war
d
s
th
e
g
eo
m
etr
y
s
h
o
wed
d
if
f
er
e
n
t
lev
els
o
f
im
p
r
o
v
em
e
n
t
in
PjB
L
en
v
ir
o
n
m
en
ts
,
d
e
p
en
d
in
g
o
n
th
eir
co
g
n
itiv
e
s
ty
les.
T
h
e
s
ec
o
n
d
g
r
o
u
p
ex
a
m
in
ed
in
d
iv
id
u
al
f
ac
to
r
s
t
h
at
in
f
l
u
en
c
e
th
e
im
p
lem
en
tatio
n
an
d
ef
f
e
ctiv
en
ess
o
f
PjB
L
.
As
an
ex
am
p
le,
Ki
m
[
1
9
]
in
d
icate
d
t
h
at
PjB
L
o
u
tco
m
es
ar
e
s
h
ap
e
d
b
y
s
tu
d
en
ts
’
in
ter
ac
tio
n
s
ty
les
an
d
th
ei
r
lev
el
o
f
lear
n
i
n
g
m
o
t
iv
atio
n
,
wh
ile
r
esear
ch
by
Yu
n
ita
et
a
l.
[
6
]
d
ictated
t
h
at
m
at
h
em
atica
l
ab
ilit
y
is
r
elate
d
to
th
e
p
r
o
ce
s
s
o
f
PjB
L
.
I
n
an
o
th
er
s
tu
d
y
,
Vir
o
et
a
l.
[
2
]
r
e
v
ea
led
th
at
teac
h
e
r
m
o
ti
v
atio
n
is
co
n
s
id
er
e
d
v
er
y
im
p
o
r
ta
n
t
f
o
r
th
e
s
u
cc
e
s
s
o
f
PjB
L
im
p
lem
en
tatio
n
.
As
a
co
n
s
eq
u
e
n
ce
,
t
h
e
o
u
tc
o
m
es
o
f
PjB
L
ar
e
in
f
lu
en
ce
d
b
y
s
ev
er
al
co
m
p
o
n
en
ts
,
in
clu
d
in
g
h
o
w
th
e
cu
r
r
ic
u
lu
m
is
ad
ap
ted
,
th
e
lev
el
o
f
t
ea
ch
er
s
u
p
p
o
r
t
an
d
tr
ain
in
g
,
ass
ess
m
en
t p
r
ac
tices,
an
d
th
e
r
ea
d
in
ess
o
f
b
o
th
e
d
u
ca
to
r
s
an
d
lear
n
e
r
s
[
8
]
.
T
h
e
th
ir
d
g
r
o
u
p
e
x
p
lo
r
e
d
th
e
in
teg
r
atio
n
o
f
PjB
L
with
o
th
er
teac
h
in
g
m
o
d
els
an
d
m
eth
o
d
s
to
en
h
an
ce
ef
f
ec
tiv
e
n
ess
.
On
e
ap
p
r
o
ac
h
is
to
p
r
o
p
o
s
e
h
y
b
r
id
teac
h
in
g
m
o
d
els
th
at
co
m
b
in
e
PjB
L
with
co
m
p
lem
en
tar
y
ap
p
r
o
ac
h
es
to
o
p
tim
ize
lear
n
in
g
o
u
tc
o
m
es.
Fo
r
in
s
tan
ce
,
Z
h
an
g
an
d
Ma
[
2
0
]
r
ec
o
m
m
en
d
ed
in
teg
r
atin
g
PjB
L
with
STE
M
ed
u
ca
tio
n
to
f
o
s
ter
s
tu
d
e
n
ts
’
p
o
s
itiv
e
attitu
d
es
to
war
d
STE
M
f
ield
s
an
d
en
co
u
r
a
g
e
f
u
tu
r
e
ca
r
ee
r
ch
o
ic
es
in
th
ese
a
r
ea
s
.
I
n
t
h
e
s
am
e
v
ein
,
r
esear
ch
b
y
Su
r
m
ilas
ar
i
et
a
l.
[
2
1
]
s
h
o
wed
th
at
a
STE
M
-
b
ased
PjB
L
m
o
d
el
wo
u
l
d
en
h
an
ce
s
tu
d
e
n
ts
’
cr
ea
tiv
e
th
in
k
in
g
i
n
m
ath
em
atics
lear
n
in
g
.
Fu
r
th
er
m
o
r
e
,
ex
p
er
i
m
en
tal
s
tu
d
ies
ex
am
in
ed
th
e
c
o
m
b
in
at
io
n
o
f
PjB
L
with
d
ig
ital
tech
n
o
lo
g
y
t
o
im
p
r
o
v
e
s
tu
d
en
t
p
er
f
o
r
m
an
ce
,
s
u
ch
as
u
s
in
g
ed
u
ca
tio
n
al
s
o
f
twar
e
to
d
ev
elo
p
lear
n
in
g
to
o
ls
[
2
2
]
,
[
2
3
]
.
Ad
d
itio
n
ally
,
Su
p
r
iad
i
et
a
l.
[
2
4
]
h
ig
h
lig
h
t
ed
th
at
i
n
teg
r
atin
g
PjB
L
with
g
u
id
ed
d
is
co
v
er
y
lear
n
in
g
is
co
n
s
id
er
ed
as
an
ef
f
ec
tiv
e
ap
p
r
o
ac
h
t
o
s
tr
en
g
th
en
in
g
s
tu
d
en
ts
’
m
at
h
em
atica
l
ab
ilit
ies.
Alt
h
o
u
g
h
p
r
i
o
r
w
o
r
k
d
e
m
o
n
s
tr
a
te
d
th
e
b
en
e
f
its
o
f
PjB
L
,
p
e
r
s
p
e
cti
v
es
o
n
i
ts
ef
f
ec
ti
v
e
n
ess
i
n
m
at
h
e
m
a
tics
ed
u
ca
t
io
n
r
e
m
ai
n
v
a
r
ie
d
.
R
ese
ar
ch
o
n
t
h
e
i
m
p
a
ct
o
f
PjB
L
co
n
f
i
r
m
e
d
th
at
its
a
p
p
lic
ati
o
n
e
n
h
a
n
c
es
s
tu
d
e
n
ts
’
m
at
h
e
m
ati
ca
l
ab
ilit
ie
s
a
n
d
i
n
cr
ea
s
es
t
h
ei
r
en
g
ag
em
en
t
i
n
le
a
r
n
in
g
.
Me
a
n
w
h
i
le
,
s
t
u
d
ies
e
x
a
m
i
n
i
n
g
th
e
f
a
ct
o
r
s
i
n
f
l
u
e
n
ci
n
g
PjB
L
i
m
p
lem
en
tat
io
n
h
i
g
h
li
g
h
te
d
e
n
a
b
l
in
g
as
we
ll
as
li
m
it
in
g
f
ac
t
o
r
s
,
s
u
c
h
as
t
ea
ch
er
r
e
ad
in
ess
,
s
t
u
d
e
n
t
p
a
r
t
ici
p
ati
o
n
,
a
n
d
i
n
s
t
it
u
ti
o
n
al
s
u
p
p
o
r
t.
A
d
d
iti
o
n
al
ly
,
r
esea
r
ch
f
o
cu
s
ed
o
n
i
m
p
r
o
v
i
n
g
PjB
L
ex
p
l
o
r
e
d
wa
y
s
t
o
a
d
d
r
ess
it
s
li
m
it
ati
o
n
s
b
y
i
n
t
eg
r
a
ti
n
g
it
wit
h
o
th
er
t
ea
c
h
i
n
g
m
et
h
o
d
s
o
r
le
v
e
r
a
g
i
n
g
tec
h
n
o
lo
g
y
.
Ho
we
v
e
r
,
a
c
o
m
m
o
n
f
i
n
d
in
g
ac
r
o
s
s
m
o
s
t
s
t
u
d
ies
is
t
h
at
P
jB
L
r
e
q
u
ir
es
ca
r
e
f
u
l
p
r
ep
ar
ati
o
n
b
y
tea
ch
er
s
an
d
s
t
r
o
n
g
i
n
s
tit
u
t
io
n
al
s
u
p
p
o
r
t
t
o
m
a
x
im
iz
e
i
ts
e
f
f
ec
ti
v
en
ess
.
B
as
ed
o
n
p
r
e
v
i
o
u
s
s
t
u
d
ies
,
PjB
L
h
as
s
h
o
wn
g
r
ea
t
p
o
t
en
tia
l
as
a
n
in
s
t
r
u
ct
io
n
al
m
et
h
o
d
b
u
t
h
as
y
e
t
t
o
b
e
wi
d
e
ly
im
p
l
em
e
n
t
ed
in
m
at
h
e
m
at
ics
ed
u
c
ati
o
n
d
u
e
t
o
v
ar
i
o
u
s
c
h
a
ll
en
g
es
.
W
h
i
le
e
x
is
t
in
g
p
u
b
l
ica
t
io
n
s
p
r
o
v
id
ed
s
u
b
s
ta
n
t
ial
e
v
i
d
en
ce
o
f
t
h
e
b
e
n
e
f
its
o
f
PjB
L
,
t
h
e
y
als
o
h
ig
h
l
ig
h
t
e
d
d
i
f
f
ic
u
l
ties
i
n
p
r
a
cti
ca
l
a
p
p
l
icat
io
n
,
p
a
r
t
ic
u
l
ar
l
y
i
n
g
en
er
al
e
d
u
ca
ti
o
n
s
e
tti
n
g
s
.
Key
a
r
e
as r
e
q
u
ir
in
g
f
u
r
t
h
e
r
i
n
v
est
ig
ati
o
n
i
n
cl
u
d
e
cle
ar
ly
i
d
e
n
ti
f
y
i
n
g
t
h
e
f
ac
t
o
r
s
i
n
f
l
u
e
n
c
in
g
t
h
e
i
m
p
le
m
e
n
t
ati
o
n
o
f
PjB
L
i
n
m
a
th
em
ati
cs,
es
p
ec
iall
y
wit
h
i
n
t
h
e
co
n
t
ex
t o
f
Vi
et
n
a
m
es
e
e
d
u
ca
t
io
n
;
ex
am
in
in
g
th
e
i
m
p
a
ct
o
f
PjB
L
o
n
s
t
u
d
e
n
ts
’
c
o
g
n
i
ti
v
e
d
e
v
el
o
p
m
e
n
t
a
n
d
l
ea
r
n
in
g
o
u
tc
o
m
es
t
h
r
o
u
g
h
e
m
p
i
r
ic
al
s
t
u
d
ies;
a
n
d
e
x
p
lo
r
i
n
g
h
y
b
r
i
d
m
o
d
els
t
h
at
i
n
t
e
g
r
ate
PjB
L
wit
h
o
t
h
e
r
t
ea
ch
in
g
m
e
th
o
d
s
to
en
h
an
ce
its
e
f
f
ec
t
iv
en
ess
.
T
h
is
s
t
u
d
y
s
ee
k
s
t
o
en
h
a
n
ce
t
h
e
f
ie
ld
b
y
ex
am
i
n
i
n
g
t
h
e
f
ac
t
o
r
s
i
n
f
l
u
e
n
c
in
g
th
e
a
p
p
lic
ati
o
n
o
f
PjB
L
i
n
m
at
h
e
m
atics
,
w
it
h
t
h
e
g
o
al
o
f
p
r
o
v
i
d
i
n
g
p
r
a
ctic
al
r
ec
o
m
m
en
d
a
ti
o
n
s
t
o
b
o
o
s
t
its
e
f
f
ec
ti
v
e
n
ess
i
n
g
e
n
er
al
e
d
u
ca
ti
o
n
.
3.
M
E
T
H
O
D
3
.
1
.
Resea
rc
h
des
ig
n
T
h
is
r
esear
ch
ad
o
p
ts
a
q
u
an
titativ
e
m
eth
o
d
o
lo
g
y
to
in
v
esti
g
ate
an
d
an
aly
ze
th
e
f
ac
to
r
s
in
f
lu
en
cin
g
th
e
im
p
lem
en
tatio
n
o
f
PjB
L
in
m
ath
em
atics.
Sp
ec
if
ically
,
ex
p
lo
r
ato
r
y
f
ac
to
r
an
al
y
s
is
(
E
FA)
is
u
tili
ze
d
to
id
en
tify
laten
t
v
ar
ia
b
les
with
in
th
e
co
llected
d
ata.
E
FA
i
s
co
m
m
o
n
ly
a
p
p
lied
to
u
n
co
v
er
th
e
u
n
d
er
ly
i
n
g
s
tr
u
ctu
r
e
o
f
a
d
ataset,
allo
win
g
f
o
r
th
e
r
ed
u
ctio
n
o
f
o
b
s
er
v
ed
v
a
r
iab
les
in
to
a
m
o
r
e
m
an
ag
ea
b
le
s
et
wh
ile
r
etain
in
g
th
e
m
o
s
t
cr
itical
in
f
o
r
m
atio
n
[
2
5
]
.
As
a
d
im
e
n
s
io
n
ality
r
ed
u
ctio
n
tec
h
n
iq
u
e
,
E
F
A
h
elp
s
id
en
tify
k
e
y
f
ac
to
r
g
r
o
u
p
s
th
at
im
p
ac
t
th
e
o
r
g
an
izatio
n
o
f
PjB
L
.
Fo
l
lo
win
g
th
e
ex
tr
ac
tio
n
o
f
f
ac
to
r
s
th
r
o
u
g
h
E
FA,
th
e
s
tu
d
y
p
r
o
ce
e
d
s
with
co
n
f
i
r
m
ato
r
y
f
ac
t
o
r
an
aly
s
is
(
C
FA)
to
v
alid
ate
th
e
p
r
o
p
o
s
ed
m
o
d
el.
T
h
e
s
tu
d
y
u
s
ed
C
FA
to
test
th
e
co
m
p
atib
il
ity
b
etwe
en
t
h
e
co
n
ce
p
tu
al
m
o
d
el
an
d
th
e
co
llected
d
ata,
v
alid
atin
g
th
e
co
n
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ec
tio
n
s
b
etwe
en
u
n
d
er
ly
i
n
g
co
n
s
tr
u
cts
an
d
m
ea
s
u
r
a
b
le
in
d
icato
r
s
[
2
5
]
.
T
o
en
s
u
r
e
th
e
r
eliab
ilit
y
o
f
th
e
an
aly
s
is
,
th
e
co
llected
d
ata
was
r
an
d
o
m
ly
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iv
i
d
ed
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n
to
t
wo
g
r
o
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p
s
.
T
h
e
f
ir
s
t
g
r
o
u
p
was
u
s
ed
f
o
r
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FA
to
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r
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l fa
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s
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h
a
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p
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je
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g
in
ma
th
ema
t
ics ed
u
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tio
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C
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n
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a
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P
h
a
m
)
4543
ex
p
lo
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e
a
n
d
i
d
en
tify
k
ey
f
ac
to
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s
with
in
th
e
r
esear
ch
m
o
d
el,
wh
ile
th
e
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ec
o
n
d
g
r
o
u
p
was
e
m
p
lo
y
ed
f
o
r
C
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to
v
alid
ate
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d
co
n
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ir
m
th
e
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tr
u
ct
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r
e
o
f
th
e
m
ea
s
u
r
em
en
t
m
o
d
el
,
en
s
u
r
in
g
its
r
eliab
ilit
y
an
d
v
a
lid
ity
.
T
h
e
ch
o
s
en
m
eth
o
d
o
l
o
g
y
in
c
r
ea
s
es
th
e
s
tu
d
y
’
s
r
ig
o
r
an
d
tr
u
s
two
r
th
i
n
ess
,
s
u
p
p
o
r
tin
g
a
d
ee
p
er
u
n
d
er
s
tan
d
in
g
o
f
th
e
elem
en
ts
in
f
lu
en
cin
g
PjB
L
in
m
ath
em
atics e
d
u
ca
tio
n
.
3
.
2
.
Sa
m
ple a
nd
da
t
a
co
llect
io
n
T
h
is
s
tu
d
y
f
o
cu
s
ed
o
n
s
ec
o
n
d
ar
y
an
d
h
i
g
h
s
ch
o
o
l
m
ath
e
m
atics
teac
h
er
s
to
ex
am
in
e
t
h
e
f
ac
to
r
s
in
f
lu
en
cin
g
th
e
im
p
lem
en
tatio
n
o
f
PjB
L
.
T
h
e
r
esear
ch
p
ar
ticip
an
ts
in
clu
d
ed
m
ath
em
atics
teac
h
er
s
f
r
o
m
th
e
No
r
th
er
n
,
C
en
tr
al,
an
d
So
u
th
er
n
r
eg
io
n
s
o
f
Vietn
am
.
T
o
en
s
u
r
e
r
ep
r
esen
tativ
en
ess
an
d
alig
n
m
en
t
with
th
e
r
esear
ch
o
b
jectiv
es,
th
e
s
tu
d
y
em
p
l
o
y
ed
a
p
u
r
p
o
s
iv
e
s
am
p
lin
g
m
eth
o
d
,
f
ac
ilit
atin
g
th
e
r
ec
r
u
itm
en
t
o
f
in
d
iv
id
u
als
wh
o
m
et
th
e
p
r
ed
eter
m
in
ed
r
esear
ch
c
r
iter
ia.
T
o
f
ac
ilit
ate
p
ar
ticip
atio
n
a
n
d
e
n
s
u
r
e
ac
ce
s
s
ib
ilit
y
,
d
ata
wer
e
g
ath
er
ed
u
s
in
g
a
Go
o
g
le
Fo
r
m
s
-
b
ased
o
n
lin
e
s
u
r
v
ey
.
B
ef
o
r
e
th
e
s
u
r
v
ey
was
ad
m
in
is
ter
ed
,
p
ar
ticip
an
ts
wer
e
th
o
r
o
u
g
h
ly
i
n
f
o
r
m
e
d
a
b
o
u
t
th
e
s
tu
d
y
’
s
o
b
j
ec
tiv
es,
th
e
ty
p
e
o
f
d
ata
to
b
e
co
llected
,
h
o
w
th
e
d
ata
wo
u
ld
b
e
s
to
r
ed
an
d
u
s
ed
,
an
d
th
eir
r
ig
h
t
to
p
a
r
ticip
ate
v
o
lu
n
tar
ily
o
r
with
d
r
aw
at
an
y
p
o
in
t.
T
h
e
s
u
r
v
e
y
to
o
k
p
lace
o
v
er
a
3
-
m
o
n
th
p
er
io
d
,
f
r
o
m
J
an
u
ar
y
to
Ma
r
c
h
2
0
2
5
.
T
h
e
s
u
r
v
e
y
c
o
n
s
is
ted
o
f
two
m
ain
p
ar
ts
.
T
h
e
f
ir
s
t
s
ec
tio
n
co
llected
b
ac
k
g
r
o
u
n
d
in
f
o
r
m
a
tio
n
ab
o
u
t
p
ar
ticip
an
ts
,
in
clu
d
i
n
g
t
h
eir
p
r
o
f
ess
io
n
al
q
u
alif
icatio
n
s
,
te
ac
h
in
g
e
x
p
er
ien
ce
,
an
d
wo
r
k
en
v
ir
o
n
m
en
t.
T
h
e
s
ec
o
n
d
s
ec
tio
n
co
n
s
is
ted
o
f
2
5
q
u
esti
o
n
s
d
esig
n
ed
t
o
ass
ess
teac
h
er
s
’
p
er
ce
p
tio
n
s
o
f
th
eir
r
ea
d
i
n
ess
to
im
p
lem
en
t
PjB
L
in
m
ath
em
atics.
A
5
-
p
o
in
t
L
ik
er
t
s
ca
le
was
u
s
ed
to
d
esig
n
th
e
q
u
est
io
n
s
,
with
r
esp
o
n
s
e
o
p
tio
n
s
r
an
g
in
g
f
r
o
m
1
(
co
m
p
letely
d
is
ag
r
ee
)
to
5
(
co
m
p
le
tely
ag
r
ee
)
.
Dr
awin
g
o
n
p
r
ev
io
u
s
s
tu
d
ies
o
n
in
f
lu
en
cin
g
f
ac
t
o
r
s
id
e
n
tifie
d
b
y
r
esear
ch
er
s
wo
r
ld
wid
e,
th
i
s
s
tu
d
y
p
r
o
p
o
s
ed
f
iv
e
k
ey
f
ac
t
o
r
s
,
r
e
p
r
esen
ted
b
y
2
5
s
tatem
en
ts
:
teac
h
er
s
’
p
r
o
je
ct
-
b
ased
teac
h
in
g
s
k
ills
,
teac
h
er
s
’
attitu
d
es,
s
tu
d
en
ts
’
ch
ar
ac
ter
is
tics
,
ed
u
ca
tio
n
p
o
licies,
an
d
f
ac
ilit
ies.
T
h
e
s
elec
tio
n
o
f
th
ese
f
ac
to
r
s
aim
ed
to
en
s
u
r
e
a
co
m
p
r
eh
e
n
s
iv
e
in
s
ig
h
t
in
to
th
e
cir
cu
m
s
tan
ce
s
im
p
ac
tin
g
th
e
s
u
cc
ess
o
f
PjB
L
in
m
ath
em
atic
s
ed
u
ca
tio
n
.
T
ab
le
1
o
u
tlin
es th
e
s
u
r
v
ey
item
s
an
d
th
eir
ass
o
ciate
d
s
o
u
r
ce
s
ca
teg
o
r
ized
b
y
co
n
s
tr
u
ct
g
r
o
u
p
.
T
ab
le
1
.
Su
r
v
e
y
q
u
esti
o
n
n
air
e
F
a
c
t
o
r
Q
u
e
st
i
o
n
n
a
i
r
e
R
e
f
e
r
e
n
c
e
s
T
e
a
c
h
e
r
s
’
P
j
B
L
sk
i
l
l
s
Q
1
.
I
u
n
d
e
r
st
a
n
d
h
o
w
t
o
i
n
t
e
g
r
a
t
e
m
a
t
h
e
m
a
t
i
c
s
c
o
n
t
e
n
t
i
n
t
o
p
r
a
c
t
i
c
a
l
a
n
d
i
n
t
e
r
d
i
s
c
i
p
l
i
n
a
r
y
p
r
o
j
e
c
t
s.
Q
2
.
I
r
e
c
o
g
n
i
z
e
t
h
e
p
r
o
c
e
ss
o
f
P
j
B
L
,
i
n
c
l
u
d
i
n
g
p
l
a
n
n
i
n
g
,
i
m
p
l
e
me
n
t
a
t
i
o
n
,
a
n
d
e
v
a
l
u
a
t
i
o
n
.
Q
3
.
I
r
e
c
o
g
n
i
z
e
t
h
a
t
P
j
B
L
i
s
m
o
r
e
e
f
f
e
c
t
i
v
e
t
h
a
n
t
r
a
d
i
t
i
o
n
a
l
me
t
h
o
d
s.
Q
4
.
I
c
a
n
a
p
p
r
o
a
c
h
P
j
B
L
i
n
a
v
a
r
i
e
t
y
o
f
w
a
y
s.
Q
5
.
I
a
m
a
b
l
e
t
o
p
l
a
n
,
o
r
g
a
n
i
z
e
,
a
n
d
c
o
o
r
d
i
n
a
t
e
st
u
d
e
n
t
g
r
o
u
p
s.
Q
6
.
I
a
m
a
b
l
e
t
o
d
e
s
i
g
n
c
r
i
t
e
r
i
a
,
t
o
o
l
s
,
a
n
d
a
ssess
me
n
t
s
f
o
r
t
h
e
p
r
o
c
e
ss
a
n
d
p
r
o
d
u
c
t
s
o
f
P
j
B
L
.
[
1
]
–
[
3
]
,
[
1
0
]
T
e
a
c
h
e
r
’
s
a
t
t
i
t
u
d
e
Q
7
.
I
b
e
l
i
e
v
e
t
h
a
t
P
j
B
L
i
s
a
n
e
f
f
e
c
t
i
v
e
met
h
o
d
f
o
r
e
n
h
a
n
c
i
n
g
st
u
d
e
n
t
l
e
a
r
n
i
n
g
o
u
t
c
o
mes
.
Q
8
.
I
a
m
e
n
t
h
u
s
i
a
s
t
i
c
a
b
o
u
t
i
mp
l
e
m
e
n
t
i
n
g
ma
t
h
e
ma
t
i
c
a
l
p
r
o
j
e
c
t
s
i
n
t
h
e
c
l
a
ss
r
o
o
m
.
Q
9
.
I
f
e
e
l
p
r
e
p
a
r
e
d
t
o
a
p
p
l
y
P
j
B
L
.
Q
1
0
.
I
b
e
l
i
e
v
e
t
h
a
t
i
m
p
l
e
m
e
n
t
i
n
g
P
j
B
L
h
e
l
p
s
st
u
d
e
n
t
s
d
e
v
e
l
o
p
e
ss
e
n
t
i
a
l
2
1
st
-
c
e
n
t
u
r
y
sk
i
l
l
s
s
u
c
h
a
s
c
r
i
t
i
c
a
l
t
h
i
n
k
i
n
g
,
c
o
mm
u
n
i
c
a
t
i
o
n
,
a
n
d
c
o
l
l
a
b
o
r
a
t
i
o
n
.
Q
1
1
.
I
a
m
c
o
n
f
i
d
e
n
t
i
n
d
e
s
i
g
n
i
n
g
a
n
d
o
r
g
a
n
i
z
i
n
g
P
j
B
L
a
c
t
i
v
i
t
i
e
s.
[
2
]
,
[
1
0
]
,
[
2
6
]
,
[
2
7
]
S
t
u
d
e
n
t
s
’
c
h
a
r
a
c
t
e
r
i
s
t
i
c
s
Q
1
2
.
S
t
u
d
e
n
t
s
w
i
t
h
a
s
t
r
o
n
g
u
n
d
e
r
st
a
n
d
i
n
g
o
f
ma
t
h
e
m
a
t
i
c
a
l
c
o
n
c
e
p
t
s
p
e
r
f
o
r
m
w
e
l
l
i
n
m
a
t
h
e
mat
i
c
a
l
p
r
o
j
e
c
t
s.
Q
1
3
.
S
t
u
d
e
n
t
s
w
i
t
h
g
o
o
d
c
o
mm
u
n
i
c
a
t
i
o
n
a
n
d
c
o
l
l
a
b
o
r
a
t
i
o
n
s
k
i
l
l
s
e
x
c
e
l
i
n
m
a
t
h
e
m
a
t
i
c
a
l
p
r
o
j
e
c
t
s.
Q
1
4
.
S
t
u
d
e
n
t
s
a
r
e
c
o
n
f
i
d
e
n
t
a
n
d
w
i
l
l
i
n
g
t
o
w
o
r
k
i
n
g
r
o
u
p
s
w
h
e
n
e
n
g
a
g
i
n
g
i
n
m
a
t
h
e
m
a
t
i
c
a
l
p
r
o
j
e
c
t
s.
Q
1
5
.
M
o
s
t
s
t
u
d
e
n
t
s rem
a
i
n
f
o
c
u
se
d
w
h
i
l
e
w
o
r
k
i
n
g
o
n
m
a
t
h
e
m
a
t
i
c
a
l
p
r
o
j
e
c
t
s.
Q
1
6
.
S
t
u
d
e
n
t
s
a
r
e
e
n
t
h
u
si
a
s
t
i
c
a
n
d
p
r
o
a
c
t
i
v
e
i
n
p
a
r
t
i
c
i
p
a
t
i
n
g
i
n
ma
t
h
e
ma
t
i
c
a
l
p
r
o
j
e
c
t
s
t
o
e
n
h
a
n
c
e
t
h
e
i
r
a
c
a
d
e
mi
c
p
e
r
f
o
r
ma
n
c
e
.
[
1
]
,
[
3
]
,
[
1
0
]
,
[
2
0
]
Ed
u
c
a
t
i
o
n
p
o
l
i
c
y
Q
1
7
.
I
r
e
c
e
i
v
e
p
o
l
i
c
i
e
s
a
n
d
g
u
i
d
e
l
i
n
e
s
f
r
o
m
t
h
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s
c
h
o
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l
a
n
d
g
o
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e
r
n
me
n
t
t
h
a
t
e
f
f
e
c
t
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l
y
su
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t
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h
e
i
mp
l
e
m
e
n
t
a
t
i
o
n
o
f
P
j
B
L
.
Q
1
8
.
P
o
l
i
c
i
e
s a
n
d
g
u
i
d
e
l
i
n
e
s
o
n
P
j
B
L
a
r
e
c
l
e
a
r
,
e
a
sy
t
o
u
n
d
e
r
st
a
n
d
,
a
n
d
s
t
r
a
i
g
h
t
f
o
r
w
a
r
d
t
o
i
m
p
l
e
me
n
t
.
Q
1
9
.
S
a
l
a
r
y
,
b
o
n
u
s
e
s,
a
n
d
mat
e
r
i
a
l
i
n
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e
n
t
i
v
e
s i
n
f
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h
e
i
mp
l
e
m
e
n
t
a
t
i
o
n
o
f
P
j
B
L
.
Q
2
0
.
R
e
g
u
l
a
r
semi
n
a
r
s
a
n
d
t
r
a
i
n
i
n
g
sessi
o
n
s
h
e
l
p
t
e
a
c
h
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r
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u
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d
a
t
e
a
n
d
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n
h
a
n
c
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t
h
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i
r
s
k
i
l
l
s
i
n
i
mp
l
e
m
e
n
t
i
n
g
P
j
B
L
.
[
1
]
–
[
3
]
,
[
2
6
]
,
[
2
7
]
F
a
c
i
l
i
t
i
e
s
Q
2
1
.
I
a
m
p
r
o
v
i
d
e
d
w
i
t
h
s
u
f
f
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t
e
q
u
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p
me
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t
,
t
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s
,
a
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d
a
p
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s f
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c
t
-
b
a
s
e
d
t
e
a
c
h
i
n
g
.
Q
2
2
.
T
h
e
e
q
u
i
p
me
n
t
,
t
o
o
l
s
,
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n
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t
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o
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s a
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e
i
n
g
o
o
d
w
o
r
k
i
n
g
c
o
n
d
i
t
i
o
n
.
Q
2
3
.
I
c
a
n
r
e
c
e
i
v
e
a
ssi
s
t
a
n
c
e
f
r
o
m
t
h
e
s
e
r
v
i
c
e
p
r
o
v
i
d
e
r
i
f
I
e
n
c
o
u
n
t
e
r
i
ss
u
e
s
w
i
t
h
t
h
e
e
q
u
i
p
me
n
t
,
t
o
o
l
s
,
o
r
a
p
p
l
i
c
a
t
i
o
n
s.
Q
2
4
.
Th
e
l
e
a
r
n
i
n
g
s
p
a
c
e
i
s
w
e
l
l
-
d
e
si
g
n
e
d
t
o
s
u
p
p
o
r
t
g
r
o
u
p
w
o
r
k
a
n
d
t
h
e
i
m
p
l
e
me
n
t
a
t
i
o
n
o
f
mat
h
e
m
a
t
i
c
a
l
p
r
o
j
e
c
t
s
.
Q
2
5
.
L
e
a
r
n
i
n
g
ma
t
e
r
i
a
l
s
a
r
e
r
e
g
u
l
a
r
l
y
u
p
d
a
t
e
d
t
o
r
e
f
l
e
c
t
i
n
n
o
v
a
t
i
o
n
s
i
n
t
e
a
c
h
i
n
g
me
t
h
o
d
s
a
n
d
t
e
c
h
n
o
l
o
g
y
.
[
1
]
,
[
3
]
T
o
v
er
if
y
th
at
th
e
s
u
r
v
ey
to
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l
was
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o
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r
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k
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with
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co
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p
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r
esp
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r
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s
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g
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e
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twis
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eth
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ain
tai
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I
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2
2
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u
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ates
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with
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u
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I
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J
E
v
al
&
R
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d
u
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I
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N:
2252
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8
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2
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C
r
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2
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d
Q
2
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e
r
em
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ed
d
u
e
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ig
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s
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s
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r
e
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2
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ain
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g
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ar
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s
ed
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d
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tili
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d
2
4
4
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er
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with
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1
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ield
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g
a
n
o
b
s
er
v
a
tio
n
-
to
-
v
a
r
iab
le
r
atio
o
f
1
1
.
6
:
1
.
Acc
o
r
d
in
g
t
o
Hair
et
a
l.
[
2
5
]
,
a
r
atio
o
f
5
:1
is
co
n
s
id
er
ed
ac
ce
p
ta
b
le,
1
0
:
1
is
av
er
ag
e,
a
n
d
2
0
:1
is
ex
ce
llen
t.
Ad
d
itio
n
ally
,
B
u
jan
g
et
a
l.
[
2
8
]
s
u
g
g
ests
th
at
s
am
p
le
s
izes c
an
b
e
d
eter
m
in
ed
b
ased
o
n
s
p
ec
if
ic
th
r
esh
o
ld
s
s
u
ch
as 5
0
,
1
0
0
,
5
0
0
,
o
r
o
v
er
1
0
0
0
o
b
s
er
v
atio
n
s
,
d
ep
en
d
i
n
g
o
n
th
e
r
esear
ch
r
e
q
u
ir
em
en
ts
.
I
n
th
is
s
tu
d
y
,
th
e
1
1
.
6
:1
r
ati
o
ex
ce
ed
s
th
e
1
0
:
1
b
en
ch
m
ar
k
,
en
s
u
r
i
n
g
th
at
th
e
s
am
p
le
s
ize
m
ee
ts
th
e
s
tan
d
ar
d
r
eq
u
ir
em
en
ts
f
o
r
E
F
A
f
ac
to
r
an
aly
s
is
.
T
h
e
E
FA
m
eth
o
d
ass
u
m
es
a
co
r
r
elatio
n
b
etwe
en
o
b
s
er
v
e
d
v
ar
iab
les;
th
er
ef
o
r
e,
it
is
ess
en
tial
to
ass
es
s
th
e
d
eg
r
ee
o
f
c
o
r
r
elatio
n
b
ef
o
r
e
co
n
d
u
ctin
g
t
h
e
an
aly
s
is
.
I
n
th
is
s
tu
d
y
,
two
im
p
o
r
tan
t
s
tatis
tica
l
in
d
ices
wer
e
ap
p
lied
to
ex
am
in
e
t
h
e
ap
p
r
o
p
r
iaten
ess
o
f
th
e
d
at
a
f
o
r
E
FA.
On
e
o
f
th
e
p
r
i
m
ar
y
in
d
ices
is
th
e
Kaiser
-
Me
y
er
-
Olk
in
(
KM
O)
co
ef
f
icien
t,
wh
ich
m
ea
s
u
r
es
th
e
ad
eq
u
ac
y
o
f
th
e
s
am
p
le
f
o
r
f
ac
to
r
an
aly
s
is
.
A
KM
O
v
alu
e
clo
s
e
to
1
.
0
in
d
icate
s
h
ig
h
s
u
itab
ilit
y
,
wh
er
ea
s
a
v
alu
e
b
elo
w
0
.
5
s
u
g
g
ests
th
at
th
e
d
ata
d
o
es
n
o
t
m
ee
t
th
e
n
ec
ess
ar
y
co
n
d
it
io
n
s
f
o
r
E
F
A
[
2
5
]
,
[
2
9
]
.
T
h
e
s
ec
o
n
d
in
d
ex
u
s
ed
is
B
ar
tlett
’
s
test
o
f
s
p
h
er
icity
,
wh
ich
ass
ess
e
s
wh
eth
er
th
er
e
is
a
s
ig
n
if
ican
t
co
r
r
elatio
n
b
et
wee
n
o
b
s
er
v
ed
v
ar
iab
les.
T
h
is
test
ex
am
in
es
th
e
h
y
p
o
th
esis
th
at
th
e
c
o
r
r
elatio
n
m
atr
ix
is
an
id
en
tity
m
atr
ix
(
i
.
e.
,
th
e
r
e
ar
e
n
o
s
ig
n
if
ica
n
t
r
el
atio
n
s
h
ip
s
b
etwe
en
v
ar
iab
les).
I
f
th
e
p
-
v
alu
e
(
s
ig
.
)
<0
.
0
5
.
T
h
e
test
r
esu
lts
d
em
o
n
s
tr
ate
th
at
th
e
co
r
r
elatio
n
s
am
o
n
g
v
ar
iab
les
m
ee
t
th
e
r
eq
u
ir
e
d
th
r
esh
o
ld
,
th
u
s
ju
s
tify
in
g
th
e
u
s
e
o
f
E
FA o
n
th
e
d
ataset
[
2
5
]
.
T
h
e
o
b
tain
ed
d
ata
wer
e
p
r
o
ce
s
s
ed
u
s
in
g
I
B
M
SP
SS
v
er
s
io
n
2
5
.
0
.
I
n
th
e
f
ac
to
r
an
a
ly
s
is
,
th
e
p
r
in
cip
al
co
m
p
o
n
e
n
t
an
aly
s
is
(
PC
A)
m
eth
o
d
was
em
p
lo
y
e
d
to
ex
tr
ac
t
f
ac
to
r
s
,
co
m
b
in
e
d
with
th
e
V
ar
im
ax
r
o
tatio
n
tech
n
iq
u
e
to
o
p
tim
ize
th
e
f
ac
to
r
s
tr
u
ctu
r
e
an
d
en
h
a
n
ce
in
ter
p
r
etab
ilit
y
.
I
n
th
is
s
tu
d
y
,
th
e
au
th
o
r
s
d
id
n
o
t
p
r
e
d
ef
in
e
a
f
ix
ed
n
u
m
b
er
o
f
f
ac
to
r
s
to
b
e
r
etain
e
d
.
Ho
wev
er
,
with
2
1
o
b
s
er
v
ed
v
ar
i
ab
les,
en
s
u
r
in
g
th
at
ea
ch
f
ac
to
r
in
clu
d
es
at
least
2
r
ep
r
esen
tativ
e
v
ar
iab
les
(
p
r
ef
er
ab
ly
3
v
a
r
iab
les)
was
a
k
ey
cr
iter
io
n
in
th
e
f
ac
to
r
an
aly
s
is
.
B
ased
o
n
th
e
r
ec
o
m
m
en
d
atio
n
s
o
f
Hair
et
a
l.
[
2
5
]
,
th
e
ex
p
ec
te
d
n
u
m
b
er
o
f
f
ac
to
r
s
was
esti
m
ated
to
b
e
b
etwe
en
4
an
d
6
.
T
o
d
eter
m
i
n
e
th
e
o
p
tim
al
n
u
m
b
er
o
f
f
ac
to
r
s
,
t
h
e
s
tu
d
y
a
p
p
lie
d
co
m
m
o
n
s
tatis
tical
cr
iter
ia,
in
clu
d
in
g
th
e
Kaiser
cr
iter
io
n
(
r
etai
n
in
g
o
n
ly
f
ac
to
r
s
with
eig
e
n
v
alu
e
s
g
r
ea
ter
t
h
an
1
)
,
th
e
s
cr
ee
p
l
o
t
(
id
en
tif
y
in
g
th
e
n
u
m
b
er
o
f
f
ac
to
r
s
b
ased
o
n
th
e
b
r
ea
k
p
o
in
t
o
f
th
e
ei
g
en
v
alu
e
cu
r
v
e)
,
an
d
th
e
e
x
p
lai
n
ed
v
a
r
ian
ce
r
atio
(
co
n
f
ir
m
i
n
g
th
at
th
e
ch
o
s
en
f
ac
to
r
s
ex
p
lai
n
m
o
s
t
o
f
th
e
v
ar
ian
ce
with
in
th
e
d
ataset
)
.
T
h
ese
cr
iter
ia
h
elp
en
s
u
r
e
th
at
th
e
ex
tr
ac
ted
f
ac
to
r
s
ar
e
s
tati
s
tically
s
ig
n
if
ican
t a
n
d
ac
cu
r
ately
r
ep
r
esen
t th
e
laten
t stru
ctu
r
e
o
f
th
e
d
ataset.
Af
ter
co
m
p
letin
g
E
F
A,
C
FA
wa
s
s
u
b
s
eq
u
en
tly
p
er
f
o
r
m
e
d
to
test
th
e
r
eliab
ilit
y
an
d
v
alid
ity
o
f
th
e
f
ac
to
r
s
id
en
tifie
d
th
r
o
u
g
h
E
F
A.
T
h
e
r
eliab
ilit
y
o
f
th
e
m
ea
s
u
r
em
en
t
m
o
d
el
was
ev
alu
ated
u
s
in
g
co
m
p
o
s
ite
r
eliab
ilit
y
(
C
R
)
an
d
av
e
r
ag
e
v
ar
ian
ce
ex
t
r
ac
ted
(
AVE
)
.
I
n
ac
co
r
d
a
n
ce
with
estab
lis
h
ed
cr
iter
ia,
C
R
v
alu
es
ex
ce
ed
in
g
0
.
7
a
n
d
AVE
v
al
u
e
s
ab
o
v
e
0
.
5
in
d
icate
s
atis
f
ac
to
r
y
co
n
v
er
g
e
n
t v
alid
ity
.
Du
r
i
n
g
th
e
m
o
d
e
l
e
v
a
lu
ati
o
n
p
r
o
ce
s
s
,
t
h
e
s
t
u
d
y
a
p
p
li
ed
m
u
lti
p
le
g
o
o
d
n
ess
-
of
-
f
it
m
e
as
u
r
e
s
t
o
ass
ess
th
e
c
o
m
p
a
ti
b
ili
ty
b
etwe
e
n
t
h
e
m
ea
s
u
r
e
m
e
n
t
m
o
d
el
a
n
d
t
h
e
e
x
p
e
r
im
e
n
ta
l
d
ata
.
K
ey
m
e
asu
r
es
in
cl
u
d
e
d
t
h
e
ch
i
-
s
q
u
a
r
e
d
i
n
d
e
x
d
iv
id
ed
b
y
t
h
e
d
eg
r
e
es
o
f
f
r
ee
d
o
m
(
C
M
I
N/DF
)
,
wh
ic
h
ass
ess
es
h
o
w
we
ll
t
h
e
m
o
d
el
f
its
t
h
e
d
a
ta
as
a
w
h
o
l
e
.
A
d
d
iti
o
n
al
ly
,
t
h
e
s
tu
d
y
u
ti
liz
e
d
th
e
g
o
o
d
n
ess
-
of
-
f
it
i
n
d
ex
(
GF
I
)
an
d
t
h
e
a
d
j
u
s
ted
g
o
o
d
n
ess
-
of
-
f
it
in
d
e
x
(
A
GFI
)
t
o
m
ea
s
u
r
e
t
h
e
d
eg
r
e
e
o
f
f
it
b
et
wee
n
t
h
e
p
r
o
p
o
s
ed
m
o
d
el
a
n
d
th
e
o
b
s
e
r
v
e
d
d
a
ta.
T
h
e
n
o
r
m
e
d
f
i
t
in
d
e
x
(
NF
I
)
a
n
d
c
o
m
p
ar
ati
v
e
f
it
i
n
d
e
x
(
C
FI
)
w
er
e
u
ti
liz
ed
t
o
ev
al
u
a
te
i
m
p
r
o
v
e
m
e
n
ts
i
n
m
o
d
el
f
it
r
el
ati
v
e
t
o
a
b
as
eli
n
e
m
o
d
el
.
A
d
d
i
ti
o
n
all
y
,
th
e
r
o
o
t
m
ea
n
s
q
u
a
r
e
e
r
r
o
r
o
f
a
p
p
r
o
x
i
m
at
io
n
(
R
MS
E
A
)
an
d
PC
L
OSE
we
r
e
ca
l
cu
lat
ed
t
o
ass
ess
t
h
e
m
o
d
e
l
’
s
f
i
t
to
t
h
e
d
at
a,
o
f
f
e
r
i
n
g
f
u
r
t
h
e
r
ev
id
e
n
ce
i
n
s
u
p
p
o
r
t
o
f
t
h
e
m
o
d
el
’
s
v
ali
d
it
y
.
T
h
e
cr
iter
ia
f
o
r
e
v
alu
atin
g
th
e
m
o
d
el
’
s
f
it
to
th
e
d
ata
wer
e
d
eter
m
in
e
d
b
ased
o
n
s
ev
er
al
s
tatis
tica
l
in
d
ices.
C
MI
N/DF
is
co
n
s
id
er
ed
a
g
o
o
d
f
it
if
≤
3
an
d
ac
ce
p
t
ab
le
if
≤
5
.
GFI
,
AGFI
,
NFI
,
a
n
d
C
FI
in
d
icate
a
g
o
o
d
f
it
wh
en
≥
0
.
9
,
wh
ile
v
a
lu
es
≥
0
.
9
5
a
r
e
co
n
s
id
er
ed
ex
ce
llen
t
f
it
[
3
0
]
.
R
MSE
A
v
alu
es
ar
e
in
ter
p
r
eted
:
<0
.
0
1
r
ep
r
esen
ts
ex
ce
llen
t
f
it,
<0
.
0
5
in
d
icate
s
g
o
o
d
f
it,
an
d
<0
.
0
8
s
u
g
g
ests
f
air
f
it.
Fin
ally
,
th
e
PC
L
OSE
in
d
ex
is
co
n
s
id
er
ed
ex
ce
llen
t
if
≥
0
.
0
5
,
wh
ile
≥
0
.
0
1
r
e
f
lects
an
ac
ce
p
tab
le
f
it
[
2
5
]
.
C
FA
was
im
p
lem
en
ted
in
th
is
r
esear
ch
with
th
e
u
s
e
o
f
I
B
M
Am
o
s
v
e
r
s
io
n
2
0
.
0
,
w
h
ich
en
a
b
les
p
r
ec
is
e
an
d
r
eli
ab
le
test
in
g
o
f
t
h
e
m
ea
s
u
r
em
en
t m
o
d
el
s
tr
u
ctu
r
e.
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
.
14
,
No
.
6
,
Dec
em
b
er
20
25
:
4
5
4
0
-
4
5
5
4
4546
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
4
.
1
.
Resul
t
s
4
.
1
.
1
.
Descript
iv
e
s
t
a
t
is
t
ic
Af
ter
f
ilter
in
g
o
u
t
n
o
is
y
d
ata
,
E
FA
was
co
n
d
u
cted
o
n
2
1
q
u
esti
o
n
s
u
s
in
g
th
e
Var
im
a
x
r
o
tatio
n
m
eth
o
d
.
T
h
e
an
aly
s
is
r
esu
lts
f
r
o
m
SP
SS
s
o
f
twar
e
p
r
o
v
id
ed
t
h
e
ch
ar
ac
ter
is
tic
v
alu
es f
o
r
ea
ch
f
ac
to
r
.
Ho
wev
e
r
,
d
u
r
in
g
d
ata
p
r
o
ce
s
s
in
g
,
t
h
e
o
b
s
er
v
ed
v
ar
ia
b
les
Q1
8
,
Q
1
9
,
Q
2
0
,
a
n
d
Q2
5
ex
h
ib
ited
c
r
o
s
s
-
lo
ad
in
g
co
ef
f
icien
ts
≥
0
.
3
ac
r
o
s
s
m
u
ltip
le
f
ac
to
r
s
.
C
o
n
s
eq
u
en
tly
,
t
h
e
r
esear
ch
te
am
d
ec
id
e
d
t
o
r
e
m
o
v
e
th
ese
f
o
u
r
v
ar
ia
b
les
an
d
r
ea
n
aly
ze
th
e
ad
ju
s
ted
d
ataset.
T
h
e
m
ea
n
an
d
s
tan
d
ar
d
d
e
v
i
atio
n
,
alo
n
g
with
o
t
h
er
d
escr
ip
tiv
e
s
tatis
tics
,
ar
e
d
is
p
lay
ed
in
T
ab
le
2
.
T
h
e
d
escr
ip
tiv
e
s
tatis
tics
tab
le
in
d
icate
th
at
th
e
m
ea
n
v
alu
es
o
f
th
e
o
b
s
er
v
ed
v
ar
iab
les
r
an
g
e
f
r
o
m
3
.
0
3
to
3
.
8
4
,
s
u
g
g
esti
n
g
a
r
elativ
ely
h
ig
h
lev
e
l
o
f
ag
r
ee
m
en
t
am
o
n
g
p
ar
ticip
an
ts
r
eg
ar
d
in
g
th
e
s
u
r
v
ey
q
u
esti
o
n
s
.
T
h
e
s
tan
d
ar
d
d
ev
iatio
n
r
an
g
es
f
r
o
m
0
.
5
7
to
0
.
8
5
,
r
e
f
lectin
g
a
m
o
d
er
ate
l
ev
el
o
f
d
is
p
er
s
io
n
,
with
n
o
v
ar
iab
le
d
is
p
lay
in
g
e
x
ce
s
s
iv
e
v
ar
iab
ilit
y
.
Ad
d
itio
n
ally
,
s
k
ewn
ess
an
d
k
u
r
to
s
is
v
alu
es
ar
e
clo
s
e
to
0
,
in
d
icatin
g
th
at
th
e
d
ata
d
is
tr
ib
u
tio
n
is
n
eith
er
h
i
g
h
ly
s
k
ew
ed
n
o
r
e
x
ce
s
s
iv
ely
p
ea
k
ed
.
T
h
is
s
u
g
g
ests
th
at
th
e
d
ataset
clo
s
ely
ap
p
r
o
x
im
ates
a
n
o
r
m
al
d
is
tr
ib
u
tio
n
,
m
ak
in
g
it
s
u
itab
le
f
o
r
f
u
r
th
er
s
tatis
tic
al
an
aly
s
es
s
u
ch
as
E
FA a
n
d
C
FA.
T
h
e
r
esu
lts
o
f
th
e
KM
O
an
d
B
ar
tlett’s
te
s
ts
in
th
is
s
tu
d
y
co
n
f
ir
m
e
d
th
e
s
u
itab
ilit
y
o
f
th
e
d
ataset
f
o
r
f
ac
to
r
an
aly
s
is
.
T
h
e
KM
O
in
d
ex
r
ea
ch
ed
an
ac
ce
p
tab
le
lev
e
l
(
0
.
7
2
4
)
,
as
s
ee
n
in
T
ab
le
3
,
d
em
o
n
s
tr
atin
g
th
at
th
e
s
am
p
le
s
ize
was
s
u
itab
le
f
o
r
E
FA.
Mo
r
eo
v
er
,
B
ar
tlett’s
test
o
f
s
p
h
er
icity
y
ield
ed
a
s
tatis
tically
s
ig
n
if
ican
t
r
esu
lt,
co
n
f
ir
m
i
n
g
th
e
a
p
p
r
o
p
r
iaten
ess
o
f
th
e
d
ata
f
o
r
f
a
cto
r
an
aly
s
is
.
with
χ²(
2
1
0
)
=
1
8
7
7
.
5
2
2
,
ρ
<0
.
0
0
0
,
d
em
o
n
s
tr
atin
g
t
h
at
th
e
o
b
s
er
v
ed
v
ar
iab
les
h
a
d
a
s
u
f
f
icien
tl
y
s
tr
o
n
g
c
o
r
r
elatio
n
to
ju
s
tify
th
e
ap
p
licatio
n
o
f
f
ac
to
r
an
aly
s
is
.
T
ab
le
2
.
Me
an
,
s
tan
d
ar
d
d
ev
ia
tio
n
,
s
k
ewn
ess
,
an
d
k
u
r
to
s
is
o
f
o
b
s
er
v
ed
v
ar
iab
les
V
a
r
i
a
b
l
e
M
e
a
n
S
t
d
.
D
e
v
i
a
t
i
o
n
S
k
e
w
n
e
ss
K
u
r
t
o
si
s
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3
.
7
2
9
5
0
.
7
5
3
9
9
-
0
.
0
8
8
0
.
2
5
5
Q2
3
.
3
8
1
1
0
.
7
4
1
3
5
-
0
.
0
1
2
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0
.
0
0
3
Q3
3
.
5
5
7
4
0
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8
1
1
9
4
-
0
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2
3
3
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0
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1
9
4
Q4
3
.
2
7
8
7
0
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5
7
0
3
6
0
.
1
9
3
-
0
.
0
8
5
Q5
3
.
5
5
7
4
0
.
6
8
5
5
3
0
.
2
1
6
0
.
1
7
4
Q6
3
.
0
2
8
7
0
.
6
6
9
1
3
-
0
.
0
3
3
0
.
7
6
6
Q7
3
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4
0
9
8
0
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7
7
7
8
2
-
0
.
0
6
7
-
0
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1
6
4
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3
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4
3
8
5
0
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8
2
1
7
2
0
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1
0
9
-
0
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2
7
Q9
3
.
5
5
7
4
0
.
8
5
1
5
2
-
0
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0
6
-
0
.
6
Q
1
0
3
.
4
9
1
8
0
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7
6
1
7
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0
8
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0
4
4
Q
1
1
3
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5
6
5
6
0
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8
1
1
3
2
-
0
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2
6
1
-
0
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1
7
6
Q
1
2
3
.
4
7
1
3
0
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7
1
0
8
8
0
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0
6
7
-
0
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2
2
4
Q
1
3
3
.
5
9
0
2
0
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7
9
3
5
3
-
0
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1
2
5
0
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3
6
9
Q
1
4
3
.
6
8
8
5
0
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7
7
0
6
8
-
0
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1
6
1
-
0
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0
2
9
Q
1
5
3
.
4
7
9
5
0
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8
0
8
6
4
0
.
0
9
-
0
.
2
2
8
Q
1
6
3
.
1
3
5
2
0
.
8
1
7
8
5
0
.
2
4
6
-
0
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1
Q
1
7
3
.
2
0
0
8
0
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7
5
1
2
9
0
.
0
0
4
0
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3
6
7
Q
2
1
3
.
8
4
0
2
0
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6
5
0
3
1
-
0
.
0
1
1
-
0
.
2
8
7
Q
2
2
3
.
3
1
5
6
0
.
8
0
3
0
3
-
0
.
1
5
2
0
.
0
1
5
Q
2
3
3
.
5
1
2
3
0
.
7
2
2
8
3
-
0
.
2
0
8
0
.
1
3
1
Q
2
4
3
.
6
0
6
6
0
.
7
6
5
0
5
-
0
.
2
5
3
-
0
.
2
4
1
T
ab
le
3
.
KM
O
an
d
B
ar
tlett
’
s
t
est
Te
st
V
a
l
u
e
K
M
O
me
a
su
r
e
o
f
sam
p
l
i
n
g
a
d
e
q
u
a
c
y
0
.
7
2
4
B
a
r
t
l
e
t
t
’
s
t
e
s
t
o
f
sp
h
e
r
i
c
i
t
y
A
p
p
r
o
x
.
C
h
i
-
sq
u
a
r
e
1
8
7
7
.
5
2
2
Df
2
1
0
S
i
g
.
0
.
0
0
0
4
.
1
.
2
.
E
x
plo
ra
t
o
ry
f
a
ct
o
r
a
n
a
ly
s
is
T
o
an
s
wer
th
e
f
ir
s
t
r
esear
ch
q
u
esti
o
n
,
th
is
s
ec
tio
n
r
ep
o
r
ts
th
e
o
u
tco
m
es
o
f
th
e
E
FA
to
i
d
en
tify
th
e
laten
t
f
ac
to
r
s
th
at
i
n
f
lu
en
ce
t
h
e
o
r
g
an
izatio
n
o
f
PjB
L
in
m
ath
em
atics
teac
h
in
g
.
I
n
T
a
b
le
4
,
th
e
e
x
tr
ac
ted
f
ac
to
r
s
ar
e
d
is
p
lay
ed
alo
n
g
s
id
e
th
eir
eig
en
v
alu
es,
ex
p
lain
ed
v
ar
ian
ce
s
,
an
d
cu
m
u
lativ
e
v
a
r
ian
ce
s
.
Fo
llo
win
g
th
e
Kaiser
cr
iter
io
n
,
o
n
ly
f
ac
t
o
r
s
with
eig
en
v
alu
es
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r
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ter
t
h
an
1
wer
e
r
etain
ed
in
th
e
m
o
d
el.
T
h
e
an
aly
s
is
r
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lts
f
r
o
m
2
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b
s
er
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ab
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tifie
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f
lu
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ich
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o
n
e
f
ac
to
r
m
o
r
e
th
an
i
n
itially
ex
p
e
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.
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ac
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[
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.
A
s
s
h
o
wn
in
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ab
le
3
,
th
e
s
ix
ex
tr
ac
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3
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7
2
9
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Est
i
m
a
t
e
Th
r
e
s
h
o
l
d
I
n
t
e
r
p
r
e
t
a
t
i
o
n
1
C
M
I
N
/
D
1
.
2
6
4
<
3
Ex
c
e
l
l
e
n
t
2
G
F
I
0
.
9
2
4
≥
.
9
0
G
o
o
d
3
A
G
F
I
0
.
9
≥
.
9
0
A
c
c
e
p
t
a
b
l
e
4
N
F
I
0
.
8
8
7
≥
.
8
0
A
c
c
e
p
t
a
b
l
e
5
C
F
I
0
.
9
7
3
≥
.
9
5
Ex
c
e
l
l
e
n
t
6
R
M
S
EA
0
.
0
3
3
≤
.
0
5
G
o
o
d
7
P
C
LO
S
E
0
.
9
8
9
≥
.
0
5
Ex
c
e
l
l
e
n
t
Facto
r
lo
ad
in
g
r
e
f
lects
th
e
ex
ten
t
to
w
h
ich
a
n
o
b
s
er
v
e
d
v
ar
ia
b
le
r
ep
r
esen
ts
a
late
n
t
f
ac
to
r
.
A
s
tan
d
ar
d
ized
f
ac
to
r
lo
ad
in
g
s
h
o
u
ld
b
e
≥
0
.
5
to
b
e
ac
ce
p
tab
le
an
d
≥
0
.
7
to
b
e
co
n
s
id
er
ed
g
o
o
d
[
2
5
]
.
Fig
u
r
e
4
s
h
o
ws
th
at
m
o
s
t
f
ac
to
r
lo
ad
in
g
s
f
all
with
in
th
e
r
an
g
e
o
f
0
.
6
9
–
1
.
0
0
,
en
s
u
r
i
n
g
s
tr
o
n
g
c
o
n
v
e
r
g
en
t
v
alid
ity
o
f
t
h
e
m
o
d
el.
Ho
wev
e
r
,
s
o
m
e
v
ar
ia
b
les
h
av
e
s
lig
h
tly
lo
wer
c
o
ef
f
icien
ts
(
e.
g
.
,
Q1
4
=
0
.
6
9
,
Q1
5
=
0
.
6
9
)
,
y
et
r
e
m
ain
with
in
th
e
ac
ce
p
tab
le
r
a
n
g
e.
T
h
e
cu
r
v
ed
ar
r
o
ws
in
th
e
f
i
g
u
r
e
r
ep
r
esen
t
th
e
co
r
r
elatio
n
s
b
etwe
en
f
ac
to
r
s
.
I
f
a
co
r
r
elatio
n
co
e
f
f
icien
t
≥
0
.
8
5
,
it
m
ay
in
d
icate
a
m
u
ltico
llin
ea
r
ity
is
s
u
e
b
etwe
en
f
ac
to
r
s
[
3
2
]
.
I
n
th
is
ca
s
e,
th
e
co
r
r
elatio
n
co
ef
f
icie
n
ts
r
an
g
e
f
r
o
m
0
.
0
0
to
0
.
1
0
,
co
n
f
ir
m
in
g
th
at
th
e
f
ac
to
r
s
ar
e
well
d
is
cr
i
m
in
ated
an
d
t
h
at
n
o
m
u
ltico
llin
ea
r
ity
is
s
u
es
ex
is
t.
T
h
e
test
in
d
ices
in
d
icate
th
at
t
h
e
m
ea
s
u
r
em
e
n
t
m
o
d
el
ac
h
ie
v
es
g
o
o
d
r
eliab
ilit
y
an
d
v
alid
ity
,
th
er
eb
y
co
n
f
ir
m
i
n
g
th
at
R
Q2
h
as b
ee
n
s
atis
f
ac
to
r
ily
an
d
s
cien
tific
ally
ad
d
r
ess
ed
.
4
.
2
.
Dis
cus
s
io
n
4
.
2
.
1
.
L
a
t
ent
co
ns
t
ruct
s
influ
encing
t
he
a
do
ptio
n o
f
pro
j
e
ct
-
ba
s
ed
lea
rning
peda
g
o
g
ies (
RQ
1
)
T
h
e
r
esu
lts
o
f
th
e
E
FA
r
ev
ea
l
ed
th
e
ex
tr
ac
tio
n
o
f
6
d
is
tin
ct
f
ac
to
r
s
,
ac
co
u
n
tin
g
f
o
r
6
8
.
4
2
8
%
o
f
th
e
to
tal
ex
p
lain
ed
v
ar
ian
ce
.
T
h
is
p
r
o
v
i
d
es
ev
id
en
ce
o
f
a
well
-
d
ef
in
ed
,
i
n
ter
p
r
etab
le,
an
d
r
o
b
u
s
t
f
ac
to
r
s
tr
u
ctu
r
e
.
T
h
e
s
ix
p
r
im
ar
y
f
ac
to
r
s
in
f
lu
en
cin
g
th
e
o
r
g
an
izatio
n
o
f
Pj
B
L
in
m
ath
em
atics
ed
u
ca
tio
n
in
clu
d
e:
i)
f
ac
ilit
ies
an
d
teac
h
in
g
s
u
p
p
o
rt
;
ii)
ca
p
ac
ity
to
o
r
g
an
ize
PjB
L
;
iii
)
p
er
ce
p
t
io
n
o
f
PjB
L
;
iv
)
r
ea
d
in
ess
f
o
r
PjB
L
;
v
)
teac
h
er
s
’
c
o
n
f
id
e
n
ce
in
ap
p
ly
in
g
PjB
L
;
an
d
v
i)
s
tu
d
e
n
ts
’
ch
ar
ac
ter
is
tics
.
T
h
e
f
ac
to
r
o
f
f
ac
ilit
ies
an
d
tea
ch
in
g
s
u
p
p
o
r
t
p
lay
s
an
in
teg
r
a
l
p
ar
t
in
t
h
e
ef
f
ec
tiv
e
im
p
lem
e
n
tatio
n
o
f
PjB
L
.
T
h
is
f
in
d
in
g
alig
n
s
with
th
e
s
tu
d
y
in
Ng
u
y
e
n
et
a
l.
[
1
]
wh
ich
d
em
o
n
s
tr
ated
th
at
p
h
y
s
i
ca
l c
o
n
d
itio
n
s
an
d
tech
n
o
lo
g
ical
s
u
p
p
o
r
t
s
ig
n
if
ican
tly
im
p
ac
t
s
tu
d
en
ts
’
ac
ad
em
ic
p
er
f
o
r
m
a
n
ce
in
Pj
B
L
en
v
ir
o
n
m
e
n
ts
.
Su
p
p
o
r
tin
g
ev
id
e
n
ce
f
r
o
m
s
ev
er
al
r
esear
ch
e
r
s
[
2
0
]
,
[
2
2
]
,
[
2
3
]
f
u
r
t
h
er
em
p
h
asizes
th
at
th
e
av
ailab
ilit
y
o
f
d
ig
ital
to
o
ls
an
d
ap
p
r
o
p
r
iate
in
f
r
astru
ctu
r
e,
s
u
ch
as
s
m
ar
t
p
h
o
n
es,
au
g
m
en
ted
r
ea
lity
s
o
f
twar
e,
an
d
o
n
lin
e
p
latf
o
r
m
s
,
ca
n
en
h
an
ce
s
tu
d
e
n
ts
’
s
p
atial
v
is
u
aliza
tio
n
,
in
tu
itiv
e
r
ea
s
o
n
in
g
,
an
d
en
g
a
g
em
e
n
t
in
PjB
L
s
ett
in
g
s
.
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