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o
m
es
a
v
ital
ar
ea
to
o
p
er
a
tio
n
alizin
g
s
u
ch
r
ef
o
r
m
s
,
as
it
s
er
v
es
as
a
f
o
u
n
d
atio
n
f
o
r
p
r
o
b
lem
-
s
o
lv
in
g
an
d
r
ea
s
o
n
in
g
y
et
r
em
ain
s
o
n
e
o
f
t
h
e
m
o
s
t c
h
allen
g
in
g
s
u
b
jects f
o
r
Fil
ip
in
o
lear
n
e
r
s
[
7
]
,
[
8
]
.
Ma
th
em
atics
in
s
tr
u
ctio
n
i
n
m
an
y
s
ch
o
o
ls
r
em
ain
s
ab
s
tr
ac
t
an
d
h
ea
v
ily
d
ep
e
n
d
e
n
t
o
n
r
o
te
p
r
o
ce
d
u
r
es.
L
ea
r
n
er
s
o
f
ten
s
tr
u
g
g
le
to
c
o
n
n
ec
t
m
ath
em
atic
al
id
ea
s
with
th
eir
liv
ed
ex
p
e
r
ien
ce
s
,
lead
in
g
to
lo
w
en
g
ag
em
e
n
t
an
d
ac
h
iev
e
m
en
t.
As
L
u
ec
k
e
[
9
]
ar
g
u
es,
teac
h
in
g
m
ath
em
atics
as
a
u
n
iv
er
s
al
an
d
cu
ltu
r
e
-
f
r
ee
d
is
cip
lin
e
ca
n
d
is
tan
ce
lear
n
er
s
f
r
o
m
its
m
ea
n
in
g
.
I
n
co
n
tr
ast,
in
teg
r
atin
g
cu
ltu
r
al
co
n
tex
t
an
d
ev
er
y
d
ay
ex
p
er
ien
ce
s
f
o
s
ter
s
a
s
en
s
e
o
f
b
elo
n
g
in
g
an
d
en
h
a
n
ce
s
co
m
p
r
eh
en
s
io
n
.
C
u
ltu
r
ally
r
elev
a
n
t
ed
u
ca
tio
n
(
C
R
E
)
r
esp
o
n
d
s
to
th
is
ch
allen
g
e
b
y
v
alid
atin
g
s
tu
d
en
ts
’
c
u
ltu
r
al
id
en
titi
es
an
d
in
teg
r
atin
g
lo
ca
l
co
n
tex
ts
in
to
teac
h
in
g
an
d
lear
n
i
n
g
.
I
t
tr
ea
t
s
cu
ltu
r
e
as
a
d
y
n
am
ic
r
eso
u
r
ce
f
o
r
ac
a
d
em
ic
s
u
cc
ess
r
ath
e
r
th
an
a
n
o
b
s
tacle
[
1
0
]
.
T
h
is
ch
allen
g
e
b
ec
o
m
es
m
o
r
e
p
r
o
n
o
u
n
ce
d
in
r
u
r
al
p
u
b
lic
s
ec
o
n
d
ar
y
s
ch
o
o
ls
,
wh
er
e
lim
ited
ac
ce
s
s
to
co
n
tex
tu
alize
d
lear
n
in
g
r
eso
u
r
ce
s
an
d
h
ea
v
y
teac
h
er
wo
r
k
l
o
ad
s
ca
n
co
n
s
tr
ain
d
if
f
er
en
tia
ted
in
s
tr
u
ctio
n
an
d
m
ak
e
cu
r
r
icu
lu
m
s
h
if
ts
m
o
r
e
d
if
f
icu
lt
to
im
p
lem
en
t.
Un
d
er
th
ese
co
n
d
itio
n
s
,
teac
h
er
s
n
ee
d
r
ea
d
y
-
to
-
u
s
e
m
ater
ials
th
at
co
n
n
ec
t
m
ath
em
atica
l
id
ea
s
to
lear
n
er
s
’
l
o
ca
l
ex
p
er
ie
n
ce
s
wh
ile
r
em
a
in
in
g
alig
n
e
d
with
cu
r
r
icu
lu
m
s
tan
d
ar
d
s
[
1
1
]
.
I
n
th
e
Ph
ilip
p
in
e
co
n
tex
t,
t
h
e
ca
ll
f
o
r
co
n
te
x
tu
alize
d
a
n
d
c
u
ltu
r
ally
r
esp
o
n
s
iv
e
in
s
tr
u
ctio
n
is
s
u
p
p
o
r
ted
n
o
t
o
n
ly
b
y
p
e
d
ag
o
g
y
b
u
t
also
b
y
p
o
licy
.
Sectio
n
1
0
o
f
th
e
I
m
p
lem
en
tin
g
R
u
le
s
an
d
R
eg
u
latio
n
s
(
I
R
R
)
o
f
R
ep
u
b
lic
Act
No
.
1
0
5
3
3
m
an
d
ates
cu
r
r
icu
l
u
m
f
l
ex
ib
ilit
y
f
o
r
lo
ca
lizatio
n
an
d
in
d
ig
en
izatio
n
.
T
h
is
d
ir
ec
tio
n
also
alig
n
s
with
UN
E
SC
O’
s
s
u
s
tain
ab
le
d
ev
elo
p
m
en
t g
o
al
(
SDG)
1
1
,
p
ar
ticu
lar
l
y
tar
g
et
1
1
.
4
,
wh
ic
h
em
p
h
asizes
p
r
o
tectin
g
an
d
p
r
o
m
o
tin
g
cu
ltu
r
al
h
er
itag
e.
He
n
ce
,
cu
ltu
r
ally
r
esp
o
n
s
iv
e
m
a
th
em
atics
teac
h
in
g
ca
n
s
tr
en
g
th
en
ac
ad
em
ic
lear
n
in
g
wh
ile
co
n
tr
ib
u
tin
g
to
th
e
p
r
eser
v
atio
n
o
f
in
tan
g
i
b
le
cu
ltu
r
al
tr
ad
itio
n
s
,
en
s
u
r
in
g
th
at
e
d
u
ca
tio
n
r
em
ai
n
s
r
elev
an
t,
in
clu
s
iv
e,
a
n
d
em
p
o
wer
in
g
[
1
2
]
.
W
ith
in
C
R
E
,
s
to
r
ies
an
d
f
o
lk
tales
o
f
f
er
a
p
ar
ticu
lar
ly
p
r
o
m
is
in
g
p
ath
way
f
o
r
co
n
te
x
tu
aliza
tio
n
b
ec
au
s
e
th
ey
ar
e
f
am
iliar
cu
ltu
r
al
f
o
r
m
s
th
r
o
u
g
h
wh
ic
h
co
m
m
u
n
ities
tr
an
s
m
it
v
alu
es,
p
r
ac
tices,
an
d
p
r
o
b
lem
-
s
o
lv
in
g
s
tr
ateg
ies.
Fo
lk
tales
s
er
v
e
as
v
ess
els
o
f
cu
lt
u
r
al
m
em
o
r
y
,
em
b
o
d
y
in
g
m
ea
n
in
g
s
r
ec
o
g
n
izab
le
to
lear
n
er
s
[
1
3
]
.
W
h
en
m
ath
e
m
atica
l
id
ea
s
ar
e
em
b
ed
d
ed
i
n
th
ese
n
ar
r
ativ
es
s
u
ch
as
p
a
tter
n
s
in
wea
v
in
g
,
p
r
o
p
o
r
tio
n
s
in
co
o
k
in
g
,
o
r
m
e
asu
r
em
en
ts
in
f
ar
m
in
g
c
o
n
ce
p
ts
b
ec
o
m
e
m
o
r
e
co
n
cr
ete
an
d
r
elata
b
le.
L
ea
r
n
er
s
ca
n
v
is
u
alize
an
d
in
te
r
p
r
et
n
u
m
b
er
s
th
r
o
u
g
h
t
h
e
len
s
o
f
t
h
eir
co
m
m
u
n
ity
’
s
liv
ed
e
x
p
er
ien
c
es.
Su
p
p
o
r
tin
g
th
is
v
iew,
s
tu
d
ies
af
f
ir
m
th
at
s
to
r
y
tellin
g
e
n
h
a
n
ce
s
en
g
ag
e
m
en
t,
co
m
p
r
eh
en
s
io
n
,
an
d
r
eten
tio
n
.
Ab
d
alla
an
d
M
o
u
s
s
a
[
1
4
]
em
p
h
asize
th
at
c
u
ltu
r
al
ly
r
esp
o
n
s
iv
e
in
s
tr
u
ctio
n
ad
d
r
ess
es
s
o
cial
b
ar
r
ier
s
to
ac
h
iev
em
en
t
b
y
g
r
o
u
n
d
in
g
lear
n
in
g
in
f
am
iliar
co
n
tex
ts
.
Similar
ly
,
Me
n
d
ez
an
d
E
s
[
1
5
]
id
en
tify
s
to
r
ies
as
ef
f
ec
tiv
e
to
o
ls
in
m
ath
em
atics
ed
u
ca
tio
n
b
ec
au
s
e
th
ey
“p
r
o
v
id
e
a
m
ea
n
in
g
f
u
l
co
n
tex
t
t
h
at
attr
ac
ts
lear
n
er
s
’
in
ter
est.”
T
h
u
s
,
in
teg
r
atin
g
lo
c
al
f
o
lk
tales
in
to
th
e
class
r
o
o
m
ca
n
u
n
ite
cu
ltu
r
e
a
n
d
c
o
g
n
itio
n
,
m
a
k
in
g
lear
n
in
g
b
o
th
in
tellectu
ally
r
i
g
o
r
o
u
s
an
d
em
o
tio
n
ally
r
eso
n
an
t.
Alo
n
g
s
id
e
s
to
r
y
-
b
ased
c
o
n
tex
t
u
aliza
tio
n
,
r
ec
en
t
s
tu
d
ies
also
h
ig
h
lig
h
t
tech
n
o
lo
g
y
an
d
i
n
q
u
ir
y
-
d
r
iv
e
n
in
n
o
v
atio
n
s
in
m
ath
em
atics
i
n
s
tr
u
ctio
n
.
Fo
r
in
s
tan
ce
,
au
g
m
en
ted
r
ea
lity
ca
n
im
p
r
o
v
e
e
lem
en
tar
y
lear
n
er
s
’
cr
itical
th
in
k
in
g
[
1
6
]
,
d
ig
itall
y
s
u
p
p
o
r
te
d
f
r
am
ewo
r
k
s
ca
n
s
tr
en
g
th
en
p
r
e
-
s
er
v
ice
teac
h
e
r
s
’
lear
n
in
g
d
esig
n
co
m
p
eten
cies
an
d
r
esear
ch
b
a
s
ed
lear
n
in
g
-
s
cien
ce
,
tech
n
o
lo
g
y
,
e
n
g
in
ee
r
i
n
g
,
a
n
d
m
ath
em
atics
(
RBL
-
STE
M
)
ap
p
r
o
ac
h
es
ca
n
e
n
h
an
ce
s
tu
d
en
ts
’
co
n
jectu
r
i
n
g
s
k
ills
[
1
7
]
.
Ho
wev
er
,
s
u
ch
a
p
p
r
o
ac
h
es
m
ay
b
e
d
if
f
ic
u
lt
to
s
u
s
tain
in
lo
w
-
r
eso
u
r
ce
s
etti
n
g
s
an
d
r
ar
ely
p
o
s
itio
n
lo
ca
l
ly
s
h
ar
ed
n
ar
r
ativ
es
as
th
e
p
r
im
ar
y
co
n
tex
t
f
o
r
m
ath
em
atica
l
s
en
s
e
-
m
ak
in
g
.
T
h
er
ef
o
r
e,
a
clea
r
g
ap
r
em
ain
s
in
d
ev
elo
p
in
g
an
d
em
p
ir
ically
ev
alu
atin
g
cu
ltu
r
ally
an
ch
o
r
ed
,
s
to
r
y
-
b
as
ed
m
ath
em
atics
m
ater
ials
alig
n
ed
with
th
e
MA
T
AT
AG
c
u
r
r
icu
lu
m
f
o
r
r
u
r
al
Gr
ad
e
7
lear
n
er
s
.
Ad
d
r
ess
in
g
th
is
g
ap
co
n
s
titu
tes
th
e
n
o
v
elty
o
f
th
e
s
tu
d
y
,
it
s
y
s
tem
atica
lly
co
n
v
er
ts
Pan
ay
f
o
lk
tales
in
to
c
u
r
r
icu
lu
m
-
ali
g
n
ed
G
r
ad
e
7
m
ath
e
m
atics
task
s
u
s
in
g
th
e
a
n
aly
s
is
,
d
e
s
ig
n
,
d
ev
el
o
p
m
en
t,
im
p
lem
en
tatio
n
,
an
d
ev
alu
ati
o
n
(
ADDI
E
)
d
e
v
elo
p
m
e
n
t
p
r
o
ce
s
s
en
r
ich
ed
b
y
Keller
’
s
a
tten
tio
n
,
r
ele
v
an
ce
,
co
n
f
id
en
ce
,
an
d
s
atis
f
ac
tio
n
(
AR
C
S
)
p
r
in
cip
les,
an
d
v
a
lid
ates
th
e
r
esu
ltin
g
m
ater
ia
l
th
r
o
u
g
h
a
m
u
lti
-
p
er
s
p
ec
tiv
e
ev
alu
atio
n
in
v
o
lv
i
n
g
teac
h
er
s
,
ex
p
er
ts
,
a
n
d
lea
r
n
er
s
o
f
f
e
r
in
g
a
r
ep
licab
le
p
at
h
way
f
o
r
cu
ltu
r
ally
r
esp
o
n
s
iv
e
m
ath
em
atics in
s
tr
u
ctio
n
with
in
th
e
MA
T
AT
AG
c
o
n
tex
t.
T
o
ex
p
lain
h
o
w
th
is
d
ev
e
lo
p
m
en
t
ef
f
o
r
t
ca
n
en
h
a
n
c
e
lear
n
er
en
g
ag
e
m
en
t
an
d
m
aster
y
,
th
e
th
eo
r
etica
l
f
o
u
n
d
atio
n
in
te
g
r
ates
s
o
cial
co
n
s
tr
u
ctiv
is
m
,
th
e
in
s
tr
u
ctio
n
al
d
esig
n
t
h
eo
r
y
(
ADDI
E
)
,
an
d
t
h
e
AR
C
S
m
o
d
el.
So
cial
c
o
n
s
tr
u
c
tiv
is
m
,
in
s
p
ir
ed
b
y
Vy
g
o
ts
k
y
,
p
o
s
its
th
at
k
n
o
wled
g
e
is
co
-
c
o
n
s
tr
u
cted
th
r
o
u
g
h
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
.
15
,
No
.
2
,
Ap
r
il
20
2
6
:
1
1
9
6
-
1
2
1
1
1198
in
ter
ac
tio
n
,
c
u
ltu
r
e,
a
n
d
lan
g
u
ag
e;
lear
n
i
n
g
is
a
s
o
cial
ac
tiv
ity
wh
er
e
m
ea
n
in
g
em
er
g
es
f
r
o
m
d
ialo
g
u
e
,
n
eg
o
tiatio
n
,
a
n
d
s
h
a
r
ed
e
x
p
er
ien
ce
[
1
8
]
–
[
2
0
]
.
Ap
p
lied
to
m
ath
em
atics
teac
h
in
g
th
r
o
u
g
h
f
o
lk
tales,
th
is
p
er
s
p
ec
tiv
e
ass
u
m
es
th
at
lear
n
er
s
co
llab
o
r
ativ
ely
b
u
ild
u
n
d
er
s
tan
d
in
g
as
th
ey
an
aly
ze
n
ar
r
ativ
e
s
itu
atio
n
s
,
p
o
s
e
p
r
o
b
lem
s
,
an
d
d
e
r
iv
e
s
o
lu
tio
n
s
.
Fo
lk
tales
f
u
n
ctio
n
as
m
ed
iatio
n
al
to
o
ls
th
at
co
n
n
ec
t
lear
n
er
s
’
cu
ltu
r
al
s
ch
em
a
with
m
ath
em
atica
l
r
ea
s
o
n
in
g
,
wh
ile
ac
tiv
ities
s
u
ch
as
g
r
o
u
p
d
is
cu
s
s
io
n
,
d
r
am
atiza
tio
n
,
a
n
d
s
to
r
y
tellin
g
s
u
p
p
o
r
t
in
ter
n
ali
za
tio
n
o
f
b
o
th
cu
ltu
r
al
n
ar
r
a
tiv
es
an
d
m
ath
em
atica
l
s
tr
u
c
tu
r
es
an
d
cu
ltiv
ate
cr
itical
th
in
k
in
g
,
c
o
m
m
u
n
icatio
n
,
an
d
co
llab
o
r
atio
n
[
2
1
]
.
B
u
ild
in
g
o
n
th
is
co
n
s
tr
u
ctiv
is
t
len
s
,
th
e
ADDI
E
m
o
d
el
p
r
o
v
id
es
a
s
y
s
tem
atic
p
r
o
ce
s
s
f
o
r
tr
an
s
f
o
r
m
in
g
lo
ca
l
f
o
l
k
tales
in
to
ef
f
ec
tiv
e
in
s
tr
u
ctio
n
al
m
ate
r
ials
[
2
2
]
.
I
n
th
e
a
n
aly
s
is
p
h
ase,
teac
h
er
s
id
en
tify
lear
n
er
s
’
n
e
ed
s
,
least
-
m
aster
e
d
co
m
p
eten
cies,
a
n
d
cu
ltu
r
al
r
eso
u
r
ce
s
th
at
ca
n
illu
m
in
at
e
k
ey
m
ath
e
m
atica
l
id
ea
s
.
Du
r
in
g
d
esig
n
an
d
d
ev
elo
p
m
en
t
,
s
to
r
y
lin
es
ar
e
alig
n
ed
with
lea
r
n
in
g
o
b
jectiv
es
an
d
co
n
v
er
te
d
in
to
m
o
d
u
les,
v
is
u
als,
an
d
i
n
ter
ac
tiv
e
task
s
th
at
en
co
u
r
ag
e
lea
r
n
er
s
to
ex
p
lo
r
e,
r
e
p
r
esen
t,
an
d
ju
s
tify
s
o
lu
tio
n
s
co
llab
o
r
ativ
ely
.
I
m
p
lem
e
n
tatio
n
th
en
f
o
cu
s
es
o
n
teac
h
er
-
f
ac
ilit
ated
u
s
e
o
f
th
e
m
ater
i
als
in
class
,
wh
ile
e
v
alu
atio
n
b
o
th
f
o
r
m
ativ
e
a
n
d
s
u
m
m
ativ
e
f
ee
d
b
ac
k
in
to
ea
r
lier
p
h
ases
to
r
ef
in
e
s
to
r
ies,
ac
tiv
ities
,
an
d
ass
es
s
m
en
ts
.
I
n
th
is
way
,
A
DDI
E
o
p
er
atio
n
alize
s
s
o
cial
co
n
s
tr
u
ctiv
is
m
b
y
en
s
u
r
in
g
th
at
ea
c
h
s
tag
e
o
f
m
ater
ial
d
ev
elo
p
m
en
t in
ten
tio
n
ally
s
u
p
p
o
r
ts
s
o
cial
in
ter
ac
tio
n
,
cu
ltu
r
al
r
elev
an
ce
,
a
n
d
c
o
n
c
ep
t
-
b
u
ild
in
g
.
T
o
s
tr
en
g
th
en
m
o
tiv
atio
n
al
o
n
g
s
id
e
lear
n
in
g
d
esig
n
,
Keller
’
s
AR
C
S
m
o
d
el
is
em
b
ed
d
ed
with
in
th
e
ADDI
E
cy
cle
[
2
3
]
.
Du
r
in
g
an
aly
s
is
an
d
d
esig
n
,
f
o
lk
tales
an
d
task
s
ar
e
s
elec
ted
to
ca
p
tu
r
e
a
tten
tio
n
th
r
o
u
g
h
v
iv
id
p
lo
ts
an
d
ch
a
r
ac
ter
s
an
d
to
en
s
u
r
e
r
elev
an
ce
b
y
lin
k
in
g
m
ath
e
m
atica
l
id
ea
s
to
f
am
iliar
co
m
m
u
n
ity
p
r
ac
tices
s
u
ch
as
f
ar
m
i
n
g
,
h
an
d
icr
af
t,
an
d
tr
a
d
in
g
[
2
4
]
.
Dev
e
lo
p
m
en
t
a
n
d
I
m
p
lem
en
tatio
n
s
u
p
p
o
r
t
c
o
n
f
id
en
c
e
b
y
s
tr
u
ctu
r
in
g
s
ca
f
f
o
ld
ed
,
c
o
o
p
er
ativ
e
ac
tiv
ities
s
u
ch
as
g
u
id
ed
q
u
esti
o
n
in
g
,
p
ee
r
e
x
p
l
an
atio
n
,
an
d
g
r
o
u
p
p
r
o
b
lem
-
s
o
lv
in
g
th
at
allo
w
le
ar
n
er
s
to
ex
p
er
ie
n
ce
in
c
r
em
e
n
tal
s
u
cc
ess
in
a
s
u
p
p
o
r
tiv
e
s
o
cial
en
v
ir
o
n
m
en
t.
Fin
ally
,
ev
alu
atio
n
an
d
r
e
f
lectiv
e
d
is
cu
s
s
io
n
s
f
o
s
ter
Satis
f
ac
tio
n
as
lear
n
e
r
s
r
ec
o
g
n
ize
th
at
th
ey
ca
n
m
aste
r
m
ath
em
atics
th
r
o
u
g
h
s
to
r
ies
r
o
o
ted
in
th
eir
o
wn
h
er
itag
e.
T
h
u
s
,
AR
C
S
an
d
s
o
cial
co
n
s
tr
u
ctiv
is
m
wo
r
k
as
m
u
tu
ally
r
ein
f
o
r
cin
g
len
s
es th
at
g
u
id
e
m
o
tiv
atio
n
al
d
ec
is
io
n
s
at
ea
ch
ADDI
E
p
h
ase
r
ath
er
th
an
f
u
n
ctio
n
in
g
as
s
ep
ar
ate
ad
d
-
o
n
s
.
An
ch
o
r
ed
in
th
ese
th
r
ee
f
r
am
e
wo
r
k
s
,
cu
ltu
r
ally
r
elev
an
t
m
at
h
em
atics
ed
u
ca
tio
n
alig
n
s
with
Dep
E
d
’
s
MA
T
AT
AG
v
is
io
n
o
f
p
r
o
d
u
cin
g
B
atan
g
Ma
k
ab
a
n
s
a
lear
n
er
s
wh
o
ar
e
ac
ad
e
m
ically
co
m
p
eten
t,
v
alu
es
-
d
r
iv
en
,
an
d
cu
ltu
r
ally
r
o
o
ted
[
2
5
]
.
L
o
ca
lized
s
to
r
ies
ca
n
p
o
s
itio
n
m
ath
em
atics
as
a
v
eh
icle
f
o
r
b
o
th
an
aly
tical
an
d
m
o
r
al
r
ea
s
o
n
in
g
,
h
el
p
in
g
lear
n
er
s
r
ec
o
g
n
ize
th
at
n
u
m
b
er
s
a
n
d
p
atter
n
s
a
r
e
em
b
ed
d
ed
in
th
eir
ev
er
y
d
a
y
en
v
ir
o
n
m
e
n
t
wh
ile
p
o
s
itio
n
in
g
teac
h
er
s
as
cu
ltu
r
al
m
ed
iato
r
s
wh
o
co
n
n
ec
t
ab
s
tr
ac
t
co
n
ce
p
ts
to
liv
ed
r
ea
liti
es
[
2
6
]
.
Yet
m
a
n
y
class
r
o
o
m
s
r
em
ain
tex
tb
o
o
k
-
d
ep
en
d
e
n
t
an
d
d
o
m
i
n
ated
b
y
W
ester
n
ex
am
p
les,
an
d
em
p
ir
ical
r
esear
ch
o
n
s
y
s
tem
atica
lly
d
esig
n
ed
,
cu
ltu
r
ally
in
teg
r
ated
m
ath
em
atics
in
s
tr
u
ctio
n
in
th
e
Ph
ilip
p
in
e
co
n
tex
t
r
em
ain
s
lim
ited
[
2
7
]
.
Hen
ce
,
th
is
s
tu
d
y
s
ee
k
s
to
d
esig
n
,
d
ev
elo
p
,
an
d
ev
alu
ate
a
f
o
lk
tale
-
b
ased
in
s
tr
u
ctio
n
al
m
ater
ial
i
n
m
ath
em
atics
g
r
o
u
n
d
e
d
in
s
o
cial
co
n
s
tr
u
ctiv
is
m
,
s
tr
u
ctu
r
ed
b
y
ADDI
E
,
a
n
d
m
o
tiv
ated
b
y
AR
C
S,
d
em
o
n
s
tr
atin
g
h
o
w
c
u
ltu
r
al
r
elev
an
ce
,
co
g
n
itiv
e
c
o
n
s
tr
u
ctio
n
,
an
d
m
o
tiv
atio
n
al
d
esig
n
ca
n
wo
r
k
t
o
g
eth
er
to
im
p
r
o
v
e
lear
n
er
s
’
co
n
ce
p
tu
al
u
n
d
er
s
tan
d
in
g
,
e
n
g
ag
em
e
n
t,
an
d
m
o
tiv
a
tio
n
.
Ultim
ately
,
th
is
r
esear
ch
f
r
am
es
ed
u
ca
tio
n
n
o
t
m
e
r
ely
as
th
e
tr
an
s
m
is
s
io
n
o
f
m
ath
em
atica
l
k
n
o
wled
g
e
b
u
t
also
as
an
a
ct
o
f
cu
ltu
r
al
p
r
eser
v
atio
n
a
n
d
tr
a
n
s
f
o
r
m
atio
n
.
T
h
r
o
u
g
h
t
h
e
s
tr
ateg
ic
u
s
e
o
f
f
o
lk
tales,
lear
n
er
s
ar
e
in
v
ited
to
r
ed
is
co
v
er
m
at
h
em
atics
as
p
ar
t
o
f
th
eir
h
er
itag
e,
e
m
b
ed
d
ed
i
n
s
to
r
ies
o
f
wis
d
o
m
,
p
r
o
b
lem
-
s
o
lv
in
g
,
a
n
d
co
m
m
u
n
ity
co
o
p
e
r
atio
n
s
o
t
h
at
co
n
ce
p
ts
b
ec
o
m
e
b
o
th
m
e
an
in
g
f
u
l
an
d
u
s
ab
le
in
th
eir
d
aily
liv
es.
Acc
o
r
d
in
g
ly
,
th
is
s
tu
d
y
lin
k
s
cu
r
r
ic
u
lu
m
d
em
an
d
s
,
r
u
r
al
im
p
lem
en
tati
o
n
co
n
s
tr
ain
ts
,
an
d
r
ec
en
t
s
ch
o
lar
s
h
ip
to
a
co
n
cr
ete
d
ev
elo
p
m
en
t
ef
f
o
r
t:
d
esig
n
in
g
an
d
ev
alu
atin
g
f
o
l
k
tale
-
b
ased
in
s
tr
u
ctio
n
al
m
ater
ials
th
at
ca
n
b
e
ad
o
p
ted
an
d
ad
a
p
ted
b
y
Gr
a
d
e
7
m
ath
em
atics
teac
h
er
s
to
s
u
p
p
o
r
t
th
e
MA
T
AT
AG
g
o
al
o
f
d
ev
el
o
p
in
g
n
u
m
e
r
ate,
v
alu
es
-
d
r
iv
en
,
a
n
d
cu
ltu
r
ally
r
o
o
te
d
lear
n
er
s
.
I
n
lig
h
t
o
f
th
e
f
o
r
e
g
o
in
g
c
o
n
tex
t,
t
h
is
s
tu
d
y
en
d
ea
v
o
r
e
d
to
r
esp
o
n
d
t
o
th
e
f
o
llo
win
g
in
q
u
ir
ies:
i)
W
h
ich
m
ath
em
atics c
o
m
p
eten
cies d
o
teac
h
er
s
p
er
ce
iv
e
as su
itab
le
f
o
r
in
teg
r
atio
n
with
lo
ca
l f
o
lk
tales?
ii)
W
h
at
in
s
tr
u
ctio
n
al
m
ater
ial
ca
n
b
e
d
esig
n
ed
a
n
d
d
ev
elo
p
e
d
i
n
teg
r
atin
g
l
o
ca
l
f
o
lk
tales
f
r
o
m
th
e
id
en
tifie
d
co
m
p
eten
cies,
an
d
wh
at
ar
e
its
d
is
tin
ctiv
e
f
ea
tu
r
es?
iii)
W
h
at
ar
e
th
e
s
tu
d
en
ts
an
d
e
x
p
er
ts
’
ev
alu
atio
n
o
f
th
e
ac
ce
p
tab
ilit
y
o
f
th
e
d
ev
elo
p
e
d
f
o
lk
tale
-
b
ased
in
s
tr
u
ctio
n
al
m
ater
ial
in
ter
m
s
o
f
th
e:
lear
n
in
g
o
b
jectiv
es;
co
n
ten
t;
o
r
g
an
izatio
n
a
n
d
p
r
esen
tatio
n
;
f
o
r
m
at
an
d
d
esig
n
; a
n
d
ass
ess
m
en
t
?
2.
M
E
T
H
O
D
T
h
is
s
ec
tio
n
o
f
th
e
p
ap
er
p
r
esen
ts
th
e
r
esear
ch
d
esig
n
,
th
e
r
esp
o
n
d
en
ts
,
th
e
d
ata
co
llectio
n
in
s
tr
u
m
en
ts
an
d
p
r
o
ce
d
u
r
es,
as
well
as
th
e
e
th
ical
co
n
s
id
er
atio
n
s
o
b
s
er
v
ed
in
th
e
co
n
d
u
ct
o
f
th
e
s
tu
d
y
,
d
etailin
g
h
o
w
th
e
in
v
esti
g
atio
n
was
s
tr
u
ctu
r
e
d
,
wh
o
p
ar
ticip
ated
,
wh
at
t
o
o
ls
wer
e
u
s
ed
to
g
ath
er
d
ata,
a
n
d
t
h
e
s
af
eg
u
ar
d
s
im
p
lem
e
n
ted
to
e
n
s
u
r
e
eth
ical
co
m
p
lian
ce
.
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
F
r
o
m
s
to
r
ies to
n
u
mb
ers
:
d
ev
elo
p
men
t o
f fo
lkta
le
-
b
a
s
ed
in
s
tr
u
ctio
n
a
l
…
(
C
h
err
y
Jo
y
B
.
De
min
g
o
y
)
1199
2
.
1
.
Resea
rc
h
d
esig
n
T
h
is
in
v
esti
g
atio
n
ad
o
p
ted
a
T
y
p
e
I
d
ev
elo
p
m
en
tal
r
esear
c
h
d
esig
n
g
u
id
ed
b
y
th
e
ADDI
E
m
o
d
el
to
co
n
ce
p
tu
alize
,
co
n
s
tr
u
ct,
an
d
ev
alu
ate
a
f
o
lk
tale
-
b
ased
in
s
tr
u
ctio
n
al
m
ater
ial
in
m
ath
em
at
ics
7
co
n
tex
tu
alize
d
th
r
o
u
g
h
lo
ca
l
f
o
lk
tales.
De
v
elo
p
m
en
tal
r
esear
ch
s
er
v
es
as
a
r
ig
o
r
o
u
s
m
eth
o
d
o
lo
g
i
ca
l
f
r
am
ewo
r
k
f
o
r
g
en
er
atin
g
,
r
ef
in
in
g
,
an
d
em
p
ir
ically
v
alid
atin
g
in
s
tr
u
ctio
n
a
l
in
n
o
v
atio
n
s
th
at
ad
v
an
ce
p
e
d
ag
o
g
ical
p
r
ac
tice
an
d
lear
n
er
e
n
g
ag
e
m
en
t
[
2
8
]
.
I
t
en
tails
a
s
y
s
tem
atic
in
q
u
ir
y
in
to
th
e
p
r
o
ce
s
s
es
o
f
d
esig
n
,
d
ev
elo
p
m
en
t,
an
d
ev
alu
atio
n
eith
e
r
as
a
n
in
te
g
r
ated
s
y
s
tem
o
r
th
r
o
u
g
h
t
h
e
ex
am
i
n
atio
n
o
f
d
is
tin
ct
p
r
o
ce
d
u
r
al
p
h
ases
.
As
ar
ticu
lated
b
y
Al
-
Kh
iam
i
et
a
l
.
[
2
9
]
,
d
ev
el
o
p
m
en
tal
r
e
s
ea
r
ch
co
n
s
titu
tes
a
s
y
s
tem
ati
c
s
tu
d
y
o
f
d
esig
n
,
d
ev
elo
p
m
e
n
t,
an
d
ev
al
u
atio
n
p
r
o
ce
s
s
es
to
estab
lis
h
an
em
p
ir
ical
f
o
u
n
d
atio
n
f
o
r
th
e
cr
ea
t
io
n
o
f
in
s
tr
u
ctio
n
a
l
an
d
n
o
n
-
in
s
tr
u
ctio
n
al
p
r
o
d
u
cts
an
d
th
e
r
ef
in
em
e
n
t o
f
m
o
d
els
g
u
id
in
g
th
eir
p
r
o
d
u
ctio
n
.
T
h
e
s
tu
d
y
em
p
lo
y
ed
t
h
e
T
y
p
e
I
d
ev
elo
p
m
en
tal
r
esear
ch
d
e
s
ig
n
,
wh
ich
em
p
h
asizes
th
e
d
escr
ip
tio
n
,
an
aly
s
is
,
an
d
ap
p
r
aisal
o
f
a
p
r
o
d
u
ct
d
e
v
elo
p
m
e
n
t
p
r
o
ce
s
s
wi
th
in
a
d
ef
in
e
d
ed
u
ca
ti
o
n
al
co
n
tex
t.
T
h
is
ap
p
r
o
ac
h
was
d
ee
m
ed
a
p
p
r
o
p
r
iate
g
iv
en
th
e
s
tu
d
y
’
s
o
b
jectiv
e
o
f
d
esig
n
in
g
a
n
d
v
alid
atin
g
a
c
u
ltu
r
ally
r
esp
o
n
s
iv
e
f
o
lk
tale
-
b
ased
in
s
tr
u
cti
o
n
al
m
ater
ial
th
at
in
teg
r
ates
m
at
h
em
atica
l
co
n
ce
p
ts
with
i
n
d
ig
en
o
u
s
n
ar
r
ativ
e
tr
ad
itio
n
s
.
T
h
e
d
e
v
elo
p
m
e
n
ta
l
p
r
o
ce
s
s
was
s
y
s
tem
atica
lly
g
u
id
e
d
b
y
th
e
ADDI
E
m
o
d
el,
co
m
p
r
is
in
g
th
e
p
h
ases
o
f
ADDI
E
to
en
s
u
r
e
m
eth
o
d
o
l
o
g
ical
r
i
g
o
r
,
th
eo
r
etica
l
g
r
o
u
n
d
in
g
,
a
n
d
iter
ativ
e
r
ef
in
em
e
n
t
o
f
th
e
in
s
tr
u
ctio
n
al
p
r
o
d
u
ct.
Mo
r
eo
v
er
,
th
e
o
v
er
all
s
tr
u
ctu
r
e
o
f
th
e
r
esear
ch
was
f
r
am
e
d
th
r
o
u
g
h
t
h
e
in
p
u
t
–
p
r
o
ce
s
s
–
o
u
t
p
u
t
(
I
PO)
m
o
d
el,
wh
ich
d
elin
ea
ted
th
e
lo
g
ical
p
r
o
g
r
ess
io
n
o
f
ac
t
iv
ities
f
r
o
m
id
en
tify
in
g
in
s
tr
u
ctio
n
al
n
ee
d
s
to
p
r
o
d
u
cin
g
an
d
v
alid
atin
g
th
e
f
in
al
m
ater
ial.
T
h
e
s
y
n
th
esis
o
f
th
e
d
ev
elo
p
m
en
tal
r
esear
ch
f
r
am
ewo
r
k
,
ADDI
E
in
s
tr
u
ctio
n
al
m
o
d
el
,
an
d
I
P
O
co
n
ce
p
tu
al
s
tr
u
ct
u
r
e
p
r
o
v
id
ed
an
e
m
p
ir
ically
g
r
o
u
n
d
e
d
an
d
th
eo
r
etica
lly
co
h
er
en
t p
ath
wa
y
f
o
r
cr
ea
tin
g
an
in
n
o
v
ativ
e
ed
u
ca
tio
n
al
r
eso
u
r
ce
[
3
0
]
.
T
h
is
in
teg
r
ativ
e
ap
p
r
o
ac
h
en
s
u
r
ed
th
at
th
e
r
esu
ltin
g
f
o
l
k
tale
-
b
ased
in
s
tr
u
ctio
n
al
m
ater
ial
was n
o
t o
n
ly
p
ed
a
g
o
g
ically
s
o
u
n
d
a
n
d
e
m
p
ir
ically
v
alid
ated
b
u
t
also
co
n
tex
t
u
ally
m
ea
n
in
g
f
u
l,
th
er
e
b
y
co
n
tr
ib
u
tin
g
to
a
m
o
r
e
cu
ltu
r
ally
attu
n
ed
a
n
d
en
g
a
g
in
g
m
ath
em
atics lea
r
n
in
g
ex
p
er
ien
ce
f
o
r
Gr
a
d
e
7
lear
n
er
s
.
2
.
2
.
Respo
nd
ent
s
T
h
e
r
esp
o
n
d
en
ts
o
f
th
is
s
tu
d
y
co
n
s
is
ted
o
f
twen
ty
-
f
iv
e
(
2
5
)
Gr
ad
e
7
teac
h
er
s
,
6
6
lear
n
er
s
f
r
o
m
f
o
u
r
p
u
b
lic
s
ec
o
n
d
a
r
y
s
ch
o
o
ls
in
th
e
m
u
n
icip
ality
o
f
Ma
ay
o
n
,
Pro
v
in
ce
o
f
C
ap
iz.
T
h
e
teac
h
er
s
,
s
p
ec
ializin
g
in
m
ath
em
atics,
E
n
g
lis
h
,
an
d
s
o
c
ial
s
cien
ce
s
,
wer
e
p
u
r
p
o
s
iv
ely
s
elec
ted
to
p
r
o
v
id
e
cr
itical
in
p
u
ts
f
o
r
th
e
d
esig
n
an
d
d
ev
elo
p
m
en
t
o
f
th
e
f
o
lk
tale
-
b
ased
in
s
tr
u
ctio
n
al
m
ater
ial,
in
teg
r
atin
g
lo
ca
l
f
o
lk
tales
in
to
m
ath
em
atics
in
s
tr
u
ctio
n
.
T
h
eir
e
x
p
er
tis
e
an
d
f
a
m
iliar
ity
with
t
h
e
lo
ca
l
ed
u
ca
tio
n
al
co
n
tex
t
wer
e
d
ee
m
ed
v
ital
i
n
id
en
tify
in
g
th
e
m
o
s
t
s
u
itab
le
l
ea
r
n
in
g
co
m
p
eten
cies
f
o
r
in
te
g
r
atio
n
,
en
s
u
r
i
n
g
th
at
th
e
m
ater
ial
r
ef
lecte
d
b
o
th
cu
ltu
r
al
au
th
en
ticity
a
n
d
p
ed
a
g
o
g
ical
s
o
u
n
d
n
ess
.
I
n
a
d
d
itio
n
,
Gr
ad
e
7
lear
n
er
s
o
f
f
icially
en
r
o
lled
in
t
h
e
f
ir
s
t
s
em
ester
o
f
th
e
s
ch
o
o
l
y
ea
r
2
0
2
4
–
2
0
2
5
p
a
r
ticip
ated
in
th
e
im
p
lem
en
tatio
n
a
n
d
ev
alu
atio
n
o
f
th
e
d
ev
elo
p
ed
f
o
lk
tale
-
b
ased
i
n
s
tr
u
ctio
n
al
m
ater
ial.
T
h
ese
lear
n
e
r
s
also
s
er
v
ed
as
r
esp
o
n
d
e
n
ts
in
ass
ess
in
g
th
e
ac
ce
p
tab
ilit
y
an
d
r
elev
a
n
ce
o
f
t
h
e
d
ev
el
o
p
ed
f
o
l
k
tale
-
b
ased
in
s
tr
u
ctio
n
al
m
ater
ials
.
T
h
e
in
clu
s
io
n
cr
iter
ia
f
o
r
lear
n
er
-
r
esp
o
n
d
en
ts
:
i
)
cu
r
r
e
n
t
en
r
o
llm
en
t
in
Gr
ad
e
7
d
u
r
in
g
t
h
e
s
p
ec
if
ied
ac
a
d
em
ic
ter
m
an
d
ii
)
v
o
lu
n
tar
y
p
ar
ticip
atio
n
in
th
e
s
tu
d
y
.
T
h
eir
f
ee
d
b
ac
k
p
r
o
v
id
e
d
em
p
ir
i
ca
l
ev
id
en
ce
o
n
th
e
f
o
lk
tale
-
b
ased
in
s
tr
u
ctio
n
al
m
ater
ial’
s
ef
f
ec
tiv
en
ess
in
en
h
an
cin
g
en
g
ag
em
e
n
t a
n
d
lea
r
n
i
n
g
m
o
tiv
atio
n
with
in
th
e
m
ath
em
atics c
lass
r
o
o
m
.
2
.
2
.
1
.
E
v
a
lua
t
o
r
T
h
e
s
tu
d
y
in
clu
d
e
d
1
0
c
o
n
t
en
t
an
d
p
ed
a
g
o
g
y
e
x
p
er
ts
’
e
v
alu
ato
r
s
wh
o
ass
ess
ed
th
e
d
ev
elo
p
e
d
f
o
lk
tale
-
b
ased
in
s
tr
u
ctio
n
al
m
ater
ials
in
ter
m
s
o
f
co
n
ten
t
v
alid
ity
,
f
u
n
ctio
n
ality
,
an
d
p
e
d
ag
o
g
ical
ap
p
r
o
p
r
iaten
ess
.
T
h
e
ev
alu
ato
r
s
wer
e
p
u
r
p
o
s
iv
ely
s
elec
ted
b
ased
o
n
th
eir
p
r
o
f
ess
io
n
al
q
u
alif
icatio
n
s
,
wh
ich
in
clu
d
ed
:
i
)
p
o
s
s
ess
io
n
o
f
a
m
aster
’
s
o
r
d
o
cto
r
ate
d
eg
r
ee
in
ed
u
ca
tio
n
o
r
a
r
elate
d
f
iel
d
;
ii
)
a
m
i
n
im
u
m
o
f
5
y
ea
r
s
o
f
teac
h
in
g
e
x
p
er
ie
n
ce
;
an
d
iii
)
ac
tiv
e
in
v
o
lv
e
m
en
t
in
teac
h
in
g
m
ath
em
ati
cs
o
r
E
n
g
lis
h
,
o
r
in
cu
r
r
icu
lu
m
a
n
d
in
s
tr
u
ctio
n
al
m
ater
ials
d
ev
elo
p
m
en
t.
T
h
e
p
an
el
o
f
ev
al
u
ato
r
s
was
co
m
p
o
s
ed
o
f
m
ath
em
atics
an
d
E
n
g
lis
h
teac
h
er
s
,
c
u
r
r
icu
lu
m
s
p
ec
ialis
ts
,
an
d
a
Dep
E
d
ed
u
ca
tio
n
p
r
o
g
r
a
m
s
u
p
er
v
is
o
r
in
m
ath
em
atics
.
T
h
eir
ex
p
er
t
ju
d
g
m
en
ts
an
d
r
e
co
m
m
en
d
atio
n
s
wer
e
th
o
r
o
u
g
h
ly
co
n
s
id
er
ed
an
d
in
teg
r
ated
in
to
th
e
r
ef
in
em
en
t
o
f
th
e
f
o
l
k
tale
-
b
ased
in
s
tr
u
cti
o
n
al
m
ater
ial
to
en
s
u
r
e
its
ac
ad
em
ic
r
ig
o
r
,
cu
ltu
r
al
alig
n
m
e
n
t,
an
d
in
s
tr
u
ctio
n
al
ef
f
icac
y
.
2
.
3
.
Da
t
a
g
a
t
hering
ins
t
rum
ent
s
T
o
f
ac
ilit
ate
s
y
s
tem
atic
d
ata
c
o
llectio
n
an
d
en
s
u
r
e
m
eth
o
d
o
l
o
g
ical
r
ig
o
r
,
t
h
r
ee
r
esear
ch
in
s
tr
u
m
en
ts
wer
e
u
tili
ze
d
in
th
is
s
tu
d
y
:
i
)
lear
n
in
g
c
o
m
p
eten
c
y
ch
ec
k
lis
t
;
ii)
ex
p
er
ts
’
ev
alu
atio
n
f
o
r
m
;
an
d
iii)
lear
n
er
s
’
ev
alu
atio
n
f
o
r
m
.
E
ac
h
in
s
tr
u
m
en
t
u
n
d
e
r
wen
t
co
n
te
n
t
an
d
f
ac
e
v
alid
atio
n
b
y
f
iv
e
f
ield
ex
p
er
ts
to
ascer
tain
its
ap
p
r
o
p
r
iaten
ess
an
d
r
elev
a
n
ce
to
th
e
s
tu
d
y
’
s
o
b
jectiv
es.
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
.
15
,
No
.
2
,
Ap
r
il
20
2
6
:
1
1
9
6
-
1
2
1
1
1200
2
.
3
.
1
.
L
ea
rning
co
m
pet
ency
chec
k
lis
t
A
r
esear
ch
er
-
d
ev
el
o
p
ed
c
h
ec
k
lis
t
was
em
p
lo
y
ed
to
id
en
tify
th
e
f
iv
e
m
o
s
t
ap
p
r
o
p
r
iate
Gr
ad
e
7
m
ath
em
atics
lear
n
in
g
c
o
m
p
et
en
cies
th
at
co
u
ld
b
e
ef
f
ec
tiv
e
ly
in
teg
r
ated
with
lo
ca
l
f
o
lk
t
ales.
T
h
e
ch
ec
k
lis
t
co
n
tain
ed
f
ir
s
t
-
q
u
a
r
ter
lear
n
i
n
g
co
m
p
eten
cies
u
n
d
e
r
th
e
MA
T
AT
AG
cu
r
r
icu
lu
m
an
d
was
r
ated
u
s
in
g
a
4
-
p
o
in
t
L
ik
er
t
s
ca
le:
4
=
s
tr
o
n
g
ly
ag
r
ee
,
3
=
ag
r
ee
,
2
=
d
is
ag
r
ee
,
an
d
1
=
s
tr
o
n
g
ly
d
is
ag
r
ee
.
T
ea
ch
er
s
wer
e
in
s
tr
u
cted
to
in
d
icate
th
e
d
eg
r
ee
to
wh
ich
th
ey
d
ee
m
ed
ea
c
h
co
m
p
eten
cy
s
u
itab
le
f
o
r
f
o
lk
ta
le
in
teg
r
atio
n
.
T
h
is
in
s
tr
u
m
en
t
s
er
v
ed
as
th
e
f
o
u
n
d
atio
n
f
o
r
s
elec
tin
g
an
d
d
e
s
ig
n
in
g
th
e
f
o
lk
tale
-
b
ased
in
s
tr
u
ctio
n
al
m
ater
ial
alig
n
ed
with
id
en
tifie
d
k
ey
co
m
p
eten
cies.
2
.
3
.
2
.
E
x
pert
s
’
a
nd
lea
rner
s
’
ev
a
lua
t
io
n f
o
rm
s
T
o
d
eter
m
in
e
th
e
ac
ce
p
tab
i
lity
an
d
p
e
d
ag
o
g
ical
s
o
u
n
d
n
ess
o
f
th
e
d
e
v
elo
p
e
d
f
o
l
k
tale
-
b
ased
in
s
tr
u
ctio
n
al
m
ater
ial,
ev
al
u
atio
n
ch
ec
k
lis
ts
ad
ap
ted
f
r
o
m
Nab
ay
r
a
[
3
1
]
a
n
d
B
an
er
jee
a
n
d
B
h
at
[
3
2
]
wer
e
u
tili
ze
d
.
T
h
e
f
o
r
m
s
co
n
s
is
ted
o
f
item
s
clu
s
ter
ed
u
n
d
er
f
i
v
e
cr
iter
ia:
o
b
jectiv
es,
co
n
ten
t
,
o
r
g
a
n
izatio
n
an
d
p
r
esen
tatio
n
,
f
o
r
m
at
an
d
d
esig
n
,
an
d
ass
ess
m
en
t.
A
5
-
p
o
in
t
r
atin
g
s
ca
le
was
u
s
ed
:
5
=
s
tr
o
n
g
ly
a
g
r
ee
,
4
=
ag
r
ee
,
3
=
n
e
u
tr
al,
2
=
d
is
ag
r
e
e,
an
d
1
=
s
tr
o
n
g
ly
d
is
a
g
r
ee
.
Mi
n
o
r
r
ev
is
io
n
s
wer
e
m
ad
e
t
o
tai
lo
r
th
e
i
n
s
tr
u
m
en
ts
to
th
e
s
tu
d
y
’
s
f
r
am
ewo
r
k
.
T
h
e
ac
ce
p
tab
ilit
y
o
f
th
e
f
o
lk
tale
-
b
ased
in
s
tr
u
ctio
n
al
m
ater
ial
wa
s
in
ter
p
r
eted
u
s
in
g
th
e
s
ca
le
as
:
4
.
5
1
–
5
.
0
0
(
h
ig
h
ly
ac
ce
p
tab
le)
,
3
.
5
1
–
4
.
5
0
(
ac
ce
p
tab
le)
,
2
.
5
1
–
3
.
5
0
(
m
o
d
er
ately
ac
ce
p
tab
le)
,
1
.
5
1
–
2
.
5
0
(
f
air
ly
ac
ce
p
tab
le
)
,
an
d
1
.
0
0
–
1
.
5
0
(
n
o
t
ac
ce
p
ta
b
le
)
.
T
h
is
ev
alu
ativ
e
p
r
o
ce
s
s
en
s
u
r
ed
th
at
b
o
th
ex
p
er
t v
alid
ato
r
s
an
d
s
tu
d
e
n
t r
esp
o
n
d
en
ts
p
r
o
v
id
e
d
f
ee
d
b
ac
k
g
r
o
u
n
d
ed
in
estab
lis
h
ed
p
ed
a
g
o
g
ical
s
tan
d
ar
d
s
.
2
.
4
.
Da
t
a
c
o
llect
io
n pro
ce
du
re
T
h
is
s
tu
d
y
ad
o
p
ted
th
e
ADDI
E
in
s
tr
u
ctio
n
al
d
esig
n
m
o
d
el
as
th
e
g
u
id
in
g
f
r
am
ewo
r
k
f
o
r
th
e
s
y
s
tem
atic
d
ev
elo
p
m
en
t
o
f
a
cu
ltu
r
ally
co
n
tex
tu
alize
d
f
o
lk
tale
-
b
ased
i
n
s
tr
u
ctio
n
al
m
ater
ial
in
Gr
ad
e
7
m
ath
em
atics.
T
h
e
m
o
d
el,
co
n
s
is
tin
g
o
f
th
e
f
iv
e
in
ter
r
elat
ed
p
h
ases
o
f
ADDI
E
,
s
er
v
e
d
as
th
e
s
tr
u
ct
u
r
al
b
ac
k
b
o
n
e
o
f
th
e
r
esear
c
h
p
r
o
ce
s
s
.
E
ac
h
p
h
ase
was
ca
r
ef
u
ll
y
ex
ec
u
ted
to
en
s
u
r
e
th
at
th
e
r
esu
ltin
g
f
o
l
k
tale
-
b
ased
in
s
tr
u
ctio
n
al
m
ater
ial
ac
h
iev
ed
b
o
th
p
e
d
ag
o
g
ical
s
o
u
n
d
n
ess
an
d
cu
ltu
r
al
r
elev
an
ce
.
2
.
4
.
1
.
Ana
ly
s
is
p
ha
s
e
T
h
e
an
aly
s
is
p
h
ase
in
v
o
lv
e
d
a
n
ex
ten
s
iv
e
r
ev
iew
o
f
th
e
Gr
a
d
e
7
m
ath
em
atics
lear
n
in
g
co
m
p
eten
cies
o
u
tlin
ed
in
th
e
MA
T
AT
AG
cu
r
r
icu
lu
m
f
o
r
th
e
f
ir
s
t
q
u
ar
ter
o
f
th
e
s
ch
o
o
l
y
ea
r
2
0
2
4
–
2
0
2
5
.
A
d
etailed
ch
ec
k
lis
t
was
f
o
r
m
u
lated
to
id
en
tify
wh
ich
co
m
p
eten
cies
co
u
ld
b
e
ef
f
ec
tiv
el
y
in
te
g
r
ated
with
lo
ca
l
f
o
lk
tales,
th
er
eb
y
cr
ea
tin
g
a
m
ea
n
in
g
f
u
l
in
ter
s
ec
tio
n
b
etwe
en
m
ath
em
atics
an
d
cu
ltu
r
e.
Su
b
ject
m
atter
ex
p
er
ts
i
n
m
ath
em
atics,
E
n
g
lis
h
,
an
d
s
o
cial
s
tu
d
ies
co
llab
o
r
ativ
ely
ex
am
in
ed
,
r
an
k
ed
,
an
d
s
el
ec
ted
th
e
to
p
f
iv
e
co
m
p
eten
cies
u
s
in
g
s
tatis
tical
m
ea
s
u
r
es
s
u
ch
as
m
ea
n
an
d
s
tan
d
ar
d
d
ev
iatio
n
.
I
n
ad
d
itio
n
,
p
r
ac
tical
asp
ec
ts
s
u
ch
as
in
s
tr
u
ctio
n
al
e
n
v
ir
o
n
m
en
t,
p
r
o
d
u
cti
o
n
lo
g
is
tics
,
an
d
co
s
t
co
n
s
id
er
atio
n
s
wer
e
e
v
alu
ated
to
e
n
s
u
r
e
th
e
p
r
o
ject’
s
v
iab
ilit
y
an
d
s
u
s
tain
ab
ilit
y
.
T
h
is
p
h
ase
estab
li
s
h
ed
th
e
p
ed
ag
o
g
ical
an
d
lo
g
is
tical
g
r
o
u
n
d
w
o
r
k
f
o
r
th
e
s
u
cc
ee
d
in
g
s
tag
es o
f
m
ater
ial
d
ev
elo
p
m
e
n
t.
2
.
4
.
2
.
Desig
n
ph
a
s
e
I
n
th
e
d
esig
n
p
h
ase,
th
e
r
ese
ar
ch
er
a
n
aly
ze
d
lear
n
e
r
c
h
ar
ac
ter
is
tics
an
d
co
n
te
n
t
r
e
q
u
ir
em
en
ts
to
en
s
u
r
e
th
at
th
e
m
ate
r
ial
ad
d
r
e
s
s
ed
b
o
th
co
g
n
itiv
e
an
d
af
f
ec
tiv
e
lear
n
in
g
n
ee
d
s
.
Dr
awin
g
f
r
o
m
Pan
a
y
s
ay
o
n
:
T
ales
f
r
o
m
Pan
ay
I
s
lan
d
,
au
th
en
tic
Pan
ay
s
an
o
n
f
o
lk
tales
wer
e
ch
o
s
en
to
s
er
v
e
as
th
e
n
ar
r
a
tiv
e
f
r
am
ewo
r
k
f
o
r
em
b
ed
d
in
g
m
ath
e
m
atica
l
co
n
ce
p
ts
s
u
ch
as
g
eo
m
etr
y
,
m
ea
s
u
r
em
en
t,
an
d
b
asic
alg
eb
r
a.
T
h
e
in
s
tr
u
ctio
n
al
b
lu
ep
r
in
t
was
s
tr
u
ctu
r
ed
t
o
i
n
clu
d
e
less
o
n
d
is
cu
s
s
io
n
s
,
in
ter
ac
tiv
e
ac
tiv
ities
,
an
d
r
ef
le
ctiv
e
q
u
esti
o
n
s
th
at
f
o
s
ter
ed
an
al
y
tical
an
d
p
r
o
b
le
m
-
s
o
lv
in
g
s
k
ills
.
T
h
e
d
esig
n
p
h
ase
em
p
h
asized
th
e
in
te
g
r
at
io
n
o
f
lo
ca
l
c
u
ltu
r
e
with
f
o
r
m
al
m
ath
em
atics
in
s
tr
u
ctio
n
,
allo
win
g
lear
n
e
r
s
to
ap
p
r
ec
iate
m
ath
em
atica
l
id
ea
s
with
in
f
am
iliar
an
d
m
ea
n
in
g
f
u
l
co
n
tex
ts
.
T
h
is
s
tag
e
en
s
u
r
e
d
t
h
at
th
e
m
ater
ia
l
alig
n
ed
with
c
u
r
r
icu
lu
m
s
t
an
d
ar
d
s
w
h
ile
also
r
ef
lectin
g
th
e
liv
e
d
ex
p
e
r
ien
ce
s
an
d
cu
ltu
r
al
h
er
itag
e
o
f
th
e
l
ea
r
n
er
s
.
2
.
4
.
3
.
Dev
elo
pm
ent
ph
a
s
e
T
h
e
d
ev
elo
p
m
en
t p
h
ase
in
v
o
l
v
ed
th
e
p
r
o
d
u
cti
o
n
o
f
t
h
e
f
o
lk
t
ale
-
b
ased
in
s
tr
u
ctio
n
al
m
ater
ia
l b
ased
o
n
th
e
f
in
alize
d
d
esig
n
b
l
u
ep
r
in
t.
L
ess
o
n
s
wer
e
wr
itten
in
clea
r
,
en
g
ag
i
n
g
lan
g
u
ag
e
,
co
m
p
lem
en
ted
b
y
cu
ltu
r
ally
in
s
p
ir
ed
illu
s
tr
atio
n
s
cr
ea
ted
b
y
a
c
o
m
m
is
s
io
n
ed
a
r
tis
t
to
e
n
h
an
ce
ae
s
th
etic
q
u
ality
a
n
d
c
o
n
tex
tu
al
ac
c
u
r
ac
y
.
T
h
e
p
r
elim
in
ar
y
v
er
s
io
n
o
f
th
e
m
ater
ial
was
s
u
b
jecte
d
to
ex
p
er
t
v
alid
atio
n
b
y
s
p
ec
ialis
ts
in
cu
r
r
icu
lu
m
d
ev
elo
p
m
e
n
t
an
d
m
ath
em
atics
ed
u
ca
tio
n
.
T
h
e
y
ass
ess
ed
th
e
m
ater
ial
f
o
r
clar
ity
,
c
o
n
ten
t
ac
cu
r
ac
y
,
r
elev
an
ce
,
an
d
o
v
er
all
in
s
tr
u
ctio
n
al
co
h
er
en
ce
.
C
o
n
s
tr
u
ctiv
e
f
ee
d
b
ac
k
was
an
aly
ze
d
a
n
d
i
n
teg
r
at
ed
in
to
s
u
cc
ess
iv
e
r
ev
is
io
n
s
,
r
esu
ltin
g
in
a
r
ef
in
ed
m
ater
ial
th
at
was
v
i
s
u
ally
a
p
p
ea
lin
g
,
cu
ltu
r
ally
s
en
s
itiv
e,
an
d
p
ed
ag
o
g
icall
y
r
o
b
u
s
t.
T
h
is
p
h
ase
e
n
s
u
r
ed
t
h
at
th
e
d
ev
elo
p
ed
m
ater
ial
e
f
f
ec
tiv
ely
b
alan
ce
d
ac
ad
em
ic
r
ig
o
r
with
c
u
ltu
r
al
ex
p
r
ess
io
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
F
r
o
m
s
to
r
ies to
n
u
mb
ers
:
d
ev
elo
p
men
t o
f fo
lkta
le
-
b
a
s
ed
in
s
tr
u
ctio
n
a
l
…
(
C
h
err
y
Jo
y
B
.
De
min
g
o
y
)
1201
2
.
4
.
4
.
I
m
plem
ent
a
t
i
o
n
ph
a
s
e
T
h
e
im
p
lem
en
tatio
n
p
h
ase
co
n
s
is
ted
o
f
th
e
p
ilo
t
test
in
g
o
f
t
h
e
d
ev
elo
p
ed
f
o
lk
tale
-
b
ased
in
s
tr
u
ctio
n
al
m
ater
ial
am
o
n
g
s
elec
ted
Gr
a
d
e
7
lear
n
er
s
with
in
th
e
Ma
a
y
o
n
Dis
tr
ict.
Prio
r
to
th
e
im
p
lem
en
tatio
n
,
f
o
r
m
al
ap
p
r
o
v
al
was
s
ec
u
r
ed
f
r
o
m
ed
u
ca
tio
n
al
au
th
o
r
ities
,
an
d
p
ar
e
n
tal
co
n
s
en
t
was
o
b
tain
ed
to
e
n
s
u
r
e
ad
h
er
e
n
ce
to
eth
ical
s
tan
d
ar
d
s
.
T
h
e
r
esear
c
h
er
an
d
t
h
e
teac
h
er
-
im
p
lem
en
t
er
co
llab
o
r
ativ
el
y
f
ac
ilit
ated
th
e
less
o
n
s
u
s
in
g
th
e
f
o
lk
tale
-
b
ased
in
s
tr
u
ctio
n
al
m
ater
ial
in
an
au
th
en
tic
class
r
o
o
m
s
ettin
g
.
T
h
r
o
u
g
h
o
u
t
th
e
p
r
o
ce
s
s
,
th
e
r
esear
ch
an
d
co
r
esear
ch
er
s
co
n
d
u
cte
d
o
n
-
s
ite
o
b
s
er
v
atio
n
s
to
e
n
s
u
r
e
f
id
elity
an
d
c
o
n
s
is
ten
cy
o
f
in
s
tr
u
ctio
n
.
Vid
eo
d
o
cu
m
e
n
tatio
n
o
f
th
e
s
ess
io
n
s
was p
r
o
v
id
ed
to
th
e
ex
p
e
r
t p
a
n
el
f
o
r
ad
d
itio
n
al
ev
alu
atio
n
.
C
o
n
d
u
cted
f
r
o
m
th
e
last
wee
k
o
f
Au
g
u
s
t
to
th
e
th
i
r
d
wee
k
o
f
Sep
tem
b
er
2
0
2
4
,
t
h
e
im
p
lem
en
tatio
n
p
er
io
d
allo
wed
am
p
le
tim
e
f
o
r
m
o
n
ito
r
in
g
s
tu
d
en
t
p
er
f
o
r
m
an
ce
,
ass
ess
in
g
in
s
tr
u
ctio
n
al
f
lo
w,
an
d
id
en
tif
y
in
g
a
r
ea
s
f
o
r
r
e
f
in
em
en
t.
2
.
4
.
5
.
E
v
a
lua
t
io
n
ph
a
s
e
T
h
e
ev
alu
atio
n
p
h
ase
f
o
cu
s
e
d
o
n
ass
ess
in
g
th
e
ac
ce
p
tab
i
lity
an
d
o
f
th
e
d
ev
elo
p
ed
in
s
tr
u
ctio
n
al
m
ater
ial.
Stan
d
ar
d
ized
ev
alu
a
tio
n
f
o
r
m
s
wer
e
d
is
tr
ib
u
ted
t
o
b
o
th
lear
n
er
s
an
d
ex
p
er
t
e
v
alu
ato
r
s
to
g
at
h
er
q
u
an
titativ
e
d
ata.
T
h
e
ev
alu
at
io
n
cr
iter
ia
in
clu
d
e
d
c
o
n
ten
t
a
cc
u
r
ac
y
,
cu
ltu
r
al
r
elev
an
ce
,
in
s
tr
u
ctio
n
al
clar
ity
,
lay
o
u
t,
an
d
en
g
a
g
em
en
t
v
alu
e.
Descr
ip
tiv
e
s
tatis
tics
s
u
ch
as
m
ea
n
,
s
tan
d
ar
d
d
ev
iati
o
n
,
an
d
r
an
k
wer
e
em
p
lo
y
ed
to
i
n
ter
p
r
et
th
e
c
o
llected
d
ata.
O
v
er
all,
th
e
ev
alu
a
tio
n
r
ev
ea
le
d
s
tr
o
n
g
p
o
s
itiv
e
r
esp
o
n
s
es
f
r
o
m
b
o
th
g
r
o
u
p
s
,
in
d
icatin
g
th
at
th
e
m
ater
ial
was
n
o
t
o
n
ly
ed
u
ca
tio
n
ally
s
o
u
n
d
b
u
t
also
cu
l
tu
r
ally
m
ea
n
in
g
f
u
l.
T
h
e
in
s
ig
h
ts
an
d
r
ec
o
m
m
e
n
d
atio
n
s
g
ath
er
ed
wer
e
s
y
s
tem
atica
lly
in
co
r
p
o
r
ated
in
to
th
e
f
in
al
v
er
s
io
n
o
f
th
e
m
ater
ial,
en
s
u
r
in
g
co
n
tin
u
o
u
s
im
p
r
o
v
em
e
n
t
an
d
alig
n
m
en
t
w
ith
p
ed
ag
o
g
ical
s
tan
d
a
r
d
s
.
T
h
e
o
v
er
all
p
r
o
ce
d
u
r
e
is
s
u
m
m
ar
ized
in
Fig
u
r
e
1
.
Fig
u
r
e
1
.
Flo
wch
ar
t
o
f
th
e
s
tu
d
y
p
r
o
ce
d
u
r
es f
r
o
m
b
eg
in
n
in
g
to
en
d
2
.
5
.
E
t
hica
l
c
o
ns
idera
t
io
n
T
h
is
s
tu
d
y
was
co
n
d
u
cted
i
n
ad
h
er
en
ce
t
o
th
e
d
ata
p
r
iv
ac
y
ac
t
o
f
2
0
1
2
(
r
ep
u
b
lic
ac
t
n
o
.
1
0
1
7
3
)
.
T
h
ese
f
r
am
ewo
r
k
s
em
p
h
asize
r
esp
ec
t
f
o
r
p
er
s
o
n
s
,
b
en
ef
ice
n
ce
,
an
d
ju
s
tice,
wh
ich
ar
e
p
r
in
cip
les
th
at
g
u
id
ed
th
e
r
esear
ch
er
in
s
af
eg
u
ar
d
in
g
th
e
r
ig
h
ts
,
d
ig
n
ity
,
an
d
welf
ar
e
o
f
all
p
ar
ticip
an
ts
th
r
o
u
g
h
o
u
t th
e
s
tu
d
y
.
Prio
r
to
d
ata
co
llectio
n
,
f
o
r
m
al
a
p
p
r
o
v
al
was
o
b
tain
ed
f
r
o
m
th
e
s
ch
o
o
ls
’
d
iv
is
io
n
o
f
f
ice
o
f
C
ap
iz
an
d
th
e
ad
m
in
is
tr
ato
r
s
o
f
t
h
e
p
ar
ticip
atin
g
s
ec
o
n
d
ar
y
s
ch
o
o
ls
.
An
o
r
ien
tatio
n
was
co
n
d
u
cted
to
in
f
o
r
m
p
ar
ticip
an
ts
ab
o
u
t
th
e
s
tu
d
y
’
s
o
b
jectiv
es,
p
r
o
ce
d
u
r
es,
b
en
ef
its
,
an
d
m
in
i
m
al
r
is
k
s
.
Par
ticip
atio
n
was
s
t
r
ictly
v
o
lu
n
tar
y
an
d
r
esp
o
n
d
en
ts
wer
e
ass
u
r
ed
o
f
th
eir
r
ig
h
t
to
with
d
r
aw
f
r
o
m
th
e
s
tu
d
y
at
an
y
p
o
i
n
t
with
o
u
t
co
n
s
eq
u
en
ce
.
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
.
15
,
No
.
2
,
Ap
r
il
20
2
6
:
1
1
9
6
-
1
2
1
1
1202
I
n
f
o
r
m
ed
co
n
s
en
t
was
o
b
tain
ed
f
r
o
m
all
teac
h
e
r
s
an
d
lear
n
er
s
as
r
esp
o
n
d
en
ts
,
wh
ile
p
ar
en
tal
o
r
g
u
ar
d
ian
co
n
s
en
t
was
s
ec
u
r
ed
f
o
r
m
in
o
r
s
.
T
h
e
co
n
s
en
t
p
r
o
ce
s
s
en
s
u
r
ed
tr
an
s
p
ar
en
c
y
an
d
u
n
d
er
s
ta
n
d
in
g
o
f
th
e
s
tu
d
y
’
s
s
co
p
e,
p
u
r
p
o
s
e,
an
d
d
ata
u
s
e.
All
co
llected
in
f
o
r
m
atio
n
was
tr
ea
ted
with
s
tr
ict
co
n
f
id
en
tial
ity
an
d
an
o
n
y
m
ity
,
wh
er
e
id
en
tifia
b
le
d
ata
wer
e
ex
clu
d
ed
,
s
ec
u
r
ely
s
to
r
e
d
,
an
d
r
ep
o
r
te
d
o
n
ly
in
ag
g
r
eg
ated
f
o
r
m
.
B
y
u
p
h
o
ld
in
g
th
ese
eth
ical
an
d
leg
al
s
tan
d
ar
d
s
,
th
e
r
esear
ch
er
e
n
s
u
r
e
d
th
at
th
e
s
tu
d
y
was
co
n
d
u
cted
with
in
teg
r
ity
,
tr
an
s
p
ar
en
cy
,
a
n
d
f
u
ll
r
esp
ec
t
f
o
r
h
u
m
a
n
p
ar
ticip
an
ts
,
th
er
e
b
y
m
ain
tain
in
g
b
o
th
th
e
m
o
r
al
s
o
u
n
d
n
ess
an
d
th
e
s
ch
o
lar
ly
r
ig
o
r
o
f
th
e
r
esear
ch
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
o
im
p
r
o
v
e
clar
ity
an
d
av
o
id
r
ed
u
n
d
a
n
cy
,
th
e
d
is
cu
s
s
io
n
s
y
n
th
esizes f
in
d
in
g
s
ar
o
u
n
d
:
i
)
co
m
p
eten
cy
s
elec
tio
n
;
ii
)
m
ater
ial
f
ea
tu
r
es
;
an
d
iii
)
ev
alu
atio
n
r
esu
lts
,
wh
ile
ex
p
licitly
lin
k
in
g
ea
ch
tab
l
e
an
d
f
ig
u
r
e
to
th
e
co
r
r
esp
o
n
d
in
g
claim
s
in
th
e
t
ex
t.
T
h
e
r
esu
lts
an
d
d
is
cu
s
s
io
n
ar
e
p
r
esen
ted
o
n
th
e
lear
n
i
n
g
co
m
p
eten
cies
in
Gr
ad
e
7
m
ath
em
atics
th
at
ar
e
b
est
in
teg
r
ated
with
lo
ca
l
f
o
lk
tales,
th
e
d
ev
elo
p
m
e
n
t
o
f
th
e
f
o
lk
tale
-
b
ased
in
s
tr
u
ctio
n
al
m
ater
ials
,
an
d
th
e
ev
alu
atio
n
o
f
th
ese
m
ater
ials
co
n
d
u
cted
b
y
ex
p
e
r
ts
an
d
s
tu
d
en
ts
.
3
.
1
.
L
ea
rning
co
m
pet
encies in
G
ra
de
7
m
a
t
hem
a
t
ics bes
t
inte
g
ra
t
ed
wit
h lo
ca
l f
o
l
k
t
a
les
T
h
e
in
teg
r
atio
n
o
f
lo
ca
l
f
o
lk
tales
in
to
m
ath
em
atics
in
s
tr
u
ctio
n
n
ec
ess
itates
th
e
id
en
tific
atio
n
o
f
lear
n
in
g
co
m
p
eten
cies
th
at
alig
n
co
n
ce
p
tu
ally
a
n
d
co
n
t
ex
tu
ally
with
cu
ltu
r
al
n
ar
r
at
iv
es.
I
n
th
is
s
tu
d
y
,
a
co
m
p
eten
c
y
ch
ec
k
lis
t
was
ad
m
in
is
ter
ed
to
2
5
Gr
ad
e
7
tea
ch
er
s
h
an
d
lin
g
m
ath
em
atics,
E
n
g
lis
h
,
an
d
s
o
cial
s
cien
ce
s
ac
r
o
s
s
f
o
u
r
p
u
b
lic
s
e
co
n
d
ar
y
s
ch
o
o
ls
in
th
e
m
u
n
ici
p
ality
o
f
Ma
ay
o
n
,
Pro
v
in
ce
o
f
C
ap
iz,
d
u
r
in
g
th
e
f
ir
s
t
s
em
ester
o
f
S.Y.
2
0
2
4
–
2
0
2
5
.
T
h
e
p
u
r
p
o
s
e
o
f
th
e
in
s
tr
u
m
en
t
was
to
ascer
tai
n
wh
ich
lear
n
in
g
co
m
p
eten
cies
in
Gr
a
d
e
7
m
at
h
em
atics
wer
e
m
o
s
t
s
u
itab
le
f
o
r
in
teg
r
atio
n
with
lo
ca
l
f
o
lk
t
ales.
Data
g
ath
er
ed
wer
e
an
aly
ze
d
u
s
in
g
m
ea
n
,
s
tan
d
ar
d
d
ev
iatio
n
,
an
d
r
an
k
to
d
eter
m
in
e
th
e
co
m
p
ete
n
cies
p
er
ce
iv
ed
as
m
o
s
t
ap
p
r
o
p
r
iate
f
o
r
in
teg
r
atio
n
.
T
h
e
r
esu
lts
wer
e
th
en
u
s
ed
as
th
e
f
o
u
n
d
atio
n
al
f
r
a
m
ewo
r
k
in
th
e
d
esig
n
an
d
d
ev
elo
p
m
e
n
t o
f
a
cu
ltu
r
ally
r
e
lev
an
t in
s
tr
u
ctio
n
al
m
ater
ial.
T
h
e
r
esu
lts
in
T
ab
le
1
r
ev
ea
led
th
at
co
m
p
eten
cies
u
n
d
er
m
ea
s
u
r
em
en
t
an
d
g
e
o
m
etr
y
,
an
d
n
u
m
b
er
an
d
alg
eb
r
a
wer
e
p
er
ce
iv
e
d
a
s
m
o
r
e
ad
ap
tab
le
to
c
u
ltu
r
al
s
to
r
y
tellin
g
.
T
h
is
f
in
d
in
g
s
u
g
g
ests
th
at
teac
h
er
s
v
alu
e
th
e
co
n
tex
t
u
al
p
o
ten
tial
o
f
f
o
lk
tales to
illu
s
tr
ate
m
ath
em
atica
l id
ea
s
th
at
in
v
o
lv
e
p
r
o
b
lem
-
s
o
lv
in
g
,
tr
a
d
e,
an
d
r
ea
l
-
life
ap
p
licatio
n
s
[
3
3
]
,
[
3
4
]
.
Un
d
er
m
ea
s
u
r
em
en
t
an
d
g
e
o
m
etr
y
,
o
n
e
co
m
p
eten
cy
was
id
en
tifie
d
:
“d
r
aw
tr
ian
g
les,
q
u
a
d
r
ilater
al
s
,
an
d
r
eg
u
lar
p
o
ly
g
o
n
s
(
5
,
6
,
8
,
o
r
1
0
s
id
es)
with
g
iv
e
n
an
g
le
m
ea
s
u
r
es”
(
M=
3
.
0
0
,
SD=0
.
7
6
,
r
an
k
=4
)
.
T
h
is
co
m
p
eten
c
y
was
co
n
s
id
er
ed
s
u
itab
le
b
ec
au
s
e
o
f
its
co
n
n
ec
tio
n
t
o
s
y
m
m
etr
ical
an
d
g
eo
m
etr
ic
p
atter
n
s
f
o
u
n
d
in
in
d
i
g
en
o
u
s
ar
t,
wea
v
in
g
,
an
d
ar
ch
itectu
r
al
m
o
tifs.
B
y
ass
o
ciatin
g
g
eo
m
etr
ic
f
i
g
u
r
es
with
cu
ltu
r
al
a
r
tifa
cts,
lear
n
er
s
ca
n
b
etter
u
n
d
e
r
s
tan
d
ab
s
tr
ac
t
m
ath
em
atica
l
f
o
r
m
s
th
r
o
u
g
h
f
am
iliar
cu
ltu
r
a
l r
ep
r
esen
tatio
n
s
[
3
5
]
.
T
ab
le
1
.
L
ea
r
n
in
g
c
o
m
p
ete
n
cies in
Gr
ad
e
7
m
at
h
em
atics b
est in
teg
r
ated
with
lo
ca
l f
o
lk
tale
s
To
p
i
c
SD
M
R
a
n
k
M
e
a
su
r
e
me
n
t
a
n
d
g
e
o
m
e
t
r
y
:
D
r
a
w
t
r
i
a
n
g
l
e
s,
q
u
a
d
r
i
l
a
t
e
r
a
l
s,
a
n
d
r
e
g
u
l
a
r
p
o
l
y
g
o
n
s
(
5
,
6
,
8
,
o
r
1
0
si
d
e
s)
w
i
t
h
g
i
v
e
n
a
n
g
l
e
m
e
a
s
u
r
e
s
0
.
7
6
3
.
0
0
4
N
u
mb
e
r
a
n
d
a
l
g
e
b
r
a
:
S
o
l
v
e
p
r
o
b
l
e
ms
i
n
v
o
l
v
i
n
g
:
p
e
r
c
e
n
t
a
g
e
i
n
c
r
e
a
se,
a
n
d
p
e
r
c
e
n
t
a
g
e
d
e
c
r
e
a
s
e
0
.
6
9
3
.
1
6
2
.
5
S
o
l
v
e
mo
n
e
y
p
r
o
b
l
e
ms
i
n
v
o
l
v
i
n
g
p
e
r
c
e
n
t
a
g
e
s (
d
i
s
c
o
u
n
t
,
c
o
mm
i
ssi
o
n
,
s
a
l
e
s
t
a
x
,
a
n
d
si
m
p
l
e
i
n
t
e
r
e
st
)
0
.
8
0
3
.
1
6
2
.
5
I
d
e
n
t
i
f
y
a
n
d
e
x
p
l
a
i
n
t
h
e
u
se
s o
f
r
a
t
e
s
0
.
7
9
2
.
9
6
5
S
o
l
v
e
p
r
o
b
l
e
ms
i
n
v
o
l
v
i
n
g
r
a
t
e
s (sp
e
e
d
)
0
.
6
5
3
.
2
0
1
C
o
r
r
esp
o
n
d
in
g
ly
,
in
n
u
m
b
er
an
d
alg
eb
r
a
,
f
o
u
r
co
m
p
ete
n
cies
with
h
ig
h
er
m
ea
n
s
co
r
es
wer
e
id
en
tifie
d
,
r
ef
lectin
g
teac
h
er
s
’
p
er
ce
p
tio
n
o
f
th
eir
s
tr
o
n
g
er
n
ar
r
ativ
e
ad
ap
tab
ilit
y
.
T
h
e
h
ig
h
est
-
r
a
n
k
e
d
co
m
p
eten
cy
was
“so
lv
e
p
r
o
b
lem
s
in
v
o
lv
i
n
g
r
ates
(
s
p
ee
d
)
”
(
M=
3
.
2
0
,
SD=0
.
6
5
,
r
a
n
k
=1
)
,
w
h
ich
alig
n
s
n
atu
r
ally
with
f
o
lk
tales
f
ea
t
u
r
in
g
jo
u
r
n
ey
s
,
m
o
v
em
en
t,
an
d
tim
e
-
r
elate
d
ch
allen
g
es.
T
h
e
co
m
p
eten
cies
“so
lv
e
p
r
o
b
lem
s
in
v
o
lv
in
g
: a
.
p
er
ce
n
tag
e
in
cr
ea
s
e,
an
d
b
.
p
e
r
ce
n
tag
e
d
ec
r
ea
s
e”
(
M=
3
.
1
6
,
SD=0
.
6
9
,
r
an
k
=2
.
5
)
an
d
“so
lv
e
m
o
n
ey
p
r
o
b
lem
s
i
n
v
o
lv
in
g
p
er
ce
n
ta
g
es
(
d
is
co
u
n
t,
co
m
m
is
s
io
n
,
s
ales
tax
,
an
d
s
im
p
le
in
ter
est)”
(
M=
3
.
1
6
,
SD=0
.
8
0
,
r
an
k
=2
.
5
)
wer
e
also
r
ated
h
ig
h
ly
,
as
teac
h
er
s
r
ec
o
g
n
ized
th
a
t
s
to
r
ies
in
v
o
lv
in
g
co
m
m
er
ce
,
tr
a
d
e,
an
d
m
o
r
al
d
ec
is
io
n
-
m
ak
in
g
ca
n
co
n
tex
t
u
a
lize
th
ese
ab
s
tr
ac
t
co
n
ce
p
ts
.
L
astl
y
,
“id
en
tify
an
d
ex
p
lain
th
e
u
s
es
o
f
r
ates”
w
as
o
b
tain
ed
(
M=
2
.
9
6
,
SD=0
.
7
9
,
r
a
n
k
=5
)
,
s
u
g
g
esti
n
g
th
at
wh
ile
co
n
ce
p
tu
ally
r
elev
an
t,
it m
ay
r
eq
u
i
r
e
m
o
r
e
co
n
cr
ete
n
a
r
r
ativ
e
ex
a
m
p
les f
o
r
ef
f
ec
tiv
e
i
n
teg
r
atio
n
.
Ov
er
all,
th
e
f
in
d
i
n
g
s
in
d
icate
th
at
m
ath
em
atica
l
co
m
p
eten
ci
es
r
o
o
ted
in
co
m
p
u
tatio
n
a
n
d
r
ea
l
-
wo
r
ld
p
r
o
b
lem
-
s
o
lv
in
g
,
p
a
r
ticu
lar
ly
th
o
s
e
r
elate
d
to
r
ates
an
d
p
er
ce
n
tag
es,
ar
e
m
o
s
t
co
m
p
atib
l
e
with
th
e
n
ar
r
ativ
e
an
d
m
o
r
al
d
im
en
s
io
n
s
o
f
lo
c
al
f
o
lk
tales.
I
n
teg
r
atin
g
th
ese
co
m
p
eten
cies
in
to
c
u
ltu
r
ally
f
am
iliar
s
to
r
ies
n
o
t
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
F
r
o
m
s
to
r
ies to
n
u
mb
ers
:
d
ev
elo
p
men
t o
f fo
lkta
le
-
b
a
s
ed
in
s
tr
u
ctio
n
a
l
…
(
C
h
err
y
Jo
y
B
.
De
min
g
o
y
)
1203
o
n
ly
s
tr
en
g
th
en
s
s
tu
d
e
n
ts
’
m
ath
em
atica
l
co
m
p
r
eh
en
s
io
n
b
u
t
also
f
o
s
ter
s
cu
ltu
r
al
ap
p
r
ec
iatio
n
an
d
en
g
ag
em
e
n
t.
T
h
is
cu
ltu
r
ally
r
esp
o
n
s
iv
e
ap
p
r
o
ac
h
alig
n
s
with
th
e
Dep
E
d
’
s
ad
v
o
ca
cy
f
o
r
c
o
n
tex
tu
alize
d
in
s
tr
u
ctio
n
th
at
p
r
o
m
o
tes m
ea
n
in
g
f
u
l a
n
d
in
cl
u
s
iv
e
lear
n
in
g
ex
p
er
ien
ce
s
[
3
6
]
.
3
.
2
.
Dev
el
o
pm
ent
o
f
a
f
o
lkta
le
-
ba
s
ed
ins
t
r
uct
io
na
l m
a
t
er
i
a
l in m
a
t
hema
t
ics
T
h
e
d
e
v
elo
p
m
e
n
t
o
f
th
e
cu
ltu
r
ally
r
elev
an
t
f
o
lk
tale
-
b
ased
in
s
tr
u
ctio
n
al
m
ater
ial
was
g
r
o
u
n
d
ed
in
th
e
in
teg
r
atio
n
o
f
m
ath
em
atica
l
c
o
n
ce
p
ts
with
in
d
ig
en
o
u
s
f
o
lk
t
ales
f
r
o
m
Pan
ay
I
s
lan
d
.
Fo
llo
win
g
an
ex
ten
s
iv
e
an
aly
s
is
o
f
t
h
e
Gr
a
d
e
7
lea
r
n
in
g
co
m
p
eten
cies
o
u
tlin
ed
in
th
e
MA
T
AT
AG
c
u
r
r
icu
lu
m
,
th
e
r
esear
ch
er
id
en
tifie
d
s
p
ec
if
ic
co
m
p
eten
c
ies
s
u
itab
le
f
o
r
co
n
tex
tu
al
in
teg
r
atio
n
with
lo
ca
l
n
ar
r
ativ
e
s
.
I
n
co
llab
o
r
atio
n
with
a
lo
ca
l
lay
o
u
t
ar
tis
t,
th
e
r
esear
ch
er
d
esig
n
ed
an
d
illu
s
tr
ated
v
is
u
al
elem
en
ts
th
at
au
th
en
tically
r
ep
r
esen
ted
t
h
e
ch
a
r
ac
ter
s
,
s
ettin
g
s
,
an
d
cu
lt
u
r
al
m
o
tifs
o
f
Pan
ay
an
o
n
f
o
lk
lo
r
e,
wh
ile
s
im
u
ltan
eo
u
s
ly
em
b
ed
d
in
g
m
ath
em
atica
l
id
ea
s
with
in
th
e
n
ar
r
ativ
e
s
tr
u
ctu
r
e.
T
h
e
s
to
r
ies
u
tili
ze
d
in
th
e
m
ater
ial
wer
e
ad
ap
ted
f
r
o
m
Ace
v
e
d
o
et
a
l.
[
3
7
]
.
Up
o
n
co
m
p
letio
n
o
f
th
e
lay
o
u
t
an
d
d
esig
n
,
th
e
m
ater
ial
u
n
d
er
wen
t
p
r
elim
in
ar
y
p
r
o
d
u
ctio
n
an
d
was
s
u
b
jecte
d
to
r
i
g
o
r
o
u
s
f
ac
e
an
d
co
n
ten
t
v
alid
atio
n
b
y
s
u
b
ject
m
atter
e
x
p
er
ts
,
ed
u
c
ato
r
s
,
an
d
cu
ltu
r
al
co
n
s
u
ltan
ts
.
Su
b
s
eq
u
en
t
r
e
v
i
s
io
n
s
wer
e
im
p
lem
en
ted
b
a
s
ed
o
n
ev
alu
ativ
e
f
ee
d
b
ac
k
to
en
h
an
ce
b
o
th
p
ed
ag
o
g
ical
s
o
u
n
d
n
ess
an
d
c
u
ltu
r
al
in
teg
r
ity
.
T
h
e
f
in
al
v
er
s
io
n
o
f
th
e
m
ater
ial
was
t
h
en
r
ep
r
o
d
u
ce
d
f
o
r
class
r
o
o
m
im
p
lem
en
tatio
n
a
n
d
ev
alu
atio
n
.
Dis
tin
ct
f
r
o
m
co
m
m
e
r
cially
av
ailab
le
in
s
tr
u
ctio
n
al
s
to
r
y
b
o
o
k
s
,
th
e
d
ev
elo
p
e
d
m
ater
ial
is
ch
ar
ac
ter
ized
b
y
th
r
ee
d
ef
i
n
in
g
f
ea
tu
r
es
t
h
at
u
n
d
er
s
co
r
e
its
cu
ltu
r
al
an
d
ed
u
ca
tio
n
a
l
r
elev
an
ce
.
First,
th
e
in
co
r
p
o
r
atio
n
o
f
Pan
ay
I
s
lan
d
f
o
lk
tales
s
er
v
es
as
an
av
e
n
u
e
f
o
r
p
r
o
m
o
tin
g
c
u
ltu
r
al
aw
ar
en
ess
an
d
h
e
r
itag
e
ap
p
r
ec
iatio
n
am
o
n
g
lea
r
n
er
s
.
As
n
o
ted
b
y
Mo
h
y
ed
d
in
[
3
8
]
,
lo
ca
l
f
o
lk
lo
r
e
f
u
n
ctio
n
s
as
a
v
ess
el
o
f
cu
ltu
r
al
id
en
tity
,
o
f
f
er
in
g
p
r
o
f
o
u
n
d
in
s
ig
h
t
in
to
co
m
m
u
n
ity
v
alu
es,
tr
ad
itio
n
s
,
an
d
w
o
r
ld
v
iews.
S
ec
o
n
d
,
t
o
r
ein
f
o
r
ce
lin
g
u
is
tic
an
d
cu
ltu
r
al
au
th
en
ticity
,
th
e
s
to
r
ies
wer
e
n
ar
r
ated
in
Hilig
ay
n
o
n
,
th
e
r
eg
io
n
al
d
ialec
t
o
f
C
ap
iz,
th
er
eb
y
estab
lis
h
in
g
a
d
ee
p
e
r
em
o
tio
n
al
an
d
c
u
ltu
r
al
r
es
o
n
an
ce
with
lear
n
e
r
s
.
C
o
m
p
lem
en
tar
y
E
n
g
lis
h
tr
an
s
latio
n
s
wer
e
p
r
o
v
id
e
d
to
en
s
u
r
e
ac
ce
s
s
ib
ilit
y
an
d
co
n
ce
p
tu
al
clar
ity
,
esp
ec
ially
f
o
r
m
ath
em
atica
l
id
ea
s
th
at
m
ay
lack
d
ir
ec
t
lin
g
u
is
tic
eq
u
iv
alen
ce
i
n
Hilig
ay
n
o
n
.
A
cc
o
r
d
in
g
to
Sh
u
k
la
[
3
9
]
,
tr
a
n
s
latio
n
o
f
ten
f
ails
to
f
u
lly
ca
p
tu
r
e
s
em
an
tic
n
u
an
c
e;
th
u
s
,
en
g
ag
in
g
with
a
cu
ltu
r
e
th
r
o
u
g
h
its
n
ativ
e
lan
g
u
a
g
e
p
r
o
v
id
es
a
m
o
r
e
au
th
en
tic
u
n
d
er
s
tan
d
i
n
g
o
f
m
ea
n
in
g
an
d
co
n
te
x
t.
Fin
all
y
,
th
e
m
ater
ial
co
n
clu
d
e
d
with
an
ass
ess
m
en
t
co
m
p
o
n
en
t
d
esig
n
ed
to
e
v
alu
ate
lear
n
er
s
’
co
m
p
r
e
h
en
s
io
n
o
f
b
o
th
th
e
s
to
r
y
an
d
th
e
em
b
e
d
d
ed
m
ath
em
atica
l
co
n
ce
p
t,
f
o
s
ter
in
g
n
o
t o
n
l
y
ac
ad
em
ic
m
aster
y
b
u
t a
ls
o
in
ter
p
r
etativ
e
an
d
r
e
f
lectiv
e
en
g
a
g
e
m
en
t.
3
.
2
.
1
.
Str
uct
ura
l
co
m
po
nent
s
o
f
t
he
f
o
l
k
t
a
le
-
ba
s
ed
ins
t
ruct
io
na
l m
a
t
er
ia
l
−
C
o
v
er
p
ag
e
:
th
e
co
v
e
r
p
ag
e
was
m
eticu
lo
u
s
ly
d
esig
n
ed
to
en
ca
p
s
u
late
th
e
m
ater
ial’
s
th
em
atic
co
r
e
th
r
o
u
g
h
cu
ltu
r
ally
i
n
s
p
ir
ed
v
is
u
al
r
ep
r
esen
tatio
n
s
.
T
h
e
in
ter
p
lay
o
f
im
a
g
er
y
,
c
o
lo
r
,
a
n
d
s
y
m
b
o
lis
m
in
tr
o
d
u
ce
s
r
ea
d
er
s
to
th
e
n
ar
r
ativ
e’
s
to
n
e,
s
ettin
g
,
an
d
m
ath
em
atica
l
f
o
cu
s
,
th
e
r
eb
y
s
tim
u
latin
g
cu
r
i
o
s
ity
an
d
co
g
n
itiv
e
e
n
g
ag
e
m
en
t
e
v
en
b
e
f
o
r
e
tex
tu
al
i
n
ter
ac
tio
n
.
T
h
is
v
is
u
al
f
r
am
in
g
aim
s
to
estab
lis
h
an
an
ticip
ato
r
y
co
n
n
ec
tio
n
,
in
v
iti
n
g
r
ea
d
e
r
s
to
ex
p
l
o
r
e
th
e
s
to
r
y
an
d
its
co
n
ce
p
t
u
al
d
ep
th
.
−
C
o
p
y
r
ig
h
t
p
ag
e
:
th
is
s
ec
tio
n
f
o
r
m
ally
estab
lis
h
es
th
e
m
ate
r
ial’
s
in
tellectu
al
p
r
o
p
e
r
ty
r
i
g
h
ts
,
en
s
u
r
in
g
leg
al
an
d
eth
ical
u
s
e.
I
t
attr
ib
u
tes
th
e
cu
ltu
r
al
o
r
ig
in
s
o
f
t
h
e
i
n
co
r
p
o
r
ated
f
o
lk
tales
an
d
ac
k
n
o
wled
g
es
th
e
co
llab
o
r
ativ
e
e
f
f
o
r
ts
o
f
th
e
d
ev
elo
p
m
e
n
t
team
,
in
cl
u
d
in
g
r
esear
ch
er
s
,
e
d
u
ca
to
r
s
,
a
n
d
ar
tis
ts
.
T
h
is
tr
an
s
p
ar
en
cy
u
n
d
e
r
s
co
r
es r
esp
ec
t f
o
r
cu
ltu
r
al
o
wn
er
s
h
ip
an
d
af
f
ir
m
s
th
e
m
ater
ial’
s
ac
ad
em
i
c
leg
itima
cy
.
−
L
ea
r
n
in
g
co
m
p
eten
cies
co
v
e
r
ed
:
ea
ch
s
to
r
y
was
p
u
r
p
o
s
ef
u
lly
alig
n
ed
with
d
esig
n
ated
Gr
ad
e
7
m
ath
em
atics
co
m
p
eten
cies
to
m
ain
tain
cu
r
r
ic
u
lar
co
h
er
en
ce
an
d
in
s
tr
u
ctio
n
al
f
o
cu
s
.
T
h
ese
co
m
p
eten
cies
ar
e
ex
p
licitly
lis
ted
i
n
th
e
m
a
ter
ial
an
d
s
er
v
e
as
th
e
b
asis
f
o
r
th
e
less
o
n
o
b
jectiv
es,
co
n
t
en
t
f
lo
w,
an
d
ass
es
s
m
en
t ta
s
k
s
.
−
C
o
n
ten
t
:
th
e
co
n
ten
t
s
ec
tio
n
p
r
esen
ts
th
e
s
elec
ted
Pan
ay
I
s
lan
d
f
o
lk
tales
alo
n
g
s
id
e
th
e
co
r
r
esp
o
n
d
in
g
m
ath
em
atica
l
less
o
n
s
an
d
ac
t
iv
ities
.
E
ac
h
s
to
r
y
is
o
r
g
a
n
iz
ed
to
i
n
tr
o
d
u
ce
th
e
n
ar
r
ativ
e,
h
ig
h
lig
h
t
th
e
em
b
ed
d
e
d
m
ath
em
atica
l
id
ea
,
an
d
p
r
o
v
id
e
g
u
id
e
d
ex
er
cises
th
at
co
n
n
ec
t
th
e
ev
en
ts
o
f
th
e
f
o
lk
tale
to
th
e
tar
g
et
co
m
p
eten
cy
.
−
Ass
es
s
m
en
t
:
t
h
e
co
n
clu
d
i
n
g
s
ec
tio
n
o
f
ea
ch
less
o
n
c
o
m
p
r
is
es
q
u
esti
o
n
s
an
d
task
s
d
ir
ec
tl
y
lin
k
ed
to
th
e
s
to
r
y
an
d
th
e
m
ath
em
atica
l
co
n
ce
p
t
it
illu
s
tr
ates.
T
h
ese
ite
m
s
ch
ec
k
lear
n
er
s
’
u
n
d
e
r
s
tan
d
in
g
o
f
b
o
th
th
e
n
ar
r
ativ
e
a
n
d
th
e
co
m
p
u
tatio
n
o
r
r
ea
s
o
n
in
g
r
eq
u
ir
ed
,
an
d
th
ey
p
r
o
v
i
d
e
im
m
ed
iate
f
ee
d
b
ac
k
o
n
th
e
attain
m
en
t
o
f
th
e
s
tated
co
m
p
eten
cy
.
As
B
ad
d
a
n
e
a
n
d
E
n
n
a
m
[
4
0
]
p
o
s
its
,
ass
ess
m
en
t
n
o
t
o
n
ly
m
ea
s
u
r
es
lear
n
in
g
b
u
t
also
d
ee
p
e
n
s
en
g
ag
em
en
t
with
liter
atu
r
e
b
y
p
r
o
m
p
tin
g
lear
n
e
r
s
to
in
te
r
p
r
et
,
ev
alu
ate,
an
d
in
ter
n
alize
tex
tu
al
m
ea
n
i
n
g
.
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
.
15
,
No
.
2
,
Ap
r
il
20
2
6
:
1
1
9
6
-
1
2
1
1
1204
3
.
2
.
2
.
T
he
un
iq
ue
f
ea
t
ures o
f
t
he
ins
t
ruct
io
na
l m
a
t
er
ia
l
T
h
e
d
e
v
elo
p
m
e
n
t
o
f
th
e
f
o
l
k
tale
-
b
ased
in
s
tr
u
ctio
n
al
m
ater
ial
was
g
u
id
ed
b
y
th
e
in
ten
t
to
c
r
ea
te
a
p
ed
ag
o
g
ical
r
eso
u
r
ce
th
at
m
er
g
es
m
ath
em
atica
l
p
r
o
f
ici
en
cy
with
cu
ltu
r
al
liter
ac
y
.
I
ts
d
esig
n
em
b
o
d
ies
d
is
tin
ct
f
ea
tu
r
es
th
at
d
if
f
e
r
en
t
iate
it
f
r
o
m
c
o
n
v
e
n
tio
n
al
m
at
h
em
atics
wo
r
k
b
o
o
k
s
,
in
teg
r
at
in
g
lo
ca
l
id
e
n
tity
,
co
n
tex
tu
al
u
n
d
er
s
tan
d
in
g
,
an
d
lear
n
er
en
g
a
g
em
en
t
with
in
a
s
in
g
le
ed
u
ca
tio
n
al
f
r
am
ew
o
r
k
.
E
ac
h
elem
en
t
o
f
th
e
m
ater
ial
was
d
elib
er
ately
s
tr
u
ctu
r
ed
to
c
u
ltiv
ate
co
g
n
itiv
e
g
r
o
wth
,
c
u
ltu
r
al
awa
r
en
e
s
s
,
an
d
m
ea
n
in
g
f
u
l
lear
n
in
g
ex
p
er
ien
ce
s
am
o
n
g
s
t
u
d
en
ts
.
a.
C
o
n
tex
tu
alize
d
,
s
to
r
y
-
b
ased
f
r
am
ewo
r
k
At
th
e
h
ea
r
t
o
f
t
h
e
m
ate
r
ial
l
ies
th
e
in
teg
r
atio
n
o
f
Pan
ay
I
s
lan
d
f
o
lk
tales
as
n
ar
r
ativ
e
a
n
ch
o
r
s
f
o
r
m
ath
em
atica
l
co
n
ce
p
ts
.
T
h
is
d
esig
n
n
o
t o
n
ly
co
n
tex
t
u
alize
s
ab
s
tr
ac
t
id
ea
s
with
in
f
am
iliar
cu
ltu
r
al
s
ettin
g
s
b
u
t
also
n
u
r
tu
r
es
a
s
en
s
e
o
f
p
r
id
e
an
d
id
en
tity
am
o
n
g
lear
n
er
s
.
B
y
em
b
ed
d
in
g
m
ath
em
atica
l
p
r
in
cip
les
in
to
lo
ca
l
s
to
r
ies,
th
e
m
ater
ial
tr
an
s
f
o
r
m
s
tr
ad
itio
n
al
p
r
o
b
lem
-
s
o
lv
i
n
g
in
to
a
cu
ltu
r
ally
r
eso
n
a
n
t
lear
n
in
g
ex
p
er
ien
ce
,
allo
win
g
lear
n
er
s
to
s
ee
m
at
h
em
atics
as
b
o
th
a
u
n
iv
er
s
al
lan
g
u
ag
e
an
d
a
r
ef
lectio
n
o
f
th
eir
co
m
m
u
n
ity
’
s
wo
r
ld
v
iew.
b.
L
in
g
u
is
tically
in
clu
s
iv
e
an
d
b
i
lin
g
u
al
ap
p
r
o
ac
h
T
h
e
m
ater
ial
em
p
lo
y
s
Hilig
ay
n
o
n
as
th
e
p
r
im
ar
y
m
ed
i
u
m
o
f
n
ar
r
atio
n
,
s
u
p
p
o
r
ted
b
y
E
n
g
lis
h
tr
an
s
latio
n
s
.
T
h
is
b
ilin
g
u
al
s
tr
u
ctu
r
e
en
h
an
ce
s
ac
ce
s
s
ib
ilit
y
f
o
r
a
d
iv
er
s
e
r
a
n
g
e
o
f
lear
n
er
s
an
d
en
s
u
r
es
th
at
m
ath
em
atica
l
co
n
ce
p
ts
ar
e
c
o
m
m
u
n
icate
d
with
p
r
ec
is
io
n
an
d
cu
ltu
r
al
au
th
e
n
ticity
.
T
h
e
u
s
e
o
f
th
e
lo
c
al
d
ialec
t
b
r
id
g
es
co
g
n
itiv
e
an
d
cu
ltu
r
al
u
n
d
e
r
s
tan
d
in
g
,
r
ein
f
o
r
cin
g
th
e
v
alu
e
o
f
lin
g
u
is
tic
d
iv
er
s
ity
in
ac
ad
em
ic
co
n
tex
ts
.
T
h
is
f
ea
tu
r
e
n
o
t
o
n
ly
p
r
eser
v
es
lo
ca
l
h
er
itag
e
b
u
t
also
en
co
u
r
ag
es
s
tu
d
en
ts
to
ap
p
r
ec
iate
th
e
in
ter
p
lay
b
etwe
en
la
n
g
u
a
g
e
an
d
k
n
o
wled
g
e,
a
p
r
in
cip
le
u
n
d
e
r
s
co
r
ed
b
y
T
az
h
ito
v
a
et
a
l
.
[
4
1
]
.
c.
Vis
u
ally
an
d
cu
ltu
r
ally
e
n
g
ag
i
n
g
d
esig
n
E
v
er
y
p
a
g
e
o
f
th
e
m
ater
ial
is
en
r
ich
ed
with
illu
s
tr
atio
n
s
th
at
m
ir
r
o
r
th
e
c
u
ltu
r
al
m
o
tifs,
ch
ar
ac
ter
s
,
an
d
s
ettin
g
s
o
f
Pan
ay
’
s
f
o
lk
l
o
r
e.
T
h
ese
v
is
u
als
s
er
v
e
as
s
e
m
io
tic
r
eso
u
r
ce
s
,
co
n
v
ey
in
g
m
ea
n
in
g
b
ey
o
n
d
tex
t
an
d
in
v
itin
g
lear
n
e
r
s
to
in
te
r
p
r
et
m
ath
em
atics
th
r
o
u
g
h
v
is
u
al,
n
ar
r
ativ
e,
a
n
d
c
u
ltu
r
al
d
im
en
s
io
n
s
.
T
h
e
m
ater
ial’
s
d
esig
n
d
r
aws
o
n
m
u
ltimo
d
al
lear
n
in
g
p
r
in
ci
p
les,
wh
er
e
im
ag
er
y
an
d
tex
t
co
llab
o
r
ate
to
d
ee
p
e
n
co
m
p
r
eh
e
n
s
io
n
,
en
h
a
n
ce
r
ec
al
l,
an
d
s
u
s
tain
en
g
ag
em
en
t.
T
h
is
ap
p
r
o
ac
h
p
o
s
itio
n
s
v
is
u
al
liter
ac
y
as
a
cr
u
cial
to
o
l in
m
ath
em
atics e
d
u
ca
tio
n
,
esp
ec
ially
in
cu
ltu
r
ally
g
r
o
u
n
d
ed
p
e
d
ag
o
g
y
.
d.
C
o
m
p
eten
cy
-
alig
n
e
d
an
d
task
-
o
r
ien
ted
s
tr
u
ctu
r
e
E
ac
h
s
to
r
y
is
d
elib
er
ately
m
a
p
p
ed
t
o
s
p
ec
if
ic
Gr
a
d
e
7
m
at
h
em
atics
co
m
p
eten
cies
d
e
r
iv
e
d
f
r
o
m
th
e
MA
T
AT
AG
c
u
r
r
icu
lu
m
,
en
s
u
r
in
g
alig
n
m
en
t
with
n
atio
n
al
s
tan
d
ar
d
s
.
T
h
e
task
s
with
in
ea
ch
less
o
n
ar
e
s
eq
u
en
ce
d
to
p
r
o
g
r
ess
f
r
o
m
c
o
m
p
r
eh
e
n
s
io
n
o
f
th
e
s
to
r
y
to
ap
p
licatio
n
o
f
m
ath
e
m
atica
l
co
n
ce
p
ts
,
cu
lm
in
atin
g
in
r
ef
lectiv
e
e
x
er
cises
th
at
i
n
teg
r
ate
b
o
th
d
o
m
ain
s
.
T
h
is
d
esig
n
en
s
u
r
es
a
s
p
ir
al
p
r
o
g
r
ess
io
n
o
f
lear
n
in
g
d
ev
elo
p
m
e
n
t,
n
o
t
o
n
ly
m
ath
e
m
atica
l
u
n
d
er
s
tan
d
in
g
b
u
t
als
o
cr
itical
th
in
k
in
g
,
p
r
o
b
lem
-
s
o
lv
in
g
,
a
n
d
cu
ltu
r
al
in
ter
p
r
etatio
n
s
k
ills
.
e.
R
ef
lectiv
e
an
d
in
teg
r
ativ
e
ass
e
s
s
m
en
t
T
h
e
co
n
clu
d
in
g
s
ec
tio
n
s
o
f
ea
ch
s
to
r
y
f
ea
tu
r
e
ass
ess
m
en
ts
th
at
b
len
d
liter
ar
y
ap
p
r
ec
iatio
n
with
m
ath
em
atica
l
r
ea
s
o
n
in
g
.
T
h
ese
ass
es
s
m
en
ts
ar
e
d
esig
n
ed
to
m
ea
s
u
r
e
b
o
th
c
o
g
n
itiv
e
m
ast
er
y
an
d
i
n
ter
p
r
etiv
e
u
n
d
er
s
tan
d
i
n
g
,
allo
win
g
lear
n
er
s
to
d
em
o
n
s
tr
ate
h
o
w
cu
ltu
r
al
n
ar
r
ativ
es
ca
n
illu
m
in
ate
m
ath
em
atica
l
id
ea
s
.
W
ell
-
d
esig
n
ed
ass
ess
m
en
ts
n
o
t
o
n
ly
e
v
alu
ate
co
m
p
r
eh
e
n
s
io
n
b
u
t
also
f
o
s
ter
d
ee
p
e
r
en
g
a
g
em
en
t
a
n
d
ap
p
r
ec
iatio
n
o
f
co
n
te
n
t
[
4
2
]
.
T
h
r
o
u
g
h
th
is
in
teg
r
ativ
e
ap
p
r
o
ac
h
,
lear
n
er
s
ar
e
en
c
o
u
r
a
g
ed
to
th
i
n
k
c
r
itically
,
m
ak
e
co
n
n
ec
tio
n
s
,
an
d
ap
p
l
y
t
h
eir
k
n
o
wled
g
e
in
c
u
ltu
r
ally
m
ea
n
in
g
f
u
l c
o
n
tex
ts
.
f.
Fin
al
o
u
tp
u
t
T
he
f
in
al
o
u
tp
u
t
o
f
th
e
s
tu
d
y
was
a
v
alid
ated
an
d
r
ef
in
ed
f
o
lk
tale
-
b
ased
in
s
tr
u
ctio
n
al
m
a
ter
ial
titl
ed
Pan
ay
s
ay
o
n
:
T
ales
f
r
o
m
Pan
ay
I
s
lan
d
in
m
ath
em
atics,
d
esig
n
ed
s
p
ec
if
ically
f
o
r
Gr
a
d
e
7
lear
n
er
s
.
T
h
e
m
ater
ial
s
u
cc
ess
f
u
lly
in
teg
r
ated
s
elec
ted
Pan
ay
an
o
n
f
o
lk
tales
with
co
r
e
m
ath
em
atica
l
co
m
p
eten
cies,
allo
win
g
s
tu
d
en
ts
to
en
g
ag
e
with
m
ath
em
atica
l
id
ea
s
th
r
o
u
g
h
cu
l
tu
r
ally
g
r
o
u
n
d
ed
n
a
r
r
ativ
es.
E
v
alu
atio
n
r
esu
lts
co
n
f
ir
m
e
d
th
at
t
h
e
f
o
lk
tale
-
b
a
s
ed
in
s
tr
u
ctio
n
al
m
ater
ial
m
et
h
ig
h
s
tan
d
ar
d
s
o
f
c
o
n
ten
t
ac
c
u
r
ac
y
,
in
s
tr
u
ctio
n
al
ef
f
ec
tiv
en
ess
,
an
d
ae
s
th
etic
ap
p
ea
l.
L
ea
r
n
e
r
s
d
em
o
n
s
tr
ated
in
cr
ea
s
ed
m
o
tiv
atio
n
,
d
ee
p
er
c
o
n
ce
p
t
u
al
u
n
d
er
s
tan
d
i
n
g
,
an
d
im
p
r
o
v
ed
p
ar
ticip
atio
n
d
u
r
in
g
ev
id
e
n
t
d
u
r
in
g
th
e
im
p
lem
en
tatio
n
.
E
x
p
er
t
v
alid
ato
r
s
af
f
ir
m
ed
th
at
th
e
m
ater
ial
p
r
o
m
o
ted
co
n
te
x
tu
al
lear
n
in
g
b
y
co
n
n
ec
tin
g
ab
s
tr
ac
t
m
ath
em
atica
l
co
n
ce
p
ts
to
f
am
iliar
cu
ltu
r
al
co
n
tex
ts
,
th
er
eb
y
en
h
an
cin
g
co
m
p
r
eh
en
s
io
n
an
d
r
eten
tio
n
.
T
o
v
is
u
ally
r
ep
r
esen
t
t
h
ese
f
e
atu
r
es,
Fig
u
r
e
2
s
h
o
ws
a
s
am
p
le
co
v
er
p
ag
e
o
f
th
e
d
ev
elo
p
e
d
m
ater
ial,
o
f
f
er
in
g
a
p
r
ev
iew
o
f
th
e
s
to
r
y
’
s
th
em
es,
to
n
e,
an
d
co
n
te
n
t
th
r
o
u
g
h
illu
s
tr
atio
n
s
th
at
s
u
g
g
est
its
s
tr
u
ctu
r
e,
ch
ar
ac
ter
s
,
an
d
s
ettin
g
;
th
is
co
h
esiv
e
d
esig
n
aim
s
to
ca
p
tu
r
e
r
ea
d
er
s
’
atten
tio
n
,
s
p
ar
k
cu
r
io
s
ity
,
an
d
en
c
o
u
r
a
g
e
d
ee
p
er
en
g
ag
em
en
t
with
th
e
s
to
r
y
.
B
u
ild
in
g
o
n
th
is
v
is
u
al
in
tr
o
d
u
cti
o
n
,
Fig
u
r
e
3
p
r
esen
ts
a
s
am
p
le
Pan
ay
s
ay
o
n
less
o
n
,
wh
er
e
a
lo
ca
l
f
o
lk
tale
is
u
s
ed
to
co
n
tex
tu
alize
th
e
tar
g
eted
m
ath
e
m
atics
co
m
p
eten
cy
.
T
h
e
m
ain
tex
t
is
in
Hilig
ay
n
o
n
,
with
an
E
n
g
lis
h
tr
an
s
latio
n
to
en
a
b
le
b
ilin
g
u
al
in
s
tr
u
c
tio
n
an
d
ac
ce
s
s
f
o
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t
J
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v
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&
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es E
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c
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2252
-
8
8
2
2
F
r
o
m
s
to
r
ies to
n
u
mb
ers
:
d
ev
elo
p
men
t o
f fo
lkta
le
-
b
a
s
ed
in
s
tr
u
ctio
n
a
l
…
(
C
h
err
y
Jo
y
B
.
De
min
g
o
y
)
1205
non
-
Hilig
ay
n
o
n
s
p
ea
k
er
s
.
T
h
is
b
ilin
g
u
al,
c
u
ltu
r
ally
r
esp
o
n
s
iv
e
d
esig
n
p
r
o
m
o
tes
lin
g
u
i
s
tic
in
clu
s
iv
ity
an
d
s
u
p
p
o
r
ts
a
co
m
p
r
eh
e
n
s
iv
e,
r
ig
o
r
o
u
s
f
r
a
m
ewo
r
k
f
o
r
m
ath
em
a
tics
ed
u
ca
tio
n
.
Fig
u
r
e
2
.
T
h
e
co
v
er
d
esig
n
o
f
Pan
ay
s
ay
o
n
Fig
u
r
e
3
.
Sam
p
le
o
f
Pan
ay
s
ay
o
n
less
o
n
3
.
2
.
3
.
Sa
m
ple st
o
ry
-
ba
s
ed
ma
t
hem
a
t
ics t
a
s
k
s
T
o
h
elp
r
ea
d
er
s
v
is
u
alize
h
o
w
lear
n
in
g
u
n
f
o
ld
s
,
th
e
d
ev
e
lo
p
ed
m
ater
ial
in
clu
d
es
s
to
r
y
-
an
ch
o
r
ed
task
s
th
at
p
r
o
g
r
ess
f
r
o
m
co
m
p
r
eh
en
s
io
n
o
f
t
h
e
f
o
l
k
tale
to
m
ath
em
atica
l
m
o
d
elin
g
an
d
s
o
lu
tio
n
ch
ec
k
i
n
g
.
All
s
to
r
ies
ar
e
an
ch
o
r
ed
o
n
t
h
e
co
m
p
eten
cies
id
en
tifie
d
as
least
m
a
s
ter
ed
as
s
h
o
wn
in
T
ab
le
1
.
E
x
am
p
les
(
ab
r
id
g
e
d
)
in
clu
d
e
:
−
Sh
ap
es
an
d
f
ig
u
r
es
(
Pan
asay
o
n
b
o
o
k
1
)
:
o
n
a
q
u
iet
m
o
r
n
i
n
g
b
y
th
e
r
iv
er
,
a
b
o
atm
an
s
k
etc
h
es
a
n
ew
b
o
at
m
ea
n
t
to
g
lid
e
s
m
o
o
th
ly
th
r
o
u
g
h
s
tr
o
n
g
cu
r
r
e
n
ts
:
h
e
p
lan
s
a
r
ec
tan
g
u
lar
d
ec
k
m
ea
s
u
r
in
g
4
m
×
1
.
5
m
,
a
p
o
in
ted
is
o
s
ce
les
tr
ian
g
u
lar
b
o
w
with
s
id
es
1
.
2
m
,
1
.
2
m
,
a
n
d
1
.
5
m
,
an
d
tr
a
p
ez
o
id
s
id
e
p
an
els
(
to
p
b
ase
4
m
,
b
o
tto
m
b
ase
3
.
4
m
,
h
eig
h
t
0
.
6
m
)
th
at
s
lan
t
in
war
d
f
o
r
b
alan
ce
.
As
y
o
u
r
ea
d
h
is
p
l
an
,
id
en
tif
y
th
e
s
h
ap
es
h
e
u
s
ed
,
class
if
y
th
e
b
o
w
tr
ian
g
le
(
b
y
s
id
es
an
d
an
g
les),
an
d
d
eter
m
in
e
th
e
m
is
s
in
g
ac
u
te
an
g
le
o
f
a
r
ig
h
t
-
tr
ian
g
le
s
u
p
p
o
r
t b
r
ac
e
in
s
id
e
th
e
b
o
at
with
leg
s
0
.
6
m
an
d
0
.
8
m
.
−
Per
ce
n
tag
e
(
Pan
a
y
s
ay
o
n
b
o
o
k
2
)
:
i
n
th
e
f
o
r
est,
th
e
m
o
n
k
ey
s
f
o
u
n
d
a
s
m
all
r
a
f
t
th
at
co
u
ld
ca
r
r
y
o
n
ly
5
0
0
k
g
,
an
d
th
ey
f
ir
s
t
lo
ad
ed
3
5
0
k
g
o
f
ca
r
g
o
o
n
to
it;
later
,
ev
en
th
o
u
g
h
th
e
b
u
tter
f
ly
war
n
ed
t
h
em
n
o
t
to
ad
d
m
o
r
e,
th
e
y
k
ep
t
s
tack
in
g
s
ac
k
s
u
n
til
th
e
lo
ad
r
ea
c
h
ed
5
6
0
k
g
,
g
o
in
g
b
e
y
o
n
d
th
e
s
af
e
lim
i
t.
W
h
at
is
th
e
p
er
ce
n
tag
e
in
c
r
ea
s
e
in
th
e
ca
r
g
o
weig
h
t
(
f
r
o
m
3
5
0
k
g
to
5
6
0
k
g
)
with
r
esp
ec
t
to
th
e
r
af
t’
s
5
0
0
k
g
ca
r
r
y
in
g
ca
p
ac
ity
?
−
Simp
le
in
ter
est
(
Pan
asay
o
n
b
o
o
k
3
)
:
in
th
e
to
wn
led
g
er
,
d
o
g
th
e
len
d
e
r
,
ca
t
th
e
s
h
o
p
k
ee
p
er
,
an
d
m
o
u
s
e
th
e
co
llecto
r
r
ev
iewe
d
ca
t’
s
r
ec
o
r
d
s
:
ca
t
h
ad
₱7
2
,
0
0
0
i
n
as
s
ets
an
d
₱3
2
,
5
0
0
in
liab
ilit
ies.
I
f
ca
t
p
lan
s
to
u
s
e
4
0
%
o
f
h
e
r
ass
ets
to
p
ay
h
er
d
e
b
ts
,
h
o
w
m
u
ch
m
o
n
ey
will
s
h
e
p
ay
,
will
it
b
e
en
o
u
g
h
to
c
o
v
er
th
e
₱3
2
,
5
0
0
liab
ilit
y
,
an
d
h
o
w
m
u
ch
d
eb
t (
i
f
an
y
)
will r
em
ain
?
−
Sp
ee
d
–
r
ate
–
tim
e
(
m
o
ti
o
n
)
(
P
an
asay
o
n
b
o
o
k
4
)
:
o
n
a
6
0
0
-
m
eter
f
o
r
est
tr
ail,
th
e
d
ee
r
d
ash
ed
at
1
2
m
/s
wh
ile
th
e
tin
y
s
n
ail
in
ch
ed
f
o
r
war
d
at
o
n
ly
0
.
0
6
m
/s
,
h
o
w
lo
n
g
will
ea
ch
tak
e
to
r
ea
ch
th
e
f
in
is
h
lin
e,
an
d
wh
en
th
e
d
ee
r
ar
r
iv
es,
h
o
w
m
a
n
y
m
eter
s
h
as th
e
s
n
ail
alr
ea
d
y
tr
av
eled
?
3
.
3
.
E
v
a
lua
t
i
o
n o
f
t
he
f
o
lkta
le
-
ba
s
ed
m
a
t
hem
a
t
ics ins
t
ruct
io
na
l m
a
t
er
ia
l
T
h
e
ev
alu
atio
n
o
f
th
e
d
e
v
elo
p
ed
cu
ltu
r
ally
r
elev
a
n
t
f
o
lk
tale
-
b
ased
in
s
tr
u
ctio
n
al
m
ater
ial
in
m
ath
em
atics
d
eter
m
in
ed
its
le
v
el
o
f
ac
ce
p
tab
ilit
y
b
ased
o
n
f
iv
e
co
r
e
d
im
en
s
io
n
s
:
lear
n
in
g
o
b
jectiv
es,
co
n
ten
t,
o
r
g
an
izatio
n
an
d
p
r
esen
tatio
n
,
f
o
r
m
at
an
d
d
esig
n
,
an
d
ass
es
s
m
en
t
as
s
ee
n
in
T
ab
l
e
2
.
A
t
o
tal
o
f
7
6
r
esp
o
n
d
en
ts
,
c
o
m
p
r
is
in
g
6
6
Gr
ad
e
7
s
tu
d
e
n
ts
an
d
1
0
co
n
ten
t
an
d
p
ed
ag
o
g
y
e
x
p
er
ts
,
p
ar
ticip
ated
u
s
in
g
a
v
alid
ated
an
d
m
o
d
if
ied
v
er
s
i
o
n
o
f
th
e
u
n
i
v
er
s
ity
’
s
ev
alu
at
io
n
f
o
r
m
f
o
r
p
r
in
te
d
in
s
tr
u
cti
o
n
al
m
ater
ia
ls
.
T
h
e
r
esu
lts
r
ev
ea
led
th
at
th
e
m
ate
r
ial
o
b
tain
ed
an
o
v
e
r
all
m
ea
n
r
atin
g
o
f
M=
4
.
5
6
,
SD=0
.
2
1
,
w
h
ich
co
r
r
esp
o
n
d
s
to
a
“
h
ig
h
ly
ac
ce
p
tab
le
”
d
escr
ip
t
io
n
.
T
h
is
in
d
icate
s
th
at
th
e
m
ater
ial
m
et
ex
p
ec
ted
p
ed
ag
o
g
i
ca
l,
lin
g
u
is
tic,
an
d
ae
s
th
etic
s
tan
d
ar
d
s
,
v
alid
atin
g
its
s
u
itab
ilit
y
f
o
r
in
s
tr
u
ctio
n
al
u
s
e
in
m
ath
em
atics
class
r
o
o
m
s
with
m
in
im
al
r
ev
is
io
n
s
r
eq
u
ir
e
d
.
Fo
r
m
at
an
d
d
esig
n
ac
h
iev
ed
th
e
h
ig
h
est
o
v
er
all
m
ea
n
(
M=
4
.
8
5
,
SD=0
.
2
3
)
,
s
ig
n
if
y
in
g
th
at
th
e
m
ater
ial’
s
lay
o
u
t,
c
o
n
s
is
ten
cy
,
an
d
illu
s
tr
atio
n
s
wer
e
ex
c
ep
tio
n
ally
well
-
ex
ec
u
te
d
.
T
h
e
u
s
e
o
f
c
u
ltu
r
ally
in
s
p
ir
ed
v
is
u
als,
co
h
e
r
en
t
c
o
lo
r
s
ch
em
es,
an
d
leg
ib
le
ty
p
o
g
r
ap
h
y
m
ad
e
t
h
e
m
ater
ial
e
n
g
a
g
in
g
,
u
s
er
-
f
r
ien
d
ly
,
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