I
nte
rna
t
io
na
l J
o
urna
l o
f
E
v
a
lua
t
io
n a
nd
Resea
rc
h in E
du
ca
t
io
n (
I
J
E
RE
)
Vo
l.
13
,
No
.
6
,
Dec
em
b
er
2
0
2
4
,
p
p
.
3
7
6
3
~
3
7
7
4
I
SS
N:
2
2
5
2
-
8
8
2
2
,
DOI
: 1
0
.
1
1
5
9
1
/
ijer
e
.
v
13
i
6
.
2
9
5
8
0
3763
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
ere.
ia
esco
r
e.
co
m
Ass
ess
ing
studen
t
s
’
ma
thema
ti
ca
l r
ea
so
ning
in
pro
bl
em
-
ba
sed
lea
rning
:
a
gende
r perspec
tive
Nurul I
s
na
ini
Ro
m
a
dh
o
n,
M
o
ha
m
ma
d F
a
iza
l A
m
ir,
M
a
ha
rdik
a
Da
r
m
a
wa
n K
us
um
a
Wa
rda
na
D
e
p
a
r
t
me
n
t
o
f
P
r
i
mar
y
S
c
h
o
o
l
T
e
a
c
h
e
r
Ed
u
c
a
t
i
o
n
,
U
n
i
v
e
r
si
t
a
s
M
u
h
a
mm
a
d
i
y
a
h
S
i
d
o
a
r
j
o
,
S
i
d
o
a
r
j
o
,
I
n
d
o
n
e
si
a
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Dec
12
,
2
0
2
3
R
ev
is
ed
Ap
r
3
,
2
0
2
4
Acc
ep
ted
May
7
,
2
0
2
4
M
a
th
e
m
a
ti
c
a
l
re
a
so
n
in
g
(
M
R)
in
p
r
o
b
lem
-
so
l
v
in
g
is
sti
ll
re
lati
v
e
l
y
l
o
w,
b
u
t
stu
d
e
n
ts
n
e
e
d
it
.
P
re
v
i
o
u
s
stu
d
ie
s
h
a
v
e
s
h
o
wn
t
h
a
t
p
r
o
b
lem
-
b
a
se
d
lea
rn
i
n
g
(P
BL)
c
a
n
imp
ro
v
e
M
R.
M
e
a
n
w
h
il
e
,
d
iffere
n
c
e
s
in
M
R
a
re
a
lso
i
n
flu
e
n
c
e
d
b
y
g
e
n
d
e
r.
Th
is
stu
d
y
a
ss
e
ss
e
s
M
R
q
u
a
n
ti
tati
v
e
ly
a
n
d
q
u
a
li
tativ
e
ly
b
y
re
v
iew
in
g
g
e
n
d
e
r
d
iffere
n
c
e
s
wh
e
n
g
i
v
e
n
P
BL
i
n
terv
e
n
ti
o
n
.
Th
e
re
se
a
r
c
h
p
a
rti
c
ip
a
n
ts
i
n
v
o
lv
e
d
we
re
fift
h
-
g
ra
d
e
p
rima
ry
st
u
d
e
n
ts.
Th
e
sa
m
p
li
n
g
tec
h
n
iq
u
e
s
u
se
d
we
re
c
o
n
v
e
n
ien
c
e
a
n
d
p
u
rp
o
siv
e
sa
m
p
li
n
g
.
T
h
is
stu
d
y
d
e
sig
n
u
se
s
a
n
e
x
p
lan
a
to
r
y
se
q
u
e
n
ti
a
l
m
ix
e
d
m
e
th
o
d
with
q
u
a
n
ti
tativ
e
d
a
t
a
c
o
ll
e
c
ti
o
n
f
o
ll
o
we
d
b
y
q
u
a
li
tati
v
e
d
a
ta.
In
stru
m
e
n
ts
li
k
e
M
R
tes
ts,
in
terv
ie
w
g
u
i
d
e
s,
a
n
d
q
u
e
sti
o
n
n
a
ires
we
re
u
se
d
to
c
o
ll
e
c
t
d
a
ta.
A
n
a
ly
sis
t
e
c
h
n
iq
u
e
s
u
se
d
f
o
r
q
u
a
n
ti
tati
v
e
d
a
ta
a
re
d
e
sc
rip
ti
v
e
sta
ti
stics
,
n
-
g
a
in
,
a
n
d
Wi
lco
x
o
n
sig
n
e
d
-
ra
n
k
tes
t,
w
h
il
e
q
u
a
li
tati
v
e
d
a
ta
is
th
e
m
a
ti
c
a
n
a
ly
sis.
T
h
e
stu
d
y
f
o
u
n
d
th
a
t
q
u
a
n
ti
tativ
e
l
y
,
P
B
L
sig
n
ifi
c
a
n
tl
y
a
ffe
c
ts
th
e
M
R
o
f
st
u
d
e
n
ts
wit
h
d
iffere
n
t
g
e
n
d
e
r
p
e
rsp
e
c
ti
v
e
s.
M
e
a
n
wh
il
e
,
q
u
a
li
tati
v
e
fin
d
in
g
s
in
M
R
v
a
rie
d
a
m
o
n
g
st
u
d
e
n
ts
o
f
d
iffere
n
t
g
e
n
d
e
rs (m
a
sc
u
li
n
e
,
fe
m
in
in
e
,
a
n
d
n
e
u
tral)
in
t
h
e
imp
li
c
a
ti
o
n
o
f
P
BL.
An
o
th
e
r
fi
n
d
in
g
is
th
a
t
stu
d
e
n
ts’
M
R
is
in
a
d
e
q
u
a
te
in
g
e
n
e
ra
li
z
in
g
th
e
sta
tem
e
n
t.
Th
e
stu
d
y
re
su
lt
s
p
ro
v
id
e
c
o
m
p
re
h
e
n
siv
e
fin
d
i
n
g
s
re
g
a
rd
i
n
g
t
h
e
d
iffere
n
c
e
s
in
M
R
o
f
stu
d
e
n
ts
wi
th
g
e
n
d
e
r
d
i
ffe
re
n
c
e
s
in
th
e
imp
l
ica
ti
o
n
s
o
f
P
BL,
wh
i
c
h
c
a
n
c
o
n
tri
b
u
te
p
ra
c
ti
c
a
l,
th
e
o
re
ti
c
a
l,
o
r
m
e
th
o
d
o
lo
g
ica
l
to
tea
c
h
e
rs,
p
ra
c
ti
ti
o
n
e
rs,
re
se
a
rc
h
e
rs,
a
n
d
sc
h
o
lars
h
ip
.
K
ey
w
o
r
d
s
:
Gen
d
er
Ma
th
em
atica
l r
ea
s
o
n
in
g
Mix
ed
m
eth
o
d
Pro
b
lem
-
b
ased
lear
n
in
g
Pro
b
lem
-
s
o
lv
in
g
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Mo
h
am
m
ad
Faizal
Am
ir
Dep
ar
tm
en
t o
f
Prim
ar
y
Sch
o
o
l T
ea
ch
er
E
d
u
ca
tio
n
,
Facu
lty
o
f
Ps
y
ch
o
lo
g
y
an
d
E
d
u
ca
tio
n
Scien
ce
s
,
Un
iv
er
s
itas
Mu
h
am
m
ad
iy
ah
Sid
o
ar
jo
R
am
e
Pil
an
g
Stre
et
No
.
4
,
W
o
n
o
ay
u
,
Sid
o
ar
jo
,
E
ast J
av
a,
I
n
d
o
n
esia
E
m
ail: f
aiza
l.a
m
ir
@
u
m
s
id
a.
ac
.
id
1.
I
NT
RO
D
UCT
I
O
N
Ma
th
em
atica
l
r
ea
s
o
n
in
g
(
MR
)
is
k
n
o
w
n
as
lo
g
ical
th
in
k
in
g
i
n
p
r
o
b
lem
-
s
o
lv
i
n
g
th
at
ca
n
n
o
t
b
e
s
o
lv
e
d
d
ir
ec
tly
[
1
]
–
[
3
]
.
MR
ca
n
h
elp
b
eg
in
n
er
s
tu
d
en
ts
s
o
lv
e
p
r
o
b
le
m
s
[
4
]
.
Fro
m
th
e
co
m
p
eten
ce
ac
h
iev
em
en
t
p
o
in
t
o
f
v
iew,
im
p
r
o
v
in
g
MR
f
o
r
p
r
o
b
lem
-
s
o
lv
in
g
is
n
ee
d
ed
f
o
r
s
t
u
d
en
ts
to
ac
h
iev
e
ad
e
q
u
ate
lea
r
n
in
g
o
u
tc
o
m
es
in
lear
n
in
g
m
ath
e
m
atics
[
5
]
.
Ac
h
iev
in
g
MR
f
o
r
p
r
o
b
lem
-
s
o
lv
in
g
in
clu
d
es
o
v
er
co
m
in
g
ac
ti
v
e
in
ter
ac
tio
n
an
d
th
in
k
in
g
s
k
ills
in
lear
n
in
g
m
ath
em
atics
ac
tiv
ities
[
6
]
.
I
n
th
is
,
teac
h
er
s
m
u
s
t
d
ev
el
o
p
MR
at
th
e
p
r
im
ar
y
s
ch
o
o
l
lev
el.
T
h
is
is
b
ec
au
s
e
t
h
e
o
p
p
o
r
tu
n
ities
teac
h
er
s
g
iv
e
s
tu
d
en
ts
in
lea
r
n
in
g
ca
n
im
p
r
o
v
e
ea
r
l
y
f
o
r
th
e
d
ev
elo
p
m
e
n
t o
f
r
ea
s
o
n
in
g
in
p
r
o
b
lem
-
s
o
lv
in
g
[
4
]
.
T
h
e
Pro
g
r
am
f
o
r
I
n
te
r
n
atio
n
al
Stu
d
en
t
Ass
es
s
m
en
t
(
PISA
)
a
n
d
T
r
en
d
s
in
I
n
ter
n
atio
n
al
Ma
th
em
atics
an
d
Scien
ce
Stu
d
y
(
T
I
MSS
)
s
tu
d
ies
r
ev
ea
l
th
at
s
tu
d
en
ts
’
M
R
in
I
n
d
o
n
esia
is
s
till
r
elativ
ely
lo
w.
T
h
is
s
h
o
ws
th
at
r
ea
s
o
n
in
g
is
an
im
p
o
r
tan
t
th
in
g
th
at
n
ee
d
s
atten
tio
n
[
7
]
.
T
h
e
PISA
r
esu
lts
also
s
h
o
wed
th
at
s
tu
d
en
ts
’
MR
in
I
n
d
o
n
esia is st
i
ll r
elativ
ely
l
o
w.
T
h
is
is
in
d
icate
d
b
y
th
e
d
e
clin
e
in
th
e
m
ea
n
m
ath
em
atics sco
r
e
f
r
o
m
3
8
6
to
379
[
8
]
.
B
ased
o
n
th
e
T
I
MSS
in
2
0
1
5
,
s
tu
d
en
ts
’
MR
lev
el
was
r
an
k
ed
4
4
o
u
t
o
f
4
9
co
u
n
tr
ies
[
9
]
.
T
h
u
s
,
s
tu
d
en
t p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
th
at
r
eq
u
ir
e
MR c
an
also
b
e
tr
o
u
b
led
.
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
.
13
,
No
.
6
,
Dec
em
b
er
2
0
2
4
:
3
7
6
3
-
3
7
7
4
3764
Pre
v
io
u
s
r
esear
ch
er
s
h
av
e
s
h
o
wn
th
at
p
r
o
b
lem
-
b
ased
le
ar
n
in
g
(
PB
L
)
im
p
r
o
v
es
m
ath
em
atica
l
r
ea
s
o
n
in
g
s
k
ills
[
1
0
]
,
[
1
1
]
.
L
a
p
u
z
[
1
0
]
ar
g
u
e
d
th
at
th
r
o
u
g
h
PB
L
,
MR
ca
n
im
p
r
o
v
e
b
ec
au
s
e
s
tu
d
en
ts
ac
q
u
ir
e
k
n
o
wled
g
e
th
r
o
u
g
h
u
n
s
tr
u
ct
u
r
ed
s
o
lu
tio
n
s
.
PB
L
p
o
s
itiv
ely
im
p
r
o
v
es
MR
b
ec
au
s
e
it
s
o
lv
es
th
e
p
r
o
b
lem
-
s
o
lv
in
g
s
tr
ateg
ies
teac
h
er
s
en
co
u
n
ter
in
lear
n
in
g
[
1
1
]
.
B
ased
o
n
t
h
e
s
tu
d
y
’
s
r
esu
lts
,
MR
ca
n
b
e
en
h
an
ce
d
b
y
im
p
licatio
n
PB
L
[
1
2
]
,
[
1
3
]
.
I
n
ad
d
itio
n
,
PB
L
is
a
lear
n
in
g
th
at
r
eq
u
i
r
es
s
tu
d
en
ts
to
th
in
k
at
a
h
ig
h
er
lev
e
l
th
r
o
u
g
h
MR
[
1
4
]
,
[
1
5
]
.
T
h
er
ef
o
r
e,
PB
L
ca
n
b
e
u
s
ed
as a
lear
n
in
g
s
o
lu
tio
n
to
co
r
r
ec
t stu
d
en
ts
'
in
ad
eq
u
ate
MR.
Pro
b
lem
-
b
ased
lear
n
in
g
is
n
o
t
alwa
y
s
a
s
u
f
f
icien
t
s
o
lu
tio
n
to
im
p
r
o
v
e
s
tu
d
en
ts
’
MR
co
m
p
r
eh
e
n
s
iv
ely
.
T
h
er
e
is
a
n
o
p
in
i
o
n
th
at
g
en
d
er
p
e
r
s
p
ec
tiv
e
is
v
ital
in
MR
[
1
6
]
.
Gen
d
er
is
a
s
o
cial
co
n
s
tr
u
ctio
n
th
at
d
if
f
e
r
en
tiates
th
e
p
s
y
ch
ic
f
u
n
ctio
n
s
o
f
m
e
n
an
d
wo
m
en
i
n
ter
m
s
o
f
attitu
d
es,
em
o
tio
n
s
,
an
d
s
o
cial
ac
tio
n
s
th
at
d
ev
elo
p
in
s
o
ciety
[
1
7
]
,
[
1
8
]
.
I
n
te
r
n
al
f
ac
to
r
s
af
f
ec
t
th
e
r
ea
s
o
n
in
g
p
r
o
c
ess
,
n
am
ely
g
en
d
er
d
if
f
er
en
ce
s
th
at
ca
u
s
e
d
if
f
e
r
e
n
ce
s
in
r
ea
s
o
n
in
g
ab
ilit
y
a
n
d
lear
n
in
g
r
esu
lts
[
1
9
]
.
T
h
e
a
n
a
ly
s
is
o
f
MR
f
r
o
m
a
g
en
d
er
p
er
s
p
ec
tiv
e
is
co
n
s
id
er
ed
ess
en
tial
b
ec
au
s
e
th
e
I
n
d
o
n
esian
g
o
v
er
n
m
en
t
s
ets
g
en
d
er
is
s
u
es
in
th
e
s
u
s
tain
ab
le
d
ev
elo
p
m
en
t
p
r
o
g
r
am
in
ed
u
ca
tio
n
,
esp
ec
ially
i
n
m
ath
em
atics,
s
o
th
at
it
ca
n
im
p
r
o
v
e
r
ea
s
o
n
in
g
s
k
ills
an
d
im
p
r
o
v
e
s
tu
d
en
t
lea
r
n
in
g
r
esu
lts
[
2
0
]
,
[
2
1
]
.
T
h
u
s
,
a
g
en
d
er
p
er
s
p
ec
tiv
e
is
n
ee
d
e
d
in
th
e
im
p
licatio
n
o
f
PB
L
to
ass
ess
s
tu
d
en
ts
’
MR b
etter
.
I
n
th
e
last
f
ew
p
er
io
d
s
,
th
e
a
v
ailab
le
s
tu
d
ies
s
till
d
i
s
cu
s
s
MR
b
y
r
ev
iewin
g
g
en
d
er
p
er
s
p
ec
tiv
e
b
u
t
h
av
e
n
o
t
ass
ess
ed
it
co
n
ce
r
n
i
n
g
PB
L
im
p
lem
en
tatio
n
.
Sev
er
al
r
esear
ch
er
s
s
tated
t
h
at
g
e
n
d
er
d
if
f
er
e
n
ce
s
in
m
en
an
d
wo
m
e
n
s
ig
n
if
ican
tl
y
af
f
ec
t
s
tu
d
en
ts
’
MR.
T
h
es
e
g
en
d
e
r
d
i
f
f
er
en
ce
s
m
ay
o
c
cu
r
in
asp
ec
ts
th
at
in
clu
d
e
m
ascu
lin
e,
f
e
m
in
in
e
,
n
eu
tr
al,
a
n
d
an
d
r
o
g
y
n
o
u
s
[
2
2
]
,
[
2
3
]
.
L
ey
v
a
[
2
4
]
s
u
g
g
ested
th
at
m
o
r
e
ex
p
lo
r
atio
n
is
n
ee
d
ed
r
e
g
ar
d
i
n
g
m
ascu
lin
e
g
e
n
d
er
in
s
tu
d
en
ts
'
m
ath
em
atica
l
ac
h
iev
em
en
t.
I
n
co
m
p
ar
is
o
n
,
Py
f
er
[
2
5
]
co
n
f
ir
m
ed
th
at
f
e
m
in
in
e
-
g
en
d
er
ed
s
tu
d
en
ts
ca
n
u
s
e
i
n
s
tr
u
m
en
tal
an
d
r
elati
o
n
al
u
n
d
er
s
tan
d
i
n
g
th
r
o
u
g
h
r
ec
o
g
n
izin
g
,
f
o
r
m
in
g
,
an
d
co
n
f
ir
m
in
g
co
n
jectu
r
es
o
n
a
p
r
o
b
lem
.
I
n
s
tr
u
m
en
tal
u
n
d
er
s
tan
d
in
g
is
d
o
n
e
b
y
m
e
m
o
r
izin
g
m
ath
e
m
atica
l
r
u
les
an
d
alg
o
r
ith
m
s
with
o
u
t
u
n
d
er
s
tan
d
i
n
g
t
h
eir
r
ea
s
o
n
s
.
I
n
co
n
tr
ast,
r
elatio
n
al
u
n
d
er
s
tan
d
i
n
g
is
d
o
n
e
b
y
u
n
d
er
s
tan
d
i
n
g
th
e
p
r
o
b
lem
an
d
im
p
lem
e
n
tin
g
p
r
o
b
lem
-
s
o
lv
in
g
s
tr
ateg
ies
ap
p
r
o
p
r
iately
an
d
co
n
s
tr
u
ctiv
e
ly
.
R
esear
ch
o
n
ass
ess
in
g
s
tu
d
en
ts
’
MR
in
th
e
im
p
licatio
n
o
f
PB
L
b
y
r
ev
iewin
g
g
e
n
d
er
d
if
f
er
en
ce
s
b
ased
o
n
its
asp
ec
ts
is
s
till
u
n
av
ailab
le.
Me
an
wh
ile,
Sm
it
et
a
l.
[
2
6
]
em
p
h
asize
d
th
e
im
p
o
r
tan
ce
o
f
ass
ess
in
g
MR
b
ased
o
n
o
u
tco
m
es
an
d
p
r
o
ce
s
s
es.
Ho
wev
er
,
PB
L
ca
n
im
p
r
o
v
e
s
tu
d
en
ts
'
MR
p
r
o
d
u
ctiv
ely
[
1
0
]
,
[
1
1
]
.
C
o
n
s
tr
u
ctin
g
lear
n
i
n
g
p
r
o
ce
s
s
es
th
at
co
n
s
id
er
d
if
f
er
en
t
g
en
d
er
p
e
r
s
p
ec
tiv
es
ca
n
also
r
esu
lt
in
d
if
f
er
en
t
MRs
[
2
7
]
.
L
ea
r
n
in
g
in
v
o
lv
in
g
m
en
an
d
wo
m
en
in
s
ch
o
o
ls
is
ex
p
e
cted
to
av
o
id
g
en
d
er
g
a
p
s
o
r
b
iases
[
2
8
]
.
T
h
is
led
u
s
to
ass
ess
th
e
in
cr
ea
s
e
o
r
d
ec
r
ea
s
e
o
f
s
tu
d
en
ts
'
MR
to
war
d
s
PB
L
im
p
lem
en
tatio
n
as
a
p
r
o
d
u
ct
an
d
to
ass
ess
s
tu
d
en
ts
'
M
R
in
ter
m
s
o
f
d
if
f
e
r
en
t
g
en
d
er
p
e
r
s
p
ec
tiv
es
as
a
p
r
o
ce
s
s
af
ter
PB
L
im
p
lem
en
ta
tio
n
.
T
h
er
e
f
o
r
e,
th
e
q
u
esti
o
n
s
o
f
th
is
s
tu
d
y
lea
d
to
two
th
in
g
s
:
i)
is
th
er
e
a
s
ig
n
i
f
ican
t
ef
f
ec
t
o
r
d
if
f
er
e
n
ce
in
s
tu
d
en
ts
'
MR
b
ef
o
r
e
an
d
a
f
ter
PB
L
im
p
lem
en
tatio
n
?
;
an
d
ii)
h
o
w
is
s
tu
d
en
ts
'
MR
d
escr
ip
tiv
ely
v
iewe
d
f
r
o
m
d
if
f
er
en
t
g
en
d
er
p
er
s
p
ec
tiv
es
af
ter
PB
L
im
p
l
em
en
tatio
n
?
T
h
e
r
esear
c
h
r
e
s
u
lts
th
r
o
u
g
h
th
ese
two
r
esear
ch
q
u
esti
o
n
s
ar
e
ex
p
ec
ted
to
p
r
o
v
id
e
p
r
ac
tical
b
en
ef
its
f
o
r
e
d
u
ca
to
r
s
:
p
r
o
v
id
e
ev
i
d
en
ce
an
d
em
p
ir
ical
way
s
th
at
PB
L
im
p
lem
en
tatio
n
ca
n
i
n
cr
ea
s
e
o
r
im
p
r
o
v
e
th
e
MR
o
f
p
r
o
b
lem
atic
s
tu
d
en
ts
.
I
n
a
d
d
itio
n
,
it
o
f
f
er
s
v
alu
ab
l
e
in
f
o
r
m
atio
n
f
o
r
p
o
licy
m
ak
er
s
to
p
ay
atten
tio
n
t
o
g
e
n
d
er
d
if
f
er
en
ce
s
co
n
ce
r
n
i
n
g
ef
f
o
r
t
s
to
im
p
r
o
v
e
MR,
esp
ec
ially
th
r
o
u
g
h
th
e
im
p
lem
en
tatio
n
o
f
PB
L
,
s
o
th
at
d
if
f
er
en
ce
s
in
g
e
n
d
er
p
er
s
p
ec
tiv
e
a
r
e
n
o
l
o
n
g
e
r
s
ee
n
as
a
b
iased
r
ev
iew
o
f
lear
n
in
g
.
2.
M
E
T
H
O
D
T
h
is
s
tu
d
y
u
s
es
an
e
x
p
lan
ato
r
y
s
eq
u
en
tial
with
a
m
ix
ed
-
m
eth
o
d
ap
p
r
o
ac
h
.
E
x
p
lan
ato
r
y
s
e
q
u
en
tial
is
a
m
eth
o
d
th
at
s
tar
ts
b
y
c
o
llectin
g
q
u
a
n
titativ
e
d
ata
an
d
th
en
co
n
tin
u
es
with
q
u
alitativ
e
d
ata
to
s
u
p
p
o
r
t
th
e
d
ata
p
r
o
ce
s
s
in
g
p
r
o
ce
s
s
s
o
th
at
th
e
s
tu
d
y
r
esu
lts
ca
n
p
r
o
v
id
e
a
co
m
p
r
eh
en
s
iv
e
d
escr
ip
tio
n
.
I
n
th
is
,
a
o
n
e
-
class
ex
p
er
im
en
tal
d
esig
n
was
u
s
ed
to
o
b
tain
q
u
a
n
titativ
e
d
ata,
f
o
llo
wed
b
y
a
n
ar
r
ativ
e
d
esig
n
t
o
o
b
tain
q
u
alitativ
e
d
ata
[
2
9
]
,
[
3
0
]
.
A
o
n
e
-
class
ex
p
er
im
en
tal
d
esig
n
was
co
n
d
u
cted
b
y
im
p
lem
en
tin
g
PB
L
in
o
n
e
e
x
p
er
im
e
n
tal
class
with
o
u
t
a
co
n
tr
o
l
g
r
o
u
p
s
o
th
at
th
e
ef
f
ec
t
o
r
s
ig
n
if
ic
an
ce
o
f
d
if
f
er
en
ce
s
i
n
PB
L
i
m
p
lem
en
tatio
n
o
n
s
tu
d
en
ts
'
M
R
co
u
ld
b
e
d
eter
m
in
ed
.
MR
was
ass
e
s
s
ed
q
u
an
titativ
ely
b
ef
o
r
e
a
n
d
af
ter
PB
L
im
p
lem
en
tatio
n
.
Me
an
wh
ile,
th
e
n
ar
r
ativ
e
d
esi
g
n
was
co
n
d
u
cted
a
f
ter
PB
L
im
p
lem
en
tatio
n
b
y
ass
ess
in
g
MR
d
escr
ip
tiv
ely
o
n
s
tu
d
en
ts
with
d
if
f
er
en
t
g
en
d
e
r
p
er
s
p
ec
tiv
es.
T
h
is
s
tu
d
y
im
p
lem
en
ted
PB
L
u
s
in
g
f
iv
e
s
tep
s
ad
ap
ted
f
r
o
m
Ar
en
d
s
[
1
4
]
,
in
clu
d
in
g
:
i
)
Or
ien
t
s
tu
d
en
ts
to
th
e
p
r
o
b
lem
.
I
n
th
i
s
s
tep
,
th
e
teac
h
er
co
n
v
ey
s
lea
r
n
in
g
o
b
jectiv
es,
m
o
tiv
ates
s
tu
d
en
ts
to
lear
n
,
a
n
d
p
r
esen
ts
au
th
en
tic
p
r
o
b
lem
s
i
n
th
e
class
r
o
o
m
;
ii)
Or
g
an
ize
s
tu
d
en
ts
f
o
r
s
tu
d
y
,
th
e
teac
h
er
o
r
g
a
n
izes
s
tu
d
en
ts
in
to
s
m
all
g
r
o
u
p
s
to
h
av
e
a
m
o
r
e
f
o
cu
s
ed
d
is
cu
s
s
io
n
to
s
o
lv
e
th
e
p
r
o
b
lem
.
I
n
th
is
s
tep
,
ea
ch
g
r
o
u
p
co
n
s
is
ts
o
f
3
-
4
s
tu
d
e
n
ts
;
iii)
Ass
is
t
in
d
ep
en
d
en
t
an
d
g
r
o
u
p
i
n
v
esti
g
atio
n
,
th
e
teac
h
er
f
ac
ilit
ates
in
d
iv
id
u
al
lear
n
in
g
t
o
u
n
d
er
s
tan
d
t
h
e
p
r
o
b
lem
s
o
th
a
t stu
d
en
ts
ca
n
h
av
e
alter
n
ativ
e
p
r
o
b
lem
s
o
lu
tio
n
s
.
Fu
r
th
er
m
o
r
e,
s
tu
d
en
ts
in
ea
ch
g
r
o
u
p
ar
e
ask
ed
to
d
is
cu
s
s
th
e
m
o
s
t
ap
p
r
o
p
r
iate
alter
n
ativ
e
p
r
o
b
lem
s
o
lu
tio
n
s
with
ea
c
h
o
th
er
;
iv
)
Dev
elo
p
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
A
s
s
es
s
in
g
s
tu
d
en
ts
’
ma
th
ema
tica
l rea
s
o
n
in
g
in
p
r
o
b
lem
-
b
a
s
ed
lea
r
n
in
g
…
(
N
u
r
u
l I
s
n
a
in
i R
o
ma
d
h
o
n
)
3765
an
d
p
r
esen
t
ar
tifa
cts
an
d
ex
h
ib
its
.
E
ac
h
g
r
o
u
p
is
m
o
tiv
ate
d
an
d
en
c
o
u
r
ag
e
d
to
p
r
esen
t
th
e
b
est
p
r
o
b
lem
-
s
o
lv
in
g
r
esu
lts
to
th
e
class
i
n
th
is
s
tep
.
Stu
d
en
ts
in
ea
ch
g
r
o
u
p
tak
e
tu
r
n
s
p
r
esen
tin
g
th
e
b
est
-
p
r
o
p
o
s
ed
p
r
o
b
lem
-
s
o
lv
in
g
s
tr
ateg
y
an
d
s
eq
u
en
ce
o
f
s
tep
s
;
v
)
An
aly
ze
an
d
ev
alu
ate
th
e
p
r
o
b
lem
-
s
o
lv
in
g
p
r
o
ce
s
s
.
I
n
th
is
s
tep
,
s
tu
d
en
ts
f
r
o
m
n
o
n
-
p
r
esen
tin
g
g
r
o
u
p
s
ar
e
g
u
id
ed
to
b
e
ab
le
to
cr
iticize
an
d
d
is
cu
s
s
th
e
wo
r
k
o
f
th
e
g
r
o
u
p
th
at
h
as b
ee
n
p
r
esen
ted
.
T
h
e
s
tu
d
y
p
a
r
ticip
an
ts
wer
e
2
1
f
if
th
-
g
r
ad
e
p
r
im
ar
y
s
ch
o
o
l
s
tu
d
en
ts
at
Sek
o
lah
Da
s
ar
Neg
er
i
B
u
lu
k
an
d
an
g
1
Prig
en
,
E
ast
J
av
a,
I
n
d
o
n
esia.
I
n
th
is
s
tu
d
y
,
s
am
p
lin
g
was
co
n
d
u
cted
t
h
r
o
u
g
h
two
tech
n
iq
u
es,
n
am
ely
,
c
o
n
v
e
n
ien
ce
a
n
d
p
u
r
p
o
s
iv
e
s
am
p
lin
g
.
C
o
n
v
en
ie
n
ce
s
am
p
lin
g
was
u
s
ed
to
o
b
tain
q
u
an
titativ
e
d
ata
o
n
s
tu
d
en
ts
'
M
R
with
g
en
d
er
d
if
f
er
en
ce
s
in
PB
L
im
p
lem
en
tatio
n
.
C
o
n
v
en
ien
ce
s
am
p
lin
g
was
co
n
s
id
er
ed
b
ec
au
s
e
th
is
s
tu
d
y
em
p
h
asizes
th
e
e
x
is
ten
ce
o
f
g
en
d
er
ch
ar
a
cter
is
tics
to
ass
es
s
s
tu
d
en
ts
'
M
R
.
I
n
a
d
d
itio
n
,
th
is
s
tu
d
y
was
co
n
d
u
cte
d
n
o
t
t
o
g
e
n
er
alize
th
e
f
in
d
in
g
s
b
u
t
t
o
d
e
s
cr
ib
e
o
r
ass
ess
s
tu
d
en
ts
'
MR
in
a
s
m
all
g
r
o
u
p
o
f
s
tu
d
ies.
T
h
e
r
esu
lts
o
f
th
e
g
e
n
d
er
p
r
esen
ce
s
tu
d
y
an
aly
s
is
r
esu
lted
in
f
o
u
r
m
ascu
lin
e,
n
i
n
e
f
em
i
n
in
e,
eig
h
t
n
eu
tr
al,
an
d
n
o
a
n
d
r
o
g
y
n
o
u
s
.
I
n
o
th
er
w
o
r
d
s
,
th
er
e
wer
e
th
r
ee
o
f
th
e
f
o
u
r
s
u
p
p
o
s
ed
g
e
n
d
e
r
ca
teg
o
r
ies
am
o
n
g
all
p
ar
ticip
an
ts
.
T
h
u
s
,
th
e
ex
is
ten
ce
o
f
t
h
r
ee
o
u
t
o
f
f
o
u
r
g
en
d
er
ca
teg
o
r
ies
was
d
ee
m
ed
s
u
f
f
icien
t
to
c
o
n
d
u
ct
a
s
tu
d
y
o
n
g
en
d
e
r
p
er
s
p
ec
tiv
e
i
n
v
o
lv
in
g
2
1
p
ar
ticip
a
n
ts
.
Me
an
wh
ile,
p
u
r
p
o
s
iv
e
s
am
p
lin
g
was
u
s
ed
to
o
b
tain
d
escr
ip
tiv
e
q
u
alitativ
e
d
ata
ab
o
u
t
MR
s
tu
d
en
ts
b
y
r
ev
iewin
g
d
if
f
er
en
ce
s
in
g
en
d
er
ca
teg
o
r
ies
af
ter
PB
L
wa
s
ap
p
lied
.
On
e
s
tu
d
e
n
t
ea
ch
wa
s
tak
en
r
an
d
o
m
ly
to
r
ep
r
esen
t
s
tu
d
en
ts
'
M
R
in
th
e
m
ascu
lin
e
(
MS)
,
f
em
in
i
n
e
(
FS
)
,
an
d
n
e
u
tr
al
(
NS)
ca
teg
o
r
ies,
r
esu
ltin
g
in
o
n
e
s
u
b
ject
in
th
e
MS,
FS
,
a
n
d
NS
ca
teg
o
r
ies.
A
s
am
p
le
s
ize
o
f
less
th
an
3
0
is
s
u
f
f
icien
t
f
o
r
o
n
e
ex
p
er
im
en
tal
class
[
3
1
]
.
I
n
ad
d
itio
n
,
co
n
v
en
ien
ce
s
am
p
lin
g
is
em
p
h
asized
n
o
t
to
g
en
er
alize
th
e
f
i
n
d
in
g
s
b
u
t
to
d
escr
ib
e
o
r
ass
ess
MR
s
tu
d
en
ts
in
a
s
m
all
r
esear
ch
g
r
o
u
p
.
Me
an
wh
ile,
p
u
r
p
o
s
iv
e
s
am
p
lin
g
aim
s
to
f
i
n
d
in
d
i
v
id
u
als o
r
a
g
r
o
u
p
o
f
in
d
iv
id
u
als wh
o
r
e
p
r
esen
t sp
ec
if
ic
ch
ar
ac
ter
is
tics
.
T
h
e
r
esear
ch
in
s
tr
u
m
en
ts
co
n
s
is
ted
o
f
MR
test
s
,
in
ter
v
iew
g
u
id
es,
an
d
g
e
n
d
er
q
u
esti
o
n
n
air
es.
MR
test
h
as
f
o
u
r
ess
ay
q
u
esti
o
n
s
b
ased
o
n
MR
ac
tiv
ities
,
ea
ch
w
ith
an
in
d
icato
r
f
o
r
f
in
d
in
g
a
r
elatio
n
s
h
ip
p
atter
n
,
p
r
o
p
o
s
in
g
a
co
n
ject
u
r
e,
v
e
r
if
y
in
g
th
e
s
tatem
en
t'
s
tr
u
th
,
an
d
g
en
er
alizin
g
th
e
s
tatem
en
t
[
1
6
]
,
a
s
p
r
esen
te
d
in
T
ab
le
1
.
I
n
ter
v
iew
g
u
id
es
co
n
tain
s
em
i
-
s
tr
u
ctu
r
ed
q
u
esti
o
n
s
ab
o
u
t
th
e
d
e
p
th
o
f
p
r
o
b
lem
-
s
o
lv
in
g
in
ea
ch
MR
ac
tiv
ity
,
n
am
ely
u
n
d
e
r
s
tan
d
in
g
th
e
p
r
o
b
lem
,
p
la
n
n
in
g
th
e
s
o
lu
tio
n
,
ca
r
r
y
in
g
o
u
t
th
e
s
o
lu
tio
n
,
an
d
ch
ec
k
in
g
b
ac
k
[
4
]
.
T
h
e
g
e
n
d
er
q
u
esti
o
n
n
air
e
h
as
3
0
item
s
o
f
th
e
B
e
m
Sex
R
o
les
I
n
v
en
to
r
y
(
B
SR
I
)
,
wh
ich
is
ad
ap
ted
f
r
o
m
Geld
en
h
u
y
s
an
d
B
o
s
ch
[
3
2
]
.
T
h
e
ad
ap
tatio
n
was
m
ad
e
b
y
ch
an
g
in
g
th
e
item
s
th
at
wer
e
p
r
ev
io
u
s
ly
in
E
n
g
lis
h
to
I
n
d
o
n
esian
.
E
ac
h
o
f
th
e
1
0
item
s
r
ep
r
esen
ts
m
ascu
lin
e,
f
em
in
in
e
,
an
d
n
eu
tr
al
g
en
d
er
d
im
en
s
io
n
s
.
T
h
e
an
d
r
o
g
y
n
o
u
s
d
im
e
n
s
io
n
o
cc
u
r
s
wh
en
th
e
m
ea
n
m
ascu
lin
e
an
d
f
em
in
i
n
e
s
co
r
es a
r
e
eq
u
al
o
r
b
alan
ce
d
.
T
h
e
g
en
d
er
d
im
en
s
io
n
s
ar
e
s
h
o
wn
in
T
ab
le
2
.
T
ab
le
1
.
Ma
th
em
atica
l r
ea
s
o
n
in
g
test
I
n
d
i
c
a
t
o
r
s
P
r
o
b
l
e
ms
F
i
n
d
i
n
g
a
r
e
l
a
t
i
o
n
s
h
i
p
p
a
t
t
e
r
n
B
a
se
d
o
n
t
h
e
f
i
g
u
r
e
s
b
e
l
o
w
.
D
e
t
e
r
mi
n
e
t
h
e
si
z
e
o
f
t
h
e
s
q
u
a
r
e
a
n
d
i
t
s
p
e
r
i
m
e
t
e
r
i
n
F
i
g
u
r
e
(
5
)
!
F
i
g
u
r
e
(
1
)
F
i
g
u
r
e
(
2
)
F
i
g
u
r
e
(
3
)
F
i
g
u
r
e
(
4
)
P
r
o
p
o
si
n
g
a
c
o
n
j
e
c
t
u
r
e
M
r
s.
Y
a
n
t
i
h
a
s a
r
e
c
t
a
n
g
l
e
-
s
h
a
p
e
d
l
a
n
d
m
e
a
s
u
r
i
n
g
1
0
m
×
8
m.
Th
e
l
a
n
d
w
i
l
l
b
e
p
l
a
n
t
e
d
w
i
t
h
2
0
m²
o
f
sp
i
n
a
c
h
a
n
d
3
0
m²
o
f
k
a
l
e
.
I
s t
h
e
r
e
a
n
y
l
a
n
d
l
e
f
t
t
o
p
l
a
n
t
c
o
r
n
?
H
o
w
m
u
c
h
l
a
n
d
i
s
l
e
f
t
?
V
e
r
i
f
y
i
n
g
t
h
e
t
r
u
t
h
o
f
t
h
e
s
t
a
t
e
me
n
t
M
r
.
A
n
t
o
n
:
M
o
m,
i
s
t
h
i
s s
q
u
a
r
e
-
s
h
a
p
e
d
c
l
o
t
h
f
o
r
sa
l
e
?
M
s.
I
n
d
a
h
:
Y
e
s,
t
h
i
s
c
l
o
t
h
i
s f
o
r
sa
l
e
,
si
r
.
M
r
.
A
n
t
o
n
:
W
h
a
t
s
i
z
e
i
s
t
h
e
c
l
o
t
h
,
M
o
m?
M
s.
I
n
d
a
h
:
M
e
a
s
u
r
e
s
2
m
×
2
m.
T
h
e
c
l
o
t
h
p
r
i
c
e
p
e
r
m²
i
s
R
p
.
1
2
,
0
0
0
.
M
r
.
A
n
t
o
n
:
S
o
,
t
h
e
mo
n
e
y
t
h
a
t
I
h
a
v
e
t
o
p
a
y
i
s
R
p
.
4
8
,
0
0
0
.
B
a
se
d
o
n
t
h
e
d
i
a
l
o
g
,
t
r
y
t
o
p
r
o
v
e
w
h
e
t
h
e
r
M
r
.
A
n
t
o
n
’
s st
a
t
e
me
n
t
i
s
t
r
u
e
.
M
r
.
A
n
t
o
n
h
a
d
t
o
p
a
y
a
t
o
t
a
l
o
f
R
p
.
4
8
,
0
0
0
.
G
e
n
e
r
a
l
i
z
i
n
g
t
h
e
st
a
t
e
me
n
t
U
n
k
n
o
w
n
:
A
r
e
a
o
f
r
i
g
h
t
t
r
i
a
n
g
l
e
=
8
4
m²
Th
e
b
a
se
o
f
t
h
e
r
i
g
h
t
t
r
i
a
n
g
l
e
=
7
m
A
sk
:
W
h
a
t
i
s
t
h
e
h
e
i
g
h
t
o
f
t
h
e
r
i
g
h
t
t
r
i
a
n
g
l
e
?
Ex
p
l
a
i
n
h
o
w
y
o
u
f
o
u
n
d
t
h
e
h
e
i
g
h
t
o
f
t
h
e
r
i
g
h
t
t
r
i
a
n
g
l
e
!
1
6
c
m
8
c
m
4
c
m
2
c
m
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
.
13
,
No
.
6
,
Dec
em
b
er
2
0
2
4
:
3
7
6
3
-
3
7
7
4
3766
I
n
d
ata
co
llectio
n
,
th
er
e
ar
e
t
wo
tech
n
iq
u
es:
test
an
d
non
-
t
est.
T
est
tech
n
iq
u
es
ar
e
ca
r
r
i
ed
o
u
t
b
y
ad
m
in
is
ter
in
g
MR
test
s
p
r
esen
ted
in
p
r
etest
an
d
p
o
s
ttes
t.
T
h
e
MR
te
s
t
i
s
u
s
ed
to
co
llect
s
t
u
d
en
ts
'
q
u
an
titativ
e
MR
d
ata.
T
h
e
f
in
al
r
esu
lts
r
eg
ar
d
in
g
MR
wer
e
ass
ess
ed
u
s
in
g
th
e
MR
ass
es
s
m
en
t
r
u
b
r
ic
wh
ich
h
as
a
L
ik
er
t
s
ca
le
o
f
0
-
4
[
1
6
]
,
as
s
h
o
wn
in
T
ab
le
3
.
Me
an
wh
ile,
n
o
n
-
t
est
tech
n
iq
u
es
wer
e
co
n
d
u
cted
b
y
ad
m
in
is
ter
in
g
q
u
esti
o
n
n
air
es
an
d
in
ter
v
iews.
T
h
e
q
u
esti
o
n
n
air
e
was
u
s
ed
to
co
llect
q
u
a
n
titativ
e
d
ata
o
n
s
tu
d
en
ts
'
g
en
d
er
ca
teg
o
r
ies
o
b
tain
e
d
b
ef
o
r
e
t
h
e
im
p
lem
e
n
tatio
n
o
f
PB
L
.
I
n
th
is
,
g
e
n
d
er
is
ca
teg
o
r
i
ze
d
in
to
m
ascu
lin
e,
f
em
in
in
e,
n
eu
tr
al,
o
r
an
d
r
o
g
y
n
o
u
s
o
n
a
s
ca
le
o
f
1
-
7
,
n
am
ely
,
1
(
n
ev
er
tr
u
e)
,
2
(
u
s
u
ally
n
o
t
t
r
u
e)
,
3
(
s
o
m
etim
es
tr
u
e)
,
4
(
o
cc
asio
n
ally
tr
u
e)
,
5
(
o
f
ten
tr
u
e)
,
6
(
u
s
u
ally
tr
u
e)
,
an
d
7
(
alwa
y
s
tr
u
e)
.
I
n
ter
v
i
ews
wer
e
u
s
ed
to
co
llect
q
u
alitativ
e
d
ata
r
e
g
ar
d
in
g
th
e
d
ep
th
o
f
MR
in
a
d
escr
ip
tiv
e
m
an
n
er
.
I
n
th
is
ca
s
e,
th
e
in
ter
v
iew
was
co
n
d
u
cte
d
af
ter
o
b
tain
in
g
s
tu
d
en
ts
'
M
R
d
ata
as th
e
o
u
tp
u
t o
f
PB
L
im
p
lem
en
tatio
n
.
T
ab
le
2
.
Gen
d
er
id
e
n
tity
b
y
3
0
item
B
em
Sex
R
o
les I
n
v
en
to
r
y
(
B
SR
I
)
M
a
s
c
u
l
i
n
e
F
e
mi
n
i
n
e
N
e
u
t
r
a
l
A
sserti
v
e
U
n
d
e
r
st
a
n
d
i
n
g
C
o
n
sc
i
e
n
t
i
o
u
s
n
e
ss
Le
a
d
e
r
s
h
i
p
a
b
i
l
i
t
y
S
y
mp
a
t
h
e
t
i
c
M
o
o
d
y
D
o
mi
n
a
n
t
Ea
g
e
r
t
o
s
o
o
t
h
e
h
u
r
t
f
e
e
l
i
n
g
s
R
e
l
i
a
b
l
e
S
t
r
o
n
g
p
e
r
so
n
a
l
i
t
y
S
e
n
s
i
t
i
v
e
t
o
t
h
e
n
e
e
d
s
o
f
o
t
h
e
r
s
Jea
l
o
u
s
F
o
r
c
e
f
u
l
C
o
m
p
a
s
si
o
n
a
t
e
C
o
n
v
e
n
t
i
o
n
a
l
A
g
g
r
e
ss
i
v
e
Lo
v
e
s
c
h
i
l
d
r
e
n
Ta
c
t
f
u
l
W
i
l
l
i
n
g
n
e
ss
t
o
t
a
k
e
a
s
t
a
n
d
A
f
f
e
c
t
i
o
n
a
t
e
C
o
n
c
e
i
t
e
d
I
n
d
e
p
e
n
d
e
n
t
G
e
n
t
l
e
S
e
c
r
e
t
i
v
e
D
e
f
e
n
d
o
w
n
b
e
l
i
e
f
s
W
a
r
m
Tr
u
t
h
f
u
l
W
i
l
l
i
n
g
t
o
t
a
k
e
r
i
sk
s
Te
n
d
e
r
A
d
a
p
t
a
b
l
e
T
ab
le
3
.
Ma
th
em
atica
l r
ea
s
o
n
in
g
test
s
co
r
in
g
r
u
b
r
ic
I
n
d
i
c
a
t
o
r
s
S
c
a
l
e
s
D
e
scri
p
t
i
o
n
s
F
i
n
d
i
n
g
a
r
e
l
a
t
i
o
n
s
h
i
p
p
a
t
t
e
r
n
4
3
2
1
0
Th
e
p
a
t
t
e
r
n
f
o
u
n
d
i
s
c
o
r
r
e
c
t
,
t
h
e
p
r
i
n
c
i
p
l
e
s
o
r
c
o
n
c
e
p
t
s
u
s
e
d
a
r
e
c
o
r
r
e
c
t
,
a
n
d
t
h
e
a
r
i
t
h
m
e
t
i
c
o
p
e
r
a
t
i
o
n
i
s
p
r
e
c
i
se
Th
e
p
a
t
t
e
r
n
f
o
u
n
d
i
s
c
o
r
r
e
c
t
,
a
n
d
t
h
e
p
r
i
n
c
i
p
l
e
s
o
r
c
o
n
c
e
p
t
s
u
s
e
d
a
r
e
c
o
r
r
e
c
t
,
b
u
t
t
h
e
a
r
i
t
h
m
e
t
i
c
o
p
e
r
a
t
i
o
n
i
s l
e
ss
p
r
e
c
i
se
Th
e
p
a
t
t
e
r
n
f
o
u
n
d
i
s
c
o
r
r
e
c
t
,
b
u
t
t
h
e
p
r
i
n
c
i
p
l
e
s
o
r
c
o
n
c
e
p
t
s
u
s
e
d
a
r
e
w
r
o
n
g
Th
e
p
a
t
t
e
r
n
f
o
u
n
d
i
s
w
r
o
n
g
N
o
a
n
sw
e
r
P
r
o
p
o
si
n
g
a
c
o
n
j
e
c
t
u
r
e
4
3
2
1
0
Th
e
c
o
n
j
e
c
t
u
r
e
g
i
v
e
n
i
s
c
o
r
r
e
c
t
,
t
h
e
r
e
i
s a
r
e
a
s
o
n
f
o
r
t
h
e
c
o
n
j
e
c
t
u
r
e
m
a
d
e
,
a
n
d
i
t
i
s
p
r
e
c
i
se
Th
e
c
o
n
j
e
c
t
u
r
e
g
i
v
e
n
i
s
c
o
r
r
e
c
t
,
t
h
e
r
e
i
s a
r
e
a
s
o
n
f
o
r
t
h
e
c
o
n
j
e
c
t
u
r
e
m
a
d
e
,
b
u
t
i
t
i
s
l
e
ss
p
r
e
c
i
se
Th
e
c
o
n
j
e
c
t
u
r
e
g
i
v
e
n
i
s
c
o
r
r
e
c
t
,
b
u
t
t
h
e
r
e
i
s
n
o
r
e
a
s
o
n
f
o
r
t
h
e
c
o
n
j
e
c
t
u
r
e
m
a
d
e
Th
e
c
o
n
j
e
c
t
u
r
e
g
i
v
e
n
i
s wr
o
n
g
N
o
a
n
sw
e
r
V
e
r
i
f
y
i
n
g
t
h
e
t
r
u
t
h
o
f
t
h
e
st
a
t
e
me
n
t
4
3
2
1
0
Th
e
st
e
p
s
i
n
t
h
e
v
e
r
i
f
i
c
a
t
i
o
n
p
r
o
c
e
s
s
a
r
e
c
o
r
r
e
c
t
,
t
h
e
p
r
i
n
c
i
p
l
e
s
o
r
c
o
n
c
e
p
t
s
u
s
e
d
a
r
e
c
o
r
r
e
c
t
,
a
n
d
t
h
e
a
r
i
t
h
me
t
i
c
o
p
e
r
a
t
i
o
n
i
s
p
r
e
c
i
s
e
Th
e
st
e
p
s
i
n
t
h
e
v
e
r
i
f
i
c
a
t
i
o
n
p
r
o
c
e
s
s
a
r
e
c
o
r
r
e
c
t
,
t
h
e
p
r
i
n
c
i
p
l
e
s
o
r
c
o
n
c
e
p
t
s
u
se
d
a
r
e
c
o
r
r
e
c
t
,
b
u
t
t
h
e
a
r
i
t
h
me
t
i
c
o
p
e
r
a
t
i
o
n
i
s
l
e
ss
p
r
e
c
i
se
Th
e
st
e
p
s
i
n
t
h
e
v
e
r
i
f
i
c
a
t
i
o
n
p
r
o
c
e
ss
a
r
e
c
o
r
r
e
c
t
,
b
u
t
t
h
e
p
r
i
n
c
i
p
l
e
s
o
r
c
o
n
c
e
p
t
s
u
s
e
d
a
r
e
w
r
o
n
g
Th
e
st
e
p
s
i
n
t
h
e
v
e
r
i
f
i
c
a
t
i
o
n
p
r
o
c
e
ss
a
r
e
w
r
o
n
g
o
r
m
o
s
t
l
y
w
r
o
n
g
N
o
a
n
sw
e
r
G
e
n
e
r
a
l
i
z
i
n
g
t
h
e
st
a
t
e
me
n
t
4
3
2
1
0
G
e
n
e
r
a
l
i
z
a
t
i
o
n
i
s
c
o
r
r
e
c
t
,
a
n
d
t
h
e
p
r
o
c
e
ss
o
f
g
e
n
e
r
a
l
i
z
i
n
g
i
s
c
o
r
r
e
c
t
a
n
d
p
r
e
c
i
se
G
e
n
e
r
a
l
i
z
a
t
i
o
n
i
s
c
o
r
r
e
c
t
,
b
u
t
t
h
e
r
e
i
s
a
sl
i
g
h
t
e
r
r
o
r
i
n
t
h
e
p
r
o
c
e
ss
o
f
m
a
k
i
n
g
a
g
e
n
e
r
a
l
i
z
a
t
i
o
n
G
e
n
e
r
a
l
i
z
a
t
i
o
n
i
s
c
o
r
r
e
c
t
,
b
u
t
t
h
e
p
r
o
c
e
ss
o
f
g
e
n
e
r
a
l
i
z
i
n
g
i
s wr
o
n
g
o
r
m
o
st
l
y
w
r
o
n
g
G
e
n
e
r
a
l
i
z
a
t
i
o
n
a
n
d
t
h
e
p
r
o
c
e
ss
o
f
g
e
n
e
r
a
l
i
z
i
n
g
i
s wr
o
n
g
o
r
m
o
st
l
y
w
r
o
n
g
N
o
a
n
sw
e
r
B
ef
o
r
e
b
ein
g
u
s
ed
,
th
e
MR
test
,
in
ter
v
iew
g
u
id
es,
an
d
g
en
d
er
q
u
esti
o
n
n
air
e
in
s
tr
u
m
e
n
ts
wer
e
test
ed
f
o
r
v
alid
ity
a
n
d
r
eliab
ilit
y
.
Valid
ity
was
test
ed
u
s
in
g
Aik
en
V.
I
tem
s
th
at
h
ad
a
v
alu
e
eq
u
a
l
to
o
r
less
th
an
0
.
5
wer
e
r
ev
is
ed
ag
ain
af
ter
test
in
g
.
Me
an
wh
ile,
r
eliab
ilit
y
wa
s
test
ed
with
C
r
o
n
b
ac
h
’
s
alp
h
a
with
a
v
alu
e
o
f
m
o
r
e
th
an
0
.
6
.
T
h
e
r
eliab
ilit
y
test
r
esu
lt
s
o
n
th
e
MR
te
s
t,
in
ter
v
iew
g
u
id
es,
an
d
g
en
d
er
q
u
esti
o
n
n
air
e
in
s
tr
u
m
en
ts
s
h
o
wed
v
alu
es
o
f
0
.
8
7
,
0
.
6
5
,
an
d
0
.
7
8
.
T
h
u
s
,
th
e
s
e
in
s
tr
u
m
en
ts
ar
e
d
ec
lar
ed
v
a
lid
an
d
r
eliab
le,
s
o
in
s
tr
u
m
en
ts
ar
e
s
u
itab
le
f
o
r
u
s
e.
Data
an
aly
s
is
was c
o
n
d
u
cted
u
s
in
g
d
if
f
er
en
t te
ch
n
iq
u
es o
n
q
u
an
titativ
e
an
d
q
u
alitativ
e
MR d
ata.
T
h
e
d
ata
an
aly
s
is
tech
n
i
q
u
es
u
s
ed
wer
e
d
escr
ip
tiv
e
s
tatis
tics
,
n
-
g
ain
,
an
d
W
ilco
x
o
n
s
ig
n
ed
-
r
a
n
k
test
in
q
u
an
titativ
e
d
ata.
Descr
ip
tiv
e
s
tatis
t
ics
ca
lcu
late
s
th
e
s
tan
d
ar
d
d
ev
iatio
n
a
n
d
m
ea
n
o
f
MR
in
th
e
p
r
etest
an
d
p
o
s
ttes
t.
Fu
r
th
er
m
o
r
e,
n
-
g
ain
was
u
s
ed
to
ca
lcu
late
th
e
m
ag
n
itu
d
e
o
f
th
e
i
n
cr
ea
s
e
in
s
tu
d
en
ts
’
MR
b
ased
o
n
p
r
etest
an
d
p
o
s
ttes
t
s
co
r
es.
T
h
e
n
-
g
ain
cr
iter
ia
ar
e
g
≤
0
.
3
(
l
o
w)
,
0
.
3
<g
≤
0
,
7
(
m
ed
iu
m
)
,
an
d
g
>0
.
7
(
h
ig
h
)
[
3
3
]
.
T
h
e
W
ilco
x
o
n
s
ig
n
ed
-
r
an
k
te
s
t
is
a
n
o
n
-
p
ar
am
etr
ic
s
tatis
tical
test
to
m
ea
s
u
r
e
th
e
s
ig
n
if
ic
an
ce
o
f
d
if
f
er
en
c
es
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
A
s
s
es
s
in
g
s
tu
d
en
ts
’
ma
th
ema
tica
l rea
s
o
n
in
g
in
p
r
o
b
lem
-
b
a
s
ed
lea
r
n
in
g
…
(
N
u
r
u
l I
s
n
a
in
i R
o
ma
d
h
o
n
)
3767
b
etwe
en
two
g
r
o
u
p
s
o
f
p
air
ed
d
ata
with
o
r
d
in
al
o
r
in
ter
v
al
s
ca
les
b
u
t
n
o
n
-
n
o
r
m
al
d
is
tr
ib
u
t
io
n
.
I
n
a
d
d
itio
n
,
th
e
W
ilco
x
o
n
s
ig
n
ed
-
r
a
n
k
test
is
an
alter
n
ativ
e
test
to
th
e
p
air
e
d
s
am
p
le
t
-
test
.
T
h
is
is
u
s
ed
to
test
th
e
h
y
p
o
th
esis
“
th
er
e
is
a
s
ig
n
if
ican
t
d
if
f
er
e
n
ce
in
th
e
m
ea
n
s
co
r
es
o
f
M
R
b
ef
o
r
e
an
d
a
f
ter
PB
L
is
ap
p
lied
.
”
I
n
q
u
alitativ
e
d
ata,
th
e
d
ata
an
aly
s
is
tech
n
i
q
u
e
u
s
ed
is
th
em
atic
an
aly
s
is
[
2
7
]
.
T
h
em
atic
a
n
aly
s
is
was
co
n
d
u
cted
b
y
f
o
c
u
s
in
g
MR
d
ata
o
n
its
ac
tiv
ities
in
f
in
d
in
g
a
r
elatio
n
s
h
ip
p
atter
n
,
p
r
o
p
o
s
in
g
a
co
n
jectu
r
e,
v
er
if
y
in
g
th
e
s
tatem
en
t
’
s
tr
u
th
,
an
d
g
en
e
r
alizin
g
th
e
s
tatem
en
t.
I
n
th
is
,
d
ata
th
at
is
in
ap
p
r
o
p
r
iate
o
r
d
o
es
n
o
t
s
u
p
p
o
r
t
MR
ac
t
iv
ities
wil
l
b
e
r
ed
u
ce
d
o
r
elim
in
ated
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
3
.
1
.
Q
ua
ntit
a
t
iv
e
f
ind
ing
s
T
ab
le
4
p
r
esen
ts
th
e
r
esu
lts
o
f
d
escr
ip
tiv
e
an
aly
s
is
o
f
s
tu
d
en
ts
'
M
R
o
b
tain
ed
b
ef
o
r
e
(
p
r
etest)
an
d
af
ter
(
p
o
s
ttes
t)
PB
L
im
p
lem
e
n
tatio
n
.
T
h
e
m
ea
n
p
r
etest
s
co
r
e
was
5
.
8
1
,
wh
ile
t
h
e
m
ea
n
p
o
s
ttes
t
s
co
r
e
was
1
1
.
5
2
.
I
n
o
t
h
er
wo
r
d
s
,
th
e
m
e
an
p
o
s
ttes
t
s
co
r
e
is
h
ig
h
er
t
h
a
n
th
e
p
r
etest
s
co
r
e.
T
h
u
s
,
it
ca
n
b
e
in
ter
p
r
ete
d
th
at
s
tu
d
en
ts
'
M
R
in
th
e
s
am
p
le
s
co
p
e
is
h
ig
h
e
r
af
ter
PB
L
im
p
lem
en
tatio
n
.
On
th
e
o
t
h
er
h
a
n
d
,
T
ab
le
5
p
r
esen
ts
th
e
r
esu
lts
o
f
th
e
n
-
g
ain
s
co
r
e
test
.
B
a
s
ed
o
n
th
e
ca
lcu
latio
n
o
f
th
e
n
-
g
ain
s
co
r
e
test
s
h
o
ws th
at
th
e
m
ea
n
v
alu
e
o
f
th
e
n
-
g
ain
s
co
r
e
f
o
r
s
tu
d
en
t’
s
MR
is
0
.
5
7
1
6
o
r
5
7
.
1
6
%,
wh
ich
is
in
th
e
m
ed
iu
m
ca
teg
o
r
y
.
T
h
is
s
h
o
ws
an
in
cr
ea
s
e
in
MR in
th
e
m
ed
iu
m
ca
teg
o
r
y
d
u
e
to
PB
L
im
p
lem
en
tatio
n
.
T
ab
le
4
.
Descr
ip
tio
n
o
f
p
r
etest a
n
d
p
o
s
ttes
t d
ata
N
M
a
x
i
m
u
m
M
i
n
i
m
u
m
S
t
d
.
de
v
i
a
t
i
o
n
M
e
a
n
P
r
e
t
e
s
t
21
9
4
1
.
5
3
7
5
.
8
1
P
o
st
t
e
s
t
21
15
6
2
.
9
0
9
1
1
.
5
2
V
a
l
i
d
N
(
l
i
s
t
w
i
se)
21
T
ab
le
5
.
N
-
g
ain
s
co
r
e
test
ca
lcu
latio
n
r
esu
lts
N
M
a
x
i
m
u
m
M
i
n
i
m
u
m
S
t
d
.
d
e
v
i
a
t
i
o
n
M
e
a
n
N
-
g
a
i
n
21
.
8
9
.
0
0
.
2
7
2
1
8
.
5
7
1
6
V
a
l
i
d
N
(
l
i
s
t
w
i
se)
21
T
a
b
l
e
6
p
r
e
s
e
n
t
s
t
h
e
r
e
s
u
lt
s
o
f
t
h
e
a
n
a
l
y
s
i
s
W
i
l
c
o
x
o
n
t
e
s
t
.
I
n
t
h
i
s
,
n
e
g
a
t
i
v
e
r
a
n
k
s
o
r
t
h
e
d
i
f
f
e
r
e
n
c
e
(
n
e
g
a
t
i
v
e
)
b
e
t
w
e
e
n
M
R
o
u
t
c
o
m
e
s
f
o
r
t
h
e
p
r
e
t
e
s
t
a
n
d
p
o
s
t
t
e
s
t
i
s
0
i
n
t
h
e
N
v
a
l
u
e
,
m
e
a
n
r
a
n
k
,
a
n
d
s
u
m
o
f
r
a
n
k
s
.
T
h
e
s
e
0
v
a
l
u
es
i
n
d
i
c
at
e
n
o
d
e
c
r
e
a
s
e
(
r
e
d
u
c
ti
o
n
)
f
r
o
m
t
h
e
p
r
e
t
es
t
v
a
l
u
e
t
o
t
h
e
p
o
s
tt
e
s
t
v
a
l
u
e
,
p
o
s
i
t
i
v
e
r
a
n
k
s
,
o
r
t
h
e
d
i
f
f
e
r
e
n
c
e
(
p
o
s
i
t
i
v
e
)
b
et
w
e
e
n
th
e
p
r
e
t
e
s
t
a
n
d
p
o
s
t
t
es
t
m
a
t
h
e
m
a
t
i
cs
l
e
a
r
n
i
n
g
o
u
t
c
o
m
es
.
T
h
e
r
e
a
r
e
2
0
p
o
s
i
t
i
v
e
d
a
ta
(
N
)
,
m
e
a
n
i
n
g
a
l
l
2
0
s
t
u
d
e
n
ts
e
x
p
e
r
i
e
n
c
e
d
i
n
c
r
e
a
s
e
d
M
R
o
u
t
c
o
m
e
s
f
r
o
m
p
r
e
t
es
t
t
o
p
o
s
tt
est
s
c
o
r
es
.
T
h
e
m
e
a
n
r
a
n
k
o
r
m
e
a
n
i
n
c
r
e
as
e
is
1
0
.
5
0
,
w
h
i
l
e
t
h
e
s
u
m
o
f
r
a
n
k
s
o
r
p
o
s
it
i
v
e
r
a
n
k
s
i
s
2
1
0
.
0
0
.
T
i
e
s
a
r
e
s
im
i
l
a
r
i
n
p
r
et
e
s
t
a
n
d
p
o
s
t
t
es
t
s
c
o
r
es
.
He
r
e
,
t
h
e
t
ie
v
al
u
e
is
1
,
s
o
i
t
ca
n
b
e
s
a
i
d
t
h
a
t
t
h
e
s
a
m
e
v
a
l
u
e
b
e
t
w
ee
n
t
h
e
p
r
e
t
es
t
a
n
d
p
o
s
t
te
s
t
is
1
.
B
as
e
d
o
n
t
h
e
t
e
s
t
s
t
a
ti
s
t
i
cs
o
u
t
p
u
t
,
t
h
e
a
s
y
m
p
’
s
k
n
o
w
n
s
i
g
n
i
f
i
c
a
n
c
e
(
2
-
t
a
i
l
e
d
)
i
s
0
.
0
0
0
b
e
c
a
u
s
e
o
f
t
h
e
v
a
l
u
e
o
f
0
.
0
0
0
<
0
.
0
5
.
I
t
c
a
n
b
e
c
o
n
c
l
u
d
e
d
t
h
a
t
t
h
e
h
y
p
o
t
h
es
i
s
is
ac
c
e
p
t
e
d
.
T
h
is
m
e
a
n
s
t
h
e
r
e
is
a
d
i
f
f
e
r
e
n
c
e
b
e
t
we
e
n
MR
o
u
t
c
o
m
e
s
f
o
r
p
r
e
t
e
s
t
a
n
d
p
o
s
t
tes
t
.
I
n
a
d
d
i
t
i
o
n
,
P
B
L
h
as
a
s
i
g
n
if
i
c
a
n
t
e
f
f
e
c
t
o
n
s
t
u
d
e
n
ts
’
M
R
.
T
ab
le
6
.
W
ilco
x
o
n
test
r
esu
lts
P
o
st
te
s
t
-
P
r
e
t
e
st
N
e
g
a
t
i
v
e
r
a
n
k
s
P
o
si
t
i
v
e
r
a
n
ks
Ti
e
s
To
t
a
l
0
a
20
b
1
c
21
a
.
P
o
st
t
e
s
t
<
P
r
e
t
e
st
.
0
0
1
0
.
5
0
b
.
P
o
st
t
e
st
>
P
r
e
te
st
.
0
0
2
1
0
.
0
0
c
.
P
o
st
t
e
s
t
=
P
r
e
t
e
s
t
Z
P
o
st
t
e
s
t
–
P
r
e
te
st
-
3
.
9
3
2
b
a
.
W
i
l
c
o
x
o
n
si
g
n
e
d
r
a
n
k
s
t
e
st
A
sy
mp
.
S
i
g
.
(
2
-
t
a
i
l
e
d
)
.
0
0
0
b
.
B
a
s
e
d
o
n
n
e
g
a
t
i
v
e
r
a
n
k
s
.
3
.
2
.
Q
ua
lit
a
t
iv
e
f
ind
ing
s
3
.
2
.
1
.
M
a
t
hem
a
t
ic
a
l r
ea
s
o
nin
g
a
na
ly
s
is
re
s
ults o
f
a
m
a
s
c
uli
ne
s
ub
j
ec
t
ca
t
eg
o
ry
(
M
S)
Fig
u
r
e
1
s
h
o
ws
th
e
r
esu
lt
o
f
th
e
wr
itten
wo
r
k
o
f
s
u
b
jects
c
ateg
o
r
ized
as
m
ascu
lin
e
(
MS)
o
b
tain
ed
f
r
o
m
th
e
MR
test
.
I
n
ad
d
itio
n
,
b
ased
o
n
th
e
in
ter
v
iew
r
esu
lts
,
ev
er
y
MR
ac
tiv
ity
ca
n
b
e
i
n
ter
p
r
eted
as
f
in
d
in
g
a
r
elatio
n
s
h
ip
p
atter
n
,
p
r
o
p
o
s
i
n
g
a
co
n
jectu
r
e,
v
e
r
if
y
in
g
th
e
s
tatem
en
t’
s
tr
u
th
,
an
d
g
en
er
ali
zin
g
th
e
s
tatem
en
t.
I
n
f
i
n
d
in
g
a
r
elatio
n
s
h
ip
p
att
er
n
,
MS
d
id
t
h
e
r
elatio
n
s
h
ip
p
atter
n
ac
tiv
ity
b
y
id
e
n
tify
in
g
th
e
len
g
th
o
f
th
e
s
q
u
ar
e
to
1
,
2
,
3
,
an
d
4
.
Kn
o
win
g
th
e
r
elatio
n
s
h
ip
p
atter
n
an
d
f
i
n
d
in
g
th
e
co
r
r
ec
t
in
f
o
r
m
atio
n
is
ess
en
tial
to
wr
itin
g
wh
at
is
k
n
o
wn
an
d
as
k
ed
in
th
e
p
r
o
b
lem
.
Fro
m
th
e
in
ter
v
iew,
MS
m
en
tio
n
ed
th
a
t
th
e
len
g
th
o
f
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
13
,
No
.
6
,
Dec
em
b
er
2
0
2
4
:
3
7
6
3
-
3
7
7
4
3768
s
id
e
o
f
th
e
s
q
u
ar
e
is
3
2
,
“
I
kn
o
w
th
e
s
iz
e
o
f
th
e
s
q
u
a
r
e
to
5
is
3
2
b
ec
a
u
s
e
th
e
s
iz
e
o
f
th
e
s
q
u
a
r
e
is
tw
ice
a
s
b
ig
a
s
th
e
s
iz
e
o
f
th
e
p
r
ev
io
u
s
o
n
e
.
”
I
n
p
r
o
p
o
s
in
g
a
co
n
jectu
r
e,
MS
p
r
o
p
o
s
ed
a
co
r
r
ec
t
co
n
jectu
r
e
b
y
ca
lc
u
latin
g
th
e
r
em
ain
in
g
lan
d
to
p
lan
t
c
o
r
n
t
h
r
o
u
g
h
th
e
r
ec
ta
n
g
u
lar
a
r
ea
f
o
r
m
u
la.
MS
s
aid
th
e
r
em
ain
in
g
lan
d
p
la
n
ted
with
co
r
n
was
3
0
m
².
“
T
h
e
ar
ea
o
f
lan
d
p
lan
ted
with
co
r
n
ca
n
b
e
ca
lcu
lated
u
s
in
g
t
h
e
r
ec
tan
g
u
lar
ar
e
a
f
o
r
m
u
la.
T
h
e
to
tal
lan
d
ar
ea
m
in
u
s
th
e
lan
d
a
r
ea
p
lan
ted
with
s
p
in
ac
h
an
d
k
ale,
s
o
8
0
m
²
-
5
0
m
²=
3
0
m
²
.
”
Fig
u
r
e
1
.
Ma
th
e
m
atica
l r
ea
s
o
n
in
g
test
r
esu
lts
o
f
m
ascu
lin
e
s
u
b
ject
ca
teg
o
r
y
(
MS)
Ma
s
cu
lin
e
v
er
if
ied
t
h
e
tr
u
t
h
o
f
Mr
.
An
t
o
n
'
s
s
tatem
en
t.
Fro
m
th
e
in
ter
v
iew,
MS
s
aid
Mr
.
An
to
n
h
a
d
to
p
ay
R
p
.
4
8
,
0
0
0
t
o
b
u
y
t
h
e
f
ab
r
ic.
“
T
h
e
ar
ea
o
f
th
e
f
a
b
r
ic
p
u
r
c
h
ased
b
y
Mr
.
A
n
to
n
is
2
m
×
2
m
=4
m
²
b
ec
au
s
e
th
e
p
r
ice
o
f
f
a
b
r
ic
p
er
m
²
is
R
p
.
1
2
,
0
0
0
,
th
en
R
p
.
1
2
,
0
0
0
×
4
=Rp
.
4
8
,
0
0
0
.
”
I
n
g
en
er
alizin
g
th
e
s
tatem
en
t,
MS
g
en
er
alize
d
th
e
s
tatem
en
t
wh
en
ca
lcu
latin
g
th
e
h
eig
h
t
v
alu
e
o
f
a
r
i
g
h
t
tr
ian
g
le.
Ho
wev
er
,
f
r
o
m
th
e
r
esu
lts
o
f
th
e
MS
in
ter
v
ie
w,
th
er
e
was
an
er
r
o
r
in
ca
lcu
latin
g
th
e
h
eig
h
t
v
alu
e
th
r
o
u
g
h
th
e
r
ig
h
t
tr
ia
n
g
le
ar
ea
f
o
r
m
u
la.
“
T
h
e
h
eig
h
t
v
al
u
e
ca
n
b
e
k
n
o
wn
u
s
in
g
th
e
ar
ea
f
o
r
m
u
la
o
f
a
r
ig
h
t
tr
ian
g
le
.
T
h
e
f
o
r
m
u
la
f
o
r
th
e
ar
ea
o
f
a
r
ig
h
t
tr
ia
n
g
le
is
1
2
x
b
a
s
e
x
h
eig
h
t.
T
h
e
ar
ea
a
n
d
b
ase
v
alu
es
ar
e
alr
ea
d
y
k
n
o
wn
,
n
a
m
ely
8
4
m
²
an
d
7
m
.
T
h
en
,
th
e
h
eig
h
t
o
f
th
e
r
ig
h
t
tr
ian
g
le
is
2
6
9
cm
.
”
MS
g
en
er
alize
s
m
ath
em
atica
l
s
tate
m
en
ts
co
r
r
ec
tly
b
u
t
ca
n
n
o
t
o
p
er
ate
d
iv
is
io
n
c
o
r
r
e
ctly
in
ca
lcu
latin
g
th
e
h
eig
h
t
v
alu
e
th
r
o
u
g
h
t
h
e
r
ig
h
t
tr
ia
n
g
le
ar
ea
f
o
r
m
u
la,
r
esu
ltin
g
in
er
r
o
r
s
in
th
e
p
r
o
b
lem
-
s
o
lv
in
g
s
tep
s
.
3
.
2
.
2
.
M
a
t
hem
a
t
ic
a
l r
ea
s
o
nin
g
a
na
ly
s
is
re
s
ults o
f
a
f
em
i
nin
e
s
u
bje
ct
ca
t
eg
o
ry
(
F
S)
Fig
u
r
e
2
s
h
o
ws
th
e
r
esu
lt
o
f
th
e
wr
itten
wo
r
k
o
f
s
u
b
jects
ca
t
eg
o
r
ized
as
f
em
in
in
e
(
FS
)
o
b
t
ain
ed
f
r
o
m
th
e
MR
test
.
I
n
ad
d
itio
n
,
b
as
ed
o
n
th
e
in
ter
v
iew
r
esu
lts
,
ev
er
y
MR
ac
tiv
ity
ca
n
b
e
in
te
r
p
r
eted
as
f
in
d
in
g
a
r
elatio
n
s
h
ip
p
atter
n
,
p
r
o
p
o
s
in
g
a
co
n
jectu
r
e,
v
er
if
y
in
g
th
e
s
tatem
en
t’
s
tr
u
th
,
an
d
g
en
er
al
izin
g
th
e
s
tatem
en
t.
I
n
f
in
d
in
g
a
r
elatio
n
s
h
ip
p
atte
r
n
,
FS
d
id
a
r
elatio
n
s
h
ip
p
atter
n
ac
tiv
ity
b
y
id
en
tif
y
in
g
th
e
l
en
g
th
o
f
th
e
s
q
u
a
r
e
to
1
,
2
,
3
,
an
d
4
.
Fro
m
th
e
in
ter
v
iew,
FS
k
n
o
ws
th
e
s
q
u
ar
e
s
ize
is
1
6
×
2
=3
2
cm
.
“
T
h
e
m
o
r
e
to
th
e
r
ig
h
t,
th
e
s
q
u
ar
e
s
ize
in
cr
ea
s
es
twice
as
b
ig
.
T
h
e
s
q
u
ar
e
s
ize
is
2
cm
,
2
×
2
=4
cm
,
4
×
2
=8
cm
,
8
×
2
=1
6
cm
,
an
d
16
×
2
=
3
2
cm
.
”
I
n
p
r
o
p
o
s
in
g
a
co
n
jectu
r
e,
FS
p
r
o
p
o
s
ed
a
co
r
r
ec
t
co
n
jectu
r
e
b
y
ca
lcu
latin
g
th
e
r
em
ain
in
g
lan
d
to
p
lan
t
co
r
n
th
r
o
u
g
h
th
e
r
e
ctan
g
u
lar
ar
ea
f
o
r
m
u
la.
T
h
is
ca
n
b
e
s
ee
n
f
r
o
m
th
e
ab
ilit
y
o
f
th
e
p
r
o
ce
s
s
to
Q
u
e
st
i
o
n
:
B
a
se
d
o
n
t
h
e
i
m
a
g
e
b
e
l
o
w
,
d
e
t
e
r
m
i
n
e
t
h
e
s
i
z
e
o
f
t
h
e
s
q
u
a
r
e
a
n
d
i
t
s
p
e
r
i
me
t
e
r
i
n
F
i
g
u
r
e
(
5
)
!
F
igur
e
(
1)
F
igur
e
(
2)
F
igur
e
(
3)
F
igur
e
(
4)
Q
u
e
st
i
o
n
:
I
s t
h
e
r
e
a
n
y
r
e
ma
i
n
i
n
g
l
a
n
d
f
o
r
p
l
a
n
t
i
n
g
c
o
r
n
?
(
y
e
s/
n
o
)
A
n
sw
e
r
:
K
n
o
w
n
:
La
n
d
s
i
z
e
1
0
m
x
8
m
2
0
m
²
o
f
l
a
n
d
i
s
p
l
a
n
t
e
d
w
i
t
h
s
p
i
n
a
c
h
3
0
m
²
o
f
l
a
n
d
i
s
p
l
a
n
t
e
d
w
i
t
h
k
a
l
e
A
sk
e
d
:
I
s t
h
e
r
e
a
n
y
l
a
n
d
l
e
f
t
t
o
p
l
a
n
t
c
o
r
n
?
A
n
sw
e
r
:
A
r
e
a
o
f
l
a
n
d
=
l
e
n
g
t
h
x
w
i
d
t
h
=
1
0
x
8
=
8
0
m
²
S
o
,
t
h
e
a
r
e
a
o
f
l
a
n
d
p
l
a
n
t
e
d
w
i
t
h
c
o
r
n
i
s =
8
0
-
(
2
0
+
3
0
)
=
8
0
-
50
=
3
0
m
²
A
n
sw
e
r
:
K
n
o
w
n
:
F
i
g
u
r
e
1
s
q
u
a
r
e
si
z
e
2
c
m
F
i
g
u
r
e
2
s
q
u
a
r
e
si
z
e
4
c
m
F
i
g
u
r
e
3
s
q
u
a
r
e
si
z
e
8
c
m
F
i
g
u
r
e
4
s
q
u
a
r
e
si
z
e
1
6
c
m
A
sk
e
d
:
W
h
a
t
i
s
t
h
e
s
i
z
e
o
f
sq
u
a
r
e
5
i
s
3
2
cm
A
n
sw
e
r
:
Th
e
sq
u
a
r
e
si
z
e
o
f
F
i
g
u
r
e
5
i
s
3
2
cm
P
e
r
i
me
t
e
r
=
4
x
si
d
e
=
4
x
3
2
=
1
2
8
Q
u
e
st
i
o
n
:
B
a
se
d
o
n
t
h
e
d
i
a
l
o
g
,
t
r
y
t
o
p
r
o
v
e
w
h
e
t
h
e
r
M
r
.
A
n
t
o
n
's
st
a
t
e
me
n
t
i
s
t
r
u
e
?
I
t
c
o
st
s
R
p
.
4
8
,
0
0
0
t
o
b
u
y
t
h
e
f
a
b
r
i
c
.
W
r
i
t
e
y
o
u
r
a
n
sw
e
r
i
n
t
h
i
s
c
o
l
u
mn
!
A
n
sw
e
r
:
K
n
o
w
n
:
Th
e
si
z
e
o
f
t
h
e
f
a
b
r
i
c
i
s
2
m
x
2
m
A
sk
e
d
:
I
s M
r
.
A
n
t
o
n
's s
t
a
t
e
me
n
t
t
r
u
e
?
Y
e
s
t
r
u
e
A
n
sw
e
r
:
Th
e
a
r
e
a
o
f
t
h
e
f
a
b
r
i
c
i
s
sq
u
a
r
e
=
si
d
e
=
2
x
2
=
4
m²
I
f
t
h
e
p
r
i
c
e
o
f
f
a
b
r
i
c
p
e
r
m²
i
s
R
p
.
1
2
,
0
0
0
Th
e
n
t
h
e
mo
n
e
y
t
h
a
t
M
r
.
A
n
t
o
n
mu
st
p
a
y
i
s
1
2
,
0
0
0
x
4
=
R
p
.
4
8
,
0
0
0
I
t
i
s c
o
n
c
l
u
d
e
d
t
h
a
t
M
r
.
A
n
t
o
n
's s
t
a
t
e
men
t
Q
u
e
st
i
o
n
:
W
h
a
t
i
s
t
h
e
h
e
i
g
h
t
o
f
t
h
e
r
i
g
h
t
t
r
i
a
n
g
l
e
?
Ex
p
l
a
i
n
h
o
w
y
o
u
f
o
u
n
d
t
h
e
h
e
i
g
h
t
o
f
t
h
e
r
i
g
h
t
t
r
i
a
n
g
l
e
!
A
n
sw
e
r
:
K
n
o
w
n
:
A
r
e
a
o
f
t
h
e
r
i
g
h
t
t
r
i
a
n
g
l
e
=
8
4
m²
Th
e
b
a
se
o
f
t
h
e
r
i
g
h
t
t
r
i
a
n
g
l
e
=
7
m
A
sk
e
d
:
W
h
a
t
i
s
t
h
e
h
e
i
g
h
t
o
f
t
h
e
r
i
g
h
t
t
r
i
a
n
g
l
e
?
2
6
9
A
n
sw
e
r
:
A
r
e
a
o
f
t
h
e
r
i
g
h
t
t
r
i
a
n
g
l
e
=
1
2
x
b
a
se
x
h
e
i
g
h
t
8
4
=
1
2
x
7
x
h
e
i
g
h
t
8
4
x
2
=
1
6
8
x
h
e
i
g
h
t
1
6
8
=
8
4
x
2
x
h
e
i
g
h
t
h
e
i
g
h
t
=
168
269
=
2
6
9
m
32
c
m
16
x
2
(
E
r
r
o
r
1)
M
S
c
a
n
ge
ne
r
a
li
z
e
s
tate
ments
c
or
r
e
c
tl
y,
but
c
a
nnot
ope
r
a
te
divi
s
ion
c
or
r
e
c
tl
y.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
A
s
s
es
s
in
g
s
tu
d
en
ts
’
ma
th
ema
tica
l rea
s
o
n
in
g
in
p
r
o
b
lem
-
b
a
s
ed
lea
r
n
in
g
…
(
N
u
r
u
l I
s
n
a
in
i R
o
ma
d
h
o
n
)
3769
u
n
d
er
s
tan
d
t
h
e
p
r
o
b
lem
well
b
ec
au
s
e
it
ca
n
f
in
d
an
d
wr
ite
d
o
wn
co
m
p
lete
im
p
o
r
ta
n
t
in
f
o
r
m
atio
n
f
r
o
m
t
h
e
p
r
o
b
lem
s
p
r
esen
ted
.
FS
s
aid
th
e
r
em
ain
in
g
lan
d
was
p
lan
te
d
with
co
r
n
,
8
0
m
²
-
5
0
m
²=
3
0
m
².
“
Mr
s
.
Yan
ti
h
as
a
lan
d
s
ize
o
f
1
0
m
×
8
m
=8
0
m
².
T
h
e
to
tal
lan
d
p
lan
ted
wit
h
s
p
in
ac
h
an
d
k
ale
is
5
0
m
²,
s
o
th
e
r
em
ain
i
n
g
lan
d
p
lan
ted
with
co
r
n
is
8
0
m
²
-
5
0
m
²=
3
0
m
²
.
”
I
n
v
er
if
y
in
g
t
h
e
tr
u
th
o
f
th
e
s
t
atem
en
t,
FS
was
wr
o
n
g
b
ec
au
s
e
th
er
e
was
a
n
er
r
o
r
in
ca
lcu
latin
g
th
e
ar
ea
o
f
th
e
clo
th
p
u
r
c
h
ased
b
y
Mr
.
An
to
n
.
FS
b
eliev
es
th
e
a
n
s
wer
is
co
r
r
ec
t
b
u
t
is
le
s
s
ca
r
ef
u
l
wh
en
ch
ec
k
in
g
a
p
r
o
b
lem
-
s
o
lv
in
g
s
o
lu
tio
n
.
FS
s
h
o
u
ld
co
n
tain
th
e
a
n
s
wer
s
th
at
h
av
e
b
ee
n
d
o
n
e
t
o
av
o
i
d
an
er
r
o
r
.
Fro
m
th
e
in
ter
v
iew,
FS
s
aid
Mr
.
An
to
n
h
ad
to
p
ay
R
p
.
4
8
,
0
0
0
to
b
u
y
f
ab
r
ic,
with
th
e
p
r
ice
p
er
m
²
b
ein
g
R
p
.
1
2
,
0
0
0
.
“
T
h
e
ar
ea
o
f
th
e
f
a
b
r
ic
t
h
at
M
r
.
An
to
n
b
o
u
g
h
t
was
1
2
×
4
=4
8
cm
²,
s
o
h
e
h
ad
to
p
ay
R
p
.
4
8
,
0
0
0
with
th
e
p
r
ice
p
er
m
²
b
ein
g
R
p
.
1
2
,
0
0
0
.
”
I
n
g
en
er
alizin
g
th
e
s
tatem
en
t
ac
tiv
ity
,
FS
g
en
er
alize
s
th
e
s
tatem
en
t
wh
en
ca
lcu
latin
g
th
e
h
eig
h
t v
alu
e
o
f
a
r
ig
h
t
tr
ian
g
le.
Ho
we
v
er
,
f
r
o
m
th
e
in
ter
v
iew,
th
er
e
was
an
er
r
o
r
in
ca
lcu
latin
g
th
e
h
eig
h
t
v
al
u
e
th
r
o
u
g
h
th
e
f
o
r
m
u
la
f
o
r
th
e
ar
ea
o
f
a
r
ig
h
t
tr
ian
g
le.
“
T
h
e
f
o
r
m
u
la
f
o
r
th
e
ar
ea
o
f
a
r
ig
h
t
tr
ian
g
le
is
1
2
x
b
ase
x
h
eig
h
t.
So
,
th
e
h
eig
h
t
v
alu
e
is
1
6
8
=2
6
9
m
”.
Fig
u
r
e
2
.
Ma
th
e
m
atica
l r
ea
s
o
n
in
g
test
r
esu
lts
o
f
f
em
in
in
e
s
u
b
ject
ca
teg
o
r
y
(
FS
)
3
.
2
.
3
.
M
a
t
hem
a
t
ic
a
l r
ea
s
o
nin
g
a
na
ly
s
is
re
s
ults o
f
a
neutr
a
l su
bje
ct
ca
t
eg
o
ry
(
NS)
Fig
u
r
e
3
s
h
o
ws
th
e
r
esu
lt
o
f
t
h
e
wr
itten
wo
r
k
o
f
s
u
b
jects
ca
teg
o
r
ized
as
n
eu
tr
al
(
NS)
o
b
ta
in
ed
f
r
o
m
th
e
MR
test
.
I
n
ad
d
itio
n
,
b
as
ed
o
n
th
e
in
ter
v
iew
r
esu
lts
,
ev
er
y
MR
ac
tiv
ity
ca
n
b
e
in
te
r
p
r
eted
as
f
in
d
in
g
a
r
elatio
n
s
h
ip
p
atter
n
,
p
r
o
p
o
s
in
g
a
co
n
jectu
r
e,
v
er
if
y
in
g
th
e
s
tatem
en
t’
s
tr
u
th
,
an
d
g
en
er
al
izin
g
th
e
s
tatem
en
t.
I
n
f
in
d
in
g
a
r
elatio
n
s
h
ip
p
atter
n
,
NS
d
id
th
e
r
elatio
n
s
h
ip
p
atter
n
ac
tiv
ity
b
y
id
en
tify
i
n
g
th
e
s
ize
o
f
th
e
s
q
u
ar
es
to
1
,
2
,
3
,
an
d
4
.
Fro
m
th
e
in
t
er
v
iew,
NS
k
n
ew
th
e
len
g
th
o
f
th
e
s
id
e
o
f
th
e
s
q
u
ar
e
was
2
×
1
6
=3
2
cm
b
u
t
was
wr
o
n
g
in
ca
lcu
latin
g
th
e
co
n
c
ep
t
o
f
p
er
im
eter
.
“
T
h
e
len
g
t
h
o
f
th
e
s
id
e
o
f
th
e
s
q
u
ar
e
is
t
wice
as
b
ig
as
th
e
p
r
ev
io
u
s
p
ictu
r
e,
s
o
2
×
1
6
=3
2
cm
.
”
I
n
p
r
o
p
o
s
in
g
a
co
n
jectu
r
e,
NS
p
r
o
p
o
s
ed
a
co
r
r
ec
t
co
n
jectu
r
e
b
y
ca
lcu
latin
g
th
e
r
em
ain
in
g
lan
d
to
p
lan
t
co
r
n
th
r
o
u
g
h
t
h
e
r
ec
tan
g
u
lar
a
r
ea
f
o
r
m
u
la.
NS
m
en
tio
n
ed
th
at
th
e
r
em
ain
in
g
lan
d
to
p
lan
t
c
o
r
n
i
s
3
0
m
².
“
T
h
e
r
e
m
ain
in
g
lan
d
f
o
r
p
lan
tin
g
co
r
n
m
ea
n
s
th
e
a
r
ea
o
f
Mr
s
.
Yan
ti'
s
lan
d
m
in
u
s
th
e
a
m
o
u
n
t o
f
la
n
d
p
lan
ted
with
s
p
in
ac
h
an
d
k
ale
,
s
o
8
0
-
(
2
0
+
3
0
)
=3
0
m
²
.
”
Q
u
e
st
i
o
n
:
B
a
se
d
o
n
t
h
e
i
ma
g
e
b
e
l
o
w
,
d
e
t
e
r
mi
n
e
t
h
e
s
i
z
e
o
f
t
h
e
s
q
u
a
r
e
a
n
d
i
t
s
p
e
r
i
m
e
t
e
r
i
n
F
i
g
u
r
e
(
5
)
!
F
igur
e
(
1)
F
igur
e
(
2)
F
i
gur
e
(
3)
F
igur
e
(
4)
Q
u
e
st
i
o
n
:
I
s t
h
e
r
e
a
n
y
r
e
ma
i
n
i
n
g
l
a
n
d
f
o
r
p
l
a
n
t
i
n
g
c
o
r
n
?
(
y
e
s/
n
o
)
A
n
sw
e
r
:
K
n
o
w
n
:
La
n
d
s
i
z
e
1
0
x
8
m
P
l
a
n
t
e
d
2
0
m
²
o
f
s
p
i
n
a
c
h
P
l
a
n
t
e
d
3
0
m
²
o
f
k
a
l
e
A
sk
e
d
:
I
s
t
h
e
r
e
a
n
y
l
a
n
d
l
e
f
t
t
o
p
l
a
n
t
c
o
r
n
?
A
n
sw
e
r
:
Y
e
s
A
r
e
a
o
f
l
a
n
d
=
l
e
n
g
t
h
x
w
i
d
t
h
=
1
0
x
8
=
8
0
m
²
S
o
,
t
h
e
a
r
e
a
o
f
l
a
n
d
p
l
a
n
t
e
d
w
i
t
h
c
o
r
n
i
s =
8
0
-
(
2
0
+
3
0
)
=
8
0
-
50
=
3
0
m
²
A
n
sw
e
r
:
K
n
o
w
n
:
F
i
g
u
r
e
1
s
q
u
a
r
e
si
z
e
2
c
m
F
i
g
u
r
e
2
s
q
u
a
r
e
si
z
e
4
c
m
F
i
g
u
r
e
3
s
q
u
a
r
e
si
z
e
8
c
m
F
i
g
u
r
e
4
s
q
u
a
r
e
si
z
e
1
6
c
m
A
sk
e
d
:
W
h
a
t
i
s
t
h
e
si
z
e
o
f
s
q
u
a
r
e
5
?
A
n
sw
e
r
:
Th
e
s
q
u
a
r
e
si
z
e
o
f
F
i
g
u
r
e
5
i
s
3
2
c
m
P
e
r
i
me
t
e
r
o
f
s
q
u
a
r
e
=
4
x
si
d
e
=
4
x
3
2
=
1
2
8
c
m
Q
u
e
st
i
o
n
:
B
a
se
d
o
n
t
h
e
d
i
a
l
o
g
,
t
r
y
t
o
p
r
o
v
e
w
h
e
t
h
e
r
M
r
.
A
n
t
o
n
's st
a
t
e
me
n
t
i
s
t
r
u
e
.
I
t
c
o
st
s
R
p
.
4
8
,
0
0
0
t
o
b
u
y
t
h
e
f
a
b
r
i
c
.
W
r
i
t
e
y
o
u
r
a
n
sw
e
r
i
n
t
h
i
s
c
o
l
u
m
n
!
A
n
sw
e
r
:
K
n
o
w
n
:
Th
e
si
z
e
o
f
t
h
e
f
a
b
r
i
c
i
s
2
m
x
2
m
A
sk
e
d
:
I
s M
r
.
A
n
t
o
n
's s
t
a
t
e
me
n
t
t
r
u
e
?
A
n
sw
e
r
:
Tr
u
e
Th
e
a
r
e
a
o
f
t
h
e
f
a
b
r
i
c
i
s
sq
u
a
r
e
=
si
d
e
x
s
i
d
e
=
1
2
x
2
=
4
8
m²
I
f
t
h
e
p
r
i
c
e
o
f
f
a
b
r
i
c
p
e
r
m²
i
s
R
p
.
1
2
,
0
0
0
Th
e
n
t
h
e
m
o
n
e
y
t
h
a
t
M
r
.
A
n
t
o
n
m
u
st
p
a
y
i
s
1
2
,
0
0
0
x
4
=
R
p
.
4
8
,
0
0
0
I
t
i
s c
o
n
c
l
u
d
e
d
t
h
a
t
M
r
.
A
n
t
o
n
's s
t
a
t
e
men
t
i
s t
r
u
e
Q
u
e
st
i
o
n
:
W
h
a
t
i
s
t
h
e
h
e
i
g
h
t
o
f
t
h
e
r
i
g
h
t
t
r
i
a
n
g
l
e
?
Ex
p
l
a
i
n
h
o
w
y
o
u
f
o
u
n
d
t
h
e
h
e
i
g
h
t
o
f
t
h
e
r
i
g
h
t
t
r
i
a
n
g
l
e
!
A
n
sw
e
r
:
K
n
o
w
n
:
A
r
e
a
o
f
t
h
e
r
i
g
h
t
t
r
i
a
n
g
l
e
=
8
4
m²
Th
e
b
a
se
o
f
t
h
e
r
i
g
h
t
t
r
i
a
n
g
l
e
=
7
m
A
sk
e
d
:
W
h
a
t
i
s
t
h
e
h
e
i
g
h
t
o
f
t
h
e
r
i
g
h
t
t
r
i
a
n
g
l
e
?
A
n
sw
e
r
:
A
r
e
a
o
f
t
h
e
r
i
g
h
t
t
r
i
a
n
g
l
e
=
1
2
x
b
a
s
e
x
h
e
i
g
h
t
8
4
=
1
2
x
7
x
h
e
i
g
h
t
8
4
x
2
=
1
6
8
x
h
e
i
g
h
t
1
6
8
=
8
4
x
2
h
e
i
g
h
t
(
E
r
r
o
r
1)
F
S
c
a
n
ve
r
if
y
the
tr
uth
of
the
s
tate
ment,
but
ther
e
is
a
n
e
r
r
or
c
a
lcula
ti
ng
the
a
r
e
a
of
the
f
a
br
ic.
(
E
r
r
o
r
2)
F
S
c
a
n
ge
ne
r
a
li
z
e
s
tate
ments
c
or
r
e
c
tl
y,
but
c
a
nnot
ope
r
a
te
divi
s
ion
c
or
r
e
c
tl
y.
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
.
13
,
No
.
6
,
Dec
em
b
er
2
0
2
4
:
3
7
6
3
-
3
7
7
4
3770
Neu
tr
al
s
u
b
ject
ca
teg
o
r
y
v
er
if
ied
th
e
tr
u
th
o
f
Mr
.
An
t
o
n
'
s
s
tatem
en
t.
Fro
m
th
e
in
te
r
v
iew,
NS
m
en
tio
n
ed
t
h
at
Mr
.
An
t
o
n
h
ad
to
p
ay
R
p
.
4
8
,
0
0
0
to
b
u
y
4
m
²
o
f
f
a
b
r
ic.
“
T
h
e
f
a
b
r
ic
s
ize
is
2
m
×
2
m
=4
m
²
an
d
th
e
p
r
ice
p
er
m
²
is
R
p
.
1
2
,
0
0
0
.
So
,
Mr
.
An
to
n
h
as
to
p
ay
4
×
R
p
.
1
2
,
0
0
0
=Rp
.
4
8
,
0
0
0
.
”
I
n
g
en
er
alizin
g
t
h
e
s
tatem
en
t,
NS
g
en
er
alize
d
th
e
m
ath
em
atica
l
s
tatem
en
t
co
r
r
e
ctly
b
u
t
d
id
n
o
t
co
r
r
ec
tly
o
p
e
r
ate
th
e
d
iv
is
io
n
i
n
ca
lcu
latin
g
th
e
h
eig
h
t v
alu
e
o
f
th
e
r
ig
h
t
tr
ian
g
le.
Fro
m
th
e
in
ter
v
iew
r
esu
lts
,
NS
g
en
er
alize
d
th
e
m
at
h
em
atica
l
s
tatem
en
t
th
r
o
u
g
h
t
h
e
f
o
r
m
u
l
a
f
o
r
th
e
ar
ea
o
f
a
r
i
g
h
t
tr
ian
g
le.
“
T
h
e
h
eig
h
t
v
alu
e
ca
n
b
e
k
n
o
wn
th
r
o
u
g
h
th
e
f
o
r
m
u
la
f
o
r
th
e
ar
ea
o
f
a
r
ig
h
t
tr
ian
g
le,
wh
ich
is
1
2
x
b
ase
x
h
eig
h
t.
T
h
e
ar
ea
o
f
a
r
ig
h
t
tr
ia
n
g
le
is
8
4
m
²
,
an
d
th
e
b
ase
is
7
m
.
So
,
th
e
h
eig
h
t
v
alu
e
is
168
7
=... m
.
”
Fig
u
r
e
3
.
Ma
th
e
m
atica
l r
ea
s
o
n
in
g
test
r
esu
lts
o
f
n
eu
tr
al
s
u
b
je
ct
ca
teg
o
r
y
(
NS)
B
ased
o
n
th
e
a
n
aly
s
is
o
f
t
h
e
r
esear
ch
r
esu
lts
,
s
ev
er
al
f
in
d
in
g
s
ca
n
b
e
lis
ted
an
d
elab
o
r
ated
q
u
an
titativ
ely
an
d
q
u
alitativ
ely
.
Qu
an
titativ
e
f
i
n
d
in
g
s
s
h
o
w
th
at
s
tu
d
en
ts
'
MR
in
cr
ea
s
ed
in
th
e
m
ed
iu
m
ca
teg
o
r
y
a
f
ter
im
p
le
m
en
tin
g
PB
L
.
I
n
th
is
,
th
e
im
p
lem
en
ta
tio
n
o
f
PB
L
s
ig
n
if
ican
tly
af
f
ec
ts
s
tu
d
en
ts
'
M
R
.
T
h
ese
f
in
d
in
g
s
ar
e
co
n
s
is
ten
t
with
p
r
ev
io
u
s
f
in
d
in
g
s
r
eg
ar
d
in
g
MR
p
r
o
b
lem
-
o
r
ie
n
ted
lear
n
in
g
in
ter
v
e
n
tio
n
s
in
ex
p
er
im
e
n
tal
r
esear
ch
d
esi
g
n
s
[
4
]
,
[
1
0
]
–
[
1
5
]
,
[
3
4
]
–
[
3
6
]
.
E
x
p
er
ts
ex
p
lain
th
at
PB
L
h
as
ch
ar
ac
ter
is
tics
o
f
p
r
o
b
lem
-
s
o
lv
in
g
s
tep
s
,
lead
in
g
to
h
ig
h
er
-
lev
el
th
in
k
in
g
d
e
v
elo
p
m
en
t
[
1
4
]
,
[
1
5
]
.
MR
f
o
r
p
r
o
b
lem
-
s
o
lv
i
n
g
is
f
ac
ilit
ated
th
r
o
u
g
h
ac
tiv
e
in
ter
ac
tio
n
u
s
in
g
th
in
k
in
g
s
k
ills
,
in
clu
d
in
g
MR d
u
r
in
g
lear
n
in
g
[
6
]
.
Q
u
a
l
i
t
at
i
v
e
f
i
n
d
i
n
g
s
s
h
o
w
t
h
a
t
s
t
u
d
e
n
ts
w
h
o
h
a
v
e
d
i
f
f
e
r
e
n
t
g
en
d
e
r
p
e
r
s
p
e
c
t
i
v
es
i
n
te
r
m
s
o
f
m
a
s
c
u
l
i
n
e,
f
e
m
i
n
i
n
e
,
a
n
d
n
e
u
t
r
a
l
h
a
v
e
d
if
f
e
r
e
n
t
M
R
.
T
h
is
f
i
n
d
i
n
g
c
a
n
b
e
s
e
e
n
a
s
c
o
n
s
is
t
e
n
t
w
it
h
p
r
e
v
i
o
u
s
s
t
u
d
i
e
s
t
h
a
t
g
e
n
d
e
r
d
i
f
f
e
r
e
n
c
e
s
a
r
e
a
f
a
c
t
o
r
o
r
c
a
n
r
e
s
u
l
t
i
n
d
i
f
f
e
r
e
n
c
es
i
n
M
R
[
1
6
]
,
[
1
9
]
,
[
2
7
]
,
[
3
7
]
–
[
4
3
]
.
I
n
t
h
i
s
,
t
h
e
r
e
w
e
r
e
n
o
s
t
u
d
e
n
t
s
w
i
t
h
a
n
d
r
o
g
y
n
o
u
s
g
e
n
d
e
r
i
d
e
n
t
i
t
y
i
n
p
r
i
m
a
r
y
s
c
h
o
o
l
.
T
h
i
s
p
h
e
n
o
m
e
n
o
n
i
s
c
a
u
s
e
d
b
y
c
h
i
l
d
r
e
n
w
h
o
a
r
e
a
t
t
h
e
e
l
e
m
e
n
ta
r
y
s
c
h
o
o
l
le
v
e
l
a
n
d
t
e
n
d
n
o
t
t
o
h
a
v
e
s
t
a
b
l
e
g
e
n
d
e
r
s
t
e
r
e
o
t
y
p
es
[
4
4
]
,
[
4
5
]
,
s
o
i
t
i
s
s
c
a
r
c
e
f
o
r
c
h
i
l
d
r
e
n
t
o
h
a
v
e
a
n
d
r
o
g
y
n
o
u
s
,
w
h
i
c
h
r
e
p
r
e
s
e
n
ts
g
e
n
d
e
r
w
it
h
eq
u
a
l
l
y
s
t
r
o
n
g
m
a
s
c
u
l
i
n
e
a
n
d
f
em
i
n
i
n
e
t
r
a
i
ts
[
4
6
]
.
Ma
s
cu
lin
e
s
u
b
ject
ca
teg
o
r
y
i
d
en
tifie
d
ca
n
f
in
d
a
r
elatio
n
s
h
ip
p
atter
n
,
p
r
o
p
o
s
e
a
c
o
n
je
ctu
r
e,
an
d
co
r
r
ec
tly
v
er
if
y
th
e
s
tatem
en
t’
s
tr
u
th
b
u
t
ar
e
wr
o
n
g
in
g
en
er
alizin
g
th
e
s
tatem
en
ts
.
FS
is
i
d
en
tifie
d
as
k
n
o
w
n
to
f
in
d
a
r
elatio
n
s
h
ip
p
atter
n
an
d
p
r
o
p
o
s
e
a
co
n
jectu
r
e
b
u
t
is
wr
o
n
g
i
n
v
er
if
y
in
g
a
n
d
g
en
e
r
alizin
g
th
e
s
tatem
en
ts
.
Me
an
wh
ile,
NS
id
en
tifie
d
ca
n
n
o
t
f
in
d
a
r
elatio
n
s
h
ip
p
atter
n
,
p
r
o
p
o
s
in
g
a
co
n
jectu
r
e
an
d
g
en
er
alizin
g
th
e
s
tatem
en
ts
,
b
u
t
ar
e
co
r
r
ec
t
in
v
er
if
y
in
g
t
h
e
tr
u
th
o
f
th
e
s
tatem
en
ts
.
No
q
u
alitativ
e
s
tu
d
y
r
esu
lts
ar
e
p
r
ec
is
ely
t
h
e
s
am
e
as
th
ese
f
in
d
in
g
s
,
wh
er
e
s
tu
d
e
n
t
MR
is
elab
o
r
ated
b
ased
o
n
th
e
p
er
s
p
ec
tiv
e
o
f
Q
u
e
st
i
o
n
:
B
a
se
d
o
n
t
h
e
i
m
a
g
e
b
e
l
o
w
,
d
e
t
e
r
m
i
n
e
t
h
e
s
i
z
e
o
f
t
h
e
s
q
u
a
r
e
a
n
d
i
t
s
p
e
r
i
me
t
e
r
i
n
F
i
g
u
r
e
(
5
)
!
F
igur
e
(
1)
F
igur
e
(
2)
F
i
gur
e
(
3)
F
igur
e
(
4)
A
n
sw
e
r
:
P
e
r
i
m
e
t
e
r
o
f
s
q
u
a
r
e
K
n
o
w
n
:
=
4
x
si
d
e
F
i
g
u
r
e
1
s
q
u
a
r
e
si
z
e
2
c
m
=
4
x
8
F
i
g
u
r
e
2
s
q
u
a
r
e
si
z
e
4
c
m
=
3
2
c
m
F
i
g
u
r
e
3
s
q
u
a
r
e
si
z
e
8
c
m
F
i
g
u
r
e
4
s
q
u
a
r
e
si
z
e
1
6
c
m
F
i
g
u
r
e
5
s
q
u
a
r
e
si
z
e
3
2
c
m
Q
u
e
st
i
o
n
:
I
s t
h
e
r
e
a
n
y
r
e
ma
i
n
i
n
g
l
a
n
d
f
o
r
p
l
a
n
t
i
n
g
c
o
r
n
?
(
y
e
s/
n
o
)
A
n
sw
e
r
:
K
n
o
w
n
:
La
n
d
s
i
z
e
1
0
x
8
m
P
l
a
n
t
e
d
2
0
m
o
f
s
p
i
n
a
c
h
P
l
a
n
t
e
d
3
0
m
o
f
k
a
l
e
A
sk
e
d
:
I
s t
h
e
r
e
a
n
y
l
a
n
d
l
e
f
t
t
o
p
l
a
n
t
c
o
r
n
?
Y
e
s
A
n
sw
e
r
:
Y
e
s
A
r
e
a
o
f
l
a
n
d
=
l
e
n
g
t
h
x
w
i
d
t
h
=
x
=
m
²
P
l
a
n
t
e
d
w
i
t
h
c
o
r
n
=
8
0
-
(
2
0
+
3
0
)
=
8
0
-
50
=
3
0
m
²
Q
u
e
st
i
o
n
:
B
a
se
d
o
n
t
h
e
d
i
a
l
o
g
,
t
r
y
t
o
p
r
o
v
e
w
h
e
t
h
e
r
M
r
.
A
n
t
o
n
's
st
a
t
e
me
n
t
i
s
t
r
u
e
.
I
t
c
o
s
t
s
R
p
.
4
8
,
0
0
0
t
o
b
u
y
t
h
e
f
a
b
r
i
c
.
W
r
i
t
e
y
o
u
r
a
n
sw
e
r
i
n
t
h
i
s c
o
l
u
m
n
!
A
n
sw
e
r
:
Th
e
a
r
e
a
o
f
t
h
e
f
a
b
r
i
c
i
s
sq
u
a
r
e
=
si
d
e
x
s
i
d
e
=
2
x
2
=
4
m
²
I
f
t
h
e
p
r
i
c
e
o
f
f
a
b
r
i
c
p
e
r
m²
i
s
R
p
.
1
2
,
0
0
0
Th
e
n
t
h
e
mo
n
e
y
t
h
a
t
M
r
.
A
n
t
o
n
mu
st
p
a
y
i
s
1
2
,
0
0
0
x
4
=
R
p
.
4
8
,
0
0
0
I
t
i
s c
o
n
c
l
u
d
e
d
t
h
a
t
M
r
.
A
n
t
o
n
's s
t
a
t
e
men
t
i
s t
r
u
e
Q
u
e
st
i
o
n
:
W
h
a
t
i
s
t
h
e
h
e
i
g
h
t
o
f
t
h
e
r
i
g
h
t
t
r
i
a
n
g
l
e
?
Ex
p
l
a
i
n
h
o
w
y
o
u
f
o
u
n
d
t
h
e
h
e
i
g
h
t
o
f
t
h
e
r
i
g
h
t
t
r
i
a
n
g
l
e
!
A
n
sw
e
r
:
Kn
o
w
n
:
A
r
e
a
o
f
t
h
e
r
i
g
h
t
t
r
i
a
n
g
l
e
=
8
4
m²
Th
e
b
a
se
o
f
t
h
e
r
i
g
h
t
t
r
i
a
n
g
l
e
=
7
m
A
r
e
a
o
f
t
h
e
r
i
g
h
t
t
r
i
a
n
g
l
e
=
1
2
x
b
a
s
e
x
h
e
i
g
h
t
8
4
=
1
2
x
7
x
h
e
i
g
h
t
8
4
x
2
=
7
x
h
e
i
g
h
t
1
6
8
=
7
x
h
e
i
g
h
t
h
e
i
g
h
t
=
168
7
=
m
(
E
r
r
o
r
1)
NS
c
a
nnot
c
a
lcula
te
the
pe
r
im
e
ter
o
f
a
s
qua
r
e
.
(
E
r
r
o
r
2)
NS
c
a
n
pr
opos
e
c
onjec
tur
e
s
c
or
r
e
c
tl
y,
but
a
r
e
incomplete
in
wr
it
in
g
pr
oble
m
s
olvi
ng,
e
s
pe
c
ially
in
ter
ms
of
f
ind
ing
the
a
r
e
a
of
a
ll
land.
(
E
r
r
o
r
3)
NS
c
a
n
ge
ne
r
a
li
z
e
s
tate
ments
c
or
r
e
c
tl
y,
but
c
a
nnot
ope
r
a
te
divi
s
ion
c
or
r
e
c
tl
y.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
A
s
s
es
s
in
g
s
tu
d
en
ts
’
ma
th
ema
tica
l rea
s
o
n
in
g
in
p
r
o
b
lem
-
b
a
s
ed
lea
r
n
in
g
…
(
N
u
r
u
l I
s
n
a
in
i R
o
ma
d
h
o
n
)
3771
g
en
d
er
d
if
f
er
en
ce
s
a
f
ter
PB
L
im
p
lem
en
tatio
n
.
Ho
wev
er
,
s
o
m
e
p
ar
ts
o
f
th
e
f
i
n
d
in
g
s
ca
n
b
e
s
aid
to
b
e
co
n
s
is
ten
t
an
d
ca
n
b
e
f
u
r
th
er
elab
o
r
ated
with
r
elate
d
s
tu
d
i
es.
MS
an
d
FS
s
u
cc
ess
f
u
lly
f
o
u
n
d
a
r
elatio
n
s
h
ip
p
atter
n
an
d
p
r
o
p
o
s
ed
a
co
n
jec
tu
r
e,
wh
ile
NS
f
ailed
.
Stu
d
e
n
ts
wh
o
s
u
cc
ee
d
ed
in
f
in
d
in
g
a
r
elatio
n
s
h
ip
p
atter
n
an
d
p
r
o
p
o
s
e
a
c
o
n
jectu
r
e
b
ec
au
s
e
s
tu
d
en
ts
s
u
cc
ee
d
ed
in
id
en
tify
in
g
im
p
o
r
tan
t
o
r
u
n
im
p
o
r
tan
t
in
f
o
r
m
atio
n
b
ased
o
n
p
r
o
b
le
m
q
u
esti
o
n
s
,
t
h
en
co
n
n
ec
tin
g
it
with
p
o
s
s
ib
le
s
tr
ateg
ies
an
d
p
r
o
b
lem
-
s
o
lv
i
n
g
[
3
7
]
,
[
3
8
]
,
[
4
7
]
.
On
ly
FS
is
wr
o
n
g
in
v
er
if
y
i
n
g
th
e
s
tatem
en
t.
Stu
d
en
ts
b
eliev
e
th
e
an
s
wer
is
co
r
r
ec
t
b
u
t
ar
e
ca
r
eless
in
r
ec
h
ec
k
in
g
th
e
s
o
lu
tio
n
[
4
8
]
.
All
s
u
b
jects
(
MS,
FS
,
an
d
NS)
f
ailed
to
g
en
er
alize
th
e
s
tatem
en
ts
.
T
h
ese
f
in
d
in
g
s
a
r
e
c
o
n
s
is
ten
t
with
s
e
v
er
al
s
tu
d
ies
[
3
]
,
[
1
6
]
,
[
4
9
]
–
[
5
2
]
.
T
h
e
ac
ti
v
ity
o
f
g
en
er
alizin
g
th
e
s
tatem
en
ts
is
th
e
m
o
s
t
d
if
f
icu
lt
to
d
o
b
ec
a
u
s
e
it
r
eq
u
ir
es
ab
s
tr
ac
tio
n
s
k
ills
[
5
3
]
–
[
5
5
]
an
d
r
elatio
n
al
u
n
d
er
s
tan
d
i
n
g
[
2
5
]
,
[
5
6
]
–
[
5
8
]
.
I
t is also
ca
u
s
ed
b
y
s
tu
d
en
ts
f
ailin
g
to
r
e
p
r
esen
t p
r
o
b
lem
s
in
m
ath
em
atica
l m
o
d
e
ls
[
4
9
]
.
T
h
e
f
in
d
in
g
s
o
f
th
is
s
tu
d
y
p
r
o
v
id
e
co
m
p
r
e
h
en
s
iv
e
n
ew
em
p
ir
ical
ev
id
en
ce
th
at
th
e
MR
o
f
s
tu
d
en
ts
with
d
if
f
er
en
t g
en
d
e
r
p
er
s
p
ec
t
iv
es
ca
n
b
e
im
p
r
o
v
e
d
o
r
in
f
lu
e
n
ce
d
s
ig
n
if
ican
tly
t
h
r
o
u
g
h
t
h
e
im
p
lem
en
tatio
n
o
f
PB
L
.
W
h
at
co
m
p
r
eh
en
s
iv
en
es
s
m
ea
n
s
is
th
at
th
e
s
tu
d
y
'
s
r
es
u
lts
p
r
o
v
id
e
q
u
an
titativ
e
em
p
i
r
ical
ev
id
en
ce
th
at
s
tu
d
en
ts
'
M
R
ca
n
b
e
in
cr
ea
s
ed
th
r
o
u
g
h
PB
L
.
I
t p
r
o
v
id
es
q
u
al
itativ
e
em
p
ir
ical
ev
id
en
ce
th
at
MR
s
tu
d
en
ts
with
d
if
f
er
en
t
g
e
n
d
er
p
er
s
p
ec
tiv
es
h
av
e
th
eir
o
wn
s
u
cc
ess
o
r
f
ail
u
r
e
in
ea
ch
MR
ac
tiv
ity
af
ter
i
m
p
lem
en
tin
g
PB
L
.
B
ased
o
n
th
ese
f
in
d
in
g
s
,
p
r
ac
tical,
th
eo
r
etica
l,
o
r
m
et
h
o
d
o
lo
g
ical
co
n
tr
ib
u
tio
n
s
o
r
i
m
p
licatio
n
s
ca
n
b
e
s
y
n
th
esized
.
R
eg
ar
d
in
g
p
r
ac
tical
ed
u
ca
tio
n
al
o
r
em
p
ir
ical
c
o
n
tr
ib
u
tio
n
s
,
th
e
f
in
d
in
g
s
ar
e
h
elp
f
u
l
f
o
r
teac
h
er
s
o
r
p
r
ac
titi
o
n
er
s
in
th
at
th
e
teac
h
in
g
m
ater
ials
th
at
ar
e
p
r
ep
ar
ed
,
esp
ec
ially
in
to
PB
L
le
ar
n
in
g
s
tep
s
b
y
also
p
ay
in
g
atten
tio
n
t
o
g
e
n
d
er
,
h
a
v
e
b
ee
n
p
r
o
v
en
to
im
p
r
o
v
e
M
R
s
tu
d
en
ts
wh
o
h
a
v
e
p
r
o
b
lem
s
.
I
n
th
is
ca
s
e,
PB
L
ca
n
b
e
a
co
n
s
id
er
atio
n
f
o
r
p
o
licy
m
ak
er
s
to
s
elec
t
an
d
m
ain
tain
as
th
e
b
est
lear
n
in
g
m
o
d
el
to
en
c
o
u
r
a
g
e
s
tu
d
en
ts
’
ac
ad
em
ic
ac
h
iev
e
m
en
t
lev
el
s
[
5
9
]
–
[
6
2
]
an
d
av
o
i
d
g
en
d
er
b
ias
in
e
d
u
ca
tio
n
[
2
8
]
,
[
4
6
]
,
[
6
3
]
–
[
6
5
]
.
T
h
er
ef
o
r
e,
th
e
f
in
d
in
g
s
ca
n
al
s
o
b
e
u
s
ed
f
o
r
p
o
licy
m
ak
e
r
s
to
m
ain
tain
PB
L
as
a
lear
n
in
g
m
o
d
el
to
ac
h
iev
e
s
tan
d
ar
d
m
ath
em
atics
co
m
p
et
en
cies
b
y
av
o
id
in
g
g
en
d
e
r
b
i
as.
R
eg
ar
d
in
g
th
e
o
r
etica
l
co
n
tr
ib
u
tio
n
,
t
h
e
s
tu
d
y
f
in
d
in
g
s
s
tr
en
g
th
en
th
e
r
esu
lts
o
f
p
r
ev
io
u
s
r
esear
ch
th
at
PB
L
ca
n
s
ig
n
if
ican
tly
im
p
r
o
v
e
MR,
as
well
a
s
in
itia
l
f
in
d
in
g
s
th
at
MR
with
a
g
en
d
er
p
er
s
p
ec
tiv
e
ca
n
b
e
in
f
lu
e
n
ce
d
th
r
o
u
g
h
PB
L
.
Fin
ally
,
t
h
e
s
tu
d
y
f
i
n
d
in
g
s
p
r
o
v
id
e
a
m
eth
o
d
o
l
o
g
ical
co
n
t
r
ib
u
tio
n
in
ter
m
s
o
f
th
e
av
aila
b
ilit
y
o
f
r
esear
ch
r
esu
lts
th
at
n
o
t
o
n
ly
ass
ess
M
R
q
u
an
titativ
ely
af
ter
im
p
lem
en
t
in
g
PB
L
,
b
u
t a
s
s
ess
MR in
d
e
p
th
an
d
d
escr
ip
tiv
ely
f
r
o
m
a
g
en
d
er
p
e
r
s
p
ec
tiv
e.
4.
CO
NCLU
SI
O
N
T
h
e
s
tu
d
y
r
esu
lts
ca
n
b
e
co
n
clu
d
e
d
q
u
an
titativ
ely
an
d
q
u
alitativ
ely
.
Qu
an
titativ
ely
,
it
ca
n
b
e
co
n
clu
d
e
d
th
at
im
p
lem
e
n
tin
g
p
r
o
b
lem
-
b
ased
lear
n
i
n
g
s
ig
n
if
ican
tly
af
f
ec
ts
s
tu
d
en
ts
’
m
ath
em
atica
l
r
ea
s
o
n
in
g
f
r
o
m
d
if
f
er
e
n
t
g
en
d
er
p
er
s
p
ec
tiv
es.
I
n
th
is
,
th
er
e
is
an
in
cr
ea
s
e
in
m
ath
em
atica
l
r
ea
s
o
n
i
n
g
b
e
f
o
r
e
a
n
d
a
f
ter
ap
p
ly
in
g
p
r
o
b
lem
-
b
ased
lear
n
i
n
g
.
Me
an
wh
ile,
it
is
q
u
alitativ
ely
co
n
clu
d
e
d
th
at
s
tu
d
en
ts
with
d
if
f
er
en
t g
en
d
er
p
er
s
p
ec
tiv
es
in
ter
m
s
o
f
m
a
s
cu
lin
e,
f
em
in
in
e
,
an
d
n
eu
tr
al
h
av
e
d
if
f
e
r
en
t
m
at
h
em
ati
ca
l
r
ea
s
o
n
in
g
af
ter
ap
p
ly
in
g
p
r
o
b
lem
-
b
ased
lea
r
n
in
g
.
Stu
d
en
ts
with
m
ascu
lin
e
g
en
d
er
id
en
tity
ca
n
f
in
d
a
r
elatio
n
s
h
ip
p
atter
n
,
p
r
o
p
o
s
e
a
c
o
n
jectu
r
e,
an
d
co
r
r
ec
tly
v
er
if
y
th
e
s
tatem
en
t’
s
tr
u
th
b
u
t
ar
e
wr
o
n
g
in
g
en
er
aliz
in
g
th
e
s
tatem
en
ts
.
Stu
d
en
ts
with
f
em
in
in
e
g
e
n
d
e
r
id
en
tity
ca
n
k
n
o
w
to
f
in
d
a
r
elatio
n
s
h
ip
p
atter
n
an
d
p
r
o
p
o
s
e
a
co
n
jectu
r
e
b
u
t
ar
e
wr
o
n
g
in
v
er
if
y
in
g
an
d
g
en
er
alizin
g
th
e
s
tatem
en
ts
.
Stu
d
en
ts
with
n
e
u
tr
al
g
e
n
d
er
id
en
tity
ca
n
n
o
t
f
in
d
a
r
elatio
n
s
h
ip
p
atter
n
,
p
r
o
p
o
s
in
g
a
co
n
jectu
r
e
an
d
g
en
er
alizi
n
g
th
e
s
tatem
en
ts
,
b
u
t
ar
e
co
r
r
ec
t
in
v
er
if
y
in
g
th
e
tr
u
th
o
f
t
h
e
s
tatem
en
ts
.
On
th
e
o
th
er
h
a
n
d
,
alth
o
u
g
h
th
e
s
tu
d
y
’
s
r
esu
lts
s
h
o
w
p
o
s
itiv
e
th
in
g
s
,
th
e
s
tu
d
y
was
ca
r
r
ied
o
u
t
with
a
r
elativ
ely
s
m
all
s
am
p
le
o
f
p
ar
ticip
an
ts
.
Ap
ar
t
f
r
o
m
th
at,
th
e
s
tu
d
y
r
esu
lts
s
h
o
w
th
at
th
er
e
ar
e
s
tu
d
en
ts
’
m
at
h
em
atica
l
r
ea
s
o
n
in
g
ac
tiv
ities
in
g
en
er
a
lizin
g
th
e
s
tatem
en
t
th
at
is
s
till
p
r
o
b
lem
atic
o
r
in
ad
eq
u
ate.
T
h
u
s
,
we
r
ec
o
m
m
en
d
th
at
th
e
n
ex
t
s
tu
d
y
c
o
n
d
u
ct
f
u
r
th
er
r
esear
ch
o
n
ass
es
s
in
g
s
tu
d
en
ts
’
m
ath
em
atica
l
r
ea
s
o
n
in
g
b
y
s
t
ill
co
n
s
id
er
in
g
d
if
f
er
en
ce
s
in
g
en
d
er
p
er
s
p
ec
tiv
e
b
u
t
th
r
o
u
g
h
p
r
o
b
lem
-
b
ase
d
lear
n
in
g
i
n
ter
v
en
tio
n
s
in
v
o
lv
in
g
a
b
r
o
a
d
er
r
esear
ch
s
am
p
le,
as
well
as
s
tr
en
g
th
e
n
in
g
g
en
e
r
alizin
g
t
h
e
s
tatem
en
t a
ctiv
ities
th
at
ar
e
m
o
r
e
m
ea
n
in
g
f
u
l a
n
d
c
o
n
s
tr
u
cti
v
e.
ACK
NO
WL
E
DG
E
M
E
NT
S
T
h
e
au
th
o
r
s
wan
t
to
th
an
k
th
e
Un
iv
er
s
itas
Mu
h
am
m
ad
iy
ah
Sid
o
ar
jo
as
th
e
f
u
n
d
er
o
f
r
es
ea
r
ch
an
d
p
u
b
licatio
n
s
,
as
well
as
a
ll
p
ar
ties
in
v
o
lv
ed
in
th
e
s
tu
d
y
,
s
o
th
at
th
e
p
ed
ag
o
g
ical
p
r
ac
tice
o
f
th
is
r
esear
ch
ca
n
b
e
ca
r
r
ied
out
.
RE
F
E
R
E
NC
E
S
[
1
]
H
.
B
r
o
n
k
h
o
r
st
,
G
.
R
o
o
r
d
a
,
C
.
S
u
h
r
e
,
a
n
d
M
.
G
o
e
d
h
a
r
t
,
“
Lo
g
i
c
a
l
r
e
a
so
n
i
n
g
i
n
f
o
r
ma
l
a
n
d
e
v
e
r
y
d
a
y
r
e
a
so
n
i
n
g
t
a
s
k
s,”
I
n
t
e
r
n
a
t
i
o
n
a
l
J
o
u
rn
a
l
o
f
S
c
i
e
n
c
e
a
n
d
M
a
t
h
e
m
a
t
i
c
s
Ed
u
c
a
t
i
o
n
,
v
o
l
.
1
8
,
n
o
.
8
,
p
p
.
1
6
7
3
–
1
6
9
4
,
2
0
2
0
,
d
o
i
:
1
0
.
1
0
0
7
/
s
1
0
7
6
3
-
019
-
1
0
0
3
9
-
8.
[
2
]
A
.
L.
P
a
l
i
n
u
ssa,
J.
S
.
M
o
l
l
e
,
a
n
d
M
.
G
a
s
p
e
r
sz
,
“
R
e
a
l
i
st
i
c
ma
t
h
e
ma
t
i
c
s
e
d
u
c
a
t
i
o
n
:
ma
t
h
e
ma
t
i
c
a
l
r
e
a
so
n
i
n
g
a
n
d
c
o
m
mu
n
i
c
a
t
i
o
n
sk
i
l
l
s
i
n
r
u
r
a
l
c
o
n
t
e
x
t
s,
”
I
n
t
e
r
n
a
t
i
o
n
a
l
J
o
u
r
n
a
l
o
f
E
v
a
l
u
a
t
i
o
n
a
n
d
Re
s
e
a
r
c
h
i
n
E
d
u
c
a
t
i
o
n
(
I
J
ERE)
,
v
o
l
.
1
0
,
n
o
.
2
,
p
p
.
5
2
2
–
5
3
4
,
2
0
2
1
,
d
o
i
:
1
0
.
1
1
5
9
1
/
i
j
e
r
e
.
v
1
0
i
2
.
2
0
6
4
0
.
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
.
13
,
No
.
6
,
Dec
em
b
er
2
0
2
4
:
3
7
6
3
-
3
7
7
4
3772
[
3
]
H
.
R
.
P
.
N
e
g
a
r
a
,
W
a
h
y
u
d
i
n
,
E
.
N
u
r
l
a
e
l
a
h
,
a
n
d
T
.
H
e
r
ma
n
,
“
I
mp
r
o
v
i
n
g
s
t
u
d
e
n
t
s’
m
a
t
h
e
m
a
t
i
c
a
l
r
e
a
so
n
i
n
g
a
b
i
l
i
t
i
e
s
t
h
r
o
u
g
h
s
o
c
i
a
l
c
o
g
n
i
t
i
v
e
l
e
a
r
n
i
n
g
u
si
n
g
G
e
o
G
e
b
r
a
,
”
I
n
t
e
r
n
a
t
i
o
n
a
l
J
o
u
rn
a
l
o
f
Em
e
r
g
i
n
g
T
e
c
h
n
o
l
o
g
i
e
s
i
n
L
e
a
rn
i
n
g
,
v
o
l
.
1
7
,
n
o
.
1
8
,
p
p
.
1
1
8
–
1
3
5
,
2
0
2
2
,
d
o
i
:
1
0
.
3
9
9
1
/
i
j
e
t
.
v
1
7
i
1
8
.
3
2
1
5
1
.
[
4
]
S
.
H
e
r
b
e
r
t
a
n
d
G
.
W
i
l
l
i
a
ms,
“
El
i
c
i
t
i
n
g
mat
h
e
ma
t
i
c
a
l
r
e
a
so
n
i
n
g
d
u
r
i
n
g
e
a
r
l
y
p
r
i
m
a
r
y
p
r
o
b
l
e
m
so
l
v
i
n
g
,
”
M
a
t
h
e
m
a
t
i
c
s
E
d
u
c
a
t
i
o
n
Re
se
a
rc
h
J
o
u
r
n
a
l
,
v
o
l
.
3
5
,
n
o
.
1
,
p
p
.
7
7
–
1
0
3
,
2
0
2
3
,
d
o
i
:
1
0
.
1
0
0
7
/
s
1
3
3
9
4
-
0
2
1
-
0
0
3
7
6
-
9.
[
5
]
E.
S
.
B
o
y
e
a
n
d
D
.
D
.
A
g
y
e
i
,
“
Ef
f
e
c
t
i
v
e
n
e
ss
o
f
p
r
o
b
l
e
m
-
b
a
se
d
l
e
a
r
n
i
n
g
s
t
r
a
t
e
g
y
i
n
i
mp
r
o
v
i
n
g
t
e
a
c
h
i
n
g
a
n
d
l
e
a
r
n
i
n
g
o
f
mat
h
e
m
a
t
i
c
s
f
o
r
p
r
e
-
serv
i
c
e
t
e
a
c
h
e
r
s
i
n
G
h
a
n
a
,
”
S
o
c
i
a
l
S
c
i
e
n
c
e
s
a
n
d
H
u
m
a
n
i
t
i
e
s
O
p
e
n
,
v
o
l
.
7
,
n
o
.
1
,
p
.
1
0
0
4
5
3
,
2
0
2
3
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
ssa
h
o
.
2
0
2
3
.
1
0
0
4
5
3
.
[
6
]
K
.
Li
t
st
e
r
,
B
.
L
.
M
a
c
d
o
n
a
l
d
,
a
n
d
J
.
F
.
S
h
u
mw
a
y
,
“
E
x
p
e
r
i
e
n
c
i
n
g
a
c
t
i
v
e
mat
h
e
m
a
t
i
c
s
l
e
a
r
n
i
n
g
:
me
e
t
i
n
g
t
h
e
e
x
p
e
c
t
a
t
i
o
n
s
f
o
r
t
e
a
c
h
i
n
g
a
n
d
l
e
a
r
n
i
n
g
i
n
m
a
t
h
e
m
a
t
i
c
s
c
l
a
ssr
o
o
ms,
”
M
a
t
h
e
m
a
t
i
c
s
En
t
h
u
si
a
st
,
v
o
l
.
1
7
,
n
o
.
2
–
3
,
p
p
.
6
1
5
–
6
4
0
,
2
0
2
0
,
d
o
i
:
1
0
.
5
4
8
7
0
/
1
5
5
1
-
3
4
4
0
.
1
4
9
9
.
[
7
]
C
.
I
.
G
u
l
t
o
m,
Tr
i
y
a
n
t
o
,
a
n
d
D
.
R
.
S
a
r
i
S
a
p
u
t
r
o
,
“
S
t
u
d
e
n
t
s’
ma
t
h
e
ma
t
i
c
a
l
r
e
a
so
n
i
n
g
s
k
i
l
l
s
i
n
s
o
l
v
i
n
g
m
a
t
h
e
m
a
t
i
c
a
l
p
r
o
b
l
e
ms,
”
J
PI
(
J
u
r
n
a
l
P
e
n
d
i
d
i
k
a
n
I
n
d
o
n
e
si
a
)
,
v
o
l
.
1
1
,
n
o
.
3
,
p
p
.
5
4
2
–
5
5
1
,
2
0
2
2
,
d
o
i
:
1
0
.
2
3
8
8
7
/
j
p
i
u
n
d
i
k
s
h
a
.
v
1
1
i
3
.
4
2
0
7
3
.
[
8
]
O
r
g
a
n
i
sa
t
i
o
n
f
o
r
E
c
o
n
o
mi
c
C
o
o
p
e
r
a
t
i
o
n
a
n
d
D
e
v
e
l
o
p
me
n
t
(
O
E
C
D
)
,
PI
S
A
2
0
1
8
res
u
l
t
s
:
W
h
e
r
e
a
l
l
s
t
u
d
e
n
t
s
c
a
n
s
u
c
c
e
d
,
v
o
l
.
I
I
.
O
EC
D
P
u
b
l
i
s
h
i
n
g
,
P
a
r
i
s
,
2
0
1
9
.
d
o
i
:
1
0
.
1
7
8
7
/
b
5
f
d
1
b
8
f
-
e
n
.
[
9
]
I
.
V
.
M
u
l
l
i
s,
M
.
O
.
M
a
r
t
i
n
,
P
.
F
o
y
,
a
n
d
M
.
H
o
p
p
e
r
,
T
I
MS
S
2
0
1
5
I
n
t
e
rn
a
t
i
o
n
a
l
Re
s
u
l
t
s
i
n
M
a
t
h
e
m
a
t
i
c
s
.
2
0
1
6
.
[
O
n
l
i
n
e
]
.
A
v
a
i
l
a
b
l
e
:
h
t
t
p
:
/
/
t
i
mss
2
0
1
5
.
o
r
g
/
t
i
mss
-
2
0
1
5
/
sc
i
e
n
c
e
/
s
t
u
d
e
n
t
-
a
c
h
i
e
v
e
me
n
t
/
d
i
s
t
r
i
b
u
t
i
o
n
-
of
-
sci
e
n
c
e
-
a
c
h
i
e
v
e
me
n
t
/
[
1
0
]
A
.
La
p
u
z
,
“
I
mp
r
o
v
i
n
g
t
h
e
c
r
i
t
i
c
a
l
t
h
i
n
k
i
n
g
s
k
i
l
l
s
o
f
se
c
o
n
d
a
r
y
sc
h
o
o
l
s
t
u
d
e
n
t
s
u
s
i
n
g
p
r
o
b
l
e
m
-
b
a
se
d
l
e
a
r
n
i
n
g
,
”
I
n
t
e
rn
a
t
i
o
n
a
l
J
o
u
rn
a
l
o
f
Ac
a
d
e
m
i
c
M
u
l
t
i
d
i
sc
i
p
l
i
n
a
r
y
Re
s
e
a
rc
h
,
v
o
l
.
4
,
n
o
.
1
,
p
p
.
1
–
7
,
2
0
1
5
.
[
1
1
]
N
u
r
y
a
mi
,
“
Li
t
e
r
a
t
u
r
e
S
t
u
d
y
o
f
Th
e
i
n
f
l
u
e
n
c
e
o
f
p
r
o
b
l
e
m
-
b
a
se
d
l
e
a
r
n
i
n
g
mo
d
e
l
o
n
s
t
u
d
e
n
t
s’
m
a
t
h
e
m
a
t
i
c
a
l
r
e
a
so
n
i
n
g
a
b
i
l
i
t
y
,
”
J
o
u
rn
a
l
o
f
S
c
i
e
n
t
i
f
i
c
Re
s
e
a
rc
h
,
Ed
u
c
a
t
i
o
n
,
a
n
d
T
e
c
h
n
o
l
o
g
y
(
J
S
RET)
,
v
o
l
.
2
,
n
o
.
1
,
p
p
.
8
4
–
9
3
,
2
0
2
3
,
d
o
i
:
1
0
.
5
8
5
2
6
/
j
sr
e
t
.
v
2
i
1
.
4
7
.
[
1
2
]
M
.
P
.
S
a
r
i
,
S
u
s
a
n
t
o
,
N
.
Y
u
l
i
a
t
i
,
E.
N
.
I
mama
h
,
a
n
d
N
.
I
.
La
i
l
y
,
“
Th
e
st
u
d
e
n
t
s’
m
a
t
h
e
m
a
t
i
c
a
l
r
e
a
so
n
i
n
g
a
b
i
l
i
t
y
b
a
se
d
o
n
p
r
o
b
l
e
m
b
a
s
e
d
l
e
a
r
n
i
n
g
mo
d
e
l
,
”
J
o
u
rn
a
l
o
f
Ph
y
si
c
s:
C
o
n
f
e
r
e
n
c
e
S
e
ri
e
s
,
v
o
l
.
1
5
3
8
,
n
o
.
1
,
2
0
2
0
,
d
o
i
:
1
0
.
1
0
8
8
/
1
7
4
2
-
6
5
9
6
/
1
5
3
8
/
1
/
0
1
2
0
7
8
.
[
1
3
]
A
.
S
y
a
f
r
i
z
a
l
,
E.
S
y
a
h
p
u
t
r
a
,
a
n
d
I
.
I
r
v
a
n
,
“
D
i
f
f
e
r
e
n
c
e
s
i
n
i
n
c
r
e
a
s
i
n
g
t
h
e
a
b
i
l
i
t
y
o
f
r
e
a
so
n
i
n
g
i
n
p
r
o
b
l
e
m
b
a
se
d
l
e
a
r
n
i
n
g
mo
d
e
l
a
n
d
c
o
m
p
u
t
e
r
-
b
a
s
e
d
g
r
o
u
p
i
n
v
e
s
t
i
g
a
t
i
o
n
,
”
M
a
l
i
k
u
ssa
l
e
h
J
o
u
r
n
a
l
o
f
M
a
t
h
e
m
a
t
i
c
s
L
e
a
r
n
i
n
g
(
MJ
ML
)
,
v
o
l
.
3
,
n
o
.
2
,
p
.
5
1
,
2
0
2
0
,
d
o
i
:
1
0
.
2
9
1
0
3
/
mj
m
l
.
v
3
i
2
.
2
4
2
2
.
[
1
4
]
R
.
I
.
A
r
e
n
d
s,
L
e
a
rn
i
n
g
t
o
t
e
a
c
h
,
1
0
t
h
e
d
.
M
c
G
r
a
w
-
H
i
l
l
E
d
u
c
a
t
i
o
n
,
2
0
1
4
.
[
1
5
]
A
n
w
a
r
,
L.
Er
u
U
g
i
,
a
n
d
S
a
r
d
i
n
,
“
T
h
e
e
f
f
e
c
t
o
f
p
r
o
b
l
e
m
b
a
s
e
d
l
e
a
r
n
i
n
g
m
o
d
e
l
a
p
p
l
i
c
a
t
i
o
n
r
e
v
i
e
w
e
d
f
r
o
m
m
a
t
h
e
mat
i
c
a
l
r
e
a
s
o
n
i
n
g
a
b
i
l
i
t
y
,
”
J
o
u
rn
a
l
o
f
P
h
y
si
c
s:
C
o
n
f
e
r
e
n
c
e
S
e
r
i
e
s
,
v
o
l
.
1
4
7
7
,
n
o
.
4
,
2
0
2
0
,
d
o
i
:
1
0
.
1
0
8
8
/
1
7
4
2
-
6
5
9
6
/
1
4
7
7
/
4
/
0
4
2
0
4
0
.
[
1
6
]
S
.
S
u
p
a
r
ma
n
,
A
.
J
u
p
r
i
,
E
.
M
u
s
d
i
,
N
.
A
mal
i
t
a
,
M
.
T
a
mu
r
,
a
n
d
J.
C
h
e
n
,
“
M
a
l
e
a
n
d
f
e
ma
l
e
s
t
u
d
e
n
t
s’
mat
h
e
ma
t
i
c
a
l
r
e
a
s
o
n
i
n
g
sk
i
l
l
s
i
n
so
l
v
i
n
g
t
r
i
g
o
n
o
m
e
t
r
y
p
r
o
b
l
e
ms,
”
Be
t
a
:
J
u
rn
a
l
T
a
d
r
i
s
M
a
t
e
m
a
t
i
k
a
,
v
o
l
.
1
4
,
n
o
.
1
,
p
p
.
3
4
–
5
2
,
M
a
y
2
0
2
1
,
d
o
i
:
1
0
.
2
0
4
1
4
/
b
e
t
a
j
t
m.
v
1
4
i
1
.
4
4
1
.
[
1
7
]
J.
F
a
t
h
a
l
l
a
h
a
n
d
P
.
P
y
a
k
u
r
e
l
,
“
A
d
d
r
e
ssi
n
g
g
e
n
d
e
r
i
n
e
n
e
r
g
y
s
t
u
d
i
e
s
,
”
E
n
e
rg
y
R
e
se
a
rc
h
a
n
d
S
o
c
i
a
l
S
c
i
e
n
c
e
,
v
o
l
.
6
5
,
p
.
1
0
1
4
6
1
,
2
0
2
0
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
e
r
ss.
2
0
2
0
.
1
0
1
4
6
1
.
[
1
8
]
A
.
Li
n
d
q
v
i
s
t
,
M
.
G
.
S
e
n
d
é
n
,
a
n
d
E.
A
.
R
e
n
st
r
ö
m,
“
W
h
a
t
i
s
g
e
n
d
e
r
,
a
n
y
w
a
y
:
a
r
e
v
i
e
w
o
f
t
h
e
o
p
t
i
o
n
s
f
o
r
o
p
e
r
a
t
i
o
n
a
l
i
si
n
g
g
e
n
d
e
r
,
”
Psy
c
h
o
l
o
g
y
a
n
d
S
e
x
u
a
l
i
t
y
,
v
o
l
.
1
2
,
n
o
.
4
,
p
p
.
3
3
2
–
3
4
4
,
2
0
2
1
,
d
o
i
:
1
0
.
1
0
8
0
/
1
9
4
1
9
8
9
9
.
2
0
2
0
.
1
7
2
9
8
4
4
.
[
1
9
]
B
.
M
.
C
a
s
e
y
a
n
d
C
.
M
.
G
a
n
l
e
y
,
“
A
n
e
x
a
m
i
n
a
t
i
o
n
o
f
g
e
n
d
e
r
d
i
f
f
e
r
e
n
c
e
s
i
n
s
p
a
t
i
a
l
s
k
i
l
l
s
a
n
d
m
a
t
h
a
t
t
i
t
u
d
e
s
i
n
r
e
l
a
t
i
o
n
t
o
m
a
t
h
e
m
a
t
i
c
s
s
u
c
c
e
s
s
:
a
b
i
o
-
p
s
y
c
h
o
-
s
o
c
i
a
l
m
o
d
e
l
,
”
D
e
v
e
l
o
p
m
e
n
t
a
l
R
e
v
i
e
w
,
v
o
l
.
6
0
,
n
o
.
A
p
r
i
l
,
p
.
1
0
0
9
6
3
,
2
0
2
1
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
d
r
.
2
0
2
1
.
1
0
0
9
6
3
.
[
2
0
]
A
.
O
.
S
a
k
a
,
“
M
a
t
h
e
ma
t
i
c
s
f
o
r
s
u
s
t
a
i
n
a
b
l
e
d
e
v
e
l
o
p
me
n
t
:
i
m
p
r
o
v
i
n
g
s
t
u
d
e
n
t
s’
l
e
a
r
n
i
n
g
t
h
r
o
u
g
h
r
i
c
h
ma
t
h
e
ma
t
i
c
a
l
t
a
sk
s
st
r
a
t
e
g
y
,
”
J
o
u
rn
a
l
P
l
u
s
E
d
u
c
a
t
i
o
n
,
v
o
l
.
3
3
,
n
o
.
S
p
e
c
i
a
l
I
ssu
e
,
p
p
.
3
3
8
–
3
5
8
,
2
0
2
3
,
d
o
i
:
1
0
.
2
4
2
5
0
/
j
p
e
/
si
/
2
0
2
3
/
a
o
s/
.
[
2
1
]
D
.
S
u
r
y
a
d
a
r
m
a
,
“
G
e
n
d
e
r
d
i
f
f
e
r
e
n
c
e
s
i
n
n
u
mer
a
c
y
i
n
I
n
d
o
n
e
s
i
a
:
e
v
i
d
e
n
c
e
f
r
o
m
a
l
o
n
g
i
t
u
d
i
n
a
l
d
a
t
a
set
,
”
E
d
u
c
a
t
i
o
n
E
c
o
n
o
m
i
c
s
,
v
o
l
.
2
3
,
n
o
.
2
,
p
p
.
1
8
0
–
1
9
8
,
2
0
1
5
,
d
o
i
:
1
0
.
1
0
8
0
/
0
9
6
4
5
2
9
2
.
2
0
1
3
.
8
1
9
4
1
5
.
[
2
2
]
R
.
K
u
s
h
a
r
y
a
d
i
a
n
d
D
.
Ju
a
n
d
i
,
“
A
n
a
l
y
si
s
o
f
st
u
d
e
n
t
s’
m
a
t
h
e
m
a
t
i
c
a
l
r
e
a
so
n
i
n
g
b
e
t
w
e
e
n
d
i
f
f
e
r
e
n
t
g
e
n
d
e
r
s,”
U
n
i
o
n
:
J
u
r
n
a
l
I
l
m
i
a
h
Pe
n
d
i
d
i
k
a
n
M
a
t
e
m
a
t
i
k
a
,
v
o
l
.
1
1
,
n
o
.
2
,
p
p
.
3
3
9
–
3
4
7
,
2
0
2
3
,
d
o
i
:
1
0
.
3
0
7
3
8
/
u
n
i
o
n
.
v
1
1
i
2
.
1
4
9
3
9
.
[
2
3
]
S
.
I
v
a
n
,
O
.
D
a
n
i
e
l
a
,
a
n
d
B
.
D
.
J
a
r
o
s
l
a
v
a
,
“
S
e
x
d
i
f
f
e
r
e
n
c
e
s
m
a
t
t
e
r
:
ma
l
e
s
a
n
d
f
e
m
a
l
e
s
a
r
e
e
q
u
a
l
b
u
t
n
o
t
t
h
e
s
a
me,
”
P
h
y
s
i
o
l
o
g
y
a
n
d
Be
h
a
v
i
o
r
,
v
o
l
.
2
5
9
,
p
.
1
1
4
0
3
8
,
2
0
2
3
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
p
h
y
s
b
e
h
.
2
0
2
2
.
1
1
4
0
3
8
.
[
2
4
]
L.
A
.
Le
y
v
a
,
“
U
n
p
a
c
k
i
n
g
t
h
e
ma
l
e
su
p
e
r
i
o
r
i
t
y
m
y
t
h
a
n
d
m
a
sc
u
l
i
n
i
z
a
t
i
o
n
o
f
mat
h
e
mat
i
c
s
a
t
t
h
e
i
n
t
e
r
se
c
t
i
o
n
s:
a
r
e
v
i
e
w
o
f
r
e
se
a
r
c
h
o
n
g
e
n
d
e
r
i
n
ma
t
h
e
ma
t
i
c
s
e
d
u
c
a
t
i
o
n
,
”
J
o
u
r
n
a
l
f
o
r
R
e
se
a
rc
h
i
n
M
a
t
h
e
m
a
t
i
c
s
Ed
u
c
a
t
i
o
n
,
v
o
l
.
4
8
,
n
o
.
4
,
p
p
.
3
9
7
–
4
3
3
,
2
0
1
7
,
d
o
i
:
1
0
.
5
9
5
1
/
j
r
e
sema
t
h
e
d
u
c
.
4
8
.
4
.
0
3
9
7
.
[
2
5
]
K
.
C
.
P
y
f
e
r
,
“
Y
o
u
d
o
ma
t
h
l
i
k
e
a
g
i
r
l
:
h
o
w
w
o
m
e
n
r
e
a
s
o
n
ma
t
h
e
ma
t
i
c
a
l
l
y
o
u
t
s
i
d
e
o
f
f
o
r
ma
l
a
n
d
sc
h
o
o
l
ma
t
h
e
mat
i
c
s
c
o
n
t
e
x
t
s
,”
Th
e
s
e
s
a
n
d
D
i
ssert
a
t
i
o
n
s
,
B
i
r
g
h
a
m
Y
o
u
n
g
U
n
i
v
e
r
si
t
y
,
2
0
2
1
.
[
2
6
]
R
.
S
m
i
t
,
K
.
H
e
ss,
A
.
Ta
r
a
s
,
P
.
B
a
c
h
man
n
,
a
n
d
H
.
D
o
b
e
r
,
“
T
h
e
r
o
l
e
o
f
i
n
t
e
r
a
c
t
i
v
e
d
i
a
l
o
g
u
e
i
n
st
u
d
e
n
t
s’
l
e
a
r
n
i
n
g
o
f
m
a
t
h
e
m
a
t
i
c
a
l
r
e
a
so
n
i
n
g
:
a
q
u
a
n
t
i
t
a
t
i
v
e
m
u
l
t
i
-
me
t
h
o
d
a
n
a
l
y
s
i
s
o
f
f
e
e
d
b
a
c
k
e
p
i
s
o
d
e
s,
”
L
e
a
rn
i
n
g
a
n
d
I
n
st
r
u
c
t
i
o
n
,
v
o
l
.
8
6
,
p
.
1
0
1
7
7
7
,
2
0
2
3
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
l
e
a
r
n
i
n
st
r
u
c
.
2
0
2
3
.
1
0
1
7
7
7
.
[
2
7
]
E.
Y
u
r
t
,
“
T
h
e
me
d
i
a
t
i
n
g
r
o
l
e
o
f
m
e
t
a
c
o
g
n
i
t
i
v
e
st
r
a
t
e
g
i
e
s
i
n
t
h
e
r
e
l
a
t
i
o
n
sh
i
p
b
e
t
w
e
e
n
g
e
n
d
e
r
a
n
d
ma
t
h
e
m
a
t
i
c
a
l
r
e
a
so
n
i
n
g
p
e
r
f
o
r
m
a
n
c
e
,
”
Psy
c
h
o
-
Ed
u
c
a
t
i
o
n
a
l
R
e
se
a
rc
h
R
e
v
i
e
w
s
,
v
o
l
.
1
1
,
n
o
.
2
,
p
p
.
9
8
–
1
2
0
,
2
0
2
2
,
d
o
i
:
1
0
.
5
2
9
6
3
/
p
e
r
r
_
b
i
r
u
n
i
_
v
1
1
.
n
2
.
0
7
.
[
2
8
]
G
.
X
i
e
a
n
d
X
.
L
i
u
,
“
G
e
n
d
e
r
i
n
ma
t
h
e
m
a
t
i
c
s
:
h
o
w
g
e
n
d
e
r
r
o
l
e
p
e
r
c
e
p
t
i
o
n
i
n
f
l
u
e
n
c
e
s
m
a
t
h
e
m
a
t
i
c
a
l
c
a
p
a
b
i
l
i
t
y
i
n
j
u
n
i
o
r
h
i
g
h
sch
o
o
l
,
”
J
o
u
rn
a
l
o
f
C
h
i
n
e
s
e
S
o
c
i
o
l
o
g
y
,
v
o
l
.
1
0
,
n
o
.
1
,
2
0
2
3
,
d
o
i
:
1
0
.
1
1
8
6
/
s
4
0
7
1
1
-
0
2
3
-
0
0
1
8
8
-
3.
[
2
9
]
J.
W
.
C
r
e
sw
e
l
l
a
n
d
T.
C
.
G
u
e
t
t
e
r
ma
n
,
E
d
u
c
a
t
i
o
n
a
l
res
e
a
rc
h
:
p
l
a
n
n
i
n
g
,
c
o
n
d
u
c
t
i
n
g
,
a
n
d
e
v
a
l
u
a
t
i
n
g
q
u
a
n
t
i
t
a
t
i
v
e
a
n
d
q
u
a
l
i
t
a
t
i
v
e
rese
a
rc
h
,
6
t
h
e
d
.
N
e
w
Jerse
y
:
P
e
a
r
so
n
,
2
0
1
8
.
[
3
0
]
J.
S
c
h
o
o
n
e
n
b
o
o
m
a
n
d
R
.
B
.
Jo
h
n
s
o
n
,
“
H
o
w
t
o
c
o
n
s
t
r
u
c
t
a
mi
x
e
d
me
t
h
o
d
s
r
e
se
a
r
c
h
d
e
si
g
n
,
”
K
Z
f
S
S
K
ö
l
n
e
r
Z
e
i
t
sc
h
ri
f
t
f
ü
r
S
o
z
i
o
l
o
g
i
e
u
n
d
S
o
z
i
a
l
p
syc
h
o
l
o
g
i
e
,
v
o
l
.
6
9
,
n
o
.
S
2
,
p
p
.
1
0
7
–
1
3
1
,
2
0
1
7
,
d
o
i
:
1
0
.
1
0
0
7
/
s
1
1
5
7
7
-
0
1
7
-
0
4
5
4
-
1.
[
3
1
]
L.
C
o
h
e
n
,
L.
M
a
n
i
o
n
,
a
n
d
K
.
M
o
r
r
i
so
n
,
Re
se
a
r
c
h
m
e
t
h
o
d
s
i
n
e
d
u
c
a
t
i
o
n
,
8
t
h
Ed
i
.
N
e
w
Y
o
r
k
:
R
o
u
t
l
e
d
g
e
,
2
0
1
8
.
[
3
2
]
M
.
G
e
l
d
e
n
h
u
y
s
a
n
d
A
.
B
o
s
c
h
,
“
A
r
a
s
c
h
a
d
a
p
t
e
d
v
e
r
si
o
n
o
f
t
h
e
3
0
-
i
t
e
m
B
e
m
S
e
x
R
o
l
e
I
n
v
e
n
t
o
r
y
(
B
S
R
I
)
,
”
J
o
u
r
n
a
l
o
f
Pe
rso
n
a
l
i
t
y
Assessm
e
n
t
,
v
o
l
.
1
0
2
,
n
o
.
3
,
p
p
.
4
2
8
–
4
3
9
,
2
0
2
0
,
d
o
i
:
1
0
.
1
0
8
0
/
0
0
2
2
3
8
9
1
.
2
0
1
8
.
1
5
2
7
3
4
3
.
[
3
3
]
S
.
A
f
i
f
a
h
,
A
.
M
u
d
z
a
k
i
r
,
a
n
d
A
.
B
.
D
.
N
a
n
d
i
y
a
n
t
o
,
“
H
o
w
t
o
c
a
l
c
u
l
a
t
e
p
a
i
r
e
d
s
a
m
p
l
e
t
-
t
e
s
t
u
s
i
n
g
SPSS
s
o
f
t
w
a
r
e
:
f
r
o
m
s
t
e
p
-
by
-
s
t
e
p
p
r
o
c
e
s
s
i
n
g
f
o
r
u
s
e
r
s
t
o
t
h
e
p
r
a
c
t
i
c
a
l
e
x
a
m
p
l
e
s
i
n
t
h
e
a
n
a
l
y
s
i
s
o
f
t
h
e
e
f
f
e
c
t
o
f
a
p
p
l
i
c
a
t
i
o
n
a
n
t
i
-
f
i
r
e
b
a
m
b
o
o
t
e
a
c
h
i
n
g
m
a
t
e
r
i
a
l
s
o
n
s
t
u
d
e
n
t
l
e
a
r
n
i
n
g
o
u
t
c
o
m
e
s
,
”
I
n
d
o
n
e
s
i
a
n
J
o
u
r
n
a
l
o
f
T
e
a
c
h
i
n
g
i
n
S
c
i
e
n
c
e
,
v
o
l
.
2
,
n
o
.
1
,
p
p
.
8
1
–
9
2
,
2
0
2
2
,
d
o
i
:
1
0
.
1
7
5
0
9
/
i
j
o
t
i
s
.
v
2
i
1
.
4
5
8
9
5
.
[
3
4
]
N
.
M
a
n
d
a
sar
i
,
“
P
r
o
b
l
e
m
-
b
a
s
e
d
l
e
a
r
n
i
n
g
mo
d
e
l
t
o
i
m
p
r
o
v
e
m
a
t
h
e
mat
i
c
a
l
r
e
a
s
o
n
i
n
g
a
b
i
l
i
t
y
,
”
J
o
u
r
n
a
l
o
f
P
h
y
s
i
c
s:
C
o
n
f
e
r
e
n
c
e
S
e
r
i
e
s
,
v
o
l
.
1
7
3
1
,
n
o
.
1
,
2
0
2
1
,
d
o
i
:
1
0
.
1
0
8
8
/
1
7
4
2
-
6
5
9
6
/
1
7
3
1
/
1
/
0
1
2
0
4
1
.
[
3
5
]
R
.
M
a
r
a
sa
b
e
ss
y
,
“
S
t
u
d
y
o
f
ma
t
h
e
ma
t
i
c
a
l
r
e
a
s
o
n
i
n
g
a
b
i
l
i
t
y
f
o
r
m
a
t
h
e
m
a
t
i
c
s
l
e
a
r
n
i
n
g
i
n
sc
h
o
o
l
s:
a
l
i
t
e
r
a
t
u
r
e
r
e
v
i
e
w
,
”
I
n
d
o
n
e
si
a
n
J
o
u
rn
a
l
o
f
T
e
a
c
h
i
n
g
i
n
S
c
i
e
n
c
e
,
v
o
l
.
1
,
n
o
.
2
,
p
p
.
7
9
–
9
0
,
2
0
2
1
,
d
o
i
:
1
0
.
1
7
5
0
9
/
i
j
o
t
i
s.
v
1
i
2
.
3
7
9
5
0
.
[
3
6
]
Y
.
H
.
Z
i
l
d
a
,
“
I
mp
r
o
v
i
n
g
l
e
a
r
n
i
n
g
a
c
t
i
v
i
t
i
e
s
a
n
d
m
a
t
h
e
m
a
t
i
c
a
l
r
e
a
so
n
i
n
g
s
k
i
l
l
s
f
o
r
c
l
a
ss
x
st
u
d
e
n
t
s
a
p
p
l
y
i
n
g
p
r
o
b
l
e
m
-
b
a
s
e
d
l
e
a
r
n
i
n
g
,
”
ED
U
C
ATI
O
:
J
u
r
n
a
l
Pe
n
d
i
d
i
k
a
n
I
n
d
o
n
e
s
i
a
,
v
o
l
.
8
,
n
o
.
1
,
p
p
.
7
9
–
8
6
,
2
0
2
2
,
d
o
i
:
1
0
.
2
9
2
1
0
/
1
2
0
2
2
2
2
2
1
9
.
Evaluation Warning : The document was created with Spire.PDF for Python.