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m
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ts
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ra
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sc
h
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th
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o
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h
o
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t
h
e
p
ro
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e
ss
o
f
les
so
n
stu
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y
wa
s
d
o
n
e
g
i
v
e
n
th
e
fo
ll
o
wi
n
g
p
h
a
se
s:
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lan
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i
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g
p
h
a
se
,
im
p
lem
e
n
tatio
n
p
h
a
se
,
a
n
d
p
o
st
-
les
so
n
re
flec
ti
o
n
a
n
d
d
isc
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ss
io
n
p
h
a
se
.
Emp
h
a
sis o
n
th
e
p
lan
n
i
n
g
p
h
a
se
wa
s g
iv
e
n
o
n
t
h
e
d
e
tails o
f
th
e
les
so
n
d
e
sig
n
w
h
ich
a
ime
d
t
o
in
te
g
ra
te
Ig
n
a
ti
a
n
v
a
lu
e
s
i
n
t
h
e
d
isc
u
ss
io
n
wh
il
e
d
e
v
e
l
o
p
i
n
g
a
lg
e
b
ra
ic
th
i
n
k
in
g
fro
m
q
u
a
si
-
v
a
riab
le
th
i
n
k
in
g
d
e
li
v
e
re
d
in
t
h
e
im
p
lem
e
n
tatio
n
p
h
a
se
.
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i
n
d
i
n
g
s
h
i
g
h
l
ig
h
ted
o
n
t
h
re
e
sta
t
e
m
e
n
ts:
i
)
Co
ll
a
b
o
ra
ti
v
e
les
so
n
p
lan
n
in
g
n
u
rtu
re
s
a
d
e
e
p
e
r
se
n
se
o
f
sc
h
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l
a
rsh
ip
a
n
d
c
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ll
e
g
ialit
y
;
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)
B
u
il
d
in
g
a
lg
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b
ra
ic
th
in
k
in
g
fr
o
m
q
u
a
si
-
v
a
riab
le
(
a
rit
h
m
e
ti
c
)
th
in
k
in
g
is
a
v
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b
le
stra
teg
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f
o
r
u
n
d
e
rsta
n
d
in
g
th
e
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o
n
c
e
p
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o
f
a
lg
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b
ra
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q
u
a
ti
o
n
;
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n
d
i
ii
)
L
o
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k
in
g
i
n
t
o
t
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e
“
b
ig
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ict
u
re
”
a
n
d
re
sp
o
n
d
i
n
g
to
re
lev
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n
t
so
c
ial
issu
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s
c
o
u
l
d
stre
n
g
t
h
e
n
m
e
a
n
in
g
-
i
n
teg
ra
ti
o
n
o
f
I
g
n
a
ti
a
n
v
a
l
u
e
s.
S
tro
n
g
c
o
ll
a
b
o
ra
ti
o
n
a
n
d
c
o
m
m
u
n
ica
ti
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n
a
m
o
n
g
tea
c
h
e
rs
in
c
re
a
ti
n
g
d
e
tailed
les
so
n
d
e
si
g
n
e
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b
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m
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a
n
in
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f
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in
g
a
m
o
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g
p
u
p
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Re
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rc
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v
e
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led
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if
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t
r
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st
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n
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re
a
ti
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m
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n
in
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fu
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teg
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n
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c
ti
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ti
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s
wh
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p
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v
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d
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fficie
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l
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g
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d
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w
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K
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:
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Ar
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k
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[
1
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.
R
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4
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.
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th
e
less
o
n
in
a
way
th
at
it
is
n
o
t
f
o
r
ce
d
[
5
]
.
T
h
is
m
ak
es
teac
h
in
g
in
th
e
m
ath
em
atics
d
ep
ar
tm
en
t
a
r
ea
l
ch
allen
g
e
asid
e
f
r
o
m
th
e
s
u
b
ject’
s
n
atu
r
e.
Fo
r
teac
h
e
r
s
n
o
t
to
u
s
e
th
is
s
tr
ateg
y
,
it
w
as
s
u
g
g
ested
th
at
a
p
r
o
b
lem
-
s
o
lv
in
g
s
tr
ateg
y
wo
u
ld
b
e
u
s
ed
in
in
teg
r
atin
g
v
alu
es
in
th
e
m
ath
class
r
o
o
m
[
6
]
,
[
7
]
.
T
h
e
co
n
ce
p
t
m
u
s
t
b
e
em
b
e
d
d
ed
in
r
ea
l
-
life
s
itu
atio
n
s
,
s
o
th
at
th
e
s
tu
d
en
t
s
ca
n
ap
p
ly
a
m
at
h
em
atica
l
al
g
o
r
ith
m
i
n
m
a
k
in
g
d
ec
is
io
n
s
.
On
e
g
o
al
o
f
th
is
s
tu
d
y
is
to
b
e
a
b
le
to
f
ig
u
r
e
o
u
t
way
s
to
f
in
d
ef
f
ec
tiv
e
way
s
t
o
in
teg
r
ate
I
g
n
atian
v
alu
es
s
m
o
o
th
ly
in
th
e
m
ath
cl
ass
r
o
o
m
.
Ma
th
em
atics
s
tar
ts
with
th
e
b
asic
k
n
o
wled
g
e
o
f
a
r
it
h
m
etic
an
d
u
tili
ze
s
th
is
as
a
f
o
u
n
d
atio
n
f
o
r
in
tr
o
d
u
cin
g
a
n
d
teac
h
in
g
alg
e
b
r
a.
T
h
e
s
h
if
t
f
r
o
m
ar
ith
m
etic
to
alg
e
b
r
a
is
d
if
f
icu
lt,
b
u
t
it
is
an
ess
en
tial
s
tep
f
o
r
m
ath
e
m
atica
l
p
r
o
g
r
ess
[
8
]
.
B
y
th
e
tim
e
p
u
p
ils
s
tar
t
lear
n
in
g
alg
e
b
r
a,
t
h
ey
ar
e
ex
p
ec
t
ed
to
h
a
v
e
r
ea
c
h
ed
p
r
o
f
icien
c
y
in
ar
ith
m
etic
co
n
c
ep
ts
.
A
s
tu
d
y
h
as
s
h
o
wn
t
h
at
s
tu
d
en
ts
’
er
r
o
r
s
in
alg
e
b
r
a
ca
n
b
e
attr
ib
u
ted
t
o
th
e
f
u
n
d
am
e
n
tal
d
if
f
er
e
n
ce
s
b
etw
ee
n
ar
ith
m
etic
an
d
al
g
eb
r
a
[
9
]
.
Fo
r
ex
am
p
le,
if
p
u
p
ils
th
in
k
alg
eb
r
aica
lly
,
th
ey
s
h
o
u
ld
s
cr
u
tin
ize
s
o
m
e
co
n
ce
p
ts
tau
g
h
t
in
ea
r
ly
-
g
r
a
d
e
m
ath
em
atics
(
ar
ith
m
etic)
to
m
an
ag
e
alg
eb
r
aic
s
y
m
b
o
lis
m
[
1
0
]
.
Pu
p
ils
ca
n
n
o
t u
n
d
e
r
s
tan
d
th
e
r
elatio
n
s
h
ip
b
etwe
en
two
q
u
a
n
t
ities
(
ar
ith
m
etic
an
d
alg
eb
r
a)
b
ec
au
s
e
o
f
th
e
f
lawe
d
f
o
u
n
d
atio
n
o
f
t
h
e
ar
ith
m
etic
-
alg
eb
r
aic
co
n
n
ec
tio
n
in
s
itu
atio
n
s
[
1
1
]
.
I
t
was
ar
g
u
ed
in
a
s
tu
d
y
th
at
s
tu
d
en
ts
h
av
e
d
if
f
icu
lty
in
m
o
v
in
g
f
o
r
war
d
to
lear
n
in
g
al
g
eb
r
a
b
ec
au
s
e
o
f
t
h
eir
p
o
o
r
f
o
u
n
d
atio
n
o
f
p
re
-
alg
eb
r
a
co
n
ce
p
ts
lik
e
o
p
er
atio
n
s
o
n
wh
o
le
n
u
m
b
er
s
an
d
f
r
ac
tio
n
s
an
d
o
p
e
r
atio
n
s
o
n
in
teg
er
s
[
1
2
]
.
T
h
e
g
en
er
alizin
g
r
elatio
n
s
h
ip
o
f
n
u
m
b
er
s
is
n
ec
ess
ar
y
f
o
r
t
h
e
d
ev
elo
p
m
en
t
o
f
alg
e
b
r
aic
th
i
n
k
in
g
a
m
o
n
g
p
u
p
ils
[
1
3
]
.
Alg
eb
r
aic
t
h
in
k
in
g
is
th
e
id
en
tify
in
g
,
cl
ass
if
y
in
g
,
a
n
d
l
ab
elin
g
o
f
s
am
en
ess
an
d
d
if
f
er
en
ce
wh
ile
m
ak
in
g
d
is
tin
ctio
n
s
in
th
e
s
tu
d
en
t'
s
m
in
d
[
1
4
]
.
T
h
e
f
o
cu
s
o
n
a
r
ith
m
etic
th
in
k
in
g
is
m
er
ely
ca
l
cu
latin
g
a
n
u
m
er
ical
an
s
wer
to
s
o
lv
e
a
p
r
o
b
lem
.
On
th
e
o
th
er
h
an
d
,
alg
eb
r
aic
th
in
k
in
g
f
o
cu
s
es o
n
r
elatio
n
s
an
d
o
p
er
atio
n
s
[
1
5
]
.
T
h
is
ar
ticle
r
ep
o
r
ts
a
less
o
n
s
tu
d
y
(
L
S)
th
at
ai
m
ed
to
u
tili
ze
q
u
asi
-
v
ar
iab
les
an
d
th
e
b
alan
cin
g
m
eth
o
d
i
n
estab
lis
h
in
g
a
r
ela
tio
n
s
h
ip
b
etwe
en
v
ar
iab
les.
L
ess
o
n
s
tu
d
y
is
o
n
e
p
r
ac
tice
wh
er
e
teac
h
er
s
ca
n
g
r
o
w
b
y
lear
n
in
g
f
r
o
m
ea
ch
o
th
e
r
,
g
iv
en
th
e
r
ig
h
t
o
p
p
o
r
tu
n
ity
a
n
d
co
n
te
x
t.
I
t
is
a
J
ap
an
ese
f
o
r
m
o
f
p
r
o
f
ess
io
n
al
d
ev
elo
p
m
en
t
th
a
t
f
o
cu
s
es
o
n
th
e
co
llab
o
r
ativ
e
s
tu
d
y
o
f
liv
e
class
r
o
o
m
less
o
n
s
an
d
h
as
s
p
r
ea
d
q
u
ick
ly
wo
r
ld
wid
e
[
1
6
]
.
I
t
is
n
o
w
b
ein
g
in
tr
o
d
u
ce
d
[
1
7
]
,
[
1
8
]
an
d
in
s
titu
tio
n
aliz
ed
in
t
h
e
Ph
ilip
p
in
es
[
1
9
]
.
I
t
is
d
ee
m
ed
th
at
en
g
ag
in
g
in
les
s
o
n
s
tu
d
y
p
r
o
v
i
d
es
o
p
p
o
r
tu
n
it
ies
f
o
r
teac
h
er
s
to
d
ev
elo
p
d
e
ep
d
is
co
u
r
s
e
o
n
th
e
teac
h
in
g
o
f
m
ath
em
atics
[
2
0
]
.
L
ess
o
n
s
tu
d
y
was
u
s
ed
in
th
is
s
tu
d
y
to
s
u
p
p
o
r
t
a
s
m
o
o
th
tr
an
s
itio
n
f
r
o
m
ar
ith
m
etic
th
i
n
k
in
g
to
al
g
eb
r
a
ic
th
in
k
in
g
an
d
to
m
ak
e
m
ea
n
in
g
f
u
l
co
n
n
ec
tio
n
s
b
etwe
en
p
r
ev
io
u
s
k
n
o
wled
g
e
an
d
n
ew
k
n
o
wled
g
e
w
h
ile
in
t
eg
r
atin
g
I
g
n
atian
v
alu
es
a
n
d
s
o
cial
is
s
u
es
in
th
e
d
is
cu
s
s
io
n
.
Fin
ally
,
th
is
s
tu
d
y
p
r
o
v
id
e
d
ev
id
e
n
ce
o
n
h
o
w
les
s
o
n
s
tu
d
y
p
r
ac
tice
af
f
ec
ts
in
s
tr
u
ctio
n
an
d
p
u
p
ils
’
way
o
f
t
h
in
k
in
g
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
L
ess
o
n
s
tu
d
y
f
alls
u
n
d
er
th
e
ca
teg
o
r
y
o
f
class
r
o
o
m
-
b
ased
r
e
s
ea
r
ch
.
I
n
th
is
lig
h
t,
th
is
s
tu
d
y
f
o
llo
ws
a
q
u
alitativ
e
ap
p
r
o
ac
h
to
r
e
n
d
er
in
-
d
ep
t
h
an
d
f
o
cu
s
ed
a
n
aly
s
is
o
f
d
ata
co
m
in
g
f
r
o
m
a
s
p
ec
if
ic
r
ese
ar
ch
less
o
n
f
o
r
th
e
wh
o
le
p
r
o
ce
s
s
o
f
les
s
o
n
s
tu
d
y
[
2
1
]
.
T
r
an
s
cr
ip
ts
an
d
v
i
d
eo
r
ec
o
r
d
in
g
s
o
f
teac
h
er
s
’
co
llab
o
r
ativ
e
p
lan
n
in
g
,
class
r
o
o
m
o
b
s
er
v
atio
n
s
,
an
d
p
o
s
t
-
less
o
n
d
is
cu
s
s
io
n
s
wer
e
an
aly
ze
d
,
t
o
g
eth
er
with
ar
tifa
cts
f
r
o
m
t
h
e
s
tu
d
en
ts
’
wo
r
k
s
d
u
r
in
g
t
h
e
r
es
ea
r
ch
less
o
n
.
T
h
em
atic
a
n
aly
s
is
was
g
en
er
ally
d
o
n
e
to
g
e
n
er
ate
th
e
f
in
d
in
g
s
f
o
r
th
e
s
tu
d
y
.
T
h
is
m
eth
o
d
i
d
en
tif
ies
an
d
an
aly
ze
s
p
atter
n
s
o
f
m
ea
n
in
g
s
in
q
u
alitativ
e
d
ata
[
2
2
]
.
T
h
e
th
em
es
th
at
em
er
g
e
a
f
ter
a
n
aly
zin
g
th
e
r
e
f
lectio
n
s
an
d
co
m
m
e
n
ts
d
u
r
in
g
th
e
p
o
s
t
-
co
n
f
er
e
n
ce
ar
e:
h
o
w
th
e
p
r
ac
tice
o
f
less
o
n
s
tu
d
y
h
el
p
ed
t
h
e
teac
h
er
s
in
d
ev
elo
p
i
n
g
t
h
e
less
o
n
;
h
o
w
alg
eb
r
aic
th
in
k
i
n
g
w
as
b
u
ilt
f
r
o
m
q
u
asi
-
v
ar
iab
le
th
i
n
k
in
g
;
h
o
w
th
e
c
o
n
ce
p
t
o
f
alg
eb
r
a
was
s
tr
en
g
th
en
ed
with
th
e
in
teg
r
atio
n
o
f
I
g
n
atian
v
alu
es
th
r
o
u
g
h
d
is
c
u
s
s
io
n
o
f
r
elev
an
t
s
o
cial
is
s
u
e;
an
d
th
e
teac
h
er
s
’
r
o
le
in
d
e
v
elo
p
in
g
cr
itical
th
i
n
k
in
g
o
f
th
e
p
u
p
ils
.
2
.
1
.
P
l
a
nn
ing
p
ha
s
e
T
h
r
ee
o
u
t
o
f
f
o
u
r
m
em
b
e
r
s
o
f
th
e
r
esear
ch
team
(
th
e
au
t
h
o
r
s
o
f
th
is
p
a
p
er
)
,
ar
e
g
r
ad
e
s
ix
m
ath
teac
h
er
s
o
f
Aten
eo
d
e
Dav
a
o
Un
iv
er
s
it
y
–
Gr
ad
e
Sch
o
o
l
U
n
it,
Ma
tin
a,
Dav
ao
C
ity
,
Ph
ili
p
p
in
es.
T
h
e
p
lan
to
co
n
d
u
ct
th
is
r
esear
ch
s
tar
ted
wh
en
th
e
au
th
o
r
s
atten
d
e
d
a
s
em
in
ar
-
wo
r
k
s
h
o
p
o
n
less
o
n
s
tu
d
y
h
eld
o
n
J
an
u
ar
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
10
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
1
2
9
8
-
1
3
0
5
1300
3
-
5
,
2
0
1
8
at
t
h
e
Aten
eo
d
e
Dav
ao
Un
iv
er
s
ity
,
Ph
ilip
p
in
e
s
.
T
h
e
wo
r
k
s
h
o
p
em
p
h
asized
th
e
im
p
o
r
tan
ce
o
f
less
o
n
s
tu
d
y
,
its
ad
v
an
tag
es,
an
d
ch
allen
g
es.
As
an
o
u
tp
u
t,
p
ar
ticip
an
ts
id
en
tifie
d
lear
n
in
g
co
n
ten
t
th
at
wo
u
ld
b
e
u
s
ed
in
t
h
e
r
esear
ch
less
o
n
.
T
h
e
less
o
n
s
tu
d
y
was
m
ater
ia
lized
with
th
e
f
u
ll
s
u
p
p
o
r
t
o
f
t
h
e
h
ea
d
m
aster
a
n
d
th
e
s
u
b
ject
ar
e
a
h
ea
d
f
o
r
m
at
h
em
atics.
T
h
e
r
esear
ch
f
o
llo
wed
th
e
ess
en
tial
p
r
o
ce
s
s
in
d
o
in
g
less
o
n
s
tu
d
y
,
n
am
ely
:
i)
p
la
n
n
in
g
p
h
ase,
ii)
im
p
lem
en
tatio
n
o
f
r
esear
c
h
l
ess
o
n
p
h
ase
an
d
,
iii)
p
o
s
t
-
less
o
n
r
ef
lectio
n
a
n
d
d
is
cu
s
s
io
n
p
h
ase
[
2
3
]
.
T
h
e
d
o
cu
m
en
tatio
n
o
f
th
is
less
o
n
s
tu
d
y
was
f
ac
ilit
ated
b
y
th
e
f
o
u
r
th
a
u
th
o
r
o
f
th
is
ar
ticle,
wh
o
s
er
v
ed
as th
e
r
eso
u
r
ce
p
er
s
o
n
d
u
r
in
g
th
e
3
-
d
ay
s
em
in
ar
wo
r
k
s
h
o
p
o
n
less
o
n
s
tu
d
y
.
T
h
is
less
o
n
s
tu
d
y
was
d
esig
n
ed
to
h
elp
p
u
p
ils
d
ev
elo
p
alg
eb
r
aic
th
in
k
in
g
,
s
p
ec
if
ically
r
ec
o
g
n
izin
g
r
elatio
n
s
h
ip
s
,
g
en
er
alizin
g
,
an
d
an
aly
zin
g
h
o
w
v
alu
es
ch
a
n
g
e
wh
en
ex
p
l
o
r
in
g
al
g
eb
r
aic
eq
u
atio
n
s
with
two
u
n
k
n
o
wn
v
ar
iab
les.
T
h
e
r
esear
ch
er
s
co
llab
o
r
ativ
el
y
p
lan
n
e
d
f
o
r
two
wee
k
s
,
at
least
twice
a
wee
k
to
d
ev
elo
p
an
ef
f
ec
tiv
e
less
o
n
p
la
n
in
ten
d
ed
f
o
r
g
r
ad
e
s
ix
p
u
p
ils
.
P
ar
t
o
f
th
e
p
lan
n
in
g
r
e
q
u
ir
ed
th
e
r
esear
ch
g
r
o
u
p
t
o
co
m
m
en
t
an
d
g
iv
e
s
u
g
g
esti
o
n
s
ab
o
u
t
th
e
less
o
n
p
r
ep
ar
e
d
b
y
a
g
r
o
u
p
m
em
b
er
a
n
d
d
is
cu
s
s
th
o
r
o
u
g
h
ly
h
o
w
th
e
g
r
o
u
p
c
o
u
ld
im
p
lem
en
t
th
e
less
o
n
lo
g
ically
a
n
d
ef
f
ec
tiv
ely
with
in
a
5
0
-
m
in
u
tes
p
er
i
o
d
.
M
o
r
eo
v
er
,
th
e
ass
ig
n
ed
teac
h
er
f
o
r
th
e
r
esear
ch
less
o
n
p
er
f
o
r
m
ed
a
n
in
itial d
r
y
r
u
n
with
th
e
p
r
esen
ce
o
f
th
e
team
an
d
s
u
b
ject
ar
ea
h
ea
d
f
o
r
m
at
h
to
an
ticip
at
e
an
d
u
n
lo
ck
s
o
m
e
d
if
f
icu
lties
th
at
th
e
teac
h
er
m
ay
en
c
o
u
n
te
r
.
2
.
2
.
I
m
ple
m
ent
a
t
io
n o
f
re
s
ea
rc
h pha
s
e
T
h
e
r
esear
ch
less
o
n
was
im
p
l
em
en
ted
o
n
Feb
r
u
ar
y
1
2
,
2
0
1
8
,
with
th
e
p
ar
ticip
atio
n
o
f
4
0
g
r
ad
e
s
ix
p
u
p
ils
f
r
o
m
C
lass
St.
Fra
n
cis
Xav
ier
o
f
th
e
Aten
eo
d
e
Dav
ao
Gr
ad
e
Sch
o
o
l.
Fo
u
r
teen
te
ac
h
er
s
o
b
s
er
v
ed
th
e
less
o
n
’
s
im
p
lem
en
tatio
n
,
f
iv
e
ad
m
in
is
tr
ato
r
s
all
f
r
o
m
Aten
eo
d
e
Dav
ao
Un
iv
er
s
ity
-
Gr
ad
e
Sch
o
o
l
Un
it
(
Ad
DU
-
GS)
,
an
d
a
p
r
o
f
ess
o
r
f
r
o
m
th
e
Un
iv
er
s
ity
o
f
th
e
Ph
ilip
p
in
es
(
UP)
.
E
ac
h
o
b
s
er
v
er
was
p
r
o
v
id
ed
with
a
co
p
y
o
f
t
h
e
less
o
n
p
lan
as
h
is
/
h
er
g
u
id
e
f
o
r
th
eir
o
b
s
er
v
atio
n
.
T
h
e
v
id
eo
ca
m
e
r
a
was
u
s
ed
to
r
ec
o
r
d
th
e
ac
t
u
al
im
p
lem
en
tatio
n
o
f
th
e
less
o
n
.
Prio
r
to
th
e
ac
tu
al
o
b
s
er
v
atio
n
,
th
e
o
b
s
er
v
e
r
s
wer
e
o
r
ien
ted
o
n
wh
at
to
d
o
d
u
r
in
g
o
b
s
er
v
at
io
n
.
Fo
c
u
s
o
n
p
u
p
ils
’
r
esp
o
n
s
es,
en
g
ag
e
m
en
t,
an
d
in
ter
ac
tio
n
s
wer
e
g
iv
en
em
p
h
asis
.
Ob
s
er
v
er
s
wer
e
also
in
f
o
r
m
ed
to
r
ef
r
ain
f
r
o
m
h
el
p
in
g
p
u
p
ils
wh
o
m
a
y
ask
f
o
r
h
elp
in
an
s
we
r
in
g
t
h
e
task
g
iv
en
to
th
em
.
T
h
e
o
b
s
er
v
er
s
wer
e
en
co
u
r
a
g
ed
to
ta
k
e
n
o
tes o
f
th
eir
in
s
ig
h
ts
a
n
d
s
u
g
g
esti
o
n
s
.
T
h
e
teac
h
er
im
p
lem
e
n
ted
th
e
r
esear
ch
less
o
n
with
in
a
5
0
-
m
in
u
te
s
p
er
io
d
.
T
h
e
less
o
n
s
tar
ted
with
ac
tiv
atin
g
p
u
p
ils
’
p
r
io
r
k
n
o
w
led
g
e,
wh
ich
h
elp
ed
th
e
p
u
p
i
ls
co
n
n
ec
t
to
t
h
e
p
r
o
p
er
less
o
n
-
th
e
alg
e
b
r
aic
eq
u
atio
n
s
with
two
u
n
k
n
o
w
n
v
ar
iab
les.
A
p
r
o
b
lem
s
itu
atio
n
r
elev
an
t
to
a
s
o
cial
is
s
u
e
was
p
r
esen
ted
as
a
v
ital
p
ar
t
o
f
th
e
less
o
n
to
co
n
n
ec
t
th
e
lear
n
in
g
ex
p
e
r
ien
ce
to
b
r
o
ad
er
asp
e
cts
an
d
in
f
u
s
e
I
g
n
a
tian
v
alu
es.
I
n
th
e
less
o
n
p
r
o
p
er
,
th
e
teac
h
e
r
p
r
o
v
id
ed
th
e
p
u
p
ils
with
ac
tiv
itie
s
th
at
wo
u
ld
b
e
d
o
n
e
b
y
p
air
.
T
h
o
u
g
h
t
-
p
r
o
v
o
k
in
g
q
u
esti
o
n
s
r
elev
an
t
t
o
th
e
g
iv
en
ac
tiv
ities
wer
e
g
iv
e
n
w
h
ich
led
th
e
p
u
p
ils
to
m
ak
e
s
tatem
en
ts
ab
o
u
t
r
elatio
n
s
h
ip
s
o
f
two
d
if
f
er
en
t
v
ar
iab
les
in
th
e
alg
eb
r
aic
eq
u
atio
n
an
d
h
y
p
o
th
esize
w
h
eth
e
r
th
e
r
elatio
n
s
h
ip
o
f
two
v
ar
iab
les
in
th
e
e
q
u
atio
n
will
alwa
y
s
h
o
ld
tr
u
e
at
all
tim
es.
T
h
e
less
o
n
was
f
o
r
m
ally
cl
o
s
ed
u
s
in
g
t
h
e
E
x
it
C
ar
d
in
wh
ich
p
u
p
ils
wer
e
g
iv
en
th
e
o
p
p
o
r
t
u
n
ity
to
a
n
s
wer
th
e
q
u
esti
o
n
s
wr
itten
o
n
a
s
tr
ip
o
f
p
ap
e
r
.
2
.
3
.
P
o
s
t
-
less
o
n r
ef
lect
io
n a
nd
dis
c
us
s
io
n pha
s
e
Af
ter
th
e
im
p
lem
e
n
tatio
n
o
f
th
e
less
o
n
,
th
e
r
esear
c
h
er
s
an
d
th
e
o
b
s
er
v
er
s
co
n
v
en
e
d
f
o
r
th
e
p
o
s
t
-
less
o
n
d
is
cu
s
s
io
n
,
in
s
ig
h
ts
,
an
d
r
ef
lectio
n
.
T
h
is
p
ar
t
is
v
ital
in
a
less
o
n
s
tu
d
y
b
ec
au
s
e
th
i
s
is
a
v
en
u
e
w
h
er
e
th
e
im
p
lem
en
ter
s
an
d
o
b
s
er
v
er
s
will
in
v
esti
g
ate
th
e
ex
ec
u
ted
less
o
n
an
d
f
o
cu
s
o
n
h
o
w
it
ca
n
b
e
im
p
r
o
v
e
d
[
2
4
]
,
[
2
5
]
.
T
h
e
r
esear
ch
less
o
n
im
p
lem
en
te
r
s
h
ar
e
d
th
e
ex
p
e
r
ien
ce
s
,
in
s
ig
h
ts
,
an
d
r
ef
lecti
o
n
s
g
ath
er
e
d
f
r
o
m
th
e
r
esear
ch
less
o
n
wh
ich
s
tar
ted
f
r
o
m
th
e
p
lan
n
in
g
p
h
ase
to
th
e
im
p
lem
en
tatio
n
o
f
t
h
e
less
o
n
.
Af
ter
war
d
,
th
e
o
b
s
er
v
er
s
s
h
ar
ed
th
eir
in
s
ig
h
ts
,
r
ef
lectio
n
s
,
o
b
s
er
v
atio
n
s
,
im
p
r
ess
io
n
s
,
an
d
r
ec
o
m
m
en
d
atio
n
s
o
n
t
h
e
im
p
lem
en
tatio
n
o
f
th
e
r
esear
c
h
less
o
n
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
r
ee
em
er
g
e
n
t
p
er
s
p
ec
tiv
es
wer
e
ev
id
en
t
in
th
e
co
n
d
u
ct
o
f
th
e
less
o
n
s
tu
d
y
:
i
)
C
o
llab
o
r
ativ
e
less
o
n
p
lan
n
in
g
a
n
d
d
e
v
elo
p
m
e
n
t
n
u
r
tu
r
es
a
d
ee
p
er
s
en
s
e
o
f
s
c
h
o
lar
s
h
ip
an
d
c
o
lleg
iality
;
ii
)
B
u
ild
in
g
alg
eb
r
aic
th
in
k
in
g
f
r
o
m
q
u
asi
-
v
a
r
iab
le
(
ar
ith
m
etic
)
th
in
k
in
g
is
a
v
iab
l
e
s
tr
ateg
y
f
o
r
s
tu
d
en
ts
to
m
ak
e
s
en
s
e
o
f
alg
eb
r
aic
eq
u
atio
n
s
;
an
d
iii
)
L
o
o
k
in
g
i
n
to
“b
ig
g
er
p
ictu
r
e”
an
d
r
esp
o
n
d
in
g
t
o
r
elev
an
t
s
o
cial
is
s
u
es
co
u
ld
s
tr
en
g
th
en
m
ea
n
in
g
-
in
te
g
r
atio
n
o
f
I
g
n
atia
n
v
alu
es
.
3
.
1
.
Co
lla
bo
ra
t
iv
e
less
o
n pla
nn
in
g
nu
rt
ures a
deeper
s
en
s
e
o
f
s
cho
la
rsh
i
p a
nd
co
lleg
ia
lity
Mo
s
t
o
f
th
e
p
o
s
itiv
e
f
ee
d
b
ac
k
s
wer
e
ab
o
u
t
h
o
w
th
e
less
o
n
p
lan
u
s
ed
in
t
h
e
r
esear
ch
l
ess
o
n
was
ca
r
ef
u
lly
an
d
co
llab
o
r
ativ
ely
done
.
T
h
e
o
b
s
er
v
er
s
n
o
tice
d
th
at
th
e
less
o
n
p
lan
was
d
ev
elo
p
e
d
th
r
o
u
g
h
r
esear
ch
an
d
co
llab
o
r
atio
n
an
d
n
o
t
ju
s
t
th
e
ty
p
ical
tex
tb
o
o
k
-
b
ased
p
lan
.
T
h
e
less
o
n
s
tu
d
y
team
g
en
er
ally
f
o
u
n
d
th
e
ex
e
r
cise
o
f
co
llab
o
r
atio
n
en
r
ich
in
g
.
Alth
o
u
g
h
ch
allen
g
es
ar
o
s
e
alo
n
g
th
e
way
,
th
e
p
r
o
ce
s
s
o
f
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
I
n
teg
r
a
tio
n
o
f I
g
n
a
tia
n
v
a
lu
es
in
th
e
d
ev
elo
p
men
t o
f a
l
g
eb
r
a
i
c
th
in
kin
g
via
… (
Ma
r
ia
n
Gra
ce
V
elo
s
o
)
1301
th
in
k
in
g
,
r
e
-
t
h
in
k
in
g
a
n
d
r
ev
is
in
g
th
e
r
esear
ch
less
o
n
p
la
n
as
a
g
r
o
u
p
r
esu
lted
in
a
le
s
s
o
n
p
lan
th
at
is
a
pr
o
d
u
ct
o
f
t
h
e
ex
p
e
r
tis
e
o
f
s
ev
er
al
m
in
d
s
.
Acc
o
r
d
in
g
to
o
n
e
o
f
th
e
less
o
n
s
tu
d
y
p
ar
ticip
an
t
s
:
“
Th
ere
w
a
s
‘
n
o
m
o
n
o
p
o
ly
o
f
kn
o
w
led
g
e’
a
mo
n
g
th
e
tea
m
mem
b
ers
.
E
ve
r
y
mem
b
er
o
f
th
e
LS
tea
m
felt c
o
mp
eten
t a
n
d
co
n
f
id
en
t
to
g
ive
h
is
/h
er b
r
ig
h
t id
e
a
s
a
n
ytime
a
lo
n
g
th
e
w
a
y
.
”
T
h
is
s
u
p
p
o
r
ted
th
e
claim
th
at
less
o
n
s
tu
d
y
d
ev
elo
p
s
co
ll
ab
o
r
atio
n
am
o
n
g
teac
h
er
s
in
p
lan
n
in
g
,
im
p
lem
en
tin
g
a
n
d
e
v
alu
atin
g
a
less
o
n
[
2
6
]
,
[
2
7
]
.
A
d
ee
p
er
s
en
s
e
o
f
co
lleg
iality
was
n
u
r
t
u
r
ed
in
th
e
p
r
o
ce
s
s
,
an
d
at
th
e
s
am
e
tim
e,
th
e
lev
e
l
o
f
k
n
o
wled
g
e
o
f
th
e
teac
h
er
p
ar
ticip
an
ts
wer
e
en
h
a
n
ce
d
d
u
e
to
d
ee
p
e
n
in
g
o
f
th
e
co
n
ten
t to
teac
h
th
r
o
u
g
h
le
s
s
o
n
s
tu
d
y
.
I
n
th
e
im
p
lem
e
n
tatio
n
o
f
th
e
r
esear
ch
less
o
n
,
o
b
s
er
v
er
s
’
co
m
m
en
ts
an
d
f
ee
d
b
ac
k
f
o
cu
s
ed
o
n
th
e
f
o
llo
win
g
:
i)
co
n
ten
t
th
at
is
f
o
cu
s
ed
o
n
d
ev
elo
p
in
g
alg
e
b
r
aic
th
in
k
in
g
f
r
o
m
q
u
asi
-
v
a
r
iab
le
th
in
k
in
g
;
ii
)
m
ea
n
in
g
t
h
at
is
f
o
c
u
s
ed
o
n
co
n
n
ec
ted
n
ess
o
f
alg
e
b
r
a
t
o
b
r
o
ad
e
r
asp
ec
ts
(
s
o
cial
is
s
u
es),
an
d
in
f
u
s
io
n
o
f
I
g
n
atian
v
alu
es,
also
teac
h
er
r
o
le
in
d
ev
elo
p
in
g
p
u
p
ils
’
cr
itical
th
in
k
in
g
.
I
t
was
o
b
s
er
v
ed
th
at
th
e
d
ay
’
s
less
o
n
o
b
jectiv
es
wer
e
n
o
t
ex
p
licitly
m
en
tio
n
ed
in
th
e
b
eg
i
n
n
in
g
th
u
s
p
o
s
tin
g
s
o
m
e
th
o
u
g
h
ts
am
o
n
g
th
e
o
b
s
er
v
e
r
s
as
to
wh
ich
wo
u
l
d
b
e
m
o
r
e
e
f
f
ec
tiv
e,
s
ay
in
g
th
e
o
b
jectiv
es
at
t
h
e
b
eg
in
n
in
g
o
r
allo
win
g
th
e
p
u
p
ils
to
d
is
co
v
e
r
it
alo
n
g
th
e
wa
y
.
I
t
was
also
em
p
h
asized
th
at
th
e
teac
h
er
’
s
ch
o
s
en
ac
tiv
it
y
to
u
s
e
in
p
r
esen
tin
g
th
e
c
o
n
ce
p
t
o
f
“b
alan
ci
n
g
”
was
s
o
m
ewh
at
ex
p
licit.
Acc
o
r
d
in
g
to
two
o
f
th
e
o
b
s
er
v
er
s
,
wh
o
wer
e
also
s
cien
ce
teac
h
er
s
,
th
o
u
g
h
th
e
co
n
ce
p
t
was
n
o
t
f
r
ee
ly
g
iv
en
,
it
m
i
g
h
t
h
av
e
b
ee
n
b
etter
if
th
e
p
u
p
ils
d
is
co
v
e
r
ed
th
e
“b
ala
n
cin
g
”
in
m
ath
em
atics th
em
s
elv
es.
T
h
e
ch
o
ice
o
f
ac
tiv
it
y
is
v
er
y
im
p
o
r
tan
t.
On
s
ev
er
al
o
c
ca
s
io
n
s
,
p
u
p
ils
wer
e
n
o
t
g
i
v
en
e
n
o
u
g
h
o
p
p
o
r
tu
n
ity
to
s
tr
ateg
ize
in
s
o
lv
in
g
th
e
p
r
o
b
lem
s
p
r
esen
ted
.
Acc
o
r
d
i
n
g
to
o
n
e
o
f
th
e
o
b
s
er
v
er
s
,
p
u
p
ils
s
h
o
u
ld
b
e
g
iv
en
am
p
le
tim
e
an
d
c
h
an
ce
to
th
in
k
cr
itically
th
em
s
elv
es.
D
ev
elo
p
in
g
cr
itic
al
th
in
k
in
g
en
t
ails
tim
e
an
d
e
f
f
ec
tiv
e
a
r
t
o
f
q
u
esti
o
n
in
g
[
2
8
]
.
I
t
was
ev
en
a
n
o
p
p
o
r
tu
n
e
tim
e
f
o
r
p
u
p
ils
to
m
ak
e
co
n
n
ec
tio
n
s
with
o
t
h
er
d
is
cip
lin
es
lik
e
s
ci
en
ce
g
i
v
en
en
o
u
g
h
tim
e
to
ex
p
lo
r
e
an
d
r
em
em
b
e
r
.
Ob
s
er
v
in
g
h
o
w
p
u
p
il
en
g
ag
e
m
en
t
tr
an
s
p
ir
e
d
al
o
n
g
th
e
p
r
o
ce
s
s
o
f
d
o
in
g
th
e
p
r
e
p
ar
ed
ta
s
k
s
,
it
was
ap
p
ar
en
t
th
at
p
u
p
il
e
n
g
ag
e
m
e
n
t
in
cr
ea
s
ed
f
r
o
m
T
ask
1
wh
er
e
th
e
s
itu
atio
n
p
r
esen
te
d
lim
ited
th
e
p
u
p
ils
to
g
iv
in
g
o
n
ly
o
n
e
e
x
ac
t
an
s
we
r
to
T
ask
2
wh
er
e
p
u
p
ils
wer
e
allo
wed
to
e
x
p
lo
r
e
an
d
elicit
s
ev
er
al
p
o
s
s
ib
le
an
s
wer
s
.
C
o
n
f
id
en
ce
am
o
n
g
p
u
p
ils
also
in
cr
ea
s
ed
as
th
ey
wer
e
g
iv
en
o
p
p
o
r
tu
n
ities
to
lis
t
d
o
wn
s
ev
er
al
p
o
s
s
ib
le
an
s
wer
s
an
d
w
h
en
t
h
ey
wer
e
alr
ea
d
y
ab
le
to
s
ee
th
e
p
atter
n
an
d
r
elatio
n
s
h
ip
o
f
th
e
v
ar
iab
les
an
d
co
n
s
tan
ts
in
v
o
lv
ed
.
3
.
2
.
B
uil
din
g
a
lg
ebra
ic
t
hin
k
ing
f
ro
m
qu
a
s
i
-
v
a
ria
ble
t
hin
k
ing
is
a
v
ia
ble
s
t
ra
t
eg
y
f
o
r
s
t
ud
ent
s
t
o
m
a
k
e
s
ens
e
o
f
a
lg
ebra
ic
equa
t
io
ns
T
h
e
p
u
p
ils
wer
e
ab
le
to
d
if
f
er
en
tiate
alg
eb
r
aic
e
x
p
r
ess
io
n
s
f
r
o
m
alg
e
b
r
aic
e
q
u
atio
n
s
ea
s
ily
g
iv
en
th
e
ac
tiv
ity
o
f
ca
teg
o
r
izin
g
ex
a
m
p
les.
T
h
e
teac
h
er
ask
in
g
f
o
r
th
e
d
if
f
er
en
ce
b
etwe
en
th
e
two
d
id
f
o
llo
w
u
p
q
u
esti
o
n
s
.
Sp
ec
if
ically
,
to
em
p
h
asize
o
n
v
is
u
al
d
if
f
e
r
en
ce
,
t
h
e
teac
h
er
ask
ed
,
“
Wh
a
t
d
o
y
o
u
s
ee
in
a
lg
eb
r
a
ic
eq
u
a
tio
n
s
th
a
t
ca
n
n
o
t b
e
fo
u
n
d
in
a
lg
eb
r
a
ic
ex
p
r
ess
io
n
s
?
”
Acc
o
r
d
in
g
to
th
e
o
b
s
er
v
er
s
,
th
is
p
r
o
ce
s
s
was
d
o
n
e
“to
o
ex
p
licitly
”.
So
m
eh
o
w,
it
was
to
o
lead
in
g
.
R
ec
o
m
m
en
d
atio
n
s
wer
e
to
allo
w
th
e
p
u
p
ils
to
ca
teg
o
r
ize
an
d
d
if
f
er
en
tiate
alg
e
b
r
aic
ex
p
r
ess
io
n
s
f
r
o
m
al
g
eb
r
aic
e
q
u
atio
n
s
th
em
s
elv
es th
r
o
u
g
h
a
r
u
m
b
le
o
f
s
u
ch
ex
a
m
p
les.
Un
d
er
s
tan
d
in
g
th
e
r
elatio
n
s
h
i
p
b
etwe
en
co
n
s
tan
ts
,
v
ar
iab
le
s
,
an
d
b
u
ild
in
g
t
h
e
co
n
ce
p
t
o
f
eq
u
alities
th
r
o
u
g
h
th
e
b
alan
ci
n
g
m
eth
o
d
s
tar
ted
with
an
ac
tiv
ity
in
v
o
l
v
in
g
an
ac
tu
al
b
ala
n
ce
weig
h
i
n
g
s
ca
le.
T
h
e
p
u
p
ils
f
o
u
n
d
ea
s
e
in
g
iv
i
n
g
co
m
b
in
a
tio
n
s
o
f
n
u
m
b
er
s
th
at
will
m
a
k
e
th
e
s
ca
le
b
alan
ce
d
.
Sam
p
l
e
o
u
tp
u
ts
wer
e
th
e
f
o
llo
win
g
:
5
0
=2
0
+
2
0
+
1
0
5
0
=2
0
+
2
0
+
5
+
5
2
0
=1
0
+
1
0
2
0
=5
+
5
+
5
+
5
Pu
p
ils
wer
e
ab
le
to
id
en
tify
th
at
th
e
f
u
lcr
u
m
in
th
e
b
alan
ce
s
ca
le
is
th
e
s
am
e
as
th
e
eq
u
al
s
ig
n
“=
”
wr
itten
in
an
eq
u
atio
n
.
I
t
is
th
e
s
y
m
b
o
l
t
h
at
tells
th
at
th
e
e
q
u
atio
n
’
s
lef
t
s
id
e’
s
v
alu
e
is
th
e
s
am
e
as
th
e
v
al
u
e
o
n
its
r
ig
h
t
s
id
e.
Pro
g
r
ess
in
g
to
wo
r
k
in
g
with
alg
eb
r
aic
e
q
u
atio
n
s
,
p
u
p
ils
wer
e
ab
le
to
id
en
tify
d
if
f
er
e
n
t
v
alu
es
o
f
th
e
v
ar
iab
les
th
at
wi
ll
m
ak
e
t
h
e
eq
u
atio
n
“
b
alan
ce
d
”.
W
h
en
th
ey
wer
e
ask
e
d
to
g
iv
e
th
e
r
elatio
n
s
h
ip
o
f
th
e
p
air
s
o
f
v
a
r
iab
les
th
ey
m
en
tio
n
ed
,
p
u
p
ils
wer
e
ab
le
to
id
en
tif
y
th
em
with
ea
s
e.
Al
th
o
u
g
h
task
1
was
lim
itin
g
,
s
im
ilar
task
2
g
av
e
t
h
e
p
u
p
ils
m
o
r
e
lib
e
r
ty
to
th
in
k
an
d
g
iv
e
en
d
less
p
o
s
s
ib
le
p
air
s
o
f
v
a
r
iab
les
o
r
co
m
b
in
atio
n
s
y
et
co
m
e
u
p
with
th
e
s
am
e
r
elatio
n
s
h
ip
b
etwe
en
th
e
v
ar
iab
les.
I
n
th
e
en
d
,
wh
en
ask
ed
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
10
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
1
2
9
8
-
1
3
0
5
1302
q
u
esti
o
n
,
“
S
o
,
w
h
en
d
o
es
th
e
r
ela
tio
n
s
h
ip
ch
a
n
g
e?
”
p
u
p
ils
wer
e
ab
le
to
d
r
aw
th
e
s
tatem
en
t
th
at,
“
Th
e
r
ela
tio
n
s
h
ip
o
f th
e
va
r
ia
b
le
ch
a
n
g
es w
h
en
th
e
va
l
u
e
o
f th
e
c
o
n
s
ta
n
ts
is
ch
a
n
g
ed
o
r
a
lter
ed
.
”
T
h
is
is
co
n
s
is
ten
t
with
th
e
r
esu
lt
wh
er
e
a
ch
ild
d
r
ew
a
p
ictu
r
e
o
f
a
b
alan
ce
s
ca
le
to
s
h
o
w
h
o
w
it
af
f
ec
ts
th
e
b
alan
ce
if
s
h
e
alter
s
th
e
ex
p
r
ess
io
n
s
o
n
ea
ch
s
id
e
[
29
]
.
3
.
2
.
1
.
G
ener
a
lizing
nu
m
er
ica
l r
ela
t
io
ns
hip
s
:
B
uil
di
ng
a
lg
ebra
ic
t
hin
k
ing
T
ab
le
1
s
h
o
ws th
e
r
esp
o
n
s
e
o
f
o
n
e
p
u
p
il in
o
n
e
o
f
th
e
g
iv
e
n
task
s
.
T
h
e
p
u
p
il u
n
d
er
s
tan
d
s
t
h
at
if
th
er
e
ar
e
1
6
0
waf
e
r
s
to
b
e
g
i
v
en
t
o
2
0
ch
il
d
r
en
,
ea
ch
ch
ild
will
r
e
ce
iv
e
an
“x
”
n
u
m
b
er
o
f
waf
e
r
s
.
Ho
wev
er
,
w
h
en
th
e
n
u
m
b
er
o
f
ch
ild
r
en
b
ec
o
m
es
4
0
ea
ch
ch
ild
will
r
ec
ei
v
e
a
“y
”
n
u
m
b
e
r
o
f
waf
er
s
.
T
h
e
p
u
p
il
was
ab
le
to
id
en
tify
th
at
th
e
v
alu
e
o
f
x
is
t
wice
y
.
T
ab
le
1
.
Pu
p
il’s
r
esp
o
n
s
e
M
a
t
h
e
ma
t
i
c
a
l
se
n
t
e
n
c
e
:
2
0
x
A
=
4
0
x
B
To
t
a
l
n
u
m
b
e
r
o
f
w
a
f
e
r
s
2
0
c
h
i
l
d
r
e
n
4
0
c
h
i
l
d
r
e
n
1
6
0
2
0
(
X
)
=
1
6
0
4
0
(
Y
)
=
1
6
0
R
e
l
a
t
i
o
n
s
h
i
p
b
e
t
w
e
e
n
A
a
n
d
B
:
X
i
s
t
w
i
c
e
Y
’
s
v
a
l
u
e
T
ab
le
2
s
h
o
ws
th
e
r
esp
o
n
s
e
o
f
an
o
th
e
r
p
u
p
il.
I
f
t
h
er
e
a
r
e
1
6
0
waf
er
s
to
b
e
g
iv
e
n
to
2
0
ch
il
d
r
en
,
ea
ch
ch
ild
will
r
ec
eiv
e
eig
h
t
waf
er
s
.
Ho
wev
er
,
if
th
er
e
ar
e
4
0
c
h
ild
r
en
,
ea
c
h
ch
ild
will
r
ec
eiv
e
o
n
ly
f
o
u
r
wa
f
er
s
.
T
h
e
p
u
p
il
m
a
d
e
t
h
e
to
tal
n
u
m
b
er
o
f
waf
e
r
s
8
0
.
I
f
it
is
g
iv
en
to
2
0
ch
ild
r
e
n
,
ea
c
h
o
n
e
will
r
ec
eiv
e
f
o
u
r
waf
er
s
an
d
if
th
er
e
ar
e
4
0
ch
ild
r
en
,
ea
ch
o
n
e
will r
ec
eiv
e
two
waf
er
s
.
T
h
e
p
u
p
il a
ls
o
m
ad
e
th
e
to
tal
n
u
m
b
er
o
f
waf
er
s
2
0
0
.
I
f
th
er
e
a
r
e
2
0
p
u
p
ils
,
ea
c
h
ch
ild
will
r
ec
eiv
e
1
0
waf
e
r
s
an
d
if
th
er
e
ar
e
4
0
p
u
p
ils
,
ea
c
h
ch
ild
will
r
ec
eiv
e
f
iv
e
waf
er
s
.
He
was a
b
le
to
s
tate
th
at
th
e
v
alu
e
o
f
B
is
½
o
f
A.
T
ab
le
2
.
Pu
p
il’s
r
esp
o
n
s
e
M
a
t
h
e
ma
t
i
c
a
l
S
e
n
t
e
n
c
e
:
2
0
x
A
=
4
0
x
B
To
t
a
l
n
u
m
b
e
r
o
f
w
a
f
e
r
s
2
0
c
h
i
l
d
r
e
n
40
c
h
i
l
d
r
e
n
1
6
0
8
2
80
4
4
2
0
0
10
5
R
e
l
a
t
i
o
n
s
h
i
p
b
e
t
w
e
e
n
A
a
n
d
B
:
B
i
s
½
o
f
A
T
ab
le
3
s
h
o
ws
th
e
r
esp
o
n
s
e
o
f
an
o
th
er
p
u
p
il
in
th
e
s
ec
o
n
d
p
ar
t
o
f
th
e
task
.
T
h
e
m
ath
em
atica
l
s
en
ten
ce
is
3
(
Y)
=
1
5
(
Z
)
.
I
f
b
o
t
h
th
e
lef
t
a
n
d
r
ig
h
ties
o
f
th
e
e
q
u
atio
n
ar
e
e
q
u
al
to
3
0
,
th
e
v
alu
e
o
f
Y
is
1
0
an
d
th
e
v
alu
e
o
f
Z
is
2
.
I
f
b
o
t
h
th
e
lef
t
an
d
r
ig
h
t
s
id
es
o
f
th
e
eq
u
atio
n
ar
e
eq
u
al
to
4
5
,
th
e
v
alu
e
o
f
Y
i
s
1
5
an
d
th
e
v
alu
e
o
f
Z
is
3
.
An
d
i
f
b
o
th
th
e
lef
t
an
d
r
ig
h
t
s
id
e
o
f
t
h
e
eq
u
atio
n
is
eq
u
al
to
6
0
,
th
e
v
alu
e
o
f
Y
i
s
2
0
an
d
th
e
v
alu
e
o
f
Z
is
4
.
T
h
e
p
u
p
il wa
s
ab
le
to
id
en
tify
th
at
th
e
v
alu
e
o
f
Z
is
o
n
e
-
f
if
th
o
f
th
e
v
alu
e
o
f
Y.
T
ab
le
3
.
Pu
p
il’s
r
esp
o
n
s
e
M
a
t
h
e
ma
t
i
c
a
l
se
n
t
e
n
c
e
:
3
(
Y
)
=
1
5
(
Z)
V
a
l
u
e
o
f
e
q
u
a
l
i
t
y
C
o
n
st
a
n
t
:
3
C
o
n
st
a
n
t
:
1
5
30
3
(
Y
)
;
Y
=
1
0
1
5
(
Z)
;
Z=
2
45
3
(
Y
)
;
Y
=
1
5
1
5
(
Z)
;
Z=
3
60
3
(
Y
)
;
Y
=
2
0
1
5
(
Z)
;
Z=
4
R
e
l
a
t
i
o
n
s
h
i
p
b
e
t
w
e
e
n
Y
a
n
d
Z
:
Z’
s
v
a
l
u
e
i
s
1
/
5
o
f
Y
’
s v
a
l
u
e
3
.
2
.
2
.
P
up
ils
’
re
s
po
n
s
es t
o
pro
ce
s
s
qu
estio
n
s
Af
ter
g
o
in
g
th
r
o
u
g
h
t
h
e
less
o
n
to
p
ic
an
d
ac
tiv
ities
,
th
e
p
u
p
ils
wer
e
ask
ed
to
a
n
s
wer
p
r
o
ce
s
s
q
u
esti
o
n
s
.
T
h
ese
p
r
o
ce
s
s
q
u
e
s
tio
n
s
wer
e
f
o
cu
s
ed
o
n
th
e
p
u
p
ils
’
r
ea
lizatio
n
s
in
th
e
lea
r
n
in
g
p
r
o
ce
s
s
.
T
h
e
f
o
llo
win
g
ar
e
th
e
p
u
p
ils
’
r
esp
o
n
s
es
wh
en
ask
ed
th
e
q
u
esti
o
n
s
:
i)
“
W
h
at
co
n
n
ec
tio
n
d
id
y
o
u
m
a
k
e
to
d
ay
th
at
m
ad
e
y
o
u
s
ay
,
'
AHA
I
g
et
it!
'
”
“I
h
a
ve
lea
r
n
ed
t
h
a
t th
ere
a
r
e
co
u
n
tles
s
w
a
ys to
crea
te
th
e
s
a
me
n
u
mb
ers
.
”
“T
h
e
co
n
n
ec
tio
n
b
etw
ee
n
X
a
n
d
Y:
w
h
en
th
e
c
o
n
s
ta
n
t is ch
a
n
g
ed
th
e
a
n
s
w
er is
ch
a
n
g
ed
.
”
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
I
n
teg
r
a
tio
n
o
f I
g
n
a
tia
n
v
a
lu
es
in
th
e
d
ev
elo
p
men
t o
f a
l
g
eb
r
a
i
c
th
in
kin
g
via
… (
Ma
r
ia
n
Gra
ce
V
elo
s
o
)
1303
ii)
“So
m
eth
in
g
th
at
I
s
till
d
o
n
o
t
u
n
d
er
s
tan
d
is
.
.
.
”
“
N
o
th
in
g
.
A
ctu
a
lly,
I
le
a
r
n
ed
a
lo
t fro
m
th
is
less
o
n
.
”
“
N
o
th
in
g
,
ju
s
t p
r
a
ctice
mo
r
e
a
n
d
mo
r
e
to
imp
r
o
ve
.
”
iii)
“I
n
wh
at
way
s
d
id
y
o
u
s
ee
to
d
ay
’
s
m
ath
em
atics c
o
n
n
ec
te
d
t
o
y
o
u
r
ev
er
y
d
ay
life
?
”
“
I
t
h
elp
s
to
u
n
d
ers
ta
n
d
th
e
c
o
n
ce
p
ts
o
f b
a
la
n
ce
mo
r
e
in
my
d
a
ily
life.”
“T
h
e
b
a
la
n
ce
is
n
ee
d
e
d
to
ma
ke
ev
eryth
in
g
eq
u
a
l a
n
d
n
o
t j
u
s
t fo
cu
s
o
n
o
n
e
s
id
e.
”
T
h
e
r
esp
o
n
s
es
in
d
icate
d
th
e
e
x
ten
t
o
f
p
u
p
ils
’
u
n
d
er
s
tan
d
in
g
o
f
th
e
less
o
n
p
r
esen
ted
a
n
d
d
is
cu
s
s
ed
.
I
t
also
s
h
o
wed
p
u
p
ils
’
co
n
f
id
e
n
ce
in
b
u
ild
i
n
g
alg
e
b
r
aic
th
in
k
in
g
f
r
o
m
a
r
ith
m
etic.
L
astl
y
,
th
e
r
esp
o
n
s
es
ex
h
ib
ited
h
o
w
th
e
p
u
p
ils
wer
e
ab
le
to
m
ak
e
a
m
ea
n
in
g
f
u
l
co
n
n
ec
tio
n
b
etwe
en
th
e
co
n
ce
p
t
o
f
alg
eb
r
a
an
d
alg
eb
r
aic
eq
u
ati
o
n
s
to
r
ea
l
life
.
3
.
3
.
L
o
o
k
ing
into
t
he
“
big
pict
ure”
a
nd
re
s
po
nd
ing
t
o
re
lev
a
nt
s
o
cia
l iss
ues
co
u
ld s
t
re
ng
t
hen m
ea
nin
g
-
inte
g
ra
t
io
n o
f
I
g
na
t
ia
n
v
a
lue
s
Ob
s
er
v
er
s
h
av
e
ap
p
r
ec
iated
th
at
th
e
in
teg
r
atio
n
o
f
th
e
I
g
n
ati
an
v
alu
e
in
t
h
e
r
esear
ch
less
o
n
p
lan
an
d
th
e
im
p
lem
en
tatio
n
its
elf
was
s
m
o
o
th
ly
d
o
n
e.
C
o
n
tr
ar
y
to
t
h
e
u
s
u
al
claim
o
f
a
m
ath
em
atic
s
teac
h
er
wh
o
f
in
d
s
d
if
f
icu
lty
i
n
f
u
s
in
g
v
alu
es
in
a
m
ath
class
[
3
0
]
,
th
e
I
g
n
atian
v
alu
e
“
fa
ith
th
a
t
d
o
es
j
u
s
tice
”
was
s
m
o
o
th
ly
an
d
clea
r
ly
m
an
if
ested
in
t
h
e
d
is
cu
s
s
io
n
o
f
“b
alan
cin
g
”
was e
x
p
li
ci
tly
id
en
tifie
d
b
y
th
e
p
u
p
ils
.
T
ea
ch
er
:
“
Ho
w
d
o
es
b
a
l
a
n
ci
n
g
w
o
r
k
in
yo
u
r
d
a
ily
life?
”
“W
h
ere
else
d
o
yo
u
ex
p
erien
ce
b
a
la
n
ce
?
Pu
p
ils
:
“
b
a
la
n
ce
d
d
iet
,
”
“b
a
l
a
n
ce
b
etw
ee
n
a
ca
d
emic
s
a
n
d
s
p
o
r
ts
,
”
“b
a
la
n
ce
i
n
ma
n
a
g
in
g
time
,
”
“b
a
la
n
ce
i
n
th
i
n
kin
g
b
efo
r
e
ma
kin
g
d
ec
is
io
n
s
,
”
“f
a
ir
n
ess
like
b
a
la
n
ce
in
tr
ea
t
in
g
o
th
ers
.
”
T
ea
ch
er
: “
S
o
w
h
ich
I
g
n
a
tia
n
V
a
lu
e
is
r
eflec
ted
in
to
d
a
y’
s
le
s
s
o
n
?
Wh
y
d
o
y
o
u
s
a
y
s
o
?
”
Pu
p
il:
“
F
a
ith
th
a
t
d
o
es
Ju
s
tice
s
in
ce
it
r
eflec
ts
fa
i
r
n
ess
in
d
ea
lin
g
w
ith
o
th
ers
a
n
d
b
a
la
n
c
e
in
livin
g
o
n
e’
s
life.”
Usi
n
g
th
e
o
r
p
h
a
n
cr
is
is
as
a
r
e
lev
an
t
s
o
cial
is
s
u
e
wh
er
e
s
o
lv
i
n
g
alg
e
b
r
aic
e
q
u
atio
n
s
ca
n
b
e
u
s
ed
g
av
e
m
o
r
e
m
ea
n
in
g
to
wh
at
th
e
p
u
p
ils
ar
e
lear
n
in
g
.
Seein
g
co
n
n
ec
tio
n
s
an
d
r
ele
v
an
ce
o
f
s
o
lv
in
g
alg
eb
r
aic
eq
u
atio
n
s
to
r
ea
l
-
life
s
itu
atio
n
s
allo
wed
p
u
p
i
ls
to
s
ee
alg
eb
r
a
in
an
ea
s
y
p
er
s
p
ec
tiv
e
r
ath
e
r
th
an
lo
o
k
in
g
at
it
to
o
v
ag
u
ely
.
T
h
o
u
g
h
th
e
p
r
esen
tatio
n
o
f
th
e
s
o
cial
is
s
u
e
was
g
iv
en
less
ti
m
e
an
d
atten
tio
n
as
it
was
wr
i
tten
in
th
e
p
lan
,
th
e
em
p
h
asis
was
m
ad
e
m
o
r
e
o
n
th
e
asp
ec
t
wh
er
e
m
at
h
em
atica
l
p
r
o
b
le
m
s
o
lv
in
g
wa
s
in
v
o
lv
ed
.
T
h
e
L
S
team
d
ec
id
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u
p
o
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u
ch
a
ch
a
n
g
e
at
t
h
e
last
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in
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te
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e
to
tim
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co
n
s
tr
ain
ts
.
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o
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ac
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d
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to
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er
v
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,
th
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r
e
ab
o
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t
th
e
o
r
p
h
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c
r
is
is
s
itu
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th
at
was
f
lash
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o
n
th
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s
cr
ee
n
was
n
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t
clea
r
e
n
o
u
g
h
f
o
r
th
e
p
u
p
ils
to
s
ee
an
d
u
n
d
er
s
tan
d
.
L
astl
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,
th
e
u
s
e
o
f
th
e
waf
er
s
as
p
ar
t
o
f
th
e
co
n
cr
ete
ap
p
r
o
ac
h
in
s
o
lv
in
g
th
e
id
en
tifie
d
p
r
o
b
lem
s
itu
atio
n
was n
o
t u
s
e
d
ef
f
ec
tiv
ely
.
L
astl
y
,
in
g
iv
in
g
b
etter
m
ea
n
in
g
to
th
e
less
o
n
th
r
o
u
g
h
its
in
teg
r
atio
n
with
th
e
I
g
n
atian
v
alu
e
an
d
s
o
c
ial
is
s
u
e,
ac
co
r
d
in
g
to
o
n
e
o
f
th
e
o
b
s
er
v
er
s
,
it
c
o
u
ld
h
a
v
e
b
ee
n
b
est
if
th
e
teac
h
e
r
allo
wed
th
e
p
u
p
ils
to
r
ef
lect
o
n
th
e
p
r
o
b
lem
s
itu
atio
n
an
d
ask
,
“
if
th
e
n
u
mb
er
o
f
ch
ild
r
en
in
tw
o
o
r
p
h
a
n
a
g
es
is
n
o
t
s
a
me,
ye
t
yo
u
h
a
ve
th
e
s
a
me
n
u
mb
er
o
f
g
o
o
d
s
to
s
h
a
r
e,
h
o
w
w
o
u
l
d
th
e
d
i
s
tr
ib
u
tio
n
to
g
o
o
d
s
b
e?
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l
th
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ch
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r
en
g
et
t
h
e
s
a
me
n
u
mb
er
o
f
g
o
o
d
ies?
”
T
h
is
r
ein
f
o
r
ce
s
th
e
co
n
ce
p
t
o
f
eq
u
ita
b
le
d
is
tr
ib
u
tio
n
o
f
w
ea
lth
,
wh
ich
is
,
to
o
,
p
ar
t
o
f
th
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s
ch
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l’
s
m
is
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io
n
.
4.
CO
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T
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p
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aliza
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aic
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m
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d
u
ctio
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to
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lg
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r
a
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lin
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with
n
u
m
b
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s
as q
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v
ar
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th
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n
ev
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tu
ally
with
liter
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s
y
m
b
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ls
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f
alg
eb
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a
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C
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I
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ev
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less
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class
ar
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two
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d
am
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tal
p
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J
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lear
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th
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C
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allen
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to
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co
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cu
s
o
n
th
e
n
atu
r
e
o
f
th
e
s
u
b
ject
m
atter
.
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th
e
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u
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ils
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is
co
v
er
an
d
ex
p
r
ess
s
u
ch
r
ef
lectio
n
s
th
e
m
s
elv
es.
T
h
e
less
o
n
s
tu
d
y
team
b
eliev
es
th
at
co
n
d
u
ctin
g
a
less
o
n
s
tu
d
y
in
d
ev
elo
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g
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ea
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f
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l
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tr
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d
ac
tiv
ity
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h
iev
e
s
u
ch
is
v
er
y
h
elp
f
u
l a
s
it p
r
o
v
id
e
s
a
n
ef
f
icien
t stru
ctu
r
e
in
d
ev
el
o
p
in
g
a
ch
o
s
en
less
o
n
to
p
ic.
ACK
NO
WL
E
DG
E
M
E
NT
S
T
h
e
au
th
o
r
s
wo
u
ld
lik
e
to
e
x
p
r
ess
th
eir
h
ea
r
tf
elt
g
r
atitu
d
e
to
all
th
o
s
e
wh
o
co
n
tr
ib
u
ted
in
th
e
co
m
p
letio
n
o
f
th
is
r
esear
ch
s
tu
d
y
.
T
o
t
h
e
Aten
eo
d
e
Dav
ao
Un
iv
er
s
ity
C
o
m
m
u
n
ity
,
f
o
r
th
e
en
d
less
s
u
p
p
o
r
t
an
d
ac
tiv
e
p
ar
tcip
atio
n
in
th
e
p
r
o
ce
s
s
,
f
r
o
m
th
e
im
p
lem
en
ta
tio
n
o
f
th
e
less
o
n
s
tu
d
y
to
th
e
co
m
p
letio
n
o
f
th
e
r
esear
ch
p
ap
e
r
.
RE
F
E
R
E
NC
E
S
[1
]
S
.
M
o
u
n
ti
n
a
n
d
R.
N
o
wa
c
e
k
,
“
Re
flec
ti
o
n
in
Ac
ti
o
n
:
A
S
ig
n
a
tu
re
I
g
n
a
ti
a
n
P
e
d
a
g
o
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y
f
o
r
th
e
2
1
st
Ce
n
tu
r
y
,
”
in
N
.
L
Ch
ick
,
A
.
Ha
y
n
ie
,
a
n
d
R
.
A
.
R
.
G
u
ru
n
g
,
E
d
s.
,
Exp
l
o
rin
g
M
o
re
S
ig
n
a
t
u
re
Ped
a
g
o
g
ies
:
Ap
p
r
o
a
c
h
e
s
to
T
e
a
c
h
in
g
Disc
ip
li
n
a
ry
H
a
b
it
s
o
f
M
i
n
d
.
S
ter
li
n
g
,
Va
.
:
S
t
y
l
u
s P
u
b
li
s
h
in
g
,
2
0
1
2
,
p
p
.
1
2
9
-
1
4
2
.
[2
]
Z.
Lu
a
n
d
V.
Ro
se
n
,
“
P
ra
c
ti
c
in
g
Ig
n
a
ti
a
n
P
e
d
a
g
o
g
y
:
A
Dig
it
a
l
Co
l
lec
ti
o
n
o
f
Re
so
u
rc
e
s,”
J
e
su
it
Hig
h
e
r
Ed
u
c
a
ti
o
n
:
A
J
o
u
rn
a
l
,
v
ol
.
4
,
n
o.
2
,
p
p
.
1
3
5
-
1
5
2
,
2
0
1
5
.
[3
]
S
a
in
t
Lo
u
is
Un
i
v
e
rsity
(
S
LU
),
Ig
n
a
ti
a
n
P
e
d
a
g
o
g
ica
l
P
a
ra
d
i
g
m
.
[
On
li
n
e
].
Av
a
il
a
b
le
:
h
tt
p
s:/
/www
.
slu
.
e
d
u
/cttl
/res
o
u
rc
e
s/ig
n
a
ti
a
n
-
p
e
d
a
g
o
g
ica
l
-
p
a
ra
d
ig
m
.
p
h
p
.
[4
]
M.
M
c
Av
o
y
,
“
Trai
n
in
g
fa
c
u
lt
y
t
o
a
d
o
p
t
t
h
e
Ig
n
a
ti
a
n
p
e
d
a
g
o
g
ica
l
p
a
ra
d
ig
m
,
I
P
P
a
n
d
it
s
in
f
lu
e
n
c
e
o
n
tea
c
h
in
g
a
n
d
lea
rn
in
g
:
P
ro
c
e
ss
a
n
d
o
u
tco
m
e
s,”
J
e
su
it
Hig
h
e
r E
d
u
c
a
ti
o
n
:
A
J
o
u
r
n
a
l
,
v
o
l
.
2
,
n
o
.
2
,
p
p
.
1
-
1
2
,
2
0
1
3
.
[5
]
L
.
Clay
we
ll
,
K
.
P
e
n
n
in
g
t
o
n
,
a
n
d
C.
S
p
a
d
e
,
“
An
E
x
p
l
o
ra
ti
o
n
o
f
t
h
e
In
flu
e
n
c
e
o
f
Ig
n
a
ti
a
n
Va
lu
e
s
o
n
F
a
c
u
lt
y
Ro
l
e
Ex
p
e
c
tatio
n
s,”
J
e
su
it
Hi
g
h
e
r E
d
u
c
a
ti
o
n
:
A
J
o
u
rn
a
l
,
v
o
l.
3
,
n
o
.
1
,
p
p
.
1
-
8
,
2
0
1
4
.
[6
]
J.W
.
M
u
l
n
i
x
,
“
Th
i
n
k
i
n
g
c
ri
t
ica
ll
y
a
b
o
u
t
c
rit
ica
l
th
i
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,
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u
c
a
ti
o
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Ph
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.
[7
]
Y
.
M
.
A
b
d
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a
n
i
a
n
d
J
.
Es
h
an
,
“
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c
h
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g
Va
l
u
e
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v
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h
e
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ro
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p
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c
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th
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m
a
ti
c
s
,
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In
ter
n
a
t
io
n
a
l
J
o
u
rn
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l
o
f
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a
tes
t
R
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se
a
rc
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L
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1
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.
[8
]
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.
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.
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ib
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n
,
V
.
C
.
Ch
u
a
,
J
.
G
a
rc
ia,
a
n
d
L
.
E.
El
ip
a
n
e
,
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F
ro
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:
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In
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in
S
e
v
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th
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ra
d
e
M
a
th
e
m
a
ti
c
s,”
P
a
p
e
r
p
re
se
n
ted
a
t
th
e
An
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a
l
M
e
e
ti
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M
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th
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ma
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Ed
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c
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Gr
o
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Au
stra
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sia
(M
E
RGA)
,
2
0
1
4
.
[9
]
G
.
E.
A.
Do
n
,
“
S
e
c
o
n
d
a
ry
S
c
h
o
o
l
S
tu
d
e
n
ts’
M
isc
o
n
c
e
p
ti
o
n
s
in
Al
g
e
b
ra
,
”
Diss
e
rtatio
n
,
Un
iv
e
rsity
o
f
To
ro
n
to
,
2
0
1
1
.
[1
0
]
S
.
S
trac
h
o
ta,
E
.
Kn
u
t
h
,
a
n
d
M.
Blan
to
n
,
“
Cy
c
les
o
f
g
e
n
e
ra
li
z
in
g
a
c
ti
v
it
ies
in
th
e
c
las
sro
o
m
,
”
In
T
e
a
c
h
in
g
a
n
d
L
e
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rn
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g
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lg
e
b
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ic T
h
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5
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2
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r
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s
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ter
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g
,
2
0
1
8
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p
p
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5
1
-
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7
8
.
[1
1
]
N.
He
rsc
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v
ics
a
n
d
L.
Li
n
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h
e
v
s
k
i,
“
A
c
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it
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v
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g
a
p
b
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twe
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m
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e
b
ra
,
”
Ed
u
c
a
ti
o
n
a
l
S
t
u
d
ies
in
M
a
t
h
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ma
ti
c
s
,
v
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l.
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7
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n
o
.
1
,
p
p
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9
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0
7
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0
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2
8
4
5
2
8
.
[1
2
]
P
.
S
in
g
h
,
C
.
T
.
Ha
n
,
N
.
A
.
Na
sir,
M
.
A
.
Ra
m
ly
,
a
n
d
T
.
S.
Ho
o
n
,
“
F
a
c
to
rs
Co
n
tri
b
u
ti
n
g
t
o
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tu
d
e
n
ts’
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o
o
r
P
e
rfo
rm
a
n
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e
in
a
M
a
th
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m
a
ti
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s
P
re
p
a
ra
to
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P
ro
g
ra
m
,
”
7
t
h
In
ter
n
a
ti
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n
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l
C
o
n
f
e
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n
c
e
o
n
Un
ive
rs
it
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L
e
a
rn
i
n
g
a
n
d
T
e
a
c
h
in
g
(In
CULT
2
0
1
4
)
Pro
c
e
e
d
in
g
s
,
2
0
1
6
,
p
p
.
3
4
9
-
3
6
0
.
[1
3
]
B
.
Do
u
g
h
e
rty
,
D
.
P
.
Bry
a
n
t,
B
.
R
.
Bry
a
n
t,
R
.
L
.
Da
rro
u
g
h
,
a
n
d
K
.
H.
P
fa
n
n
e
n
stiel
,
“
De
v
e
lo
p
in
g
c
o
n
c
e
p
ts
a
n
d
g
e
n
e
ra
li
z
a
ti
o
n
s
to
b
u
i
ld
a
lg
e
b
ra
ic
th
in
k
in
g
:
Th
e
re
v
e
rsib
i
li
ty
,
flex
i
b
il
i
t
y
,
a
n
d
g
e
n
e
ra
li
z
a
ti
o
n
a
p
p
ro
a
c
h
,
”
In
ter
v
e
n
ti
o
n
in
S
c
h
o
o
l
a
n
d
Cli
n
ic
,
v
o
l.
5
0
,
n
o
.
5
,
p
p
.
2
7
3
-
2
8
1,
2
0
1
5
.
[1
4
]
G.
Eg
o
d
a
wa
tt
e
,
“
S
e
c
o
n
d
a
ry
sc
h
o
o
l
stu
d
e
n
ts’
m
isc
o
n
c
e
p
ti
o
n
s
i
n
a
l
g
e
b
ra
,”
Un
p
u
b
li
s
h
e
d
P
h
.
D.
T
h
e
sis
,
Un
iv
e
rsity
o
f
To
ro
n
to
,
Ca
n
a
d
a
,
2
0
1
1
.
[1
5
]
M
.
Blan
t
o
n
,
A
.
S
tep
h
e
n
s,
E
.
Kn
u
t
h
,
A
.
M
.
G
a
rd
in
e
r,
I
.
Isle
r,
a
n
d
J
.
S.
Kim
,
“
Th
e
d
e
v
e
l
o
p
m
e
n
t
o
f
c
h
il
d
re
n
'
s
a
lg
e
b
ra
ic
th
in
k
in
g
:
Th
e
imp
a
c
t
o
f
a
c
o
m
p
re
h
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n
siv
e
e
a
rly
a
lg
e
b
ra
i
n
terv
e
n
ti
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n
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n
th
ir
d
g
ra
d
e
,
”
J
o
u
rn
a
l
f
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Res
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rc
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M
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s E
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l.
4
6
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1,
p
p
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-
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1
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0
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.
[1
6
]
J
.
D
.
Ve
rm
u
n
t,
M
.
Vri
k
k
i
,
N
.
v
a
n
Ha
lem
,
P
.
Warwic
k
,
a
n
d
N.
M
e
rc
e
r
,
“
Th
e
imp
a
c
t
o
f
Les
so
n
S
tu
d
y
p
ro
fe
ss
io
n
a
l
d
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v
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lo
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m
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t
o
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t
h
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q
u
a
li
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f
tea
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lea
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,
”
T
e
a
c
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a
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T
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u
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ti
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l.
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[1
7
]
L.
S
.
Lo
m
ib
a
o
,
“
E
n
h
a
n
c
i
n
g
m
a
th
e
m
a
ti
c
s
tea
c
h
e
r
s’
q
u
a
li
ty
t
h
ro
u
g
h
Les
so
n
S
t
u
d
y
,
”
S
p
ri
n
g
e
rPl
u
s
,
v
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l.
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,
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p
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1
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.
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1305
[1
8
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L
.
E.
El
ip
a
n
e
,
“
T
o
wa
rd
s
t
h
e
e
m
b
o
d
ime
n
t
o
f
c
o
m
p
e
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y
sta
n
d
a
rd
s:
In
c
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p
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g
t
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lem
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ts
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f
Les
so
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d
y
in
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e
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re
-
se
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a
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P
h
il
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p
p
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e
s,”
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h
e
Asia
-
P
a
c
if
ic
Ed
u
c
a
t
io
n
Res
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a
rc
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1
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2
,
p
p
.
3
6
5
-
7
4
,
2
0
1
2
.
[1
9
]
L
.
E.
El
i
p
a
n
e
,
“
I
n
tro
d
u
c
i
n
g
Les
so
n
S
tu
d
y
a
s
a
P
ro
fe
ss
io
n
a
l
De
v
e
lo
p
m
e
n
t
M
o
d
e
l
i
n
th
e
Isla
n
d
s
o
f
t
h
e
P
h
i
li
p
p
in
e
s,”
Ad
v
a
n
c
e
d
S
c
ien
c
e
L
e
tt
e
rs
,
v
o
l.
2
3
,
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o
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2
,
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p
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1
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1
1
6
6
/as
l.
2
0
1
7
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7
5
1
4
.
[2
0
]
L.
El
i
p
a
n
e
,
L.
Na
c
in
o
,
R.
P
e
re
d
a
,
P.
Re
p
e
ru
g
a
,
a
n
d
M
.
To
r
io
,
“
De
v
e
lo
p
in
g
De
e
p
M
a
th
e
m
a
ti
c
s
Tea
c
h
in
g
Disc
o
u
rse
Th
ro
u
g
h
Re
se
a
rc
h
Les
so
n
s
,”
Pro
c
e
e
d
in
g
s
o
f
th
e
8
th
In
ter
n
a
ti
o
n
a
l
C
o
n
fer
e
n
c
e
o
n
E
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c
a
ti
o
n
R
e
se
a
rc
h
,
2
0
1
3
,
p
p
.
2
8
6
-
292
.
[2
1
]
C.
Lew
is,
R.
P
e
rr
y
,
J.
H
u
rd
,
“
A d
e
e
p
e
r
lo
o
k
a
t
les
so
n
stu
d
y
”
E
d
u
c
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ti
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n
a
l
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a
d
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rs
h
i
p
,
v
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l.
61
,
n
o
.
5
,
p
.
18
,
2
0
0
4
.
[2
2
]
H.
Jo
ffe
,
T
h
e
ma
ti
c
a
n
a
lys
is,
Qu
a
li
ta
ti
v
e
re
se
a
rc
h
me
th
o
d
s
in
m
e
n
ta
l
h
e
a
lt
h
a
n
d
p
sy
c
h
o
th
e
ra
p
y
.
Jo
h
n
Wi
ley
&
S
o
n
s,
Lt
d
2
0
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2
,
d
o
i:
1
0
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7
8
1
1
1
9
9
7
3
2
4
9
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c
h
1
5
.
[2
3
]
M
.
L.
F
e
rn
a
n
d
e
z
,
“
In
v
e
stig
a
ti
n
g
h
o
w
a
n
d
wh
a
t
p
ro
s
p
e
c
ti
v
e
tea
c
h
e
rs
lea
rn
th
r
o
u
g
h
m
icro
tea
c
h
in
g
les
so
n
stu
d
y
,”
T
e
a
c
h
in
g
a
n
d
T
e
a
c
h
e
r E
d
u
c
a
ti
o
n
,
v
o
l
.
2
6
,
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o
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2
,
p
p
.
3
5
1
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,
2
0
1
0
,
d
o
i:
1
0
.
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0
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6
/j
.
tate
.
2
0
0
9
.
0
9
.
0
1
2
.
[2
4
]
S
.
B.
G
u
ti
e
re
z
,
“
Tea
c
h
e
rs’
re
fle
c
ti
v
e
p
ra
c
ti
c
e
in
les
so
n
stu
d
y
:
A
to
o
l
fo
r
i
m
p
r
o
v
i
n
g
i
n
stru
c
ti
o
n
a
l
p
r
a
c
ti
c
e
,
”
Al
b
e
rta
J
o
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[2
9
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P
.
An
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d
J.
S
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rs
,
“
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s:
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n
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