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[
1
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Evaluation Warning : The document was created with Spire.PDF for Python.
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14
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Octo
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20
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9
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403
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4030
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t
ici
p
ati
o
n
a
n
d
im
p
r
o
v
e
k
n
o
wl
ed
g
e
r
ete
n
t
io
n
[
1
7
]
.
W
h
e
r
e
it
was
f
o
u
n
d
th
at
w
h
e
n
p
h
y
s
i
ca
l
a
cti
v
ity
w
as
c
o
m
b
i
n
e
d
wi
th
m
at
h
,
t
h
e
s
t
u
d
e
n
ts
p
e
r
f
o
r
m
ed
a
lo
t
b
e
tte
r
th
a
n
th
o
s
e
w
h
o
d
i
d
t
h
e
o
p
p
o
s
i
te
[
1
8
]
.
Ga
m
e
-
b
ase
d
l
ea
r
n
i
n
g
r
ei
n
v
e
n
ts
t
h
e
f
o
r
m
s
o
f
e
d
u
c
ati
o
n
b
y
u
ti
liz
in
g
g
am
es
a
n
d
g
a
m
e
-
l
ik
e
f
e
at
u
r
es
t
o
m
o
t
iv
at
e
a
n
d
e
n
g
a
g
e
s
tu
d
e
n
ts
.
As
it
t
u
r
n
e
d
o
u
t
,
s
tu
d
e
n
ts
p
r
e
f
e
r
a
n
d
a
r
e
m
o
r
e
a
c
tiv
e
i
n
g
a
m
e
-
b
ase
d
lea
r
n
i
n
g
[
1
9
]
.
Ga
m
es
h
a
v
e
a
p
o
s
iti
v
e
ef
f
ec
t
o
n
t
h
e
v
a
r
i
o
u
s
e
m
o
ti
o
n
s
o
f
t
h
e
s
tu
d
en
ts
a
n
d
it
s
i
m
i
la
r
l
y
h
as
a
p
o
s
iti
v
e
i
n
f
lu
en
ce
o
n
s
t
u
d
e
n
ts
’
le
v
els
o
f
m
o
ti
v
ati
o
n
,
en
g
ag
e
m
e
n
t
,
at
tit
u
d
e
,
e
n
j
o
y
m
e
n
t,
a
n
d
s
tate
o
f
f
l
o
w
[
2
0
]
.
Ma
t
h
e
m
at
ic
al
m
a
n
i
p
u
l
ati
v
es
a
r
e
t
o
o
ls
d
es
ig
n
ed
f
o
r
s
tu
d
en
t
s
t
o
ex
p
l
o
r
e
a
n
d
g
r
as
p
th
e
id
ea
o
f
m
a
th
em
ati
cs
th
r
o
u
g
h
t
h
e
s
en
s
es
[
2
1
]
.
H
o
w
ev
er
,
th
er
e
is
n
o
d
o
u
b
t
t
h
a
t
s
t
u
d
e
n
ts
u
n
d
e
r
s
ta
n
d
a
n
d
w
o
r
k
m
at
h
e
m
a
tic
all
y
,
ev
e
n
s
o
,
wit
h
th
e
h
e
lp
o
f
m
a
n
i
p
u
lati
v
es
[
2
2
]
.
I
t
h
as
co
m
e
o
u
t
m
a
n
i
p
u
l
ati
v
es
t
h
at
wh
e
n
u
s
ed
m
a
k
es
s
t
u
d
e
n
ts
u
n
d
er
s
ta
n
d
an
d
d
e
v
el
o
p
s
h
ig
h
er
o
r
d
e
r
t
h
i
n
k
in
g
s
k
ills
[
2
3
]
.
So
m
e
t
y
p
es
o
f
m
a
n
ip
u
l
ati
v
es
in
c
lu
d
e
th
e
u
s
e
o
f
alg
e
b
r
a
tiles
,
n
u
m
b
e
r
l
in
es,
a
n
d
n
u
m
b
er
c
h
i
p
s
wit
h
r
esp
ec
t t
o
a
d
d
iti
o
n
a
n
d
s
u
b
tr
ac
t
io
n
[
2
4
]
–
[
2
6
]
.
I
n
th
e
Ph
ilip
p
in
es,
th
e
m
is
s
io
n
o
f
th
e
Dep
ar
t
m
en
t
o
f
E
d
u
c
atio
n
(
Dep
E
d
)
s
tates
th
at
ev
e
r
y
s
tu
d
en
t
s
h
o
u
ld
b
e
a
f
f
o
r
d
ed
th
e
r
ig
h
t
t
o
p
o
s
s
ess
a
q
u
ality
,
eq
u
itab
le,
cu
ltu
r
ally
r
elev
a
n
t
a
n
d
co
m
p
l
ete
b
asic
ed
u
ca
tio
n
[
2
7
]
.
Giv
en
Dep
E
d
’
s
u
n
d
er
s
tan
d
in
g
o
f
its
m
an
d
ate
to
p
r
o
v
id
e
in
s
ig
h
t a
n
d
g
u
id
an
ce
in
p
r
o
m
o
tin
g
an
d
e
n
s
u
r
in
g
th
e
q
u
ality
o
f
b
asic
ed
u
ca
tio
n
th
r
o
u
g
h
o
u
t
th
e
Ph
ilip
p
in
es
’
r
eg
io
n
,
it
c
o
n
tin
u
es
to
en
g
ag
e
in
v
ar
io
u
s
ass
es
s
m
en
ts
aim
ed
at
ad
d
r
ess
i
n
g
th
e
ch
allen
g
e
o
f
im
p
r
o
v
in
g
an
d
p
r
o
g
r
ess
in
g
to
war
d
s
th
e
in
ter
n
atio
n
aliza
tio
n
o
f
th
e
b
asic
ed
u
ca
tio
n
al
q
u
a
lity
.
On
e
o
f
th
ese
ass
e
s
s
m
e
n
ts
is
th
e
Pro
g
r
am
m
e
f
o
r
I
n
ter
n
atio
n
al
Stu
d
en
t
Ass
es
s
m
en
t
(
PISA)
,
wh
er
e
it
ex
am
in
es
th
e
p
r
o
f
icien
cy
o
f
s
tu
d
e
n
ts
in
th
e
th
r
e
e
d
o
m
ain
s
–
r
ea
d
in
g
,
m
ath
em
atics
,
an
d
s
cien
ce
liter
ac
y
.
As
in
d
icate
d
b
y
th
e
r
esu
l
ts
o
f
PISA,
th
e
Ph
ilip
p
in
es
h
a
s
n
o
t
b
ee
n
a
b
le
to
ex
ce
l
th
e
m
ath
em
atics
d
o
m
ain
.
I
n
th
e
2
0
2
2
ass
ess
m
en
t,
it
ac
h
iev
ed
an
av
er
a
g
e
o
f
3
5
5
p
o
in
ts
wh
ic
h
was
co
n
s
id
er
ab
ly
less
th
an
th
e
4
7
2
p
o
in
ts
th
at
th
e
Or
g
an
izatio
n
f
o
r
E
co
n
o
m
ic
C
o
-
o
p
e
r
atio
n
an
d
Dev
elo
p
m
e
n
t
(
OE
C
D
)
m
em
b
er
s
o
b
tain
ed
.
At
b
est,
o
n
l
y
1
6
%
o
f
th
e
s
tu
d
en
ts
wh
o
wer
e
1
5
y
ea
r
s
o
l
d
c
o
u
ld
o
b
tain
lev
el
2
,
wh
ich
h
as b
ee
n
d
esig
n
ated
as th
e
m
in
im
u
m
lev
el
r
eq
u
ir
e
d
f
o
r
u
n
d
er
s
tan
d
i
n
g
an
d
f
i
n
d
in
g
s
i
m
p
le
m
ath
em
atica
l
co
n
ten
t.
Fo
r
co
m
p
a
r
is
o
n
p
u
r
p
o
s
es,
th
e
av
er
ag
e
f
o
r
th
e
OE
C
D
ar
ea
i
s
6
9
%
.
I
n
ad
d
itio
n
,
n
o
Fil
ip
in
o
s
tu
d
en
ts
r
ea
ch
ed
th
e
h
ig
h
est lev
els o
f
p
r
o
f
icien
cy
(
lev
el
5
o
r
6
)
wh
ich
r
eq
u
ir
e
a
d
v
an
ce
d
p
r
o
b
lem
s
o
l
v
in
g
an
d
m
o
d
elin
g
m
ath
em
atics
[
2
8
]
.
T
h
is
s
u
g
g
ests
a
s
ig
n
if
ican
t
g
ap
to
en
a
b
le
lear
n
er
s
to
d
e
v
elo
p
h
ig
h
-
o
r
d
er
m
at
h
em
atica
l
co
m
p
eten
cies.
D
a
a
n
T
a
l
i
g
a
m
a
n
I
n
t
e
g
r
a
t
e
d
Se
c
o
n
d
a
r
y
S
c
h
o
o
l
(
D
T
I
S
S
)
i
s
a
r
e
m
o
t
e
i
n
d
i
g
e
n
o
u
s
p
e
o
p
l
e
s
e
d
u
c
a
t
i
o
n
(
I
P
E
d
)
s
e
c
o
n
d
a
r
y
s
c
h
o
o
l
i
n
B
u
t
u
a
n
C
i
t
y
,
P
h
i
li
p
p
i
n
e
s
,
es
t
ab
l
i
s
h
e
d
t
o
s
e
r
v
e
M
a
n
o
b
o
i
n
d
i
g
e
n
o
u
s
s
t
u
d
e
n
ts
b
y
p
r
o
v
i
d
i
n
g
c
u
l
t
u
r
a
l
l
y
r
e
l
e
v
a
n
t
an
d
a
c
c
e
s
s
i
b
l
e
e
d
u
c
a
t
i
o
n
.
T
h
e
s
c
h
o
o
l
i
s
c
o
m
m
it
t
e
d
t
o
f
o
s
t
e
r
i
n
g
q
u
a
l
i
t
y
e
d
u
c
a
t
i
o
n
t
h
a
t
i
n
t
e
g
r
a
te
s
i
n
d
i
g
e
n
o
u
s
k
n
o
w
l
e
d
g
e
s
y
s
t
e
m
s
w
h
i
le
a
d
d
r
e
s
s
in
g
t
h
e
u
n
i
q
u
e
l
e
a
r
n
i
n
g
n
e
e
d
s
o
f
i
t
s
s
t
u
d
e
n
ts
.
O
n
e
o
f
t
h
e
s
i
g
n
i
f
i
ca
n
t
c
h
a
l
l
e
n
g
es
i
n
I
PE
d
s
c
h
o
o
l
s
is
e
n
s
u
r
i
n
g
t
h
a
t
m
at
h
e
m
a
t
i
c
al
c
o
n
c
e
p
t
s
,
s
u
c
h
a
s
a
lg
e
b
r
a
,
a
r
e
t
a
u
g
h
t
i
n
a
m
a
n
n
e
r
t
h
a
t
a
l
i
g
n
s
w
i
t
h
s
t
u
d
e
n
t
s
’
c
u
l
t
u
r
a
l
b
a
c
k
g
r
o
u
n
d
s
a
n
d
l
e
a
r
n
i
n
g
s
t
y
l
es
.
R
e
c
o
g
n
i
zi
n
g
t
h
e
s
e
c
h
a
l
l
e
n
g
es
,
t
h
e
D
e
p
E
d
a
n
d
i
n
d
i
g
e
n
o
u
s
p
e
o
p
l
e
s
(
I
P
)
l
e
a
d
e
r
s
f
o
r
m
u
l
a
te
d
t
h
e
N
a
t
i
o
n
a
l
I
n
d
i
g
e
n
o
u
s
P
e
o
p
l
es
E
d
u
c
a
t
i
o
n
P
o
l
i
cy
F
r
a
m
e
w
o
r
k
(
D
e
p
E
d
O
r
d
e
r
6
2
,
s
.
2
0
1
1
)
.
T
h
i
s
p
o
l
i
c
y
a
d
o
p
t
s
a
r
i
g
h
t
s
-
b
a
s
e
d
a
p
p
r
o
a
c
h
t
o
e
d
u
c
a
t
i
o
n
,
e
m
p
h
a
s
i
z
i
n
g
t
h
e
n
e
e
d
f
o
r
a
n
i
n
c
l
u
s
i
v
e
c
u
r
r
i
c
u
l
u
m
g
r
o
u
n
d
e
d
i
n
t
h
e
s
o
c
i
a
l
a
n
d
c
u
l
t
u
r
a
l
c
o
n
t
e
x
t
o
f
I
P
l
e
a
r
n
e
r
s
.
D
e
s
p
it
e
t
h
es
e
e
f
f
o
r
t
s
,
d
a
t
a
f
r
o
m
p
r
e
v
i
o
u
s
s
u
m
m
a
t
i
v
e
as
s
e
s
s
m
e
n
ts
a
t
D
T
I
SS
i
n
d
i
c
at
e
t
h
a
t
7
6
%
o
f
s
t
u
d
e
n
ts
c
o
n
t
i
n
u
e
t
o
s
t
r
u
g
g
l
e
w
i
t
h
m
a
t
h
e
m
at
i
cs
,
p
a
r
t
i
c
u
la
r
l
y
a
l
g
e
b
r
a
,
a
s
r
e
f
l
e
ct
e
d
i
n
t
h
e
i
r
l
ea
s
t
-
l
ea
r
n
e
d
c
o
m
p
e
t
e
n
c
i
es
.
A
l
g
e
b
r
a
i
c
c
o
n
c
e
p
t
s
a
n
d
p
r
o
c
e
d
u
r
e
s
h
a
v
e
b
e
e
n
i
d
e
n
t
i
f
i
ed
a
s
t
h
e
m
o
s
t
c
h
al
l
e
n
g
i
n
g
a
r
e
as
f
o
r
s
t
u
d
e
n
ts
,
i
m
p
e
d
i
n
g
t
h
e
i
r
ab
i
l
i
t
y
t
o
p
r
o
g
r
e
s
s
i
n
t
h
e
s
u
b
j
ec
t
.
S
i
n
c
e
t
h
e
K
t
o
1
2
c
u
r
r
i
c
u
l
u
m
f
o
l
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r
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c
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m
p
le
x
i
n
h
i
g
h
e
r
g
r
a
d
e
s
[
2
9
]
.
H
o
w
e
v
e
r
,
t
h
e
r
e
i
s
l
i
m
i
t
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l
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ti
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r
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ie
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c
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a
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b
a
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d
l
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r
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n
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i
n
a
d
d
r
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n
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th
e
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p
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i
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te
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i
f
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i
c
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lt
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a
m
o
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i
n
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o
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s
s
t
u
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n
I
P
E
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h
o
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l
s
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is
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p
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t
s
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ct
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i
q
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c
a
ti
o
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a
l
s
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i
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g
.
T
h
is
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ar
c
h
f
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o
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h
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a
cti
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ase
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o
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ts
i
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a
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eb
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o
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c
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p
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r
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u
r
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C
o
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ce
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t
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a
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e
r
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d
m
at
h
em
atic
al
id
e
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t
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tai
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it
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m
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m
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ica
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it
h
m
s
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d
p
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u
r
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a
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.
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k
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ab
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ak
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d
d
er
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e
th
e
r
e
q
u
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d
an
s
w
er
s
[
3
0
]
.
T
o
ad
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r
ess
s
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d
en
ts
’
d
if
f
icu
lti
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in
alg
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o
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ac
tiv
ities
,
s
u
ch
as
DaM
ath
an
d
Ma
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Ma
th
ex
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DaM
ath
,
d
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f
r
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t
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e
tr
ad
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Fil
ip
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o
b
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Dam
a,
was
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r
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o
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atin
g
m
ath
em
atic
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I
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2252
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8
8
2
2
B
o
o
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g
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l
g
eb
r
a
ma
s
tery th
r
o
u
g
h
a
ctivity
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b
a
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lea
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n
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ig
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les
… (
R
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N
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4031
g
am
e
p
iece
s
an
d
ass
ig
n
in
g
d
if
f
er
en
t
m
ath
em
atica
l
r
u
les
to
ea
ch
g
r
id
[
3
1
]
.
Me
an
wh
ile
,
Ma
ze
Ma
th
ex
er
c
is
es
co
m
b
in
ed
p
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o
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with
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h
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ally
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ter
ac
tiv
e,
h
an
d
s
-
o
n
ac
tiv
ities
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d
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th
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n
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o
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ter
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h
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e
s
p
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ically
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n
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p
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b
r
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g
r
a
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e
7
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laws
o
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x
p
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e
n
ts
;
g
r
ad
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8
:
s
o
lv
in
g
s
y
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tem
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o
f
lin
ea
r
eq
u
atio
n
s
in
two
v
ar
ia
b
les
;
an
d
g
r
ad
e
9
:
laws
o
f
r
ad
icals.
T
h
e
s
tu
d
y
aim
ed
to
ex
am
in
e
th
e
im
p
ac
t
o
f
ac
tiv
it
y
-
b
ased
lear
n
in
g
o
n
s
tu
d
en
ts
’
co
n
ce
p
tu
al
u
n
d
e
r
s
tan
d
in
g
an
d
p
r
o
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d
u
r
al
s
k
ills
in
th
ese
to
p
ics.
Sp
ec
if
ically
,
it
s
o
u
g
h
t
to
d
eter
m
in
e
wh
eth
er
s
ig
n
if
ican
t
im
p
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v
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e
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cu
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ed
in
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d
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s
tan
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k
ills
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ased
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g
an
d
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h
e
em
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th
em
es in
s
tu
d
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r
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eg
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d
in
g
th
eir
e
x
p
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ien
ce
s
wi
th
th
e
ac
tiv
ities
.
2.
M
E
T
H
O
D
2
.
1
.
Resea
rc
h
des
ig
n
T
h
e
r
esear
ch
d
esig
n
u
s
ed
i
n
th
is
s
tu
d
y
was
m
ix
ed
-
m
eth
o
d
s
r
esear
ch
.
Mix
ed
m
eth
o
d
s
r
esear
ch
is
a
m
eth
o
d
o
l
o
g
ical
ap
p
r
o
ac
h
wh
er
ein
a
r
esear
ch
er
ca
n
u
tili
ze
b
o
th
q
u
alitativ
e
an
d
q
u
a
n
titativ
e
m
eth
o
d
o
l
o
g
ies,
d
ata
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llectio
n
to
o
ls
,
a
n
d
d
ata
an
aly
s
is
.
I
t
s
ee
k
s
to
in
teg
r
ate
b
o
th
to
en
h
a
n
ce
th
e
ex
p
lan
ati
o
n
o
f
th
e
o
b
jectiv
e
ad
d
r
ess
ed
[
3
2
]
.
I
t
em
p
l
o
y
s
q
u
asi
-
ex
p
er
im
en
tal
q
u
an
titativ
e
r
esear
ch
[
3
3
]
.
T
h
is
q
u
asi
-
ex
p
er
im
en
tal
r
esear
ch
em
p
lo
y
ed
a
p
r
e
-
test
p
o
s
t
-
test
d
esig
n
t
h
at
co
m
p
ar
es
two
m
ea
s
u
r
es
o
f
th
e
d
e
p
en
d
e
n
t
v
ar
iab
le
(
s
tu
d
en
t
p
er
f
o
r
m
an
ce
)
tak
en
o
n
th
e
s
am
e
g
r
o
u
p
o
r
in
d
iv
id
u
al,
o
n
e
b
ef
o
r
e
an
d
th
e
o
th
er
o
n
e
af
te
r
th
e
ac
tiv
ities
,
to
ev
alu
ate
th
e
im
p
ac
t
th
e
ac
tiv
i
ties
h
ad
o
n
th
e
g
r
o
u
p
.
Par
ticip
an
ts
ar
e
test
ed
b
ef
o
r
e
th
e
ac
tiv
ities
(
p
r
e
-
test
)
to
estab
lis
h
a
b
aselin
e
an
d
ag
ain
af
ter
th
e
ac
tiv
ities
(
p
o
s
t
-
test
)
t
o
m
ea
s
u
r
e
th
e
ch
an
g
es [
3
4
]
.
Q
u
alitativ
ely
,
it u
s
ed
th
em
atic
an
aly
s
is
o
f
s
tu
d
en
t
r
e
s
p
o
n
s
es
to
lear
n
m
o
r
e
ab
o
u
t
h
o
w
th
ey
ex
p
er
ien
ce
d
an
d
p
er
c
eiv
ed
th
e
ac
tiv
ities
,
wh
ich
h
elp
s
to
clar
if
y
its
im
p
ac
ts
.
T
h
em
atic
an
aly
s
is
is
th
e
p
r
o
ce
s
s
o
f
id
en
tify
in
g
p
atter
n
s
o
r
th
em
es
with
in
q
u
alitativ
e
d
ata
[
3
5
]
.
A
t
h
o
r
o
u
g
h
ass
ess
m
en
t
o
f
th
e
ac
t
iv
ities
’
ef
f
icac
y
is
p
r
o
v
id
ed
b
y
th
is
b
len
d
o
f
q
u
an
titativ
e
an
d
q
u
alitativ
e
m
eth
o
d
s
.
B
ec
au
s
e
o
f
its
v
ar
i
o
u
s
ad
v
an
ta
g
es,
th
is
r
esear
ch
p
ar
ad
ig
m
is
o
f
ten
em
p
lo
y
ed
in
ed
u
ca
tio
n
al
r
esea
r
ch
,
it o
f
f
er
s
th
e
b
est k
n
o
wled
g
e
o
f
a
r
esear
ch
p
r
o
b
lem
.
2
.
2
.
Sa
m
pli
ng
t
ec
hn
iqu
e
a
n
d pa
rt
icipa
nts
T
h
i
s
s
t
u
d
y
u
t
i
li
z
es
a
s
t
r
at
i
f
i
e
d
r
a
n
d
o
m
s
a
m
p
l
i
n
g
t
e
c
h
n
i
q
u
e
,
w
h
i
c
h
i
n
v
o
l
v
e
s
d
i
v
i
d
i
n
g
t
h
e
p
o
p
u
l
a
t
i
o
n
i
n
t
o
s
m
a
l
le
r
s
u
b
g
r
o
u
p
s
k
n
o
w
n
as
s
tr
a
t
a
.
F
o
r
t
h
i
s
s
t
u
d
y
,
t
h
e
s
t
r
at
a
co
m
p
r
i
s
e
t
h
e
t
h
r
e
e
g
r
a
d
e
l
e
v
el
s
o
f
D
T
I
S
S
–
g
r
a
d
es
7
,
8
,
a
n
d
9
.
T
h
e
s
a
m
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f
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a
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w
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ate
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p
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t
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u
m
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i
t
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n
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a
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r
a
t
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a
s
i
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l
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r
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n
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o
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a
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c
h
n
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q
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t
h
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n
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p
l
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d
t
o
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el
e
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t
t
h
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o
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n
t
s
.
I
n
th
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p
ar
tic
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lar
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d
y
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esear
ch
p
r
o
p
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tili
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t
h
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o
ch
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an
f
o
r
m
u
la
f
o
r
f
i
n
ite
p
o
p
u
latio
n
[
3
6
]
,
wh
ich
is
′
=
/
(
1
+
(
2
⋅
(
1
−
)
/
(
2
⋅
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,
wh
er
e
′
is
th
e
s
am
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le
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ize
,
is
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ize
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r
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lim
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p
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(
2
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2
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s
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n
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i
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g
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th
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c
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o
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n
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;
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th
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ex
p
ec
ted
p
r
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ce
o
r
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p
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tio
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th
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p
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an
d
is
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d
esire
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m
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o
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.
N
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N
=1
4
4
.
Settin
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ize
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3
3
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To
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3
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A
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air
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s
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p
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s
t
-
test
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h
is
q
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esti
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4
8
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p
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test
th
at
ass
es
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d
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’
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n
ce
p
tu
al
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n
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er
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tan
d
i
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g
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d
p
r
o
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ed
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r
al
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k
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e
law
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o
f
ex
p
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n
e
n
ts
,
s
o
lv
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g
s
y
s
tem
s
o
f
lin
ea
r
eq
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atio
n
s
in
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ar
iab
les,
an
d
laws
o
f
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ad
icals.
T
h
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twelv
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2
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ch
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4
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ile
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2
4
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.
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h
e
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esear
ch
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p
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s
o
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ly
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ed
th
e
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esti
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s
in
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f
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p
ec
if
icatio
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f
o
llo
win
g
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Dep
E
d
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lear
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c
o
m
p
eten
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in
th
e
ab
o
v
em
e
n
tio
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ed
to
p
ics.
Prio
r
to
d
ata
co
llectio
n
,
th
e
q
u
esti
o
n
n
air
e
was
v
alid
ated
f
o
r
v
alid
i
ty
an
d
r
eliab
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y
to
co
n
f
ir
m
th
at
it
m
et
th
e
r
eq
u
ir
em
en
t
[
3
7
]
.
T
h
e
in
s
tr
u
m
e
n
t
u
n
d
er
wen
t
co
n
ten
t
v
alid
atio
n
b
y
th
r
ee
ex
p
er
ts
in
m
ath
em
atics
ed
u
ca
tio
n
to
en
s
u
r
e
th
at
th
e
item
s
ac
cu
r
ately
r
ef
lecte
d
th
e
in
ten
d
e
d
lear
n
in
g
co
m
p
eten
cies.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
14
,
No
.
5
,
Octo
b
er
20
25
:
4
0
2
9
-
403
9
4032
T
h
e
v
alid
ato
r
s
ex
am
in
e
d
th
e
q
u
esti
o
n
n
air
e
f
o
r
clar
ity
,
r
ele
v
an
ce
,
an
d
a
p
p
r
o
p
r
iaten
ess
o
f
th
e
item
s
f
o
r
th
e
tar
g
eted
g
r
ad
e
lev
els.
Feed
b
ac
k
f
r
o
m
th
e
v
alid
ato
r
s
was
u
s
ed
to
r
ef
in
e
th
e
i
n
s
tr
u
m
en
t
b
ef
o
r
e
its
ad
m
in
is
tr
atio
n
.
T
o
estab
lis
h
r
e
liab
ilit
y
,
a
p
ilo
t te
s
t w
as c
o
n
d
u
cted
am
o
n
g
a
g
r
o
u
p
o
f
3
0
s
tu
d
en
ts
wh
o
wer
e
n
o
t
p
ar
t o
f
th
e
ac
tu
al
s
tu
d
y
b
u
t h
a
d
s
im
ilar
ch
ar
ac
ter
is
tics
to
th
e
p
ar
ticip
an
ts
.
T
h
e
r
eliab
ilit
y
o
f
th
e
in
s
tr
u
m
en
t w
as
m
ea
s
u
r
ed
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s
in
g
C
r
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ac
h
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s
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lp
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a,
y
ield
i
n
g
a
co
e
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f
icien
t
o
f
0
.
8
2
,
in
d
icatin
g
g
o
o
d
in
ter
n
a
l
co
n
s
is
ten
cy
[
3
8
]
.
T
o
co
n
tr
o
l
co
n
f
o
u
n
d
in
g
v
a
r
iab
les,
th
e
r
esear
ch
er
im
p
l
em
en
ted
a
co
n
s
is
ten
t
test
in
g
en
v
ir
o
n
m
en
t
b
y
ad
m
in
is
ter
in
g
th
e
p
r
e
-
test
an
d
p
o
s
t
-
test
u
n
d
er
s
im
ilar
co
n
d
itio
n
s
,
in
clu
d
in
g
th
e
s
am
e
ti
m
e
allo
tm
en
t,
s
am
e
class
r
o
o
m
s
ettin
g
s
,
s
am
e
in
s
tr
u
ctio
n
s
,
ac
tiv
ities
wer
e
co
n
d
u
cted
u
n
if
o
r
m
ly
an
d
s
am
e
s
et
o
f
ac
tiv
ities
.
T
h
at
is
,
th
e
r
esear
ch
er
ad
m
in
is
ter
ed
th
e
p
r
e
-
test
f
o
r
1
h
o
u
r
to
th
e
s
tu
d
en
ts
.
No
te
th
at
th
e
p
r
e
-
test
m
ea
n
s
th
e
ass
es
s
m
en
t
b
ef
o
r
e
th
e
ac
tiv
ities
.
T
h
e
r
esu
l
ts
o
f
th
e
p
r
e
-
test
wer
e
th
en
as
s
ess
ed
.
T
h
e
ac
tiv
ities
wer
e
g
i
v
en
e
v
er
y
Frid
ay
o
f
th
e
wee
k
f
o
r
o
n
e
h
o
u
r
.
T
h
e
ac
tiv
ities
r
u
n
f
o
r
o
n
e
m
o
n
th
.
Du
r
in
g
t
h
e
ac
tiv
ities
,
th
e
r
esear
c
h
er
g
av
e
v
ar
iety
o
f
ac
tiv
ities
to
th
e
s
tu
d
en
ts
s
u
ch
as Da
Mat
h
an
d
Ma
ze
.
T
h
e
r
esear
ch
er
ag
ain
ad
m
in
is
ter
ed
a
p
o
s
t
-
test
.
T
h
e
s
co
r
e
s
o
f
th
e
s
tu
d
en
ts
wer
e
co
n
s
o
lid
a
ted
f
o
r
d
ata
an
aly
s
is
.
Fin
ally
,
th
e
s
tu
d
en
ts
wer
e
ask
ed
o
n
th
eir
ex
p
e
r
ien
ce
s
an
d
p
er
ce
p
tio
n
s
o
f
th
e
ac
tiv
ities
th
ey
en
co
u
n
ter
ed
.
T
h
e
ac
tiv
ities
wer
e
DaM
ath
o
n
laws
o
f
ex
p
o
n
en
ts
an
d
r
a
d
icals
an
d
Ma
ze
o
n
laws
o
f
ex
p
o
n
e
n
ts
,
s
y
s
tem
o
f
lin
ea
r
eq
u
atio
n
s
in
two
v
ar
iab
les,
an
d
laws
o
f
r
ad
icals.
Fig
u
r
e
1
s
h
o
ws
th
e
DaM
ath
o
n
L
aws
o
f
ex
p
o
n
e
n
ts
wh
er
e
s
tu
d
en
ts
ca
n
p
lay
an
d
eith
er
s
im
p
lif
y
,
m
u
lti
p
ly
,
o
r
d
iv
id
e
ex
p
r
ess
io
n
s
o
n
th
e
ch
ip
s
.
Fig
u
r
e
2
s
h
o
ws
th
e
Ma
ze
o
n
s
o
lv
in
g
s
y
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o
f
lin
ea
r
eq
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atio
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s
in
two
v
ar
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d
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f
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wh
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e
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ts
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o
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lify
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ical
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p
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ess
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n
til th
ey
r
ea
ch
e
d
th
e
f
in
is
h
lin
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Fig
u
r
e
1
.
Mo
d
if
ied
DaM
ath
o
n
laws o
f
ex
p
o
n
en
ts
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
B
o
o
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a
l
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r
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tery th
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o
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R
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)
4033
Fig
u
r
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2
.
Ma
ze
o
n
s
o
lv
in
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s
y
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tem
s
o
f
lin
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r
eq
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atio
n
s
in
tw
o
v
ar
iab
les an
d
laws o
f
r
ad
ical
s
2
.
4
.
Ana
ly
s
is
T
h
e
s
c
o
r
e
s
a
n
d
t
h
e
m
e
a
n
p
e
r
c
en
t
a
g
e
s
c
o
r
e
(
M
PS
)
b
e
f
o
r
e
a
n
d
a
f
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e
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t
h
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a
c
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d
.
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a
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r
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i
a
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n
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y
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,
t
h
e
p
a
i
r
e
d
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a
m
p
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e
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-
te
s
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w
a
s
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s
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d
.
S
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p
a
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-
s
a
m
p
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t
-
t
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t
i
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a
p
a
r
a
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r
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c
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es
t
,
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h
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a
s
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u
m
p
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w
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r
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c
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c
k
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d
t
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n
s
u
r
e
t
h
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v
a
l
i
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i
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f
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t
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r
es
u
l
ts
a
n
d
o
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c
e
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h
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a
s
s
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m
p
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o
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a
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m
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t
,
t
h
e
n
t
h
e
t
e
s
t
c
a
n
b
e
u
s
ed
[
3
9
]
.
T
h
e
p
a
i
r
e
d
s
a
m
p
l
e
s
t
-
t
e
s
t
is
u
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ac
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3.
RE
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1
3
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id
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tifie
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Ad
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R
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4
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h
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ests
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ly
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0
4
3
.
3
3
1
.
6
4
G
r
a
d
e
9
C
o
n
c
e
p
t
u
a
l
1
3
.
6
9
5
7
.
0
4
2
.
2
9
P
r
o
c
e
d
u
r
a
l
8
.
5
4
3
5
.
5
8
2
.
3
0
3
.
2
.
Af
t
er
a
ct
i
v
it
y
-
ba
s
ed
lea
rning
T
ab
le
3
p
r
esen
ts
th
e
im
p
r
o
v
em
en
t
in
m
ea
n
s
co
r
es
f
r
o
m
th
e
p
r
e
-
test
to
th
e
p
o
s
t
-
test
,
s
h
o
win
g
a
co
n
s
is
ten
t
in
cr
ea
s
e
in
b
o
th
co
n
ce
p
tu
al
u
n
d
er
s
tan
d
in
g
an
d
p
r
o
ce
d
u
r
al
s
k
ills
ac
r
o
s
s
al
l
g
r
ad
e
lev
els.
T
h
e
s
ig
n
if
ican
t g
ain
s
in
s
tu
d
en
ts
’
s
co
r
es su
g
g
est th
at
ac
tiv
ity
-
b
ased
teac
h
in
g
h
as a
p
o
s
itiv
e
im
p
ac
t o
n
th
eir
alg
eb
r
a
p
r
o
f
icien
c
y
.
T
h
ese
f
in
d
in
g
s
h
ig
h
lig
h
t
t
h
e
ef
f
ec
tiv
e
n
ess
o
f
h
an
d
s
-
o
n
an
d
in
ter
ac
tiv
e
le
ar
n
in
g
s
tr
ateg
ies
in
en
h
an
cin
g
s
tu
d
en
ts
’
m
ath
em
at
ical
p
er
f
o
r
m
a
n
ce
.
T
ab
le
3
.
Descr
ip
tiv
e
s
tatis
tics
in
co
n
ce
p
t
u
al
u
n
d
er
s
tan
d
in
g
a
n
d
p
r
o
ce
d
u
r
al
s
k
ills
s
co
r
es a
f
ter
ac
tiv
ity
-
b
ased
lear
n
in
g
G
r
a
d
e
l
e
v
el
S
k
i
l
l
s
M
e
a
n
M
P
S
S
t
a
n
d
a
r
d
d
e
v
i
a
t
i
o
n
G
r
a
d
e
7
C
o
n
c
e
p
t
u
a
l
1
9
.
2
9
8
0
.
3
8
2
.
5
5
P
r
o
c
e
d
u
r
a
l
1
7
.
7
9
7
4
.
1
3
1
.
6
7
G
r
a
d
e
8
C
o
n
c
e
p
t
u
a
l
1
9
.
0
7
7
9
.
4
6
2
.
4
9
P
r
o
c
e
d
u
r
a
l
1
8
.
4
0
7
6
.
6
7
1
.
6
4
G
r
a
d
e
9
C
o
n
c
e
p
t
u
a
l
2
1
.
2
3
8
8
.
4
6
2
.
0
9
P
r
o
c
e
d
u
r
a
l
1
9
.
0
8
7
9
.
5
0
2
.
7
2
T
h
e
MPS
o
f
g
r
ad
e
7
in
c
o
n
c
ep
tu
al
u
n
d
e
r
s
tan
d
in
g
in
c
r
ea
s
es
f
r
o
m
4
1
.
0
8
to
8
0
.
3
8
,
wh
ile
p
r
o
ce
d
u
r
al
s
k
ills
M
PS
in
cr
ea
s
es
f
r
o
m
3
4
.
8
3
to
7
4
.
1
3
af
ter
th
e
ac
tiv
ities
.
T
h
ese
s
u
g
g
est
th
at
im
p
r
o
v
e
m
en
ts
h
ap
p
en
af
ter
th
e
ac
tiv
ities
ar
e
ap
p
lied
.
Similar
o
b
s
er
v
atio
n
s
ca
n
b
e
m
ad
e
f
o
r
g
r
ad
e
8
s
tu
d
en
t
s
.
T
h
e
co
n
ce
p
tu
al
u
n
d
er
s
tan
d
i
n
g
MPS
in
cr
ea
s
es
f
r
o
m
4
9
.
4
6
to
7
9
.
4
6
,
wh
ile
p
r
o
ce
d
u
r
al
s
k
ills
MPS
in
cr
ea
s
es
f
r
o
m
4
3
.
3
3
to
7
6
.
6
7
af
ter
th
e
ac
tiv
ities
.
T
h
e
g
r
ad
e
9
s
tu
d
e
n
ts
p
er
f
o
r
m
ed
e
x
ce
llen
tly
in
t
h
e
co
n
ce
p
tu
al
with
a
m
ea
n
s
co
r
e
o
f
2
1
.
2
3
with
MPS
o
f
8
8
.
4
6
.
T
h
e
s
tu
d
en
ts
’
p
r
o
ce
d
u
r
al
m
ea
n
s
c
o
r
e
also
im
p
r
o
v
es,
r
is
in
g
f
r
o
m
8
.
5
4
to
1
9
.
0
8
with
MPS
o
f
7
9
.
5
0
.
T
h
e
s
tan
d
a
r
d
d
ev
iatio
n
s
o
f
g
r
a
d
e
s
7
a
n
d
8
s
co
r
es
af
ter
ac
tiv
ity
-
b
ased
teac
h
in
g
in
co
n
ce
p
tu
al
ar
e
h
ig
h
e
r
th
a
n
in
th
e
p
r
o
ce
d
u
r
al,
wh
ich
m
ea
n
s
th
at
th
e
s
co
r
es
in
co
n
ce
p
tu
al
ar
e
m
o
r
e
d
is
p
er
s
ed
co
m
p
ar
ed
to
th
e
s
co
r
es
in
t
h
e
p
r
o
ce
d
u
r
al.
H
o
wev
er
,
t
h
e
p
r
o
ce
d
u
r
al
s
co
r
es in
g
r
a
d
e
9
ar
e
m
o
r
e
d
is
p
er
s
ed
th
an
in
co
n
ce
p
tu
al
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I
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2252
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8
8
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2
B
o
o
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g
a
l
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eb
r
a
ma
s
tery th
r
o
u
g
h
a
ctivity
-
b
a
s
ed
lea
r
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in
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n
a
n
in
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ig
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o
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s
p
eo
p
les
… (
R
o
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N
a
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l A
p
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4035
s
co
r
es.
T
h
ese
f
in
d
in
g
s
alig
n
with
ex
is
tin
g
liter
atu
r
e
em
p
h
asizin
g
th
e
ef
f
icac
y
o
f
ac
tiv
ity
-
b
ased
lear
n
i
n
g
i
n
m
ath
em
atics
ed
u
ca
tio
n
.
A
s
tu
d
y
b
y
An
war
[
4
1
]
h
ig
h
lig
h
te
d
th
at
lear
n
er
ten
d
t
o
b
e
m
o
r
e
in
ter
ested
in
ac
tiv
ity
-
b
ased
teac
h
in
g
co
m
p
ar
e
d
t
o
tr
ad
itio
n
al
lectu
r
e
m
eth
o
d
s
,
wh
ich
ca
n
lea
d
to
in
c
r
ea
s
ed
m
ath
em
atics
ac
h
iev
em
en
t.
Fu
r
t
h
er
m
o
r
e,
g
a
m
e
-
b
ased
lear
n
in
g
ex
p
er
ien
ce
s
p
o
s
itiv
ely
in
f
lu
en
ce
p
r
im
ar
y
s
tu
d
en
ts
’
attitu
d
es
to
war
d
m
ath
em
atics,
th
er
e
b
y
i
m
p
r
o
v
i
n
g
th
eir
en
g
a
g
em
en
t a
n
d
u
n
d
e
r
s
tan
d
in
g
[
4
2
]
.
T
h
e
s
ig
n
if
ican
t
im
p
r
o
v
em
e
n
t
o
b
s
er
v
ed
ac
r
o
s
s
all
g
r
ad
e
lev
els
in
th
e
p
o
s
t
-
test
in
d
icate
s
th
at
p
ar
ticip
an
ts
ac
h
iev
ed
s
u
b
s
tan
tial
p
r
o
g
r
ess
in
b
o
th
c
o
n
ce
p
t
u
a
l
u
n
d
er
s
tan
d
i
n
g
a
n
d
p
r
o
ce
d
u
r
al
s
k
ills
in
alg
eb
r
a.
T
h
is
s
u
g
g
ests
th
at
ac
tiv
ity
-
b
as
ed
lear
n
in
g
ef
f
ec
tiv
el
y
en
h
an
c
es
s
tu
d
en
ts
’
ab
ilit
y
to
g
r
asp
a
n
d
ap
p
ly
alg
e
b
r
aic
co
n
ce
p
ts
.
As p
r
ev
io
u
s
ly
h
ig
h
li
g
h
ted
,
h
a
n
d
s
-
o
n
lear
n
in
g
ac
tiv
ities
n
o
t o
n
ly
im
p
r
o
v
e
ac
a
d
em
ic
p
er
f
o
r
m
an
ce
b
u
t
also
f
o
s
ter
g
r
ea
ter
s
tu
d
e
n
t in
te
r
est an
d
en
g
a
g
em
en
t in
lear
n
in
g
ab
s
tr
ac
t m
ath
em
atica
l c
o
n
ce
p
ts
lik
e
alg
eb
r
a.
3
.
3
.
T
he
ef
f
ec
t
o
f
Da
M
a
t
h a
nd
m
a
ze
a
ct
iv
it
ies in t
he
co
n
ce
ptua
l und
er
s
t
a
nd
ing
a
nd
p
ro
ce
du
ra
l
s
k
ills
T
ab
le
4
h
ig
h
lig
h
ts
a
clea
r
i
m
p
r
o
v
e
m
en
t
in
s
tu
d
e
n
ts
’
s
co
r
es,
s
h
o
win
g
p
o
s
itiv
e
m
ea
n
d
if
f
er
en
ce
s
b
etwe
en
th
eir
p
o
s
t
-
test
an
d
p
r
e
-
test
r
esu
lts
in
b
o
th
c
o
n
c
ep
tu
al
u
n
d
er
s
tan
d
in
g
an
d
p
r
o
ce
d
u
r
al
s
k
ills
.
On
av
er
ag
e,
s
tu
d
en
ts
s
co
r
ed
7
to
1
1
p
o
in
ts
h
ig
h
er
a
f
ter
e
n
g
ag
in
g
in
ac
tiv
ity
-
b
ased
lea
r
n
in
g
,
r
ef
lectin
g
s
ig
n
if
ican
t
p
r
o
g
r
ess
.
T
h
is
s
u
g
g
ests
th
at
i
n
ter
ac
tiv
e
an
d
h
a
n
d
s
-
o
n
lear
n
in
g
m
eth
o
d
s
tr
u
l
y
h
el
p
s
tu
d
e
n
ts
g
r
asp
alg
e
b
r
aic
co
n
ce
p
ts
m
o
r
e
ef
f
ec
tiv
ely
a
n
d
ap
p
ly
th
em
with
g
r
ea
ter
c
o
n
f
i
d
en
ce
.
T
h
e
-
v
alu
es
ar
e
all
0
.
0
0
,
wh
ic
h
ar
e
less
th
an
th
e
s
ig
n
if
ican
ce
lev
el
0
.
0
1
.
T
h
is
r
esu
lt
in
d
icate
s
th
a
t
th
er
e
is
a
s
ig
n
if
ican
t
d
if
f
er
e
n
c
e
b
etwe
en
th
e
s
tu
d
en
ts
’
co
n
ce
p
tu
al
u
n
d
e
r
s
tan
d
in
g
b
ef
o
r
e
an
d
af
ter
th
e
ac
tiv
ity
-
b
ased
lear
n
in
g
.
Similar
ly
,
th
er
e
is
a
s
ig
n
if
ican
t
d
if
f
er
en
ce
b
etwe
en
th
e
s
tu
d
en
ts
’
p
r
o
ce
d
u
r
al
s
k
ills
b
ef
o
r
e
an
d
af
ter
th
e
ac
tiv
ity
-
b
ased
lear
n
i
n
g
.
Hen
ce
,
ac
tiv
ity
-
b
ased
lear
n
in
g
is
ef
f
ec
tiv
e
in
h
elp
in
g
s
t
u
d
en
ts
im
p
r
o
v
e
th
eir
ac
ad
em
ic
p
er
f
o
r
m
an
ce
in
alg
eb
r
a.
T
h
ese
r
esu
lts
f
u
r
th
er
s
u
p
p
o
r
t
th
e
f
in
d
in
g
s
o
f
Sh
lo
u
l
[
4
3
]
,
wh
ich
r
e
v
ea
led
th
at
p
r
o
ject
-
b
ased
lear
n
i
n
g
e
n
h
an
ce
s
cr
itical
th
in
k
in
g
a
n
d
m
ath
em
atica
l
en
g
ag
em
en
t,
lead
in
g
to
h
ig
h
er
p
er
f
o
r
m
an
ce
in
alg
eb
r
a
.
Similar
ly
,
Hiltrim
ar
tin
et
a
l.
[
4
4
]
co
n
f
ir
m
e
d
th
at
e
n
g
ag
in
g
s
tu
d
en
ts
in
s
tr
u
ctu
r
ed
ac
tiv
ity
-
b
ased
lear
n
in
g
ap
p
r
o
a
ch
es si
g
n
if
ican
tly
im
p
r
o
v
es m
ath
em
atica
l a
b
ilit
ies
Hen
ce
,
ac
tiv
ity
-
b
ased
lear
n
in
g
is
a
p
o
we
r
f
u
l
way
to
h
elp
s
tu
d
en
ts
b
u
ild
th
eir
alg
e
b
r
a
s
k
ills
with
co
n
f
id
en
ce
.
B
y
m
ak
in
g
lear
n
in
g
m
o
r
e
i
n
ter
ac
tiv
e
an
d
h
an
d
s
-
o
n
,
it
allo
ws
s
tu
d
en
ts
to
tr
u
ly
u
n
d
er
s
tan
d
m
ath
em
atica
l
co
n
ce
p
ts
r
ath
er
th
an
ju
s
t
m
em
o
r
ize
p
r
o
ce
d
u
r
es.
T
h
is
ap
p
r
o
ac
h
n
o
t
o
n
l
y
s
tr
en
g
th
en
s
th
ei
r
p
r
o
b
lem
-
s
o
lv
in
g
ab
ilit
ies
b
u
t
also
m
ak
es
alg
eb
r
a
m
o
r
e
en
g
ag
in
g
an
d
e
n
jo
y
ab
le,
lead
i
n
g
to
b
etter
ac
ad
em
ic
p
er
f
o
r
m
an
ce
.
T
ab
le
4
.
Descr
ip
tiv
e
s
tatis
tics
in
co
n
ce
p
t
u
al
u
n
d
er
s
tan
d
in
g
a
n
d
p
r
o
ce
d
u
r
al
s
k
ills
s
co
r
es a
f
ter
ac
tiv
ity
-
b
ased
lear
n
in
g
G
r
a
d
e
l
e
v
e
l
S
k
i
l
l
s
M
e
a
n
SD
t
S
i
g
G
r
a
d
e
7
C
o
n
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e
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l
9
.
4
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3
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.
9
3
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P
r
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e
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r
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l
9
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.
3
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6
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r
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e
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C
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1
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S
i
g
n
i
f
i
c
a
n
t
a
t
0
.
0
1
l
e
v
e
l
o
f
si
g
n
i
f
i
c
a
n
c
e
3
.
4
.
T
hem
a
t
ic
a
na
ly
s
is
o
f
s
t
ud
ent
s
’
ex
perience
s
wit
h
Da
M
a
t
h a
nd
M
a
ze
a
ct
iv
it
ie
s
T
h
er
e
ar
e
th
r
ee
em
er
g
in
g
t
h
e
m
es
in
s
tu
d
en
ts
’
r
esp
o
n
s
es
wh
en
ask
ed
a
b
o
u
t
th
ei
r
ex
p
e
r
ie
n
ce
s
with
DaM
ath
an
d
Ma
ze
a
ctiv
ities
.
T
h
ese
t
h
em
es
ar
e
en
g
ag
e
m
en
t
an
d
e
n
jo
y
m
e
n
t,
i
n
cr
ea
s
ed
co
n
f
id
en
ce
,
a
n
d
im
p
r
o
v
e
d
u
n
d
er
s
tan
d
in
g
.
T
h
e
f
ir
s
t
th
em
e
is
en
g
ag
em
e
n
t
an
d
en
jo
y
m
e
n
t.
Mo
s
t
o
f
th
e
s
tu
d
e
n
ts
ex
p
r
ess
ed
th
at
th
e
ac
tiv
ities
allo
wed
th
em
to
en
jo
y
an
d
f
ee
l e
n
g
ag
ed
with
t
h
e
to
p
ics.
Fo
r
ex
a
m
p
le,
o
n
e
s
tu
d
en
t said
v
er
b
atim
,
with
th
e
co
r
r
esp
o
n
d
in
g
tr
an
s
la
tio
n
in
E
n
g
lis
h
:
“
Ma
lin
g
a
w
ko
ka
y
d
u
la
ma
n
s
iya
u
g
k
a
mi
mis
mo
ma
ka
b
a
lo
k
u
n
g
s
a
kto
b
a
mi
o
r
d
ili.
”
“
I
en
jo
y
th
e
a
ctivity,
a
n
d
I
ca
n
tell if
I
’
m
co
r
r
ec
t o
r
n
o
t b
ec
a
u
s
e
it is
h
a
n
d
s
-
on.
”
(
T
r
a
n
s
latio
n
)
T
h
e
s
ec
o
n
d
t
h
em
e
is
th
e
in
c
r
ea
s
e
in
co
n
f
id
e
n
ce
o
f
th
e
s
tu
d
en
ts
.
So
m
e
o
f
th
e
s
tu
d
e
n
ts
ex
p
r
ess
ed
th
at
th
ey
b
ec
am
e
m
o
r
e
co
n
f
id
en
t in
lea
r
n
in
g
b
y
h
av
i
n
g
ac
tiv
ities
in
cl
ass
.
On
e
s
tu
d
en
t said
th
at:
“
Dili
ko
ma
u
la
w
ma
ma
li
u
g
m
a
s
co
n
fid
en
t
ko
,
a
h
,
a
n
g
imp
o
r
ta
n
te
ma
ka
b
a
lo
k
o
s
a
to
p
ic
ka
y
d
u
la
ma
n
s
iya
.
”
“
I
a
m
n
o
t
a
s
h
a
med
o
f
ma
kin
g
mis
ta
ke
s
.
I
b
ec
o
me
mo
r
e
co
n
fid
en
t.
Th
e
imp
o
r
ta
n
t
th
in
g
is
th
a
t
I
lea
r
n
ed
.
”
(
T
r
an
s
latio
n
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
14
,
No
.
5
,
Octo
b
er
20
25
:
4
0
2
9
-
403
9
4036
T
h
e
f
in
al
th
em
e
is
th
e
im
p
r
o
v
ed
u
n
d
e
r
s
tan
d
in
g
o
f
th
e
s
tu
d
e
n
ts
.
Mo
s
t
o
f
th
e
s
tu
d
en
ts
h
av
e
ex
p
r
ess
ed
th
at
th
ey
u
n
d
er
s
tan
d
th
e
c
o
n
ce
p
ts
well
an
d
k
n
o
w
h
o
w
to
ap
p
ly
t
h
e
p
r
o
ce
d
u
r
es
in
s
o
lv
in
g
p
r
o
b
le
m
s
b
ec
au
s
e
o
f
th
e
ac
tiv
ities
.
T
h
ese
ac
tiv
it
ies
al
lo
w
th
em
to
in
ter
ac
t
with
th
e
m
ater
ial,
r
esu
ltin
g
in
an
im
p
r
o
v
ed
u
n
d
er
s
tan
d
i
n
g
o
f
th
e
less
o
n
.
On
e
s
tu
d
en
t said
th
at:
“
Ma
s
n
a
ka
s
a
b
o
t
ko
s
a
less
o
n
,
s
a
co
n
ce
p
ts
s
a
to
p
ic
u
g
s
a
p
a
g
s
o
lve
ka
r
o
n
n
g
a
n
a
y
d
u
la
.
Da
li
r
a
s
iya
ma
s
a
b
ta
n
.
”
“
Th
e
a
ctivities h
elp
ed
me
u
n
d
ers
ta
n
d
th
e
less
o
n
w
ell
a
n
d
h
o
w
to
a
p
p
ly
th
em.
”
(
T
r
an
s
latio
n
)
T
h
e
r
esu
lts
ar
e
s
u
p
p
o
r
ted
with
s
o
m
e
s
tu
d
ies
th
at
ac
tiv
ity
-
b
ased
lear
n
in
g
s
ig
n
if
ican
tly
im
p
r
o
v
es
th
e
ac
ad
em
ic
p
er
f
o
r
m
an
ce
o
f
s
tu
d
en
ts
in
m
ath
em
atics
[
1
6
]
.
T
h
e
ac
tiv
ities
h
elp
ed
s
tu
d
en
ts
to
b
e
m
o
r
e
i
n
v
o
lv
e
d
with
th
e
to
p
ics,
r
esu
ltin
g
in
an
in
cr
ea
s
e
in
s
tu
d
en
ts
’
u
n
d
er
s
tan
d
in
g
[
1
9
]
.
No
t o
n
ly
d
o
th
eir
s
co
r
es
im
p
r
o
v
e,
b
u
t
s
o
d
o
th
eir
attitu
d
es a
n
d
in
ter
e
s
ts
f
o
r
m
ath
-
r
elate
d
to
p
ics [
2
0
]
.
T
h
e
r
esu
lts
o
f
th
is
s
tu
d
y
a
r
e
co
n
s
is
ten
t
with
th
e
liter
atu
r
e
th
at
ac
tiv
ity
-
b
ased
lear
n
in
g
b
o
o
s
ts
u
p
s
tu
d
en
ts
’
p
er
f
o
r
m
a
n
ce
in
m
ath
em
atics.
T
h
e
in
cr
ea
s
ed
in
v
o
lv
em
en
t
d
o
es
n
o
t
o
n
ly
im
p
r
o
v
e
th
eir
s
co
r
es
b
u
t
also
u
ltima
tely
cr
ea
tes
a
p
o
s
it
iv
e
p
er
ce
p
tio
n
to
war
d
s
p
r
ac
ticin
g
m
ath
em
atics
th
at
m
ak
es
it
m
o
r
e
in
ter
esti
n
g
an
d
less
f
ea
r
f
u
l.
T
h
e
f
i
n
d
in
g
s
,
in
th
is
ca
s
e,
u
n
d
er
s
co
r
e
th
e
r
o
le
o
f
ac
tiv
ity
-
b
ased
lear
n
i
n
g
s
tr
ateg
ies
in
th
e
d
ev
elo
p
m
e
n
t o
f
b
o
th
t
h
e
co
g
n
i
tiv
e
an
d
em
o
tio
n
al
asp
ec
ts
o
f
t
h
e
s
tu
d
en
ts
.
4.
CO
NCLU
SI
O
N
T
h
is
s
tu
d
y
in
v
esti
g
ated
th
e
e
f
f
ec
t
o
f
ac
tiv
ity
-
b
ased
lear
n
in
g
o
n
th
e
c
o
n
ce
p
t
u
al
u
n
d
er
s
tan
d
in
g
a
n
d
p
r
o
ce
d
u
r
al
s
k
ills
o
f
ju
n
io
r
h
ig
h
s
ch
o
o
l
s
tu
d
en
ts
in
an
i
n
d
ig
e
n
o
u
s
lear
n
in
g
en
v
ir
o
n
m
e
n
t.
T
h
e
r
esu
lts
s
h
o
wed
a
s
ig
n
if
ican
t
im
p
ac
t
o
f
ac
tiv
ity
-
b
ased
lear
n
in
g
o
n
u
n
d
er
s
tan
d
i
n
g
alg
eb
r
aic
co
n
ce
p
ts
an
d
ap
p
ly
in
g
p
r
o
ce
d
u
r
es,
p
ar
ticu
lar
ly
in
th
e
least
-
lear
n
ed
to
p
ics
am
o
n
g
i
n
d
ig
e
n
o
u
s
lear
n
er
s
.
T
h
e
im
p
r
o
v
em
e
n
t
was
ev
id
en
t
in
th
e
m
ar
k
ed
d
if
f
e
r
en
ce
b
etwe
en
p
r
e
-
test
an
d
p
o
s
t
-
test
s
co
r
es,
d
em
o
n
s
tr
atin
g
t
h
at
in
ter
ac
tiv
e
,
h
an
d
s
-
o
n
ac
tiv
ities
s
u
ch
as
DaM
ath
a
n
d
Ma
ze
Ma
th
ar
e
e
f
f
ec
tiv
e
i
n
m
a
k
in
g
ab
s
tr
ac
t
alg
e
b
r
aic
c
o
n
ce
p
ts
m
o
r
e
ac
ce
s
s
ib
le
to
in
d
ig
en
o
u
s
s
tu
d
en
ts
.
I
n
in
d
ig
en
o
u
s
lear
n
i
n
g
c
o
n
tex
ts
,
wh
e
r
e
tr
ad
itio
n
al
teac
h
in
g
m
eth
o
d
s
m
ay
n
o
t
alwa
y
s
alig
n
with
s
tu
d
en
ts
’
c
u
ltu
r
al
b
ac
k
g
r
o
u
n
d
s
an
d
lear
n
in
g
s
ty
les,
ac
tiv
ity
-
b
ased
lear
n
in
g
p
r
o
v
ed
to
b
e
an
ef
f
ec
tiv
e
s
tr
ateg
y
.
B
y
s
h
if
ti
n
g
f
r
o
m
lectu
r
e
-
b
ased
in
s
tr
u
ctio
n
to
s
tu
d
en
t
-
ce
n
ter
ed
,
in
ter
ac
tiv
e
lear
n
in
g
,
s
tu
d
en
ts
wer
e
m
o
r
e
e
n
g
ag
e
d
,
an
d
th
ei
r
d
if
f
icu
lties
in
al
g
eb
r
a
wer
e
r
e
d
u
ce
d
.
Mo
r
eo
v
e
r
,
t
h
is
ap
p
r
o
ac
h
n
o
t
o
n
l
y
im
p
r
o
v
e
d
alg
eb
r
a
m
aster
y
b
u
t
also
f
o
s
ter
ed
co
n
f
id
en
ce
,
m
o
tiv
atio
n
,
an
d
a
m
o
r
e
p
o
s
itiv
e
attitu
d
e
to
war
d
m
ath
em
atics,
wh
ich
is
cr
u
cial
in
in
d
ig
en
o
u
s
ed
u
ca
tio
n
s
ettin
g
s
wh
er
e
lear
n
in
g
d
is
p
ar
ities
o
f
ten
ex
is
t
d
u
e
to
s
o
cio
-
cu
ltu
r
al
f
ac
to
r
s
.
Fro
m
th
e
f
in
d
in
g
s
o
f
th
is
s
tu
d
y
,
ed
u
ca
tio
n
al
in
s
titu
tio
n
s
s
er
v
in
g
in
d
ig
e
n
o
u
s
s
tu
d
en
ts
m
ig
h
t
co
n
s
id
er
im
p
lem
en
tin
g
cu
ltu
r
ally
r
esp
o
n
s
iv
e
ac
tiv
ity
-
b
ased
lear
n
in
g
s
tr
ateg
ies
with
in
th
e
c
u
r
r
icu
lu
m
to
en
h
a
n
ce
b
o
t
h
co
n
ce
p
tu
al
u
n
d
e
r
s
tan
d
in
g
an
d
p
r
o
ce
d
u
r
al
s
k
ills
.
T
ea
ch
er
s
s
h
o
u
ld
b
e
tr
ain
ed
an
d
r
etr
ain
e
d
i
n
th
ese
ap
p
r
o
ac
h
es
to
b
r
id
g
e
th
e
g
a
p
b
etwe
en
m
ath
em
atica
l
lear
n
in
g
an
d
in
d
ig
e
n
o
u
s
s
tu
d
e
n
ts
’
way
s
o
f
u
n
d
er
s
tan
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m
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[
1
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M
.
V
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3
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[
4
]
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.
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5
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C
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.
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p
e
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[
6
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K
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M
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