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E
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11
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20
22
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t
en
d
to
b
e
p
ass
iv
e
in
clas
s
r
o
o
m
lear
n
in
g
ac
tiv
ities
.
W
h
er
ea
s
,
s
o
f
ar
class
ical
le
ar
n
in
g
h
as
b
ee
n
g
iv
e
n
in
m
a
th
em
atics
class
,
th
e
teac
h
er
d
u
r
in
g
t
h
e
lear
n
in
g
p
r
o
ce
s
s
co
n
s
id
er
s
th
e
co
n
d
itio
n
o
f
th
e
s
tu
d
e
n
ts
to
b
e
in
th
e
s
a
m
e
co
n
d
itio
n
,
b
o
th
in
ter
m
s
o
f
in
itial
ab
ilit
ies,
l
ea
r
n
in
g
s
ty
les,
tem
p
er
am
e
n
t
an
d
th
e
ec
o
n
o
m
ic
b
ac
k
g
r
o
u
n
d
o
f
th
e
s
tu
d
e
n
ts
'
f
am
ilies
.
As
we
k
n
o
w
th
at
m
ath
em
atics
class
co
m
es
f
r
o
m
h
eter
o
g
en
e
o
u
s
s
tu
d
en
ts
[
1
9
]
,
[
2
0
]
.
I
n
co
n
n
ec
tio
n
with
th
is
co
n
d
itio
n
,
it
is
n
ec
e
s
s
ar
y
to
u
n
d
er
s
tan
d
th
e
teac
h
er
'
s
u
n
d
er
s
tan
d
in
g
o
f
th
e
s
tr
at
eg
ies
th
at
m
u
s
t
b
e
u
s
ed
in
m
ath
em
atics lea
r
n
in
g
.
Hen
ce
,
s
tu
d
en
ts
ca
n
u
n
d
er
s
tan
d
m
ath
em
atica
l c
o
n
ce
p
ts
m
ea
n
in
g
f
u
lly
.
Hu
m
an
p
er
s
o
n
ality
is
d
iv
id
ed
in
to
two
p
er
s
o
n
ality
ty
p
es
b
ased
o
n
th
e
attitu
d
e
o
f
th
e
h
u
m
an
s
o
u
l
,
th
ey
ar
e
ex
tr
o
v
er
ted
an
d
in
tr
o
v
er
ted
h
u
m
a
n
s
[
2
2
]
,
[
2
3
]
.
T
h
is
h
u
m
an
p
e
r
s
o
n
ality
is
a
p
er
s
o
n
'
s
r
ea
ctio
n
to
s
o
m
eth
in
g
,
b
u
t if
th
ese
r
ea
ctio
n
s
ar
e
ca
r
r
ied
o
u
t c
o
n
tin
u
o
u
s
ly
it will tu
r
n
in
to
h
ab
its
[
2
4
]
–
[
2
7
]
.
An
e
x
tr
o
v
e
r
t is
an
attitu
d
e
th
at
d
ir
ec
ts
p
s
y
ch
ic
en
er
g
y
o
u
twar
d
s
o
th
at
a
p
er
s
o
n
is
o
r
ien
ted
to
war
d
s
s
o
m
eth
in
g
o
b
jectiv
e,
an
d
awa
y
f
r
o
m
th
e
s
u
b
jectiv
e
[
2
3
]
,
[
2
8
]
–
[
3
1
]
.
E
x
tr
o
v
er
te
d
p
e
o
p
l
e
ar
e
m
o
r
e
i
n
f
lu
en
ce
d
b
y
th
ei
r
s
u
r
r
o
u
n
d
in
g
s
th
an
th
eir
in
n
e
r
wo
r
ld
[
2
6
]
,
[
3
2
]
.
E
x
tr
o
v
er
ts
a
r
e
ch
a
r
ac
ter
ized
b
y
an
av
e
r
s
io
n
to
ac
tiv
ities
th
at
t
ak
e
a
l
o
n
g
tim
e
a
n
d
tak
e
ac
tio
n
r
ath
e
r
th
an
c
o
n
tem
p
late.
R
ea
lizin
g
th
e
d
if
f
e
r
en
t
c
o
n
d
iti
o
n
s
f
o
r
ea
ch
s
tu
d
en
t,
th
e
teac
h
er
ca
n
ass
is
t
s
tu
d
en
ts
in
lear
n
in
g
an
d
th
e
teac
h
er
ca
n
ad
ju
s
t
th
e
n
ee
d
s
d
esire
d
b
y
s
tu
d
e
n
ts
.
On
e
o
f
th
e
ch
ar
ac
ter
is
tics
o
f
s
tu
d
en
ts
is
s
tu
d
en
ts
with
ex
tr
o
v
er
te
d
p
e
r
s
o
n
alities
[
2
3
]
.
Stu
d
en
ts
in
th
is
ca
teg
o
r
y
te
n
d
to
o
p
e
n
th
e
m
s
elv
es
to
o
m
u
ch
to
th
e
o
u
ts
id
e
wo
r
ld
wh
ich
is
in
f
lu
en
ce
d
b
y
th
eir
o
b
jectiv
e
wo
r
ld
[
2
9
]
–
[
3
1
]
,
ten
d
to
lik
e
to
in
te
r
ac
t
an
d
s
o
cialize
[
2
6
]
,
[
3
3
]
.
Stu
d
en
ts
with
ex
tr
o
v
er
ted
p
e
r
s
o
n
alities
wil
l
b
e
b
etter
at
l
ea
r
n
in
g
if
g
iv
en
g
u
id
an
ce
an
d
d
ir
ec
tio
n
in
th
e
lear
n
in
g
p
r
o
ce
s
s
[
3
4
]
.
T
h
er
e
f
o
r
e,
ex
tr
o
v
e
r
t
s
tu
d
en
ts
s
h
o
u
ld
g
et
s
p
ec
ial
atten
tio
n
s
o
th
at
th
eir
tem
p
er
am
en
t
o
r
p
er
s
o
n
ality
ca
n
b
e
u
s
ed
as
an
ad
v
an
tag
e
[
2
8
]
,
[
3
5
]
,
[
3
6
]
s
o
th
at
th
ey
ca
n
b
e
d
ev
el
o
p
ed
b
etter
.
T
o
f
u
lf
ill
th
e
n
ee
d
s
o
f
ex
tr
o
v
er
ted
s
tu
d
e
n
ts
in
lear
n
in
g
m
ath
e
m
atics,
o
n
e
o
f
th
e
lear
n
in
g
m
eth
o
d
s
th
at
ca
n
b
e
u
s
ed
is
th
e
tu
to
r
ial
m
eth
o
d
.
T
h
e
tu
to
r
ial
m
eth
o
d
is
lear
n
in
g
in
th
e
f
o
r
m
o
f
ac
ad
em
ic
tu
to
r
in
g
b
y
tu
to
r
s
to
lear
n
in
g
citiz
en
s
to
h
elp
s
m
o
o
th
th
e
p
r
o
ce
s
s
o
f
in
d
e
p
e
n
d
en
t
lear
n
in
g
f
o
r
citizen
s
to
l
ea
r
n
in
d
i
v
id
u
ally
o
r
i
n
g
r
o
u
p
s
r
elate
d
to
teac
h
in
g
m
ater
ials
[
3
7
]
–
[
3
9
]
.
I
n
th
e
t
u
to
r
ial
m
eth
o
d
,
s
tu
d
en
ts
g
et
in
d
iv
id
u
al
lear
n
i
n
g
s
er
v
ices
s
o
th
at
th
e
s
p
ec
if
ic
p
r
o
b
lem
s
th
e
y
f
ac
e
ca
n
b
e
s
er
v
ed
s
p
ec
if
ically
as
well
[
4
0
]
.
Als
o
,
s
tu
d
en
ts
ca
n
lear
n
at
a
s
p
ee
d
th
at
s
u
its
th
eir
ab
ilit
ies wit
h
o
u
t h
av
in
g
to
b
e
i
n
f
lu
en
ce
d
b
y
t
h
e
lear
n
in
g
s
p
ee
d
o
f
o
th
er
s
tu
d
e
n
ts
[
4
1
]
–
[
4
3
]
.
B
ased
o
n
th
ese
co
n
d
itio
n
s
,
it
is
n
ec
ess
ar
y
to
tak
e
ac
tio
n
to
o
p
tim
ize
s
tu
d
e
n
t
lear
n
i
n
g
o
u
tco
m
es
th
r
o
u
g
h
ap
p
r
o
p
r
iate
lear
n
in
g
m
eth
o
d
s
.
T
h
e
r
ef
o
r
e,
it
is
n
ec
e
s
s
ar
y
to
r
esear
ch
to
s
ee
th
e
in
cr
ea
s
e
in
lear
n
in
g
o
u
tco
m
es
o
f
s
tu
d
en
ts
with
ex
t
r
o
v
er
t
i
n
m
ath
e
m
atics
u
s
in
g
a
p
p
r
o
p
r
iate
lear
n
i
n
g
m
eth
o
d
s
.
I
n
co
n
n
ec
tio
n
with
th
is
co
n
d
itio
n
,
th
e
p
u
r
p
o
s
e
o
f
th
is
s
tu
d
y
is
to
im
p
r
o
v
e
th
e
lea
r
n
in
g
ac
h
iev
em
en
t
o
f
ex
tr
o
v
er
t
s
tu
d
en
ts
b
y
u
s
in
g
th
e
tu
to
r
ial
m
eth
o
d
o
n
alg
eb
r
aic
o
p
er
atio
n
s
m
ater
ial.
So
th
at
th
e
b
asic
co
n
tr
ib
u
tio
n
o
f
th
e
r
esear
ch
is
th
at
tu
to
r
ial
lear
n
in
g
ca
n
b
e
u
s
ed
as
an
alter
n
ativ
e
lear
n
in
g
f
o
r
th
e
r
est
o
f
th
e
ex
tr
o
v
er
ts
,
esp
ec
ially
in
alg
eb
r
aic
m
ater
ial.
Alg
eb
r
a
was
ch
o
s
en
b
ec
au
s
e
alg
eb
r
a
is
o
n
e
o
f
th
e
b
r
an
ch
es o
f
m
ath
e
m
atics th
at
i
s
im
p
o
r
tan
t to
lear
n
[
4
4
]
.
Als
o
,
al
g
eb
r
a
is
u
s
ed
to
c
h
an
g
e
p
r
o
b
lem
s
in
ev
er
y
d
ay
li
f
e
in
to
m
ath
em
atica
l sen
ten
ce
s
[
4
5
]
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
T
h
is
was
s
in
g
le
s
u
b
ject
r
esear
ch
with
s
in
g
le
ca
s
e
ex
p
er
im
e
n
t
d
esig
n
.
I
t
was
ca
r
r
ied
o
u
t
o
n
a
s
in
g
le
s
u
b
ject
to
k
n
o
w
th
e
m
ag
n
itu
d
e
o
f
th
e
ef
f
ec
t
o
f
r
ep
ea
ted
tr
e
atm
en
t
o
n
th
e
b
eh
a
v
io
r
th
at
y
o
u
wan
t
to
ch
an
g
e
with
in
a
ce
r
tain
tim
e
[
4
6
]
–
[
4
8
]
.
T
h
is
r
esear
ch
u
s
ed
A
-
B
d
esig
n
;
w
h
er
e
A
is
th
e
b
ase
lin
e
co
n
d
itio
n
,
i.e
.
,
th
e
co
n
d
itio
n
wh
e
n
th
e
tr
ea
tm
en
t
h
as
n
o
t
b
ee
n
g
iv
en
o
r
th
e
in
itial
co
n
d
itio
n
.
C
o
n
d
itio
n
B
is
an
in
ter
v
en
tio
n
co
n
d
itio
n
,
th
at
is
,
th
e
co
n
d
itio
n
wh
en
an
in
ter
v
en
tio
n
h
as
b
ee
n
g
iv
en
a
n
d
th
e
tar
g
et
b
e
h
av
io
r
is
m
ea
s
u
r
ed
u
n
d
er
th
at
c
o
n
d
itio
n
.
T
h
e
m
e
asu
r
em
en
t
o
f
A
-
B
d
esig
n
is
d
o
n
e
in
a
ce
r
tain
p
er
io
d
f
o
r
e
x
am
p
le
wee
k
ly
,
p
e
r
d
ay
,
h
o
u
r
ly
,
an
d
th
e
co
m
p
ar
i
s
o
n
is
n
o
t
d
o
n
e
b
etwe
en
in
d
iv
id
u
als
b
u
t
co
m
p
ar
e
d
to
th
e
s
am
e
s
u
b
ject
u
n
d
er
d
if
f
er
en
t c
o
n
d
itio
n
s
[
4
7
]
.
T
h
e
r
esear
ch
s
u
b
jects
wer
e
s
elec
ted
u
s
in
g
a
p
u
r
p
o
s
iv
e
tech
n
iq
u
e,
m
ea
n
in
g
th
at
t
h
e
r
esear
c
h
s
u
b
jects
h
ad
to
b
e
ad
j
u
s
ted
to
th
e
c
h
a
r
ac
ter
is
tics
o
f
th
e
s
tu
d
y
,
t
h
e
p
u
r
p
o
s
e
o
f
th
e
s
tu
d
y
,
an
d
t
h
e
s
u
b
jectiv
ity
o
f
th
e
r
esear
ch
er
s
to
s
elec
t
s
u
b
jects
with
o
u
t
leav
in
g
th
e
r
esear
ch
er
s
'
co
d
e
o
f
eth
ics
[
4
9
]
,
[
5
0
]
.
T
h
e
r
esear
ch
s
u
b
je
ct
u
s
ed
was
a
s
tu
d
en
t
with
an
e
x
tr
o
v
er
t.
Fu
r
th
er
m
o
r
e,
ac
c
o
r
d
in
g
to
th
e
r
esear
ch
c
o
d
e
o
f
et
h
ics,
th
is
s
u
b
ject
is
r
ef
er
r
ed
t
o
as
E
.
T
o
f
in
d
o
u
t
th
at
s
tu
d
en
ts
h
av
e
ex
t
r
o
v
er
te
d
p
er
s
o
n
alities
,
th
e
r
esear
ch
e
r
s
g
av
e
p
er
s
o
n
ality
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
Lea
r
n
in
g
a
ch
ieve
men
t
o
f e
xtro
ve
r
ted
s
tu
d
en
ts
in
a
lg
eb
r
a
ic
o
p
era
tio
n
s
b
y
tu
to
r
ia
l
… (
S
r
i A
d
i Wid
o
d
o
)
101
test
s
wh
ich
wer
e
tak
en
f
r
o
m
p
r
ef
er
e
n
ce
s
o
f
ex
tr
o
v
er
t
a
n
d
in
tr
o
v
er
ted
o
n
th
e
Keir
s
ey
T
em
p
er
am
en
t
So
r
ter
(
KT
S)
[
5
1
]
,
[
5
2
]
.
T
h
is
KT
S
o
r
ig
in
ally
co
n
tain
ed
7
0
item
s
[
5
3
]
,
b
u
t
in
th
is
s
tu
d
y
,
o
n
ly
ex
t
r
o
v
er
t
a
n
d
in
t
r
o
v
er
t
in
d
icato
r
s
wer
e
tak
en
s
o
th
at
o
n
ly
1
0
item
s
.
Data
co
llectio
n
tech
n
iq
u
es
in
t
h
is
s
tu
d
y
wer
e
ca
r
r
ie
d
o
u
t
b
y
u
s
in
g
o
b
s
er
v
atio
n
an
d
test
s
.
Ob
s
er
v
atio
n
in
th
is
s
tu
d
y
is
u
s
ed
to
o
b
s
er
v
e
an
d
r
ec
o
r
d
all
th
e
b
eh
av
io
r
o
f
th
e
s
u
b
je
ct
d
u
r
in
g
th
e
s
tu
d
y
.
Ob
s
er
v
atio
n
s
wer
e
m
ad
e
b
y
d
escr
ib
i
n
g
th
e
in
d
ica
to
r
s
th
e
r
esear
ch
er
wan
ted
to
ac
h
iev
e.
Ob
s
er
v
atio
n
in
d
icato
r
s
ar
e
:
i
)
th
e
s
u
b
ject
is
en
th
u
s
iast
ic
d
u
r
in
g
lear
n
in
g
;
ii
)
th
e
s
u
b
ject
u
n
d
er
s
tan
d
s
th
e
in
s
tr
u
ctio
n
s
an
d
m
ater
ia
l
p
r
esen
ted
b
y
th
e
r
esear
ch
er
;
an
d
iii
)
th
e
s
u
b
ject
ca
n
wo
r
k
o
n
t
h
e
q
u
esti
o
n
s
g
i
v
en
.
T
h
er
e
ar
e
two
test
s
u
s
ed
in
th
is
s
tu
d
y
,
n
am
ely
KT
S
an
d
lear
n
in
g
ac
h
iev
em
en
t
test
s
.
KT
S
is
u
s
ed
to
d
eter
m
in
e
th
e
r
esear
ch
s
u
b
jec
t
is
in
an
ex
tr
o
v
er
ted
co
n
d
itio
n
.
As
p
r
e
v
io
u
s
ly
w
r
itten
,
to
f
i
n
d
o
u
t
ex
t
r
o
v
er
te
d
s
tu
d
en
ts
,
1
0
item
s
in
clu
d
ed
in
th
e
i
n
tr
o
v
e
r
t
an
d
e
x
tr
o
v
er
t
p
r
ef
er
en
ce
s
in
KT
S
wer
e
u
s
ed
[
5
1
]
–
[
5
3
]
.
L
ea
r
n
in
g
ac
h
iev
em
en
t
test
is
u
s
ed
b
y
r
esear
ch
er
s
to
d
eter
m
i
n
e
th
e
ab
ilit
y
o
f
ex
t
r
o
v
er
te
d
s
tu
d
en
t
s
in
u
n
d
er
s
tan
d
in
g
alg
eb
r
aic
o
p
e
r
atio
n
s
.
T
h
e
test
u
s
ed
is
in
th
e
f
o
r
m
o
f
a
n
e
s
s
ay
.
T
h
is
test
is
s
tr
u
ctu
r
ed
b
y
r
ef
e
r
r
in
g
t
o
th
e
in
d
icato
r
s
o
f
alg
e
b
r
aic
o
p
e
r
at
io
n
s
,
n
am
ely
:
i
)
Stu
d
e
n
ts
ca
n
r
ec
o
g
n
ize
an
d
o
p
er
ate
alg
e
b
r
aic
ad
d
itio
n
a
n
d
s
u
b
tr
ac
tio
n
o
p
er
atio
n
s
;
ii
)
S
tu
d
en
ts
ca
n
r
ec
o
g
n
ize
a
n
d
o
p
er
ate
alg
e
b
r
aic
m
u
ltip
licat
io
n
o
p
e
r
atio
n
s
;
iii
)
Stu
d
en
ts
ca
n
r
ec
o
g
n
ize
an
d
o
p
er
ate
alg
eb
r
aic
p
o
wer
o
p
er
at
io
n
s
;
an
d
iv
)
Stu
d
en
ts
ca
n
r
ec
o
g
n
ize
an
d
o
p
er
ate
alg
eb
r
aic
d
iv
is
io
n
o
p
er
atio
n
s
.
T
h
e
d
ata
an
aly
s
is
tech
n
iq
u
e
u
s
ed
in
th
is
s
tu
d
y
in
clu
d
es
an
al
y
s
is
in
co
n
d
itio
n
s
an
d
an
aly
s
i
s
b
etwe
en
co
n
d
itio
n
s
[
5
4
]
.
I
n
-
co
n
d
itio
n
an
aly
s
is
is
an
an
aly
s
is
p
er
f
o
r
m
ed
at
b
aselin
e
co
n
d
itio
n
s
an
d
i
n
ter
v
en
tio
n
co
n
d
itio
n
s
.
T
h
e
co
m
p
o
n
e
n
ts
u
s
ed
to
p
er
f
o
r
m
th
e
a
n
aly
s
is
in
th
ese
co
n
d
itio
n
s
in
clu
d
e
:
i
)
Dete
r
m
in
in
g
th
e
len
g
th
o
f
th
e
c
o
n
d
itio
n
;
ii
)
D
eter
m
in
in
g
th
e
esti
m
atio
n
o
f
t
h
e
tr
en
d
;
iii
)
Dete
r
m
in
in
g
th
e
s
tab
ilit
y
tr
en
d
;
iv
)
Dete
r
m
in
in
g
th
e
tr
e
n
d
o
f
th
e
d
ata
tr
ail
;
v
)
Dete
r
m
in
in
g
th
e
le
v
el
o
f
s
tab
ilit
y
an
d
r
a
n
g
e
;
an
d
vi
)
Dete
r
m
in
e
th
e
lev
el
o
f
ch
a
n
g
e
[
4
7
]
,
[
4
8
]
.
An
an
aly
s
is
b
etwe
en
co
n
d
itio
n
s
was
ca
r
r
ied
o
u
t
to
s
ee
t
h
e
d
if
f
er
en
ce
b
etwe
en
th
e
b
aselin
e
p
h
ase
an
d
th
e
i
n
ter
v
en
tio
n
p
h
ase
[
5
4
]
.
T
h
e
co
m
p
o
n
en
ts
u
s
ed
to
ca
r
r
y
o
u
t
th
is
co
n
d
itio
n
a
n
aly
s
is
in
clu
d
e
:
i
)
Dete
r
m
in
in
g
th
e
n
u
m
b
er
o
f
v
ar
iab
les
ch
an
g
ed
;
ii
)
Dete
r
m
in
in
g
ch
an
g
es
in
tr
en
d
d
ir
ec
tio
n
;
iii
)
Dete
r
m
in
in
g
ch
a
n
g
es
in
s
tab
ilit
y
tr
en
d
s
;
iv
)
Dete
r
m
in
in
g
th
e
lev
el
o
f
ch
a
n
g
e
;
an
d
v
)
Dete
r
m
in
in
g
th
e
o
v
er
lap
o
f
b
aselin
e
co
n
d
itio
n
s
.
an
d
in
t
er
v
en
tio
n
[
4
7
]
,
[
4
8
]
.
3.
RE
SU
L
T
S
AND
D
I
SCU
SS
I
O
N
3
.
1
.
Resul
t
T
h
e
r
esu
lts
o
f
th
e
KT
S
test
f
o
u
n
d
th
at
s
u
b
ject
E
h
ad
an
ex
tr
o
v
er
t
p
r
ef
e
r
en
ce
as
was
th
e
g
o
al
o
f
th
is
s
tu
d
y
.
T
h
e
r
esu
lts
o
f
th
e
m
ea
s
u
r
em
en
t
o
f
s
u
b
ject
E
in
u
n
d
er
s
tan
d
in
g
alg
eb
r
aic
o
p
er
atio
n
m
ater
ial
d
u
r
in
g
th
e
b
aselin
e
an
d
in
ter
v
en
tio
n
s
tag
es
ar
e
p
r
esen
ted
in
Fig
u
r
e
1
.
T
h
e
f
ig
u
r
e
s
h
o
ws
d
ata
an
aly
s
is
in
s
in
g
le
s
u
b
ject
r
esear
ch
u
s
in
g
a
n
aly
s
is
u
n
d
er
co
n
d
itio
n
s
an
d
tech
n
iq
u
es b
et
wee
n
co
n
d
itio
n
s
.
Fig
u
r
e
1
.
Sco
r
e
s
tu
d
en
t o
f
ex
tr
o
v
er
t in
b
aselin
e
an
d
in
ter
v
en
t
io
n
3
.
1
.
1
.
Ana
ly
s
is
un
der
co
nd
it
i
o
ns
I
n
th
is
an
al
y
s
is
th
e
s
tep
s
u
s
e
d
ar
e
:
i
)
d
eter
m
in
in
g
th
e
len
g
th
o
f
th
e
co
n
d
itio
n
;
i
)
d
ete
r
m
in
in
g
th
e
esti
m
atio
n
o
f
th
e
tr
en
d
;
iii
)
d
eter
m
in
in
g
th
e
s
tab
ilit
y
tr
en
d
;
iv
)
d
eter
m
in
in
g
t
h
e
tr
en
d
o
f
th
e
d
ata
tr
ail
;
v
)
d
eter
m
in
in
g
th
e
lev
el
o
f
s
ta
b
ilit
y
an
d
r
an
g
e
;
an
d
vi
)
d
e
ter
m
in
e
th
e
lev
el
o
f
c
h
an
g
e
.
T
h
e
f
ir
s
t
s
tep
is
d
eter
m
in
in
g
th
e
le
n
g
th
o
f
t
h
e
co
n
d
itio
n
.
F
ig
u
r
e
2
s
h
o
ws
th
at
th
e
b
aselin
e
p
h
ase
(
A
1
)
was
ca
r
r
ied
o
u
t
f
o
r
f
o
u
r
s
ess
io
n
s
.
L
ik
ewise,
th
e
in
ter
v
en
tio
n
p
h
ase
(
B
1
)
was
also
c
ar
r
ied
o
u
t
i
n
f
o
u
r
s
ess
io
n
s
.
At
th
e
en
d
o
f
ea
ch
s
ess
io
n
,
a
test
is
g
iv
en
to
m
ea
s
u
r
e
th
e
ex
tr
o
v
er
ted
s
tu
d
en
ts
'
ab
ilit
y
to
u
n
d
er
s
tan
d
alg
eb
r
aic
ar
ith
m
etic
o
p
er
atio
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
11
,
No
.
1
,
Ma
r
ch
20
22
:
99
-
1
07
102
T
h
e
s
ec
o
n
d
s
tep
is
d
eter
m
in
in
g
th
e
esti
m
atio
n
o
f
th
e
tr
en
d
.
E
s
tim
atio
n
o
f
th
e
tr
en
d
o
f
th
e
d
ata
o
n
a
g
r
ap
h
is
v
er
y
im
p
o
r
ta
n
t
in
s
i
n
g
le
-
s
u
b
ject
r
esear
ch
,
it
aim
s
to
p
r
o
v
id
e
an
o
v
er
v
iew
o
f
t
h
e
b
eh
a
v
io
r
o
f
t
h
e
s
u
b
ject
b
ein
g
s
tu
d
ied
.
E
s
tim
a
tio
n
o
f
th
e
tr
en
d
in
th
is
s
tu
d
y
u
s
in
g
th
e
s
p
lit
-
m
id
d
le
m
eth
o
d
[
5
5
]
–
[
5
7
]
.
T
h
is
m
eth
o
d
is
ca
r
r
ied
o
u
t
b
ased
o
n
th
e
m
ed
ian
v
alu
e
o
f
th
e
o
r
d
in
al
d
ata
p
o
in
ts
.
T
h
e
tr
en
d
d
ir
ec
tio
n
in
r
esear
ch
ca
n
b
e
s
ee
n
in
Fig
u
r
e
2
.
I
t
c
an
b
e
s
ee
n
th
at
th
e
b
aseli
n
e
p
h
ase
h
as
a
co
n
s
tan
t
tr
en
d
d
i
r
ec
tio
n
,
an
d
in
th
e
in
ter
v
en
tio
n
p
h
ase,
th
er
e
is
a
ten
d
en
cy
to
war
d
s
an
u
p
war
d
tr
en
d
.
Fig
u
r
e
2
.
E
s
tim
atio
n
o
f
th
e
tr
e
n
d
T
h
e
th
ir
d
s
tep
is
d
eter
m
in
in
g
t
h
e
s
tab
ilit
y
tr
en
d
.
T
h
e
s
tab
ilit
y
tr
en
d
s
h
o
ws
th
e
d
e
g
r
ee
o
f
v
ar
iat
io
n
o
r
th
e
s
ize
o
f
th
e
r
an
g
e
o
f
ce
r
tain
d
ata
g
r
o
u
p
s
.
I
f
th
e
d
ata
r
an
g
e
is
s
m
al
l
o
r
th
e
lev
el
o
f
v
ar
iatio
n
is
lo
w,
th
e
d
ata
is
s
aid
to
b
e
s
tab
le.
I
n
g
en
er
al,
s
in
g
le
-
s
u
b
ject
s
tu
d
ies
m
o
s
tly
u
s
e
a
s
tab
ilit
y
ten
d
e
n
cy
o
f
1
5
%,
s
o
th
e
ca
lcu
latio
n
o
f
th
e
b
aselin
e
c
o
n
d
itio
n
s
(
A)
f
o
r
s
tab
ilit
y
r
an
g
e
i
s
th
e
h
ig
h
s
co
r
e
s
tab
ilit
y
cr
iter
ia
=5
2
0
.
1
5
=
7
.
8
.
Nex
t
to
d
eter
m
in
e
th
e
m
ea
n
le
v
el
is
(
4
6
+
5
4
+4
8
+5
2
)
:4
=5
0
.
As
a
r
esu
lt
o
f
t
h
e
u
p
p
er
lim
it
is
m
ea
n
lev
el
+
h
alf
o
f
th
e
s
tab
ilit
y
=5
0
+3
.
9
=5
3
.
9
,
an
d
th
e
lo
wer
lim
it
is
th
e
m
e
an
lev
el
-
h
alf
o
f
th
e
s
tab
ilit
y
=
5
0
–
3
.
9
=4
6
.
1
.
Fro
m
th
is
ca
lcu
latio
n
,
a
g
r
a
p
h
ca
n
b
e
m
ad
e
as sh
o
wn
in
Fig
u
r
e
3
.
Fu
r
th
er
m
o
r
e
,
th
e
ca
lcu
latio
n
o
f
th
e
s
tab
ilit
y
tr
en
d
i
n
th
e
in
te
r
v
en
tio
n
p
h
ase
is
r
an
g
e
is
th
e
h
ig
h
s
co
r
e
s
tab
ilit
y
cr
iter
ia=
9
2
0
.
1
5
=1
3
.
8
.
Nex
t
to
d
eter
m
i
n
e
th
e
m
e
an
lev
el
is
(
9
0
+8
4
+8
8
+9
2
)
:4
=
8
8
.
5
.
As
a
r
esu
lt
o
f
th
e
u
p
p
er
lim
it
is
m
ea
n
lev
el
+
h
alf
o
f
th
e
s
tab
ilit
y
=8
8
.
5
+
6
.
9
=9
5
.
4
,
an
d
th
e
lo
wer
lim
it
is
m
ea
n
lev
el
–
h
alf
o
f
th
e
s
tab
ilit
y
=8
8
.
5
–
6
.
9
=8
1
.
8
.
Fro
m
th
is
ca
lcu
latio
n
,
a
g
r
a
p
h
was
m
ad
e
as sh
o
wn
in
Fig
u
r
e
4
.
Fig
u
r
e
3
.
Dete
r
m
i
n
in
g
th
e
s
tab
ilit
y
tr
en
d
b
aselin
e
Fig
u
r
e
4
.
Dete
r
m
i
n
in
g
th
e
s
tab
ilit
y
tr
en
d
in
ter
v
e
n
tio
n
B
ased
o
n
Fig
u
r
es
3
an
d
4
,
it
is
f
o
u
n
d
th
at
th
e
p
e
r
ce
n
tag
e
tr
e
n
d
o
f
d
ata
p
o
in
t
s
tab
ilit
y
in
th
e
b
aselin
e
p
h
ase
is
m
an
y
d
ata
p
o
in
ts
ex
is
t
in
a
r
an
g
e
d
iv
id
e
d
b
y
t
h
e
n
u
m
b
er
o
f
d
ata
p
o
in
ts
in
o
th
er
wo
r
d
s
th
at
2
:6
=
0
.
3
3
3
o
r
3
3
.
3
%.
I
f
th
e
p
er
ce
n
tag
e
o
f
s
tab
ilit
y
o
f
8
5
%
-
9
0
%
is
s
aid
to
b
e
s
tab
le
[
5
8
]
.
W
h
en
it
is
b
elo
w,
it
is
s
aid
to
b
e
u
n
s
tab
le
(
v
ar
iab
le)
.
B
ec
au
s
e
th
e
ca
lc
u
latio
n
r
esu
lt
f
o
r
th
e
b
aselin
e
p
h
ase
is
3
3
.
3
%,
th
en
th
is
p
h
ase
is
s
aid
to
b
e
u
n
s
tab
le
(
v
ar
ia
b
le)
.
T
h
is
c
o
n
d
itio
n
d
if
f
er
s
f
r
o
m
th
e
in
te
r
v
en
tio
n
p
h
ase
with
th
e
p
er
ce
n
tag
e
o
f
s
tab
ilit
y
is
1
0
0
%,
th
is
s
h
o
ws th
at
th
e
in
te
r
v
en
tio
n
is
in
a
s
tab
le
co
n
d
itio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
Lea
r
n
in
g
a
ch
ieve
men
t
o
f e
xtro
ve
r
ted
s
tu
d
en
ts
in
a
lg
eb
r
a
ic
o
p
era
tio
n
s
b
y
tu
to
r
ia
l
… (
S
r
i A
d
i Wid
o
d
o
)
103
T
h
e
f
o
u
r
th
s
tep
is
to
d
eter
m
in
e
th
e
tr
en
d
o
f
t
h
e
d
ata
tr
ail.
T
o
f
in
d
o
u
t
th
e
tr
en
d
f
r
o
m
tr
ail
d
ata,
y
o
u
ca
n
s
ee
th
e
esti
m
ated
tr
en
d
d
ir
ec
tio
n
.
I
n
th
e
s
ec
o
n
d
s
tag
e,
it
is
s
ee
n
th
at
th
e
esti
m
ated
tr
en
d
to
war
d
s
th
e
b
aselin
e
is
co
n
s
tan
t
s
o
th
at
th
e
tr
en
d
o
f
t
h
e
d
ata
t
r
ail
o
n
th
e
b
aselin
e
is
also
co
n
s
tan
t.
T
h
e
tr
en
d
esti
m
atio
n
to
war
d
s
in
ter
v
en
tio
n
s
ee
m
s
to
b
e
in
cr
ea
s
in
g
s
o
t
h
at
th
e
d
ata
t
r
ail
tr
en
d
at
th
e
b
aselin
e
also
i
n
cr
ea
s
es.
T
h
e
f
if
th
s
tep
is
d
eter
m
in
in
g
th
e
lev
el
o
f
s
tab
ilit
y
an
d
r
an
g
e.
T
o
d
eter
m
in
e
th
e
le
v
el
o
f
s
tab
ilit
y
an
d
r
an
g
e,
as
p
r
ev
io
u
s
ly
ca
lcu
lated
,
it
was
f
o
u
n
d
th
at
in
t
h
e
b
aselin
e
(
A
1
)
th
e
d
ata
was
v
ar
iab
le
o
r
u
n
s
tab
le
with
a
s
co
r
e
r
an
g
e
b
etwe
en
4
6
a
n
d
5
4
.
I
n
i
n
ter
v
en
tio
n
(
B
)
with
a
s
co
r
e
r
a
n
g
e
o
f
5
2
t
o
9
2
,
th
e
d
ata
was s
tab
le.
T
h
e
last
s
tep
is
to
d
eter
m
in
e
th
e
lev
el
o
f
ch
an
g
e.
T
o
d
eter
m
in
e
th
e
lev
el
o
f
c
h
an
g
e
b
y
m
ar
k
in
g
th
e
f
ir
s
t
d
ata
(
d
ay
1
)
a
n
d
th
e
last
d
ata
(
d
a
y
6
)
in
th
e
b
aselin
e
p
h
ase
(
A)
.
T
h
en
,
t
h
e
d
if
f
e
r
en
ce
b
etwe
en
th
e
two
d
ata
is
ca
lcu
lated
an
d
th
e
d
ir
e
ctio
n
is
in
cr
ea
s
in
g
o
r
d
ec
r
ea
s
in
g
an
d
a
s
ig
n
(
+)
is
g
iv
en
if
it
im
p
r
o
v
es,
(
-
)
g
ets
wo
r
s
e,
an
d
(
=)
if
th
er
e
is
n
o
c
h
an
g
e.
L
ik
ewise,
to
ca
lcu
late
th
e
lev
el
o
f
ch
an
g
e
in
th
e
i
n
ter
v
en
tio
n
p
h
ase
(
B
)
.
Fro
m
Fig
u
r
e
1
,
it
is
f
o
u
n
d
th
at
in
th
e
b
aselin
e
f
o
r
th
e
f
ir
s
t
d
ay
,
th
e
s
co
r
e
was
4
6
an
d
th
e
s
co
r
e
o
n
th
e
last
d
ay
was
5
2
,
s
o
th
e
d
if
f
e
r
en
ce
was
(
+6
)
.
I
n
th
e
in
ter
v
e
n
tio
n
f
o
r
th
e
f
ir
s
t
d
ay
,
th
e
s
co
r
e
was
9
0
a
n
d
th
e
s
co
r
e
o
n
th
e
last
d
ay
was 9
2
,
s
o
th
e
d
if
f
er
e
n
ce
was (
+2
)
.
3
.
1
.
2
.
Ana
ly
s
is
bet
wee
n c
o
nd
it
io
ns
I
n
th
is
an
aly
s
is
,
th
e
s
tep
s
u
s
e
d
ar
e
:
i
)
d
eter
m
in
in
g
th
e
n
u
m
b
er
o
f
v
ar
iab
les
ch
an
g
ed
;
ii
)
d
eter
m
in
in
g
ch
an
g
es
in
tr
en
d
d
i
r
ec
tio
n
;
iii
)
d
eter
m
in
in
g
c
h
an
g
es
in
s
tab
ilit
y
tr
en
d
s
;
iv
)
d
eter
m
in
in
g
t
h
e
lev
el
o
f
ch
an
g
e
;
an
d
iv
)
d
eter
m
in
in
g
th
e
o
v
er
l
ap
o
f
b
aselin
e
co
n
d
itio
n
s
an
d
in
ter
v
en
tio
n
.
T
h
e
in
itial
ac
tiv
ity
to
an
aly
ze
th
e
n
u
m
b
er
o
f
v
a
r
iab
les
ch
an
g
e
d
in
th
is
s
tu
d
y
was
to
u
s
e
p
ee
r
tu
to
r
in
g
tec
h
n
iq
u
es
to
im
p
r
o
v
e
th
e
lear
n
in
g
ac
h
iev
em
en
t
o
f
ex
t
r
o
v
er
te
d
s
tu
d
en
ts
in
alg
e
b
r
aic
o
p
er
atio
n
s
.
T
h
u
s
,
o
n
ly
o
n
e
v
ar
iab
le
will
b
e
ch
a
n
g
ed
in
th
is
s
tu
d
y
.
T
h
e
s
ec
o
n
d
s
te
p
is
d
eter
m
in
i
n
g
ch
a
n
g
es
in
tr
en
d
d
ir
ec
ti
o
n
.
T
o
d
eter
m
in
e
ch
an
g
es
in
c
o
n
d
itio
n
s
,
it
ca
n
b
e
s
ee
n
in
th
e
tab
le
o
f
ch
an
g
es
in
d
ir
ec
tio
n
tr
en
d
s
r
elat
ed
to
ex
tr
o
v
er
te
d
s
tu
d
en
t
ac
h
i
ev
em
en
t
in
s
o
lv
in
g
alg
eb
r
aic
o
p
er
atio
n
q
u
esti
o
n
s
as
in
T
ab
le
1
.
I
t
ca
n
b
e
s
ee
n
t
h
at
th
e
lear
n
in
g
ac
h
iev
em
e
n
t
o
f
ex
tr
o
v
er
t
s
tu
d
en
ts
in
alg
eb
r
a
o
p
er
atio
n
s
in
th
e
b
a
s
elin
e
p
h
ase
A1
ten
d
s
to
b
e
in
a
f
ix
ed
d
ir
ec
tio
n
(
=)
,
w
h
ile
in
th
e
B
1
ef
f
icien
cy
co
n
d
itio
n
it
ten
d
s
to
in
cr
ea
s
e
(
+)
.
I
n
c
o
n
n
ec
tio
n
with
th
is
co
n
d
itio
n
,
it
ca
n
b
e
co
n
cl
u
d
ed
t
h
a
t
th
e
p
r
o
v
is
io
n
o
f
lear
n
in
g
in
ter
v
en
tio
n
s
u
s
in
g
p
ee
r
tu
to
r
s
h
as a
p
o
s
itiv
e
ef
f
ec
t
o
n
th
e
c
h
an
g
e
d
v
ar
iab
les.
T
h
e
th
ir
d
s
tep
is
d
eter
m
i
n
in
g
ch
an
g
es
in
s
tab
ilit
y
tr
en
d
s
.
T
o
d
eter
m
in
e
ch
a
n
g
es
in
s
tab
ilit
y
tr
en
d
s
,
it
ca
n
b
e
s
ee
n
f
r
o
m
th
e
s
tab
ilit
y
tr
en
d
in
t
h
e
b
aselin
e
(
A)
a
n
d
in
ter
v
en
tio
n
(
B
)
p
h
ases
in
th
e
s
u
m
m
ar
y
an
aly
s
is
u
n
d
er
c
o
n
d
itio
n
s
.
Fro
m
th
e
s
u
m
m
ar
y
o
f
th
e
an
aly
s
is
u
n
d
e
r
co
n
d
itio
n
s
,
c
h
an
g
es
in
t
h
e
s
tab
ilit
y
tr
en
d
ca
n
b
e
s
ee
n
in
T
ab
le
1
.
T
ab
le
1
.
C
h
an
g
es in
s
tab
ilit
y
tr
en
d
s
C
o
m
p
a
r
i
so
n
o
f
c
o
n
d
i
t
i
o
n
s
A
/
B
C
h
a
n
g
e
s
i
n
s
t
a
b
i
l
i
t
y
t
r
e
n
d
s
U
n
st
a
b
l
e
t
o
st
a
b
l
e
(
V
a
r
i
a
b
l
e
t
o
s
t
a
b
l
e
)
T
h
e
f
o
u
r
th
s
tep
is
d
eter
m
in
i
n
g
th
e
lev
el
o
f
ch
an
g
e.
T
o
d
et
er
m
in
e
th
e
lev
el
o
f
ch
a
n
g
e,
it
is
d
o
n
e
b
y
d
eter
m
in
in
g
t
h
e
d
ata
p
o
in
t
in
th
e
b
aselin
e
co
n
d
itio
n
(
A)
in
t
h
e
last
s
ess
io
n
,
wh
ich
is
5
2
,
a
n
d
th
e
f
ir
s
t
s
ess
io
n
in
th
e
in
ter
v
en
tio
n
co
n
d
itio
n
(
B
)
,
wh
ich
is
9
0
.
T
h
en
ca
lcu
late
th
e
d
if
f
er
en
ce
b
etwe
e
n
th
e
two
,
n
am
ely
(
5
2
–
9
0
)
,
s
o
th
at
th
e
d
if
f
er
en
c
e
is
(
3
8
)
.
T
h
e
last
s
tep
is
d
ete
r
m
in
in
g
th
e
o
v
er
lap
o
f
b
aselin
e
an
d
in
ter
v
en
tio
n
co
n
d
itio
n
s
.
T
o
d
eter
m
in
e
t
h
e
o
v
er
lap
o
f
d
ata
at
b
aselin
e
co
n
d
itio
n
s
(
A)
with
th
e
i
n
te
r
v
en
tio
n
(
B
)
b
y
:
i)
L
o
o
k
in
g
b
ac
k
at
th
e
lo
wer
a
n
d
u
p
p
er
lim
its
in
th
e
b
aselin
e
co
n
d
itio
n
s
;
ii)
C
alcu
latin
g
th
e
n
u
m
b
er
o
f
d
ata
p
o
in
ts
in
th
e
i
n
ter
v
en
tio
n
c
o
n
d
itio
n
(
B
)
wh
ich
is
in
t
h
e
co
n
d
itio
n
r
a
n
g
e
(
A)
.
Af
ter
o
b
s
er
v
in
g
it,
all
d
ata
p
o
i
n
ts
in
th
e
in
ter
v
en
tio
n
co
n
d
itio
n
a
r
e
n
o
t
in
th
e
b
aselin
e
r
an
g
e,
s
o
in
th
is
s
ec
t
io
n
,
th
e
n
u
m
b
er
i
s
0
;
iii)
T
h
e
r
e
s
u
lt
s
o
b
tain
ed
ar
e
d
iv
id
ed
b
y
th
e
n
u
m
b
er
o
f
d
ata
p
o
in
ts
in
co
n
d
i
tio
n
(
B
)
t
h
en
m
u
ltip
lied
b
y
1
0
0
.
Sin
ce
th
er
e
ar
e
m
an
y
d
ata
p
o
in
ts
f
o
r
th
e
in
ter
v
en
tio
n
c
o
n
d
itio
n
s
th
at
a
r
e
n
o
t
in
th
e
b
aselin
e
co
n
d
itio
n
,
t
h
e
r
esu
lt
o
f
th
is
s
tag
e
is
0
%.
I
n
co
n
n
ec
tio
n
with
th
is
o
v
er
lap
p
er
ce
n
tag
e
,
th
e
s
m
aller
th
e
o
v
e
r
lap
p
er
ce
n
tag
e,
th
e
b
etter
th
e
ef
f
ec
t
o
f
th
e
in
ter
v
en
tio
n
o
n
tar
g
et
b
e
h
a
v
io
r
.
3
.
2
.
Dis
cu
s
s
io
n
Ma
th
em
atics
h
as
an
im
p
o
r
tan
t
r
o
le
in
life
,
in
ad
d
itio
n
t
o
f
u
n
ctio
n
in
g
as
a
to
o
l
to
s
o
lv
e
p
r
o
b
lem
s
,
th
in
k
lo
g
ically
,
an
d
r
atio
n
all
y
,
m
ath
em
atics
also
f
u
n
ctio
n
s
as
a
to
o
l
to
f
ac
ilit
ate
r
el
atio
n
s
h
ip
s
b
etwe
en
in
d
iv
id
u
als
an
d
as
a
to
o
l
f
o
r
c
o
m
m
u
n
icatio
n
[
1
9
]
,
[
2
0
]
,
[
5
9
]
.
T
h
is
is
o
n
e
o
f
th
e
r
ea
s
o
n
s
m
ath
em
atics
is
g
iv
en
f
r
o
m
p
r
e
-
s
ch
o
o
l
o
r
k
in
d
e
r
g
ar
ten
to
u
n
iv
er
s
ity
[
6
0
]
,
[
6
1
]
,
t
h
is
co
n
d
itio
n
also
ap
p
lies
in
I
n
d
o
n
esia.
So
th
at
in
ev
itab
ly
,
s
tu
d
en
ts
ca
n
n
o
t a
v
o
id
m
ath
em
atica
l p
r
o
b
lem
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
11
,
No
.
1
,
Ma
r
ch
20
22
:
99
-
1
07
104
T
h
is
s
tu
d
y
d
escr
ib
es
th
e
co
n
d
itio
n
o
f
e
x
tr
o
v
e
r
ted
s
tu
d
e
n
ts
f
r
o
m
th
e
b
aselin
e
co
n
d
itio
n
to
th
e
in
ter
v
en
tio
n
c
o
n
d
itio
n
.
T
h
e
te
s
t
r
esu
lts
g
iv
en
in
th
e
b
aselin
e
f
o
r
f
o
u
r
s
ess
io
n
s
s
h
o
wed
th
at
th
e
co
n
d
itio
n
o
f
s
u
b
ject
E
was
in
an
u
n
s
tab
le
co
n
d
itio
n
(
v
ar
iab
le
)
.
T
h
is
c
an
b
e
s
ee
n
f
r
o
m
th
e
r
esu
lts
o
f
d
eter
m
in
in
g
th
e
s
tab
ilit
y
tr
en
d
a
n
d
th
e
r
esu
lts
o
f
th
e
ca
lcu
latio
n
o
f
th
e
lev
el
o
f
s
tab
ilit
y
an
d
r
a
n
g
e.
T
h
e
f
i
n
d
in
g
s
o
b
tain
ed
in
b
aselin
e
co
n
d
itio
n
s
an
d
m
u
s
t
r
ec
eiv
e
s
p
ec
ial
atten
tio
n
in
clu
d
e
:
i
)
T
h
e
s
u
b
ject
s
till
h
as
p
r
o
b
lem
s
s
o
lv
in
g
p
r
o
b
lem
s
i
n
alg
e
b
r
aic
o
p
er
ati
o
n
s
;
ii
)
T
h
e
s
u
b
ject
s
till
h
as
d
if
f
icu
lty
u
n
d
er
s
tan
d
i
n
g
t
h
e
p
r
o
ce
s
s
o
f
m
u
ltip
ly
in
g
co
r
r
ec
tly
;
iii
)
T
h
e
s
u
b
ject
s
till
h
as
d
if
f
icu
lty
in
d
escr
ib
i
n
g
an
d
s
o
lv
in
g
p
o
wer
p
r
o
b
lem
s
o
f
alg
eb
r
aic
f
o
r
m
s
;
an
d
iv
)
T
he
s
u
b
ject
s
till
h
as d
if
f
icu
lty
d
iv
i
d
in
g
f
o
r
ce
r
tai
n
f
o
r
m
s
th
at
h
av
e
m
o
r
e
th
a
n
o
n
e
v
ar
iab
le
in
o
n
e
tr
ib
e.
T
h
e
in
s
tab
ilit
y
in
s
u
b
ject
E
n
e
ed
s
to
b
e
g
iv
en
i
n
ter
v
e
n
tio
n
s
o
th
at
s
u
b
ject
E
b
ec
o
m
es
s
tab
le
an
d
th
e
s
u
b
ject
u
n
d
e
r
s
tan
d
s
th
e
c
o
n
ce
p
ts
th
at
ex
is
t
in
m
ath
em
atics.
T
h
er
e
is
th
is
r
esear
c
h
th
at
th
e
in
ter
v
en
tio
n
g
iv
en
to
s
u
b
ject
E
is
lear
n
in
g
m
ath
e
m
atics
u
s
in
g
th
e
tu
to
r
ial
m
eth
o
d
.
I
n
th
e
i
n
ter
v
en
tio
n
p
h
ase,
w
h
ich
was
ca
r
r
ied
o
u
t
f
o
r
f
o
u
r
s
ess
io
n
s
,
it
s
h
o
wed
th
at
s
u
b
ject
E
was
in
a
s
tab
le
co
n
d
itio
n
.
T
h
is
ca
n
b
e
s
ee
n
f
r
o
m
th
e
r
esu
lts
o
f
d
eter
m
in
in
g
th
e
s
tab
ilit
y
tr
en
d
an
d
th
e
r
esu
lts
o
f
th
e
ca
lcu
lat
io
n
o
f
th
e
lev
el
o
f
s
tab
ilit
y
an
d
r
an
g
e
wh
ich
ca
n
b
e
co
n
clu
d
ed
t
h
at
t
h
e
s
u
b
ject
i
s
in
a
s
tab
le
co
n
d
itio
n
.
I
n
ad
d
itio
n
to
s
ee
in
g
th
e
s
t
ab
ilit
y
tr
en
d
,
lev
el
o
f
s
tab
ilit
y
,
an
d
r
an
g
e
in
s
u
b
ject
E
,
lear
n
in
g
m
ath
em
atics
u
s
in
g
th
e
tu
to
r
ia
l
m
eth
o
d
is
co
n
s
id
er
ed
s
u
cc
es
s
f
u
l,
it
ca
n
b
e
s
ee
n
in
th
e
r
es
u
lts
o
f
th
e
an
aly
s
is
b
etwe
en
th
e
co
n
d
itio
n
s
o
b
tain
ed
th
at
th
e
lev
el
o
f
ch
an
g
e
is
(
-
3
8
)
,
th
is
s
h
o
ws
th
at
th
e
u
s
e
o
f
th
e
tu
to
r
ial
m
eth
o
d
h
as
a
s
ig
n
if
ica
n
t
ef
f
e
ct.
Po
s
itiv
e
o
n
t
h
e
lear
n
in
g
a
ch
iev
em
en
t
o
f
al
g
eb
r
aic
o
p
er
atio
n
s
.
So
th
at
i
n
g
en
er
al
s
u
b
ject
E
with
ex
tr
o
v
er
ted
tem
p
er
am
en
t
co
n
d
itio
n
s
ca
n
r
ec
o
g
n
ize
an
d
o
p
er
ate
alg
eb
r
aic
ad
d
itio
n
an
d
s
u
b
tr
ac
tio
n
o
p
er
atio
n
s
,
r
ec
o
g
n
ize
an
d
o
p
er
ate
al
g
eb
r
aic
m
u
ltip
licatio
n
o
p
er
atio
n
s
,
r
ec
o
g
n
ize
a
n
d
o
p
e
r
ate
alg
eb
r
aic
p
o
we
r
o
p
e
r
atio
n
s
,
an
d
r
ec
o
g
n
ize
an
d
o
p
e
r
ate
alg
eb
r
aic
d
iv
is
io
n
o
p
e
r
atio
n
s
.
T
h
e
r
esu
lt
s
o
f
th
is
s
tu
d
y
in
d
icate
th
at
th
e
p
r
o
v
is
io
n
o
f
in
t
er
v
en
tio
n
th
r
o
u
g
h
th
e
tu
to
r
ial
lear
n
in
g
m
eth
o
d
ca
n
i
m
p
r
o
v
e
lear
n
in
g
o
u
tco
m
es
f
o
r
ex
tr
o
v
er
ted
s
u
b
j
ec
ts
,
esp
ec
ially
in
alg
e
b
r
aic
o
p
er
atio
n
s
.
I
n
tu
to
r
ial
lear
n
in
g
,
s
tu
d
e
n
ts
ar
e
g
iv
e
n
l
ea
r
n
in
g
g
u
id
an
ce
in
th
e
f
o
r
m
o
f
g
iv
in
g
d
ir
ec
tio
n
s
,
ass
is
tan
c
e,
in
s
tr
u
ctio
n
s
,
an
d
m
o
tiv
atio
n
s
o
th
at
s
tu
d
en
ts
le
ar
n
e
f
f
icien
tly
a
n
d
ef
f
ec
tiv
el
y
[
6
2
]
–
[
6
4
]
.
Dir
ec
tio
n
s
in
t
u
to
r
i
al
lear
n
in
g
ca
n
b
e
in
ter
p
r
eted
as
d
ir
ec
tio
n
s
g
iv
en
to
s
tu
d
en
ts
to
ac
h
iev
e
th
eir
r
e
s
p
ec
tiv
e
g
o
als
(
in
th
is
ca
s
e,
le
ar
n
in
g
o
b
jectiv
es).
Ass
i
s
tan
ce
in
tu
to
r
ial
lear
n
in
g
ca
n
b
e
in
ter
p
r
eted
b
y
h
elp
in
g
s
tu
d
en
ts
lear
n
th
e
s
u
b
ject
m
a
tter
.
I
n
s
tr
u
ctio
n
s
i
n
tu
to
r
ial
lear
n
in
g
ar
e
p
r
o
v
id
in
g
in
f
o
r
m
atio
n
ab
o
u
t
h
o
w
to
s
tu
d
y
th
e
m
ater
ial,
wh
ile
m
o
tiv
atio
n
in
tu
to
r
ial
lear
n
in
g
is
ca
r
r
ied
o
u
t
b
y
m
o
v
in
g
s
tu
d
e
n
ts
'
ac
tiv
itie
s
in
l
ea
r
n
in
g
m
ater
ial,
d
o
in
g
ass
ig
n
m
en
ts
,
an
d
tak
in
g
ass
es
s
m
en
ts
.
Peer
s
ca
n
g
u
id
e
tu
to
r
ial
lear
n
i
n
g
[
6
5
]
–
[
6
7
]
.
T
ea
c
h
er
s
ca
n
b
e
co
m
e
tu
to
r
s
f
o
r
s
tu
d
e
n
ts
if
s
tu
d
en
ts
ar
e
d
ee
m
ed
n
o
t
y
et
wo
r
th
y
to
d
eliv
er
th
e
m
ater
ial
to
b
e
r
ep
o
r
ted
.
T
h
i
s
g
u
id
an
ce
p
r
o
ce
s
s
m
ak
es
th
e
clo
s
en
ess
b
etwe
en
s
tu
d
en
ts
an
d
tu
to
r
s
ca
n
b
e
f
o
r
m
ed
s
o
th
at
s
tu
d
e
n
ts
ca
n
f
r
ee
ly
ask
q
u
esti
o
n
s
d
ir
ec
tl
y
to
th
e
t
u
to
r
.
W
ith
th
is
co
n
d
itio
n
,
th
e
lear
n
in
g
atm
o
s
p
h
er
e
b
ec
o
m
es
aliv
e
d
u
e
to
ac
tiv
e
lear
n
in
g
in
t
er
ac
tio
n
s
,
an
d
th
e
m
ath
em
atics m
ater
ial
d
eliv
er
e
d
b
y
th
e
tu
to
r
t
o
s
tu
d
en
ts
b
ec
o
m
es m
o
r
e
m
ea
n
i
n
g
f
u
l.
C
h
ar
ac
ter
is
tics
o
f
ex
tr
o
v
e
r
t
s
t
u
d
en
ts
wh
o
h
a
v
e
to
r
ea
d
q
u
esti
o
n
s
o
r
r
ea
d
m
ater
ial
m
o
r
e
t
h
an
o
n
ce
s
o
th
at
ex
tr
o
v
er
t
s
tu
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en
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u
n
d
er
s
t
an
d
b
etter
wh
at
is
b
ein
g
lear
n
ed
[
6
8
]
,
[
6
9
]
.
Als
o
,
ex
tr
o
v
er
te
d
s
tu
d
en
t
s
wh
o
ar
e
alwa
y
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in
a
h
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r
r
y
t
o
s
o
lv
e
p
r
o
b
lem
s
ar
e
v
er
y
p
r
o
n
e
t
o
m
ak
e
m
is
tak
es
in
s
o
lv
in
g
p
r
o
b
lem
s
[
7
0
]
.
T
h
is
is
v
er
y
d
if
f
er
en
t
f
r
o
m
in
tr
o
v
er
ted
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tu
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en
ts
wh
o
ten
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to
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e
ab
le
t
o
m
an
ag
e
th
e
in
f
o
r
m
atio
n
t
h
ey
f
ac
e
[
6
9
]
,
[
7
1
]
.
T
h
e
co
n
d
itio
n
o
f
ex
tr
o
v
er
t
s
tu
d
en
ts
,
if
n
o
t
g
iv
en
a
tu
to
r
o
r
s
u
p
er
v
is
o
r
,
ca
n
r
esu
lt
in
th
e
p
r
o
ce
s
s
o
f
lear
n
in
g
m
ath
em
atics
b
ein
g
h
am
p
er
ed
b
ec
au
s
e
ex
tr
o
v
er
t
s
tu
d
en
ts
h
av
e
a
lo
n
g
ten
d
en
c
y
to
u
n
d
er
s
tan
d
m
ath
em
atics
m
ater
ial
b
ec
au
s
e
th
e
p
r
o
ce
s
s
o
f
r
ea
d
in
g
m
ater
ial
m
u
s
t
b
e
d
o
n
e
r
e
p
ea
ted
ly
,
r
ea
d
in
g
m
at
h
em
atica
l
p
r
o
b
lem
s
th
at
m
u
s
t b
e
d
o
n
e
r
e
p
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ted
ly
,
an
d
s
tu
d
en
ts
ex
tr
o
v
er
ts
ar
e
p
r
o
n
e
to
m
is
tak
es.
4.
CO
NCLU
SI
O
N
T
h
is
s
tu
d
y
co
n
clu
d
e
d
th
at
tu
to
r
ial
lear
n
in
g
af
f
ec
ts
ex
tr
o
v
er
t
s
tu
d
en
t
lear
n
in
g
ac
h
ie
v
em
en
t
in
alg
eb
r
aic
o
p
er
at
io
n
m
ater
ial.
T
h
e
ef
f
ec
t
o
f
tu
to
r
ial
lear
n
in
g
ca
n
b
e
s
ee
n
f
r
o
m
th
e
ch
a
n
g
e
in
d
ata
f
r
o
m
th
e
b
aselin
e
p
h
ase
to
th
e
in
ter
v
en
tio
n
p
h
ase.
I
n
th
e
al
g
eb
r
a
o
p
e
r
atio
n
test
o
n
th
e
b
aselin
e
co
n
d
itio
n
s
,
th
e
s
u
b
ject
o
b
tain
ed
an
a
v
er
ag
e
s
co
r
e
o
f
5
0
.
W
h
ile
in
th
e
in
ter
v
e
n
tio
n
p
h
ase
th
e
s
u
b
ject
ex
p
er
ie
n
c
ed
a
ch
an
g
e
in
th
e
av
er
ag
e
s
co
r
e
to
8
8
.
5
.
Fro
m
t
h
ese
d
ata,
it
ca
n
b
e
s
ee
n
th
at
th
e
lear
n
in
g
ac
h
iev
e
m
en
t
o
f
e
x
tr
o
v
er
te
d
s
tu
d
en
ts
h
as c
h
an
g
ed
b
y
3
8
.
5
.
W
ith
th
e
r
esu
lts
o
f
th
is
s
tu
d
y
,
it i
s
s
u
g
g
ested
th
at
th
e
u
s
e
o
f
tu
to
r
ial
l
e
ar
n
in
g
ca
n
b
e
u
s
ed
as
an
alter
n
ativ
e
lear
n
in
g
m
et
h
o
d
f
o
r
ex
tr
o
v
er
t
s
tu
d
e
n
ts
.
Fu
r
th
er
m
o
r
e
,
it
is
n
ec
ess
ar
y
to
p
ay
atten
tio
n
to
th
e
u
s
e
o
f
lear
n
in
g
tu
to
r
ials
to
im
p
r
o
v
e
e
x
tr
o
v
er
t stu
d
en
ts
'
ab
ilit
ies in
o
th
er
m
ater
ials
.
RE
F
E
R
E
NC
E
S
[
1
]
O
.
O
l
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a
r
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Je
t
h
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A
.
M
o
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o
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p
p
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2
0
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Evaluation Warning : The document was created with Spire.PDF for Python.
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in
a
lg
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r
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)
105
[
2
]
C
.
M
.
Zu
b
a
i
n
u
r
,
A
.
V
e
l
o
o
,
a
n
d
R
.
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h
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l
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d
,
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h
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e
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f
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c
m
a
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a
p
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mat
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t
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p
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h
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n
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re
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Pro
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6
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:
1
0
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1
0
6
3
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4
9
1
5
7
1
0
.
[
3
]
M
.
R
a
t
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i
sn
a
a
n
d
A
.
T
a
r
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m,
“
S
t
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s
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M
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s
E
d
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c
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t
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(
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,
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U
S
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:
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o
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[
4
]
M
.
V
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,
S
.
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k
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[
5
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N
.
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[
6
]
J.
D
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o
s
k
y
,
K
.
A
.
R
a
w
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o
n
,
E
.
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.
M
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sh
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.
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n
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n
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D
.
T.
W
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l
l
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n
g
h
a
m,
“
I
mp
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o
v
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n
g
S
t
u
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t
s’
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e
a
r
n
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n
g
W
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t
h
Ef
f
e
c
t
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v
e
Le
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n
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n
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Te
c
h
n
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q
u
e
s
,
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9
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6
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[
7
]
A
.
L.
S
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n
,
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r
h
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m,
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n
d
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.
F
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t
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,
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A
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a
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ma
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t
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y
,
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o
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rn
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l
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P
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si
c
s:
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:
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-
6
5
9
6
/
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3
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5
/
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0
6
9
.
[
8
]
Tr
i
sn
i
a
w
a
t
i
,
M
.
Ti
t
i
M
u
a
n
i
f
a
h
,
N
.
R
h
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sy
i
d
a
,
S
.
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d
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W
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d
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d
o
,
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d
M
.
A
r
d
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n
i
n
g
r
u
m
,
“
E
x
p
l
o
r
a
t
i
o
n
t
o
w
a
r
d
s a
t
t
i
t
u
d
e
o
f
st
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d
e
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t
s
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n
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t
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o
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d
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c
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t
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ma
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t
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c
s
l
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a
r
n
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n
g
,
”
J
o
u
r
n
a
l
o
f
Ph
y
s
i
c
s:
C
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n
f
e
re
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S
e
ri
e
s
,
v
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l
.
1
3
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5
,
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o
.
1
,
p
.
1
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0
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3
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.
2
0
1
9
,
d
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:
1
0
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1
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8
8
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2
-
6
5
9
6
/
1
3
1
5
/
1
/
0
1
2
0
3
3
.
[
9
]
W
a
w
a
n
,
E
.
F
.
N
i
n
g
si
h
,
S
.
A
.
W
i
d
o
d
o
,
Le
o
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.
M
.
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.
R
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