I
nte
rna
t
io
na
l J
o
urna
l o
f
E
v
a
lua
t
io
n a
nd
Resea
rc
h in E
du
ca
t
io
n (
I
J
E
RE
)
Vo
l.
14
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
5
,
p
p
.
583
~
588
I
SS
N:
2
2
5
2
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8
8
2
2
,
DOI
: 1
0
.
1
1
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9
1
/
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e
.
v
14
i
1
.
2
9
9
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1
583
J
o
ur
na
l ho
m
ep
a
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e
:
h
ttp
:
//ij
ere.
ia
esco
r
e.
co
m
The media
ting
effect of
study ha
bi
t
s betwe
en paren
t
a
l
inv
o
lv
ement and
a
lg
ebra
ic proble
m
-
so
lv
ing
achiev
ement
I
m
da
d Ali,
Sa
m
ira
n Da
s
D
e
p
a
r
t
me
n
t
o
f
M
a
t
h
e
m
a
t
i
c
s,
C
e
n
t
r
a
l
I
n
st
i
t
u
t
e
o
f
T
e
c
h
n
o
l
o
g
y
K
o
k
r
a
j
h
a
r
,
A
s
sam,
I
n
d
i
a
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Ja
n
1
3
,
2
0
2
4
R
ev
is
ed
J
u
l 2
6
,
2
0
2
4
Acc
ep
ted
Au
g
1
1
,
2
0
2
4
Alg
e
b
ra
is
t
h
e
m
a
jo
r
b
ra
n
c
h
o
f
m
a
th
e
m
a
ti
c
s
th
a
t
d
e
a
ls
with
n
u
m
b
e
rs,
a
n
d
sy
m
b
o
ls
a
re
m
o
stl
y
u
se
d
in
p
ro
b
l
e
m
-
so
lv
in
g
.
S
t
u
d
e
n
ts
o
fte
n
stru
g
g
le
to
lea
r
n
m
a
th
e
m
a
ti
c
s
d
u
e
to
th
e
d
iffi
c
u
l
ti
e
s
o
f
so
lv
i
n
g
a
l
g
e
b
ra
ic
p
ro
b
le
m
s
a
t
th
e
se
c
o
n
d
a
ry
lev
e
l.
S
e
v
e
ra
l
fa
c
to
rs
a
ffe
c
t
stu
d
e
n
t
p
ro
b
lem
-
so
lv
i
n
g
a
c
h
iev
e
m
e
n
t
(P
S
A).
Th
e
p
re
se
n
t
stu
d
y
a
ims
to
e
x
a
m
in
e
th
e
m
e
d
iati
n
g
e
ffe
c
t
o
f
stu
d
y
h
a
b
it
s
(S
H)
i
n
th
e
re
latio
n
sh
i
p
b
e
twe
e
n
p
a
re
n
tal
in
v
o
l
v
e
m
e
n
t
(P
I)
a
n
d
a
lg
e
b
ra
ic
P
S
A.
F
o
r
t
h
is
p
u
r
p
o
se
,
a
stu
d
y
h
a
b
it
s
sc
a
le
a
n
d
a
p
a
re
n
tal
in
v
o
lv
e
m
e
n
t
sc
a
le
a
re
u
se
d
,
a
n
d
a
p
ro
b
lem
-
so
l
v
in
g
tes
t
is
d
o
n
e
fo
r
a
lg
e
b
ra
ic
p
ro
b
lem
-
so
lv
i
n
g
.
I
n
t
h
is
c
o
rre
latio
n
a
l
stu
d
y
,
Ba
ro
n
a
n
d
Ke
n
n
y
’s
se
ries
o
f
re
g
re
ss
io
n
m
o
d
e
ls
is
u
se
d
t
o
tes
t
th
e
m
e
d
iatin
g
e
ffe
c
t
o
f
S
H.
Th
e
fin
d
in
g
s
re
v
e
a
led
th
a
t
th
a
t
P
I,
S
H an
d
a
lg
e
b
ra
ic P
S
A are
p
o
siti
v
e
ly
c
o
rre
late
d
.
Also
,
it
is
c
o
n
firme
d
t
h
a
t
S
H
m
e
d
iate
s
t
h
e
re
latio
n
s
h
ip
b
e
twe
e
n
P
I
a
n
d
a
lg
e
b
ra
ic
P
S
A
b
e
c
a
u
se
th
e
re
is
n
o
lo
n
g
e
r
a
n
y
si
g
n
if
ica
n
t
e
ffe
c
t
o
f
P
I
o
n
P
S
A
a
fter
S
H
is
in
c
lu
d
e
d
i
n
th
e
m
o
d
e
l.
It
is
re
c
o
m
m
e
n
d
e
d
th
a
t
stu
d
e
n
ts’
p
r
o
b
le
m
-
so
lv
in
g
sk
il
ls
b
e
d
e
v
e
lo
p
e
d
t
h
ro
u
g
h
th
e
ir
b
e
tt
e
r
stu
d
y
h
a
b
it
s.
I
n
c
re
a
sin
g
p
a
re
n
tal
su
p
p
o
rt
m
a
y
p
r
o
m
o
te stu
d
e
n
ts b
e
t
ter S
H,
wh
ich
in
t
u
rn
b
e
tt
e
r
a
c
h
iev
e
m
e
n
t
in
p
ro
b
lem
-
so
lv
i
n
g
.
P
a
re
n
ts
a
n
d
tea
c
h
e
rs
sh
o
u
l
d
m
o
n
it
o
r
a
n
d
e
n
c
o
u
ra
g
e
stu
d
e
n
ts’
stu
d
y
h
a
b
i
ts
fo
r
b
e
tt
e
r
p
e
rfo
rm
a
n
c
e
in
p
r
o
b
lem
-
so
lv
in
g
a
n
d
m
a
th
e
m
a
ti
c
s a
s a
wh
o
le.
K
ey
w
o
r
d
s
:
Alg
eb
r
a
Par
en
tal
in
v
o
lv
em
e
n
t
Pro
b
lem
-
s
o
lv
in
g
Seco
n
d
ar
y
s
ch
o
o
l
Stu
d
y
h
ab
its
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
I
m
d
ad
Ali
Dep
ar
tm
en
t o
f
Ma
th
em
atics,
C
en
tr
al
I
n
s
titu
te
o
f
T
ec
h
n
o
lo
g
y
Ko
k
r
ajh
a
r
R
an
g
alik
h
ata,
Ko
k
r
aj
h
ar
B
T
AD,
Ass
am
7
8
3
3
7
0
,
I
n
d
ia
E
m
ail: a
li.im
d
ad
9
9
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
Ma
th
em
atics
s
er
v
es
as
th
e
b
ac
k
b
o
n
e
in
th
e
a
d
v
an
ce
m
e
n
t
o
f
m
o
d
e
r
n
s
cien
ce
an
d
tech
n
o
l
o
g
y
.
I
t
is
a
b
asic
s
u
b
ject
tau
g
h
t
g
lo
b
ally
in
p
r
im
ar
y
an
d
s
ec
o
n
d
ar
y
s
ch
o
o
l
ed
u
ca
tio
n
.
I
n
I
n
d
ian
e
d
u
ca
tio
n
al
s
y
s
tem
,
m
ath
em
atics
is
tau
g
h
t
as
a
co
m
p
u
ls
o
r
y
s
u
b
ject
f
r
o
m
p
r
im
ar
y
to
s
ec
o
n
d
ar
y
s
ch
o
o
ls
(
u
p
to
1
0
th
s
tan
d
a
r
d
)
.
I
t
is
co
m
m
o
n
p
e
r
ce
p
tio
n
th
at
m
at
h
em
atics
is
m
o
r
e
d
if
f
icu
lt
s
u
b
ject
in
s
ch
o
o
l
ed
u
ca
tio
n
[
1
]
.
T
ea
ch
er
s
,
p
ar
e
n
ts
,
s
ch
o
o
l
au
th
o
r
ities
,
an
d
th
e
ed
u
ca
tio
n
al
s
y
s
tem
ar
e
o
f
ten
wo
r
r
ied
ab
o
u
t
th
e
s
tu
d
en
ts
’
p
er
f
o
r
m
an
ce
i
n
m
ath
em
atic.
T
h
e
im
p
o
r
tan
ce
o
f
m
ath
e
m
atics
is
co
m
p
ar
ativ
ely
h
ig
h
e
r
th
an
t
h
e
o
th
er
s
u
b
jects
in
th
e
ed
u
ca
tio
n
al
s
y
s
tem
[
2
]
.
T
h
e
s
ec
o
n
d
ar
y
s
ch
o
o
l
lev
el
m
ath
em
atics
cu
r
r
icu
lu
m
in
clu
d
es
ar
ith
m
etic,
alg
eb
r
a
,
g
eo
m
etr
y
,
s
tatis
tics
,
tr
ig
o
n
o
m
etr
y
,
m
en
s
u
r
atio
n
an
d
p
r
o
b
ab
i
lity
;
all
ar
e
in
ter
co
n
n
ec
ted
to
ea
ch
o
th
er
.
Alg
e
b
r
a
is
th
e
b
asic
f
ield
o
f
m
ath
e
m
atics,
wh
ich
is
r
e
g
ar
d
e
d
as
t
h
e
la
n
g
u
ag
e
o
f
m
ath
e
m
atics
th
at
u
s
es
letter
s
,
s
y
m
b
o
ls
,
an
d
n
u
m
b
er
s
in
p
r
o
b
lem
-
s
o
lv
i
n
g
[
3
]
.
As
a
lan
g
u
ag
e,
lear
n
in
g
alg
eb
r
a
h
elp
s
u
s
to
u
n
d
er
s
tan
d
m
ath
em
atics
[
4
]
.
L
ea
r
n
in
g
alg
e
b
r
a
d
ev
elo
p
s
s
tu
d
en
ts
’
p
r
o
b
lem
-
s
o
lv
i
n
g
s
k
ills
,
r
ea
s
o
n
in
g
,
an
d
cr
itical
th
in
k
in
g
ab
ilit
ies.
H
o
wev
er
,
d
u
e
to
th
e
ab
s
tr
ac
t
n
atu
r
e
o
f
alg
eb
r
a,
s
tu
d
e
n
ts
f
ac
e
d
if
f
icu
lties
in
m
ath
em
atics
lear
n
in
g
.
T
h
e
d
if
f
icu
lty
in
lear
n
in
g
m
at
h
em
atics
is
d
u
e
to
th
e
en
co
u
n
ter
i
n
g
o
f
al
g
eb
r
aic
p
r
o
b
lem
s
o
lv
in
g
[
5
]
.
Pro
b
lem
-
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
.
1
,
Feb
r
u
a
r
y
2
0
2
5
:
58
3
-
588
584
s
o
lv
in
g
is
o
n
e
o
f
th
e
p
r
o
m
in
e
n
t
asp
ec
ts
o
f
th
e
m
ath
em
atics
teac
h
in
g
an
d
lear
n
in
g
p
r
o
ce
s
s
[
6
]
,
[
7
]
.
P
r
o
b
lem
-
s
o
lv
in
g
ab
ilit
y
in
alg
eb
r
a
is
clo
s
ely
r
elate
d
to
m
ath
em
atica
l
ac
h
iev
em
en
t
[
8
]
.
R
esear
ch
h
a
s
d
em
o
n
s
tr
ated
th
at
a
n
u
m
b
e
r
o
f
f
ac
to
r
s
ar
e
ass
o
ciate
d
with
p
r
o
b
lem
-
s
o
lv
in
g
ac
h
iev
em
e
n
t
[
9
]
.
T
h
e
ass
o
ciatin
g
f
ac
to
r
s
o
f
ac
h
iev
em
en
t
ar
e
a
f
f
ec
tin
g
o
r
c
o
g
n
itiv
e
as
well
as
en
v
ir
o
n
m
e
n
tal
an
d
p
e
d
ag
o
g
ical
o
n
es
[
1
0
]
.
T
h
o
u
g
h
p
r
o
b
lem
-
s
o
lv
in
g
ac
h
iev
em
e
n
t (
PS
A)
is
a
co
g
n
itiv
e
p
r
o
ce
s
s
,
th
e
ass
o
ciatin
g
f
ac
to
r
s
ca
n
n
o
t b
e
ig
n
o
r
e
d
,
s
o
u
n
d
er
s
tan
d
in
g
th
e
co
n
n
ec
tio
n
b
etwe
en
t
h
e
ass
o
ciatin
g
f
ac
to
r
s
an
d
PS
A
is
a
p
r
o
m
in
e
n
t a
r
ea
o
f
s
tu
d
y
.
I
n
ed
u
ca
tio
n
al
r
esear
ch
,
s
tu
d
e
n
ts
’
s
tu
d
y
h
ab
its
an
d
p
ar
en
tal
in
v
o
l
v
em
en
t
ar
e
th
e
m
o
s
t
r
el
ev
an
t
an
d
in
f
lu
en
tial
f
ac
to
r
s
in
p
r
o
b
lem
-
s
o
lv
in
g
ac
h
ie
v
em
en
t
[
1
1
]
.
R
esear
ch
h
as
d
em
o
n
s
tr
ated
th
a
t
s
tu
d
y
h
ab
its
an
d
p
ar
en
tal
in
v
o
lv
em
en
t
a
r
e
th
e
m
o
s
t
s
ig
n
if
ican
t
af
f
ec
tiv
e
f
ac
t
o
r
s
ass
o
ciate
d
with
ac
ad
em
ic
ac
h
iev
em
en
t
[
1
2
]
–
[
1
4
]
.
Fo
r
in
s
tan
ce
,
it
was
f
o
u
n
d
th
at
E
th
io
p
ian
s
ix
th
-
g
r
ad
e
s
tu
d
en
ts
’
s
tu
d
y
h
ab
its
,
s
elf
-
co
n
ce
p
t,
an
d
p
a
r
en
tal
in
v
o
lv
em
e
n
t a
r
e
th
e
m
o
s
t in
f
lu
en
tial f
ac
to
r
s
o
f
ac
ad
em
ic
ac
h
iev
em
en
t a
n
d
h
a
v
e
a
s
ig
n
if
ican
t r
elatio
n
s
h
ip
with
th
eir
ac
ad
em
ic
ac
h
iev
em
e
n
t
[
1
3
]
.
Mo
r
eo
v
er
,
th
e
r
elatio
n
s
h
ip
b
etwe
en
s
tu
d
y
h
ab
its
an
d
p
ar
en
tal
in
v
o
lv
em
en
t
was
s
tu
d
ied
am
o
n
g
th
e
n
in
th
-
g
r
ad
e
s
ec
o
n
d
ar
y
s
ch
o
o
l
s
tu
d
e
n
ts
in
th
e
Gan
jam
d
is
tr
ict
o
f
Od
is
h
a
in
I
n
d
ia
an
d
f
o
u
n
d
to
h
a
v
e
a
s
ig
n
if
ican
t
r
el
atio
n
s
h
ip
with
th
eir
ac
h
ie
v
em
en
t
[
1
4
]
.
I
n
t
o
d
a
y
’
s
e
d
u
c
a
t
i
o
n
a
l
e
n
v
i
r
o
n
m
e
n
t
,
s
t
u
d
e
n
ts
’
s
t
u
d
y
h
a
b
i
ts
(
S
H
)
a
r
e
t
h
e
m
o
s
t
i
m
p
o
r
t
a
n
t
a
s
p
e
c
t
o
f
a
c
h
i
e
v
e
m
e
n
t
[
1
5
]
,
[
1
6
]
.
S
H
a
r
e
b
e
h
a
v
i
o
r
s
a
n
d
d
i
s
p
o
s
i
ti
o
n
s
th
a
t
c
a
n
i
n
c
r
e
as
e
m
o
t
i
v
at
i
o
n
a
n
d
m
a
k
e
s
t
u
d
y
i
n
g
a
n
e
x
t
r
e
m
e
l
y
f
r
u
i
t
f
u
l e
n
d
e
a
v
o
r
t
h
at
l
e
a
d
s
t
o
h
i
g
h
e
r
l
e
a
r
n
i
n
g
s
k
i
l
ls
[
1
7
]
.
T
h
e
s
e
b
e
h
a
v
i
o
r
s
a
n
d
s
k
ill
s
c
a
n
a
ls
o
i
m
p
r
o
v
e
a
s
t
u
d
e
n
t
’
s
le
a
r
n
i
n
g
,
p
r
o
b
l
e
m
-
s
o
l
v
i
n
g
a
b
i
l
i
t
y
a
n
d
a
c
a
d
e
m
i
c
a
ch
i
e
v
e
m
e
n
t
[
1
8
]
.
R
e
s
e
a
r
c
h
h
as
id
e
n
t
i
f
i
e
d
t
h
a
t
b
e
t
te
r
S
H
h
a
v
e
a
s
i
g
n
i
f
i
c
a
n
t
r
o
l
e
i
n
m
a
t
h
e
m
a
ti
c
s
a
c
h
i
e
v
e
m
e
n
t
[
1
9
]
.
S
t
u
d
e
n
t
s
’
b
et
t
e
r
S
H
p
r
o
m
o
t
e
s
a
d
e
e
p
e
r
u
n
d
e
r
s
t
a
n
d
i
n
g
o
f
m
a
t
h
e
m
at
i
c
al
c
o
n
c
e
p
t
s
,
e
n
a
b
l
i
n
g
s
t
u
d
e
n
ts
t
o
a
p
p
r
o
a
c
h
p
r
o
b
l
e
m
-
s
o
l
v
i
n
g
t
a
s
k
s
wi
t
h
c
o
n
f
i
d
e
n
c
e.
S
e
v
e
r
a
l
r
e
ce
n
t
s
t
u
d
i
es
h
a
v
e
ex
p
l
o
r
e
d
t
h
e
f
a
c
t
t
h
at
s
t
u
d
y
h
a
b
i
t
s
a
r
e
o
n
e
o
f
t
h
e
m
o
s
t
s
i
g
n
if
i
c
a
n
t
p
r
e
d
i
c
t
o
r
s
o
f
m
a
t
h
e
m
a
t
i
ca
l
p
r
o
b
l
e
m
-
s
o
l
v
i
n
g
[
1
5
]
,
[
1
6
]
,
[
1
8
]
.
A
l
s
o
,
R
e
y
es
e
t
a
l
.
[
1
5
]
m
e
n
t
i
o
n
e
d
t
h
a
t
S
H
is
t
h
e
m
e
d
i
at
o
r
b
e
t
w
e
e
n
t
h
e
c
o
g
n
i
t
i
v
e
o
r
a
f
f
ec
t
i
v
e
f
a
ct
o
r
s
a
n
d
ac
a
d
e
m
i
c
a
ch
i
e
v
e
m
e
n
t
.
I
n
a
s
t
r
u
c
t
u
r
al
s
t
u
d
y
,
H
s
i
e
h
e
t
a
l
.
[
1
2
]
e
s
t
a
b
li
s
h
e
d
t
h
a
t
SH
m
e
d
ia
t
e
d
th
e
r
e
l
a
ti
o
n
s
h
i
p
b
et
w
e
e
n
p
a
r
e
n
ta
l
i
n
v
o
l
v
e
m
e
n
t
a
n
d
a
ca
d
e
m
i
c
ac
h
i
e
v
e
m
e
n
t
.
T
h
u
s
,
it
i
s
o
n
e
o
f
t
h
e
m
o
s
t
i
n
f
l
u
e
n
t
ia
l
f
ac
t
o
r
s
i
n
m
a
t
h
e
m
a
t
i
ca
l
a
c
h
i
e
v
em
e
n
t
s
[
2
0
]
,
[
2
1
]
.
I
n
th
e
p
r
esen
t
er
a,
p
ar
e
n
tal
in
v
o
l
v
em
en
t
(
PI)
h
as
b
ee
n
a
n
ew
f
o
c
u
s
o
f
ed
u
ca
tio
n
a
l
r
esear
ch
.
Acc
o
r
d
in
g
t
o
Fu
en
tes
et
a
l.
[
2
2
]
,
s
tu
d
en
ts
’
ed
u
ca
tio
n
al
d
ev
elo
p
m
en
ts
ca
n
b
e
i
n
f
lu
en
ce
d
b
y
p
ar
e
n
tal
in
v
o
lv
em
e
n
t.
T
h
eir
in
v
o
lv
em
en
t
an
d
attitu
d
e
to
war
d
s
th
e
s
u
b
ject
en
h
an
ce
th
e
lear
n
in
g
ac
h
iev
em
en
t
o
f
a
s
tu
d
en
t
[
2
3
]
–
[
2
5
]
.
R
esear
ch
e
r
s
h
av
e
ac
tiv
ely
p
r
o
m
o
ted
p
ar
en
t
in
v
o
lv
e
m
en
t
in
an
e
f
f
o
r
t
to
in
cr
ea
s
e
th
eir
ch
ild
r
en
’
s
ac
ad
em
ic
s
u
cc
ess
[
2
6
]
,
[
2
7
]
.
Par
en
ts
ac
tiv
ely
p
ar
ticip
atin
g
in
th
eir
ch
ild
r
en
’
s
ed
u
ca
tio
n
an
d
attem
p
tin
g
to
r
eso
lv
e
th
eir
p
r
o
b
lem
s
m
ay
en
co
u
r
ag
e
b
ette
r
SH
an
d
ca
n
r
esu
lt
in
b
etter
ac
h
iev
em
en
ts
f
o
r
ch
ild
r
en
[
1
3
]
,
[
2
8
]
.
No
wad
ay
s
,
th
e
im
p
o
r
tan
ce
o
f
p
ar
en
tal
i
n
v
o
lv
em
en
t
h
as
em
er
g
ed
as
o
n
e
o
f
th
e
s
ig
n
if
ican
t
f
ac
to
r
s
co
n
n
ec
ted
to
m
ath
e
m
atics
ac
h
iev
em
en
t
[
2
9
]
,
[
3
0
]
.
Par
en
ts
’
ac
ad
em
ic
s
u
p
p
o
r
t
an
d
an
ticip
atio
n
th
r
o
u
g
h
o
u
t
th
eir
c
h
ild
r
en
’
s
ed
u
ca
tio
n
f
o
s
ter
a
p
o
s
itiv
e
attitu
d
e
to
war
d
m
ath
em
atics,
wh
ic
h
m
ay
en
h
a
n
ce
th
eir
ab
ilit
y
to
s
o
lv
e
m
ath
em
atica
l
wo
r
d
p
r
o
b
lem
s
a
n
d
d
ev
elo
p
al
g
eb
r
aic
th
in
k
in
g
[
3
1
]
.
Stu
d
ies
h
av
e
f
o
u
n
d
th
at
PI
h
as
a
p
o
s
itiv
e
r
elatio
n
s
h
ip
with
s
tu
d
en
t
ac
h
ie
v
em
en
t
i
n
m
ath
em
atics
[
3
0
]
,
[
3
2
]
.
T
h
u
s
,
PI
is
o
n
e
o
f
th
e
en
v
ir
o
n
m
en
tal
f
ac
to
r
s
to
b
e
in
v
esti
g
ated
in
co
n
n
ec
tio
n
with
m
ath
em
atica
l a
ch
iev
em
en
t.
2.
T
H
E
P
R
E
SE
NT
S
T
UD
Y
T
h
e
liter
atu
r
e
ex
h
i
b
ited
th
at
s
tu
d
y
h
a
b
its
an
d
p
ar
e
n
tal
in
v
o
lv
em
en
t
a
r
e
th
e
in
f
l
u
en
tial
f
ac
to
r
s
o
f
m
ath
em
atica
l
ac
h
iev
em
e
n
t.
H
o
wev
er
,
th
e
r
elatio
n
s
h
ip
b
etwe
en
s
tu
d
y
h
ab
its
,
p
ar
e
n
tal
in
v
o
lv
em
e
n
t
an
d
alg
eb
r
aic
p
r
o
b
lem
-
s
o
lv
in
g
is
r
ar
ely
s
tu
d
ied
.
Als
o
,
th
e
m
e
d
iatin
g
r
o
le
o
f
s
tu
d
y
h
ab
its
b
etwe
en
PI
an
d
alg
eb
r
aic
PS
A
is
r
elativ
ely
n
ew
in
th
e
f
ield
o
f
m
ath
em
atics
ed
u
ca
tio
n
.
T
h
er
e
f
o
r
e,
th
e
aim
o
f
th
e
s
tu
d
y
to
estab
lis
h
th
e
m
ed
iatin
g
r
o
le
o
f
s
tu
d
y
h
a
b
its
b
etwe
en
p
ar
e
n
tal
in
v
o
lv
em
en
t
an
d
alg
eb
r
aic
p
r
o
b
lem
-
s
o
lv
in
g
ac
h
ie
v
em
en
t
.
R
esear
ch
er
s
s
u
g
g
est
th
at
s
tu
d
y
h
a
b
its
ca
n
b
e
co
n
s
id
er
ed
as
o
n
e
o
f
th
e
m
o
s
t
i
n
f
lu
en
tial
p
r
e
d
icto
r
s
o
f
p
r
o
b
lem
-
s
o
lv
in
g
ac
h
iev
em
e
n
t
[
1
8
]
,
[
1
9
]
,
[
2
1
]
.
Als
o
,
s
ev
er
al
s
tu
d
ies
[
1
2
]
,
[
1
5
]
h
ig
h
lig
h
te
d
th
e
m
ed
iatin
g
r
elatio
n
s
h
ip
b
etwe
en
PI
an
d
ac
h
iev
em
en
t.
On
th
e
o
th
er
h
an
d
,
p
ar
en
tal
in
v
o
lv
em
e
n
t
h
as
b
ee
n
id
en
tif
ied
is
o
n
e
o
f
th
e
im
p
o
r
tan
t
f
ac
to
r
s
in
m
ath
em
atica
l
d
o
m
ai
n
[
2
2
]
,
[
3
1
]
.
T
h
e
r
elatio
n
s
h
ip
b
etwe
en
PI
an
d
m
ath
em
atica
l
ac
h
iev
e
m
en
t
h
as
s
ig
n
if
ie
d
b
y
s
ev
er
al
s
tu
d
ies
[
3
0
]
,
[
3
2
]
.
C
o
n
s
id
er
in
g
all
th
e
f
ac
t
th
at,
i
t
is
h
y
p
o
th
esized
th
at
s
tu
d
y
h
ab
its
m
ed
iate
th
e
r
elatio
n
s
h
ip
b
etwe
en
p
ar
en
tal
in
v
o
l
v
em
en
t
an
d
alg
e
b
r
aic
p
r
o
b
lem
-
s
o
lv
in
g
ac
h
iev
em
e
n
t
.
T
h
e
h
y
p
o
th
esized
m
o
d
el
is
p
r
esen
ted
in
th
e
Fig
u
r
e
1
.
3.
M
E
T
H
O
D
A
co
r
r
elatio
n
al
r
esear
ch
d
esig
n
is
u
s
ed
to
ca
r
r
y
o
u
t
th
e
s
tu
d
y
.
I
t
is
an
ess
en
tial
to
o
l
to
d
et
er
m
in
e
th
e
ef
f
ec
t
o
f
two
o
r
m
o
r
e
in
d
ep
e
n
d
en
t
v
ar
iab
les
o
n
o
n
e
d
ep
en
d
e
n
t
v
ar
iab
le
[
3
3
]
.
I
n
th
is
s
tu
d
y
,
th
is
d
esig
n
is
u
s
e
d
to
in
v
esti
g
ate
th
e
ef
f
ec
t
o
f
in
d
ep
en
d
en
t
v
ar
iab
les SH a
n
d
PI
o
n
th
e
d
ep
en
d
en
t v
ar
ia
b
le
alg
e
b
r
aic
PS
A.
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
Th
e
med
ia
tin
g
effec
t o
f stu
d
y
h
a
b
its
b
etw
ee
n
p
a
r
en
ta
l in
v
o
l
ve
men
t a
n
d
a
lg
eb
r
a
ic
…
(
I
md
a
d
A
li
)
585
Fig
u
r
e
1
.
Hy
p
o
th
esized
m
o
d
el
3
.
1
.
Sa
m
ple
I
n
a
s
tu
d
y
,
th
e
s
am
p
le
is
th
e
p
o
r
tio
n
o
f
th
e
p
o
p
u
latio
n
th
at
is
ch
o
s
en
to
r
ep
r
esen
t th
e
to
tal
p
o
p
u
latio
n
.
I
n
o
u
r
s
tu
d
y
ar
ea
,
th
e
t
o
tal
p
o
p
u
latio
n
is
1
2
,
2
2
7
.
H
o
we
v
er
,
ac
co
r
d
in
g
to
C
o
ch
r
an
’
s
f
o
r
m
u
la
f
o
r
f
in
ite
p
o
p
u
latio
n
[
3
4
]
,
th
e
r
e
q
u
ir
ed
s
am
p
le
(
wh
ich
ca
n
r
ep
r
esen
t
th
e
to
tal
p
o
p
u
latio
n
)
is
3
7
4
o
r
m
o
r
e
f
o
r
1
2
,
2
2
7
s
tu
d
en
ts
.
Hen
ce
,
we
h
av
e
c
o
n
s
id
er
ed
4
0
0
class
I
X
s
ec
o
n
d
ar
y
s
ch
o
o
l
s
tu
d
e
n
ts
in
th
e
Mo
r
ig
ao
n
d
is
tr
ict
o
f
Ass
am
,
I
n
d
ia.
T
h
e
s
am
p
le
f
o
r
th
e
s
tu
d
y
is
r
an
d
o
m
ly
s
elec
ted
f
o
r
th
e
s
tu
d
y
p
u
r
p
o
s
e.
3
.
2
.
I
ns
t
rum
ent
s
I
n
s
u
r
v
e
y
r
e
s
ea
r
c
h
,
q
u
e
s
t
i
o
n
n
a
i
r
e
s
a
r
e
a
c
o
m
m
o
n
a
p
p
r
o
a
c
h
t
o
s
t
a
ti
s
t
i
c
al
a
n
a
l
y
s
is
.
T
h
e
u
s
e
o
f
q
u
e
s
t
i
o
n
n
a
i
r
es
is
c
o
n
s
i
d
e
r
e
d
a
p
p
r
o
p
r
i
a
t
e
i
n
t
h
is
r
e
s
ea
r
c
h
i
n
o
r
d
e
r
t
o
g
e
t
s
u
f
f
i
c
ie
n
t
r
es
p
o
n
s
e
s
f
r
o
m
t
h
e
r
e
s
p
o
n
d
e
n
t
s
[
3
5
]
.
T
h
e
r
e
s
e
a
r
c
h
e
r
s
d
e
v
e
l
o
p
e
d
s
e
l
f
-
a
d
m
i
n
is
t
e
r
ed
q
u
e
s
t
i
o
n
n
a
i
r
es
t
h
a
t
a
r
e
u
s
e
d
f
o
r
s
t
u
d
e
n
t
s
’
S
H
,
P
I
a
n
d
a
p
r
o
b
l
e
m
-
s
o
l
v
i
n
g
t
e
s
t
i
n
th
i
s
s
t
u
d
y
.
A
l
l
it
e
m
s
o
f
t
h
e
q
u
e
s
t
i
o
n
n
a
i
r
e
s
a
r
e
v
a
l
i
d
a
te
d
b
y
t
h
e
e
x
p
e
r
t
e
d
u
c
a
t
o
r
s
.
T
h
e
s
tu
d
y
h
ab
its
s
ca
le
co
n
s
is
t
s
o
f
1
0
item
s
o
f
th
e
L
ik
er
t
f
iv
e
-
p
o
in
t
ty
p
e.
Fo
r
ea
ch
item
,
n
u
m
er
ical
s
co
r
es
ar
e
co
n
s
id
er
ed
“
5
-
s
tr
o
n
g
ly
a
g
r
ee
”,
“4
-
ag
r
ee
”,
“
3
-
n
e
u
tr
al”,
“2
-
d
is
ag
r
ee
”,
a
n
d
“1
-
s
tr
o
n
g
ly
d
is
ag
r
ee
”.
On
e
ex
am
p
le
o
f
th
e
item
is
“I
s
tu
d
y
th
e
tex
tb
o
o
k
s
ev
er
al
tim
es
to
u
n
d
er
s
tan
d
m
ath
e
m
atica
l
p
r
o
b
lem
s
.
”
T
h
e
C
r
o
n
b
ac
h
alp
h
a
r
eliab
ilit
y
o
f
th
e
s
ca
le
is
0
.
9
1
.
Als
o
,
th
e
p
a
r
en
tal
in
v
o
lv
e
m
en
t
s
ca
le
co
n
s
is
ts
o
f
1
0
item
s
o
f
th
e
L
ik
er
t
f
iv
e
-
p
o
in
t
ty
p
e.
Fo
r
ea
ch
item
,
n
u
m
er
ical
s
co
r
es
ar
e
co
n
s
id
er
ed
“
5
-
s
tr
o
n
g
ly
ag
r
ee
”
to
“1
-
s
tr
o
n
g
ly
d
is
ag
r
ee
”.
An
ex
am
p
le
o
f
a
n
item
is
“M
y
p
ar
en
ts
h
elp
m
e
wh
en
I
f
ac
e
d
if
f
icu
lty
in
m
at
h
em
atics
.
”
Als
o
,
th
e
C
r
o
n
b
ac
h
alp
h
a
r
eliab
ilit
y
o
f
t
h
e
s
ca
le
is
0
.
8
2
.
T
o
k
n
o
w
s
tu
d
en
ts
’
alg
eb
r
aic
PS
A
a
te
s
t
i
s
d
o
n
e
b
ased
o
n
alg
eb
r
a.
T
h
e
test
co
n
s
is
ts
o
f
2
0
item
s
b
ased
o
n
9
th
g
r
ad
e
s
ec
o
n
d
ar
y
ed
u
ca
tio
n
b
o
a
r
d
o
f
ass
am
(
SEBA
)
tex
t
b
o
o
k
.
T
h
e
item
s
o
f
th
e
te
s
t
ar
e
o
f
m
u
ltip
le
-
ch
o
ice
q
u
esti
o
n
h
av
in
g
f
o
u
r
al
ter
n
ativ
e
o
p
tio
n
s
f
o
r
ea
ch
q
u
e
s
tio
n
.
Ou
t
o
f
th
o
s
e
f
o
u
r
o
p
tio
n
s
,
o
n
ly
o
n
e
o
p
tio
n
is
co
r
r
ec
t.
Fo
r
th
e
co
r
r
ec
t
o
p
ti
o
n
1
m
ar
k
is
g
i
v
en
,
an
d
f
o
r
th
e
wr
o
n
g
o
p
tio
n
,
0
m
ar
k
s
a
r
e
g
iv
en
.
T
h
e
test
item
s
ar
e
v
alid
ated
with
th
e
h
elp
o
f
ex
p
er
t
m
ath
e
m
atics
teac
h
er
an
d
ed
u
ca
to
r
s
with
m
o
r
e
th
an
1
0
y
ea
r
s
o
f
ex
p
er
ien
ce
.
T
h
e
r
eliab
ilit
y
C
r
o
n
b
ac
h
alp
h
a
is
0
.
8
8
ac
ce
p
tab
le
.
3
.
3
.
Da
t
a
a
na
ly
s
is
T
h
e
s
tatis
tical
p
r
o
d
u
ct
an
d
s
er
v
ice
s
o
lu
tio
n
(
SP
SS
)
v
er
s
io
n
2
6
.
0
is
u
s
ed
to
an
al
y
s
is
th
e
co
llected
d
ata.
T
h
e
d
escr
ip
tiv
e
s
tatis
tic
s
ar
e
u
s
ed
an
d
th
e
n
o
r
m
ality
test
s
ar
e
also
d
o
n
e.
T
h
e
co
r
r
elatio
n
b
etwe
en
SH,
PI,
an
d
alg
eb
r
aic
PS
A
is
d
eter
m
in
ed
b
y
u
s
in
g
Pear
s
o
n
co
r
r
el
atio
n
.
B
ar
o
n
a
n
d
Ken
n
y
[
3
6
]
s
tep
s
ar
e
u
s
ed
t
o
estab
lis
h
th
e
m
ed
iatin
g
ef
f
ec
t
o
f
SH.
At
f
ir
s
t,
alg
e
b
r
aic
PS
A
is
r
eg
r
ess
ed
o
n
PI
an
d
in
th
e
s
ec
o
n
d
s
tep
,
SH
is
r
eg
r
ess
ed
o
n
PI.
I
n
th
e
t
h
ir
d
s
tep
,
PS
A
i
s
r
eg
r
ess
ed
o
n
b
o
th
th
e
in
d
ep
e
n
d
en
t
v
a
r
iab
le
PI
an
d
th
e
m
ed
iatin
g
v
ar
iab
le
SH.
Acc
o
r
d
in
g
t
o
B
ar
o
n
a
n
d
Ken
n
y
[
3
6
]
,
th
e
f
o
l
lo
win
g
r
eq
u
ir
em
en
ts
s
h
o
u
ld
b
e
s
atis
f
ied
f
o
r
t
h
e
m
ed
iatio
n
e
f
f
ec
t.
I
n
th
e
f
ir
s
t
s
tep
,
PI
m
u
s
t
h
av
e
an
ef
f
ec
t
o
n
PS
A
in
th
e
r
eg
r
ess
io
n
an
a
ly
s
is
.
I
n
th
e
s
ec
o
n
d
s
tep
,
PI
m
u
s
t
h
av
e
an
ef
f
ec
t
o
n
alg
eb
r
aic
SH.
I
n
t
h
e
th
i
r
d
s
t
ep
,
SH
s
h
o
u
ld
h
av
e
an
ef
f
ec
t
o
n
alg
e
b
r
aic
PS
A.
Fin
ally
,
th
e
th
ir
d
r
eg
r
ess
io
n
an
aly
s
is
s
h
o
u
ld
s
h
o
w
a
s
m
aller
ef
f
ec
t o
f
PI
o
n
alg
e
b
r
aic
PS
A
th
an
th
e
s
ec
o
n
d
.
4.
RE
SU
L
T
S
AND
D
I
SCU
SS
I
O
N
I
n
T
a
b
le
1
,
th
e
d
escr
ip
tiv
e
s
tatis
tics
o
f
SH,
PI,
an
d
PS
A
a
r
e
s
h
o
wn
.
Sk
ewn
ess
an
d
k
u
r
t
o
s
is
v
alu
es
r
an
g
in
g
f
r
o
m
-
1
to
1
in
d
icate
th
at
th
e
v
ar
iab
les
h
av
e
a
n
o
r
m
al
d
is
tr
ib
u
tio
n
.
Als
o
,
th
e
v
ar
iab
les
(
SH,
PI,
an
d
PS
A)
ar
e
s
ig
n
if
ican
tly
c
o
r
r
el
ated
to
ea
c
h
o
t
h
er
at
0
.
0
1
.
T
h
e
co
r
r
elatio
n
is
m
o
d
er
ate
as
r
>0
.
3
an
d
lar
g
e
as
r
>0
.
5
[
3
7
]
.
PS
A
is
f
o
u
n
d
a
la
r
g
e
p
o
s
itiv
e
co
r
r
elatio
n
with
SH
(
r
=0
.
8
0
9
,
p
<
0
.
0
1
)
an
d
PI
(
r
=0
.
5
1
3
,
p
<0
.
0
1
)
.
Als
o
,
SH is a
lar
g
e
p
o
s
itiv
e
co
r
r
elatio
n
with
PI
(
r
=
0
.
6
1
9
,
p
<
0
.
0
1
)
.
I
n
th
is
s
tu
d
y
,
a
s
er
ies
o
f
r
eg
r
ess
io
n
an
aly
s
es
was
u
s
ed
to
test
th
e
m
ed
iatin
g
ef
f
e
ct
o
f
m
ath
e
m
atics
SH
o
n
th
e
in
f
l
u
en
ce
o
f
PI
o
n
alg
eb
r
aic
PS
A,
wh
ich
was
s
u
g
g
ested
b
y
B
ar
o
n
an
d
Ken
n
y
[
3
6
]
.
T
h
e
r
esu
lts
o
f
r
eg
r
ess
io
n
an
aly
s
es
ar
e
s
h
o
w
n
in
T
ab
le
2
.
I
n
th
e
f
ir
s
t
s
tep
,
alg
eb
r
aic
PS
A
is
r
eg
r
ess
ed
o
n
PI
an
d
th
e
r
esu
lt
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
.
1
,
Feb
r
u
a
r
y
2
0
2
5
:
58
3
-
588
586
f
o
u
n
d
a
s
tatis
tically
s
ig
n
if
ican
t
r
elatio
n
s
h
ip
(
B
=5
,
t=1
1
.
9
1
9
,
P<0
.
0
0
1
)
.
T
h
e
p
r
ed
icto
r
v
ar
ia
b
le
PI
ex
p
lain
s
th
e
2
6
.
3
%
v
ar
ian
ce
o
f
alg
e
b
r
aic
P
SA.
I
n
t
h
e
s
ec
o
n
d
s
tep
,
SH
is
r
eg
r
ess
ed
o
n
PI
a
n
d
f
o
u
n
d
a
s
ig
n
if
ican
t
p
o
s
itiv
e
r
elatio
n
s
h
ip
(
B
=0
.
7
3
9
,
t=1
5
.
7
4
,
P<0
.
0
0
1
)
.
T
h
e
p
r
ed
icto
r
v
a
r
iab
le
PI
ex
p
lain
s
th
e
3
8
.
4
%
o
f
v
ar
ian
ce
o
f
SH.
Als
o
in
th
e
th
ir
d
s
tep
,
alg
eb
r
a
ic
PS
A
is
r
eg
r
ess
ed
o
n
PI
an
d
SH.
I
t
is
f
o
u
n
d
th
at
SH
h
av
e
a
s
ig
n
if
ican
t
ef
f
ec
t
o
n
alg
e
b
r
aic
PS
A
(
B
=6
.
5
1
3
,
t=2
1
.
2
4
9
,
P<0
.
0
0
1
)
.
I
n
th
is
r
eg
r
ess
io
n
m
o
d
el,
th
e
p
r
ed
icto
r
v
ar
iab
le
SH
ex
p
lain
s
th
e
6
5
.
5
%
v
ar
ian
ce
o
f
alg
eb
r
aic
PS
A.
On
th
e
o
th
er
h
a
n
d
,
PI
h
av
e
n
o
s
ig
n
if
ican
t
ef
f
ec
t
o
n
alg
eb
r
aic
PS
A
(
B
=0
.
1
8
3
,
t=
0
.
5
0
1
,
P=0
.
6
1
7
)
.
B
u
t
PI
was
f
o
u
n
d
s
ig
n
if
ican
t
ef
f
ec
t
o
n
alg
e
b
r
aic
PS
A
in
s
ec
o
n
d
r
eg
r
ess
io
n
an
aly
s
is
.
T
h
is
in
d
icate
s
th
at
t
h
e
ef
f
ec
t
o
f
PI
o
n
alg
e
b
r
aic
PS
A
is
n
o
lo
n
g
er
ex
is
t
wh
en
SH
is
s
im
u
ltan
eo
u
s
ly
co
n
s
id
er
ed
,
wh
ich
s
atis
f
ies
th
e
s
u
g
g
ested
B
ar
o
n
an
d
K
en
n
y
[
3
6
]
co
n
d
itio
n
o
f
m
e
d
iatio
n
.
Hen
ce
th
e
h
y
p
o
th
esis
is
ac
ce
p
ted
.
T
h
e
m
ed
iatin
g
ef
f
ec
t
o
f
SH in
th
e
r
elatio
n
s
h
ip
b
etwe
en
PI
a
n
d
alg
e
b
r
aic
PS
A.
T
ab
le
1
.
C
o
r
r
elatio
n
an
d
d
escr
ip
tiv
e
s
tatis
tic
s
f
o
r
SH,
PI,
an
d
PS
A
PI
SH
PSA
PI
1
0
.
6
1
9
0
.
5
1
3
SH
1
0
.
8
0
9
PSA
1
M
e
a
n
3
.
5
3
.
4
4
1
1
.
6
S
t
a
n
d
a
r
d
d
e
v
i
a
t
i
o
n
0
.
5
5
0
.
6
6
5
.
3
9
S
k
e
w
n
e
ss
-
0
.
7
4
-
0
.
5
9
-
0
.
0
2
K
u
r
t
o
si
s
-
0
.
2
7
-
0
.
7
2
-
0
.
9
*
*
.
C
o
r
r
e
l
a
t
i
o
n
i
s
si
g
n
i
f
i
c
a
n
t
a
t
t
h
e
0
.
0
1
l
e
v
e
l
(
2
-
t
a
i
l
e
d
)
T
ab
le
2
.
Me
d
iatio
n
ef
f
ec
t
o
f
S
H
in
th
e
r
elatio
n
s
h
ip
b
etwe
en
PI
an
d
PS
A
M
o
d
e
l
F
P
R
2
B
S
t
d
.
e
r
r
o
r
β
t
P
1.
R
e
g
r
e
sse
d
o
f
P
S
A
o
n
P
I
C
o
n
st
a
n
t
1
4
2
.
0
6
4
0
.
0
0
0
0
.
2
6
3
-
5
.
8
3
9
1
.
4
8
4
-
3
.
9
3
4
**
0
.
0
0
0
PI
5
.
0
0
0
0
.
4
1
9
0
.
5
1
3
1
1
.
9
1
9
**
0
.
0
0
0
2.
R
e
g
r
e
sse
d
o
f
S
H
o
n
P
I
C
o
n
st
a
n
t
2
4
7
.
7
4
6
0
.
0
0
0
0
.
3
8
4
0
.
8
5
4
0
.
1
6
6
5
.
1
4
**
0
.
0
0
0
PI
0
.
7
3
9
0
.
0
4
7
0
.
6
1
9
1
5
.
7
4
**
0
.
0
0
0
3.
R
e
g
r
e
sse
d
o
f
P
S
A
o
n
S
H
a
n
d
P
I
C
o
n
st
a
n
t
-
1
1
.
4
0
3
1
.
0
5
-
1
0
.
8
6
5
**
0
.
0
0
0
PI
3
7
7
.
2
1
0
0
.
0
0
0
0
.
6
5
5
0
.
1
8
3
0
.
3
6
6
0
.
0
1
9
0
.
5
0
1
0
.
6
1
7
SH
6
.
5
1
3
0
.
3
0
7
0
.
7
9
8
2
1
.
2
4
9
**
0
.
0
0
0
**
P
<
0
.
0
0
1
I
t
is
wid
ely
ac
ce
p
ted
th
at
s
tu
d
en
ts
’
p
r
o
b
lem
-
s
o
lv
in
g
ac
h
ie
v
em
en
t
is
af
f
ec
ted
b
y
m
an
y
f
ac
to
r
s
[
3
8
]
.
I
n
th
e
p
r
esen
t
s
tu
d
y
,
SH
an
d
PI
ar
e
th
e
af
f
ec
tiv
e
f
ac
to
r
s
th
at
h
av
e
s
ig
n
if
ican
t
r
elatio
n
s
h
ip
with
alg
eb
r
aic
PS
A.
I
n
th
e
f
ir
s
t
r
e
g
r
ess
io
n
a
n
aly
s
is
PI
h
as
s
ig
n
if
ican
t
e
f
f
ec
t
o
n
a
lg
eb
r
aic
PS
A.
T
h
e
p
o
s
itiv
e
co
r
r
elatio
n
in
d
icate
d
th
at
in
cr
ea
s
in
g
p
ar
e
n
tal
in
v
o
l
v
em
en
t
p
r
o
m
o
tes
th
eir
c
h
ild
r
en
'
s
P
SA
.
T
h
e
r
esu
lt
is
co
n
s
is
ten
t
with
th
e
s
tu
d
y
s
h
o
win
g
th
at
PI
is
s
ig
n
if
ican
tly
r
elate
d
to
m
ath
e
m
atica
l
ac
h
iev
em
en
t
[
1
3
]
,
[
2
8
]
.
R
esear
ch
by
T
an
g
et
a
l.
[
3
0
]
f
o
u
n
d
a
p
o
s
itiv
e
co
n
n
ec
tio
n
b
etwe
en
PI
an
d
m
ath
em
atics
ac
h
iev
em
en
t
at
th
e
h
ig
h
s
ch
o
o
l
l
ev
el.
I
n
r
elatio
n
to
th
is
estab
lis
h
m
en
t,
o
th
er
s
tu
d
i
es
also
in
d
icate
th
at
PI
is
o
n
e
o
f
th
e
p
r
ed
icto
r
s
o
f
m
ath
em
atica
l
ac
h
iev
em
en
t
[
1
3
]
,
[
3
9
]
.
T
h
u
s
,
p
ar
e
n
tal
s
u
p
p
o
r
t
h
as
s
ig
n
if
ican
t
c
o
n
tr
ib
u
tio
n
to
th
eir
ch
ild
r
e
n
’
m
at
h
em
atica
l
ac
h
iev
em
en
t
wh
ich
lead
s
to
th
eir
ac
a
d
em
ic
s
u
cc
ess
.
I
n
th
e
s
ec
o
n
d
r
eg
r
ess
io
n
an
a
ly
s
is
,
it
is
f
o
u
n
d
th
at
PI
h
as
an
ef
f
ec
t
o
n
SH.
T
h
is
in
d
i
ca
tes
th
at
in
cr
ea
s
in
g
PI
is
s
ig
n
if
ican
tly
in
f
lu
en
ce
th
eir
ch
ild
r
en
’
s
SH.
T
h
is
is
co
n
s
is
ten
t
with
ea
r
lie
r
s
tu
d
ies
[
1
3
]
,
[
1
4
]
[
3
1
]
,
[
3
2
]
.
W
h
en
p
a
r
en
ts
en
co
u
r
ag
e
m
ath
em
atica
l
ex
p
lo
r
atio
n
,
p
r
o
v
id
e
r
eso
u
r
ce
s
,
an
d
s
h
o
w
in
ter
est
in
lear
n
in
g
m
ath
em
atics,
ch
ild
r
e
n
ar
e
lik
ely
to
d
e
v
elo
p
s
tr
o
n
g
s
tu
d
y
h
ab
its
in
th
e
s
u
b
ject.
T
h
ese
s
u
p
p
o
r
t
a
n
d
in
ter
est in
th
eir
ch
ild
r
e
n
’
s
ed
u
ca
tio
n
m
ay
o
f
ten
lead
to
b
etter
s
tu
d
y
h
ab
its
an
d
ac
ad
em
ic
s
u
cc
ess
.
H
o
wev
er
,
th
e
ef
f
ec
t
o
f
PI
o
n
a
lg
eb
r
aic
PS
A
is
n
o
l
o
n
g
e
r
ex
i
s
t
wh
en
SH
is
co
n
s
id
er
ed
at
t
h
e
s
am
e
in
th
e
th
ir
d
r
eg
r
ess
io
n
an
aly
s
is
.
Acc
o
r
d
in
g
B
ar
o
n
an
d
Ken
n
y
[
3
6
]
,
n
o
s
ig
n
if
ican
t
ef
f
ec
t
o
f
PI
o
n
alg
eb
r
aic
PS
A
af
ter
in
clu
d
in
g
SH
in
th
e
m
o
d
el
co
n
f
ir
m
th
at
SH
p
lay
s
a
m
ed
iatin
g
r
o
le
in
th
e
r
elatio
n
s
h
ip
b
etwe
en
PI
an
d
PS
A.
T
h
is
m
ea
n
s
th
at
th
e
ef
f
e
ct
o
f
PI
o
n
alg
eb
r
aic
PS
A
to
o
k
p
lace
th
r
o
u
g
h
th
e
m
e
d
iatio
n
o
f
SH.
T
h
is
r
esu
lt
alig
n
s
with
a
p
r
io
r
s
tu
d
y
[
1
5
]
m
en
tio
n
e
d
th
at
SH
is
a
p
r
ed
icto
r
o
f
ac
h
iev
em
e
n
t
an
d
p
la
y
s
a
m
ed
iatin
g
r
o
l
e
b
etwe
en
th
e
af
f
ec
tiv
e
v
a
r
iab
le
s
an
d
ac
h
iev
em
en
t a
t th
e
s
ec
o
n
d
ar
y
lev
el.
Als
o
,
Hsi
eh
et
a
l.
[
1
2
]
estab
lis
h
ed
th
e
s
im
ilar
r
esu
lt
th
at
SH
m
ed
iat
ed
th
e
r
elatio
n
s
h
ip
b
etwe
en
PI
an
d
ac
h
iev
em
en
t
in
a
s
tr
u
ctu
r
al
s
tu
d
y
.
T
h
u
s
,
in
cr
ea
s
in
g
p
ar
e
n
tal
s
u
p
p
o
r
t
m
ay
p
r
o
m
o
te
s
tu
d
en
ts
b
etter
SH
[
4
0
]
,
wh
ich
in
tu
r
n
b
et
ter
ac
h
iev
em
en
t
in
p
r
o
b
lem
-
s
o
lv
in
g
[
2
5
]
.
Mo
r
e
o
v
er
,
th
e
d
ir
ec
t
p
o
s
itiv
e
ef
f
ec
t
o
f
SH
o
n
alg
eb
r
aic
PS
A
in
d
icate
s
th
at
s
tu
d
en
ts
with
b
etter
s
tu
d
y
h
a
b
its
ca
n
a
ch
iev
e
m
o
r
e
in
p
r
o
b
lem
-
s
o
lv
i
n
g
an
d
m
at
h
em
atics
as
a
wh
o
le
[
1
3
]
,
[
3
0
]
,
[
3
2
]
.
T
h
is
p
o
s
itiv
e
c
o
r
r
elatio
n
b
et
wee
n
SH
an
d
m
at
h
em
atica
l
PS
A
h
as
b
ee
n
estab
lis
h
ed
p
r
ev
io
u
s
ly
[
1
4
]
,
[
1
8
]
.
So
m
e
o
th
er
s
tu
d
ies
h
av
e
id
e
n
tifie
d
th
at
s
tu
d
en
ts
with
b
etter
s
tu
d
y
h
a
b
its
h
av
e
d
if
f
er
i
n
g
ac
h
iev
e
m
en
t
i
n
m
ath
em
atics f
r
o
m
th
o
s
e
with
p
o
o
r
s
tu
d
y
h
a
b
its
an
d
th
eir
ac
a
d
em
ic
ac
h
iev
em
e
n
t
[
1
6
]
,
[
4
1
]
.
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
Th
e
med
ia
tin
g
effec
t o
f stu
d
y
h
a
b
its
b
etw
ee
n
p
a
r
en
ta
l in
v
o
l
ve
men
t a
n
d
a
lg
eb
r
a
ic
…
(
I
md
a
d
A
li
)
587
5.
CO
NCLU
SI
O
N
T
h
e
s
tu
d
y
in
v
esti
g
ates
th
e
m
ed
iatin
g
ef
f
ec
t
o
f
SH
in
th
e
r
el
atio
n
s
h
ip
b
etwe
en
PI
an
d
alg
e
b
r
aic
PS
A.
T
h
e
s
tu
d
y
f
o
u
n
d
a
s
ig
n
if
ican
t
p
o
s
itiv
e
r
elatio
n
s
h
ip
am
o
n
g
th
e
v
ar
iab
les
(
s
tu
d
y
h
ab
its
an
d
p
ar
e
n
tal
in
v
o
lv
em
e
n
t)
,
an
d
alg
eb
r
aic
P
SA.
T
h
e
f
in
d
in
g
r
e
v
ea
led
th
at
SH
h
as
a
s
ig
n
if
ican
t
p
o
s
itiv
e
ef
f
ec
t
o
n
alg
eb
r
aic
PS
A
an
d
m
ed
iates
th
e
r
elatio
n
s
h
ip
b
etwe
en
PI
an
d
alg
e
b
r
aic
PS
A.
B
ased
o
n
th
e
f
in
d
in
g
s
,
s
tu
d
en
ts
’
b
etter
s
tu
d
y
h
ab
its
f
o
r
lear
n
in
g
m
a
y
im
p
r
o
v
e
th
eir
alg
eb
r
aic
PS
A
an
d
m
ath
em
atics
as
a
wh
o
le.
Als
o
,
p
ar
en
ts
an
d
teac
h
er
s
s
h
o
u
ld
b
e
m
o
r
e
co
n
ce
r
n
ed
ab
o
u
t th
eir
ch
ild
r
en
’
s
SH f
r
o
m
a
n
ea
r
ly
a
g
e
wh
ile
lear
n
i
n
g
m
ath
em
atics.
I
t
is
r
ec
o
m
m
e
n
d
ed
th
at
s
tu
d
e
n
ts
’
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
b
e
d
ev
elo
p
ed
t
h
r
o
u
g
h
t
h
eir
b
e
tter
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in
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f
ield
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.
RE
F
E
R
E
NC
E
S
[
1
]
K
.
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a
f
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d
A
.
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3
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4
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[
5
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L.
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Ph
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[
6
]
J.
R
.
P
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M
.
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[
7
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P
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,
S
.
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[
8
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.
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[
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.
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.
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[
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1
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