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Ma
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ch
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Ma
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Par
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C
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A
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R
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G.
Sag
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C
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,
W
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as State
Un
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s
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I
lo
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C
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,
Ph
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p
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1.
I
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RO
D
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O
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Ma
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p
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icien
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d
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1
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Ack
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d
if
f
e
r
s
u
b
s
tan
tially
f
r
o
m
th
o
s
e
in
STE
M
b
o
ar
d
i
n
g
s
c
h
o
o
ls
.
As
a
r
esu
lt,
th
er
e
r
e
m
ain
s
lim
ited
em
p
ir
ical
clar
ity
o
n
h
o
w
t
h
ese
s
o
cio
-
ec
o
lo
g
ical
f
ac
to
r
s
jo
in
tl
y
s
h
ap
e
m
ath
em
atics
o
u
tco
m
e
s
in
r
esid
en
tial
STE
M
en
v
ir
o
n
m
en
ts
,
an
d
wh
eth
er
th
eir
ef
f
ec
ts
ar
e
tr
an
s
m
itted
th
r
o
u
g
h
af
f
ec
tiv
e
m
ec
h
an
is
m
s
s
u
ch
as m
ath
em
atics in
ter
est.
Ho
wev
er
,
d
esp
ite
th
is
s
u
s
tain
ed
in
s
titu
tio
n
al
em
p
h
asis
,
p
er
s
is
ten
t
ch
allen
g
es
in
s
tu
d
en
t
en
g
ag
em
e
n
t
an
d
m
ath
e
m
atics
ac
h
iev
em
en
t
r
em
ain
e
v
id
en
t.
T
h
is
is
s
u
e
is
n
o
t
co
n
f
in
ed
to
th
e
Ph
ilip
p
in
e
Scien
ce
Hig
h
Sch
o
o
l
–
W
ester
n
Vis
ay
as
C
am
p
u
s
(
PS
HS
–
W
V
C
)
b
u
t
m
ir
r
o
r
s
b
r
o
ad
er
n
atio
n
al
tr
en
d
s
.
I
n
ter
n
atio
n
al
lar
g
e
-
s
ca
le
ass
ess
m
en
ts
,
m
o
s
t
n
o
tab
ly
th
e
Pro
g
r
a
m
m
e
f
o
r
I
n
ter
n
atio
n
al
Stu
d
en
t
A
s
s
es
s
m
en
t
(
PISA)
,
co
n
s
is
ten
tly
in
d
icate
th
at
Fil
ip
in
o
lear
n
er
s
p
e
r
f
o
r
m
am
o
n
g
th
e
lo
west
g
l
o
b
ally
in
m
ath
em
atics,
with
a
s
u
b
s
tan
tial p
r
o
p
o
r
tio
n
f
ailin
g
to
attain
b
asic p
r
o
f
icien
cy
in
p
r
o
b
lem
-
s
o
lv
in
g
a
n
d
lo
g
ical
r
ea
s
o
n
in
g
[
5
]
.
Alar
m
in
g
ly
,
s
im
ilar
p
atter
n
s
em
er
g
e
ev
e
n
with
in
PS
HS,
an
ac
ad
em
ically
s
elec
tiv
e
s
y
s
tem
,
wh
er
e
in
ter
n
al
r
ea
d
i
n
ess
ass
es
s
m
en
ts
f
r
eq
u
en
tly
r
ep
o
r
t
m
ea
n
m
at
h
em
atics
s
co
r
es
r
an
g
in
g
f
r
o
m
5
0
%
to
5
5
%
[
6
]
.
T
h
ese
f
in
d
i
n
g
s
s
u
g
g
est
th
at
u
n
d
er
p
er
f
o
r
m
a
n
ce
ca
n
n
o
t
b
e
s
u
f
f
icien
tly
ex
p
lain
ed
b
y
cu
r
r
icu
lar
r
ig
o
r
,
in
s
tr
u
ctio
n
al
tim
e,
o
r
s
tu
d
e
n
t
s
elec
tiv
ity
alo
n
e,
th
er
e
b
y
d
ir
ec
tin
g
atten
tio
n
to
war
d
n
o
n
-
c
o
g
n
itiv
e
a
n
d
co
n
tex
tu
al
d
eter
m
in
an
ts
o
f
l
ea
r
n
in
g
.
T
h
e
co
n
te
m
p
o
r
a
r
y
ed
u
ca
tio
n
al
lan
d
s
ca
p
e
f
u
r
th
e
r
ex
ac
er
b
ates
th
ese
ch
allen
g
es.
T
h
e
h
eig
h
te
n
ed
a
ca
d
em
ic
d
em
a
n
d
s
ch
ar
ac
ter
is
t
ic
o
f
2
1
s
t
-
ce
n
tu
r
y
s
ch
o
o
lin
g
ex
p
o
s
e
s
tu
d
en
ts
to
in
cr
ea
s
ed
co
g
n
itiv
e
lo
a
d
,
co
m
p
r
ess
ed
s
ch
ed
u
les,
a
n
d
s
u
s
t
ain
ed
p
e
r
f
o
r
m
an
ce
p
r
ess
u
r
e,
wh
ich
ar
e
ass
o
ciate
d
with
elev
ated
lev
els
o
f
s
tr
ess
,
an
x
iety
,
s
leep
d
is
r
u
p
tio
n
,
an
d
d
ec
lin
in
g
ac
a
d
em
ic
f
o
cu
s
[
7
]
.
Su
c
h
co
n
d
itio
n
s
h
av
e
b
ee
n
s
h
o
wn
to
u
n
d
e
r
m
in
e
en
g
a
g
em
en
t
an
d
ac
h
iev
e
m
e
n
t,
p
a
r
ticu
lar
ly
i
n
c
o
g
n
itiv
ely
d
em
an
d
in
g
s
u
b
jects
s
u
ch
as m
ath
em
atics,
wh
ile
s
im
u
ltan
eo
u
s
ly
wid
en
i
n
g
s
o
cio
e
co
n
o
m
ic
a
n
d
ac
h
ie
v
em
en
t d
is
p
ar
ities
[
8
]
.
W
ith
in
th
is
co
n
tex
t,
th
e
r
esid
e
n
tial
s
ch
o
o
l
m
o
d
el
o
f
PS
HS
–
W
VC
p
r
esen
ts
a
d
is
t
in
ctiv
e
en
v
ir
o
n
m
en
t
in
wh
ich
th
ese
p
r
ess
u
r
es
ar
e
in
ten
s
if
ied
.
W
h
ile
th
e
m
o
d
el
en
h
an
ce
s
p
ee
r
in
ter
ac
tio
n
an
d
in
s
titu
tio
n
al
im
m
er
s
io
n
,
it
also
co
n
s
tr
ain
s
d
ir
ec
t
p
ar
en
tal
in
v
o
lv
em
e
n
t,
r
en
d
er
i
n
g
s
tu
d
en
ts
m
o
r
e
d
ep
en
d
e
n
t
o
n
p
ee
r
n
etwo
r
k
s
an
d
s
ch
o
o
l
-
b
ased
s
u
p
p
o
r
t
s
y
s
tem
s
.
C
o
n
s
eq
u
e
n
tly
,
m
ath
em
atics
p
er
f
o
r
m
an
ce
in
t
h
is
s
ettin
g
em
er
g
es
f
r
o
m
th
e
c
o
m
p
lex
in
ter
ac
ti
o
n
o
f
in
te
r
n
al
p
s
y
ch
o
lo
g
ica
l
p
r
o
ce
s
s
es
an
d
ex
ter
n
al
s
o
cio
-
en
v
i
r
o
n
m
e
n
tal
in
f
lu
en
ce
s
,
with
t
h
e
r
esid
en
tia
l
co
n
tex
t
a
m
p
lify
in
g
th
eir
r
ec
i
p
r
o
ca
l
ef
f
ec
ts
[
9
]
–
[
1
1
]
.
Yet,
e
m
p
ir
ical
wo
r
k
th
at
ex
p
licitly
m
o
d
els
th
ese
in
ter
t
win
ed
in
f
lu
en
ce
s
with
in
STE
M
b
o
ar
d
in
g
s
ch
o
o
ls
r
em
ain
s
lim
ited
,
p
ar
ticu
lar
ly
in
ter
m
s
o
f
test
in
g
in
teg
r
ated
d
ir
e
ct
-
an
d
-
in
d
ir
ec
t p
ath
way
s
r
ath
e
r
th
an
r
e
p
o
r
tin
g
b
r
o
ad
ass
o
ciatio
n
s
.
Ag
ain
s
t
th
is
b
ac
k
d
r
o
p
,
th
e
p
r
esen
t
s
tu
d
y
ex
am
in
es
th
e
in
f
lu
en
ce
o
f
s
o
cio
-
ec
o
lo
g
ical
an
d
af
f
ec
tiv
e
f
ac
to
r
s
o
n
th
e
m
ath
em
atics
p
er
f
o
r
m
a
n
ce
o
f
s
ch
o
lar
s
at
th
e
PS
HS
–
W
V
C
.
Sp
ec
if
ically
,
i
t
in
v
esti
g
ates
h
o
w
p
ar
en
tal
in
v
o
lv
em
e
n
t,
p
ee
r
in
f
lu
en
ce
,
s
ch
o
o
l
s
u
p
p
o
r
t,
an
d
g
r
ad
e
lev
el
s
h
ap
e
s
tu
d
en
ts
’
in
ter
est
in
m
ath
em
atics
an
d
,
in
tu
r
n
,
th
eir
ac
ad
em
ic
o
u
tco
m
es.
E
x
is
tin
g
em
p
ir
ical
ev
id
en
ce
s
u
g
g
ests
th
at
en
v
ir
o
n
m
en
tal
s
u
p
p
o
r
ts
ex
er
t
b
o
t
h
d
ir
ec
t
an
d
i
n
d
ir
ec
t
ef
f
ec
ts
o
n
ac
h
iev
em
en
t,
f
r
eq
u
en
tly
o
p
e
r
atin
g
th
r
o
u
g
h
a
f
f
ec
t
iv
e
p
ath
way
s
s
u
ch
as
in
ter
est,
m
o
tiv
atio
n
,
an
d
s
elf
-
b
elief
[
1
2
]
,
[
1
3
]
.
Su
p
p
o
r
tiv
e
lear
n
in
g
en
v
i
r
o
n
m
e
n
ts
f
o
s
ter
co
n
f
id
en
ce
an
d
en
g
ag
em
e
n
t,
wh
ile
s
u
s
tain
ed
in
ter
est
in
m
ath
em
atics
p
r
o
m
o
t
es
p
er
s
is
ten
ce
,
r
esil
ien
ce
,
an
d
ad
ap
tiv
e
co
p
i
n
g
in
th
e
f
ac
e
o
f
ac
ad
em
ic
d
if
f
ic
u
lty
[
1
4
]
–
[
1
6
]
.
Fro
m
th
is
p
er
s
p
ec
tiv
e,
m
at
h
em
atics
ac
h
iev
em
en
t
is
b
est
co
n
ce
p
tu
alize
d
as
a
d
y
n
a
m
ic
o
u
tco
m
e
o
f
in
ter
ac
tin
g
en
v
ir
o
n
m
en
tal,
em
o
tio
n
al,
an
d
m
o
ti
v
atio
n
al
p
r
o
ce
s
s
es
r
ath
er
th
an
as a
p
r
o
d
u
ct
o
f
in
s
tr
u
ctio
n
al
ex
p
o
s
u
r
e
alo
n
e
[
1
7
]
.
T
o
th
eo
r
etica
lly
an
ch
o
r
th
e
s
e
r
elatio
n
s
h
ip
s
,
th
e
s
tu
d
y
in
teg
r
ates
s
o
cial
co
g
n
itiv
e
th
eo
r
y
an
d
B
r
o
n
f
en
b
r
e
n
n
er
’
s
ec
o
lo
g
ical
s
y
s
tem
s
th
eo
r
y
in
to
a
u
n
if
ie
d
co
n
ce
p
tu
al
f
r
am
ewo
r
k
.
So
ci
al
co
g
n
itiv
e
th
eo
r
y
p
o
s
its
th
at
ac
ad
em
ic
ac
h
iev
e
m
en
t
r
esu
lts
f
r
o
m
r
ec
ip
r
o
ca
l
in
ter
ac
tio
n
s
am
o
n
g
p
er
s
o
n
al
b
elief
s
,
b
e
h
av
io
r
al
en
g
ag
em
e
n
t,
an
d
en
v
i
r
o
n
m
e
n
tal
co
n
d
itio
n
s
,
with
s
elf
-
ef
f
icac
y
f
u
n
ctio
n
in
g
as
a
ce
n
tr
al
d
eter
m
in
an
t
o
f
lear
n
in
g
o
u
tco
m
es
[
1
8
]
.
W
ith
in
th
is
f
r
am
ewo
r
k
,
m
ath
em
atics
in
ter
est
o
p
er
ates
as
a
cr
itical
m
ed
iatin
g
co
n
s
tr
u
ct
th
at
lin
k
s
in
ter
n
al
d
is
p
o
s
itio
n
s
to
o
b
s
er
v
ab
le
ac
ad
em
ic
b
eh
av
io
r
s
,
as
s
tu
d
en
ts
with
s
tr
o
n
g
er
co
n
f
id
en
ce
a
n
d
p
o
s
itiv
e
af
f
ec
t
to
war
d
m
ath
em
atics
ar
e
m
o
r
e
lik
ely
to
en
g
a
g
e
d
ee
p
l
y
,
p
er
s
is
t
th
r
o
u
g
h
d
if
f
icu
lty
,
an
d
ac
h
iev
e
h
ig
h
er
lev
els
o
f
p
er
f
o
r
m
an
ce
[
1
9
]
.
C
o
m
p
lem
en
tin
g
th
is
p
er
s
p
ec
tiv
e,
B
r
o
n
f
en
b
r
en
n
e
r
’
s
ec
o
lo
g
ical
s
y
s
tem
s
th
eo
r
y
s
itu
ates
lear
n
in
g
with
in
n
ested
an
d
i
n
ter
co
n
n
ec
ted
s
y
s
tem
s
o
f
in
f
l
u
en
ce
,
r
an
g
in
g
f
r
o
m
im
m
ed
iate
in
ter
ac
tio
n
s
with
p
ee
r
s
,
teac
h
er
s
,
an
d
d
o
r
m
ito
r
y
life
(
m
icr
o
s
y
s
tem
)
to
th
e
r
elatio
n
al
lin
k
ag
es
am
o
n
g
th
ese
co
n
tex
ts
(
m
eso
s
y
s
tem
)
,
s
u
ch
as
h
o
m
e
–
s
ch
o
o
l
co
m
m
u
n
icatio
n
a
n
d
p
ee
r
–
tea
ch
er
co
llab
o
r
atio
n
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
B
ey
o
n
d
n
u
mb
ers
:
a
p
a
th
a
n
a
ly
s
is
o
n
h
o
w
ed
u
ca
tio
n
a
l e
co
s
ystem
a
n
d
ma
th
…
(
C
h
a
r
ma
ig
n
e
A
.
E
s
la
b
r
a
)
1039
[
2
0
]
,
[
2
1
]
.
I
n
th
e
r
esid
e
n
tial
s
ettin
g
o
f
PS
HS
–
W
V
C
,
th
ese
s
y
s
tem
s
co
n
v
er
g
e
with
h
eig
h
ten
ed
i
n
ten
s
ity
,
cr
ea
tin
g
a
lear
n
in
g
ec
o
lo
g
y
in
wh
ich
p
ee
r
n
o
r
m
s
,
co
llab
o
r
at
iv
e
p
r
ac
tices,
an
d
in
s
titu
tio
n
al
s
u
p
p
o
r
t
s
tr
u
ctu
r
es
p
lay
a
p
ar
ticu
la
r
ly
s
alien
t r
o
le.
B
u
ild
in
g
o
n
th
is
in
teg
r
ated
th
eo
r
etica
l
len
s
,
th
e
s
tu
d
y
p
r
o
p
o
s
es
th
at
m
ath
em
atics
in
ter
es
t
m
ed
iates
th
e
r
elatio
n
s
h
ip
b
etwe
en
e
n
v
ir
o
n
m
en
tal
s
u
p
p
o
r
ts
p
ar
e
n
tal
in
v
o
lv
em
en
t,
p
ee
r
in
f
lu
en
ce
,
a
n
d
s
ch
o
o
l
s
u
p
p
o
r
t
—
p
ar
en
tal
in
v
o
lv
e
m
en
t,
p
ee
r
i
n
f
lu
en
ce
,
an
d
s
ch
o
o
l
s
u
p
p
o
r
t
—
an
d
ac
ad
em
ic
p
er
f
o
r
m
an
ce
,
wh
ile
co
n
tex
tu
al
f
ac
to
r
s
s
u
ch
as c
u
r
r
icu
lar
in
ten
s
ity
an
d
s
ch
o
lar
tier
lev
el
m
o
d
er
ate
th
ese
p
ath
way
s
.
T
h
is
m
o
d
el
r
ec
o
g
n
izes th
at
id
en
tical
s
u
p
p
o
r
t
m
ec
h
a
n
is
m
s
m
ay
y
ield
d
i
f
f
er
en
tial
e
f
f
ec
t
s
d
ep
en
d
in
g
o
n
s
tu
d
e
n
ts
’
ac
a
d
em
ic
lo
ad
,
s
tr
ess
ex
p
o
s
u
r
e,
a
n
d
co
p
in
g
ca
p
ac
ity
[
2
2
]
,
[
2
3
]
.
B
y
elu
cid
atin
g
b
o
th
th
e
m
ec
h
a
n
is
m
s
an
d
co
n
d
itio
n
s
u
n
d
er
wh
ich
s
o
cio
-
ec
o
lo
g
ical
an
d
af
f
ec
tiv
e
f
ac
to
r
s
in
ter
ac
t,
th
e
s
tu
d
y
s
ee
k
s
to
ad
v
an
ce
a
m
o
r
e
n
u
a
n
ce
d
u
n
d
e
r
s
tan
d
in
g
o
f
m
ath
em
atics
ac
h
iev
em
en
t
with
in
s
p
ec
ialized
,
h
ig
h
-
d
em
a
n
d
ed
u
ca
tio
n
al
co
n
tex
ts
an
d
to
in
f
o
r
m
th
e
d
ev
elo
p
m
e
n
t o
f
ta
r
g
eted
,
c
o
n
t
ex
t
-
s
en
s
itiv
e
in
ter
v
en
tio
n
s
th
at
ex
ten
d
b
ey
o
n
d
p
u
r
ely
p
ed
ag
o
g
ical
r
ef
o
r
m
.
T
h
e
n
o
v
elty
o
f
th
is
s
tu
d
y
lies
in
its
h
o
lis
tic
an
d
in
teg
r
ativ
e
ap
p
r
o
ac
h
to
u
n
d
e
r
s
tan
d
in
g
m
a
th
em
atics
p
er
f
o
r
m
an
ce
with
in
a
r
esid
e
n
tial
STE
M
en
v
ir
o
n
m
e
n
t
s
u
ch
as
PS
HS
–
W
VC
.
Un
lik
e
e
ar
lier
r
esear
ch
th
at
co
n
ce
n
tr
ated
o
n
co
g
n
itiv
e
o
r
in
s
tr
u
ctio
n
al
d
eter
m
in
a
n
ts
,
t
h
is
s
tu
d
y
b
r
id
g
es
p
s
y
ch
o
l
o
g
i
ca
l
an
d
ec
o
lo
g
ical
p
er
s
p
ec
tiv
es,
em
p
h
asizin
g
h
o
w
m
ath
em
atics
in
ter
est
m
ed
iates
th
e
ef
f
ec
ts
o
f
en
v
ir
o
n
m
e
n
tal
in
f
lu
en
ce
s
in
a
s
ettin
g
wh
er
e
s
tu
d
en
ts
liv
e,
s
t
u
d
y
,
an
d
s
o
cialize
p
r
im
ar
ily
o
n
ca
m
p
u
s
.
B
y
f
o
r
e
g
r
o
u
n
d
in
g
th
e
in
ter
d
ep
e
n
d
en
c
e
o
f
m
ath
em
atics in
ter
est,
p
ee
r
a
n
d
s
ch
o
o
l su
p
p
o
r
ts
,
an
d
th
e
i
n
ten
s
if
ied
m
icr
o
s
y
s
tem
an
d
m
es
o
s
y
s
tem
d
y
n
am
ics
o
f
a
r
esid
en
tial
s
ch
o
o
l,
th
e
s
tu
d
y
o
f
f
er
s
a
c
o
m
p
r
e
h
en
s
iv
e
f
r
a
m
ewo
r
k
f
o
r
ex
p
lain
in
g
wh
y
s
o
m
e
s
tu
d
e
n
ts
th
r
iv
e
u
n
d
er
p
r
ess
u
r
e
wh
ile
o
t
h
er
s
s
tr
u
g
g
le.
Ultim
ately
,
th
e
f
i
n
d
in
g
s
ar
e
ex
p
ec
te
d
to
in
f
o
r
m
t
h
e
d
ev
elo
p
m
en
t
o
f
s
tu
d
en
t
-
ce
n
ter
ed
,
ev
id
e
n
ce
-
b
a
s
ed
s
tr
ateg
ies
th
at
p
r
o
m
o
te
b
o
th
ac
ad
em
ic
s
u
cc
ess
an
d
p
s
y
c
h
o
lo
g
ical
welln
ess
.
T
h
r
o
u
g
h
th
is
s
y
n
th
esis
,
th
e
r
e
s
ea
r
ch
co
n
tr
ib
u
tes
to
a
d
ee
p
er
u
n
d
er
s
tan
d
in
g
o
f
m
ath
em
atic
s
lear
n
in
g
as
b
o
th
a
co
g
n
itiv
e
a
n
d
em
o
tio
n
al
p
r
o
ce
s
s
,
s
h
ap
ed
b
y
t
h
e
d
y
n
am
ic
in
te
r
ac
tio
n
b
etwe
en
th
e
in
d
iv
id
u
al
an
d
th
ei
r
lear
n
in
g
ec
o
lo
g
y
,
a
n
in
s
ig
h
t
cr
u
cial
f
o
r
s
u
s
tain
in
g
ex
ce
llen
ce
an
d
well
-
b
ein
g
i
n
h
ig
h
-
p
er
f
o
r
m
in
g
e
d
u
ca
tio
n
al
in
s
titu
tio
n
s
lik
e
PS
HS
–
W
VC
.
T
h
is
s
tu
d
y
s
o
u
g
h
t
to
d
eter
m
in
e
h
o
w
p
ar
e
n
tal
in
v
o
lv
em
e
n
t,
p
ee
r
in
f
lu
e
n
ce
,
s
ch
o
o
l
s
u
p
p
o
r
t,
a
n
d
m
ath
em
atics
in
ter
est
co
llectiv
ely
an
d
in
d
iv
i
d
u
ally
a
f
f
ec
ted
th
e
m
ath
em
atics
p
er
f
o
r
m
a
n
ce
o
f
s
ch
o
lar
s
at
th
e
PS
HS
–
W
VC
.
I
t
aim
ed
to
p
r
o
v
id
e
d
ee
p
er
in
s
ig
h
ts
in
to
th
e
way
s
s
o
cial
an
d
m
o
tiv
ati
o
n
al
f
ac
to
r
s
in
ter
ac
t
t
o
s
h
ap
e
s
tu
d
en
ts
’
ac
ad
em
ic
ac
h
iev
em
en
t.
I
n
p
u
r
s
u
it
o
f
t
h
is
o
b
jectiv
e,
th
e
s
tu
d
y
was
g
u
id
e
d
b
y
th
e
f
o
llo
win
g
r
esear
ch
q
u
esti
o
n
s
:
−
W
h
at
ar
e
th
e
p
r
ev
ailin
g
lev
e
ls
o
f
p
ar
en
tal
in
v
o
l
v
em
en
t,
p
ee
r
in
f
lu
e
n
ce
,
s
ch
o
o
l
s
u
p
p
o
r
t,
m
ath
em
atics
in
ter
est,
an
d
m
ath
em
atics a
ch
i
ev
em
en
t a
m
o
n
g
th
e
s
ch
o
lar
s
o
f
th
e
PS
HS
?
−
W
h
ich
s
tr
u
ctu
r
al
m
o
d
el
m
o
s
t
ac
cu
r
ately
r
ep
r
esen
ts
th
e
r
el
atio
n
s
h
ip
s
am
o
n
g
p
a
r
en
tal
in
v
o
lv
em
en
t,
p
ee
r
in
f
lu
en
ce
,
an
d
s
ch
o
o
l
s
u
p
p
o
r
t
an
d
s
tu
d
e
n
ts
’
m
ath
e
m
atics
ac
h
iev
em
en
t,
s
p
ec
if
ically
d
is
tin
g
u
is
h
in
g
:
i
)
th
eir
d
ir
ec
t
ef
f
ec
ts
o
n
m
ath
em
atic
s
ac
h
iev
em
en
t
an
d
ii
)
th
eir
i
n
d
ir
ec
t
ef
f
ec
ts
o
n
m
ath
e
m
atics
ac
h
iev
em
en
t
th
r
o
u
g
h
m
ath
em
atics in
ter
est
as a
m
ed
iatin
g
v
ar
ia
b
le?
2.
M
E
T
H
O
D
2
.
1
.
Resea
rc
h
d
esig
n
T
h
is
s
t
u
d
y
s
o
u
g
h
t
t
o
ass
ess
th
e
le
v
els
o
f
p
a
r
e
n
ta
l
i
n
v
o
l
v
em
e
n
t
,
p
e
e
r
i
n
f
l
u
e
n
c
e,
s
c
h
o
o
l
s
u
p
p
o
r
t
,
m
at
h
e
m
a
tics
i
n
te
r
es
t,
an
d
m
a
t
h
e
m
at
ics
ac
h
i
ev
em
en
t
a
m
o
n
g
s
ch
o
l
ar
s
o
f
t
h
e
PS
HS
–
W
VC
.
I
t
f
u
r
t
h
er
ai
m
e
d
t
o
d
et
e
r
m
i
n
e
t
h
e
m
o
s
t
a
p
p
r
o
p
r
i
ate
s
t
r
u
ct
u
r
a
l
m
o
d
el
t
h
at
r
e
p
r
es
en
ts
th
e
p
at
te
r
n
s
o
f
ass
o
c
iati
o
n
a
m
o
n
g
t
h
es
e
v
a
r
i
ab
les
,
i
n
c
lu
d
i
n
g
b
o
t
h
d
i
r
e
c
t a
n
d
i
n
d
i
r
e
ct
r
e
lat
io
n
s
h
i
p
s
,
i
n
r
el
ati
o
n
to
s
t
u
d
e
n
ts
’
m
at
h
e
m
a
ti
cs
p
e
r
f
o
r
m
a
n
ce
.
T
o
ad
d
r
ess
t
h
es
e
o
b
jec
ti
v
es
,
t
h
e
s
tu
d
y
em
p
lo
y
e
d
s
t
r
u
c
tu
r
a
l
e
q
u
at
io
n
m
o
d
eli
n
g
(
S
E
M
)
wi
th
p
at
h
an
al
y
s
is
as
th
e
p
r
im
ar
y
a
n
a
ly
tic
al
te
c
h
n
iq
u
e.
Pat
h
an
al
y
s
is
is
a
r
o
b
u
s
t
s
ta
ti
s
tica
l
ap
p
r
o
ac
h
f
o
r
e
x
a
m
i
n
i
n
g
c
o
m
p
l
e
x
r
e
lat
io
n
al
s
tr
u
ct
u
r
es
b
y
est
im
ati
n
g
t
h
e
m
a
g
n
it
u
d
e
a
n
d
d
i
r
ec
ti
o
n
o
f
ass
o
cia
ti
o
n
s
a
m
o
n
g
v
ar
ia
b
l
es,
i
n
cl
u
d
i
n
g
i
n
d
i
r
e
ct
p
at
h
w
a
y
s
th
r
o
u
g
h
m
e
d
ia
ti
n
g
c
o
n
s
tr
u
cts.
P
r
o
c
ed
u
r
e
e
n
s
u
r
e
d
t
h
at
s
ch
o
l
ar
s
f
r
o
m
e
ac
h
ti
er
l
ev
el
a
n
d
g
e
n
d
e
r
g
r
o
u
p
wer
e
a
d
e
q
u
at
el
y
r
e
p
r
ese
n
t
e
d
,
t
h
e
r
e
b
y
s
tr
en
g
t
h
en
in
g
t
h
e
g
e
n
e
r
aliz
a
b
ili
ty
a
n
d
m
e
th
o
d
o
l
o
g
ic
al
r
i
g
o
r
o
f
t
h
e
s
t
u
d
y
.
2
.
2
.
Respo
nd
ent
s
T
h
e
r
esp
o
n
d
en
ts
wer
e
2
5
1
r
a
n
d
o
m
ly
s
elec
ted
PS
HS
–
W
V
C
s
ch
o
lar
s
in
Me
tr
o
p
o
lis
Av
en
u
e,
I
l
o
ilo
C
ity
,
ch
o
s
en
th
r
o
u
g
h
p
r
o
p
o
r
t
io
n
ate
s
tr
atif
ied
r
an
d
o
m
s
am
p
lin
g
to
en
s
u
r
e
r
ep
r
esen
tatio
n
ac
r
o
s
s
s
tr
ata.
T
h
e
m
in
im
u
m
r
eq
u
ir
ed
s
am
p
le
s
ize
was
f
ir
s
t
co
m
p
u
ted
u
s
in
g
G*
Po
wer
f
o
r
m
u
ltip
le
lin
ea
r
r
eg
r
ess
io
n
with
f
iv
e
p
r
ed
icto
r
s
,
ass
u
m
in
g
m
ed
iu
m
ef
f
ec
t
s
ize
(
f
²=
0
.
1
5
)
,
α
=0
.
0
5
,
an
d
p
o
wer
=0
.
9
5
,
wh
ich
y
ie
ld
s
N=
1
3
8
as
th
e
m
in
im
u
m
(
i.e
.
,
th
e
s
m
allest
N
th
at
m
ee
ts
th
e
s
p
ec
if
ied
p
o
wer
an
d
er
r
o
r
r
ates)
[
2
4
]
.
B
ec
au
s
e
th
e
an
aly
s
is
also
in
v
o
lv
es
p
ath
an
aly
s
is
/SEM
,
ad
eq
u
ac
y
was
f
u
r
th
e
r
ch
ec
k
e
d
ag
ain
s
t
SEM
-
f
o
c
u
s
ed
p
o
wer
an
d
lo
wer
-
b
o
u
n
d
g
u
id
an
ce
,
wh
e
r
e
s
am
p
le
n
ee
d
s
d
ep
en
d
o
n
m
o
d
el
co
m
p
lex
ity
,
d
esire
d
p
o
wer
,
an
d
ef
f
ec
t
s
izes;
n
o
tab
ly
,
p
o
wer
-
b
ased
an
d
m
o
d
el
-
s
tr
u
ctu
r
e
lo
wer
-
b
o
u
n
d
ap
p
r
o
ac
h
es
s
u
p
p
o
r
t
u
s
in
g
s
am
p
les
well
ab
o
v
e
m
in
im
al
r
eg
r
ess
io
n
co
u
n
ts
wh
en
esti
m
atin
g
c
o
v
a
r
ian
ce
-
s
tr
u
ctu
r
e
m
o
d
els
[
2
5
]
,
[
2
6
]
.
Mo
r
e
o
v
er
,
s
im
u
latio
n
e
v
id
en
ce
s
h
o
ws
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
.
15
,
No
.
2
,
Ap
r
il
20
2
6
:
1
0
3
7
-
1
0
5
0
1040
SEM
s
o
lu
tio
n
s
b
ec
o
m
e
m
o
r
e
s
tab
le
(
p
o
wer
,
b
ias,
an
d
p
r
o
p
er
s
o
lu
tio
n
s
)
as
N
in
c
r
ea
s
es
an
d
th
at
m
an
y
co
m
m
o
n
SEM
s
o
f
ten
b
en
e
f
it
f
r
o
m
s
am
p
les
ar
o
u
n
d
/ab
o
v
e
2
0
0
,
d
ep
en
d
in
g
o
n
co
n
d
itio
n
s
[
2
7
]
.
T
h
er
ef
o
r
e,
th
e
ac
h
iev
ed
N=
2
5
1
is
ad
eq
u
ate
b
ec
au
s
e
it
ex
ce
ed
s
th
e
G*
Po
we
r
m
in
im
u
m
(
1
3
8
)
a
n
d
alig
n
s
with
SEM
g
u
id
an
ce
f
av
o
r
in
g
lar
g
e
r
s
am
p
les f
o
r
s
ta
b
le
p
ar
am
eter
esti
m
atio
n
a
n
d
m
o
d
el
test
in
g
.
2
.
3
.
Da
t
a
g
a
t
hering
ins
t
rum
ent
T
o
s
y
s
tem
atica
lly
ca
p
tu
r
e
th
e
q
u
an
titativ
e
d
ata
r
e
q
u
ir
ed
f
o
r
th
is
s
tu
d
y
,
th
r
ee
p
r
im
ar
y
d
a
ta
s
o
u
r
ce
s
wer
e
u
tili
ze
d
:
two
s
tan
d
ar
d
ized
L
ik
er
t
-
s
ca
le
q
u
esti
o
n
n
air
es
an
d
o
n
e
s
et
o
f
o
f
f
icial
ac
ad
em
ic
r
ec
o
r
d
s
.
T
h
ese
in
s
tr
u
m
en
ts
wer
e
s
elec
ted
to
en
s
u
r
e
co
m
p
r
e
h
en
s
iv
e
m
ea
s
u
r
em
en
t
o
f
th
e
co
r
e
v
ar
iab
les
s
u
ch
as
m
ath
em
atics
in
ter
est,
ed
u
ca
tio
n
al
ec
o
s
y
s
te
m
f
ac
to
r
s
,
an
d
m
ath
em
atics a
ch
iev
em
en
t a
n
d
wer
e
s
u
b
jecte
d
to
ex
p
er
t
v
alid
atio
n
an
d
r
eliab
ilit
y
test
in
g
to
g
u
ar
a
n
tee
m
eth
o
d
o
lo
g
ical
r
i
g
o
r
.
2
.
3
.
1
.
M
a
t
hem
a
t
ics
inte
re
s
t
i
nv
ent
o
ry
T
h
e
m
ath
em
atics
in
ter
est
in
v
en
to
r
y
(
M
I
I
)
was
u
s
ed
to
ass
ess
th
e
lev
el
o
f
in
ter
est
in
m
ath
em
atics
am
o
n
g
PS
HS
s
ch
o
lar
s
.
T
h
e
in
s
tr
u
m
en
t
was
an
ch
o
r
e
d
in
th
e
f
o
u
r
-
p
h
ase
m
o
d
el
o
f
in
ter
est
d
ev
elo
p
m
en
t
p
r
o
p
o
s
ed
b
y
Mic
h
ae
lis
an
d
W
ein
tr
o
p
[
2
8
]
,
e
m
p
h
asizin
g
th
e
ad
v
an
ce
d
s
tag
es
in
wh
ic
h
cu
r
io
s
ity
b
ec
o
m
es
s
elf
-
r
eg
u
lated
a
n
d
tr
a
n
s
f
o
r
m
s
in
to
a
s
tab
le
p
e
r
s
o
n
al
in
ter
est
th
at
d
r
iv
es
d
ee
p
er
lear
n
in
g
.
T
h
e
MI
I
c
o
n
s
is
ted
o
f
3
0
s
tatem
en
ts
s
u
ch
as
1
5
p
o
s
itiv
ely
wo
r
d
ed
a
n
d
1
5
n
eg
ati
v
ely
wo
r
d
e
d
ad
ap
te
d
f
r
o
m
th
e
to
o
l
d
ev
elo
p
ed
b
y
San
g
k
u
la
[
2
9
]
.
R
esp
o
n
s
es
wer
e
r
ec
o
r
d
ed
o
n
a
4
-
p
o
i
n
t
L
ik
er
t
s
ca
le:
1
(
s
tr
o
n
g
ly
d
is
ag
r
ee
)
,
2
(
d
is
ag
r
ee
)
,
3
(
ag
r
ee
)
,
an
d
4
(
s
tr
o
n
g
ly
a
g
r
ee
)
.
Neg
ativ
ely
p
h
r
ased
item
s
wer
e
r
e
v
er
s
e
-
co
d
e
d
to
m
ain
t
ain
co
n
s
is
ten
cy
i
n
in
ter
p
r
etatio
n
.
T
o
estab
lis
h
th
e
in
s
tr
u
m
en
t’
s
co
n
ten
t v
alid
ity
,
it wa
s
ev
alu
ated
b
y
th
r
ee
ex
p
e
r
ts
in
m
ath
em
atic
s
ed
u
ca
tio
n
,
a
n
d
a
p
p
r
o
p
r
iate
r
ev
is
io
n
s
wer
e
m
ad
e
in
ac
co
r
d
an
c
e
with
th
eir
f
ee
d
b
ac
k
.
2
.
3
.
2
.
E
du
ca
t
io
na
l
ec
o
s
y
s
t
em
inv
ent
o
ry
T
h
e
ed
u
ca
tio
n
al
ec
o
s
y
s
tem
in
v
en
to
r
y
(
E
E
I
)
was
ad
m
in
is
ter
ed
to
m
ea
s
u
r
e
th
e
le
v
el
o
f
e
d
u
ca
tio
n
al
s
u
p
p
o
r
t
p
er
c
eiv
ed
b
y
th
e
s
ch
o
lar
s
.
Ad
ap
ted
f
r
o
m
th
e
wo
r
k
o
f
Z
h
u
an
g
an
d
L
iu
[
3
0
]
,
t
h
e
E
E
I
co
m
p
r
is
ed
4
5
item
s
o
r
g
an
ize
d
in
to
th
r
e
e
co
r
e
d
im
en
s
io
n
s
:
f
am
ily
s
u
p
p
o
r
t,
p
ee
r
in
f
l
u
en
ce
,
a
n
d
s
ch
o
o
l
s
u
p
p
o
r
t
.
E
ac
h
d
im
en
s
io
n
co
n
tain
e
d
1
5
s
tatem
en
ts
,
o
f
wh
ich
8
wer
e
p
o
s
itiv
ely
p
h
r
ased
an
d
7
wer
e
n
eg
ativ
ely
p
h
r
ased
.
Similar
to
th
e
MI
I
,
r
esp
o
n
s
e
s
wer
e
r
ated
o
n
a
4
-
p
o
in
t
L
i
k
er
t
s
ca
le
r
an
g
in
g
f
r
o
m
1
(
s
t
r
o
n
g
ly
d
is
ag
r
ee
)
to
4
(
s
tr
o
n
g
ly
a
g
r
ee
)
,
with
r
e
v
er
s
e
s
co
r
in
g
a
p
p
lied
t
o
n
e
g
ativ
e
ly
wo
r
d
e
d
item
s
to
en
s
u
r
e
in
t
er
p
r
etiv
e
ac
c
u
r
ac
y
.
T
h
e
E
E
I
u
n
d
er
wen
t
e
x
p
er
t
v
alid
atio
n
b
y
th
r
ee
r
eg
is
ter
ed
g
u
id
an
ce
co
u
n
s
elo
r
s
,
all
o
f
wh
o
m
h
o
ld
d
o
cto
r
al
d
eg
r
ee
s
in
p
h
ilo
s
o
p
h
y
,
to
e
n
s
u
r
e
clar
ity
,
co
n
ten
t r
elev
a
n
ce
,
a
n
d
co
n
s
tr
u
ct
v
alid
ity
.
T
o
estab
lis
h
th
e
r
eliab
ilit
y
o
f
b
o
th
in
s
tr
u
m
e
n
ts
,
a
p
ilo
t
t
est
was
co
n
d
u
cted
u
s
in
g
o
n
e
r
an
d
o
m
ly
s
elec
ted
s
ec
tio
n
f
r
o
m
ea
ch
g
r
ad
e
lev
el
th
r
o
u
g
h
s
im
p
le
r
a
n
d
o
m
s
am
p
lin
g
.
T
h
e
p
ilo
t
test
y
ield
ed
C
r
o
n
b
ac
h
’
s
alp
h
a
v
alu
es
o
f
0
.
8
9
9
an
d
0
.
9
1
0
f
o
r
th
e
MI
I
a
n
d
E
E
I
,
r
e
s
p
ec
tiv
ely
.
T
h
e
q
u
esti
o
n
n
air
e
s
wer
e
d
is
tr
ib
u
ted
elec
tr
o
n
ically
th
r
o
u
g
h
Go
o
g
l
e
Fo
r
m
s
,
an
d
th
e
r
esu
lts
wer
e
s
tatis
tically
an
aly
ze
d
to
co
n
f
ir
m
th
eir
in
ter
n
al
co
n
s
is
ten
cy
.
2
.
3
.
3
.
O
f
f
icia
l
a
ca
dem
ic
re
c
o
rds
I
t
s
er
v
ed
as
th
e
b
asis
f
o
r
m
ea
s
u
r
in
g
m
ath
em
atics
ac
h
ie
v
em
e
n
t
,
wh
ich
was
d
er
iv
e
d
f
r
o
m
th
e
s
ch
o
lar
s
’
ac
tu
al
m
ath
em
atics
g
r
ad
es
o
b
tain
ed
f
r
o
m
in
s
titu
tio
n
al
r
e
co
r
d
s
.
T
h
ese
d
ata
co
m
p
lem
e
n
ted
th
e
s
elf
-
r
ep
o
r
t
m
ea
s
u
r
es
an
d
p
r
o
v
id
ed
an
o
b
jectiv
e
in
d
icato
r
o
f
s
tu
d
en
ts
’
ac
ad
em
ic
p
er
f
o
r
m
a
n
ce
.
T
h
e
i
n
teg
r
atio
n
o
f
th
ese
in
s
tr
u
m
en
ts
,
as
s
u
m
m
ar
ized
in
T
ab
le
1
,
allo
wed
t
h
e
s
tu
d
y
to
tr
ian
g
u
late
s
elf
-
r
ep
o
r
ted
af
f
ec
t
iv
e
an
d
co
n
tex
tu
al
d
ata
with
ac
tu
al
ac
a
d
em
ic
o
u
tco
m
es.
T
h
is
alig
n
m
e
n
t
en
s
u
r
ed
th
at
th
e
an
aly
s
is
ca
p
tu
r
e
d
n
o
t
o
n
ly
s
tu
d
en
ts
’
in
ter
est
an
d
p
er
ce
iv
ed
s
u
p
p
o
r
t
s
y
s
tem
s
b
u
t
also
h
o
w
th
ese
f
ac
to
r
s
tr
an
s
lated
in
to
m
ea
s
u
r
a
b
le
ac
h
iev
em
e
n
t
in
m
ath
em
atics.
B
y
clea
r
ly
d
ef
i
n
in
g
t
h
e
v
a
r
iab
les,
r
esp
o
n
s
e
s
ca
les,
an
d
lev
els
o
f
m
ea
s
u
r
em
en
t,
th
e
s
tu
d
y
estab
lis
h
ed
a
s
o
lid
q
u
an
titativ
e
f
o
u
n
d
atio
n
f
o
r
s
u
b
s
eq
u
en
t statis
tical
an
aly
s
es a
n
d
in
ter
p
r
etatio
n
o
f
r
esu
lts
.
T
ab
le
1
.
I
n
s
tr
u
m
en
ts
,
v
a
r
iab
le
s
,
an
d
lev
el
o
f
m
ea
s
u
r
em
e
n
t
I
n
st
r
u
me
n
t
s
V
a
r
i
a
b
l
e
s wi
t
h
i
n
d
i
c
a
t
o
r
s
R
e
s
p
o
n
se
s/
L
i
k
e
r
t
s
c
a
l
e
Le
v
e
l
o
f
m
e
a
s
u
r
e
m
e
n
t
M
I
I
M
a
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2
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4
.
P
r
o
ce
du
re
a
nd
inte
rv
ent
io
n
T
h
e
s
tu
d
y
was
co
n
d
u
cted
in
t
h
r
ee
s
y
s
tem
atic
s
tag
es
s
u
ch
a
s
th
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p
r
elim
in
ar
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p
h
ase,
d
ata
co
llectio
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,
an
d
d
ata
a
n
a
ly
s
is
to
en
s
u
r
e
m
e
th
o
d
o
lo
g
ical
r
ig
o
r
,
eth
ical
co
m
p
lian
ce
,
an
d
th
e
v
alid
ity
o
f
f
in
d
in
g
s
.
2
.
4
.
1
.
P
re
lim
ina
ry
p
ha
s
e
Prio
r
to
d
ata
co
llectio
n
,
th
e
r
esear
ch
er
co
m
p
leted
th
e
r
eq
u
ir
ed
eth
ical
r
ev
iew
p
r
o
ce
s
s
u
n
d
er
th
e
PS
HS
s
y
s
tem
an
d
o
b
tain
ed
f
o
r
m
al
ap
p
r
o
v
al
f
r
o
m
b
o
th
th
e
in
s
titu
tio
n
al
r
esear
ch
a
n
d
eth
ics
co
m
m
ittees.
Au
th
o
r
izatio
n
to
c
o
n
d
u
ct
th
e
s
tu
d
y
was
lik
ewise
s
ec
u
r
e
d
f
r
o
m
th
e
s
ch
o
o
l
ad
m
in
is
tr
at
io
n
,
in
cl
u
d
in
g
th
e
ca
m
p
u
s
d
i
r
ec
to
r
,
th
e
cu
r
r
ic
u
lu
m
a
n
d
i
n
s
tr
u
ctio
n
d
iv
is
io
n
c
h
ief
,
a
n
d
th
e
m
ath
em
atics
u
n
it
h
ea
d
.
Fo
llo
win
g
ap
p
r
o
v
al,
th
e
r
esear
ch
in
s
tr
u
m
en
ts
u
n
d
er
wen
t
a
co
m
p
r
eh
e
n
s
iv
e
v
alid
atio
n
p
r
o
ce
s
s
to
e
n
s
u
r
e
th
eir
ac
cu
r
ac
y
,
clar
ity
,
an
d
a
p
p
r
o
p
r
iaten
ess
f
o
r
th
e
s
tu
d
y
’
s
o
b
jectiv
es.
T
h
e
MI
I
an
d
th
e
EEI
wer
e
ev
al
u
ated
b
y
a
p
an
el
o
f
ex
p
er
ts
in
ed
u
ca
tio
n
an
d
p
s
y
ch
o
lo
g
y
.
T
h
eir
f
ee
d
b
ac
k
g
u
id
e
d
th
e
r
ef
in
em
e
n
t
an
d
r
e
v
is
io
n
o
f
th
e
in
s
tr
u
m
en
ts
t
o
s
tr
en
g
th
en
th
eir
co
n
te
n
t
v
alid
ity
an
d
alig
n
m
en
t
with
th
e
s
t
u
d
y
c
o
n
s
tr
u
cts.
A
p
ilo
t
test
was
th
en
co
n
d
u
cted
am
o
n
g
a
s
m
all
g
r
o
u
p
o
f
s
tu
d
e
n
ts
wh
o
wer
e
n
o
t
p
ar
t
o
f
th
e
m
ain
s
am
p
le
to
ass
es
s
th
e
in
s
t
r
u
m
en
ts
’
r
eliab
ilit
y
an
d
in
ter
n
al
co
n
s
is
ten
cy
.
On
c
e
v
alid
atio
n
was
co
n
f
ir
m
ed
,
t
h
e
r
esear
ch
er
d
is
tr
ib
u
ted
an
i
n
f
o
r
m
atio
n
s
h
ee
t
to
p
ar
ticip
an
ts
d
etailin
g
th
e
s
tu
d
y
’
s
p
u
r
p
o
s
e,
p
r
o
ce
d
u
r
es,
an
d
eth
ical
co
n
s
id
er
atio
n
s
.
I
n
f
o
r
m
ed
co
n
s
en
t
f
o
r
m
s
wer
e
also
p
r
o
v
id
ed
,
em
p
h
asizin
g
v
o
lu
n
ta
r
y
p
ar
ticip
atio
n
,
co
n
f
id
en
tiality
,
an
d
th
e
r
ig
h
t
to
with
d
r
aw
at
an
y
s
tag
e
with
o
u
t
ac
ad
e
m
ic
r
ep
e
r
cu
s
s
io
n
s
.
T
h
e
f
in
al
d
ata
c
o
llectio
n
s
ch
ed
u
le
an
d
v
en
u
e
wer
e
co
m
m
u
n
icate
d
v
ia
em
ail
u
s
in
g
b
lin
d
ca
r
b
o
n
co
p
y
(
B
C
C
)
f
o
r
p
r
iv
ac
y
,
c
o
m
p
lem
e
n
ted
b
y
in
-
p
e
r
s
o
n
r
em
i
n
d
er
s
.
2
.
4
.
2
.
Da
t
a
co
llect
io
n p
ha
s
e
T
h
e
d
ata
co
llectio
n
was
ca
r
r
ied
o
u
t
at
th
e
n
ew
au
d
ito
r
iu
m
o
f
th
e
PS
HS
–
W
V
C
.
B
ef
o
r
e
ad
m
in
is
tr
atio
n
,
th
e
r
esear
ch
er
d
is
cu
s
s
ed
th
e
s
tu
d
y
’
s
o
b
jectiv
es,
im
p
o
r
tan
ce
,
an
d
d
ata
p
r
o
tectio
n
m
ea
s
u
r
es,
r
eiter
atin
g
th
at
p
a
r
ticip
atio
n
w
as
v
o
lu
n
tar
y
an
d
th
at
all
r
esp
o
n
s
es
wo
u
ld
r
em
ain
an
o
n
y
m
o
u
s
an
d
co
n
f
id
en
tial,
in
ac
co
r
d
a
n
ce
with
in
s
titu
tio
n
al
eth
ical
s
tan
d
ar
d
s
.
E
ac
h
p
ar
ticip
an
t
was
ass
ig
n
ed
a
u
n
iq
u
e
q
u
ick
r
esp
o
n
s
e
(
QR
)
co
d
e
th
at
lin
k
ed
d
ir
ec
tly
to
two
o
n
lin
e
q
u
esti
o
n
n
air
e
s
:
th
e
MI
I
an
d
th
e
EEI
.
B
y
s
ca
n
n
in
g
th
e
co
d
e,
p
ar
ticip
an
ts
ac
ce
s
s
ed
th
e
s
u
r
v
ey
f
o
r
m
s
th
r
o
u
g
h
Go
o
g
le
Fo
r
m
s
an
d
s
u
b
m
itted
th
eir
r
esp
o
n
s
es
elec
tr
o
n
ically
.
T
h
e
d
ata
wer
e
au
to
m
atica
lly
co
m
p
iled
in
Go
o
g
le
Sh
ee
ts
,
wh
er
e
th
e
r
esear
ch
er
r
ev
iewe
d
en
tr
ies f
o
r
m
is
s
in
g
o
r
in
co
n
s
is
ten
t
r
esp
o
n
s
es.
I
n
co
m
p
lete
s
u
b
m
is
s
io
n
s
wer
e
eith
er
clar
if
ied
o
r
ex
clu
d
e
d
to
m
ain
tain
d
ata
in
teg
r
ity
.
Af
ter
v
er
if
y
in
g
th
e
r
esp
o
n
s
es,
th
e
r
esear
ch
er
o
b
tain
ed
au
th
o
r
izatio
n
f
r
o
m
th
e
s
ch
o
o
l
r
eg
is
tr
ar
to
ac
ce
s
s
th
e
p
ar
ticip
an
ts
’
m
ath
em
atics
g
r
a
d
es
f
o
r
th
e
f
ir
s
t
an
d
s
ec
o
n
d
q
u
ar
ter
s
o
f
s
ch
o
o
l
y
ea
r
2
0
2
3
–
2
0
2
4
.
T
o
p
r
o
tect
co
n
f
id
en
tiality
,
ea
ch
r
esp
o
n
d
en
t
was
ass
ig
n
ed
a
r
a
n
d
o
m
ly
g
en
e
r
ated
i
d
en
tific
atio
n
co
d
e
with
n
o
p
er
s
o
n
al
id
en
tifie
r
s
.
All
n
am
es,
s
ec
tio
n
s
,
an
d
em
ail
ad
d
r
ess
es
wer
e
r
em
o
v
e
d
f
r
o
m
th
e
d
ataset,
an
d
b
o
t
h
d
ig
ital
an
d
p
r
in
ted
co
p
ies o
f
th
e
d
ata
wer
e
s
ec
u
r
ely
s
to
r
ed
in
co
m
p
lian
c
e
with
eth
ical
r
esear
ch
p
r
o
to
co
ls
.
2
.
4
.
3
.
Da
t
a
a
na
ly
s
is
ph
a
s
e
T
h
e
an
aly
s
is
o
f
d
ata
in
v
o
lv
ed
th
e
ap
p
licatio
n
o
f
b
o
th
d
escr
ip
tiv
e
an
d
in
f
er
e
n
tial
s
tatis
tical
m
eth
o
d
s
.
Descr
ip
tiv
e
s
tati
s
tics
,
s
p
ec
if
ically
th
e
m
ea
n
an
d
s
tan
d
ar
d
d
ev
iatio
n
,
wer
e
u
s
ed
to
d
ete
r
m
in
e
th
e
lev
els
o
f
m
ath
em
atics
in
ter
est,
m
ath
em
atics
ac
h
iev
em
en
t,
an
d
th
e
d
eg
r
ee
o
f
s
u
p
p
o
r
t
p
r
o
v
id
e
d
b
y
th
e
s
tu
d
en
ts
’
ed
u
ca
tio
n
al
ec
o
s
y
s
tem
in
clu
d
in
g
p
a
r
en
tal
in
v
o
lv
em
e
n
t,
p
e
er
in
f
lu
e
n
ce
,
a
n
d
s
ch
o
o
l
s
u
p
p
o
r
t.
Fo
r
in
f
er
en
tial
an
aly
s
is
,
p
ath
an
aly
s
is
u
s
in
g
SP
SS
A
MO
S
wa
s
em
p
lo
y
ed
t
o
in
v
esti
g
ate
b
o
th
th
e
d
ir
ec
t
an
d
in
d
ir
ec
t
e
f
f
ec
ts
am
o
n
g
t
h
e
s
tu
d
y
v
ar
iab
les.
T
h
e
o
v
er
all
m
o
d
el
f
it
was
ev
alu
ated
u
s
in
g
m
u
ltip
le
in
d
ices:
ch
i
-
s
q
u
ar
e
(
χ²
)
,
r
o
o
t
m
ea
n
s
q
u
ar
e
e
r
r
o
r
o
f
a
p
p
r
o
x
i
m
atio
n
(
R
MSE
A)
,
g
o
o
d
n
ess
-
of
-
f
it
in
d
e
x
(
GFI
)
,
ad
ju
s
ted
g
o
o
d
n
ess
-
of
-
f
it
in
d
ex
(
AGFI
)
,
co
m
p
ar
ativ
e
f
it
in
d
e
x
(
C
FI)
,
T
u
ck
er
–
L
ewis
in
d
ex
(
T
L
I
)
,
an
d
n
o
r
m
ed
f
it
in
d
ex
(
NFI
)
.
Acc
ep
tab
le
f
it
th
r
esh
o
ld
s
wer
e
estab
lis
h
ed
a
s
:
p
>0
.
0
5
f
o
r
th
e
χ²
test
,
R
M
SEA≤
0
.
0
8
,
an
d
v
alu
es
o
f
≥
0
.
9
0
f
o
r
GFI
,
AGFI
,
C
FI,
T
L
I
,
an
d
NFI
.
Mo
d
el
p
ar
s
im
o
n
y
was
f
u
r
th
e
r
ass
ess
ed
u
s
in
g
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s
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s
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th
at
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is
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with
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co
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f
id
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,
a
n
d
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to
eth
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r
esear
ch
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tan
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f
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f
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d
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’
m
a
th
em
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r
m
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.
3.
RE
SU
L
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S AN
D
D
I
SCU
SS
I
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3
.
1
.
L
ev
el
s
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f
pa
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e
nta
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i
nv
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lv
e
m
ent
,
pe
er
in
f
l
ue
nc
e,
s
c
ho
o
l
s
u
p
po
rt
,
m
a
t
h
em
a
t
i
cs
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nte
re
s
t
,
a
n
d
m
a
t
hem
a
t
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s
a
c
hi
ev
em
e
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T
ab
le
2
s
u
m
m
ar
izes
th
e
lev
els
o
f
p
ar
en
tal
in
v
o
lv
em
en
t,
p
ee
r
in
f
lu
en
ce
,
s
ch
o
o
l
s
u
p
p
o
r
t,
m
a
th
em
atics
in
ter
est,
an
d
m
ath
e
m
atics
ac
h
iev
em
en
t
am
o
n
g
t
h
e
2
5
1
r
e
s
p
o
n
d
en
ts
.
T
h
e
r
esu
lts
p
r
o
v
id
e
a
co
m
p
r
eh
en
s
iv
e
v
iew
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f
t
h
e
ed
u
ca
tio
n
al
ec
o
s
y
s
tem
th
at
s
h
ap
es
s
tu
d
en
ts
’
en
g
ag
e
m
en
t
a
n
d
p
er
f
o
r
m
an
ce
in
m
ath
e
m
atics.
I
n
ter
m
s
o
f
m
ath
em
atics
in
ter
est,
s
tu
d
en
ts
ex
h
ib
ited
a
h
ig
h
lev
el
(
M=
2
.
8
3
,
SD=0
.
4
5
)
.
T
h
i
s
s
u
g
g
ests
th
at
th
ey
g
en
er
ally
d
em
o
n
s
tr
ate
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th
u
s
iasm
an
d
cu
r
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s
ity
to
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le
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n
in
g
m
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em
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Hig
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icate
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th
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d
v
alu
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t
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ex
p
l
o
r
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g
m
ath
em
ati
ca
l
co
n
ce
p
ts
,
wh
ich
o
f
ten
tr
a
n
s
lates
to
s
u
s
tain
ed
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
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d
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c
,
Vo
l
.
15
,
No
.
2
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Ap
r
il
20
2
6
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0
3
7
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0
5
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ef
f
o
r
t
a
n
d
p
er
s
ev
er
an
ce
in
p
r
o
b
lem
-
s
o
lv
in
g
task
s
.
Su
ch
in
ter
est
is
ess
en
tial
f
o
r
m
ain
tain
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g
f
o
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u
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d
r
esil
ien
ce
wh
en
f
ac
ed
with
c
h
allen
g
in
g
to
p
ics [
3
1
]
.
W
ith
in
th
e
ed
u
ca
tio
n
al
ec
o
s
y
s
tem
,
th
e
th
r
ee
d
im
en
s
io
n
s
s
u
c
h
p
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r
in
f
lu
en
ce
,
p
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tal
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v
o
lv
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en
t,
an
d
s
ch
o
o
l
s
u
p
p
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r
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e
all
r
ated
as
h
i
g
h
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ef
lectin
g
a
s
u
p
p
o
r
tiv
e
s
o
cial
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d
lear
n
in
g
en
v
ir
o
n
m
e
n
t
f
o
r
s
tu
d
en
ts
.
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ec
if
ically
,
p
ee
r
in
f
lu
en
ce
o
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tain
e
d
a
m
ea
n
s
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r
e
o
f
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9
9
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3
5
,
in
d
ic
atin
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th
at
s
tu
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ce
iv
e
t
h
eir
class
m
ates
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d
f
r
ien
d
s
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p
o
s
itiv
e
co
n
tr
ib
u
to
r
s
to
th
eir
lear
n
in
g
p
r
o
ce
s
s
.
A
s
tr
o
n
g
p
ee
r
n
etwo
r
k
o
f
ten
f
o
s
ter
s
co
llab
o
r
atio
n
,
s
h
ar
ed
m
o
tiv
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n
,
a
n
d
c
o
n
s
tr
u
ctiv
e
co
m
p
etitio
n
,
all
o
f
wh
ich
ca
n
r
ein
f
o
r
ce
co
n
f
id
en
ce
an
d
e
n
g
ag
e
m
en
t
i
n
m
ath
e
m
atics
[
3
2
]
.
Similar
l
y
,
p
a
r
en
tal
i
n
v
o
lv
e
m
en
t
r
eg
is
ter
ed
a
h
ig
h
lev
e
l
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2
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9
9
,
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.
4
0
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T
h
is
f
in
d
in
g
i
m
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lies
th
at
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ar
e
n
ts
m
ain
tain
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tiv
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p
a
r
ticip
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n
in
th
eir
c
h
ild
r
en
’
s
ac
ad
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ic
d
ev
elo
p
m
en
t,
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et
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er
th
r
o
u
g
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en
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o
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r
ag
e
m
en
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g
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o
r
m
o
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ito
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r
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ess
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o
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s
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ten
t
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p
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r
o
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o
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ad
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ic
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ir
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tio
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,
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n
in
g
s
tu
d
en
ts
’
d
r
iv
e
to
p
er
f
o
r
m
well
[
3
3
]
.
Me
a
n
wh
ile,
s
ch
o
o
l
s
u
p
p
o
r
t
s
h
o
wed
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e
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est
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h
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e
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y
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ar
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les
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3
7
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ig
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ch
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id
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s
tr
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ctio
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r
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s
,
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d
ac
ad
em
ic
ass
is
tan
ce
p
lay
a
v
ital
r
o
le
in
s
u
s
tain
in
g
s
tu
d
en
ts
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m
o
tiv
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n
an
d
c
o
n
f
i
d
en
c
e.
A
s
tr
o
n
g
s
u
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tem
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o
m
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l
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m
o
tes
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ad
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co
m
p
eten
ce
an
d
em
o
tio
n
al
s
tab
ilit
y
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allo
win
g
s
tu
d
en
ts
to
th
r
iv
e
with
in
a
s
tr
u
ctu
r
ed
lear
n
in
g
en
v
ir
o
n
m
en
t [
3
4
]
.
R
eg
ar
d
in
g
m
ath
e
m
atics
ac
h
iev
em
en
t,
as
m
ea
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r
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d
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y
o
f
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icial
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ad
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ic
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ata,
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tu
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e
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ts
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o
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o
r
m
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n
ce
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1
.
8
2
,
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.
5
4
)
.
T
h
is
r
ef
lects
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g
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er
ally
ad
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u
ate
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r
a
s
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o
f
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atica
l
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n
ce
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ts
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d
s
k
ills
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th
o
u
g
h
o
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p
o
r
tu
n
ities
r
em
ain
f
o
r
f
u
r
t
h
er
en
h
an
ce
m
e
n
t
in
h
ig
h
er
-
o
r
d
er
r
ea
s
o
n
in
g
an
d
p
r
o
b
lem
-
s
o
lv
in
g
.
T
h
e
h
ig
h
l
ev
els
o
f
in
ter
est,
m
o
tiv
atio
n
,
an
d
ed
u
ca
tio
n
al
s
u
p
p
o
r
t
o
b
s
er
v
ed
am
o
n
g
th
e
p
ar
ticip
an
ts
m
ay
h
a
v
e
co
n
tr
ib
u
ted
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is
f
av
o
r
ab
le
p
er
f
o
r
m
an
ce
o
u
tco
m
e
[
3
5
]
,
[
3
6
]
.
Ov
er
all,
th
ese
f
in
d
in
g
s
r
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ea
l
th
at
s
tu
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en
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it
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r
o
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a
well
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r
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n
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e
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u
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tio
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s
ch
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ls
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T
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tr
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g
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ath
em
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ter
est
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itiv
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tem
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ter
ac
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s
ac
ad
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e
n
r
ich
m
en
t
s
tr
ateg
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p
ar
ticu
lar
ly
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o
s
e
th
at
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ee
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e
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ce
p
tu
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er
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ter
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aly
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k
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T
ab
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2
.
Par
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lv
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t
,
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ch
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l su
p
p
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r
t,
m
ath
em
atics in
ter
est,
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d
m
ath
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atics
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h
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t
V
a
r
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a
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t
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M
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3
H
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P
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9
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P
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9
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2
G
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Ta
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3
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2
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3
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t,
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n
d
m
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in
ter
est
in
p
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g
s
tu
d
e
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ts
’
m
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em
atics
ac
h
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em
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t.
T
h
e
r
esu
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d
em
o
n
s
tr
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th
at
t
h
e
m
o
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el
ac
h
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e
d
an
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n
t
f
it
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th
e
o
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s
er
v
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d
ata,
as
in
d
icate
d
b
y
th
e
ab
s
o
lu
te,
in
cr
em
e
n
tal,
an
d
p
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r
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im
o
n
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u
s
f
it
m
ea
s
u
r
es.
Acc
o
r
d
in
g
to
Go
r
etzk
o
et
a
l.
[
3
7
]
,
th
e
ass
ess
m
en
t
o
f
m
o
d
el
f
it
s
h
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ately
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2
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el’
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ap
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[
3
8
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3
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m
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’
s
ex
p
lan
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r
y
s
tr
en
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th
[
4
0
]
.
T
h
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in
d
ices
co
llectiv
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g
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at
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p
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Evaluation Warning : The document was created with Spire.PDF for Python.
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1043
Mo
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m
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lim
it
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f
5
[
4
1
]
.
T
h
is
s
u
g
g
ests
th
at
th
e
m
o
d
el
ac
h
iev
es
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o
p
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alan
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ess
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m
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lex
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C
o
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th
e
co
n
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g
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ce
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a
b
s
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te,
in
cr
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tal,
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f
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er
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f
th
e
u
n
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er
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ata
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alig
n
with
th
e
r
esu
lts
o
f
Z
u
lk
i
f
li
et
a
l.
[
4
2
]
wh
o
em
p
h
asized
th
at
ele
v
ated
v
alu
es
o
f
th
e
C
FI
an
d
T
L
I
in
d
icate
b
o
th
th
eo
r
etica
l so
u
n
d
n
ess
an
d
em
p
ir
ical
r
o
b
u
s
tn
ess
in
SEM
.
Ov
er
all,
th
e
g
o
o
d
n
ess
-
of
-
f
it
in
d
ices
af
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ir
m
th
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m
at
h
em
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o
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ce
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h
e
test
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ct
u
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n
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ath
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t
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y
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s
.
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el
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ied
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p
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i,
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r
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p
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t,
m
ath
em
atics
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ter
est,
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d
m
ath
em
atics
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h
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e
n
t.
M
o
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esti
m
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was
p
er
f
o
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m
ed
u
s
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g
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ax
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li
k
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esti
m
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ich
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ap
p
r
o
p
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iate
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iv
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n
th
e
s
am
p
le
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ize,
d
is
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ib
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tio
n
al
p
r
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p
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ties
o
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th
e
d
ata,
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d
t
h
e
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tin
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o
u
s
n
atu
r
e
o
f
th
e
o
b
s
er
v
ed
v
ar
ia
b
les.
T
ab
le
3
.
Fit
in
d
ices a
n
d
s
tatis
ti
ca
l m
ea
s
u
r
es o
f
th
e
s
tr
u
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m
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C
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t
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M
e
a
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A
c
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p
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M
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s
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>
0
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0
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0
.
2
9
2
R
M
S
EA
<
0
.
0
8
0
.
0
2
9
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F
I
>
0
.
9
0
0
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9
8
9
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n
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I
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0
.
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0
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6
6
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0
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9
0
0
.
9
8
9
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0
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0
0
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7
6
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>
0
.
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0
0
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9
4
3
P
a
r
si
mo
n
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o
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s f
i
t
2
/
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1
.
2
1
3
N
o
t
e
:
a
c
c
e
p
t
a
b
l
e
v
a
l
u
e
s
a
r
e
b
a
s
e
d
o
n
Zu
l
k
i
f
l
i
e
t
a
l
.
[
4
2
]
Fo
llo
win
g
esti
m
atio
n
,
th
e
m
o
d
el
was
s
u
b
jecte
d
to
a
co
m
p
r
eh
en
s
iv
e
ev
al
u
atio
n
u
s
in
g
m
u
ltip
le
g
o
o
d
n
ess
-
of
-
f
it
in
d
ices
en
co
m
p
ass
in
g
ab
s
o
lu
te,
i
n
cr
em
en
t
al,
an
d
p
ar
s
im
o
n
i
o
u
s
cr
iter
ia.
T
h
e
co
n
v
er
g
e
n
ce
o
f
th
ese
in
d
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with
in
r
ec
o
m
m
e
n
d
ed
th
r
esh
o
ld
s
in
d
icate
d
th
at
th
e
h
y
p
o
th
esized
m
o
d
el
a
d
eq
u
ately
r
e
p
r
esen
ted
th
e
em
p
ir
ical
d
ata.
C
o
n
s
eq
u
en
tly
,
n
o
p
o
s
t
h
o
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m
o
d
if
icat
io
n
s
,
s
u
ch
as
f
r
ee
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g
a
d
d
itio
n
al
p
ar
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eter
s
o
r
co
r
r
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g
er
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ter
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s
,
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e
in
tr
o
d
u
ce
d
,
as
s
u
ch
d
ata
-
d
r
iv
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ad
ju
s
tm
en
ts
m
ay
co
m
p
r
o
m
is
e
th
eo
r
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l
co
h
er
en
ce
a
n
d
in
f
late
m
o
d
el
f
it
ar
tific
ially
.
Alth
o
u
g
h
alter
n
ativ
e
n
ested
m
o
d
els
wer
e
co
n
ce
p
tu
ally
ex
am
in
e
d
,
th
e
h
y
p
o
th
esized
m
o
d
el
was
r
etain
ed
as
th
e
f
in
al
s
o
lu
tio
n
b
ec
au
s
e
it
ac
h
iev
ed
an
o
p
tim
al
b
alan
ce
b
etwe
en
p
ar
s
im
o
n
y
,
ex
p
lan
ato
r
y
p
o
we
r
,
an
d
t
h
eo
r
etica
l
p
lau
s
ib
ilit
y
.
T
h
is
s
y
s
tem
atic
an
d
tr
a
n
s
p
a
r
en
t
m
o
d
el
test
in
g
p
r
o
ce
s
s
s
tr
en
g
th
en
s
th
e
i
n
ter
n
al
v
alid
ity
o
f
th
e
f
i
n
d
in
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s
a
n
d
s
u
p
p
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ts
th
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r
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b
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s
tn
ess
o
f
th
e
in
f
er
r
e
d
s
tr
u
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r
al
r
elatio
n
s
h
ip
s
.
Me
an
wh
ile,
Fig
u
r
e
1
illu
s
tr
ates
th
e
b
est
-
f
itti
n
g
s
tr
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m
o
d
el
th
at
i
d
en
ti
f
ies
th
e
s
ig
n
if
ican
t
p
ath
way
s
am
o
n
g
f
iv
e
in
ter
r
ela
ted
v
ar
ia
b
les:
s
ch
o
o
l
s
u
p
p
o
r
t,
p
ee
r
in
f
lu
en
ce
,
p
ar
e
n
t
in
v
o
lv
e
m
en
t,
m
ath
e
m
atics
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ter
est,
an
d
m
ath
em
atics
ac
a
d
em
ic
p
er
f
o
r
m
a
n
ce
.
T
h
e
m
o
d
el
r
ev
ea
ls
h
o
w
b
o
t
h
in
s
titu
tio
n
al
an
d
s
o
cial
f
ac
to
r
s
jo
in
tly
co
n
tr
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u
te
to
s
tu
d
e
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ts
’
en
g
ag
em
e
n
t a
n
d
s
u
cc
ess
in
m
a
th
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atics.
3
.
3
.
P
a
t
h
a
na
ly
s
is
o
f
t
he
ex
o
g
eno
us
v
a
ria
bles
’
direct
a
nd
m
edia
t
ed
ef
f
ec
t
s
o
n t
he
endo
g
eno
us
co
ns
t
ruct
T
ab
le
4
p
r
esen
ts
th
e
d
ec
o
m
p
o
s
itio
n
o
f
ef
f
ec
ts
am
o
n
g
th
e
p
r
e
d
icto
r
co
n
s
tr
u
cts
s
u
ch
as
p
ee
r
in
f
lu
en
ce
,
s
ch
o
o
l
s
u
p
p
o
r
t,
a
n
d
th
e
m
e
d
i
atin
g
co
n
s
tr
u
ct
m
ath
em
atics
i
n
ter
est
an
d
t
h
e
o
u
tco
m
e
v
ar
i
ab
le,
m
ath
em
atics
ac
h
iev
em
en
t,
as
o
u
tlin
ed
in
t
h
e
f
in
al
s
tr
u
ctu
r
al
m
o
d
el.
T
h
e
an
aly
s
is
d
is
tin
g
u
is
h
es
b
etw
ee
n
d
ir
ec
t
ef
f
ec
ts
,
wh
ich
r
ep
r
esen
t
th
e
im
m
ed
iate
im
p
ac
t
o
f
o
n
e
v
ar
iab
le
o
n
an
o
th
er
,
an
d
in
d
ir
ec
t
ef
f
ec
ts
,
wh
ich
o
p
er
ate
th
r
o
u
g
h
m
ed
iatin
g
m
ec
h
a
n
is
m
s
s
u
ch
as
m
ath
em
atics
in
ter
est.
I
n
th
is
m
o
d
el,
m
ath
em
atics
in
ter
est
f
u
n
ctio
n
s
as
th
e
p
r
im
ar
y
m
ed
iato
r
tr
an
s
m
itti
n
g
p
ar
t
o
f
th
e
in
f
lu
en
ce
o
f
s
ch
o
o
l
s
u
p
p
o
r
t
t
o
ac
h
iev
e
m
en
t,
wh
e
r
ea
s
p
ee
r
in
f
l
u
en
ce
co
n
tr
ib
u
tes
o
n
ly
a
d
ir
ec
t
p
ath
way
.
T
h
is
p
r
o
v
id
es
a
co
m
p
r
e
h
en
s
iv
e
u
n
d
er
s
tan
d
i
n
g
o
f
h
o
w
s
tu
d
en
ts
’
p
er
s
o
n
al
d
is
p
o
s
itio
n
s
an
d
en
v
ir
o
n
m
e
n
ta
l su
p
p
o
r
ts
in
ter
ac
t to
s
h
a
p
e
th
e
ir
ac
ad
em
ic
o
u
tc
o
m
es in
m
ath
em
atics.
Sp
ec
if
ically
,
th
e
tab
le
h
ig
h
lig
h
ts
h
o
w
m
ath
em
atics
in
ter
est
s
er
v
es
as
an
i
n
ter
n
al
m
o
tiv
ati
o
n
al
d
r
iv
er
th
at
en
h
an
ce
s
e
n
g
ag
em
e
n
t,
p
er
s
is
ten
ce
,
an
d
c
o
g
n
itiv
e
p
r
o
ce
s
s
in
g
in
lear
n
i
n
g
.
L
ik
ew
is
e,
p
ee
r
in
f
lu
e
n
ce
co
n
tr
ib
u
tes
s
o
cially
an
d
em
o
tio
n
ally
b
y
f
o
s
ter
in
g
co
llab
o
r
atio
n
,
h
ea
lth
y
co
m
p
etitio
n
,
a
n
d
s
h
ar
ed
lear
n
in
g
ex
p
er
ien
ce
s
th
at
s
tr
en
g
th
e
n
ac
ad
em
ic
co
n
f
id
e
n
ce
.
Me
an
wh
il
e,
s
ch
o
o
l
s
u
p
p
o
r
t
ex
er
ts
a
d
u
a
l
in
f
lu
en
ce
d
ir
ec
tly
th
r
o
u
g
h
q
u
ality
in
s
tr
u
ctio
n
an
d
r
eso
u
r
ce
s
,
an
d
in
d
ir
ec
tl
y
b
y
p
r
o
m
o
tin
g
p
ar
e
n
tal
in
v
o
lv
em
en
t,
wh
ich
r
ein
f
o
r
ce
s
lear
n
i
n
g
b
e
h
av
io
r
s
an
d
m
o
tiv
atio
n
at
h
o
m
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
.
15
,
No
.
2
,
Ap
r
il
20
2
6
:
1
0
3
7
-
1
0
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1044
Fig
u
r
e
1
.
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est
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f
itti
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o
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ig
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at
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ab
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Dec
o
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o
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ts
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etwe
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o
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a
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b
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D
i
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t
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f
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t
(
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d
i
r
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β)
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t
a
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p
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v
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3
3
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P
e
e
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e
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t
0
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h
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6
S
c
h
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p
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Usi
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d
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b
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co
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f
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(
β
)
q
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tifie
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tio
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ip
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o
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itiv
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co
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in
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icate
f
ac
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ativ
e
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f
ec
ts
a
n
d
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eg
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o
n
es
d
e
n
o
te
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h
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ito
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y
in
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l
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.
I
n
t
h
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all
co
ef
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icien
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e
p
o
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itiv
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s
h
o
win
g
th
at
ea
ch
v
a
r
iab
le
co
n
s
tr
u
ctiv
ely
co
n
tr
ib
u
tes
to
m
ath
em
atics
ac
h
iev
em
en
t.
T
h
is
d
e
m
o
n
s
tr
at
es
th
at
m
o
tiv
ated
s
tu
d
en
ts
,
s
u
p
p
o
r
ted
b
y
p
ee
r
s
an
d
in
s
titu
tio
n
s
,
ar
e
m
o
r
e
lik
ely
to
p
er
f
o
r
m
b
etter
ac
ad
em
icall
y
.
Ov
e
r
a
ll
,
t
h
e
f
i
n
d
in
g
s
e
m
p
h
asi
ze
t
h
e
i
n
t
e
r
c
o
n
n
ec
t
ed
n
at
u
r
e
o
f
p
s
y
c
h
o
l
o
g
ic
al,
s
o
cial
,
a
n
d
s
tr
u
ct
u
r
al
f
a
ct
o
r
s
i
n
m
at
h
e
m
at
ics
l
ea
r
n
in
g
.
A
ch
ie
v
e
m
e
n
t
d
o
es
n
o
t
r
es
u
l
t
f
r
o
m
is
o
lat
e
d
in
f
l
u
e
n
ce
s
b
u
t
f
r
o
m
t
h
e
s
y
n
e
r
g
is
tic
in
t
er
ac
t
io
n
o
f
i
n
t
er
est
,
p
e
e
r
co
l
lab
o
r
a
ti
o
n
,
a
n
d
s
ch
o
o
l
-
b
ase
d
s
u
p
p
o
r
t
s
y
s
te
m
s
.
St
r
e
n
g
t
h
e
n
i
n
g
t
h
es
e
d
o
m
ai
n
s
ca
n
f
o
s
te
r
h
o
lis
tic
a
n
d
s
u
s
t
ai
n
a
b
l
e
i
m
p
r
o
v
e
m
e
n
ts
i
n
s
t
u
d
e
n
ts
’
m
at
h
e
m
at
ic
al
c
o
m
p
e
te
n
c
e
an
d
o
v
e
r
al
l s
u
c
ce
s
s
.
3
.
3
.
1
.
Dire
ct
ef
f
ec
t
o
f
m
a
t
hem
a
t
ics inte
re
s
t
o
n ma
t
hem
a
t
ics a
chiev
em
ent
Ma
th
em
atics
in
ter
est
d
em
o
n
s
tr
ated
a
s
tr
o
n
g
an
d
s
ig
n
i
f
ican
t
d
ir
ec
t
p
o
s
itiv
e
ef
f
ec
t
o
n
m
a
th
em
atics
ac
h
iev
em
en
t
(
β=0
.
3
3
9
,
p
=
0
.
0
2
1
)
.
T
h
is
f
in
d
in
g
i
n
d
icate
s
th
at
s
tu
d
en
ts
wh
o
d
is
p
lay
g
en
u
in
e
cu
r
i
o
s
ity
,
en
jo
y
m
en
t,
an
d
en
t
h
u
s
iasm
to
war
d
m
ath
em
atics
ten
d
to
ac
h
iev
e
h
ig
h
er
ac
a
d
em
ic
o
u
tco
m
es.
A
h
ig
h
lev
el
o
f
in
ter
est
en
co
u
r
ag
es
d
ee
p
er
en
g
ag
em
e
n
t,
p
er
s
is
ten
ce
in
lear
n
in
g
,
an
d
in
tr
in
s
ic
m
o
ti
v
atio
n
f
ac
to
r
s
th
at
co
n
tr
ib
u
te
to
en
h
a
n
ce
d
p
r
o
b
le
m
-
s
o
lv
in
g
s
k
ills
an
d
c
o
n
ce
p
t
u
al
u
n
d
e
r
s
tan
d
in
g
.
Stu
d
e
n
ts
wh
o
f
in
d
m
at
h
em
atics
en
jo
y
ab
le
ar
e
also
m
o
r
e
lik
ely
to
in
v
est
ef
f
o
r
t,
e
x
p
lo
r
e
ch
a
llen
g
in
g
p
r
o
b
lem
s
,
a
n
d
s
u
s
tain
f
o
cu
s
e
v
en
in
t
h
e
f
ac
e
o
f
d
i
f
f
icu
lty
[
4
3
]
.
T
h
is
r
esu
lt
r
ein
f
o
r
ce
s
p
r
ev
io
u
s
r
esear
ch
s
u
g
g
esti
n
g
th
at
v
al
u
in
g
an
d
e
n
jo
y
in
g
m
ath
em
atics
p
r
o
m
o
tes
r
esil
ien
ce
,
cr
ea
tiv
ity
,
an
d
lo
n
g
-
te
r
m
ac
ad
em
ic
s
u
cc
ess
[
4
4
]
.
Hen
ce
,
cu
ltiv
atin
g
s
tu
d
en
ts
’
in
ter
est
in
m
ath
em
atics
is
f
u
n
d
am
en
tal
n
o
t
o
n
ly
f
o
r
b
o
o
s
tin
g
p
er
f
o
r
m
an
ce
b
u
t
also
f
o
r
n
u
r
tu
r
in
g
life
lo
n
g
ap
p
r
ec
iatio
n
a
n
d
co
n
f
id
en
ce
in
th
e
s
u
b
ject.
3
.
3
.
2
.
Dire
ct
ef
f
ec
t
o
f
peer
in
f
luence
o
n m
a
t
hem
a
t
ics a
chiev
em
ent
Peer
in
f
lu
en
ce
ex
h
ib
ited
a
s
ig
n
if
ican
t
d
ir
ec
t
p
o
s
itiv
e
ef
f
ec
t
o
n
m
ath
em
atics
ac
h
iev
em
en
t
(
β=0
.
1
8
7
,
p=
0
.
0
4
1
)
.
T
h
is
s
u
g
g
ests
th
at
s
tu
d
en
ts
wh
o
in
ter
ac
t
with
ac
ad
em
ically
m
o
tiv
ated
p
ee
r
s
ten
d
to
ad
o
p
t
p
r
o
d
u
ctiv
e
s
tu
d
y
h
ab
its
,
h
ig
h
er
m
o
tiv
atio
n
,
an
d
g
r
ea
ter
c
o
n
f
id
en
ce
in
th
eir
m
at
h
em
atica
l
ab
ilit
ies.
Po
s
itiv
e
p
ee
r
in
ter
ac
tio
n
s
o
f
te
n
lead
t
o
co
llab
o
r
ativ
e
lear
n
in
g
e
x
p
e
r
ien
ce
s
,
wh
er
e
s
tu
d
en
ts
ex
ch
an
g
e
id
ea
s
,
clar
if
y
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
B
ey
o
n
d
n
u
mb
ers
:
a
p
a
th
a
n
a
ly
s
is
o
n
h
o
w
ed
u
ca
tio
n
a
l e
co
s
ystem
a
n
d
ma
th
…
(
C
h
a
r
ma
ig
n
e
A
.
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s
la
b
r
a
)
1045
m
is
co
n
ce
p
tio
n
s
,
an
d
s
u
p
p
o
r
t
o
n
e
an
o
th
e
r
’
s
ac
ad
em
ic
g
o
a
ls
[
4
5
]
.
Su
ch
s
o
cial
d
y
n
am
ic
s
r
ed
u
ce
lear
n
in
g
-
r
elate
d
an
x
iety
,
e
n
h
an
ce
s
elf
-
ef
f
icac
y
,
a
n
d
f
o
s
ter
a
s
en
s
e
o
f
b
elo
n
g
in
g
i
n
th
e
class
r
o
o
m
.
T
h
ese
f
in
d
in
g
s
em
p
h
asize
th
e
v
alu
e
o
f
p
ee
r
s
u
p
p
o
r
t
s
y
s
tem
s
an
d
g
r
o
u
p
-
b
ased
lear
n
in
g
s
tr
ateg
ies
in
en
h
an
cin
g
b
o
th
ac
ad
em
ic
an
d
em
o
tio
n
al
asp
ec
ts
o
f
m
at
h
em
atics
lear
n
in
g
[
4
6
]
.
T
h
er
e
f
o
r
e,
p
r
o
m
o
ti
n
g
p
o
s
itiv
e
p
ee
r
en
v
ir
o
n
m
en
ts
ca
n
s
er
v
e
as a
p
o
wer
f
u
l m
ec
h
an
is
m
f
o
r
im
p
r
o
v
in
g
s
tu
d
e
n
ts
’
m
at
h
em
atics p
er
f
o
r
m
an
ce
.
3
.
3
.
3
.
Dire
ct
ef
f
ec
t
o
f
s
cho
o
l
s
up
po
rt
o
n pa
re
nta
l inv
o
lv
em
ent
Sch
o
o
l
s
u
p
p
o
r
t
d
em
o
n
s
tr
ated
a
s
ig
n
if
ican
t
p
o
s
itiv
e
d
ir
ec
t
ef
f
ec
t
o
n
p
ar
en
tal
in
v
o
lv
em
e
n
t
(
β=0
.
2
2
1
,
p=
0
.
0
2
6
)
.
T
h
is
in
d
icate
s
th
at
wh
en
s
ch
o
o
ls
m
ain
tain
o
p
e
n
co
m
m
u
n
icatio
n
,
t
r
an
s
p
ar
en
cy
,
an
d
in
clu
s
iv
ity
,
p
ar
en
ts
ar
e
m
o
r
e
lik
ely
to
en
g
ag
e
ac
tiv
ely
in
th
eir
ch
ild
r
e
n
’
s
ed
u
ca
tio
n
al
d
ev
elo
p
m
en
t.
I
n
itiativ
es
s
u
ch
a
s
r
eg
u
lar
teac
h
er
-
p
a
r
en
t
co
n
s
u
ltatio
n
s
,
p
r
o
g
r
ess
u
p
d
ates,
a
n
d
p
ar
ticip
ato
r
y
s
ch
o
o
l
p
r
o
g
r
am
s
s
tr
en
g
th
en
p
ar
en
ts
’
s
en
s
e
o
f
co
llab
o
r
atio
n
an
d
ac
co
u
n
tab
ilit
y
[
4
7
]
.
Su
ch
p
a
r
tn
er
s
h
ip
s
en
ab
le
p
ar
e
n
ts
to
p
r
o
v
id
e
c
o
n
s
is
ten
t
g
u
id
an
ce
an
d
en
co
u
r
ag
em
e
n
t
at
h
o
m
e,
r
ein
f
o
r
cin
g
s
tu
d
en
ts
’
lear
n
in
g
ex
p
e
r
ien
ce
s
.
T
h
is
f
in
d
in
g
h
ig
h
lig
h
ts
th
e
im
p
o
r
tan
ce
o
f
in
s
titu
tio
n
al
e
f
f
o
r
ts
in
b
u
ild
in
g
s
tr
o
n
g
h
o
m
e
–
s
ch
o
o
l
co
n
n
ec
tio
n
s
th
at
cr
ea
te
a
s
u
p
p
o
r
tiv
e
ec
o
s
y
s
tem
f
o
r
s
tu
d
e
n
t
s
u
cc
ess
[
4
8
]
.
W
h
en
s
ch
o
o
ls
ef
f
ec
tiv
ely
en
g
ag
e
p
ar
e
n
ts
as
ed
u
ca
ti
o
n
al
p
ar
t
n
er
s
,
th
ey
am
p
lify
b
o
th
ac
ad
em
ic
an
d
s
o
cio
-
em
o
tio
n
al
b
en
ef
its
f
o
r
s
tu
d
en
ts
.
3
.
3
.
4
.
Dire
ct
a
nd
ind
irec
t
ef
f
ec
t
s
o
f
s
cho
o
l su
pp
o
rt
o
n m
a
t
hem
a
t
ics a
chiev
em
ent
Sch
o
o
l
s
u
p
p
o
r
t
e
x
h
ib
ited
b
o
t
h
d
ir
ec
t
a
n
d
i
n
d
ir
ec
t
p
o
s
itiv
e
ef
f
ec
ts
o
n
m
ath
em
atics
ac
h
iev
em
en
t.
T
h
e
d
ir
ec
t
ef
f
ec
t
(
β=0
.
1
4
7
,
p
=
0
.
0
3
9
)
i
n
d
icate
s
th
at
a
s
u
p
p
o
r
tiv
e
s
ch
o
o
l
e
n
v
ir
o
n
m
en
t
ch
ar
ac
ter
ized
b
y
ef
f
ec
tiv
e
teac
h
in
g
,
ad
e
q
u
ate
le
ar
n
in
g
f
ac
ilit
ies,
an
d
co
n
s
is
ten
t
ac
ad
em
ic
g
u
id
an
ce
d
ir
ec
tly
en
h
an
ce
s
s
tu
d
en
ts
’
p
er
f
o
r
m
an
ce
in
m
ath
e
m
atics.
I
n
ad
d
itio
n
to
t
h
is
,
s
ch
o
o
l
s
u
p
p
o
r
t
also
d
em
o
n
s
tr
ated
an
in
d
ir
ec
t
ef
f
ec
t
(
β=0
.
0
8
4
)
th
r
o
u
g
h
m
ath
e
m
atics
in
ter
est,
h
ig
h
lig
h
tin
g
th
e
m
ed
iatin
g
r
o
le
o
f
s
tu
d
e
n
ts
’
in
tr
in
s
ic
en
g
ag
em
en
t
with
th
e
s
u
b
ject.
W
h
en
s
ch
o
o
ls
p
r
o
v
id
e
s
tim
u
latin
g
in
s
tr
u
c
tio
n
al
p
r
ac
tices
an
d
cr
ea
te
en
co
u
r
ag
in
g
lear
n
in
g
co
n
d
itio
n
s
,
th
e
y
cu
ltiv
ate
s
tu
d
en
ts
’
cu
r
io
s
ity
an
d
en
jo
y
m
e
n
t
in
m
ath
em
atics
[
4
9
]
.
T
h
is
h
eig
h
ten
ed
in
ter
est
s
u
b
s
eq
u
en
tly
p
r
o
m
o
tes
g
r
ea
te
r
ef
f
o
r
t,
p
er
s
is
ten
ce
,
an
d
p
o
s
itiv
e
attitu
d
es
to
war
d
lear
n
in
g
,
wh
ich
tr
an
s
late
in
t
o
im
p
r
o
v
e
d
ac
h
iev
em
en
t.
T
h
e
to
tal
ef
f
ec
t
(
β=0
.
2
3
1
)
th
er
e
f
o
r
e
u
n
d
er
s
co
r
es
th
e
d
u
al
in
f
l
u
en
ce
o
f
s
ch
o
o
l
s
u
p
p
o
r
t,
b
o
th
in
d
ir
ec
tly
im
p
r
o
v
in
g
p
er
f
o
r
m
an
ce
an
d
i
n
d
ir
ec
tly
e
n
h
an
cin
g
it th
r
o
u
g
h
i
n
cr
ea
s
ed
m
ath
em
atica
l in
ter
est.
T
h
e
s
tr
o
n
g
er
in
f
lu
en
ce
o
f
s
ch
o
o
l
s
u
p
p
o
r
t
r
elativ
e
to
p
ee
r
d
y
n
am
ics
ca
n
b
e
u
n
d
e
r
s
to
o
d
with
in
th
e
d
is
tin
ctiv
e
in
s
titu
tio
n
al
co
n
tex
t
o
f
PS
HS
–
W
V
C
a
s
an
eli
te,
r
esid
en
tial
STE
M
s
ch
o
o
l.
I
n
s
u
ch
s
ettin
g
s
,
ac
ad
em
ic
s
tr
u
ctu
r
es,
cu
r
r
icu
l
ar
r
ig
o
r
,
an
d
in
s
titu
tio
n
al
ex
p
ec
tatio
n
s
ar
e
h
ig
h
ly
s
tan
d
a
r
d
ized
an
d
d
ee
p
l
y
em
b
ed
d
e
d
in
s
tu
d
en
ts
’
d
aily
r
o
u
tin
es.
T
ea
ch
in
g
q
u
ality
,
ass
ess
m
en
t
p
r
ac
tices,
ac
ce
s
s
to
l
ea
r
n
in
g
r
eso
u
r
ce
s
,
an
d
s
tr
u
ctu
r
ed
ac
a
d
em
ic
s
u
p
p
o
r
t
s
y
s
tem
s
ex
er
t
co
n
tin
u
o
u
s
an
d
f
o
r
m
al
in
f
l
u
en
ce
o
n
lear
n
er
s
’
ac
ad
em
ic
b
eh
av
io
r
s
,
o
f
ten
s
u
r
p
ass
in
g
th
e
v
ar
iab
ilit
y
o
f
p
ee
r
ef
f
ec
ts
[
5
0
]
.
Un
lik
e
in
c
o
n
v
e
n
tio
n
al
s
ch
o
o
ls
wh
er
e
p
ee
r
g
r
o
u
p
s
m
ay
s
ig
n
if
ican
tly
s
h
ap
e
ac
ad
em
ic
n
o
r
m
s
,
PS
HS
s
ch
o
lar
s
ar
e
im
m
er
s
ed
in
an
en
v
ir
o
n
m
en
t
wh
er
e
ac
ad
em
ic
ex
ce
llen
ce
is
in
s
titu
tio
n
ally
r
ein
f
o
r
ce
d
th
r
o
u
g
h
s
tr
u
ctu
r
ed
s
ch
ed
u
les,
clo
s
e
teac
h
er
m
o
n
ito
r
i
n
g
,
a
n
d
ex
p
licit
p
er
f
o
r
m
an
ce
ex
p
ec
ta
tio
n
s
.
C
o
n
s
eq
u
en
tly
,
in
s
titu
tio
n
al
s
u
p
p
o
r
t
m
ec
h
an
is
m
s
b
e
co
m
e
th
e
d
o
m
i
n
an
t
d
r
iv
er
s
o
f
a
ch
iev
em
e
n
t,
s
h
ap
in
g
n
o
t o
n
ly
wh
at
s
tu
d
e
n
ts
lear
n
b
u
t a
ls
o
h
o
w
th
e
y
ap
p
r
o
ac
h
le
ar
n
in
g
task
s
.
Mo
r
eo
v
er
,
th
e
r
esid
en
tial
n
at
u
r
e
o
f
PS
HS
–
W
VC
f
u
r
th
er
am
p
lifie
s
th
e
r
o
le
o
f
i
n
s
titu
tio
n
al
s
u
p
p
o
r
t.
Stu
d
en
ts
’
ac
ad
em
ic,
s
o
cial,
an
d
p
e
r
s
o
n
al
ex
p
er
ien
ce
s
o
c
cu
r
lar
g
el
y
with
in
th
e
s
am
e
s
ch
o
o
l
ec
o
s
y
s
tem
,
b
lu
r
r
in
g
th
e
b
o
u
n
d
ar
ies b
etwe
en
class
r
o
o
m
in
s
tr
u
ctio
n
a
n
d
i
n
f
o
r
m
al
lear
n
in
g
s
p
ac
es.
Facu
l
ty
g
u
id
an
ce
,
ac
ce
s
s
to
ac
ad
em
ic
f
ac
ilit
ies,
an
d
s
ch
o
o
l
-
o
r
g
an
ized
lear
n
in
g
s
u
p
p
o
r
ts
ar
e
co
n
s
is
ten
tly
p
r
esen
t
ac
r
o
s
s
b
o
th
f
o
r
m
al
a
n
d
in
f
o
r
m
al
co
n
tex
ts
,
r
ein
f
o
r
ci
n
g
lear
n
in
g
b
eh
a
v
io
r
s
b
ey
o
n
d
p
ee
r
-
d
r
iv
e
n
in
ter
ac
tio
n
s
[
5
1
]
.
W
h
ile
p
ee
r
s
r
em
ain
im
p
o
r
tan
t
as
co
llab
o
r
at
o
r
s
an
d
s
o
u
r
ce
s
o
f
m
o
tiv
atio
n
,
th
eir
in
f
lu
en
ce
m
ay
b
e
m
o
r
e
h
o
m
o
g
en
eo
u
s
in
an
elite
en
v
ir
o
n
m
en
t
wh
er
e
s
tu
d
en
ts
alr
ea
d
y
s
h
ar
e
h
ig
h
ac
ad
e
m
ic
o
r
ien
tatio
n
an
d
s
im
ilar
ac
h
ie
v
em
en
t
g
o
als
[
5
2
]
.
As
a
r
esu
lt,
p
ee
r
ef
f
ec
ts
m
ay
e
x
h
ib
it
less
v
ar
iab
ilit
y
an
d
wea
k
er
p
r
e
d
ictiv
e
p
o
wer
c
o
m
p
ar
e
d
to
th
e
s
tr
u
ctu
r
e
d
,
s
u
s
tain
ed
,
an
d
s
y
s
tem
-
wid
e
in
f
lu
en
ce
o
f
s
ch
o
o
l su
p
p
o
r
t.
3
.
3
.
5
.
Dire
ct
ef
f
ec
t
o
f
s
cho
o
l
s
up
po
rt
o
n m
a
t
hem
a
t
ics inte
re
s
t
Fin
ally
,
s
ch
o
o
l
s
u
p
p
o
r
t
d
em
o
n
s
tr
ated
a
s
tr
o
n
g
an
d
s
tatis
tic
ally
s
ig
n
if
ican
t
d
ir
ec
t
p
o
s
itiv
e
ef
f
ec
t
o
n
m
ath
em
atics
in
ter
est
(
β=0
.
2
4
7
,
p
=
0
.
0
1
3
)
.
T
h
is
f
in
d
i
n
g
s
u
g
g
ests
th
at
a
s
u
p
p
o
r
tiv
e
an
d
well
-
o
r
g
a
n
ized
ac
ad
em
ic
en
v
ir
o
n
m
en
t
ch
ar
a
cter
ized
b
y
co
m
p
eten
t
teac
h
er
s
,
en
g
ag
in
g
in
s
tr
u
ctio
n
al
p
r
ac
tices,
ac
ce
s
s
ib
le
lear
n
in
g
r
eso
u
r
ce
s
,
a
n
d
c
o
n
ti
n
u
o
u
s
e
n
co
u
r
ag
em
en
t
p
lay
s
a
p
iv
o
tal
r
o
le
in
f
o
s
ter
in
g
s
tu
d
en
ts
’
cu
r
io
s
ity
a
n
d
en
th
u
s
iasm
f
o
r
m
ath
em
atics.
A
p
o
s
itiv
e
an
d
n
u
r
tu
r
in
g
s
ch
o
o
l
clim
ate
n
o
t
o
n
ly
p
r
o
v
i
d
es
em
o
tio
n
al
s
ec
u
r
ity
b
u
t
also
p
r
o
m
o
tes
in
tellectu
al
en
g
ag
em
e
n
t,
h
elp
in
g
s
h
if
t
s
tu
d
en
ts
’
p
er
ce
p
tio
n
s
o
f
m
at
h
em
atics
f
r
o
m
a
s
o
u
r
ce
o
f
an
x
iety
t
o
o
n
e
o
f
en
jo
y
m
e
n
t
an
d
in
tellectu
al
g
r
o
wth
[
5
3
]
.
W
h
en
lear
n
er
s
f
ee
l
v
alu
e
d
an
d
s
u
p
p
o
r
ted
,
th
e
y
ar
e
m
o
r
e
in
clin
ed
to
p
ar
ticip
at
e
ac
tiv
ely
,
ap
p
r
o
ac
h
m
ath
em
a
tical
task
s
with
co
n
f
id
en
ce
,
an
d
s
u
s
tain
a
d
ee
p
er
in
ter
est
in
th
e
s
u
b
ject
[
5
4
]
.
Hen
ce
,
cu
ltiv
atin
g
s
ch
o
o
l
en
v
ir
o
n
m
e
n
ts
th
at
s
tim
u
late
cu
r
io
s
ity
an
d
r
ein
f
o
r
ce
p
o
s
itiv
e
attitu
d
es
to
war
d
lear
n
in
g
is
v
ital
f
o
r
e
n
h
an
ci
n
g
b
o
th
im
m
ed
iate
ac
ad
em
ic
p
er
f
o
r
m
an
ce
an
d
l
o
n
g
-
ter
m
m
ath
em
atica
l p
r
o
f
icien
c
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
2
5
2
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8
8
2
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t
J
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v
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&
R
es E
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c
,
Vo
l
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15
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No
.
2
,
Ap
r
il
20
2
6
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1
0
3
7
-
1
0
5
0
1046
Hig
h
-
q
u
ality
in
s
tr
u
ctio
n
,
ca
r
ef
u
lly
s
ca
f
f
o
ld
ed
lear
n
in
g
ex
p
er
ien
ce
s
,
a
n
d
co
n
s
is
ten
t
ac
ad
em
ic
f
ee
d
b
ac
k
p
o
s
itio
n
th
e
in
s
titu
tio
n
as
th
e
p
r
im
ar
y
s
o
u
r
ce
o
f
in
tellectu
al
s
tim
u
latio
n
,
s
h
ap
in
g
s
tu
d
en
ts
’
cu
r
io
s
ity
an
d
en
g
ag
em
e
n
t
m
o
r
e
p
o
wer
f
u
lly
th
an
in
f
o
r
m
al
p
ee
r
in
te
r
ac
tio
n
s
.
B
ec
au
s
e
th
e
s
ch
o
o
l
cu
ltu
r
e
e
x
p
licitly
em
p
h
asizes
ac
ad
em
ic
e
x
ce
llen
ce
an
d
d
ee
p
c
o
g
n
itiv
e
en
g
a
g
em
en
t,
in
s
titu
tio
n
al
i
n
f
lu
en
ce
s
r
em
ain
s
tab
le
an
d
h
ig
h
ly
s
alien
t
in
s
tu
d
en
ts
’
lear
n
in
g
ex
p
er
ien
ce
s
[
5
5
]
.
M
o
r
eo
v
e
r
,
th
e
r
elativ
ely
h
o
m
o
g
en
eo
u
s
ac
ad
em
ic
o
r
ien
tatio
n
o
f
PS
HS
s
ch
o
lar
s
r
ed
u
ce
s
th
e
d
is
tin
ct
im
p
ac
t
o
f
p
ee
r
in
f
lu
en
ce
,
as
p
ee
r
s
lar
g
el
y
r
ein
f
o
r
ce
alr
ea
d
y
estab
lis
h
ed
ac
h
iev
em
en
t
-
d
r
iv
e
n
n
o
r
m
s
r
at
h
er
th
an
in
tr
o
d
u
ci
n
g
n
ew
m
o
tiv
atio
n
al
d
ir
ec
tio
n
s
[
5
6
]
.
C
o
m
b
in
ed
with
th
e
r
esid
en
tial
n
atu
r
e
o
f
th
e
s
ch
o
o
l,
wh
er
e
lear
n
e
r
s
ar
e
co
n
tin
u
o
u
s
ly
im
m
er
s
ed
in
in
s
titu
tio
n
-
led
ac
ad
em
ic
p
r
ac
tices
an
d
ex
p
ec
tatio
n
s
,
s
ch
o
o
l
s
u
p
p
o
r
t
b
ec
o
m
es
th
e
d
o
m
in
an
t
f
o
r
ce
in
n
u
r
t
u
r
in
g
m
ath
em
atics
in
ter
est
[
5
7
]
.
T
h
u
s
,
in
th
is
elite
STE
M
-
f
o
cu
s
ed
co
n
tex
t,
th
e
in
s
titu
tio
n
al
en
v
ir
o
n
m
en
t
s
er
v
es
as
th
e
ce
n
tr
al
ca
taly
s
t f
o
r
s
u
s
tain
in
g
s
tu
d
en
t
s
’
en
th
u
s
iasm
an
d
lo
n
g
-
ter
m
c
o
m
m
itm
en
t to
m
at
h
em
atics.
4.
CO
NCLU
SI
O
N
T
h
is
s
tu
d
y
d
em
o
n
s
tr
ates
th
at
m
ath
em
atics
ac
h
iev
em
en
t
am
o
n
g
PS
HS
–
W
VC
s
ch
o
lar
s
is
s
h
ap
ed
b
y
a
n
etwo
r
k
o
f
i
n
ter
co
n
n
ec
ted
f
ac
to
r
s
,
with
m
at
h
em
atics
in
ter
est
an
d
s
ch
o
o
l
s
u
p
p
o
r
t
em
e
r
g
i
n
g
as
th
e
s
tr
o
n
g
est
p
r
ed
icto
r
s
th
r
o
u
g
h
b
o
th
d
ir
e
ct
an
d
in
d
ir
ec
t
p
ath
way
s
.
Peer
in
f
lu
en
ce
an
d
p
ar
en
tal
in
v
o
lv
em
e
n
t
f
u
r
th
e
r
r
ein
f
o
r
ce
th
ese
ef
f
ec
ts
b
y
s
tr
en
g
th
en
i
n
g
m
o
tiv
atio
n
,
d
is
cip
lin
e,
an
d
ac
ad
em
ic
p
er
s
is
ten
ce
.
T
h
e
f
in
d
in
g
s
ad
d
r
ess
th
e
r
esear
ch
o
b
jectiv
es
b
y
c
o
n
f
ir
m
i
n
g
th
at
ac
h
ie
v
em
en
t
in
m
ath
em
atics
is
n
o
t
d
r
iv
en
b
y
co
g
n
itiv
e
ab
ilit
y
alo
n
e,
b
u
t
b
y
th
e
in
te
r
ac
tio
n
o
f
p
er
s
o
n
al
en
g
a
g
em
en
t
an
d
s
u
p
p
o
r
tiv
e
s
o
cial
–
in
s
titu
tio
n
al
co
n
tex
ts
.
I
n
th
e
r
esid
en
tial
PS
HS
s
etti
n
g
,
wh
er
e
ac
a
d
em
ic
life
,
p
ee
r
in
ter
ac
tio
n
,
a
n
d
s
ch
o
o
l
s
tr
u
ctu
r
es
ar
e
clo
s
ely
in
teg
r
ated
,
th
ese
in
f
lu
en
ce
s
a
r
e
in
ten
s
if
ied
,
h
ig
h
lig
h
tin
g
th
e
cr
itical
r
o
le
o
f
an
en
v
ir
o
n
m
en
t
th
at
n
u
r
tu
r
es
cu
r
io
s
ity
,
co
llab
o
r
atio
n
,
a
n
d
s
u
s
tain
ed
en
g
ag
e
m
en
t
in
m
at
h
e
m
atics.
T
h
e
r
esu
lts
u
n
d
er
s
co
r
e
th
e
s
ig
n
if
ican
ce
o
f
cu
ltiv
atin
g
in
ter
est
-
d
r
iv
en
le
ar
n
in
g
an
d
r
o
b
u
s
t
s
ch
o
o
l
s
u
p
p
o
r
t
s
y
s
tem
s
as
k
ey
lev
er
s
f
o
r
im
p
r
o
v
in
g
m
ath
em
atica
l p
er
f
o
r
m
an
ce
.
T
h
e
s
tu
d
y
is
lim
ited
b
y
its
f
o
cu
s
o
n
a
s
in
g
le
PS
H
S
ca
m
p
u
s
an
d
r
elian
ce
o
n
s
elf
-
r
ep
o
r
ted
m
ea
s
u
r
es,
wh
ich
m
ay
a
f
f
ec
t
g
e
n
er
aliza
b
ilit
y
an
d
in
t
r
o
d
u
ce
r
esp
o
n
s
e
b
ias.
No
n
eth
eless
,
th
e
f
in
d
i
n
g
s
h
av
e
im
p
o
r
ta
n
t
im
p
licatio
n
s
f
o
r
p
o
licy
a
n
d
p
r
ac
tice,
s
u
g
g
esti
n
g
th
at
STE
M
s
ch
o
o
ls
s
h
o
u
ld
p
r
io
r
itize
h
o
li
s
tic
s
tr
ateg
ies
th
at
in
teg
r
ate
in
ter
est
-
b
ased
p
ed
ag
o
g
ies,
p
ee
r
-
s
u
p
p
o
r
ted
lear
n
in
g
cu
ltu
r
es,
an
d
s
tr
o
n
g
h
o
m
e
–
s
ch
o
o
l
p
ar
tn
er
s
h
ip
s
.
Fo
r
PS
HS
s
p
ec
if
ically
,
in
ter
est
-
b
ased
p
ed
ag
o
g
ies
m
ay
in
clu
d
e
p
r
o
b
lem
-
b
ased
lea
r
n
in
g
a
n
ch
o
r
ed
o
n
r
ea
l
-
wo
r
ld
STE
M
ch
allen
g
es,
r
esear
ch
-
d
r
iv
en
m
ath
em
atics
p
r
o
jects
alig
n
ed
with
s
cien
c
e
an
d
en
g
i
n
ee
r
in
g
ap
p
licatio
n
s
,
m
ath
m
o
d
elin
g
t
ask
s
co
n
n
ec
ted
t
o
n
atio
n
al
d
e
v
elo
p
m
en
t
is
s
u
es,
an
d
en
r
ich
m
en
t
ac
tiv
ities
s
u
ch
as
m
ath
cir
cles
o
r
Oly
m
p
iad
-
s
ty
le
co
llab
o
r
ativ
e
p
r
o
b
lem
s
o
lv
in
g
.
Fu
t
u
r
e
r
esear
ch
m
a
y
ex
t
en
d
th
is
s
tr
u
ctu
r
al
m
o
d
el
to
o
th
e
r
PS
HS
ca
m
p
u
s
es
o
r
STE
M
-
o
r
ien
ted
s
ch
o
o
ls
,
em
p
lo
y
lo
n
g
itu
d
in
al
d
esig
n
s
to
tr
ac
k
ch
an
g
es
in
in
ter
est
an
d
ac
h
iev
em
e
n
t
o
v
er
tim
e,
an
d
ex
p
er
im
en
tally
test
th
e
lo
n
g
-
ter
m
im
p
ac
t
o
f
PS
HS
-
alig
n
ed
in
ter
est
-
b
ased
p
ed
ag
o
g
ies.
Su
ch
s
tu
d
ie
s
wo
u
ld
f
u
r
t
h
er
s
tr
en
g
th
en
ev
i
d
en
ce
-
b
ased
i
n
ter
v
en
tio
n
s
th
at
s
u
p
p
o
r
t
s
u
s
tain
e
d
ex
ce
llen
ce
in
m
ath
em
atics with
in
r
esid
en
tial ST
E
M
lear
n
in
g
en
v
ir
o
n
m
en
ts
.
ACK
NO
WL
E
DG
M
E
N
T
T
h
e
r
esear
ch
e
r
s
wh
o
leh
ea
r
ted
ly
ex
ten
d
th
eir
d
ee
p
est
g
r
atit
u
d
e
to
th
e
Dep
ar
tm
en
t
o
f
Scien
ce
an
d
T
ec
h
n
o
lo
g
y
–
Scien
ce
E
d
u
ca
t
io
n
I
n
s
titu
te
(
DOST
–
SEI
)
f
o
r
its
g
en
er
o
u
s
f
in
an
cial
ass
is
tan
ce
an
d
s
ch
o
lar
s
h
ip
s
u
p
p
o
r
t,
wh
ich
m
ad
e
t
h
e
co
m
p
letio
n
o
f
th
is
s
tu
d
y
p
o
s
s
ib
le.
Sin
ce
r
e
a
p
p
r
ec
iatio
n
is
also
g
iv
en
to
W
est
Vis
ay
as
State
Un
iv
er
s
ity
f
o
r
its
v
alu
ab
le
c
o
llab
o
r
atio
n
,
g
u
id
an
ce
,
an
d
e
n
d
o
r
s
em
e
n
t
th
r
o
u
g
h
o
u
t
t
h
e
co
n
d
u
ct
o
f
th
e
r
esear
ch
.
T
h
e
r
esear
ch
er
s
f
u
r
th
er
ac
k
n
o
wled
g
e
th
e
u
n
wav
er
in
g
en
co
u
r
ag
e
m
en
t
an
d
co
n
tr
ib
u
tio
n
s
o
f
all
in
d
iv
id
u
als an
d
in
s
titu
tio
n
s
wh
o
s
e
s
u
p
p
o
r
t w
as in
s
tr
u
m
en
tal
in
th
e
s
u
cc
ess
f
u
l r
ea
lizatio
n
o
f
th
is
wo
r
k
.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
T
h
is
s
tu
d
y
was
s
u
p
p
o
r
te
d
b
y
th
e
Dep
ar
tm
en
t
o
f
Scien
c
e
an
d
T
ec
h
n
o
lo
g
y
–
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ce
E
d
u
ca
tio
n
I
n
s
titu
te
(
DOST
–
SEI
)
,
i
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co
l
lab
o
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atio
n
with
th
e
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est
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ay
as
State
Un
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er
s
ity
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s
ity
R
esear
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elo
p
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(
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D
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)
,
th
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(
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to
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ip
d
is
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tes,
an
d
f
ac
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co
llab
o
r
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.
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