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14
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1
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Feb
r
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20
25
:
423
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432
424
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th
e
m
ain
f
o
cu
s
o
f
lear
n
in
g
a
ctiv
ities
at
all
lev
el
s
.
Hig
h
er
e
d
u
ca
tio
n
s
tu
d
en
ts
n
ee
d
o
p
p
o
r
tu
n
ities
to
tack
le
co
m
p
lex
p
r
o
b
lem
s
,
r
ef
lect
o
n
th
eir
t
h
in
k
in
g
,
an
d
ap
p
ly
d
e
v
elo
p
m
e
n
t
s
tr
ateg
ies
to
o
th
er
co
n
te
x
ts
.
B
y
s
o
lv
in
g
m
ath
p
r
o
b
lem
s
,
s
tu
d
en
ts
d
ev
elo
p
cr
itical
th
i
n
k
in
g
s
k
ills
,
p
er
s
is
ten
ce
,
c
u
r
io
s
ity
,
an
d
c
o
n
f
id
e
n
ce
in
u
n
f
am
ilia
r
s
itu
atio
n
s
o
u
ts
id
e
th
e
class
r
o
o
m
.
Go
o
d
m
ath
em
atica
l
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
en
co
m
p
ass
s
ev
er
al
el
em
en
ts
,
in
clu
d
i
n
g
u
n
d
er
s
tan
d
i
n
g
p
r
o
b
lem
in
f
o
r
m
atio
n
,
d
e
v
is
in
g
p
r
o
b
lem
-
s
o
l
v
in
g
s
tr
ateg
ies
u
s
in
g
m
ath
em
a
tical
p
r
o
ce
d
u
r
es,
an
d
d
r
awin
g
lo
g
ical
c
o
n
clu
s
io
n
s
b
ased
o
n
th
e
p
r
o
b
lem
c
o
n
tex
t.
Stu
d
en
ts
ca
n
b
e
p
r
esen
te
d
with
p
r
o
b
lem
-
s
o
lv
in
g
q
u
esti
o
n
s
to
en
h
a
n
ce
th
ese
s
k
i
lls
.
R
esp
o
n
d
i
n
g
t
o
t
h
e
u
r
g
e
n
c
y
o
f
th
e
n
ee
d
t
o
b
o
o
s
t
p
r
o
d
u
cti
v
it
y
a
n
d
c
o
m
p
eti
ti
v
e
n
ess
in
th
e
2
1
s
t
ce
n
t
u
r
y
er
a
,
t
h
e
g
o
v
e
r
n
m
e
n
t
h
as
u
ti
liz
e
d
d
i
g
it
al
t
ec
h
n
o
lo
g
y
,
a
n
d
e
d
u
c
ati
o
n
h
as
e
v
o
l
v
e
d
i
n
t
o
e
d
u
c
ati
o
n
4
.
0
wi
th
v
ar
i
o
u
s
tec
h
n
o
lo
g
i
ca
l
i
n
n
o
v
ati
o
n
s
,
es
p
ec
i
all
y
th
e
im
p
l
em
e
n
ta
ti
o
n
o
f
i
n
f
o
r
m
ati
o
n
a
n
d
co
m
m
u
n
i
ca
t
io
n
te
ch
n
o
l
o
g
y
(
I
C
T
)
in
t
h
e
p
r
o
c
ess
o
f
lea
r
n
i
n
g
m
at
h
e
m
at
ics
,
as
s
tat
ed
b
y
E
ls
a
y
ar
y
[
8
]
e
d
u
c
at
o
r
s
m
u
s
t
c
o
n
ti
n
u
e
to
tr
ai
n
s
t
u
d
e
n
ts
t
o
in
n
o
v
ate
u
s
i
n
g
I
C
T
in
b
le
n
d
ed
le
ar
n
i
n
g
,
w
h
i
c
h
h
as
r
ec
ei
v
e
d
p
ar
tic
u
l
ar
a
tte
n
t
io
n
i
n
r
e
ce
n
t
y
ea
r
s
.
B
le
n
d
e
d
lea
r
n
i
n
g
is
e
f
f
ec
ti
v
el
y
u
s
e
d
to
co
m
p
le
m
e
n
t
th
e
l
ea
r
n
in
g
p
r
o
c
ess
,
an
d
t
wo
o
f
t
h
e
t
o
o
ls
u
s
e
d
to
s
u
p
p
o
r
t
p
r
o
b
l
em
-
s
o
l
v
i
n
g
i
n
le
ar
n
i
n
g
m
at
h
e
m
at
ic
s
i
n
a
b
l
en
d
ed
l
ea
r
n
in
g
e
n
v
i
r
o
n
m
e
n
t
a
r
e
E
d
m
o
d
o
a
n
d
G
eo
Ge
b
r
a
.
B
len
d
ed
lear
n
in
g
is
an
ed
u
ca
tio
n
al
tech
n
iq
u
e
th
at
co
m
b
in
es
in
-
p
er
s
o
n
class
r
o
o
m
in
s
tr
u
ctio
n
with
o
n
lin
e
or
d
ig
ital
lear
n
in
g
r
eso
u
r
ce
s
[
9
]
–
[
1
1
]
.
B
len
d
e
d
lear
n
i
n
g
h
as
s
ev
er
al
b
en
e
f
its
in
p
r
o
v
id
in
g
o
p
p
o
r
tu
n
ities
f
o
r
in
s
tr
u
cto
r
s
to
in
c
o
r
p
o
r
ate
v
ar
io
u
s
teac
h
in
g
s
tr
ateg
ies
an
d
tech
n
o
l
o
g
ies
in
to
t
h
eir
cu
r
r
i
cu
lu
m
an
d
teac
h
in
g
m
ater
ials
,
m
ak
in
g
th
e
lear
n
in
g
ex
p
er
ien
ce
m
o
r
e
d
y
n
a
m
ic
an
d
ex
citin
g
,
o
n
e
o
f
wh
ich
i
s
u
s
in
g
Geo
Geb
r
a.
Geo
Geb
r
a
is
a
to
o
l
f
o
r
ex
p
lo
r
in
g
m
ath
em
atica
l
co
n
ce
p
ts
,
v
is
u
alizin
g
an
d
an
aly
zin
g
d
ata,
an
d
d
ev
elo
p
in
g
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
[
1
2
]
.
Geo
Geb
r
a
also
p
r
o
v
id
es
a
p
latf
o
r
m
f
o
r
s
h
ar
i
n
g
an
d
c
o
llab
o
r
atin
g
o
n
m
ath
co
n
ten
t,
s
u
ch
as
less
o
n
s
,
ac
tiv
ities
,
an
d
ass
es
s
m
en
ts
.
A
d
ev
ice
th
at
ca
n
b
e
clo
u
d
ed
in
th
e
Geo
Geb
r
a
-
ass
is
ted
lear
n
in
g
p
r
o
ce
s
s
is
E
d
m
o
d
o
.
E
d
m
o
d
o
is
a
web
-
b
ased
p
latf
o
r
m
an
d
m
o
b
ile
ap
p
licatio
n
th
at
m
ak
es it a
cc
ess
ib
le
to
u
s
er
s
o
n
v
ar
io
u
s
d
ev
ices
[
1
3
]
,
[
1
4
]
.
E
d
m
o
d
o
is
also
in
t
eg
r
ated
with
o
th
e
r
ed
u
ca
tio
n
a
l
to
o
ls
lik
e
Go
o
g
le
Dr
iv
e,
Mic
r
o
s
o
f
t
Of
f
ice,
an
d
T
u
r
n
itin
.
Ov
e
r
all,
E
d
m
o
d
o
a
n
d
Geo
Geb
r
a
ar
e
v
alu
ab
le
t
o
o
l
s
f
o
r
ed
u
ca
t
o
r
s
an
d
p
o
ten
tial
s
tu
d
en
ts
to
co
n
n
ec
t
an
d
co
llab
o
r
ate
in
b
len
d
e
d
lear
n
in
g
.
B
len
d
ed
lear
n
in
g
is
an
e
d
u
ca
tio
n
al
ap
p
r
o
ac
h
co
m
b
in
in
g
t
r
ad
itio
n
a
l c
lass
r
o
o
m
in
s
tr
u
ctio
n
with
d
i
g
ital a
n
d
in
ter
n
et
-
b
ased
ed
u
ca
t
io
n
al
r
eso
u
r
ce
s
.
T
ea
ch
in
g
m
ater
ials
an
d
co
m
p
u
ter
-
ass
is
ted
lear
n
in
g
p
r
o
ce
s
s
es,
s
u
ch
as
Geo
Geb
r
a,
h
av
e
p
r
o
v
e
n
ef
f
ec
tiv
e
in
s
tr
en
g
t
h
en
in
g
th
e
lear
n
in
g
a
n
d
u
n
d
er
s
tan
d
in
g
o
f
c
o
m
p
lex
m
ath
em
atica
l
co
n
ce
p
ts
v
is
u
ally
[
1
5
]
.
R
esear
ch
f
in
d
in
g
s
s
h
o
w
th
a
t
co
m
p
u
ter
-
ass
is
ted
teac
h
in
g
m
ater
ials
,
in
clu
d
in
g
Geo
G
eb
r
a,
ca
n
b
r
o
ad
e
n
m
ath
em
atica
l
k
n
o
wled
g
e
a
n
d
m
ak
e
it
ea
s
ier
t
o
ex
p
lo
r
e
s
u
b
je
ct
m
atter
[
1
2
]
.
Stu
d
en
ts
ca
n
b
e
tter
u
n
d
e
r
s
tan
d
th
e
in
f
o
r
m
atio
n
p
r
esen
ted
b
y
in
c
o
r
p
o
r
ati
n
g
m
ath
em
atica
l
f
u
n
c
tio
n
s
in
to
th
e
s
o
f
twar
e.
As
a
r
esu
lt,
s
tu
d
en
ts
ca
n
d
ev
elo
p
r
ea
s
o
n
in
g
s
k
ills
,
g
e
n
er
alize
d
ata,
an
d
g
e
n
er
ate
co
n
clu
s
io
n
s
b
ased
o
n
th
e
u
s
ef
u
ln
ess
o
f
cu
r
r
e
n
t
p
r
o
ce
d
u
r
es.
R
esear
ch
er
s
p
r
o
p
o
s
e
u
s
in
g
E
d
m
o
d
o
to
im
p
r
o
v
e
lear
n
in
g
i
n
th
e
b
len
d
ed
l
ea
r
n
in
g
[
1
6
]
.
T
h
is
s
o
f
twar
e
ca
n
b
e
ea
s
ily
ac
ce
s
s
ed
an
d
u
s
ed
o
n
m
o
b
ile
p
h
o
n
e
s
o
r
co
m
p
u
ter
s
,
m
a
k
in
g
it
m
o
r
e
co
n
v
e
n
ien
t
an
d
ex
citin
g
f
o
r
s
tu
d
en
ts
to
s
tu
d
y
co
n
tin
u
o
u
s
ly
.
Ad
d
itio
n
ally
,
r
esear
ch
er
s
will
test
th
e
ef
f
icac
y
o
f
em
p
lo
y
i
n
g
s
o
f
twar
e
to
lear
n
an
tid
er
iv
ati
v
e
in
teg
r
al
an
d
in
d
ef
in
ite
i
n
teg
r
al
c
o
n
te
n
t
wh
ile
u
s
in
g
ca
lcu
lu
s
t
o
s
o
lv
e
p
r
o
b
lem
s
.
Mo
r
e
r
esear
c
h
is
n
ee
d
e
d
o
n
th
e
ap
p
licatio
n
o
f
tech
n
o
lo
g
y
in
m
ath
em
atics
ed
u
ca
tio
n
,
p
ar
ticu
lar
ly
r
eg
ar
d
i
n
g
en
h
a
n
cin
g
p
r
o
b
lem
-
s
o
lv
in
g
ab
ilit
ies.
On
e
ar
ea
th
at
h
as
y
et
to
r
ec
eiv
e
atten
tio
n
(
s
tate
o
f
th
e
ar
t
)
in
lear
n
in
g
m
ath
e
m
atics
is
th
e
Fu
s
io
n
E
d
m
o
d
o
an
d
Geo
Geb
r
a
as su
p
p
o
r
ter
s
o
f
b
len
d
e
d
lear
n
in
g
.
T
h
is
s
tu
d
y
aim
ed
to
in
v
esti
g
ate
th
e
ef
f
ec
tiv
en
ess
o
f
p
r
o
b
l
em
-
b
ased
m
ath
em
atics
lear
n
i
n
g
th
r
o
u
g
h
b
len
d
ed
lear
n
in
g
with
t
h
e
h
elp
o
f
E
d
m
o
d
o
an
d
Ge
o
Geb
r
a
in
im
p
r
o
v
in
g
p
r
o
b
lem
-
s
o
lv
i
n
g
s
k
ills
in
m
ath
em
atics
lear
n
in
g
.
T
h
e
f
o
r
m
u
latio
n
o
f
t
h
e
p
r
o
b
lem
s
d
is
cu
s
s
ed
in
th
is
s
tu
d
y
ar
e:
i)
W
h
at
ar
e
th
e
cr
iter
ia
f
o
r
im
p
r
o
v
in
g
th
e
p
r
o
b
lem
-
s
o
lv
in
g
ab
ilit
y
o
f
s
tu
d
en
ts
wh
o
lear
n
with
b
len
d
ed
lear
n
in
g
u
s
in
g
E
d
m
o
d
o
an
d
Geo
Geb
r
a
(
B
L
-
UE
G)
an
d
b
len
d
e
d
lear
n
in
g
u
s
in
g
E
d
m
o
d
o
with
o
u
t
Geo
Geb
r
a
(
B
L
-
E
W
G)
?
ii)
I
s
th
er
e
a
d
is
ce
r
n
ib
le
d
if
f
er
en
ce
b
etwe
en
B
L
-
UE
G
an
d
B
L
-
E
W
G
in
h
o
w
th
ey
af
f
ec
t
th
e
d
ev
elo
p
m
e
n
t
o
f
p
r
o
b
lem
-
s
o
lv
in
g
a
b
ilit
ies?
iii)
C
an
th
e
in
c
r
ea
s
e
in
p
r
o
b
lem
-
s
o
lv
in
g
a
b
ilit
ies
b
e
d
is
tin
g
u
is
h
ed
b
etwe
en
s
tu
d
e
n
ts
wh
o
u
s
e
B
L
-
UE
G
an
d
th
o
s
e
wh
o
u
s
e
B
L
-
E
W
G
as a
to
o
l in
lear
n
i
n
g
m
ath
e
m
atics?
2.
M
E
T
H
O
D
2
.
1
.
Resea
rc
h desi
g
n
T
h
is
s
tu
d
y
u
s
ed
a
q
u
a
n
titativ
e
ap
p
r
o
ac
h
an
d
a
q
u
asi
-
ex
p
er
im
en
tal
p
r
e
-
test
an
d
p
o
s
t
-
test
co
n
tr
o
l
g
r
o
u
p
d
esig
n
[
1
7
]
.
T
h
e
lear
n
i
n
g
m
o
d
el
is
th
e
r
esear
ch
'
s
in
d
ep
en
d
en
t
v
ar
ia
b
le
wh
ile
p
r
o
b
l
em
-
s
o
lv
in
g
ap
titu
d
e
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
len
d
ed
lea
r
n
in
g
in
ma
t
h
ema
t
ica
:
th
e
fu
s
io
n
o
f G
eo
Geb
r
a
a
n
d
E
d
mo
d
o
fo
r
en
h
a
n
ce
d
…
(
A
n
to
n
N
a
s
r
u
lla
h
)
425
is
th
e
d
ep
en
d
en
t
v
a
r
iab
le.
T
h
e
ex
p
er
im
e
n
tal
g
r
o
u
p
u
s
ed
B
L
-
UE
G,
wh
er
ea
s
th
e
co
n
tr
o
l
g
r
o
u
p
u
s
ed
B
L
-
E
W
G.
T
h
e
p
u
r
p
o
s
e
o
f
g
iv
in
g
th
e
p
r
e
-
an
d
p
o
s
t
-
test
is
to
ass
e
s
s
th
e
i
n
cr
ea
s
e
in
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
in
b
o
th
g
r
o
u
p
s
.
T
o
co
n
d
u
ct
r
esear
ch
,
th
e
r
esear
ch
er
f
ir
s
t
ex
p
lain
ed
th
e
f
e
atu
r
es
an
d
ca
p
ab
ilit
ies
o
f
E
d
m
o
d
o
an
d
Geo
Geb
r
a.
B
len
d
ed
lear
n
in
g
is
th
en
u
tili
ze
d
,
b
len
d
in
g
in
-
c
lass
an
d
o
u
t
-
of
-
class
lear
n
in
g
u
s
in
g
th
e
E
d
m
o
d
o
an
d
Geo
Geb
r
a
p
r
o
g
r
am
s
an
d
d
is
tr
ib
u
tin
g
lear
n
in
g
m
ater
ials
s
u
ch
as
m
ater
ials
,
v
id
eo
s
,
ass
i
g
n
m
en
ts
,
an
d
ex
a
m
r
esu
lts
.
Acc
o
r
d
in
g
to
th
e
f
ield
s
tu
d
ies
[
1
7
]
–
[
1
9
]
,
t
h
is
to
o
l
was
s
elec
ted
b
ec
au
s
e
it
is
wel
l
-
k
n
o
wn
to
s
tu
d
en
ts
an
d
ca
n
f
ac
ilit
ate
o
r
g
an
izatio
n
an
d
co
m
m
u
n
icatio
n
wh
ile
s
tu
d
y
in
g
.
2
.
2
.
Sa
m
ple
T
h
is
r
esear
ch
was
co
n
d
u
cted
at
o
n
e
o
f
th
e
p
r
i
v
ate
u
n
i
v
er
s
ities
in
B
an
ten
-
I
n
d
o
n
esia
,
n
am
ely
Un
iv
er
s
itas
B
in
a
B
an
g
s
a.
T
h
e
m
ath
em
atics
co
d
e
f
o
r
ca
lc
u
lu
s
is
KOM
1
4
1
2
1
5
(
3
c
r
ed
its
)
f
o
r
2
nd
s
em
ester
.
T
h
e
f
ac
t
th
at
th
is
r
esear
ch
w
as
co
n
d
u
cted
at
a
u
n
iv
er
s
ity
m
ak
es
it
d
if
f
icu
lt
to
r
an
d
o
m
i
ze
ea
ch
co
u
r
s
e
an
d
ap
p
ly
it
to
co
n
tr
o
l
an
d
ex
p
er
i
m
en
tal
g
r
o
u
p
s
.
On
e
ef
f
ec
tiv
e
m
eth
o
d
is
to
u
s
e
a
q
u
asi
-
q
u
a
n
titativ
e
ex
p
er
im
en
tal
s
tu
d
y
[
1
6
]
,
wh
ich
allo
ws
co
n
tr
o
l
o
v
e
r
ce
r
tain
f
ac
to
r
s
t
h
at
ca
n
r
esu
lt
in
a
f
lawe
d
e
x
p
er
im
e
n
t
[
2
0
]
.
T
h
e
r
esear
ch
p
r
o
ce
s
s
d
o
es
n
o
t
cr
ea
te
n
ew
g
r
o
u
p
s
o
f
s
tu
d
en
ts
b
u
t
r
ath
e
r
u
s
es
ex
is
tin
g
g
r
o
u
p
s
to
id
en
tif
y
ex
p
er
ien
ce
g
r
o
u
p
s
an
d
c
o
n
tr
o
l
g
r
o
u
p
s
with
s
im
ilar
ch
a
r
ac
ter
is
tics
.
T
h
is
r
esear
c
h
in
v
o
lv
ed
7
2
two
-
s
em
ester
s
tu
d
en
ts
at
a
p
r
iv
ate
u
n
iv
er
s
ity
in
B
an
ten
,
I
n
d
o
n
esi
a,
with
d
etails
o
f
3
6
s
tu
d
en
ts
in
th
e
ex
p
er
im
e
n
tal
class
(
1
1
m
ale
an
d
2
5
f
e
m
ale)
an
d
3
6
s
tu
d
en
ts
in
th
e
co
n
tr
o
l
class
(
1
0
m
ale
an
d
2
6
f
em
a
le)
.
R
esear
ch
p
ar
ticip
an
ts
wer
e
s
elec
ted
th
r
o
u
g
h
p
u
r
p
o
s
iv
e
s
am
p
lin
g
,
wh
er
e
two
class
es
with
th
e
s
am
e
ab
ili
ti
es
wer
e
s
elec
ted
.
Ver
if
icatio
n
o
f
th
e
s
im
ilar
ity
o
f
ab
ilit
ies
was
ca
r
r
ied
o
u
t
u
s
in
g
an
in
d
ep
e
n
d
en
t
t
-
test
,
y
iel
d
in
g
t
(
7
2
)
=0
.
6
8
a
n
d
p
>0
.
0
5
,
s
h
o
win
g
th
at
th
e
ex
p
er
im
en
tal
an
d
co
n
tr
o
l
class
es
'
s
k
ill
s
wer
e
o
n
p
ar
.
A
b
ala
n
ce
d
d
is
tr
ib
u
tio
n
o
f
s
k
ills
is
s
i
g
n
if
ican
t
to
en
s
u
r
e
th
at
th
e
tr
ea
tm
en
t o
f
th
e
lear
n
in
g
m
o
d
el
an
d
to
o
ls
u
s
ed
in
cr
e
ase
p
r
o
b
lem
-
s
o
lv
i
n
g
ab
ilit
ies.
2
.
3
.
I
ns
t
rum
ent
At
th
e
d
ata
co
llectio
n
s
tag
e,
t
h
e
test
in
s
tr
u
m
en
t
was
d
es
ig
n
ed
to
m
ea
s
u
r
e
s
tu
d
en
ts
’
p
r
o
b
l
em
-
s
o
lv
in
g
ab
ilit
ies.
T
h
is
test
co
n
s
is
ts
o
f
f
iv
e
ess
ay
q
u
esti
o
n
s
f
o
cu
s
ed
o
n
ev
alu
atin
g
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
,
in
clu
d
in
g
t
h
e
d
ev
elo
p
m
e
n
t
an
d
ap
p
licatio
n
o
f
p
r
o
b
lem
-
s
o
lv
in
g
s
tr
ateg
ies,
as
well
as
r
ef
lectio
n
o
n
th
e
p
r
o
ce
s
s
[
2
1
]
.
B
ef
o
r
e
im
p
lem
en
tatio
n
,
th
e
v
alid
ity
a
n
d
r
eliab
ilit
y
o
f
th
is
test
in
s
tr
u
m
en
t w
er
e
ch
ec
k
e
d
th
r
o
u
g
h
a
s
er
ies o
f
test
s
.
T
h
e
v
alid
ity
an
d
r
eliab
ilit
y
o
f
th
e
in
s
tr
u
m
en
t
ar
e
th
e
m
ai
n
f
o
cu
s
o
f
atten
tio
n
i
n
th
is
r
esear
ch
.
A
s
er
ies
o
f
test
s
wer
e
co
n
d
u
cted
t
o
m
ea
s
u
r
e
th
e
in
s
tr
u
m
en
t
’
s
v
alid
ity
,
in
clu
d
in
g
a
co
n
ten
t
v
al
id
ity
test
in
v
o
lv
in
g
ass
es
s
m
en
ts
f
r
o
m
ex
p
e
r
ts
in
th
e
r
elate
d
f
ield
.
E
x
p
e
r
ts
p
r
o
v
id
e
in
p
u
t
o
n
th
e
q
u
esti
o
n
s
in
t
h
e
q
u
esti
o
n
n
ai
r
e
t
o
en
s
u
r
e
th
e
in
s
tr
u
m
e
n
t
’
s
s
u
itab
ilit
y
to
th
e
r
esear
ch
o
b
jectiv
es
an
d
th
e
ac
cu
r
ac
y
o
f
m
ea
s
u
r
i
n
g
th
e
v
a
r
iab
les
o
f
in
ter
est.
I
n
a
d
d
itio
n
,
test
v
alid
ity
is
ass
ess
ed
u
s
in
g
two
ap
p
r
o
ac
h
es,
n
am
ely
c
o
n
ten
t
v
al
id
ity
an
d
em
p
ir
ical
v
alid
ity
.
T
h
e
ass
ess
m
en
t
o
f
th
e
co
n
te
n
t
v
alid
ity
o
f
t
h
e
in
s
tr
u
m
e
n
t
in
v
o
lv
e
d
m
ath
em
atics
ed
u
ca
ti
o
n
ex
p
er
ts
.
T
h
e
in
s
tr
u
m
e
n
t p
ass
ed
th
e
co
n
ten
t
v
alid
ity
test
,
in
d
icatin
g
th
at
th
e
i
n
s
tr
u
m
en
t
m
et
th
e
r
esea
r
ch
o
b
jectiv
es.
Fo
r
em
p
ir
ical
v
alid
ity
,
p
r
o
d
u
ct
-
m
o
m
en
t
s
tatis
tical
co
r
r
elatio
n
an
aly
s
is
is
u
s
ed
.
T
h
e
tr
ial
was
co
n
d
u
cte
d
o
n
3
0
s
tu
d
en
ts
wh
o
h
ad
p
r
e
v
io
u
s
ly
s
tu
d
ied
th
e
v
o
lu
m
e
in
teg
r
al
o
f
r
o
tatin
g
o
b
jects.
E
m
p
ir
ical
v
al
id
ity
is
ass
ess
ed
b
y
co
m
p
ar
in
g
s
tu
d
en
t
ex
am
r
esu
lts
with
th
e
av
er
ag
e
d
aily
e
x
am
r
esu
lts
o
f
th
e
p
r
e
v
io
u
s
s
e
m
ester
.
T
h
e
r
esu
lts
s
h
o
w
th
at
th
e
p
r
o
b
lem
-
s
o
lv
in
g
ab
ilit
y
test
is
co
n
s
id
er
e
d
v
alid
,
with
an
in
s
tr
u
m
en
t
v
ali
d
ity
co
ef
f
icien
t
o
f
0
.
4
5
5
,
m
o
r
e
s
ig
n
if
ican
t th
a
n
th
e
b
en
ch
m
a
r
k
o
f
0
.
3
6
1
.
T
h
e
p
r
o
b
lem
-
s
o
lv
in
g
ab
ilit
y
t
est
in
s
tr
u
m
en
t
u
s
ed
in
th
e
r
es
ea
r
ch
h
as
u
n
d
er
g
o
n
e
a
s
er
ies
o
f
v
alid
ity
an
d
r
eliab
ilit
y
test
s
to
en
s
u
r
e
th
e
r
eliab
ilit
y
an
d
v
alid
ity
o
f
th
e
d
ata
co
llected
.
R
eliab
ilit
y
test
in
g
was
ca
r
r
ied
o
u
t
u
s
in
g
th
e
r
etest
m
eth
o
d
,
wh
er
e
th
e
q
u
esti
o
n
n
air
e
was
d
is
tr
ib
u
ted
to
r
esp
o
n
d
en
ts
at
two
d
if
f
er
en
t
tim
es
to
ch
ec
k
th
e
c
o
n
s
is
ten
cy
o
f
th
e
a
n
s
wer
s
.
C
r
o
n
b
ac
h
’
s
alp
h
a
co
e
f
f
icien
t
was
also
ap
p
lied
to
m
ea
s
u
r
e
th
e
in
ter
n
al
co
n
s
is
ten
cy
o
f
q
u
esti
o
n
s
in
th
e
in
s
tr
u
m
en
t.
T
h
e
r
eliab
ilit
y
t
est
r
esu
lts
s
h
o
w
a
m
o
d
er
ate
r
eliab
ilit
y
ca
teg
o
r
y
,
with
a
C
r
o
n
b
ac
h
’
s
alp
h
a
s
co
r
e
o
f
0
.
4
8
5
.
T
h
u
s
,
th
is
test
in
s
tr
u
m
en
t
is
co
n
s
id
er
ed
v
alid
an
d
r
eliab
le
f
o
r
m
ea
s
u
r
in
g
s
tu
d
en
ts
’
p
r
o
b
le
m
-
s
o
lv
in
g
ab
ilit
ies in
th
is
r
esear
ch
.
Sev
er
al
s
tep
s
wer
e
im
p
lem
e
n
ted
d
u
r
in
g
th
e
d
esig
n
an
d
i
m
p
lem
en
tatio
n
o
f
t
h
e
s
tu
d
y
as
co
n
tr
o
l
m
ea
s
u
r
es
f
o
r
co
n
f
o
u
n
d
in
g
v
ar
iab
les.
On
e
m
eth
o
d
o
f
c
o
n
tr
o
l
is
th
e
s
elec
tio
n
o
f
a
co
n
tr
o
l
g
r
o
u
p
t
h
at
is
co
m
p
ar
ab
le
to
th
e
e
x
p
er
im
e
n
tal
g
r
o
u
p
.
Statis
tical
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aly
s
is
,
s
u
ch
as
an
aly
s
is
o
f
co
v
ar
ian
c
e,
is
also
ap
p
lied
to
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n
tr
o
l
c
o
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o
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n
d
i
n
g
v
ar
iab
les
d
u
r
in
g
th
e
d
ata
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aly
s
is
p
r
o
c
ess
.
T
h
is
ap
p
r
o
ac
h
aim
s
to
en
s
u
r
e
th
at
d
if
f
er
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ce
s
in
r
esu
lts
b
etwe
en
th
e
ex
p
er
i
m
en
tal
an
d
co
n
tr
o
l
g
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o
u
p
s
ca
n
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e
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p
licitly
attr
ib
u
ted
to
th
e
tr
ea
tm
en
t
g
iv
en
a
n
d
n
o
t c
au
s
ed
b
y
ex
ter
n
al
f
ac
to
r
s
th
at
m
ig
h
t in
f
lu
e
n
ce
th
e
r
esear
ch
r
esu
lts
.
I
t
s
h
o
u
ld
b
e
n
o
ted
th
at
th
is
r
esear
ch
h
as
r
ec
eiv
ed
eth
ical
ap
p
r
o
v
al
f
r
o
m
t
h
e
u
n
iv
e
r
s
ity
in
B
an
ten
.
T
h
is
ap
p
r
o
v
al
e
n
s
u
r
es
th
at
r
esear
ch
is
co
n
d
u
cted
p
er
eth
ical
s
tan
d
ar
d
s
,
in
clu
d
in
g
p
r
o
tectin
g
p
ar
ticip
a
n
ts
’
r
ig
h
ts
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d
welf
a
r
e.
Data
v
al
id
ity
m
an
ag
em
en
t
is
ca
r
r
ied
o
u
t
ca
r
e
f
u
lly
th
r
o
u
g
h
d
etail
ed
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ata
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llectio
n
,
p
r
o
ce
s
s
in
g
an
d
an
aly
s
is
s
tag
es,
tak
in
g
in
t
o
ac
co
u
n
t th
e
p
r
o
ce
d
u
r
es a
n
d
m
ea
s
u
r
in
g
t
o
o
ls
u
s
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
es E
d
u
c
,
Vo
l
.
14
,
No
.
1
,
Feb
r
u
a
r
y
20
25
:
423
-
432
426
2
.
4
.
Resea
rc
h pro
ce
du
re
T
h
e
r
e
s
e
a
r
c
h
p
r
o
c
e
d
u
r
e
w
a
s
c
a
r
r
i
e
d
o
u
t
i
n
t
w
o
s
t
a
g
e
s
:
p
r
ep
a
r
a
t
i
o
n
a
n
d
i
m
p
l
e
m
e
n
t
a
t
i
o
n
.
F
i
e
l
d
a
n
d
l
i
t
e
r
at
u
r
e
s
t
u
d
i
es
w
e
r
e
c
o
n
d
u
c
t
e
d
b
e
t
t
e
r
t
o
u
n
d
e
r
s
t
a
n
d
t
h
e
r
e
s
e
a
r
c
h
p
r
o
b
l
e
m
d
u
r
i
n
g
t
h
e
p
r
e
p
a
r
a
t
o
r
y
s
t
a
g
e
.
V
a
l
i
d
it
y
a
n
d
r
e
l
i
a
b
il
i
t
y
we
r
e
c
o
n
f
i
r
m
e
d
i
n
t
h
e
r
e
s
e
a
r
c
h
i
n
s
t
r
u
m
e
n
t
u
s
i
n
g
c
o
n
t
e
n
t
a
n
d
e
m
p
i
r
i
c
a
l
v
a
l
i
d
i
t
y
m
e
t
h
o
d
s
.
First,
ex
p
er
ts
with
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
ev
alu
ate
th
e
ab
ilit
y
o
f
th
e
in
s
tr
u
m
en
t
to
m
ea
s
u
r
e
p
r
o
b
lem
-
s
o
lv
in
g
a
b
ilit
ies.
B
as
ed
o
n
th
ei
r
f
ee
d
b
ac
k
,
n
ec
ess
ar
y
ad
ju
s
tm
en
ts
wer
e
m
ad
e
to
th
e
in
s
tr
u
m
en
t,
a
n
d
it
was
ev
alu
ated
o
n
p
u
p
ils
wh
o
wer
e
n
o
t
in
v
o
lv
e
d
in
th
e
s
tu
d
y
.
T
h
e
n
,
em
p
i
r
ical
v
alid
ity
a
n
d
r
eliab
ilit
y
wer
e
ev
alu
ated
u
s
in
g
s
tatis
tical
an
a
ly
s
is
.
T
h
e
in
s
tr
u
m
en
t
is
p
r
ep
ar
ed
f
o
r
r
esear
c
h
o
n
ce
it
h
as
b
ee
n
d
ee
m
ed
v
alid
an
d
d
e
p
en
d
a
b
le.
T
h
e
s
ec
o
n
d
is
th
e
im
p
lem
e
n
tatio
n
s
tag
e,
wh
er
e
th
e
r
esear
ch
er
s
s
elec
t
s
tu
d
y
p
ar
ticip
a
n
ts
,
an
d
th
e
m
an
ag
em
en
t
o
f
r
esear
ch
p
er
m
its
ar
e
h
an
d
ed
o
v
er
to
t
h
e
r
ele
v
an
t
p
ar
ties
.
Par
ticip
an
ts
wer
e
s
elec
ted
b
ased
o
n
o
b
s
er
v
atio
n
,
an
d
a
p
r
e
-
test
in
l
ea
r
n
in
g
was
g
iv
en
b
ef
o
r
e
tr
ea
t
m
en
t.
T
h
e
p
o
s
t
-
test
was
th
en
c
ar
r
ied
o
u
t
af
ter
th
e
ca
lcu
lu
s
lear
n
in
g
p
r
o
ce
s
s
'
s
co
n
clu
s
io
n
in
th
e
r
o
tatin
g
m
ater
i
al
v
o
lu
m
e.
2
.
5
.
Da
t
a
a
na
ly
s
is
No
r
m
ality
an
d
h
o
m
o
g
en
eity
a
s
s
es
s
m
en
ts
wer
e
m
ad
e
b
ef
o
r
e
u
s
in
g
q
u
a
n
titativ
e
s
tatis
tical
test
s
.
T
h
e
Ko
lm
o
g
o
r
o
v
-
Sm
ir
n
o
v
test
was
u
s
ed
to
g
au
g
e
n
o
r
m
ality
an
d
L
ev
en
e
’
s
to
ca
lcu
late
h
o
m
o
g
en
eity
.
T
h
e
in
cr
ea
s
e
in
s
tu
d
en
ts
’
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
in
b
o
th
g
r
o
u
p
s
was m
ea
s
u
r
ed
u
s
in
g
n
o
r
m
alize
d
N
-
Gain
as
(
1
)
[
2
1
]
,
[
2
2
]
.
(
)
=
−
−
(
1
)
T
h
e
n
o
r
m
alize
d
g
ain
s
co
r
e
in
ter
p
r
etatio
n
cr
iter
ia
an
d
r
eq
u
i
r
em
en
ts
ar
e
d
escr
ib
ed
in
T
a
b
le
1
.
T
h
is
s
tu
d
y
in
v
o
lv
ed
d
escr
ip
tiv
e
an
d
h
y
p
o
th
etica
l
r
esear
ch
q
u
esti
o
n
s
.
Fo
r
d
escr
ip
tiv
e
r
esear
ch
q
u
esti
o
n
s
,
a
d
escr
ip
tiv
e
s
tatis
tical
an
aly
s
i
s
s
u
ch
as
m
ea
n
,
s
tan
d
ar
d
d
e
v
iatio
n
,
an
d
s
k
ewn
ess
was
u
s
ed
to
ex
p
lain
th
e
d
ev
elo
p
m
e
n
t
o
f
p
r
o
b
lem
-
s
o
l
v
in
g
ab
ilit
ies
in
b
o
th
class
es.
T
h
e
s
tan
d
ar
d
s
f
o
r
e
n
h
an
cin
g
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
in
b
o
th
g
r
o
u
p
s
ar
e
s
h
o
wn
in
T
ab
le
1
,
an
d
h
y
p
o
th
esis
test
in
g
was
u
s
ed
to
ad
d
r
ess
th
e
s
ec
o
n
d
an
d
th
i
r
d
s
tu
d
y
o
b
jectiv
es.
Pair
ed
-
s
am
p
le
t
-
te
s
ts
an
d
in
d
e
p
en
d
e
n
t
t
-
test
s
wer
e
also
u
s
ed
.
T
h
e
p
r
e
-
test
,
p
o
s
t
-
test
,
an
d
N
-
Gain
d
ata
wer
e
f
ir
s
t
test
ed
f
o
r
n
o
r
m
ality
an
d
h
o
m
o
g
e
n
eity
.
T
h
e
d
ata
wer
e
th
en
ex
am
in
e
d
u
s
in
g
th
e
s
tatis
tical
tech
n
iq
u
es o
f
th
e
p
air
e
d
s
am
p
l
e
t
-
test
an
d
th
e
in
d
e
p
en
d
e
n
t t
-
t
est
[
2
1
]
,
[
2
3
]
.
T
ab
le
1
.
I
n
ter
p
r
etatio
n
o
f
t
h
e
c
r
iter
ia,
n
o
r
m
alize
d
g
ain
s
co
r
e
G
a
i
n
sc
o
r
e
I
n
t
e
r
p
r
e
t
a
t
i
o
n
g
≥
0
.
7
H
i
g
h
0
.
3
0
≤
g
<
0
.
7
0
M
e
d
i
u
m
g
<
0
.
3
0
Lo
w
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
is
s
tu
d
y
'
s
p
r
im
ar
y
g
o
al
is
to
co
m
p
a
r
e
h
o
w
well
B
L
-
UE
G
an
d
B
L
-
E
W
G
wo
r
k
to
im
p
r
o
v
e
s
tu
d
en
ts
'
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
.
T
h
r
ee
s
tu
d
y
s
u
b
jects
h
av
e
b
ee
n
cr
e
ated
b
y
co
m
p
ar
in
g
t
h
e
ef
f
ec
ti
v
en
ess
o
f
B
L
-
UE
G
an
d
B
L
-
E
W
G.
T
h
e
f
o
llo
win
g
s
ec
tio
n
d
escr
ib
es
a
d
escr
ip
tiv
e
m
o
d
el
o
f
th
e
s
tatis
tical
an
aly
s
is
r
esu
lts
u
s
ed
to
im
p
r
o
v
e
s
tu
d
e
n
ts
'
p
r
o
b
lem
-
s
o
lv
in
g
ab
ilit
ies.
T
h
e
f
ir
s
t r
esear
ch
q
u
esti
o
n
h
as b
ee
n
f
o
u
n
d
an
d
d
is
cu
s
s
ed
th
r
o
u
g
h
d
escr
ip
tiv
e
s
tatis
tical
an
aly
s
i
s
,
an
d
th
e
f
in
d
in
g
s
ar
e
p
r
esen
ted
in
T
ab
le
2
.
T
ab
le
2
p
r
o
v
id
es
a
d
escr
ip
tiv
e
s
tatis
tical
an
aly
s
i
s
o
f
im
p
r
o
v
in
g
s
tu
d
en
ts
'
p
r
o
b
lem
-
s
o
lv
in
g
ab
ilit
ies
u
s
in
g
B
L
-
UE
G
an
d
B
L
-
E
W
G.
T
h
e
r
esear
ch
f
in
d
in
g
s
s
h
o
wed
th
at
s
tu
d
en
ts
wh
o
u
s
ed
B
L
-
U
E
G
s
h
o
wed
a
m
o
r
e
s
ig
n
if
ican
t
im
p
r
o
v
em
e
n
t
in
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
(
m
ea
n
N
-
Gain
=0
.
6
7
)
th
an
th
o
s
e
w
h
o
u
s
ed
B
L
-
E
W
G
(
m
ea
n
N
-
Gain
=0
.
5
6
)
.
B
o
th
class
es
d
em
o
n
s
tr
ate
im
p
r
o
v
em
e
n
t
cr
iter
ia
th
at
f
all
in
to
th
e
m
e
d
iu
m
ca
teg
o
r
y
.
T
h
e
d
is
tr
ib
u
tio
n
o
f
im
p
r
o
v
em
e
n
t
d
ata
o
n
B
L
-
UE
G
(
s
=0
.
2
6
)
is
m
o
r
e
d
iv
er
s
e
th
an
th
at
o
f
B
L
-
E
W
G
(
s
=0
.
1
5
)
.
B
o
th
class
es
g
o
t
a
n
eg
ativ
e
s
k
ewn
ess
s
co
r
e,
wh
ich
s
h
o
ws
th
at
th
e
g
r
ap
h
o
f
in
cr
ea
s
in
g
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
ten
d
s
to
b
e
n
e
g
ativ
e.
T
h
is
tr
en
d
in
d
i
ca
tes th
at
th
e
s
co
r
es f
o
r
en
h
an
cin
g
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
f
o
cu
s
o
n
h
ig
h
s
co
r
es.
T
ab
le
2
.
Descr
ip
tiv
e
p
r
o
b
lem
-
s
o
lv
in
g
ab
ilit
y
im
p
r
o
v
em
e
n
t b
ased
o
n
th
e
m
o
d
el
M
o
d
e
l
N
-
G
a
i
n
M
e
a
n
S
t
d
.
D
e
v
i
a
t
i
o
n
S
k
e
w
n
e
ss
BL
-
U
EG
0
.
6
7
0
.
2
6
-
0
.
2
9
BL
-
EWG
0
.
5
6
0
.
1
5
-
0
.
1
6
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
len
d
ed
lea
r
n
in
g
in
ma
t
h
ema
t
ica
:
th
e
fu
s
io
n
o
f G
eo
Geb
r
a
a
n
d
E
d
mo
d
o
fo
r
en
h
a
n
ce
d
…
(
A
n
to
n
N
a
s
r
u
lla
h
)
427
B
ef
o
r
e
s
tatis
tical
an
aly
s
is
,
we
test
ed
th
e
d
ata
f
r
o
m
b
o
th
class
es,
in
clu
d
in
g
t
h
e
p
r
e
-
test
,
p
o
s
t
-
test
,
an
d
N
-
G
ain
v
alu
es,
f
o
r
n
o
r
m
ality
an
d
h
o
m
o
g
en
eity
.
T
h
e
r
esu
lts
o
f
th
e
n
o
r
m
ality
test
f
o
r
b
o
th
ty
p
es
ar
e
s
h
o
wn
i
n
T
ab
le
3
.
B
ef
o
r
e
d
o
in
g
th
e
p
ai
r
ed
-
s
am
p
le
t
-
test
an
d
p
air
e
d
-
s
am
p
le
t
-
test
,
th
e
n
o
r
m
ality
te
s
t
r
esu
lts
f
r
o
m
th
e
Ko
lm
o
g
o
r
o
v
-
Sm
ir
n
o
v
test
f
o
r
ea
ch
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ill
s
co
r
e
f
r
o
m
t
h
e
two
class
es
ar
e
s
h
o
wn
.
T
h
e
t
-
test
in
d
ep
en
d
en
tly
an
s
wer
ed
th
e
s
ec
o
n
d
a
n
d
th
ir
d
r
esear
ch
q
u
esti
o
n
s
.
T
ab
le
3
d
is
p
lay
s
th
e
o
u
tco
m
es
o
f
th
e
Ko
lm
o
g
o
r
o
v
-
Sm
ir
n
o
v
test
(
Sig
.
)
,
wh
ich
was
p
er
f
o
r
m
ed
o
n
th
e
p
r
e
-
test
,
p
o
s
t
-
test
,
an
d
N
-
Ga
in
s
co
r
es
f
o
r
b
o
t
h
g
r
o
u
p
s
.
T
h
e
f
in
d
in
g
s
s
h
o
w
th
at
th
e
d
ata
h
as
a
n
o
r
m
al
d
is
tr
ib
u
tio
n
b
ec
au
s
e
th
e
Ko
lm
o
g
o
r
o
v
-
Sm
ir
n
o
v
(
Sig
.
)
s
co
r
e
f
o
r
th
e
th
r
ee
s
co
r
es
in
b
o
th
class
es
s
u
r
p
ass
e
s
0
.
0
5
.
T
h
u
s
,
b
o
th
g
r
o
u
p
s
'
p
r
e
-
test
,
p
o
s
t
-
test
,
an
d
N
-
Gain
s
co
r
es
wer
e
f
r
o
m
p
o
p
u
latio
n
s
with
n
o
r
m
al
d
is
tr
ib
u
tio
n
s
.
T
ab
le
4
d
is
p
lay
s
th
e
r
esu
lts
o
f
th
e
L
ev
en
e
test
,
wh
ich
was u
s
ed
to
d
eter
m
i
n
e
th
e
h
o
m
o
g
en
e
ity
o
f
th
e
d
ata.
T
ab
le
3
.
R
esu
lts
o
f
th
e
n
o
r
m
al
cy
test
M
o
d
e
l
Te
st
K
o
l
m
o
g
o
r
o
v
-
S
m
i
r
n
o
v
t
e
st
a
S
t
a
t
i
st
i
c
df
S
i
g
.
BL
-
U
EG
Pre
-
t
e
st
0
.
1
3
2
36
0
.
0
6
4
P
o
st
-
t
e
st
0
.
1
3
4
36
0
.
0
6
7
N
-
G
a
i
n
0
.
1
4
3
36
0
.
2
0
0
*
BL
-
EWG
Pre
-
t
e
st
0
.
1
4
1
36
0
.
0
7
6
P
o
st
-
t
e
st
0
.
1
4
3
36
0
.
0
7
8
N
-
G
a
i
n
0
.
0
7
4
36
0
.
2
0
0
*
T
ab
le
4
.
T
est th
e
h
o
m
o
g
en
eity
o
f
d
ata
in
b
o
th
class
es
Pre
-
t
e
st
P
o
st
-
t
e
st
N
-
G
a
i
n
Le
v
a
n
e
s
t
a
t
i
s
t
i
c
0
.
7
4
8
0
.
1
6
4
0
.
8
4
2
d
f
1
1
1
1
d
f
2
70
70
70
S
i
g
.
0
.
3
6
0
.
6
8
0
.
4
5
T
ab
le
4
s
h
o
ws
s
ig
n
if
ican
t
v
alu
es
f
o
r
p
r
e
-
test
,
p
o
s
t
-
test
,
an
d
N
-
Gain
s
co
r
es
f
o
r
b
o
th
class
es
th
at
ar
e
g
r
ea
ter
th
a
n
0
.
0
5
,
in
d
icatin
g
t
h
at
th
e
v
a
r
ian
ce
s
o
f
th
ese
s
co
r
es
ar
e
th
e
s
am
e.
T
ab
le
4
d
e
m
o
n
s
tr
ates
th
at
th
e
d
ata
co
n
f
o
r
m
s
to
th
e
v
ar
ian
c
e
h
o
m
o
g
en
eity
ass
u
m
p
tio
n
.
Hen
ce
,
u
s
in
g
a
t
-
test
is
tr
u
s
two
r
th
y
.
T
ab
les
5
-
7
d
is
p
lay
th
e
r
esu
lts
o
f
th
e
p
air
e
d
s
am
p
le
t
-
test
f
r
o
m
th
e
an
aly
s
is
ca
r
r
ied
o
u
t u
s
in
g
th
e
SP
SS
p
r
o
g
r
a
m
.
T
h
e
f
in
d
in
g
s
o
f
p
air
1
a
r
e
s
h
o
wn
in
T
ab
le
6
,
s
p
ec
if
ically
t
h
e
co
m
p
ar
is
o
n
o
f
th
e
s
tu
d
e
n
ts
s
tu
d
y
in
g
with
B
L
-
UE
G
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
b
etwe
en
th
e
p
r
e
-
test
an
d
p
o
s
t
-
test
,
wh
ich
ac
h
iev
e
d
a
s
ig
n
if
ican
t
lev
el
o
f
0
.
0
0
1
,
wh
ich
is
les
s
th
an
α
=0
.
0
5
.
As
a
r
esu
lt,
u
s
in
g
B
L
-
UE
G
d
r
am
atica
lly
im
p
ac
ts
h
o
w
well
s
tu
d
en
ts
lear
n
to
s
o
lv
e
p
r
o
b
lem
s
.
T
ab
le
7
s
h
o
w
s
th
e
r
elatio
n
s
h
ip
b
etwe
en
th
e
p
r
e
-
test
an
d
p
o
s
t
-
test
r
esu
lts
.
A
co
r
r
elatio
n
v
alu
e
o
f
0
.
5
4
2
was
o
b
tain
ed
f
o
r
p
ai
r
1
with
a
s
ig
n
if
ican
ce
lev
el
o
f
0
.
0
0
1
,
wh
ic
h
is
s
u
b
s
tan
tial
ly
lo
wer
th
an
0
.
0
5
,
in
d
icatin
g
a
s
u
b
s
tan
tial
p
o
s
itiv
e
lin
k
b
etwe
en
t
h
e
s
tu
d
en
ts
wh
o
h
ad
ta
k
en
B
L
-
UE
G
co
u
r
s
es
b
ef
o
r
e
an
d
a
f
ter
th
e
test
.
T
ab
le
5
.
Pair
ed
s
am
p
les s
tatis
tics
P
a
i
r
1
P
a
i
r
2
Pre
BL
-
U
EG
P
o
st
_
BL
-
U
EG
Pre
BL
-
EWG
P
o
st
BL
-
EWG
M
e
a
n
2
5
.
6
8
1
2
7
4
.
6
7
1
6
3
3
.
4
2
8
7
6
8
.
6
1
3
2
N
36
36
36
36
SD
1
3
.
4
0
3
7
6
1
3
.
1
3
7
4
7
1
1
.
4
6
7
8
2
1
2
.
6
0
7
4
7
S
E.
M
e
a
n
2
.
3
3
7
8
4
2
.
1
1
2
5
3
1
.
8
2
7
8
5
2
.
2
3
5
4
3
T
ab
le
6
.
T
h
e
t
-
test
o
n
p
air
ed
s
am
p
les f
o
r
b
o
th
class
es
P
a
i
r
1
P
a
i
r
2
P
r
e
_
B
L
-
U
EG
-
P
o
st
_
B
L
-
U
EG
P
r
e
_
B
L
-
EWG
-
P
o
s
t
_
B
L
-
EWG
M
e
a
n
−
4
7
.
1
2
4
8
0
−
3
5
.
3
7
6
7
4
SD
1
3
.
1
2
6
2
7
8
.
3
4
2
1
5
t
−
2
0
.
7
3
4
−
2
1
.
7
6
7
df
36
36
S
i
g
.
0
.
0
0
1
0
.
0
0
8
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
20
25
:
423
-
432
428
T
ab
le
7
.
Pair
ed
s
am
p
le
c
o
r
r
ela
tio
n
s
P
a
i
r
1
P
a
i
r
2
P
r
e
_
B
L
-
U
EG
& P
o
st
_
B
L
-
U
EG
P
r
e
_
B
L
-
EWG
&
P
o
s
t
_
B
L
-
EWG
N
36
36
C
o
r
r
e
l
a
t
i
o
n
0
.
5
4
2
0
.
7
1
4
S
i
g
.
0
.
0
0
1
0
.
0
0
3
T
h
e
an
aly
s
is
's
f
in
d
in
g
s
f
r
o
m
T
ab
le
6
also
d
em
o
n
s
tr
ate
p
air
2
,
wh
ich
co
m
p
ar
es
th
e
s
tu
d
en
ts
wh
o
s
tu
d
y
with
B
L
-
E
W
G
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
p
r
etest
-
p
o
s
ttes
t
,
as
h
av
in
g
a
s
ig
n
if
ican
t
lev
el
o
f
0
.
0
0
8
,
less
th
an
α
=0
.
0
5
.
As
a
r
esu
lt,
u
s
in
g
B
L
-
E
W
G
d
r
am
atica
lly
im
p
ac
ts
h
o
w
well
p
u
p
ils
lear
n
t
o
s
o
lv
e
p
r
o
b
lem
s
.
I
n
co
n
tr
ast,
r
esu
lts
f
o
r
p
air
2
in
T
ab
le
7
r
ev
ea
led
a
co
r
r
elatio
n
s
co
r
e
o
f
0
.
7
1
4
an
d
a
s
ig
n
if
ican
t
lev
el
o
f
0
.
0
0
,
wh
ich
is
s
u
b
s
tan
tially
lo
wer
t
h
an
0
.
0
5
,
in
d
icatin
g
a
s
tr
o
n
g
p
o
s
itiv
e
lin
k
b
etwe
en
th
e
s
tu
d
en
ts
wh
o
s
tu
d
ied
BL
-
E
W
G
p
r
o
b
lem
-
s
o
lv
in
g
t
ec
h
n
iq
u
es
b
ef
o
r
e
a
n
d
af
ter
th
e
test
.
T
h
e
in
d
ep
e
n
d
en
t
t
-
test
is
u
s
ed
in
th
e
f
o
llo
win
g
an
aly
s
is
to
ev
alu
ate
h
y
p
o
th
eses
ab
o
u
t
d
if
f
er
en
ce
s
b
etwe
en
s
tu
d
en
ts
wh
o
s
tu
d
y
with
B
L
-
UE
G
an
d
s
tu
d
en
ts
wh
o
s
tu
d
y
with
B
L
-
E
W
G
in
en
h
an
cin
g
p
r
o
b
lem
-
s
o
l
v
in
g
ab
ilit
ies
as sh
o
wn
in
T
ab
l
e
8
.
T
h
e
test
f
in
d
in
g
s
f
r
o
m
T
a
b
le
8
in
d
icate
th
at
t
(
7
0
)
=
2
.
8
6
with
a
s
ig
n
if
ican
t
lev
el
(
Sig
.
(
2
-
tailed
)
)
o
f
0
.
0
0
3
is
m
u
c
h
lo
wer
th
a
n
0
.
0
5
.
As
a
r
esu
lt,
th
er
e
is
a
s
ig
n
if
ican
t
d
if
f
e
r
en
ce
b
etwe
en
th
e
im
p
r
o
v
e
m
en
t
in
p
r
o
b
lem
-
s
o
lv
in
g
ab
ilit
ies
o
f
s
tu
d
en
ts
s
tu
d
y
in
g
with
B
L
-
UE
G
an
d
th
o
s
e
s
tu
d
y
in
g
with
B
L
-
E
W
G.
T
ab
le
2
d
em
o
n
s
tr
ates
th
at
s
tu
d
e
n
ts
wh
o
s
tu
d
ied
with
B
L
-
UE
G
s
aw
a
p
r
o
b
lem
-
s
o
lv
in
g
ab
ilit
y
in
cr
ea
s
e
o
f
0
.
6
7
,
wh
ich
was h
ig
h
er
th
an
t
h
e
0
.
5
6
r
is
e
i
n
s
tu
d
en
ts
wh
o
s
tu
d
ied
with
B
L
-
E
W
G
r
eg
ar
d
in
g
p
r
o
b
lem
-
s
o
lv
in
g
ab
ilit
y
.
B
len
d
ed
le
ar
n
in
g
in
th
e
f
u
s
i
o
n
o
f
E
d
m
o
d
o
an
d
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t
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r
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em
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r
o
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g
h
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ar
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s
m
eth
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d
s
.
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l
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te
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ic
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as
s
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tr
a
c
la
s
s
t
im
e.
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er
a
l
ap
p
l
ic
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s
a
r
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r
eq
u
ir
ed
to
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u
p
p
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r
t
th
e
b
l
en
d
ed
lea
r
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in
g
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e
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s
b
y
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f
er
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q
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an
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E
d
m
o
d
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p
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s
PP
T
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PD
F
c
o
n
t
en
t
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an
d
lea
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s
,
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i
le
th
e
d
ev
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i
s
a
Geo
Geb
r
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to
o
l
to
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o
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e
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r
o
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l
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s
r
eg
ar
d
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e
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g
r
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m
e
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r
o
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t
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o
b
jec
t
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a
s
p
r
e
s
en
ted
in
F
ig
u
r
e
1
.
T
ab
le
8
.
N
-
Gain
c
o
m
p
ar
is
o
n
t
est f
o
r
b
o
th
class
es
Le
v
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n
e
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s t
e
st
f
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e
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t
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t
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r
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e
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t
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g
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u
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u
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Fig
u
r
e
1
.
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ea
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in
g
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s
: b
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ed
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in
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th
e
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o
f
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d
m
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d
Geo
Geb
r
a
T
h
e
Geo
Geb
r
a
to
o
l
s
u
p
p
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r
ts
m
an
y
r
ep
r
esen
tatio
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s
o
f
m
ath
em
atica
l
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n
ce
p
ts
,
in
clu
d
in
g
alg
eb
r
aic,
v
is
u
al,
an
d
n
u
m
e
r
ical
s
p
r
ea
d
s
h
ee
t
r
ep
r
esen
tatio
n
s
.
Usi
n
g
Geo
Geb
r
a
d
o
es
n
o
t
r
eq
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ir
e
p
r
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g
r
a
m
m
in
g
a
n
d
allo
ws
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tu
d
en
ts
to
h
elp
s
o
lv
e
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lem
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o
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t
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l
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m
e
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jects
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s
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ec
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len
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th
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d
m
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all
o
f
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in
ter
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tio
n
s
o
cc
u
r
,
wh
ich
ca
n
m
o
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s
tu
d
en
ts
wh
en
th
er
e
is
n
o
t
e
n
o
u
g
h
tim
e
in
class
.
T
h
e
E
d
m
o
d
o
lear
n
in
g
ap
p
licatio
n
o
f
f
er
s
i
n
ter
ac
tio
n
b
etwe
en
s
tu
d
en
ts
an
d
lectu
r
er
s
as sh
o
w
n
in
Fig
u
r
e
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
E
v
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&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
B
len
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lea
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in
ma
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ica
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io
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f G
eo
Geb
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a
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(
A
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429
Af
t
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u
ct
in
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cr
ip
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T
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l
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2
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,
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t
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f
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d
th
a
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as
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m
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ca
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r
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in
s
tu
d
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n
t
s
'
p
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m
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Geo
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r
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t
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d
m
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r
a
l
v
o
lu
m
e
o
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r
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ta
t
in
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o
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jec
t
s
.
I
n
ad
d
it
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n
,
T
ab
l
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5
p
r
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en
t
s
th
e
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n
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ly
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s
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s
u
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t
s
s
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win
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d
if
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e
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en
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e
d
ev
elo
p
m
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t
o
f
p
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b
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in
g
s
k
il
l
s
b
et
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en
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er
wen
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a
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m
o
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s
.
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n
th
e
B
L
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d
B
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cla
s
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s
,
T
a
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s
h
o
ws
a
s
u
b
s
t
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t
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l
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o
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it
iv
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a
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o
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tio
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et
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tu
d
en
t
s
'
p
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e
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d
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o
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t
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t
e
s
t
p
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em
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s
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lv
in
g
s
k
i
ll
s
.
B
L
-
U
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G
ca
n
b
e
s
ee
n
in
th
e
le
ar
n
in
g
p
r
o
ce
s
s
,
a
n
d
s
tu
d
en
t
s
ac
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el
y
d
i
s
c
u
s
s
t
h
e
m
at
er
i
al
a
s
s
h
o
wn
in
Fig
u
r
e
s
1
an
d
2
.
I
m
p
r
o
v
in
g
p
r
o
b
lem
-
s
o
lv
in
g
a
b
ilit
ies
ca
n
b
e
ac
h
iev
e
d
b
y
tea
ch
in
g
s
tu
d
e
n
ts
h
o
w
to
c
o
m
m
u
n
icate
th
eir
id
ea
s
ef
f
e
cti
v
e
ly
.
I
t
is
im
p
o
r
ta
n
t
to
n
o
te
th
at
p
r
o
b
lem
-
s
o
lv
i
n
g
s
k
ills
ca
n
also
b
e
o
b
s
er
v
ed
t
h
r
o
u
g
h
th
e
lear
n
in
g
p
r
o
ce
s
s
an
d
th
e
d
eliv
er
y
o
f
s
tu
d
en
ts
'
id
ea
s
.
T
h
is
lear
n
in
g
p
r
o
ce
s
s
alig
n
s
with
s
o
cial
co
g
n
itiv
e
th
eo
r
y
,
wh
ich
s
tates th
at
lear
n
in
g
ca
n
o
cc
u
r
o
n
ly
b
y
o
b
s
er
v
in
g
o
th
er
s
[
2
1
]
.
B
ased
o
n
th
e
a
n
aly
s
is
p
r
esen
ted
in
T
a
b
le
5
,
th
e
u
s
e
o
f
B
L
-
UE
G
s
ig
n
if
ican
tly
im
p
r
o
v
e
s
s
tu
d
en
ts
'
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
co
m
p
ar
ed
to
lea
r
n
in
g
B
L
-
E
W
G.
T
h
e
ap
p
licatio
n
o
f
B
L
-
UE
G
ef
f
ec
tiv
ely
teac
h
es
m
ath
em
atics.
B
L
-
UE
G
en
ab
les
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o
te
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m
m
u
n
icatio
n
a
n
d
p
r
o
v
id
es
a
p
o
s
itiv
e
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n
in
g
ex
p
er
ien
ce
f
o
r
s
tu
d
en
ts
to
d
is
cu
s
s
p
r
o
b
lem
-
s
o
lv
in
g
.
Ge
o
Geb
r
a
-
ass
is
ted
lear
n
in
g
v
id
eo
s
im
p
r
o
v
e
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
[
2
4
]
,
[
2
5
]
.
I
n
a
d
d
itio
n
,
o
n
lin
e
q
u
i
zz
es
u
s
in
g
E
d
m
o
d
o
ar
e
co
n
v
en
ien
t
an
d
f
lex
ib
le
b
ec
au
s
e
th
ey
ca
n
b
e
d
o
n
e
an
y
wh
er
e
an
d
an
y
tim
e
[
2
6
]
–
[
2
8
]
.
Pre
v
i
o
u
s
r
esear
ch
r
esu
lts
also
s
tated
th
at
u
s
in
g
Ge
o
Geb
r
a
en
co
u
r
ag
es
f
r
eq
u
e
n
t
p
r
o
b
lem
-
s
o
lv
in
g
an
d
co
m
m
u
n
icatio
n
s
k
ills
am
o
n
g
s
tu
d
en
ts
[
2
9
]
.
T
h
e
lear
n
in
g
p
r
o
ce
s
s
an
d
th
e
Qu
iz
o
n
th
e
Ap
p
licatio
n
o
f
BL
-
UE
G
ar
e
illu
s
tr
ated
in
Fig
u
r
e
s
2
a
n
d
3
.
T
h
e
en
v
ir
o
n
m
e
n
t
o
f
th
e
in
te
g
r
ated
lear
n
i
n
g
p
r
o
ce
s
s
with
E
d
m
o
d
o
an
d
Geo
Geb
r
a
is
s
h
o
wn
in
Fig
u
r
e
2
.
Her
e,
th
e
two
p
latf
o
r
m
s
wo
r
k
to
g
eth
er
t
o
estab
lis
h
a
co
m
p
r
eh
e
n
s
iv
e
lear
n
in
g
e
n
v
ir
o
n
m
en
t.
Stu
d
e
n
ts
ca
n
u
s
e
in
ter
ac
tiv
e
lear
n
in
g
to
o
ls
lik
e
Geo
Geb
r
a
to
in
v
esti
g
ate
m
ath
em
atica
l
id
ea
s
th
r
o
u
g
h
p
r
ac
tical
ap
p
licatio
n
s
.
Me
an
wh
ile,
E
d
m
o
d
o
s
er
v
es
as
a
v
ir
tu
al
f
o
r
u
m
wh
er
e
s
tu
d
en
ts
ca
n
in
ter
ac
t
,
co
m
m
u
n
icate
,
a
n
d
ac
ce
s
s
co
u
r
s
e
m
ater
ials
in
a
p
l
an
n
ed
way
.
T
h
e
p
ictu
r
e
s
h
o
w
s
an
attem
p
t
to
b
u
ild
a
p
r
o
s
p
e
r
o
u
s
an
d
in
teg
r
ate
d
lear
n
in
g
ex
p
er
ien
ce
i
n
a
b
len
d
ed
lear
n
in
g
m
eth
o
d
b
y
co
m
b
i
n
in
g
th
ese
two
p
latf
o
r
m
s
.
Fig
u
r
e
2
.
T
h
e
atm
o
s
p
h
e
r
e
o
f
th
e
b
len
d
e
d
lear
n
in
g
p
r
o
ce
s
s
u
s
es E
d
m
o
d
o
an
d
Geo
Ge
b
r
a
Fig
u
r
e
3
.
Dis
p
lay
th
e
m
ater
ial
an
d
q
u
iz
r
esu
lts
o
n
th
e
E
d
m
o
d
o
ap
p
licatio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
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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
20
25
:
423
-
432
430
Fig
u
r
e
3
s
h
o
ws
th
e
ap
p
ea
r
a
n
ce
o
f
m
ater
ials
an
d
test
s
c
o
r
es
in
t
h
e
E
d
m
o
d
o
a
p
p
licat
io
n
.
Her
e,
E
d
m
o
d
o
is
an
o
n
lin
e
lear
n
in
g
p
latf
o
r
m
t
h
at
m
ak
es
q
u
izz
es
an
d
p
r
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n
o
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n
g
m
ater
ials
ea
s
ier
.
Ap
ar
t
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m
q
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iz
r
esu
lts
th
at
r
ev
ea
l
in
f
o
r
m
atio
n
ab
o
u
t
s
tu
d
en
t
s
u
cc
ess
,
th
e
f
ig
u
r
e
also
d
is
p
lay
s
a
clea
r
a
n
d
co
m
p
r
eh
e
n
s
iv
e
p
r
esen
tatio
n
o
f
teac
h
in
g
m
ater
ials
.
Fig
u
r
e
3
h
elp
s
teac
h
er
s
m
o
n
ito
r
s
t
u
d
en
t
p
r
o
g
r
ess
an
d
p
r
o
v
id
e
r
elev
an
t c
o
m
m
en
ts
b
y
s
u
m
m
ar
izin
g
s
tu
d
e
n
ts
’
u
n
d
e
r
s
tan
d
in
g
o
f
th
e
less
o
n
m
ater
ial.
I
n
cr
ea
s
ed
m
ath
e
m
atica
l
p
r
o
b
lem
-
s
o
lv
in
g
a
b
ilit
ies
ca
n
b
e
ass
o
ciate
d
with
d
if
f
er
en
t
lear
n
in
g
ac
tiv
ities
an
d
e
n
v
ir
o
n
m
en
ts
i
n
th
e
B
L
-
UE
G
an
d
B
L
-
E
W
G
class
es.
Geo
Geb
r
a
So
f
twar
e
in
th
e
B
L
-
UE
G
class
p
r
o
v
id
es
s
tu
d
en
ts
with
a
m
o
r
e
ex
citin
g
an
d
co
m
p
r
eh
en
s
iv
e
lear
n
in
g
ex
p
er
ien
ce
,
r
esu
ltin
g
in
b
et
ter
p
r
o
b
lem
-
s
o
lv
i
n
g
s
k
ills
.
T
h
e
Geo
Geb
r
a
r
esear
c
h
s
tates
th
at
m
ath
em
atica
l
ab
ili
ties
ca
n
im
p
r
o
v
e
r
ea
s
o
n
i
n
g
an
d
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
[
3
0
]
.
On
th
e
o
th
e
r
h
an
d
,
lear
n
in
g
in
th
e
co
n
tr
o
l
cl
ass
u
s
es
s
o
m
eth
in
g
d
if
f
e
r
en
t
th
an
E
d
m
o
d
o
a
n
d
Geo
Geb
r
a,
wh
ich
lim
its
s
tu
d
e
n
ts
’
o
p
p
o
r
tu
n
ities
to
ex
p
l
o
r
e
t
h
eir
id
ea
s
an
d
r
esu
lts
in
m
o
r
e
r
ig
id
th
in
k
in
g
.
T
o
im
p
r
o
v
e
p
r
o
b
le
m
-
s
o
lv
in
g
s
k
ill
s
,
Pó
ly
a
[
4
]
s
u
g
g
ests
f
o
u
r
s
tep
s
: u
n
d
er
s
tan
d
in
g
th
e
p
r
o
b
lem
,
p
lan
n
in
g
s
o
lu
tio
n
s
,
im
p
lem
en
tin
g
p
lan
s
,
an
d
r
ef
l
ec
tin
g
.
T
ea
ch
er
s
,
c
o
lleag
u
es,
o
r
teac
h
in
g
m
ater
ials
ca
n
s
er
v
e
as
m
o
d
els
f
o
r
p
r
o
b
lem
-
s
o
lv
in
g
b
eh
a
v
io
r
.
T
h
e
u
s
e
o
f
attr
ac
tiv
e
an
d
m
o
tiv
a
tin
g
m
o
d
els,
s
u
ch
as
th
o
s
e
p
r
esen
ted
in
E
d
m
o
d
o
an
d
Geo
Geb
r
a,
ca
n
h
elp
s
tu
d
e
n
ts
f
o
cu
s
o
n
th
e
p
r
o
ce
s
s
o
f
lear
n
in
g
m
ath
em
atics.
B
y
o
b
s
er
v
in
g
th
e
b
eh
av
io
r
o
f
th
e
lear
n
in
g
p
r
o
ce
s
s
d
is
p
lay
e
d
d
u
r
in
g
th
e
p
r
o
b
lem
-
s
o
lv
in
g
p
r
o
ce
s
s
,
s
tu
d
e
n
ts
ca
n
ab
s
o
r
b
an
d
co
n
s
id
er
th
e
co
g
n
itiv
e
f
ac
to
r
s
th
at
p
lay
a
r
o
le
in
th
e
p
r
o
b
lem
-
s
o
lv
in
g
[
4
]
.
T
h
e
in
cr
ea
s
e
in
p
r
o
b
lem
-
s
o
lv
i
n
g
ab
ilit
ies
b
etwe
en
s
tu
d
en
ts
wh
o
s
tu
d
y
with
B
L
-
UE
G
an
d
B
L
-
E
W
G
is
s
ig
n
if
ican
tly
d
if
f
er
en
t,
as
s
h
o
wn
in
T
ab
le
8
.
BL
-
UE
G
p
r
o
v
es
to
b
e
m
o
r
e
ef
f
ec
tiv
e
in
en
h
an
cin
g
s
tu
d
en
ts
’
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
th
an
B
L
-
E
W
G.
T
h
ese
f
in
d
in
g
s
s
u
p
p
o
r
t
p
r
e
v
io
u
s
r
esear
ch
th
at
s
h
o
wed
t
h
e
ef
f
ec
tiv
en
ess
o
f
E
d
m
o
d
o
lear
n
in
g
i
n
th
e
b
le
n
d
ed
lear
n
in
g
f
ield
[
2
7
]
.
T
h
e
u
s
e
o
f
a
p
r
o
b
lem
-
b
ased
lear
n
in
g
m
o
d
el
with
B
L
-
UE
G
s
ig
n
if
i
ca
n
tly
im
p
r
o
v
es
p
r
o
b
lem
-
s
o
l
v
in
g
a
b
ilit
ies,
r
esu
ltin
g
in
g
o
o
d
f
ea
tu
r
es
f
o
r
th
e
av
er
ag
e
v
alu
e
o
f
p
r
o
b
lem
-
s
o
l
v
in
g
s
k
ills
,
co
n
s
is
ten
t
with
p
r
ev
io
u
s
r
esear
ch
f
ield
s
[
2
9
]
,
[
3
0
]
.
Alth
o
u
g
h
th
e
d
if
f
icu
lties
s
tu
d
en
ts
m
ay
en
c
o
u
n
ter
a
r
e
tied
to
r
eso
u
r
ce
s
an
d
o
th
e
r
cir
cu
m
s
tan
ce
s
,
th
is
r
esear
ch
p
o
s
itiv
ely
im
p
ac
ts
th
e
ad
v
an
ce
m
en
t o
f
lear
n
in
g
tech
n
o
lo
g
ies an
d
th
e
le
ar
n
in
g
e
n
v
ir
o
n
m
en
t f
o
r
s
tu
d
e
n
ts
[
2
5
]
.
T
h
e
2
1
s
t
ce
n
tu
r
y
’
s
lead
in
g
r
eso
u
r
ce
f
o
r
life
lo
n
g
lear
n
in
g
h
as
b
ee
n
r
ec
o
g
n
ized
as
th
e
b
len
d
ed
lear
n
in
g
a
p
p
r
o
ac
h
c
o
m
b
in
i
n
g
E
d
m
o
d
o
an
d
Geo
Geb
r
a.
Ho
w
ev
er
,
s
tu
d
e
n
t
p
s
y
ch
o
lo
g
ical
is
s
u
es
m
ig
h
t
im
p
e
d
e
lear
n
in
g
,
p
ar
ticu
la
r
ly
in
ter
m
s
o
f
r
ea
d
in
ess
f
o
r
lear
n
in
g
.
Geo
Geb
r
a
ca
n
ass
is
t
lectu
r
er
s
an
d
s
tu
d
en
ts
in
s
o
lv
in
g
m
ath
p
r
o
b
lem
s
m
o
r
e
q
u
ick
ly
s
o
th
at
s
tu
d
en
ts
ar
e
in
s
p
ir
ed
t
o
co
n
ce
n
t
r
ate
o
n
s
tu
d
y
in
g
i
n
th
ese
cir
cu
m
s
tan
ce
s
.
T
ea
ch
er
s
m
u
s
t
also
s
et
an
ex
ce
llen
t
ex
am
p
le
f
o
r
th
eir
s
tu
d
en
ts
an
d
u
s
e
v
ar
io
u
s
teac
h
in
g
tech
n
iq
u
es
to
k
ee
p
th
em
in
ter
ested
in
th
eir
less
o
n
s
.
Stu
d
en
ts
ca
n
s
tay
f
o
cu
s
ed
an
d
en
g
a
g
ed
b
y
u
s
in
g
ad
d
iti
o
n
al
r
eso
u
r
ce
s
an
d
ap
p
s
.
T
h
e
r
esu
lts
o
f
th
is
s
tu
d
y
h
av
e
co
n
s
eq
u
en
ce
s
f
o
r
lectu
r
er
s
wh
o
wan
t
to
en
c
o
u
r
a
g
e
s
tu
d
en
ts
to
s
o
lv
e
p
r
o
b
lem
s
as th
ey
lea
r
n
m
ath
e
m
atics.
4.
CO
NCLU
SI
O
N
T
h
e
r
esu
lts
s
h
o
wed
th
at
th
e
in
cr
ea
s
e
in
p
r
o
b
lem
-
s
o
lv
in
g
ab
il
ities
in
b
o
th
class
es
was
in
th
e
m
ed
iu
m
ca
teg
o
r
y
.
Pro
b
lem
-
b
ased
m
a
th
em
atics
lear
n
in
g
th
r
o
u
g
h
B
L
-
UE
G
an
d
B
L
-
E
W
G
s
ig
n
if
ican
tly
im
p
ac
te
d
s
tu
d
en
ts
’
p
r
o
b
lem
-
s
o
lv
in
g
ab
il
ities
.
Sp
ec
if
ically
,
th
e
B
L
-
UE
G
g
r
o
u
p
s
h
o
wed
s
ig
n
i
f
ican
tly
m
o
r
e
im
p
r
o
v
em
e
n
t
th
an
th
e
B
L
-
E
W
G
g
r
o
u
p
.
Ho
wev
er
,
th
is
r
esear
ch
o
n
ly
in
cl
u
d
ed
two
-
s
em
ester
u
n
iv
er
s
ity
in
B
an
ten
s
tu
d
en
ts
wh
o
to
o
k
ca
lcu
lu
s
co
u
r
s
es
o
n
v
o
lu
m
es
o
f
r
o
tatin
g
o
b
ject
s
.
Fu
r
th
er
r
esear
ch
is
r
eq
u
ir
e
d
to
ex
a
m
in
e
o
th
e
r
co
m
p
o
n
en
ts
o
f
m
ath
em
atica
l
ab
ilit
y
b
ec
au
s
e
th
is
s
tu
d
y
’
s
m
ea
s
u
r
in
g
o
f
m
at
h
em
atica
l
ap
titu
d
e
is
r
estricte
d
to
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
.
Ad
d
itio
n
ally
,
th
er
e
is
a
n
ee
d
f
o
r
f
u
r
th
er
ex
p
lo
r
atio
n
an
d
d
ev
el
o
p
m
en
t
o
f
alter
n
ativ
e
b
len
d
ed
lear
n
in
g
m
o
d
els to
a
d
d
r
ess
th
e
lim
itatio
n
s
id
en
tifie
d
in
th
is
s
tu
d
y
.
ACK
NO
WL
E
DG
E
M
E
NT
S
R
esear
ch
er
s
wo
u
ld
lik
e
to
th
an
k
all
p
ar
ties
wh
o
h
av
e
h
el
p
ed
.
R
esear
ch
er
s
also
th
an
k
Un
iv
er
s
itas
B
in
a
B
an
g
s
a
f
o
r
p
r
o
v
id
in
g
a
l
o
ca
tio
n
f
o
r
r
esear
c
h
er
s
to
co
llect
d
ata.
T
h
an
k
y
o
u
to
th
e
Dir
ec
to
r
ate
o
f
R
esear
ch
an
d
C
o
m
m
u
n
ity
Ser
v
ice
(
in
I
n
d
o
n
esia
n
ca
lled
:
Dir
ek
t
o
r
at
R
is
et
d
an
Pen
g
ab
d
ian
k
e
p
ad
a
Ma
s
y
ar
a
k
at
o
r
DR
T
PM
)
f
o
r
p
r
o
v
id
in
g
f
u
n
d
in
g
f
o
r
th
is
r
esear
c
h
.
Ma
s
ter
C
o
n
tr
ac
t
Nu
m
b
er
:
1
0
6
/E5
/
PG.0
2
.
0
0
.
PL/2
0
2
4
;
Der
iv
ativ
e
C
o
n
tr
ac
t N
u
m
b
e
r
:
0
4
9
/SP
2
H/R
T
-
MO
NO/L
L
4
/2
0
2
4
.
RE
F
E
R
E
NC
E
S
[
1
]
K
.
H
o
o
g
l
a
n
d
a
n
d
D
.
T
o
u
t
,
“
C
o
m
p
u
t
e
r
-
b
a
s
e
d
a
ssessm
e
n
t
o
f
mat
h
e
mat
i
c
s
i
n
t
o
t
h
e
t
w
e
n
t
y
-
f
i
r
s
t
c
e
n
t
u
r
y
:
p
r
e
ss
u
r
e
s
a
n
d
t
e
n
si
o
n
s,”
Z
D
M
,
v
o
l
.
5
0
,
n
o
.
4
,
p
p
.
6
7
5
–
6
8
6
,
A
u
g
.
2
0
1
8
,
d
o
i
:
1
0
.
1
0
0
7
/
s
1
1
8
5
8
-
0
1
8
-
0
9
4
4
-
2.
[
2
]
L.
I
.
G
o
n
z
á
l
e
z
-
P
é
r
e
z
a
n
d
M
.
S
.
R
a
m
í
r
e
z
-
M
o
n
t
o
y
a
,
“
C
o
mp
o
n
e
n
t
s
o
f
e
d
u
c
a
t
i
o
n
4
.
0
i
n
2
1
st
c
e
n
t
u
r
y
s
k
i
l
l
s
f
r
a
m
e
w
o
r
k
s
:
sy
s
t
e
m
a
t
i
c
r
e
v
i
e
w
,
”
S
u
s
t
a
i
n
a
b
i
l
i
t
y
,
v
o
l
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I
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20
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423
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432
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Evaluation Warning : The document was created with Spire.PDF for Python.