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3
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[
4
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also
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t G
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SDG
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)
[
5
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.
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s
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m
at
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m
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s
.
A
cc
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g
to
r
ef
er
en
ce
[
6
]
,
s
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ab
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to
f
u
ll
y
u
n
d
er
s
ta
n
d
t
h
e
m
a
ter
ial
th
e
y
ar
e
lear
n
i
n
g
.
Ho
w
e
v
er
,
th
e
lear
n
er
te
n
d
s
to
f
o
llo
w
t
h
e
s
o
lu
tio
n
o
f
t
h
e
g
iv
e
n
p
r
o
b
le
m
,
s
o
w
h
e
n
th
e
g
iv
en
p
r
o
b
le
m
s
l
ig
h
tl
y
d
if
f
er
en
t
f
r
o
m
g
iv
e
n
ex
a
m
p
le,
t
h
e
lea
r
n
er
h
as
d
if
f
ic
u
lt
y
s
o
lv
i
n
g
i
t.
A
cc
o
r
d
in
g
to
th
e
s
u
r
v
e
y
,
th
e
m
o
s
t
co
m
m
o
n
m
eth
o
d
o
f
tea
ch
in
g
i
n
s
c
h
o
o
ls
i
s
lis
ten
i
n
g
to
teac
h
er
ex
p
lan
atio
n
s
.
W
h
e
n
s
t
u
d
en
ts
d
o
n
o
t u
n
d
er
s
ta
n
d
th
e
g
i
v
en
e
x
p
lan
atio
n
,
t
h
e
y
w
i
ll a
s
k
t
h
e
tea
ch
er
to
g
iv
e
f
u
r
th
er
ex
p
lan
atio
n
.
A
lt
h
o
u
g
h
t
h
is
m
e
th
o
d
is
u
s
ed
b
y
al
m
o
s
t
teac
h
e
r
w
h
i
le
t
ea
ch
i
n
g
,
th
i
s
m
et
h
o
d
d
o
es
n
o
t
g
u
ar
an
tee
all
th
e
s
tu
d
e
n
ts
ca
n
f
o
llo
w
t
h
e
les
s
o
n
w
ell.
I
n
ad
d
itio
n
,
t
h
er
e
is
a
te
n
d
en
c
y
f
o
r
s
t
u
d
en
ts
to
f
ee
l
s
at
u
r
ated
q
u
ick
l
y
.
T
h
ese
ar
e
ca
lled
d
y
s
ca
lcu
l
ia,
w
h
er
e
d
y
s
ca
lc
u
lia
i
s
a
p
er
s
o
n
’
s
in
ab
il
it
y
to
lear
n
m
at
h
e
m
a
tics
[
6
]
.
A
cc
o
r
d
in
g
to
r
e
f
er
en
ce
[
9
]
,
d
y
s
ca
lc
u
lia
ex
p
er
ie
n
ce
d
b
y
ea
c
h
p
er
s
o
n
is
d
if
f
er
en
t,
an
d
its
e
f
f
ec
t
o
n
ea
ch
s
ta
g
e
o
f
h
u
m
a
n
d
e
v
elo
p
m
en
t
al
s
o
d
if
f
er
en
t.
T
h
is
h
ap
p
en
s
b
ec
au
s
e
o
f
v
i
s
u
a
l
-
s
p
atial
a
n
d
la
n
g
u
a
g
e
-
p
r
o
ce
s
s
in
g
d
if
f
ic
u
lt
ies.
V
is
u
al
-
s
p
atial
d
if
f
icu
l
ties
ar
e
a
p
er
s
o
n
’
s
p
r
o
b
lem
i
n
p
r
o
ce
s
s
i
n
g
w
h
at
i
s
s
ee
n
.
L
a
n
g
u
a
g
e
-
p
r
o
ce
s
s
in
g
d
i
f
f
icu
lties
ar
e
a
p
er
s
o
n
’
s
p
r
o
b
lem
i
n
p
r
o
ce
s
s
i
n
g
a
n
d
u
n
d
er
s
tan
d
i
n
g
w
h
at
i
s
b
ein
g
h
ea
r
d
.
A
cc
o
r
d
in
g
to
r
ef
r
e
n
ce
[
1
0
]
th
er
e
ar
e
f
ac
to
r
s
in
w
h
ich
o
n
e’
s
lear
n
i
n
g
s
t
y
le
is
al
s
o
r
elate
d
to
p
s
y
ch
o
lo
g
ical,
w
h
ich
d
ep
en
d
s
o
n
th
e
r
ea
d
in
e
s
s
o
f
a
p
er
s
o
n
to
th
in
k
,
f
ee
l,
h
ea
r
a
n
d
p
r
ac
tice.
W
h
en
s
o
m
eo
n
e
h
as
co
n
s
id
er
ed
s
o
m
e
th
i
n
g
u
n
attr
ac
tiv
e
t
h
e
n
lear
n
in
g
w
i
ll
b
e
ea
s
il
y
f
o
r
g
o
tte
n
,
b
ec
au
s
e
it
is
n
o
t
r
ep
ea
ted
(
tr
ain
ed
)
.
T
h
er
ef
o
r
e,
it
tak
es
a
n
ap
p
licatio
n
o
r
te
ac
h
in
g
ap
p
licatio
n
th
a
t
ca
n
d
eliv
er
t
h
e
m
ater
ial
b
y
attr
ac
ti
n
g
an
d
f
ac
ili
tatin
g
t
h
e
lear
n
er
to
u
n
d
er
s
ta
n
d
it.
2.
RE
S
E
ARCH
M
E
T
H
O
D
I
n
th
i
s
r
esear
ch
,
m
e
th
o
d
th
at
u
s
ed
is
g
a
m
e
d
ev
elo
p
m
e
n
t
li
f
e
c
y
cle
(
GD
L
C
)
,
w
h
er
e
t
h
er
e
is
in
itiat
io
n
,
p
r
e
-
p
r
o
d
u
ctio
n
,
p
r
o
d
u
ctio
n
,
test
in
g
an
d
r
elea
s
e
[
1
1
]
.
Fig
u
r
e
1
s
h
o
w
s
th
e
g
a
m
e
co
n
te
n
ts
ar
e
m
ad
e
u
s
in
g
g
a
m
if
icatio
n
m
et
h
o
d
an
d
ex
p
er
t s
y
s
te
m
.
Fig
u
r
e
1.
Ga
m
e
d
ev
elo
p
m
e
n
t l
if
e
c
y
c
le
co
n
te
n
t s
y
s
te
m
A
cc
o
r
d
in
g
to
r
e
f
r
en
ce
[
1
1
]
-
[
1
5
]
,
g
a
m
i
f
icatio
n
i
s
a
cr
ea
tiv
e
w
a
y
o
f
lear
n
in
g
th
at
h
as
a
tr
e
m
en
d
o
u
s
p
o
w
er
o
f
in
f
lu
e
n
ce
to
i
m
p
r
o
v
e
th
e
lev
el
o
f
lear
n
in
g
in
d
ep
e
n
d
en
ce
an
d
i
m
p
r
o
v
e
s
o
m
eo
n
e
m
a
th
e
m
atic
s
k
il
ls
,
s
u
b
s
eq
u
e
n
t
l
y
ex
p
er
t
s
y
s
te
m
is
n
ee
d
ed
to
cr
ea
te
c
o
n
t
en
t
f
r
o
m
m
at
h
e
m
atica
l
lear
n
in
g
.
At
th
e
ti
m
e
o
f
t
h
e
test
,
th
is
s
t
u
d
y
w
a
s
co
n
d
u
cted
u
s
i
n
g
p
r
e
-
tes
t
an
d
p
o
s
t
-
tes
t,
w
h
er
e
t
h
e
r
es
u
lt
o
b
tain
ed
v
ie
w
ed
b
ased
o
n
ex
p
er
i
m
e
n
tal
r
es
u
lt
s
at
t
h
e
b
e
g
in
n
i
n
g
an
d
at
th
e
en
d
a
f
ter
t
h
e
u
s
er
tr
ied
th
e
cr
ea
ted
g
a
m
e.
T
h
is
is
m
ad
e
to
p
r
o
v
e
w
h
eth
er
t
h
e
g
a
m
e
cr
ea
t
ed
ca
n
i
m
p
r
o
v
e
s
o
m
eo
n
e
m
at
h
e
m
a
tic
s
k
ill
o
r
n
o
t.
I
n
m
a
k
in
g
a
g
a
m
e,
it
r
eq
u
ir
e
s
a
s
tr
o
n
g
attr
ac
tio
n
,
b
ec
au
s
e
it
d
ea
ls
w
i
th
h
u
m
a
n
p
s
y
c
h
o
l
o
g
y
.
E
v
er
y
o
n
e
w
h
o
p
la
y
s
g
a
m
es
m
u
s
t
h
av
e
a
di
f
f
er
e
n
t
f
ee
l
in
g
ab
o
u
t
a
g
a
m
e,
b
u
t
h
o
w
d
o
w
e
g
et
s
o
m
eo
n
e
to
s
u
r
v
i
v
e
i
n
g
a
m
e
p
la
y
r
eq
u
ir
es
a
g
o
o
d
u
s
er
in
ter
f
ac
e
(
UI
)
,
u
s
er
ex
p
er
ien
c
e
(
UX)
an
d
g
a
m
e
p
la
y
ex
p
er
i
en
ce
(
GX)
.
T
h
er
ef
o
r
e,
a
s
u
r
v
e
y
i
s
also
m
ad
e
t
o
o
b
tain
th
e
r
es
u
lts
o
f
th
e
e
v
al
u
a
tio
n
.
3.
SI
M
I
L
AR
AP
P
L
I
CA
T
I
O
N
CO
M
P
ARIS
O
N
ANALYS
I
S
T
h
er
e
ar
e
s
ev
er
al
ap
p
licatio
n
s
th
at
b
ee
n
d
e
v
elo
p
ed
b
ef
o
r
e,
as
a
p
ar
t
o
f
th
e
g
a
m
e
d
ev
elo
p
m
e
n
t
li
f
e
c
y
cle,
an
al
y
s
is
to
s
i
m
ilar
ap
p
licatio
n
b
ee
n
d
o
n
e.
T
h
er
e
ar
e
3
ap
p
licatio
n
th
at
b
ee
n
an
al
y
s
is
w
h
ic
h
ar
e
Ma
g
i
c
Ma
th
,
Ma
h
ir
m
ate
m
ati
k
a
k
ela
s
6
SD,
k
u
m
p
u
la
n
s
o
al
i
n
ter
ak
ti
f
k
ela
s
6
A
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
5
,
Octo
b
er
2
0
1
8
:
3
8
6
0
–
3
8
6
5
3862
T
ab
le
1
.
Sim
i
lar
A
p
p
licatio
n
C
o
m
p
ar
is
o
n
s
M
a
g
i
c
M
a
t
h
M
a
h
i
r
M
a
t
e
mat
i
k
a
K
e
l
a
s 6
S
D
K
u
mp
u
l
a
n
S
o
a
l
I
n
t
e
r
a
k
t
i
f
K
e
l
a
s 6
A
F
e
a
t
u
r
e
s
D
e
scri
b
e
t
h
e
l
e
sso
n
,
a
n
i
ma
t
i
o
n
,
a
n
d
h
a
s
e
x
e
r
c
i
se
s
D
e
scri
b
e
t
h
e
l
e
sso
n
a
n
d
h
a
s
e
x
e
r
c
i
se
s
Ex
e
r
c
i
se
,
e
n
c
y
c
l
o
p
e
d
i
a
,
a
t
l
a
s
w
o
r
l
d
,
so
f
t
w
a
r
e
u
t
i
l
i
t
y
T
e
a
c
h
i
n
g
t
o
o
l
C
o
mp
o
n
e
n
t
A
n
i
mat
i
o
n
,
i
m
a
g
e
,
t
e
x
t
,
so
u
n
d
A
n
i
mat
i
o
n
,
i
m
a
g
e
,
t
e
x
t
i
mag
e
,
h
y
p
e
r
l
i
n
k
,
t
e
x
t
D
a
t
a
b
a
se
Y
e
s
Y
e
s
Y
e
s
G
r
a
p
h
i
c
2
d
i
me
n
s
i
o
n
s
2
d
i
me
n
s
i
o
n
s
2
d
i
me
n
s
i
o
n
s
Ex
e
r
c
i
se
s
Y
e
s
Y
e
s
Y
e
s
L
a
n
g
u
a
g
e
I
n
d
o
n
e
si
a
I
n
d
o
n
e
si
a
I
n
d
o
n
e
si
a
I
n
st
a
l
l
a
t
i
o
n
Y
e
s
Y
e
s
Y
e
s
4.
RE
SU
L
T
S
A
ND
AN
AL
Y
SI
S
T
h
e
u
s
e
ca
s
e
o
f
th
e
ap
p
licatio
n
ca
n
b
e
v
ie
w
ed
in
Fi
g
u
r
e
2
.
I
t
s
h
o
w
s
h
o
w
t
h
e
u
s
er
in
ter
ac
t
w
ith
t
h
e
s
y
s
te
m
a
n
d
s
h
o
w
s
ev
er
al
f
ea
t
u
r
es th
at
i
m
p
le
m
e
n
ted
i
n
th
e
ap
p
licatio
n
.
Fig
u
r
e
2
.
Ma
th
e
m
a
tic
lear
n
i
n
g
ap
p
licatio
n
u
s
e
ca
s
e
T
h
e
s
tr
ateg
y
is
to
in
v
ite
th
e
u
s
er
s
to
lear
n
Ma
th
e
m
atic
s
b
y
u
til
izin
g
m
u
lt
i
m
ed
ia
ele
m
e
n
ts
,
s
u
ch
as
i
m
a
g
es,
s
o
u
n
d
,
te
x
t,
an
d
a
n
i
m
atio
n
.
Su
b
m
is
s
io
n
o
f
m
a
ter
i
al
is
g
i
v
e
n
i
n
th
e
f
o
r
m
o
f
an
i
m
atio
n
s
o
th
a
t
th
e
m
ater
ial
ca
n
b
e
m
o
r
e
ea
s
il
y
u
n
d
er
s
to
o
d
a
s
s
h
o
w
n
i
n
Fi
g
u
r
e
3
.
I
n
th
e
'
Sa
m
p
le
P
r
o
b
lem
s
an
d
Dis
c
u
s
s
io
n
s
'
s
ec
tio
n
,
th
is
ap
p
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d.
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ter
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m
a
k
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ter
ested
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s
?
T
ab
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.
T
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ch
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d
Stu
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e.
Ho
w
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c
h
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s
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g
ap
p
licatio
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h
elp
y
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u
to
lear
n
m
at
h
e
m
a
tic?
T
ab
le
6
.
Stu
d
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d
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ch
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p
p
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elp
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in
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6.
CO
NCLU
SI
O
N
T
h
is
g
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m
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d
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elp
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p
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m
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atic
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ater
ial.
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lti
m
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ts
s
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c
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as
tex
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m
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g
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s
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d
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m
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n
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ter
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ased
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.
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[7
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il
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.
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A
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1
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.,
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2
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ld
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,
J.,
e
t
a
l
.
,
“
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a
m
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ica
ti
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3
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.
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4
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.
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.
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