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The self
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K
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:
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d
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ca
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t
Ma
th
em
atica
l
Pro
b
lem
s
o
lv
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g
Self
-
ef
f
icac
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Un
d
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s
tan
d
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ater
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T
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s
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c
c
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a
rticle
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d
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CC B
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C
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r
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p
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A
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:
B
aid
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Dep
ar
tm
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t o
f
Ma
th
em
atics E
d
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ca
tio
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Facu
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T
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T
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E
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Un
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Mu
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Ma
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E
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b
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m
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@
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1.
I
NT
RO
D
UCT
I
O
N
Ma
th
em
atics
is
th
e
f
o
u
n
d
a
tio
n
f
o
r
m
a
n
y
p
r
o
f
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io
n
s
,
esp
ec
ially
s
cien
ce
,
tech
n
o
lo
g
y
,
an
d
en
g
in
ee
r
in
g
.
Ho
wev
e
r
,
m
ath
em
atics
is
o
f
ten
co
n
s
id
er
ed
d
if
f
icu
lt,
an
d
m
a
n
y
s
tu
d
e
n
ts
leav
e
s
cien
ce
,
tech
n
o
lo
g
y
,
en
g
in
ee
r
in
g
,
an
d
m
ath
em
atics
(
STE
M)
d
is
cip
lin
es
[
1
]
.
As
a
r
esu
lt,
ca
r
ee
r
s
i
n
en
g
in
ee
r
in
g
a
n
d
tech
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g
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,
as
well
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th
o
s
e
th
at
r
eq
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ir
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m
ath
em
atics,
a
r
e
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.
Alth
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g
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lly
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r
h
ate
m
ath
em
atics
as
an
ac
ad
em
ic
d
is
cip
lin
e
[
2
]
,
[
3
]
.
Ho
wev
er
,
m
o
s
t
s
tu
d
en
ts
s
till
n
ee
d
h
elp
to
lear
n
m
ath
em
atics.
Pro
b
lem
s
i
n
lea
r
n
in
g
m
ath
em
atics
r
elate
to
wh
at
an
d
h
o
w
to
teac
h
m
ath
em
atics
an
d
w
h
at
is
ess
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tial
f
o
r
s
tu
d
en
ts
to
lear
n
in
an
d
th
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o
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g
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m
ath
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ati
cs.
T
h
e
g
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als
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f
lear
n
in
g
m
ath
em
atics
in
clu
d
e
u
n
d
er
s
tan
d
i
n
g
m
ater
ial
co
n
c
ep
ts
an
d
s
o
lv
in
g
p
r
o
b
lem
s
[
4
]
.
Ma
th
e
m
atica
l
p
r
o
b
lem
-
s
o
lv
in
g
r
ef
er
s
to
th
e
p
r
o
ce
s
s
o
f
u
s
in
g
m
ath
em
atica
l
co
n
ce
p
ts
an
d
s
tr
ateg
ies
to
s
o
lv
e
co
m
p
lex
p
r
o
b
lem
s
o
r
n
o
n
-
r
o
u
ti
n
e
p
r
o
b
lem
s
an
d
is
r
elate
d
to
a
s
eq
u
en
tial a
n
d
s
y
s
tem
atic
p
r
o
ce
s
s
o
f
o
b
tai
n
in
g
b
etter
a
n
d
c
o
r
r
ec
t r
esu
lts
[
5
]
–
[
8
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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J
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Th
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ca
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2629
B
ased
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r
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s
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ath
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tates
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m
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atica
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ab
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f
s
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in
I
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ar
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s
till
b
elo
w
th
e
in
ter
n
atio
n
al
a
v
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ag
e
[
9
]
,
[
1
0
]
.
T
h
e
r
esu
lts
in
d
icate
th
at
s
tu
d
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'
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.
T
h
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p
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b
lem
-
s
o
lv
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g
s
k
ills
o
f
s
tu
d
en
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ca
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b
e
i
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f
lu
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ce
d
b
y
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f
f
ac
to
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s
.
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ak
in
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s
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tiv
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th
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ar
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af
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s
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co
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n
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an
d
af
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[
1
1
]
.
T
h
e
c
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itiv
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asp
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t,
s
p
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if
ically
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R
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[
1
2
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.
T
h
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[
1
3
]
.
W
h
en
in
d
iv
id
u
als
en
co
u
n
ter
a
p
r
o
b
lem
,
t
h
eir
in
itial
ap
p
r
o
ac
h
in
v
o
lv
es
s
ee
k
in
g
to
c
o
m
p
r
e
h
en
d
it
th
o
r
o
u
g
h
ly
.
Fu
r
th
e
r
m
o
r
e,
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
ca
n
also
b
e
in
f
lu
en
ce
d
b
y
m
etac
o
g
n
itio
n
,
th
e
n
ee
d
f
o
r
co
g
n
itio
n
,
an
d
i
n
tellig
en
ce
[
1
4
]
.
Af
f
ec
tiv
e
v
ar
ia
b
les
m
ay
n
o
t
h
av
e
a
d
ir
ec
t
im
p
ac
t
o
n
p
r
o
b
l
em
-
s
o
lv
in
g
s
k
ills
,
b
u
t
th
ey
ca
n
ex
er
t
an
in
d
ir
ec
t
in
f
lu
en
ce
.
I
n
d
iv
id
u
als
wh
o
lack
co
n
f
id
en
ce
in
th
eir
p
r
o
b
lem
-
s
o
lv
in
g
ab
ilit
ies
ten
d
to
i
n
v
est
less
tim
e
in
tack
lin
g
p
r
o
b
lem
s
,
m
ak
in
g
th
e
p
r
o
b
lem
-
s
o
lv
in
g
p
r
o
ce
s
s
m
o
r
e
ch
allen
g
in
g
f
o
r
th
em
.
Am
o
n
g
th
e
c
r
u
cial
v
ar
iab
les d
is
cu
s
s
ed
in
th
is
s
tu
d
y
th
at
h
av
e
a
r
elatio
n
s
h
ip
with
af
f
ec
tiv
e
asp
ec
ts
is
s
elf
-
ef
f
icac
y
(
SE)
[
1
5
]
.
Self
-
co
n
f
id
en
ce
(
s
elf
-
ef
f
icac
y
a
n
d
s
elf
-
co
n
ce
p
t)
ar
e
two
f
ac
to
r
s
th
at
s
ig
n
if
ican
tly
in
f
lu
e
n
ce
m
o
tiv
atio
n
an
d
s
tu
d
e
n
t
lear
n
in
g
o
u
tco
m
es
f
r
o
m
a
c
o
g
n
itiv
e,
s
o
cial,
o
r
p
s
y
c
h
o
lo
g
ical
p
er
s
p
ec
tiv
e
[
1
6
]
–
[
1
8
]
.
Self
-
c
o
n
ce
p
t
a
n
d
SE
ar
e
s
elf
-
p
er
ce
p
tio
n
s
r
elate
d
to
co
m
p
eten
cies
th
at
in
f
lu
en
ce
s
tu
d
en
t
s
u
cc
ess
in
e
d
u
ca
tio
n
[
1
7
]
,
[
1
9
]
.
Self
-
co
n
ce
p
t
ab
ilit
y
is
a
m
en
tal
r
e
p
r
esen
tat
io
n
o
f
a
s
tu
d
en
t'
s
ab
ilit
ies
in
th
e
ac
ad
em
ic
f
ield
in
g
en
er
al
o
r
in
a
p
ar
ticu
lar
ac
ad
em
ic
f
ield
.
SE
is
d
ef
in
ed
as
th
e
b
elief
in
o
n
e'
s
ca
p
ac
ity
to
ac
co
m
p
lis
h
task
s
o
r
d
em
o
n
s
tr
ate
s
k
ills
e
f
f
ec
tiv
ely
[
2
0
]
.
SE
r
ef
er
s
to
s
tu
d
en
ts
'
b
elief
th
at
th
ey
ca
n
m
aster
a
g
iv
en
ac
ad
em
ic
task
at
a
s
p
ec
if
ied
lev
el
[
1
7
]
,
[
1
9
]
,
an
in
d
i
v
id
u
al'
s
b
elief
in
th
eir
ab
ilit
y
to
s
u
cc
ess
f
u
lly
p
er
f
o
r
m
a
s
p
ec
if
ic
task
o
r
ac
h
iev
e
a
d
esire
d
o
u
tco
m
e
[
1
1
]
,
[
2
1
]
,
[
2
2
]
.
I
t
p
la
y
s
a
cr
u
cial
r
o
le
in
m
o
tiv
atio
n
,
lea
r
n
i
n
g
,
an
d
b
eh
a
v
io
r
al
ch
an
g
e.
S
E
b
elief
s
in
f
lu
en
ce
h
o
w
in
d
iv
id
u
als
th
i
n
k
,
f
ee
l,
an
d
b
e
h
av
e,
af
f
ec
tin
g
th
ei
r
ef
f
o
r
t
,
p
er
s
is
ten
ce
,
a
n
d
em
o
tio
n
al
r
e
s
p
o
n
s
es
in
v
a
r
io
u
s
task
s
an
d
ch
allen
g
i
n
g
s
itu
atio
n
s
[
2
2
]
Ma
th
SE
r
ef
er
s
to
a
ch
ild
'
s
b
elief
in
th
eir
ab
ilit
y
to
p
er
f
o
r
m
well
in
m
ath
em
atics
an
d
p
lay
s
a
m
e
d
iatin
g
r
o
le
in
t
h
e
r
elatio
n
s
h
ip
b
etwe
en
p
ar
en
tin
g
s
ty
le
a
n
d
m
ath
an
x
iety
,
s
u
g
g
esti
n
g
th
at
en
h
a
n
cin
g
c
h
ild
r
en
'
s
b
elief
in
th
eir
m
at
h
ab
ilit
ies
ca
n
h
el
p
allev
iate
m
ath
an
x
iety
[
2
1
]
.
Stu
d
en
ts
'
SE
p
er
ce
p
tio
n
in
m
ath
em
atics,
alo
n
g
with
r
ea
d
in
g
co
m
p
r
eh
e
n
s
io
n
an
d
m
ath
em
at
ics
attitu
d
e,
p
lay
s
a
s
ig
n
if
ican
t
r
o
le
in
t
h
eir
ab
ilit
y
to
s
o
lv
e
n
o
n
-
r
o
u
tin
e
m
at
h
em
atica
l
p
r
o
b
lem
s
[
1
1
]
an
d
is
a
s
ig
n
if
ican
t
p
r
e
d
icto
r
o
f
s
tu
d
en
ts
'
ac
ad
em
ic
ac
h
iev
e
m
en
t,
p
ar
ticu
lar
l
y
in
th
eir
p
er
f
o
r
m
an
ce
in
m
ath
em
atics tests
an
d
co
u
r
s
es [
2
2
]
.
SE
is
th
e
b
elief
in
f
in
d
in
g
,
o
r
g
an
izin
g
,
a
n
d
ca
r
r
y
in
g
o
u
t
a
t
ask
to
ac
h
iev
e
a
g
o
al.
C
o
n
f
id
en
ce
h
elp
s
d
ea
l
with
p
r
o
b
lem
s
in
ev
er
y
d
ay
life
.
T
h
e
lev
el
o
f
s
tu
d
e
n
t
SE
is
clo
s
ely
r
elate
d
to
s
o
lv
in
g
p
r
o
b
lem
s
o
r
ass
ig
n
ed
task
s
an
d
lear
n
i
n
g
ac
h
iev
em
en
t
[
2
3
]
,
[
2
4
]
.
Stu
d
en
ts
with
h
ig
h
SE
a
b
ilit
ies
will
f
o
cu
s
m
o
r
e
o
n
f
in
d
in
g
s
o
lu
tio
n
s
to
p
r
o
b
lem
s
th
an
th
in
k
in
g
a
b
o
u
t
th
ei
r
d
ef
icien
cies
[
2
5
]
,
[
2
6
]
.
Stu
d
en
ts
in
th
e
h
ig
h
SE
ca
teg
o
r
y
ca
n
m
aster
t
h
e
th
r
ee
in
d
icato
r
s
o
f
s
tu
d
en
ts
'
m
ath
em
atica
l
u
n
d
e
r
s
tan
d
in
g
a
b
ilit
ies:
tr
an
s
latio
n
,
in
ter
p
r
etatio
n
,
an
d
ex
p
lo
r
atio
n
.
Stu
d
en
ts
in
th
e
lo
w
SE
ca
te
g
o
r
ies
o
n
ly
m
aster
tr
an
s
latio
n
b
u
t
ca
n
n
o
t
ac
h
iev
e
in
ter
p
r
etatio
n
an
d
ex
p
lo
r
atio
n
in
d
icato
r
s
.
T
h
u
s
,
s
tu
d
en
ts
w
h
o
h
av
e
h
ig
h
o
r
lo
w
SE
ca
n
m
aster
in
d
icato
r
s
o
f
m
ath
em
atica
l u
n
d
e
r
s
tan
d
in
g
i
n
d
eter
m
in
in
g
to
p
r
o
b
lem
-
s
o
lv
e
an
d
h
a
v
e
a
g
o
o
d
s
elf
-
co
n
ce
p
t [
2
7
]
.
Sev
er
al
s
tu
d
ies
o
n
SE
ar
e
ass
o
ciate
d
with
p
r
o
b
lem
-
s
o
lv
in
g
[
1
1
]
,
teac
h
er
p
r
o
f
ess
io
n
al
d
e
v
elo
p
m
en
t
[
2
8
]
,
an
d
th
e
m
ajo
r
ity
is
ass
o
ciate
d
with
m
o
tiv
atio
n
an
d
p
er
f
o
r
m
a
n
ce
[
2
1
]
,
[
2
2
]
,
[
2
9
]
,
[
3
0
]
.
Giv
en
th
e
r
em
ar
k
ab
le
im
p
o
r
tan
ce
o
f
SE
in
th
e
ac
q
u
is
itio
n
o
f
m
ath
e
m
atica
l
k
n
o
wled
g
e
an
d
p
r
o
b
lem
-
s
o
lv
in
g
ab
ilit
ies,
co
u
p
led
with
th
e
r
estricte
d
n
u
m
b
er
o
f
r
esear
ch
in
v
esti
g
atio
n
s
f
o
cu
s
in
g
o
n
SE
am
o
n
g
e
d
u
ca
tio
n
al
s
tu
d
en
ts
,
esp
ec
ially
in
th
e
ar
ea
o
f
u
n
d
e
r
s
tan
d
in
g
c
o
n
ten
t
a
n
d
s
o
lv
in
g
p
r
o
b
lem
s
,
it
is
im
p
er
ativ
e
t
o
co
n
d
u
ct
r
esear
ch
in
th
is
d
o
m
ain
.
E
d
u
ca
tio
n
s
tu
d
e
n
ts
h
o
ld
a
c
r
u
cial
p
o
s
itio
n
i
n
m
o
l
d
in
g
th
e
m
ath
em
atica
l
co
m
p
ete
n
cies
an
d
p
r
o
b
lem
-
s
o
lv
in
g
p
r
o
f
icien
cies
o
f
f
o
r
th
c
o
m
in
g
g
en
er
atio
n
s
.
T
h
u
s
,
co
m
p
r
e
h
en
d
i
n
g
th
eir
SE
lev
els
in
th
ese
ar
ea
s
is
e
s
s
en
tial
f
o
r
en
h
an
cin
g
teac
h
in
g
m
eth
o
d
o
lo
g
ies
an
d
ad
v
an
cin
g
ed
u
ca
tio
n
al
r
esu
lts
.
T
h
r
o
u
g
h
ex
p
lo
r
in
g
SE
with
in
th
is
s
p
ec
if
ic
g
r
o
u
p
an
d
s
ettin
g
,
v
alu
ab
l
e
in
s
ig
h
ts
ca
n
b
e
ac
q
u
ir
ed
in
to
th
e
elem
en
ts
th
at
im
p
ac
t
th
eir
ac
ad
em
ic
p
er
f
o
r
m
an
ce
,
th
er
e
b
y
co
n
tr
ib
u
tin
g
t
o
th
e
f
o
r
m
u
latio
n
o
f
e
f
f
icien
t
in
ter
v
en
tio
n
s
a
n
d
s
tr
ateg
ies to
b
o
ls
ter
th
eir
ed
u
c
atio
n
al
jo
u
r
n
e
y
.
W
h
ile
p
r
ev
io
u
s
r
esear
ch
h
a
s
ex
ten
s
iv
ely
ex
am
in
e
d
SE
in
r
elatio
n
to
m
o
tiv
atio
n
,
ac
ad
em
ic
p
er
f
o
r
m
an
ce
,
an
d
teac
h
er
d
ev
elo
p
m
e
n
t,
s
tu
d
ies
f
o
cu
s
in
g
o
n
th
e
in
ter
p
la
y
b
etwe
en
SE
in
co
n
ten
t
co
m
p
r
eh
e
n
s
io
n
an
d
m
ath
em
at
ical
p
r
o
b
lem
-
s
o
lv
i
n
g
ab
ilit
ies
am
o
n
g
ed
u
ca
tio
n
s
tu
d
en
ts
r
e
m
ain
lim
ited
.
T
h
is
s
tu
d
y
f
ills
th
at
g
ap
b
y
in
v
esti
g
atin
g
h
o
w
SE
in
u
n
d
er
s
tan
d
in
g
s
u
b
ject
m
atter
c
o
r
r
elate
s
with
SE
in
s
o
lv
in
g
m
ath
em
atica
l
p
r
o
b
lem
s
,
p
ar
ti
cu
lar
ly
am
o
n
g
m
ath
em
atics
a
n
d
b
i
o
lo
g
y
ed
u
ca
tio
n
s
tu
d
e
n
ts
.
Fu
r
th
er
m
o
r
e,
b
y
an
aly
zin
g
d
is
cip
lin
e
-
s
p
ec
if
ic
v
ar
iatio
n
s
in
SE
lev
els,
th
is
s
tu
d
y
p
r
o
v
id
es
n
ew
in
s
ig
h
ts
i
n
to
h
o
w
SE
d
if
f
er
s
b
etwe
en
s
tu
d
en
ts
f
r
o
m
d
is
tin
ct
ac
ad
em
ic
b
ac
k
g
r
o
u
n
d
s
an
d
h
o
w
th
ese
d
if
f
er
e
n
ce
s
m
ay
in
f
lu
en
ce
f
u
tu
r
e
in
s
tr
u
ctio
n
al
s
tr
ateg
ies.
T
h
e
f
i
n
d
in
g
s
ar
e
e
x
p
ec
ted
to
co
n
tr
i
b
u
te
to
th
e
d
ev
elo
p
m
en
t
o
f
tar
g
eted
in
ter
v
en
tio
n
s
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
.
4
,
Au
g
u
s
t
20
25
:
2
6
2
8
-
2
6
3
9
2630
aim
ed
at
s
tr
en
g
th
en
i
n
g
SE
an
d
en
h
an
ci
n
g
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
am
o
n
g
f
u
tu
r
e
ed
u
ca
to
r
s
,
u
ltima
tely
im
p
r
o
v
in
g
m
at
h
em
atics
in
s
tr
u
ctio
n
q
u
ality
in
e
d
u
ca
tio
n
al
s
ettin
g
s
.
B
ased
o
n
th
is
d
escr
ip
ti
o
n
,
th
is
p
ap
er
aim
s
to
an
s
wer
th
e
f
o
llo
win
g
q
u
esti
o
n
s
:
i)
W
h
at
is
th
e
SE
o
f
b
io
lo
g
y
a
n
d
m
ath
em
atics
ed
u
ca
tio
n
s
tu
d
en
ts
in
u
n
d
e
r
s
tan
d
in
g
th
e
m
at
er
ial,
an
d
t
h
eir
SE
in
s
o
lv
in
g
m
ath
e
m
atica
l p
r
o
b
lem
s
?
ii)
I
s
th
er
e
a
s
ig
n
if
ican
t
r
elatio
n
s
h
ip
b
etwe
en
th
e
SE
o
f
m
at
h
em
atics
an
d
b
io
lo
g
y
ed
u
ca
tio
n
s
tu
d
en
ts
in
u
n
d
er
s
tan
d
i
n
g
th
e
m
ater
ial
an
d
th
e
SE
o
f
ed
u
ca
tio
n
s
tu
d
en
ts
in
s
o
lv
in
g
m
at
h
em
atics p
r
o
b
l
em
s
?
iii)
I
s
th
er
e
a
s
ig
n
if
ican
t
d
if
f
er
en
ce
in
th
e
SE
o
f
m
ath
em
atics
an
d
b
io
lo
g
y
ed
u
ca
tio
n
s
tu
d
en
ts
in
u
n
d
er
s
tan
d
i
n
g
th
e
m
ater
ial
an
d
s
tu
d
en
t'
s
SE
in
s
o
lv
in
g
m
ath
em
atics p
r
o
b
lem
s
?
2.
M
E
T
H
O
D
2
.
1
.
T
y
pes
a
nd
a
pp
ro
a
che
s
T
h
is
ty
p
e
o
f
r
esear
ch
was
a
s
u
r
v
ey
with
a
q
u
an
titativ
e
ap
p
r
o
ac
h
.
T
h
is
is
b
ec
au
s
e
th
e
r
esear
ch
o
b
jectiv
es
ar
e
to
d
escr
ib
e
th
e
lev
el
o
f
s
tu
d
en
ts
'
SE,
an
aly
ze
th
e
r
elatio
n
s
h
ip
s
am
o
n
g
r
el
ev
an
t
v
ar
iab
les,
an
d
test
d
if
f
er
en
ce
s
in
SE
r
elate
d
to
u
n
d
er
s
tan
d
i
n
g
m
ater
ial
an
d
s
o
lv
in
g
m
ath
em
atica
l
p
r
o
b
lem
s
am
o
n
g
s
tu
d
en
ts
in
b
io
lo
g
y
an
d
m
at
h
em
atics
ed
u
ca
tio
n
p
r
o
g
r
am
s
[
3
1
]
.
T
h
e
q
u
an
titativ
e
ap
p
r
o
ac
h
is
ap
p
r
o
p
r
iate
as
it
allo
ws
f
o
r
th
e
c
o
llectio
n
o
f
n
u
m
er
ica
l
d
ata
an
d
th
e
ap
p
licatio
n
o
f
s
tatis
tical
tech
n
iq
u
es
to
ex
am
in
e
p
atter
n
s
an
d
test
h
y
p
o
th
eses
.
2
.
2
.
P
a
rt
icipa
nt
T
h
e
r
esear
ch
p
ar
ticip
an
ts
wer
e
s
tu
d
en
ts
f
r
o
m
Mu
h
am
m
ad
i
y
a
h
Ma
lan
g
’
s
Facu
lty
o
f
T
ea
ch
e
r
T
r
ain
in
g
an
d
E
d
u
ca
tio
n
,
with
1
5
5
(
6
2
%)
s
tu
d
y
in
g
m
ath
em
atics
ed
u
ca
tio
n
an
d
7
4
(
4
4
.
6
%)
s
tu
d
y
in
g
b
io
lo
g
y
.
T
h
ese
p
ar
ticip
an
ts
ar
e
ap
p
r
o
p
r
iate
f
o
r
s
u
r
v
ey
r
esear
ch
with
a
s
am
p
le
s
ize
o
f
m
o
r
e
th
an
3
0
%
[
3
1
]
,
[
3
2
]
.
T
h
ese
two
s
tu
d
y
p
r
o
g
r
am
s
wer
e
ch
o
s
en
b
ec
au
s
e
th
ey
f
all
in
to
th
e
m
a
th
em
atics
an
d
s
cien
ce
ca
teg
o
r
y
,
wh
ich
in
clu
d
es
s
tu
d
en
ts
wh
o
h
av
e
tak
en
m
ath
em
atics/s
tat
is
tic
s
o
r
r
esear
ch
m
eth
o
d
s
co
u
r
s
es.
Gr
ad
e
lev
el,
p
er
ce
p
tio
n
o
f
o
n
e'
s
ab
ilit
ies,
an
d
lev
el
o
f
m
o
tiv
at
io
n
ar
e
a
co
n
f
o
u
n
d
in
g
f
ac
to
r
i
n
r
esear
ch
o
n
s
tu
d
e
n
t
SE
[
3
3
]
–
[
3
5
]
.
As
a
r
esu
lt,
th
e
r
esear
ch
p
ar
ticip
an
ts
wer
e
in
ad
jace
n
t
s
em
ester
s
:
m
ath
e
m
atics
ed
u
ca
tio
n
s
tu
d
en
ts
in
s
em
ester
s
4
an
d
6
,
an
d
b
i
o
lo
g
y
ed
u
ca
tio
n
s
tu
d
en
t
s
in
s
em
ester
s
6
an
d
8
,
r
esp
ec
tiv
ely
.
T
h
e
av
er
a
g
e
ac
ad
e
m
ic
ac
h
iev
em
en
t
i
n
d
ex
o
f
s
tu
d
en
ts
wh
o
p
ar
ticip
ated
was
r
elativ
ely
s
im
ilar
to
m
ath
em
atics
an
d
b
io
lo
g
y
ed
u
ca
tio
n
,
n
am
ely
3
.
4
6
an
d
3
.
6
3
,
r
esp
ec
tiv
ely
.
Fu
r
th
er
m
o
r
e
,
th
e
h
ea
d
s
o
f
t
h
e
m
ath
em
atics
an
d
b
io
lo
g
y
ed
u
ca
tio
n
s
tu
d
y
p
r
o
g
r
am
s
g
av
e
th
eir
p
er
m
is
s
io
n
f
o
r
t
h
is
r
esear
ch
.
All
p
ar
ticip
an
ts
v
o
lu
n
tar
ily
co
m
p
leted
th
e
Go
o
g
le
Fo
r
m
ask
in
g
ab
o
u
t
th
eir
SE
i
n
u
n
d
er
s
tan
d
i
n
g
th
e
m
ater
ial
an
d
s
o
lv
in
g
p
r
o
b
le
m
s
.
All p
ar
ticip
an
ts
'
id
en
titi
es a
r
e
s
tr
ictly
co
n
f
id
en
tial.
2
.
3
.
I
ns
t
rum
ent
s
T
h
e
r
esear
ch
in
s
tr
u
m
en
t
u
s
e
d
in
th
is
s
tu
d
y
was
a
s
tu
d
e
n
t
SE
q
u
esti
o
n
n
air
e
f
o
r
u
n
d
er
s
tan
d
in
g
m
ater
ial,
wh
ich
co
n
s
is
ted
o
f
e
ig
h
t
s
tatem
en
t
item
s
,
an
d
s
o
lv
in
g
m
ath
em
atics
p
r
o
b
lem
s
,
wh
ich
co
m
p
r
is
ed
n
i
n
e
s
tatem
en
t
item
s
.
E
ac
h
item
h
a
s
a
ch
o
ice
o
f
lev
el
o
f
c
o
n
f
id
e
n
ce
/co
n
f
id
e
n
ce
b
etwe
en
0
a
n
d
1
0
[
3
6
]
.
All
item
s
wer
e
f
o
u
n
d
to
b
e
v
alid
th
r
o
u
g
h
Per
s
o
n
c
o
r
r
elatio
n
al
an
aly
s
is
with
a
p
-
v
alu
e
<
0
.
0
5
.
T
h
e
SE
in
s
tr
u
m
en
t
in
u
n
d
er
s
tan
d
i
n
g
m
ater
ial
h
as
a
r
eliab
ilit
y
v
alu
e
o
f
0
.
9
3
(
M
cDo
n
ald
’
s
ω
)
o
r
0
.
7
8
(
C
r
o
n
b
ac
h
’
s
α
)
,
in
d
icatin
g
r
eliab
ilit
y
.
T
h
e
v
alid
ity
o
f
t
h
e
s
tu
d
en
t
SE
q
u
esti
o
n
n
air
e
in
u
n
d
er
s
tan
d
i
n
g
th
e
m
ater
ial
f
r
o
m
item
s
1
to
8
was
0
.
6
1
,
0
.
7
6
,
0
.
8
4
,
0
.
8
9
,
0
.
8
9
,
0
.
8
2
,
0
.
7
1
,
an
d
0
.
5
6
.
Me
an
w
h
ile,
th
e
v
alid
ity
o
f
s
tu
d
en
ts
’
SE
item
s
in
s
o
lv
in
g
m
ath
em
atics
p
r
o
b
lem
s
was
0
.
6
6
,
0
.
7
1
,
0
.
7
5
,
0
.
8
7
,
0
.
8
9
,
0
.
5
8
,
0
.
7
6
,
0
.
7
0
,
an
d
0
.
6
1
.
T
h
e
i
n
s
tr
u
m
en
t
is
r
eliab
le,
as in
d
icate
d
b
y
a
Mc
D
o
n
ald
’
s
ω
v
alu
e
o
f
0
.
9
3
o
r
a
C
r
o
n
b
ac
h
α
v
alu
e
o
f
0
.
7
5
.
2
.
4
.
Da
t
a
a
na
ly
s
is
B
ef
o
r
e
an
aly
s
is
,
th
e
d
ata
w
as
v
alid
ated
.
Valid
atio
n
wa
s
d
o
n
e
in
two
way
s
:
id
en
ti
f
y
in
g
a
n
d
ev
alu
atin
g
o
u
tlier
d
ata
th
at
m
ay
h
u
r
t
th
e
a
n
aly
s
is
an
d
d
eter
m
in
in
g
th
e
v
alid
ity
an
d
r
eliab
ilit
y
o
f
th
e
in
s
tr
u
m
en
ts
.
All
in
s
tr
u
m
en
ts
a
r
e
r
eliab
le,
an
d
all
item
s
ar
e
v
alid
.
Acc
o
r
d
in
g
to
th
e
r
esu
lts
o
f
id
en
tify
in
g
an
d
ev
alu
atin
g
o
u
tlier
d
ata
,
7
b
io
l
o
g
y
s
tu
d
en
ts
o
u
t
o
f
7
4
m
a
d
e
er
r
o
r
s
wh
en
f
illi
n
g
o
u
t
th
e
in
s
tr
u
m
en
t,
in
clu
d
in
g
en
ter
in
g
m
o
r
e
th
a
n
o
n
e
v
alu
e
in
o
n
e
o
f
th
e
in
s
tr
u
m
en
t
ite
m
s
.
So
,
v
alid
d
ata
c
o
m
es
f
r
o
m
1
5
5
m
ath
em
atics
ed
u
ca
tio
n
s
tu
d
e
n
ts
an
d
6
7
b
io
l
o
g
y
ed
u
ca
tio
n
s
tu
d
e
n
ts
.
Descr
ip
tiv
e
s
tatis
tic
s
(
m
ea
n
an
d
s
tan
d
ar
d
d
e
v
iatio
n
(
SD)
)
f
o
r
all
v
ar
iab
les
wer
e
ca
lcu
lated
ab
o
u
t
s
tu
d
en
t
SE
in
u
n
d
er
s
tan
d
in
g
th
e
m
ate
r
ial
an
d
s
o
lv
i
n
g
m
ath
em
atica
l
p
r
o
b
le
m
s
.
T
h
en
,
th
e
ca
teg
o
r
ies
ar
e
h
ig
h
,
m
o
d
er
ate,
an
d
l
o
w.
H
ig
h
ca
teg
o
r
y
if
t
h
e
s
co
r
e
,
>
+
0
.
5
,
m
o
d
er
ate
if
th
e
s
co
r
e
is
−
0
.
5
≤
≤
+
0
.
5
,
an
d
lo
w
if
th
e
s
co
r
e
is
−
0
.
5
<
.
T
h
e
co
r
r
elatio
n
al
test
u
s
es
Per
s
o
n
co
r
r
elatio
n
to
test
wh
eth
er
th
er
e
is
a
s
ig
n
if
ican
t
r
elatio
n
s
h
ip
b
etwe
e
n
s
tu
d
en
t’
s
SE
in
u
n
d
er
s
tan
d
i
n
g
th
e
m
ater
ial
an
d
s
o
lv
in
g
m
ath
em
atica
l
p
r
o
b
l
em
s
.
I
n
d
ep
en
d
en
t
s
am
p
le
t
-
tes
ts
wer
e
u
s
ed
to
tes
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
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v
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&
R
es E
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c
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SS
N:
2252
-
8
8
2
2
Th
e
s
elf
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effica
cy
o
f e
d
u
ca
tio
n
s
tu
d
en
ts
in
u
n
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ers
ta
n
d
i
n
g
ma
teri
a
ls
a
n
d
ma
th
ema
tica
l
…
(
B
a
id
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r
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)
2631
wh
eth
er
th
er
e
wer
e
s
ig
n
if
ica
n
t
d
if
f
er
en
ce
s
b
etwe
en
s
tu
d
e
n
t
SE
in
u
n
d
e
r
s
tan
d
in
g
t
h
e
m
ater
ial
an
d
s
o
l
v
in
g
m
ath
em
atic
p
r
o
b
lem
s
f
o
r
m
at
h
em
atics
an
d
b
i
o
lo
g
y
ed
u
ca
ti
o
n
s
tu
d
en
ts
.
T
h
e
t
-
tes
t
is
a
p
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u
l
s
tatis
tical
test
th
at
ca
n
b
e
u
s
ed
t
o
d
eter
m
i
n
e
wh
eth
er
two
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ets
o
f
s
am
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le
d
ata
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e
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ig
n
if
ican
tly
d
if
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er
e
n
t
f
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o
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ea
ch
o
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er
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en
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ey
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e
d
if
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er
e
n
t
s
izes
an
d
u
n
eq
u
al
v
a
r
ian
ce
s
[
3
7
]
,
[
3
8
]
.
All
test
s
u
s
ed
th
e
lev
el
o
f
s
tatis
tica
l
s
ig
n
if
ican
ce
at
p
<0
.
0
5
a
n
d
u
s
e
d
J
ASP s
o
f
twar
e
v
er
s
io
n
0
.
1
6
.
3
.
0
f
o
r
W
in
d
o
ws.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
3
.
1
.
Resul
t
s
T
h
e
r
esu
lts
o
f
th
is
s
tu
d
y
ar
e
p
r
esen
ted
b
ased
o
n
th
e
r
esear
ch
o
b
jectiv
es,
wh
ich
in
clu
d
e
d
escr
ib
in
g
th
e
lev
el
o
f
s
tu
d
en
ts
'
SE,
an
aly
zin
g
th
e
r
elatio
n
s
h
ip
s
b
etwe
en
r
el
ev
an
t
v
a
r
iab
les,
an
d
ex
a
m
in
in
g
d
if
f
er
en
ce
s
in
SE
r
elate
d
to
u
n
d
er
s
tan
d
in
g
m
ath
em
atica
l
co
n
ce
p
ts
an
d
s
o
l
v
in
g
m
ath
em
atica
l
p
r
o
b
lem
s
.
T
h
e
an
aly
s
is
co
m
p
ar
es
s
tu
d
en
ts
f
r
o
m
b
io
lo
g
y
an
d
m
ath
em
atics
ed
u
ca
tio
n
p
r
o
g
r
am
s
,
p
r
o
v
id
in
g
a
clea
r
er
p
i
ctu
r
e
o
f
h
o
w
th
eir
ac
ad
em
ic
b
ac
k
g
r
o
u
n
d
m
i
g
h
t
i
n
f
lu
en
ce
th
eir
co
n
f
i
d
en
ce
in
d
ea
lin
g
with
m
ath
em
atica
l
c
o
n
ten
t
an
d
p
r
o
b
lem
-
s
o
lv
in
g
task
s
.
3
.
1
.
1
.
Descript
io
n o
f
s
elf
-
ef
f
i
ca
cy
un
dersta
nd
ing
m
a
t
er
ia
l a
nd
s
o
lv
ing
m
a
t
hema
t
ica
l p
ro
blem
s
I
n
g
en
er
al,
s
tatis
tical
d
escr
ip
tio
n
s
o
f
SE
in
u
n
d
er
s
tan
d
i
n
g
m
ater
ial
an
d
s
o
lv
in
g
m
a
th
em
atica
l
p
r
o
b
lem
s
ar
e
p
r
esen
ted
in
T
a
b
le
1
.
B
ased
o
n
T
ab
le
1
,
t
h
e
m
ea
n
SE
o
f
m
ath
em
atics
an
d
b
io
lo
g
y
ed
u
ca
tio
n
s
tu
d
en
ts
in
u
n
d
er
s
tan
d
in
g
th
e
m
ater
ial
an
d
s
o
lv
in
g
m
ath
p
r
o
b
lem
s
is
r
elativ
ely
s
im
ilar
.
T
h
is
f
in
d
in
g
s
u
g
g
ests
th
at,
o
n
av
e
r
ag
e,
b
o
th
g
r
o
u
p
s
o
f
s
tu
d
e
n
ts
ten
d
to
e
x
h
ib
it
c
o
m
p
ar
ab
le
le
v
els
o
f
SE
in
th
ese
s
p
ec
if
ic
asp
ec
ts
o
f
th
eir
ac
ad
em
ic
p
u
r
s
u
its
.
Fu
r
th
er
,
th
is
f
in
d
in
g
h
i
g
h
lig
h
ts
th
e
im
p
o
r
tan
ce
o
f
p
r
o
m
o
tin
g
SE
b
elief
s
am
o
n
g
s
tu
d
en
ts
in
u
n
d
er
s
tan
d
in
g
th
e
m
ater
ial
an
d
s
o
lv
in
g
m
ath
p
r
o
b
lem
s
,
as
it
ca
n
p
o
s
itiv
ely
in
f
lu
en
ce
th
eir
ac
ad
em
ic
p
er
f
o
r
m
an
ce
,
m
o
ti
v
atio
n
,
an
d
o
v
e
r
all
lear
n
in
g
ex
p
er
ien
ce
.
Ad
d
itio
n
ally
,
it
u
n
d
er
s
co
r
es
th
e
s
ig
n
if
ican
ce
o
f
i
d
en
tify
in
g
an
d
ad
d
r
ess
in
g
in
d
iv
id
u
al
d
if
f
e
r
en
ce
s
in
SE
to
en
s
u
r
e
th
at
all
s
tu
d
en
ts
r
ec
eiv
e
th
e
s
u
p
p
o
r
t
n
ee
d
ed
t
o
th
r
iv
e
ac
ad
em
ically
in
th
eir
r
esp
ec
tiv
e
d
i
s
cip
lin
es.
B
ased
o
n
th
e
m
ea
n
s
an
d
SD
,
ca
teg
o
r
ies
o
f
h
ig
h
,
m
e
d
iu
m
,
an
d
lo
w
ar
e
estab
lis
h
ed
f
o
r
SE
in
u
n
d
er
s
t
an
d
in
g
th
e
m
ater
ial
a
n
d
s
o
lv
i
n
g
m
ath
p
r
o
b
lem
s
.
T
h
e
r
esu
lts
o
f
th
e
d
escr
ip
tiv
e
an
aly
s
is
r
eg
ar
d
in
g
SE
in
u
n
d
e
r
s
tan
d
in
g
th
e
m
ater
ial
an
d
SE
in
p
r
o
b
lem
-
s
o
lv
in
g
f
o
r
m
ath
e
m
atics a
n
d
b
io
lo
g
y
e
d
u
ca
tio
n
s
tu
d
e
n
ts
ar
e
p
r
esen
te
d
in
T
ab
le
s
2
a
n
d
3
,
r
esp
ec
tiv
e
ly
.
T
ab
le
1
.
Me
an
an
d
SD o
f
SE
in
u
n
d
e
r
s
tan
d
in
g
t
h
e
m
ater
ial
a
n
d
s
o
lv
in
g
m
ath
em
atica
l p
r
o
b
l
em
s
V
a
r
i
a
b
l
e
M
a
t
h
e
ma
t
i
c
s
s
t
u
d
e
n
t
s
B
i
o
l
o
g
y
s
t
u
d
e
n
t
s
M
e
a
n
s
SD
M
e
a
n
s
SD
S
E
in
u
n
d
e
r
s
t
a
n
d
i
n
g
t
h
e
ma
t
e
r
i
a
l
46
.
25
1
4
.
9
3
48
.
78
14
.
41
S
E
in
p
r
o
b
l
e
ms s
o
l
u
t
i
o
n
58
.
63
17
.
48
58
.
41
17
.
11
T
ab
le
2
.
Descr
ip
tiv
e
s
tatis
tics
f
o
r
m
ath
e
m
atics st
u
d
en
ts
V
a
r
i
a
b
l
e
SE
-
u
n
d
e
r
s
t
a
n
d
t
h
e
ma
t
e
r
i
a
l
SE
-
p
r
o
b
l
e
m
-
so
l
v
i
n
g
Lo
w
M
o
d
e
r
a
t
e
H
i
g
h
Lo
w
M
o
d
e
r
a
t
e
H
i
g
h
V
a
l
i
d
25
1
0
1
29
23
1
0
6
26
M
i
ss
i
n
g
0
0
0
0
0
0
M
e
a
n
s
22
.
480
46
.
284
66
.
724
33
.
957
58
.
264
81
.
962
SD
6
.
4
3
0
8
.
0
2
9
4
.
7
2
8
6
.
6
5
7
9
.
9
0
3
4
.
7
7
1
M
i
n
i
m
u
m
9
.
0
0
0
32
.
000
62
.
000
19
.
000
43
.
000
75
.
000
M
a
x
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m
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m
31
.
000
61
.
000
78
.
000
42
.
000
73
.
000
90
.
000
T
ab
le
3
.
Descr
ip
tiv
e
s
tatis
tics
o
f
b
io
lo
g
y
s
tu
d
e
n
ts
V
a
r
i
a
b
l
e
SE
-
u
n
d
e
r
s
t
a
n
d
t
h
e
ma
t
e
r
i
a
l
SE
-
p
r
o
b
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e
m
-
so
l
v
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n
g
Lo
w
M
o
d
e
r
a
t
e
H
i
g
h
Lo
w
M
o
d
e
r
a
t
e
H
i
g
h
V
a
l
i
d
35
18
14
10
45
12
M
i
ss
i
n
g
0
0
0
0
0
0
M
e
a
n
s
3
7
.
2
2
9
5
6
.
7
7
8
6
7
.
3
5
7
3
0
.
7
0
0
5
8
.
4
6
7
8
1
.
3
3
3
SD
8
.
8
2
2
3
.
8
8
9
3
.
2
9
6
4
.
2
9
6
1
0
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5
6
7
4
.
7
9
3
M
i
n
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m
u
m
1
1
.
0
0
0
5
0
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0
0
0
6
3
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0
0
0
2
4
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0
0
0
4
4
.
0
0
0
7
6
.
0
0
0
M
a
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m
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m
4
8
.
0
0
0
6
2
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0
0
0
7
5
.
0
0
0
3
5
.
0
0
0
7
5
.
0
0
0
8
9
.
0
0
0
B
ased
o
n
T
ab
le
2
,
th
e
d
escr
ip
tiv
e
s
tatis
tics
with
a
s
am
p
le
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f
1
5
5
s
tu
d
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ts
s
h
o
win
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at
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ts
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v
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le
in
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n
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er
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at
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atics
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ater
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s
h
o
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at
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th
e
lo
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teg
o
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er
e
ar
e
2
5
s
tu
d
en
ts
with
an
av
er
ag
e
o
f
2
2
.
4
8
0
;
in
th
e
m
e
d
iu
m
ca
teg
o
r
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,
th
er
e
ar
e
1
0
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s
tu
d
en
ts
with
an
a
v
er
ag
e
o
f
4
6
.
2
8
4
,
wh
ile
f
o
r
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
14
,
No
.
4
,
Au
g
u
s
t
20
25
:
2
6
2
8
-
2
6
3
9
2632
h
ig
h
ca
teg
o
r
y
,
th
er
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9
s
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d
en
ts
with
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a
v
er
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e
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f
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6
.
7
2
4
.
As
well
as
th
e
s
tu
d
en
t
SE
v
ar
iab
le
in
s
o
lv
in
g
m
ath
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r
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lem
s
s
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o
ws th
at
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er
e
ar
e
2
3
s
tu
d
e
n
ts
in
th
e
lo
w
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teg
o
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y
with
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a
v
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e
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f
3
3
.
9
3
7
.
I
n
th
e
m
ed
i
u
m
ca
teg
o
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er
e
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e
1
0
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s
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ts
,
with
an
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er
ag
e
o
f
5
8
.
2
6
4
.
th
e
d
escr
ip
tiv
e
an
al
y
s
is
p
r
o
v
id
es
in
s
ig
h
ts
in
to
th
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d
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tr
ib
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n
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f
s
tu
d
e
n
ts
'
SE
s
co
r
es
in
u
n
d
e
r
s
tan
d
in
g
m
ath
e
m
atics
m
ater
ial
an
d
s
o
lv
in
g
m
ath
p
r
o
b
lem
s
.
T
h
e
f
in
d
in
g
s
r
ev
ea
l
v
ar
iatio
n
s
in
s
tu
d
en
ts
'
co
n
f
id
en
ce
lev
els,
with
s
o
m
e
s
tu
d
en
ts
h
av
in
g
lo
wer
SE
,
s
o
m
e
d
em
o
n
s
tr
atin
g
m
o
d
er
ate
SE
,
an
d
o
th
e
r
s
d
is
p
lay
in
g
h
ig
h
er
SE
in
b
o
th
asp
ec
ts
.
T
h
ese
f
in
d
in
g
s
ar
e
im
p
o
r
tan
t
f
o
r
teac
h
er
s
as
th
e
y
ca
n
h
el
p
id
en
tif
y
s
tu
d
e
n
ts
wh
o
m
ay
r
eq
u
ir
e
a
d
d
itio
n
al
s
u
p
p
o
r
t
a
n
d
in
te
r
v
en
tio
n
s
to
en
h
an
ce
th
eir
SE
in
m
ath
em
at
ics,
th
u
s
p
o
ten
tially
im
p
r
o
v
in
g
th
eir
ac
ad
em
ic
p
er
f
o
r
m
a
n
ce
a
n
d
o
v
er
all
lear
n
in
g
ex
p
er
ien
ce
[
2
2
]
–
[
2
5
]
.
B
ased
o
n
T
ab
le
3
,
th
e
d
escr
ip
tiv
e
s
tatis
tic
s
s
h
o
ws
th
at
s
tu
d
en
ts
’
SE
v
ar
iab
le
in
u
n
d
e
r
s
tan
d
in
g
m
ath
em
atics
m
ater
ial,
s
h
o
ws
t
h
at
in
th
e
lo
w
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teg
o
r
y
,
th
er
e
ar
e
3
5
s
tu
d
en
ts
with
an
av
er
a
g
e
o
f
3
7
.
2
2
9
;
in
th
e
m
ed
iu
m
ca
teg
o
r
y
ar
e
1
8
s
tu
d
en
ts
with
an
av
er
ag
e
o
f
5
6
.
7
7
8
;
wh
ile
f
o
r
th
e
h
ig
h
ca
t
eg
o
r
y
,
th
er
e
ar
e
1
4
s
tu
d
en
ts
with
an
av
er
ag
e
o
f
6
7
.
3
5
7
.
As
well
as
th
e
s
tu
d
en
t
SE
v
ar
iab
le
in
s
o
lv
in
g
m
ath
p
r
o
b
lem
s
s
h
o
ws
th
at
in
th
e
lo
w
ca
teg
o
r
y
,
th
er
e
ar
e
ten
s
tu
d
en
ts
with
an
av
er
ag
e
o
f
3
0
.
7
0
0
;
in
t
h
e
m
ed
iu
m
ca
teg
o
r
y
,
t
h
er
e
ar
e
4
5
s
tu
d
en
ts
with
an
av
er
ag
e
o
f
5
8
.
4
6
7
;
an
d
in
t
h
e
h
i
g
h
ca
te
g
o
r
y
,
th
er
e
a
r
e
1
2
s
tu
d
en
ts
with
an
av
er
ag
e
o
f
8
1
.
3
3
3
.
T
h
e
d
escr
ip
tiv
e
an
al
y
s
is
p
r
o
v
i
d
es
in
s
ig
h
ts
in
to
th
e
d
is
tr
ib
u
ti
o
n
o
f
s
tu
d
en
ts
'
SE
s
co
r
es,
in
d
i
ca
tin
g
v
a
r
iatio
n
s
in
th
eir
co
n
f
id
e
n
ce
lev
els
wh
en
it
co
m
es
to
u
n
d
er
s
tan
d
in
g
m
ath
em
atics
m
ater
ial
an
d
s
o
lv
in
g
m
ath
p
r
o
b
lem
s
.
T
h
e
f
in
d
i
n
g
s
h
ig
h
lig
h
t
th
e
im
p
o
r
tan
ce
o
f
ad
d
r
ess
in
g
an
d
n
u
r
tu
r
in
g
s
tu
d
e
n
ts
'
SE
,
esp
ec
iall
y
in
ar
ea
s
wh
er
e
it
ap
p
ea
r
s
to
b
e
lack
in
g
,
as
it
ca
n
s
ig
n
if
ican
tly
im
p
ac
t
th
eir
lear
n
in
g
o
u
tco
m
es
an
d
o
v
er
all
p
er
f
o
r
m
a
n
ce
in
m
ath
em
atics [
39
]
.
T
h
e
r
esu
lts
o
f
th
e
d
escr
ip
tiv
e
an
aly
s
is
s
h
o
ws
th
at
s
tu
d
en
t
SE
in
u
n
d
er
s
tan
d
in
g
th
e
m
ater
ial
an
d
s
tu
d
en
t
SE
in
s
o
lv
in
g
m
ath
p
r
o
b
lem
s
f
o
r
b
io
lo
g
y
an
d
m
ath
e
m
atics
ed
u
ca
tio
n
s
tu
d
en
ts
in
cl
u
d
e
lo
w,
m
ed
i
u
m
,
an
d
h
ig
h
ca
teg
o
r
ies.
T
h
is
is
i
n
lin
e
with
th
e
r
esear
ch
t
h
at
th
e
in
f
lu
en
ce
o
n
b
asic
p
r
o
g
r
a
m
m
in
g
c
o
n
ce
p
ts
is
en
o
r
m
o
u
s
,
esp
ec
ially
f
o
r
s
tu
d
en
ts
with
m
o
d
er
ate
an
d
lo
w
SE
[
40
]
,
[
41
]
.
T
h
e
i
n
f
lu
en
ce
o
f
s
tu
d
en
ts
'
SE
an
d
lear
n
in
g
c
o
n
ce
p
ts
ca
n
in
cr
e
ase
th
e
ef
f
icac
y
o
f
s
tu
d
e
n
ts
'
s
elf
-
lear
n
in
g
,
d
em
o
n
s
tr
ate
d
b
y
co
n
ce
p
tu
al
u
n
d
er
s
tan
d
i
n
g
,
h
i
g
h
-
lev
el
c
o
g
n
itiv
e
s
k
ills
,
p
r
ac
tice,
an
d
c
o
m
m
u
n
icatio
n
[
40
]
,
[
41
]
.
3
.
1
.
2
.
Co
rr
ela
t
io
n
bet
wee
n
s
elf
-
ef
f
ica
cy
un
dersta
nd
i
ng
ma
t
er
ia
l a
nd
s
o
lv
ing
ma
t
hem
a
t
ica
l pro
blem
s
B
ef
o
r
e
co
n
d
u
ctin
g
t
h
e
Pear
s
o
n
co
r
r
elatio
n
,
th
e
m
u
ltiv
ar
iate
n
o
r
m
ality
o
f
th
e
d
ata
was
test
ed
u
s
in
g
th
e
Sh
ap
ir
o
-
W
ilk
test
,
y
ield
in
g
a
r
esu
lt
o
f
0
.
9
1
with
a
p
-
v
a
lu
e
o
f
less
th
an
0
.
0
1
.
T
h
u
s
,
it
in
d
icatin
g
t
h
at
th
e
d
ata
is
n
o
r
m
ally
d
is
tr
ib
u
ted
.
T
h
e
r
esu
lts
o
f
th
e
c
o
r
r
elati
o
n
al
an
aly
s
is
b
etwe
en
SE
in
u
n
d
e
r
s
tan
d
in
g
th
e
m
ater
ial
an
d
SE
in
s
o
lv
in
g
p
r
o
b
lem
s
u
s
in
g
t
h
e
Per
s
o
n
co
r
r
elatio
n
f
o
r
m
ath
em
atics
an
d
b
io
lo
g
y
s
tu
d
e
n
ts
ar
e
p
r
esen
ted
in
T
a
b
le
4
.
T
ab
le
4
.
Pear
s
o
n
’
s
c
o
r
r
elatio
n
SE
Ma
th
em
atic
an
d
b
io
lo
g
y
s
tu
d
en
ts
V
a
r
i
a
b
l
e
S
E_
P
M
ma
t
S
E_
P
M
b
i
o
SE
-
M
M
mat
SE
-
M
M
b
i
o
1
.
S
E_
P
M
ma
t
P
e
a
r
so
n
’
s r
—
p
-
v
a
l
u
e
—
2
.
S
E_
P
M
b
i
o
P
e
a
r
so
n
’
s r
-
0
.
0
3
—
p
-
v
a
l
u
e
0
.
8
4
—
3
.
S
E
-
M
M
ma
t
P
e
a
r
so
n
’
s r
0
.
7
0
0
.
1
6
—
p
-
v
a
l
u
e
<
0
.
0
0
1
0
.
1
9
—
4
.
S
E
-
M
M
b
i
o
P
e
a
r
so
n
’
s r
0
.
0
6
0
.
0
5
9
.
6
3
e
-
3
—
p
-
v
a
l
u
e
0
.
6
2
0
.
6
9
0
.
9
4
—
N
o
t
e
:
S
E
_
M
M
m
a
t
(
S
E
_
M
M
b
i
o
)
i
s
a
b
r
i
e
f
f
r
o
m
SE
m
a
t
h
e
m
a
t
i
c
s
(
b
i
o
l
o
g
y
)
e
d
u
c
a
t
i
o
n
st
u
d
e
n
t
s
i
n
u
n
d
e
r
s
t
a
n
d
i
n
g
t
h
e
ma
t
e
r
i
a
l
.
S
E
_
P
M
m
a
t
(
S
E
_
P
M
b
i
o
)
i
s
a
b
r
i
e
f
f
r
o
m
SE
mat
h
e
m
a
t
i
c
s
(
b
i
o
l
o
g
y
)
e
d
u
c
a
t
i
o
n
st
u
d
e
n
t
i
n
m
a
t
h
e
m
a
t
i
c
a
l
p
r
o
b
l
e
m
-
s
o
l
v
i
n
g
.
B
ased
o
n
th
e
r
esu
lts
o
f
th
e
Pear
s
o
n
co
r
r
elatio
n
test
in
T
ab
le
4
,
it
in
d
icate
s
a
s
tr
o
n
g
co
r
r
elatio
n
b
etwe
en
m
ath
em
atics
ed
u
ca
t
io
n
s
tu
d
en
ts
’
SE
in
u
n
d
e
r
s
tan
d
in
g
m
at
h
em
atica
l
co
n
ce
p
t
s
an
d
th
eir
SE
in
p
r
o
b
lem
-
s
o
lv
in
g
,
with
a
Pear
s
o
n
’
s
r
o
f
0
.
7
0
an
d
a
p
-
v
alu
e
o
f
less
th
an
0
.
0
1
.
Stu
d
en
ts
with
h
ig
h
SE
in
u
n
d
er
s
tan
d
i
n
g
m
at
h
em
atics
m
ater
ial
also
ten
d
t
o
h
a
v
e
h
i
g
h
SE
in
s
o
lv
in
g
m
ath
p
r
o
b
lem
s
.
T
h
is
is
in
lin
e
with
r
esear
ch
wh
ich
s
tates
th
at
s
tu
d
en
ts
'
SE
in
u
n
d
e
r
s
tan
d
in
g
th
e
m
ater
ial
a
n
d
SE
in
s
o
l
v
in
g
m
at
h
em
atica
l
p
r
o
b
lem
s
is
h
i
g
h
[
42
]
,
[
43
]
.
Ad
d
itio
n
ally
,
th
is
c
o
r
r
elatio
n
h
as
b
ee
n
s
h
o
wn
t
o
h
a
v
e
a
p
o
s
itiv
e
im
p
ac
t
o
n
s
tu
d
en
ts
'
ac
ad
em
ic
p
er
f
o
r
m
a
n
ce
,
wh
er
e
h
ig
h
SE
is
ass
o
ciate
d
with
b
etter
ac
ad
em
i
c
ac
h
iev
em
en
t
in
m
ath
em
atics
co
u
r
s
es
[
44
]
,
[
45
]
.
Mo
r
eo
v
e
r
,
SE
h
as
also
b
ee
n
p
r
o
v
en
to
h
av
e
a
p
o
s
itiv
e
in
f
l
u
en
ce
o
n
s
tu
d
e
n
ts
'
lear
n
in
g
m
o
tiv
atio
n
an
d
ac
ad
e
m
ic
p
er
f
o
r
m
an
c
e
[
2
2
]
,
[
45
]
,
[
46
]
.
T
h
e
im
p
licatio
n
s
o
f
th
is
r
esear
ch
u
n
d
er
s
co
r
e
th
e
im
p
o
r
ta
n
ce
o
f
ad
o
p
tin
g
lear
n
in
g
a
p
p
r
o
ac
h
es
th
at
s
tim
u
late
th
e
d
e
v
elo
p
m
e
n
t
o
f
SE
in
b
o
th
asp
ec
ts
[
4
]
,
[
42
]
,
[
45
]
,
[
47
]
Pro
v
id
in
g
a
p
p
r
o
p
r
iate
s
u
p
p
o
r
t
a
n
d
g
u
id
an
ce
in
b
u
ild
in
g
s
elf
-
co
n
f
i
d
en
c
e
in
u
n
d
e
r
s
tan
d
in
g
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
s
elf
-
effica
cy
o
f e
d
u
ca
tio
n
s
tu
d
en
ts
in
u
n
d
ers
ta
n
d
i
n
g
ma
teri
a
ls
a
n
d
ma
th
ema
tica
l
…
(
B
a
id
u
r
i
)
2633
m
ath
em
atica
l
co
n
ce
p
ts
an
d
f
ac
in
g
p
r
o
b
lem
-
s
o
lv
in
g
task
s
ca
n
h
elp
en
h
a
n
ce
th
e
q
u
ali
ty
o
f
lear
n
in
g
an
d
ac
ad
em
ic
p
er
f
o
r
m
an
ce
f
o
r
m
at
h
em
atics e
d
u
ca
tio
n
s
tu
d
e
n
ts
.
Me
a
n
w
h
il
e,
th
er
e
is
n
o
s
i
g
n
i
f
ica
n
t
r
el
ati
o
n
s
h
ip
am
o
n
g
th
e
o
t
h
e
r
v
a
r
ia
b
l
es.
T
h
er
e
is
n
o
s
ig
n
i
f
ic
a
n
t
co
r
r
el
ati
o
n
b
e
twe
en
b
i
o
l
o
g
y
ed
u
c
ati
o
n
s
tu
d
e
n
ts
'
SE
in
u
n
d
e
r
s
t
an
d
i
n
g
m
a
th
em
ati
ca
l
m
a
ter
ial
a
n
d
p
r
o
b
l
em
-
s
o
l
v
i
n
g
i
n
m
at
h
e
m
a
tics
.
T
h
is
i
n
s
i
g
n
if
ic
an
t
co
r
r
el
ati
o
n
i
n
d
i
ca
t
es
t
h
at
t
h
e
s
t
u
d
e
n
t'
s
l
ev
el
o
f
c
o
n
f
id
e
n
ce
i
n
u
n
d
er
s
ta
n
d
i
n
g
m
at
h
em
ati
ca
l
m
ate
r
ia
l
is
n
o
t
cl
o
s
el
y
r
el
at
ed
t
o
th
e
ir
l
e
v
el
o
f
c
o
n
f
i
d
en
ce
i
n
s
o
l
v
i
n
g
m
a
th
em
ati
ca
l
p
r
o
b
l
em
s
.
T
h
e
le
v
el
o
f
SE
i
n
u
n
d
e
r
s
t
an
d
i
n
g
m
at
h
e
m
at
ica
l
m
at
er
ial
d
o
es
n
o
t
d
i
r
e
ctl
y
i
n
f
l
u
e
n
c
e
th
e
s
t
u
d
e
n
t'
s
ab
i
lit
y
t
o
s
o
l
v
e
m
at
h
e
m
a
tic
al
p
r
o
b
l
em
s
.
T
h
is
f
i
n
d
i
n
g
p
r
o
v
i
d
es
a
n
u
n
d
e
r
s
t
an
d
i
n
g
o
f
th
e
d
i
f
f
er
e
n
ce
s
b
et
we
en
ac
a
d
e
m
i
c
d
is
c
ip
li
n
es
a
n
d
f
ac
t
o
r
s
t
h
a
t
m
a
y
i
n
f
l
u
e
n
c
e
SE
i
n
t
h
e
c
o
n
te
x
t
o
f
u
n
d
e
r
s
ta
n
d
i
n
g
m
a
th
e
m
a
tic
al
m
a
te
r
ia
l
an
d
s
o
l
v
i
n
g
m
at
h
e
m
a
tic
al
p
r
o
b
le
m
s
[
2
2
]
.
T
h
e
i
m
p
lic
ati
o
n
s
o
f
t
h
es
e
r
es
u
lts
ca
n
g
u
i
d
e
th
e
d
ev
el
o
p
m
e
n
t
o
f
m
o
r
e
ap
p
r
o
p
r
ia
te
t
ea
c
h
i
n
g
s
tr
ate
g
i
es
a
n
d
u
n
d
e
r
s
c
o
r
e
t
h
e
i
m
p
o
r
ta
n
ce
o
f
g
ai
n
i
n
g
d
ee
p
e
r
i
n
s
ig
h
ts
i
n
t
o
b
i
o
l
o
g
y
ed
u
c
ati
o
n
s
tu
d
en
ts
'
SE
i
n
u
n
d
e
r
s
ta
n
d
i
n
g
m
at
h
em
ati
ca
l
m
at
er
i
al
an
d
s
o
l
v
i
n
g
m
at
h
e
m
a
tic
al
p
r
o
b
le
m
s
.
T
h
er
e
is
n
o
s
ig
n
if
ican
t
co
r
r
e
latio
n
b
etwe
en
b
io
lo
g
y
an
d
m
ath
em
atics
ed
u
ca
tio
n
s
tu
d
e
n
ts
'
SE
in
u
n
d
er
s
tan
d
i
n
g
m
ath
em
atica
l
m
ater
ial
an
d
p
r
o
b
lem
-
s
o
l
v
in
g
in
m
ath
em
atics.
T
h
is
f
in
d
i
n
g
in
d
icate
s
t
h
at
th
e
s
tu
d
en
t'
s
lev
el
o
f
co
n
f
id
en
ce
in
u
n
d
er
s
tan
d
in
g
m
ath
e
m
atica
l
co
n
ce
p
ts
a
n
d
s
o
lv
i
n
g
m
ath
e
m
atica
l
p
r
o
b
lem
s
is
n
o
t
clo
s
ely
r
elate
d
to
t
h
e
two
f
ield
s
o
f
s
tu
d
y
.
T
h
e
r
esu
lts
em
p
h
asize
th
e
im
p
o
r
tan
ce
o
f
u
n
d
e
r
s
tan
d
in
g
th
e
d
if
f
er
en
ce
s
b
etwe
en
ac
a
d
em
ic
d
is
cip
lin
es
an
d
in
d
iv
id
u
al
c
h
ar
ac
ter
is
tics
o
f
s
tu
d
en
ts
th
at
m
ay
in
f
lu
en
ce
SE
in
u
n
d
er
s
tan
d
i
n
g
m
ath
em
atica
l
m
ater
ial
an
d
s
o
lv
in
g
m
ath
e
m
atica
l
p
r
o
b
lem
s
[
2
2
]
.
T
h
e
im
p
licatio
n
s
o
f
th
is
r
esear
ch
h
ig
h
lig
h
t
th
e
n
ec
ess
ity
f
o
r
ad
ap
tin
g
m
o
r
e
ap
p
r
o
p
r
iate
teac
h
in
g
ap
p
r
o
ac
h
es
to
en
h
an
ce
s
tu
d
en
ts
'
m
ath
em
atica
l u
n
d
e
r
s
tan
d
in
g
a
b
ilit
ies in
b
io
lo
g
y
an
d
m
ath
e
m
atics.
3
.
1
.
3
.
Dif
f
er
ence
s
elf
-
ef
f
ica
c
y
un
dersta
nd
ing
m
a
t
er
ia
l a
nd
s
o
lv
ing
m
a
t
he
m
a
t
ica
l pro
bl
em
s
T
h
e
r
esu
lts
o
f
th
e
an
aly
s
is
o
f
n
o
r
m
ality
b
etwe
en
SE
in
u
n
d
e
r
s
tan
d
in
g
th
e
m
ater
ial
a
n
d
SE
in
s
o
lv
in
g
p
r
o
b
lem
s
u
s
in
g
t
h
e
test
o
f
No
r
m
ality
Sh
ap
ir
o
W
ilk
f
o
r
b
io
l
o
g
y
an
d
m
ath
s
tu
d
en
ts
a
r
e
p
r
esen
ted
in
T
ab
le
5
.
T
h
e
n
o
r
m
ality
test
r
esu
lts
with
Sh
ap
ir
o
W
ilk
s
h
o
w
th
at
th
e
d
ata
is
n
o
r
m
ally
d
is
tr
ib
u
ted
.
T
h
u
s
,
th
e
d
ata
m
ee
ts
th
e
r
eq
u
ir
e
m
en
ts
f
o
r
t
h
e
t
-
test
.
As
p
r
esen
ted
in
T
ab
le
6
,
it
was
f
o
u
n
d
th
at
th
er
e
is
n
o
s
ig
n
if
i
ca
n
t
d
if
f
er
en
ce
in
th
e
lev
el
o
f
SE
am
o
n
g
b
io
lo
g
y
e
d
u
ca
tio
n
s
tu
d
e
n
ts
wh
en
u
n
d
e
r
s
tan
d
in
g
m
at
h
em
atica
l
m
ater
ial
an
d
wh
en
s
o
lv
in
g
m
ath
em
atica
l
p
r
o
b
lem
s
(
p
>
0
.
0
5
)
.
T
h
is
f
in
d
in
g
in
d
icate
s
th
at
b
io
lo
g
y
ed
u
ca
tio
n
s
tu
d
en
ts
f
ee
l
eq
u
ally
co
n
f
id
en
t
in
b
o
th
asp
ec
ts
.
T
h
is
is
in
lin
e
with
r
esear
ch
wh
ich
s
tates
th
at
t
h
er
e
is
n
o
s
ig
n
i
f
ican
t
d
if
f
e
r
e
n
ce
in
th
e
c
r
ea
tiv
e
p
r
o
b
lem
-
s
o
lv
in
g
ab
ilit
y
an
d
SE
o
f
elem
en
tar
y
s
ch
o
o
l
s
tu
d
en
ts
,
an
d
th
e
r
e
is
n
o
s
tatis
tically
s
ig
n
if
ican
t
d
if
f
er
en
ce
in
th
e
lev
el
o
f
SE
o
f
s
tu
d
en
ts
co
n
ce
r
n
in
g
th
e
p
r
ef
er
r
ed
s
tr
ateg
y
f
o
r
m
a
n
ag
in
g
lear
n
in
g
ac
tiv
ities
[
4
5
]
,
[
4
8
]
.
T
h
e
im
p
licatio
n
s
o
f
t
h
is
f
in
d
in
g
em
p
h
asize
th
e
im
p
o
r
tan
ce
o
f
in
te
g
r
ated
teac
h
in
g
b
etwe
en
m
ath
em
atics
an
d
b
io
lo
g
y
,
as we
ll
as
ef
f
o
r
ts
to
e
n
h
an
ce
s
tu
d
en
ts
'
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
.
T
h
er
ef
o
r
e
,
th
e
r
esu
lts
o
f
th
is
a
n
aly
s
is
ca
n
c
o
n
tr
ib
u
te
to
im
p
r
o
v
in
g
th
e
q
u
ality
o
f
lea
r
n
in
g
an
d
f
o
s
ter
in
g
SE
am
o
n
g
b
io
lo
g
y
e
d
u
ca
tio
n
s
tu
d
en
ts
in
th
e
co
n
te
x
t o
f
m
at
h
em
atics.
T
ab
le
5
.
T
est o
f
n
o
r
m
ality
(
Sh
ap
ir
o
-
W
ilk
)
V
a
r
i
a
b
l
e
W
P
SE
-
mat
e
r
i
a
l
B
i
o
0
.
9
7
2
0
.
1
3
0
M
a
t
h
0
9
8
7
0
.
1
5
3
SE
-
p
r
o
b
l
e
m
-
s
o
l
v
i
n
g
B
i
o
0
9
6
8
0
.
0
7
8
M
a
t
h
0
.
9
6
4
0
.
0
7
5
N
o
t
e
:
S
i
g
n
i
f
i
c
a
n
t
r
e
s
u
l
t
s s
u
g
g
e
st
a
d
e
v
i
a
t
i
o
n
f
r
o
m
n
o
r
m
a
l
i
t
y
.
T
ab
le
6
.
I
n
d
ep
e
n
d
en
t sam
p
les
t
-
test
f
o
r
SE
V
a
r
i
a
b
l
e
t
df
p
SE
mat
h
e
m
a
t
i
c
s
st
u
d
e
n
t
s
-
7
.
0
2
3
0
8
<
0
.
0
0
1
SE
b
i
o
l
o
g
y
st
u
d
e
n
t
s
-
0
.
0
8
1
3
2
0
.
9
3
a
N
o
t
e
:
S
t
u
d
e
n
t
'
s t
-
t
e
s
t
.
ᵃ
L
e
v
e
n
e
's
t
e
s
t
i
s
si
g
n
i
f
i
c
a
n
t
(
p
<
0
.
0
5
)
On
th
e
o
th
er
h
an
d
,
th
e
r
e
is
a
s
ig
n
if
ican
t
d
if
f
er
e
n
ce
in
th
e
lev
el
o
f
SE
am
o
n
g
m
ath
em
atics
ed
u
ca
tio
n
s
tu
d
en
ts
wh
en
u
n
d
e
r
s
tan
d
in
g
m
ath
em
atica
l
m
ater
ial
an
d
wh
en
f
ac
in
g
m
ath
e
m
atica
l
p
r
o
b
l
em
-
s
o
lv
in
g
.
T
h
is
is
co
n
s
is
ten
t w
ith
r
esear
ch
f
in
d
in
g
s
s
u
g
g
esti
n
g
th
at
th
is
d
if
f
er
e
n
ce
m
ay
b
e
attr
ib
u
ted
to
v
ar
iat
io
n
s
in
th
e
lear
n
in
g
co
n
tex
t,
th
e
lev
el
o
f
d
if
f
ic
u
lty
in
p
r
o
b
lem
-
s
o
lv
in
g
,
an
d
t
h
e
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
d
ev
elo
p
ed
b
y
s
tu
d
en
ts
[
49
]
–
[
51
]
.
I
t
in
d
icate
s
th
at
s
tu
d
en
ts
ten
d
to
b
e
m
o
r
e
co
n
f
i
d
e
n
t
in
ap
p
ly
in
g
th
eir
m
ath
em
at
ical
k
n
o
wled
g
e
to
s
o
lv
e
co
n
cr
ete
p
r
o
b
le
m
s
r
ath
e
r
th
an
in
u
n
d
e
r
s
tan
d
in
g
th
e
th
eo
r
y
o
r
co
n
ce
p
ts
o
f
m
at
h
em
at
ics.
T
h
is
f
in
d
in
g
is
ess
en
tial
to
b
e
u
n
d
er
s
to
o
d
in
th
e
co
n
tex
t
o
f
m
ath
em
atics
ed
u
ca
tio
n
as
it
ca
n
p
r
o
v
id
e
in
s
ig
h
ts
in
to
ar
ea
s
th
at
n
ee
d
m
o
r
e
atten
tio
n
to
en
h
an
c
e
s
tu
d
en
ts
'
SE
.
T
ea
ch
er
s
n
ee
d
to
p
ay
atten
tio
n
to
th
ese
d
if
f
er
en
ce
s
an
d
d
ev
elo
p
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
.
4
,
Au
g
u
s
t
20
25
:
2
6
2
8
-
2
6
3
9
2634
ap
p
r
o
p
r
iate
teac
h
in
g
s
tr
ateg
ie
s
to
en
h
a
n
ce
s
tu
d
e
n
ts
'
SE
in
m
ath
em
atica
l
p
r
o
b
lem
-
s
o
lv
i
n
g
.
T
h
er
ef
o
r
e,
it
is
ex
p
ec
ted
t
h
at
s
tu
d
en
ts
will
b
e
b
etter
p
r
ep
a
r
ed
t
o
f
ac
e
r
ea
l
-
wo
r
ld
m
at
h
em
atica
l
ch
allen
g
es
an
d
f
ee
l
m
o
r
e
co
n
f
id
en
t i
n
ap
p
l
y
in
g
th
ei
r
m
a
th
em
atica
l k
n
o
wled
g
e
in
m
o
r
e
co
m
p
lex
s
itu
atio
n
s
.
As
s
h
o
wn
in
T
ab
le
7
,
t
h
er
e
is
a
s
ig
n
if
ican
t
d
if
f
e
r
en
ce
in
SE
b
etwe
en
m
ath
e
m
atics
an
d
b
io
lo
g
y
ed
u
ca
tio
n
s
tu
d
en
ts
in
u
n
d
e
r
s
tan
d
in
g
m
ath
em
atica
l
m
ater
i
al
an
d
s
o
lv
in
g
m
ath
em
atica
l
p
r
o
b
lem
s
,
with
a
p
-
v
alu
e
o
f
less
th
an
0
.
0
5
.
F
u
r
th
er
m
o
r
e,
th
e
SE
i
n
u
n
d
er
s
tan
d
in
g
m
ath
em
atica
l
m
ater
ial
am
o
n
g
b
io
lo
g
y
ed
u
ca
tio
n
s
tu
d
en
ts
is
h
ig
h
er
th
an
th
at
o
f
m
ath
e
m
atics
ed
u
ca
tio
n
s
tu
d
e
n
ts
.
On
th
e
o
th
er
h
a
n
d
,
th
e
SE
in
s
o
lv
in
g
m
ath
em
atica
l
p
r
o
b
le
m
s
am
o
n
g
m
ath
e
m
atics
ed
u
ca
tio
n
s
tu
d
en
ts
is
h
ig
h
er
th
an
th
at
o
f
b
i
o
lo
g
y
ed
u
ca
tio
n
s
tu
d
en
ts
.
T
h
e
d
if
f
er
en
ce
in
SE
b
etwe
en
b
io
lo
g
y
a
n
d
m
ath
em
atics
ed
u
c
atio
n
s
tu
d
en
ts
i
n
u
n
d
er
s
tan
d
i
n
g
m
ath
em
atica
l
m
ater
ial
m
ay
b
e
attr
ib
u
ted
to
f
ac
to
r
s
s
u
ch
as
d
if
f
er
en
t
lear
n
in
g
co
n
te
x
ts
,
p
r
io
r
lear
n
in
g
ex
p
er
ien
ce
s
,
p
s
y
c
h
o
l
o
g
ical
f
ac
to
r
s
,
an
d
p
er
ce
p
tio
n
s
ab
o
u
t
m
ath
em
atics
[
52
]
,
[
53
]
.
T
h
ese
f
in
d
in
g
s
p
r
o
v
id
e
im
p
o
r
tan
t
in
s
ig
h
ts
in
t
o
h
o
w
teac
h
i
n
g
ap
p
r
o
ac
h
es
an
d
p
s
y
ch
o
lo
g
ical
s
u
p
p
o
r
t
ca
n
b
e
tailo
r
ed
t
o
h
elp
en
h
an
ce
s
tu
d
en
ts
'
SE
in
u
n
d
er
s
tan
d
in
g
m
ath
e
m
atics
an
d
s
o
lv
in
g
m
ath
em
atica
l
p
r
o
b
lem
s
[
54
]
–
[
56
]
,
esp
ec
ially
f
o
r
s
tu
d
en
ts
wh
o
s
e
m
ain
f
ie
ld
o
f
s
tu
d
y
is
d
if
f
er
e
n
t
f
r
o
m
m
ath
em
atics.
I
n
ten
s
iv
e
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
tr
ain
in
g
an
d
m
o
r
e
r
elev
an
t
in
t
eg
r
atio
n
o
f
m
ath
em
atics
in
to
t
h
e
b
io
lo
g
y
ed
u
ca
tio
n
cu
r
r
icu
l
u
m
ca
n
h
el
p
ad
d
r
ess
th
ese
d
if
f
er
en
ce
s
an
d
s
tr
en
g
t
h
en
s
tu
d
en
ts
'
SE
in
tack
lin
g
co
m
p
lex
a
n
d
ab
s
tr
ac
t
m
ath
e
m
atica
l
task
s
,
th
u
s
p
r
o
m
o
tin
g
th
e
im
p
r
o
v
em
en
t o
f
b
io
lo
g
y
ed
u
ca
tio
n
s
tu
d
e
n
ts
'
SE
in
m
ath
em
atica
l p
r
o
b
lem
-
s
o
lv
in
g
.
T
ab
le
7
.
I
n
d
ep
e
n
d
en
t sam
p
les
t
-
test
SE
m
ath
em
atics a
n
d
b
io
l
o
g
y
s
tu
d
e
n
ts
V
a
r
i
a
b
l
e
t
df
p
SE
u
n
d
e
r
st
a
n
d
i
n
g
ma
t
e
r
i
a
l
2
.
4
2
2
2
0
0
.
0
2
SE
p
r
o
b
l
e
m s
o
l
v
i
n
g
-
3
.
4
8
2
2
0
<
0
.
0
5
N
o
t
e
.
S
t
u
d
e
n
t
's
t
-
t
e
st
.
3
.
2
.
Dis
cu
s
s
io
n
B
ased
o
n
th
e
r
esu
lts
o
f
th
e
d
e
s
cr
ip
tiv
e
an
aly
s
is
s
h
o
w
th
at
s
t
u
d
en
t
SE
in
u
n
d
er
s
tan
d
i
n
g
th
e
m
ater
ial,
an
d
s
tu
d
e
n
t
SE
in
s
o
lv
in
g
m
at
h
p
r
o
b
lem
s
f
o
r
p
r
o
s
p
ec
tiv
e
b
i
o
lo
g
y
an
d
m
ath
em
atics
ed
u
ca
t
io
n
teac
h
er
s
tu
d
en
ts
in
clu
d
e
lo
w,
m
o
d
er
ate,
an
d
h
ig
h
ca
teg
o
r
ies.
T
h
is
is
co
n
s
is
t
en
t
with
r
esear
ch
s
h
o
win
g
th
at
th
e
in
f
lu
en
ce
o
n
b
asic
p
r
o
g
r
am
m
i
n
g
co
n
ce
p
ts
is
s
ig
n
if
ican
t,
p
ar
ticu
lar
ly
a
m
o
n
g
s
tu
d
en
ts
with
m
ed
iu
m
an
d
lo
w
SE
[
40
]
.
Stu
d
en
t
SE
an
d
lear
n
in
g
co
n
c
ep
ts
h
av
e
th
e
p
o
ten
tial
to
in
cr
ea
s
e
s
tu
d
en
ts
'
in
d
ep
en
d
en
t
lear
n
in
g
ef
f
icac
y
,
as
ev
id
en
ce
d
b
y
co
n
ce
p
tu
al
u
n
d
er
s
tan
d
in
g
,
h
ig
h
-
lev
el
co
g
n
itiv
e
s
k
ills
,
p
r
ac
tice,
an
d
co
m
m
u
n
icatio
n
[
41
]
.
Ma
th
em
atics
ed
u
ca
tio
n
s
tu
d
en
ts
'
SE
in
u
n
d
e
r
s
tan
d
in
g
t
h
e
m
ater
ial
an
d
s
o
lv
in
g
p
r
o
b
lem
s
is
p
r
im
ar
ily
m
o
d
er
ate,
with
lo
w
a
n
d
h
i
g
h
ca
teg
o
r
ies
b
ein
g
r
elativ
ely
eq
u
al,
in
d
icatin
g
ad
e
q
u
ate
co
n
f
id
e
n
ce
in
m
ath
em
atica
l
ab
ilit
ies.
T
h
er
e
is
litt
le
v
ar
iatio
n
in
s
tu
d
en
t
co
n
f
id
en
ce
lev
els,
as
ev
id
en
c
ed
b
y
t
h
e
m
in
im
al
d
if
f
er
en
ce
s
b
etwe
en
lo
w
a
n
d
h
ig
h
ca
teg
o
r
ies
[
51
]
,
[
57
]
.
Acc
o
r
d
in
g
to
s
tu
d
ies,
s
tu
d
en
ts
with
v
ar
y
i
n
g
m
ath
em
atica
l
ab
ilit
ies
ex
h
ib
it
v
ar
y
in
g
le
v
els
o
f
SE
in
p
r
o
b
le
m
-
s
o
lv
in
g
,
with
h
i
g
h
-
a
b
ilit
y
s
tu
d
en
ts
ex
ce
llin
g
in
p
r
o
b
lem
-
s
o
lv
in
g
s
tep
s
,
m
ed
iu
m
-
ab
ilit
y
s
tu
d
en
ts
d
e
m
o
n
s
tr
ati
n
g
p
a
r
tial
u
n
d
er
s
tan
d
in
g
,
an
d
l
o
w
-
ab
ilit
y
s
tu
d
en
ts
s
tr
u
g
g
lin
g
to
d
esig
n
an
d
im
p
le
m
en
t e
f
f
ec
tiv
e
s
o
lu
tio
n
s
.
B
io
l
o
g
y
e
d
u
c
ati
o
n
s
t
u
d
en
ts
'
SE
i
n
p
r
o
b
l
em
-
s
o
l
v
i
n
g
is
c
o
m
p
ar
ab
le
t
o
m
a
th
em
ati
cs
e
d
u
ca
ti
o
n
s
t
u
d
e
n
ts
,
wit
h
t
h
e
m
a
jo
r
it
y
f
al
li
n
g
i
n
t
o
th
e
m
o
d
er
ate
c
at
eg
o
r
y
[
58
]
.
H
o
we
v
er
,
s
ig
n
i
f
i
ca
n
t
d
i
f
f
er
e
n
ce
s
e
m
e
r
g
e
i
n
S
E
f
o
r
u
n
d
er
s
ta
n
d
i
n
g
t
h
e
m
ate
r
i
al,
wi
th
b
i
o
l
o
g
y
s
t
u
d
e
n
ts
e
x
h
i
b
iti
n
g
lo
w
le
v
els
o
f
c
o
n
f
i
d
e
n
c
e
[
59
]
.
T
h
is
s
u
g
g
ests
t
h
at
,
wh
i
le
s
t
u
d
e
n
ts
m
ay
f
e
el
ca
p
ab
l
e
o
f
s
o
l
v
i
n
g
b
i
o
l
o
g
i
ca
l
p
r
o
b
l
e
m
s
,
t
h
e
y
la
c
k
c
o
n
f
i
d
e
n
ce
i
n
th
eir
u
n
d
er
s
ta
n
d
i
n
g
o
f
th
e
m
at
er
i
al
.
T
h
e
d
is
p
a
r
i
ty
i
n
SE
le
v
els
b
etw
ee
n
p
r
o
b
le
m
-
s
o
l
v
i
n
g
a
n
d
m
at
e
r
ia
l
u
n
d
er
s
t
a
n
d
i
n
g
h
i
g
h
li
g
h
ts
t
h
e
n
e
ed
f
o
r
t
a
r
g
ete
d
i
n
te
r
v
e
n
ti
o
n
s
to
b
o
o
s
t
s
t
u
d
e
n
ts
'
c
o
n
f
id
en
ce
in
e
f
f
ec
t
iv
el
y
u
n
d
er
s
ta
n
d
i
n
g
b
i
o
l
o
g
ic
al
co
n
ce
p
ts
,
p
o
te
n
ti
all
y
t
h
r
o
u
g
h
ta
il
o
r
ed
i
n
s
tr
u
ct
io
n
al
ap
p
r
o
ac
h
es
t
h
a
t
a
d
d
r
ess
t
h
es
e
s
p
e
ci
f
ic
SE
p
er
ce
p
t
io
n
s
.
T
ea
ch
er
s
m
u
s
t
f
o
c
u
s
o
n
a
n
d
s
t
r
e
n
g
t
h
e
n
s
t
u
d
e
n
t
SE
in
tw
o
a
r
e
as:
u
n
d
e
r
s
t
an
d
i
n
g
m
a
te
r
i
al
a
n
d
p
r
o
b
le
m
-
s
o
lv
i
n
g
.
T
h
is
c
an
b
e
ac
c
o
m
p
lis
h
e
d
b
y
i
m
p
le
m
e
n
t
i
n
g
lea
r
n
i
n
g
s
tr
ate
g
ies
t
h
at
in
cr
ea
s
e
s
t
u
d
e
n
t
co
n
f
i
d
e
n
c
e,
p
r
o
v
i
d
e
c
o
n
s
t
r
u
cti
v
e
f
e
ed
b
a
c
k
,
a
n
d
f
o
s
te
r
a
le
ar
n
i
n
g
e
n
v
ir
o
n
m
e
n
t
t
h
at
e
n
c
o
u
r
a
g
es
ex
p
l
o
r
at
io
n
a
n
d
ex
p
e
r
i
m
e
n
t
ati
o
n
.
T
h
e
s
tu
d
y
'
s
co
r
r
elatio
n
al
an
aly
s
is
r
esu
lts
s
h
o
w
th
at
th
er
e
is
a
s
tr
o
n
g
r
elatio
n
s
h
ip
b
etwe
en
m
ath
em
atics
ed
u
ca
tio
n
s
tu
d
e
n
ts
'
SE
in
u
n
d
er
s
tan
d
in
g
m
a
th
em
atica
l
co
n
ce
p
ts
an
d
th
ei
r
SE
in
p
r
o
b
lem
-
s
o
lv
in
g
.
T
h
is
r
esu
lt
is
co
n
s
is
ten
t
with
th
e
f
in
d
in
g
s
o
f
p
r
io
r
r
esear
ch
,
wh
ich
s
tated
th
at
s
tu
d
en
ts
'
SE
in
u
n
d
er
s
tan
d
i
n
g
th
e
m
ater
ial
an
d
SE
in
s
o
lv
in
g
m
ath
em
at
ical
p
r
o
b
lem
s
is
s
ig
n
if
ican
tl
y
h
ig
h
[
42
]
,
[
43
]
.
Acc
o
r
d
in
g
to
th
e
r
esu
lt,
m
ath
em
atica
l
SE
is
ass
o
ciate
d
with
en
g
ag
em
en
t,
p
er
s
is
ten
ce
,
an
d
ac
ad
em
i
c
p
er
f
o
r
m
an
ce
[
3
4
]
,
[
60
]
.
Fu
r
th
er
m
o
r
e,
e
n
co
u
r
ag
in
g
in
d
ep
en
d
en
t
lear
n
i
n
g
o
f
p
r
o
b
lem
-
s
o
lv
in
g
task
s
ca
n
im
p
r
o
v
e
s
elf
-
m
o
n
ito
r
in
g
an
d
s
elf
-
r
eg
u
latio
n
,
e
v
en
tu
ally
i
m
p
r
o
v
i
n
g
p
er
f
o
r
m
an
ce
in
m
ath
em
atics
lear
n
in
g
[
61
]
.
T
h
ese
f
in
d
in
g
s
also
s
h
o
w
th
at
lear
n
in
g
s
tr
ateg
ies
th
at
im
p
r
o
v
e
s
tu
d
e
n
ts
'
u
n
d
er
s
tan
d
in
g
o
f
m
ath
e
m
atica
l
co
n
ce
p
ts
ca
n
im
p
r
o
v
e
th
eir
p
r
o
b
lem
-
s
o
lv
in
g
ab
ilit
ies.
L
ea
r
n
in
g
s
tr
ateg
ies
th
at
em
p
h
asize
a
th
o
r
o
u
g
h
u
n
d
er
s
tan
d
i
n
g
o
f
m
ath
e
m
atica
l
co
n
ce
p
ts
,
s
u
ch
as
th
e
u
s
e
o
f
co
n
cr
ete
ex
am
p
les,
p
r
o
b
lem
-
b
ased
lear
n
in
g
,
an
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t
J
E
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&
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2252
-
8
8
2
2
Th
e
s
elf
-
effica
cy
o
f e
d
u
ca
tio
n
s
tu
d
en
ts
in
u
n
d
ers
ta
n
d
i
n
g
ma
teri
a
ls
a
n
d
ma
th
ema
tica
l
…
(
B
a
id
u
r
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)
2635
v
is
u
al
r
ep
r
esen
tatio
n
s
,
ca
n
a
s
s
is
t
s
tu
d
en
ts
in
d
ev
elo
p
in
g
a
s
o
lid
f
o
u
n
d
atio
n
f
o
r
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
.
T
ea
ch
er
s
m
u
s
t
n
o
t
o
n
ly
f
o
c
u
s
o
n
d
ev
elo
p
in
g
m
ath
em
ati
ca
l
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
b
u
t
also
o
n
in
s
till
in
g
co
n
f
id
en
ce
in
s
tu
d
en
ts
’
u
n
d
er
s
tan
d
in
g
o
f
th
e
f
u
n
d
am
e
n
tal
co
n
ce
p
ts
.
T
ea
c
h
er
s
ca
n
h
elp
s
tu
d
en
ts
s
u
cc
ee
d
in
m
ath
em
atics b
y
p
r
o
v
id
in
g
s
u
p
p
o
r
t a
n
d
f
ee
d
b
ac
k
th
at
s
tr
en
g
t
h
en
s
th
eir
SE
in
b
o
th
o
f
th
ese
ar
ea
s
.
Fu
r
th
er
m
o
r
e
,
th
e
an
aly
s
is
f
o
u
n
d
n
o
s
ig
n
if
ican
t
r
elatio
n
s
h
ip
b
etwe
en
b
io
lo
g
y
ed
u
ca
tio
n
s
t
u
d
en
ts
’
SE
in
u
n
d
er
s
tan
d
i
n
g
m
ath
em
ati
ca
l
m
ater
ial
an
d
s
o
lv
in
g
m
ath
em
atica
l
p
r
o
b
lem
s
.
T
h
e
r
e
is
n
o
s
ig
n
if
ican
t
d
if
f
er
en
ce
in
SE
b
etwe
en
m
ath
em
atics
an
d
b
i
o
lo
g
y
ed
u
c
atio
n
s
tu
d
en
ts
wh
e
n
it
co
m
e
s
to
u
n
d
er
s
tan
d
in
g
m
ath
em
atics
m
ater
ial
an
d
s
o
lv
in
g
m
at
h
p
r
o
b
lem
s
.
Desp
ite
s
tu
d
en
ts
’
s
tr
o
n
g
b
elief
s
in
th
e
ir
u
n
d
e
r
s
tan
d
in
g
o
f
b
io
lo
g
y
,
th
is
co
n
f
id
en
ce
h
as
litt
le
im
p
ac
t
o
n
t
h
eir
m
ath
e
m
atica
l
p
r
o
b
lem
-
s
o
lv
in
g
a
b
ilit
ies.
T
h
is
s
u
g
g
ests
th
at
SE
in
o
n
e
s
u
b
ject
is
n
o
t
alwa
y
s
r
elate
d
to
s
k
ills
o
r
b
elief
s
in
an
o
t
h
er
[
62
]
.
W
h
ile
SE
in
m
ath
em
atics
is
im
p
o
r
tan
t f
o
r
p
r
o
b
lem
-
s
o
lv
in
g
,
it
m
ay
n
o
t
b
e
d
ir
ec
tly
a
p
p
lica
b
le
ac
r
o
s
s
d
is
cip
lin
es
[
58
]
,
[
61
]
,
[
63
]
.
Acc
o
r
d
i
n
g
to
r
esear
ch
,
s
tu
d
en
ts
’
co
n
f
id
en
ce
in
u
n
d
e
r
s
tan
d
in
g
a
n
d
s
o
lv
in
g
m
ath
e
m
atica
l
p
r
o
b
lem
s
is
n
o
t
d
is
cip
lin
e
-
s
p
ec
if
ic,
im
p
ly
in
g
th
at
h
ig
h
co
n
f
id
en
ce
in
m
at
h
em
atica
l
ab
ilit
ies
d
o
es
n
o
t
g
u
ar
an
tee
th
e
s
am
e
lev
el
o
f
co
n
f
id
en
ce
in
b
io
lo
g
y
ed
u
ca
tio
n
.
T
ask
d
if
f
icu
lty
,
em
o
tio
n
al
in
tellig
en
ce
,
an
d
m
etac
o
g
n
itiv
e
awa
r
en
ess
ar
e
im
p
o
r
tan
t
f
ac
t
o
r
s
th
at
s
h
ap
e
s
tu
d
en
ts
’
attitu
d
es
an
d
a
b
ilit
ies
in
m
ath
em
atics
an
d
o
th
er
d
is
cip
lin
es
[
64
]
,
[
65
]
.
As
a
r
esu
lt,
im
p
r
o
v
in
g
SE
a
n
d
m
at
h
em
atics
s
k
ills
m
ay
n
ec
ess
itate
a
m
u
lti
-
d
is
cip
lin
ar
y
ap
p
r
o
ac
h
.
T
h
ese
f
in
d
in
g
s
h
a
v
e
s
ig
n
if
ican
t
ed
u
ca
tio
n
al
im
p
licatio
n
s
b
ec
au
s
e
th
ey
d
em
o
n
s
tr
ate
th
at
ap
p
r
o
ac
h
es
to
in
cr
ea
s
in
g
s
tu
d
en
ts
’
SE
in
o
n
e
s
u
b
ject
c
an
n
o
t
alwa
y
s
b
e
ap
p
lied
d
ir
ec
tly
to
o
th
er
s
u
b
jects.
T
ea
c
h
er
s
m
u
s
t
co
n
s
id
er
th
e
s
p
ec
if
ic
f
ac
to
r
s
th
at
in
f
lu
en
ce
s
tu
d
en
t
SE
in
ea
ch
s
u
b
ject,
as we
ll
as
d
ev
elo
p
ap
p
r
o
p
r
iate
le
ar
n
in
g
s
tr
ateg
ies
to
b
o
o
s
t
s
tu
d
en
t
SE
in
th
at
c
o
n
tex
t.
Fu
r
th
er
m
o
r
e,
th
ese
f
in
d
i
n
g
s
em
p
h
asize
th
e
im
p
o
r
ta
n
c
e
o
f
an
in
teg
r
ated
lear
n
in
g
ap
p
r
o
ac
h
i
n
wh
ich
s
tu
d
en
ts
ar
e
g
iv
en
o
p
p
o
r
tu
n
i
ties
to
d
ev
elo
p
th
eir
SE
in
v
ar
io
u
s
asp
ec
ts
o
f
lear
n
in
g
,
s
u
c
h
as
m
ater
ial
c
o
m
p
r
eh
en
s
io
n
an
d
p
r
o
b
lem
-
s
o
l
v
in
g
a
b
ilit
ies.
I
n
th
is
way
,
e
d
u
ca
tio
n
ca
n
b
ec
o
m
e
m
o
r
e
h
o
lis
tic,
ass
i
s
tin
g
s
tu
d
en
ts
in
d
ev
elo
p
in
g
th
e
s
k
ills
r
eq
u
ir
ed
f
o
r
s
u
cc
ess
in
a
v
ar
iety
o
f
f
ield
s
.
T
h
e
t
-
tes
t
r
esu
lts
r
e
v
ea
led
n
o
s
ig
n
if
ican
t
d
if
f
er
e
n
ce
in
SE
in
u
n
d
er
s
tan
d
in
g
m
ate
r
ial
an
d
p
r
o
b
lem
-
s
o
lv
in
g
am
o
n
g
b
io
lo
g
y
ed
u
ca
tio
n
s
tu
d
en
ts
.
T
h
is
m
ea
n
s
th
a
t
b
io
lo
g
y
s
tu
d
en
ts
ar
e
eq
u
ally
co
n
f
id
en
t
in
th
eir
ab
ilit
y
to
u
n
d
er
s
tan
d
m
ater
ia
l
an
d
s
o
lv
e
p
r
o
b
lem
s
.
T
h
ese
f
in
d
in
g
s
ar
e
co
n
s
is
ten
t
with
p
r
ev
io
u
s
r
esear
ch
in
d
icatin
g
th
at
s
tu
d
en
ts
’
SE
in
b
io
lo
g
y
was
n
o
t
s
ig
n
if
i
ca
n
tly
r
elate
d
to
th
eir
p
er
f
o
r
m
an
ce
[
66
]
.
T
h
is
d
em
o
n
s
tr
ates
th
at
th
er
e
is
n
o
s
ig
n
if
ican
t
d
i
f
f
er
en
ce
in
S
E
f
o
r
c
o
m
p
r
eh
en
d
in
g
t
h
e
m
ater
ial
an
d
s
o
lv
in
g
p
r
o
b
lem
s
[
67
]
,
[
68
]
.
T
h
is
in
f
o
r
m
atio
n
ca
n
h
el
p
teac
h
er
s
an
d
ed
u
ca
tio
n
al
p
o
licy
m
ak
er
s
d
e
v
elo
p
m
o
r
e
h
o
lis
tic
an
d
in
teg
r
ated
lear
n
i
n
g
s
tr
ateg
ies
th
at
co
m
b
in
e
m
ate
r
ial
u
n
d
er
s
tan
d
in
g
an
d
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
in
b
io
lo
g
y
ed
u
ca
tio
n
.
Me
an
wh
ile,
th
e
r
e
ar
e
s
ig
n
if
ican
t
d
if
f
e
r
en
ce
s
b
etwe
en
m
ath
em
atics
ed
u
ca
tio
n
s
tu
d
en
ts
.
T
h
is
d
em
o
n
s
tr
ates
th
at
m
ath
em
atic
s
ed
u
ca
tio
n
s
tu
d
e
n
ts
h
av
e
v
a
r
y
in
g
lev
els
o
f
SE
in
b
o
th
u
n
d
er
s
tan
d
in
g
m
ater
ial
an
d
s
o
lv
in
g
p
r
o
b
lem
s
[
45
]
,
[
61
]
,
[
69
]
.
On
e
p
o
s
s
ib
le
in
ter
p
r
e
tatio
n
is
th
at
m
ath
em
atics
ed
u
ca
tio
n
s
tu
d
en
ts
m
a
y
h
av
e
g
r
ea
ter
s
elf
-
co
n
f
id
en
ce
in
u
n
d
er
s
tan
d
in
g
m
ath
em
atica
l
m
ater
ial
th
an
i
n
s
o
lv
in
g
co
n
cr
ete
m
ath
em
atica
l
p
r
o
b
lem
s
[
45
]
,
[
70
]
.
T
h
e
lev
el
o
f
d
if
f
ic
u
lty
o
f
th
e
p
r
o
b
lem
o
r
th
e
ty
p
e
o
f
p
r
o
b
lem
en
c
o
u
n
t
er
ed
in
th
e
co
n
tex
t
o
f
m
ath
em
atics
lear
n
in
g
m
ay
in
f
lu
en
ce
a
s
tu
d
e
n
t
’
s
co
n
f
id
en
ce
in
s
o
lv
in
g
it.
T
h
ese
f
in
d
in
g
s
h
ig
h
lig
h
t
th
e
im
p
o
r
tan
ce
o
f
co
n
s
id
er
in
g
n
o
n
-
ac
ad
em
ic
f
ac
to
r
s
in
s
h
a
p
in
g
s
tu
d
en
t
SE.
Alth
o
u
g
h
th
e
s
u
b
ject
m
atter
d
if
f
er
s
s
ig
n
if
ican
tly
b
etwe
en
b
io
lo
g
y
an
d
m
ath
em
atics,
o
t
h
er
f
ac
to
r
s
s
u
ch
as
p
ee
r
an
d
f
am
ily
s
u
p
p
o
r
t,
p
er
ce
p
tio
n
o
f
one
’
s
ab
ilit
ies,
an
d
lev
el
o
f
m
o
tiv
atio
n
ap
p
ea
r
to
h
av
e
a
g
r
ea
ter
in
f
l
u
en
ce
o
n
SE
[
3
3
]
,
[
3
5
]
.
T
h
ese
f
in
d
in
g
s
ca
n
h
elp
teac
h
er
s
an
d
cu
r
r
icu
lu
m
d
ev
elo
p
e
r
s
d
ev
elo
p
m
o
r
e
f
o
cu
s
ed
lear
n
in
g
s
tr
ateg
ies
to
in
cr
ea
s
e
m
ath
em
atics a
n
d
b
io
l
o
g
y
s
tu
d
en
ts
’
SE
in
u
n
d
e
r
s
tan
d
in
g
t
h
e
m
ater
ial
an
d
s
o
lv
in
g
m
ath
em
a
tical
p
r
o
b
lem
s
.
T
h
e
o
t
h
er
f
in
d
in
g
s
r
e
v
ea
l
th
at
th
er
e
is
a
s
ig
n
if
ican
t
d
if
f
e
r
en
c
e
in
SE
lev
els
b
etwe
en
m
at
h
e
m
atics
an
d
b
io
lo
g
y
ed
u
ca
tio
n
s
tu
d
en
ts
w
h
en
it
co
m
es
t
o
u
n
d
er
s
tan
d
in
g
m
ath
e
m
atics
m
ater
ial
an
d
s
o
lv
in
g
m
ath
em
atics
p
r
o
b
lem
s
.
Acc
o
r
d
in
g
to
r
esea
r
ch
,
SE
in
f
lu
e
n
ce
s
s
tu
d
en
ts
’
s
elf
-
co
n
f
id
en
ce
an
d
p
er
ce
p
tio
n
s
o
f
m
ath
em
atica
l
m
ater
ial
an
d
p
r
o
b
lem
-
s
o
lv
i
n
g
[
59
]
,
[
71
]
.
T
h
ese
f
i
n
d
in
g
s
s
h
ed
lig
h
t
o
n
h
o
w
v
ar
io
u
s
s
tu
d
y
p
r
o
g
r
am
s
ca
n
in
f
lu
en
ce
s
tu
d
en
ts
’
p
er
ce
p
tio
n
s
an
d
co
n
f
i
d
en
ce
wh
en
d
ea
lin
g
with
m
ath
em
atica
l
m
ate
r
ial
an
d
p
r
o
b
lem
s
.
T
h
e
r
esear
ch
p
ap
e
r
id
en
tifie
s
s
ev
e
r
al
f
ac
to
r
s
th
at
co
n
t
r
ib
u
te
to
t
h
e
d
if
f
er
e
n
ce
in
SE
lev
els
b
et
wee
n
m
ath
em
atics
an
d
b
io
lo
g
y
ed
u
ca
tio
n
s
tu
d
en
ts
.
Ma
th
em
atics
ed
u
ca
tio
n
s
t
u
d
en
ts
ten
d
to
h
av
e
h
ig
h
er
SE
d
u
e
to
in
cr
ea
s
ed
ex
p
o
s
u
r
e
to
m
ath
em
atica
l
m
ater
ial
an
d
in
ten
s
iv
e
p
r
ac
tice,
wh
ich
b
o
o
s
ts
th
eir
co
n
f
id
en
ce
in
s
o
lv
in
g
m
ath
em
atica
l
p
r
o
b
lem
s
[
62
]
,
[
72
]
.
B
io
lo
g
y
s
tu
d
en
ts
,
o
n
th
e
o
th
er
h
an
d
,
m
a
y
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66
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73
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[
1
]
Y
.
Li
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.
H
.
S
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2
]
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[
3
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4
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Z.
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.
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.
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