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Me
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C
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Nu
s
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Dep
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Facu
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Na
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s
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Un
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Neg
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No
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,
Su
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L
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Dis
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Ma
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C
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to
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id
1.
I
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UCT
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O
N
Me
taco
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ess
en
tial
in
s
u
p
p
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s
tu
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ts
'
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p
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s
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lv
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ab
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o
v
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all
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iev
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n
t.
Stu
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co
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ten
tly
s
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wn
th
at
s
tu
d
en
ts
with
ex
ce
llen
t
m
etac
o
g
n
itio
n
ten
d
ed
t
o
u
s
e
ef
f
ec
tiv
e
p
r
o
b
lem
-
s
o
lv
in
g
s
tr
ateg
ies
[
1
]
–
[
3
]
.
T
h
e
a
war
en
ess
o
f
th
is
s
k
ill
s
ig
n
i
f
ican
tly
en
h
an
ce
d
in
f
o
r
m
atio
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p
r
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s
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with
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m
m
em
o
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y
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a
n
d
also
f
ac
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in
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o
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m
atio
n
,
p
e
r
ce
p
tio
n
,
an
d
m
em
o
r
y
[
4
]
–
[
6
]
.
A
m
eta
-
an
aly
s
is
o
n
m
etac
o
g
n
itio
n
in
d
icate
d
th
at
wh
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awa
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en
ess
o
cc
u
r
r
e
d
in
a
n
in
d
iv
id
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al,
it
co
u
l
d
r
em
ain
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elativ
ely
u
n
ch
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ed
th
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o
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t
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ev
el
o
p
m
en
tal
s
tag
es
an
d
in
to
el
d
er
ly
y
ea
r
s
[
7
]
.
T
h
er
ef
o
r
e,
t
h
is
co
g
n
itiv
e
co
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s
tr
u
ctio
n
was stro
n
g
ly
c
o
r
r
elate
d
t
o
in
d
iv
i
d
u
al
in
tellig
en
ce
[
6
]
.
Sev
er
al
s
tu
d
ies
h
av
e
c
o
n
f
ir
m
ed
th
e
cr
u
cial
r
o
le
o
f
m
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o
g
n
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n
i
n
p
r
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b
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-
s
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l
v
in
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s
k
ills
an
d
g
en
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al
in
tellig
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[
7
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.
Fo
r
in
s
tan
ce
,
B
er
ar
d
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-
C
o
letta
et
a
l.
[
8
]
f
o
u
n
d
t
h
at
p
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p
le
with
h
i
g
h
er
m
etac
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ex
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ited
s
ig
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if
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tly
b
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p
r
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b
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-
s
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lv
in
g
s
tr
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in
tr
ain
in
g
an
d
task
tr
an
s
f
er
co
m
p
ar
ed
to
th
o
s
e
with
lo
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ab
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R
ick
ey
an
d
Stacey
[
9
]
also
s
u
g
g
ested
th
at
th
e
en
h
a
n
ce
m
en
t
o
f
m
eta
co
g
n
itio
n
im
p
r
o
v
ed
p
r
o
b
lem
-
s
o
lv
in
g
ab
ilit
ies.
C
ik
r
ici
an
d
Od
ac
i
[
1
0
]
d
escr
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b
ed
m
etac
o
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itio
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as
a
cr
u
cial
co
m
p
o
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e
n
t
f
o
r
ad
v
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ce
d
m
en
tal
p
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f
o
r
m
an
ce
an
d
ef
f
ec
tiv
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lear
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in
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p
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s
s
.
Me
taco
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ca
n
b
e
ass
es
s
ed
in
s
tu
d
e
n
ts
d
u
r
in
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p
r
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s
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d
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s
.
Sch
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d
Den
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n
[
1
1
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d
ev
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o
p
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m
et
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o
g
n
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awa
r
e
n
ess
in
v
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(
MA
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I
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J
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&
R
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d
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c
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Vo
l
.
14
,
No
.
1
,
Feb
r
u
a
r
y
20
25
:
229
-
239
230
co
m
p
r
is
ed
m
etac
o
g
n
itiv
e
co
m
p
o
n
e
n
ts
,
n
am
ely
d
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k
n
o
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[
1
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d
e
n
ts
a
t
t
e
n
t
i
o
n
[
1
4
]
.
T
h
i
s
s
i
t
u
at
i
o
n
c
a
n
e
it
h
e
r
b
e
i
m
a
g
i
n
ar
y
o
r
a
u
t
h
e
n
t
i
c
,
a
i
d
i
n
g
s
t
u
d
e
n
t
s
t
o
r
e
c
a
l
l
t
h
e
e
x
i
s
t
i
n
g
k
n
o
w
l
e
d
g
e
a
c
q
u
i
r
e
d
t
h
r
o
u
g
h
e
x
p
e
r
i
e
n
c
e
,
s
u
c
h
a
s
i
n
f
o
r
m
a
l
p
r
o
b
l
e
m
-
s
o
l
v
i
n
g
p
r
o
c
e
d
u
r
e
s
.
I
t
c
a
n
a
l
s
o
f
o
s
t
e
r
a
m
e
a
n
i
n
g
f
u
l
l
ea
r
n
i
n
g
p
r
o
c
e
s
s
[
1
3
]
,
a
s
a
p
p
r
o
p
r
i
a
t
e
le
a
r
n
i
n
g
c
o
n
t
e
x
t
g
u
i
d
e
s
t
o
w
a
r
d
a
ct
i
v
e
t
h
i
n
k
i
n
g
p
r
o
c
e
s
s
es
[
1
5
]
.
T
h
e
u
s
e
o
f
c
o
n
tex
tu
al
m
ath
p
r
o
b
lem
is
ess
en
tial
f
o
r
e
n
ab
lin
g
s
tu
d
en
ts
to
d
e
v
elo
p
m
o
r
e
co
m
p
lex
th
in
k
in
g
p
atter
n
s
,
as th
ey
en
g
a
g
e
b
o
th
f
o
r
m
al
a
n
d
in
f
o
r
m
al
m
ath
em
atica
l k
n
o
wled
g
e.
Fu
r
t
h
er
m
o
r
e
,
b
y
s
o
lv
i
n
g
co
n
tex
tu
al
m
ath
em
atica
l
p
r
o
b
lem
,
s
tu
d
en
ts
a
r
e
e
n
co
u
r
a
g
ed
to
u
n
leash
th
eir
f
u
ll
p
s
y
c
h
o
lo
g
ical
p
o
ten
tial,
s
p
ec
if
ically
r
eg
ar
d
in
g
co
g
n
itiv
e
p
r
o
ce
s
s
es
[
1
]
.
T
h
e
o
b
jectiv
e
is
to
m
o
tiv
ate
s
tu
d
en
ts
to
u
n
d
er
s
tan
d
th
e
s
u
b
ject
m
atter
[
1
6
]
,
[
1
7
]
,
as
th
is
en
h
an
ce
s
th
eir
m
etac
o
g
n
itio
n
in
s
o
lv
in
g
co
n
tex
tu
al
p
r
o
b
lem
[
1
8
]
,
[
1
9
]
.
Pr
o
b
lem
-
s
o
lv
in
g
is
a
co
m
p
lex
p
r
o
ce
s
s
th
at
in
clu
d
es
s
ev
er
al
co
g
n
itiv
e
o
p
er
atio
n
s
,
s
u
ch
as
g
ath
e
r
in
g
an
d
s
elec
tin
g
in
f
o
r
m
atio
n
,
h
eu
r
is
tic,
an
d
m
etac
o
g
n
itiv
e
s
tr
ateg
ies
[
2
0
]
.
Me
taco
g
n
itio
n
is
an
im
p
o
r
tan
t
s
tr
ateg
y
ass
o
ciate
d
with
ac
ad
em
ic
ac
h
iev
em
e
n
t
an
d
p
r
o
b
lem
-
s
o
l
v
in
g
a
b
ilit
y
s
in
ce
it
co
m
p
r
is
es
s
elf
-
ex
am
in
atio
n
,
co
g
n
itiv
e
s
tr
ateg
ies,
awa
r
en
ess
,
an
d
th
o
u
g
h
tf
u
l
p
lan
n
i
n
g
[
2
1
]
.
Me
t
ac
o
g
n
itiv
e
-
b
ased
c
o
n
tex
tu
al
l
ea
r
n
in
g
ef
f
ec
tiv
ely
en
h
an
ce
s
p
r
o
b
lem
-
s
o
lv
in
g
an
d
m
ath
em
atica
l
c
o
m
m
u
n
icatio
n
s
k
ills
,
m
ak
in
g
it
a
r
ec
o
m
m
en
d
ed
m
eth
o
d
f
o
r
teac
h
in
g
m
ath
em
atica
l
[
1
8
]
.
A
n
e
m
p
i
r
i
c
al
s
t
u
d
y
c
o
n
d
u
c
t
e
d
a
t
St
a
t
e
S
e
n
i
o
r
H
i
g
h
S
c
h
o
o
l
3
J
a
y
a
p
u
r
a
,
P
a
p
u
a
,
I
n
d
o
n
e
s
i
a
,
s
u
g
g
e
s
te
d
t
h
a
t
s
t
u
d
e
n
t
s
h
a
d
p
o
o
r
m
a
t
h
e
m
a
t
i
c
a
l
p
r
o
b
l
e
m
-
s
o
l
v
i
n
g
s
k
i
ll
s
.
Fu
r
t
h
e
r
m
o
r
e
,
i
n
t
e
r
v
i
e
ws
wi
t
h
t
ea
c
h
e
r
s
s
h
o
w
e
d
t
h
at
s
t
u
d
e
n
ts
s
ti
l
l
s
t
r
u
g
g
l
e
d
w
i
t
h
d
ai
l
y
e
x
e
r
c
is
e
s
d
u
e
t
o
t
h
e
c
o
m
p
le
x
i
t
y
o
f
u
n
d
e
r
s
t
a
n
d
i
n
g
t
h
e
n
a
r
r
a
t
i
v
e
s
o
f
q
u
es
t
i
o
n
s
.
T
h
i
s
r
e
s
u
lt
w
a
s
c
o
n
s
i
s
t
e
n
t
w
i
t
h
T
j
a
l
l
a
a
n
d
P
u
t
r
i
y
a
n
i
[
2
2
]
,
s
t
a
t
in
g
t
h
a
t
s
t
u
d
e
n
t
s
g
e
n
e
r
a
l
l
y
h
a
d
p
o
o
r
m
e
t
a
c
o
g
n
i
t
i
o
n
a
n
d
f
r
e
q
u
e
n
t
l
y
s
t
r
u
g
g
l
e
d
wi
t
h
a
ct
i
v
i
ti
e
s
r
e
q
u
i
r
i
n
g
m
eta
c
o
g
n
i
t
i
v
e
aw
a
r
e
n
es
s
,
s
p
e
ci
f
i
c
a
l
l
y
,
s
o
l
v
i
n
g
o
f
m
a
t
h
e
m
a
t
i
ca
l
p
r
o
b
l
e
m
.
T
h
e
r
e
f
o
r
e
,
t
h
e
c
u
r
r
e
n
t
s
t
u
d
y
a
i
m
e
d
t
o
d
e
v
e
l
o
p
a
n
a
l
t
e
r
n
a
t
i
v
e
m
e
t
h
o
d
t
o
h
e
l
p
s
t
u
d
e
n
t
s
s
o
l
v
e
m
at
h
e
m
a
t
ic
a
l
p
r
o
b
l
e
m
,
u
s
i
n
g
c
o
n
t
e
x
t
u
al
m
a
t
h
q
u
e
s
ti
o
n
s
.
T
h
e
u
s
e
o
f
c
o
n
t
e
x
t
u
a
l
q
u
e
s
t
i
o
n
s
c
o
u
l
d
e
n
h
a
n
c
e
t
h
e
m
o
t
i
v
a
t
i
o
n
t
o
s
o
l
v
e
p
r
o
b
l
em
a
n
d
c
o
m
p
r
e
h
e
n
d
l
e
a
r
n
i
n
g
m
a
t
e
r
i
a
ls
.
A
n
o
t
h
e
r
o
b
j
e
c
t
i
v
e
wa
s
t
o
i
m
p
r
o
v
e
s
t
u
d
e
n
t
s
'
m
e
t
a
c
o
g
n
i
t
i
o
n
a
n
d
e
n
v
i
r
o
n
m
e
n
t
a
l
a
w
a
r
e
n
ess
.
T
h
i
s
w
a
s
i
n
li
n
e
w
i
t
h
M
u
m
u
a
n
d
T
a
n
u
j
a
y
a
[
2
3
]
,
s
h
o
w
i
n
g
t
h
a
t
t
h
e
u
s
e
o
f
e
n
v
i
r
o
n
m
e
n
t
a
l
m
a
t
h
p
r
o
b
l
e
m
r
e
l
e
v
a
n
t
t
o
t
h
e
c
o
n
t
ex
t
o
f
s
t
u
d
e
n
t
s
c
o
u
l
d
i
m
p
r
o
v
e
m
e
t
a
c
o
g
n
i
t
i
o
n
a
n
d
a
w
a
r
e
n
e
s
s
o
f
e
n
v
i
r
o
n
m
e
n
t
a
l
p
r
o
b
l
e
m
.
S
e
v
e
r
a
l
s
t
u
d
i
es
h
a
v
e
d
e
s
c
r
i
b
e
d
t
h
e
i
m
p
o
r
t
a
n
c
e
o
f
m
e
t
a
c
o
g
n
iti
v
e
a
w
a
r
e
n
es
s
i
n
l
e
a
r
n
i
n
g
m
a
th
e
m
a
t
i
c
a
l
,
s
p
e
c
i
f
i
ca
l
l
y
i
n
m
a
t
h
e
m
a
ti
c
a
l
p
r
o
v
i
n
g
[
2
4
]
,
i
n
f
o
r
m
a
l
d
e
d
u
c
t
i
v
e
t
h
i
n
k
i
n
g
i
n
g
e
o
m
e
t
r
i
c
e
x
e
r
c
i
s
es
[
2
5
]
,
[
2
6
]
,
l
i
t
e
r
a
c
y
[
1
8
]
,
[
2
7
]
,
[
2
8
]
,
p
r
o
b
l
e
m
-
s
o
l
v
i
n
g
[
2
9
]
–
[
3
2
]
,
p
o
s
i
t
i
o
n
i
n
g
a
n
d
e
m
o
t
i
o
n
i
n
m
a
t
h
e
m
a
ti
c
a
l
ac
t
i
v
i
t
i
es
[
1
0
]
,
[
3
3
]
,
a
n
d
e
n
h
a
n
c
i
n
g
m
a
t
h
e
m
a
t
i
ca
l
s
k
i
ll
s
[
3
4
]
,
[
3
5
]
.
W
h
i
l
e
t
h
es
e
i
n
v
es
t
i
g
a
t
i
o
n
s
s
o
l
e
l
y
d
es
c
r
i
b
e
d
m
et
a
c
o
g
n
i
t
i
v
e
p
r
o
c
e
s
s
es
o
f
s
t
u
d
e
n
ts
a
n
d
t
h
e
i
r
r
el
a
ti
o
n
s
h
ip
s
w
it
h
m
a
t
h
e
m
at
i
c
a
l
p
r
o
b
l
em
-
s
o
l
v
i
n
g
a
n
d
t
h
i
n
k
i
n
g
s
k
i
l
ls
,
t
h
e
c
u
r
r
e
n
t
s
t
u
d
y
f
o
c
u
s
e
d
o
n
m
e
t
a
c
o
g
n
i
t
i
v
e
a
c
t
i
v
i
t
i
es
i
n
s
o
l
v
i
n
g
c
o
n
t
e
x
t
u
a
l
m
a
t
h
e
m
a
t
i
c
al
p
r
o
b
l
e
m
.
T
h
i
s
a
r
e
a
o
f
s
t
u
d
y
w
a
s
r
e
l
e
v
a
n
t
a
s
i
t
r
e
p
r
e
s
e
n
t
e
d
t
h
e
c
a
p
a
c
i
t
y
o
f
s
t
u
d
e
n
t
s
t
o
r
e
g
u
l
a
t
e
i
n
f
o
r
m
a
t
i
o
n
p
r
o
c
e
s
s
i
n
g
i
n
t
h
e
i
r
l
o
n
g
-
t
e
r
m
m
e
m
o
r
y
.
I
n
a
d
d
i
t
i
o
n
,
t
h
is
s
k
il
l
e
x
h
i
b
it
s
r
ela
t
i
v
e
c
o
n
s
i
s
t
e
n
c
y
t
h
r
o
u
g
h
o
u
t
t
h
e
d
e
v
e
l
o
p
m
e
n
t
a
l
t
r
aj
e
c
t
o
r
y
o
f
a
n
i
n
d
i
v
i
d
u
a
l
i
n
t
o
a
d
v
a
n
c
e
d
a
g
e
.
T
h
i
s
s
t
u
d
y
a
n
a
l
y
z
e
d
a
n
d
d
e
s
c
r
i
b
e
d
m
e
t
a
c
o
g
n
it
i
v
e
a
c
t
i
v
i
t
i
es
o
f
h
i
g
h
s
c
h
o
o
l
s
t
u
d
e
n
ts
i
n
s
o
l
v
i
n
g
c
o
n
t
e
x
t
u
a
l
m
a
t
h
e
m
at
i
c
a
l
p
r
o
b
l
e
m
.
I
n
a
d
d
i
t
i
o
n
,
t
h
e
i
n
d
i
c
a
to
r
p
r
o
p
o
s
e
d
b
y
W
i
l
s
o
n
a
n
d
C
l
a
r
k
e
[
1
2
]
,
w
h
i
c
h
i
n
t
e
g
r
a
t
e
d
t
h
e
P
o
l
y
a
p
r
o
b
l
e
m
-
s
o
l
v
i
n
g
s
t
a
g
es
w
as
a
d
o
p
t
e
d
t
o
ev
a
l
u
a
t
e
s
t
u
d
e
n
t
s
'
m
e
t
a
c
o
g
n
i
ti
o
n
.
2.
M
E
T
H
O
D
Descr
ip
tiv
e
an
d
q
u
alitativ
e
m
eth
o
d
s
wer
e
s
p
ec
if
ically
u
s
ed
in
th
is
s
tu
d
y
to
ef
f
ec
tiv
el
y
d
escr
ib
e
s
tu
d
en
ts
’
m
etac
o
g
n
itiv
e
ac
tiv
it
ies in
s
o
lv
in
g
co
n
tex
tu
al
m
ath
em
atica
l p
r
o
b
lem
.
T
h
ese
m
eth
o
d
s
wer
e
also
u
s
ed
d
u
e
to
t
h
e
n
at
u
r
e
o
f
th
e
co
ll
ec
ted
d
ata,
wh
ic
h
p
r
im
a
r
ily
co
n
s
is
ted
o
f
tex
tu
al
in
f
o
r
m
at
io
n
in
t
h
e
f
o
r
m
o
f
s
en
ten
ce
s
[
3
6
]
.
A
s
im
ilar
m
e
th
o
d
h
ad
b
ee
n
u
s
ed
in
s
o
m
e
s
tu
d
ies
o
n
m
etac
o
g
n
itio
n
[
1
4
]
,
[
3
7
]
,
[
3
8
]
.
T
h
e
p
ar
ticip
an
ts
co
m
p
r
is
ed
elev
en
th
g
r
ad
er
s
f
r
o
m
State
Sen
io
r
Hig
h
Sch
o
o
l
3
J
ay
ap
u
r
a,
I
n
d
o
n
esia.
C
o
n
tex
tu
al
m
ath
em
atica
l
p
r
o
b
lem
-
s
o
lv
in
g
test
was
ad
m
in
is
ter
ed
to
2
5
s
tu
d
en
ts
in
th
e
f
ir
s
t
s
tag
e
o
f
p
ar
ticip
an
t
s
elec
tio
n
,
wh
ile
th
o
s
e
wh
o
s
u
cc
ess
f
u
lly
co
m
p
leted
t
h
e
test
an
d
p
r
o
v
id
ed
th
in
k
-
alo
u
d
r
esp
o
n
s
es
wer
e
ch
o
s
en
i
n
th
e
s
ec
o
n
d
s
tag
e.
T
h
e
th
r
ee
s
tu
d
en
ts
wh
o
f
u
lf
illed
th
ese
cr
iter
ia
wer
e
id
en
tifie
d
as
PK,
VP,
an
d
E
DM
.
Oth
er
s
tu
d
ies with
s
im
ilar
o
b
jectiv
e
an
d
s
am
p
le
s
ize
wer
e
[
3
9
]
–
[
4
3
]
.
Data
co
llectio
n
was
ca
r
r
ied
o
u
t
u
s
in
g
test
in
s
tr
u
m
en
ts
an
d
th
in
k
-
alo
u
d
m
eth
o
d
s
,
as
well
as
in
ter
v
iew
g
u
id
elin
es,
wh
ich
wer
e
v
alid
a
ted
b
y
m
ath
em
atica
l
e
x
p
er
t
at
th
e
State
Un
iv
e
r
s
ity
o
f
Ma
la
n
g
.
T
h
e
v
alid
atio
n
r
esu
lts
s
h
o
wed
th
at
th
e
in
s
tr
u
m
en
t
was
s
u
itab
le
f
o
r
ac
h
iev
i
n
g
th
e
s
tu
d
y
o
b
jectiv
es.
I
n
ter
v
i
ews
wer
e
co
n
d
u
cted
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
S
tu
d
en
ts
meta
co
g
n
itive
a
ctivities in
co
n
textu
a
l m
a
th
em
a
tica
l
p
r
o
b
lem
s
o
lvin
g
(
Yu
s
tin
u
s
Wa
n
g
g
u
w
a
y
)
231
to
clar
if
y
th
e
r
esu
lts
o
f
th
e
wr
itten
test
an
d
ca
p
tu
r
e
m
etac
o
g
n
itiv
e
th
o
u
g
h
ts
o
r
p
r
o
ce
s
s
es
o
f
s
tu
d
en
ts
.
T
h
e
in
ter
v
iews
wer
e
also
ca
r
r
ied
o
u
t
to
c
o
n
f
ir
m
th
e
r
esu
lts
o
f
th
e
th
in
k
-
alo
u
d
p
r
o
ce
s
s
,
wh
ich
h
ad
b
ee
n
v
id
e
o
r
ec
o
r
d
e
d
.
T
h
is
m
eth
o
d
was
ad
o
p
ted
b
ec
a
u
s
e
n
o
t
all
m
etac
o
g
n
itiv
e
in
d
icato
r
s
wer
e
ev
id
en
t
in
th
e
wr
itten
r
esp
o
n
s
es,
an
d
s
o
m
e
th
in
k
i
n
g
p
r
o
ce
s
s
es
co
u
ld
n
o
t
b
e
ad
eq
u
ately
tr
an
s
cr
ib
e
d
in
to
an
an
s
wer
s
h
ee
t.
T
h
e
co
n
tex
t o
f
m
ath
em
atica
l p
r
o
b
l
em
is
s
h
o
wn
in
Fig
u
r
e
1
.
Fig
u
r
e
1
.
C
o
n
tex
t
u
al
m
ath
em
a
tical
ex
er
cise
T
h
e
d
ata
an
aly
s
is
ad
h
e
r
ed
t
o
th
e
m
o
d
el
o
u
tlin
e
d
b
y
Miles
et
a
l.
[
4
4
]
,
an
d
was
co
n
d
u
cte
d
in
ter
ac
tiv
ely
an
d
co
n
tin
u
o
u
s
ly
u
n
til
d
ata
s
atu
r
atio
n
was
ac
h
iev
ed
.
T
h
e
an
aly
s
is
was
co
m
p
leted
th
r
o
u
g
h
th
r
ee
s
tag
es,
n
am
ely
d
ata
r
e
d
u
ctio
n
,
s
h
o
w,
an
d
v
er
if
icatio
n
o
r
c
o
n
clu
s
io
n
d
r
awin
g
.
A
tr
ia
n
g
u
latio
n
m
eth
o
d
was
u
s
ed
to
en
s
u
r
e
d
ata
cr
ed
ib
il
ity
an
d
v
alid
ity
ass
ess
m
en
t.
So
u
r
ce
tr
ia
n
g
u
latio
n
was
s
p
ec
if
ically
ad
o
p
ted
,
wh
er
ein
th
e
r
eliab
ilit
y
o
f
in
f
o
r
m
atio
n
o
b
tain
e
d
f
r
o
m
o
b
s
er
v
a
tio
n
s
an
d
in
ter
v
iews wa
s
co
m
p
ar
ed
an
d
v
e
r
if
ied
.
T
h
e
an
aly
s
is
co
m
m
en
ce
d
wit
h
th
e
d
is
tr
ib
u
tio
n
o
f
test
s
to
th
e
p
ar
ticip
an
ts
,
wh
o
wer
e
in
s
tr
u
cted
to
en
g
ag
e
in
th
in
k
-
alo
u
d
p
r
o
ce
s
s
.
T
h
e
v
id
eo
r
ec
o
r
d
i
n
g
s
o
f
p
ar
t
icip
an
t
m
etac
o
g
n
itio
n
in
s
o
lv
i
n
g
co
n
tex
t
u
al
m
ath
p
r
o
b
lem
,
wer
e
s
u
b
s
eq
u
e
n
tly
an
aly
ze
d
.
T
h
e
th
in
k
-
alo
u
d
r
e
s
u
lts
an
d
in
ter
v
iews
f
r
o
m
e
a
ch
p
ar
ticip
an
t
wer
e
an
aly
ze
d
b
ased
o
n
th
e
m
o
d
i
f
ied
m
etac
o
g
n
itiv
e
in
d
icato
r
s
p
r
o
p
o
s
ed
b
y
W
ils
o
n
an
d
C
lar
k
e
[
1
2
]
.
T
ab
le
1
p
r
esen
ts
th
e
d
escr
ip
tio
n
c
o
d
e
f
o
r
m
etac
o
g
n
itiv
e
ac
tiv
ities
in
s
o
lv
in
g
c
o
n
tex
tu
al
m
at
h
em
atica
l p
r
o
b
lem
.
T
ab
le
1
.
Descr
ip
tio
n
c
o
d
e
f
o
r
s
tu
d
en
ts
’
m
etac
o
g
n
itiv
e
ac
tiv
it
ies in
s
o
lv
in
g
co
n
te
x
tu
al
m
ath
em
atica
l p
r
o
b
lem
M
e
t
a
c
o
g
n
i
t
i
v
e
a
c
t
i
v
i
t
i
e
s
W
i
l
s
o
n
a
n
d
C
l
a
r
k
e
[
1
2
]
I
n
d
i
c
a
t
o
r
s
C
o
d
e
M
e
t
a
c
o
g
n
i
t
i
v
e
a
w
a
r
e
n
e
ss
(
A
M
)
A
c
t
i
v
i
t
i
e
s
r
e
l
a
t
e
d
t
o
i
n
d
i
v
i
d
u
a
l
a
w
a
r
e
n
e
ss
d
u
r
i
n
g
p
r
o
b
l
e
m
-
so
l
v
i
n
g
p
r
o
c
e
ss
u
si
n
g
sp
e
c
i
f
i
c
c
o
n
t
e
n
t
k
n
o
w
l
e
d
g
e
a
n
d
t
h
e
k
n
o
w
l
e
d
g
e
a
b
o
u
t
p
e
r
s
o
n
a
l
l
e
a
r
n
i
n
g
o
r
p
r
o
b
l
e
m
-
so
l
v
i
n
g
s
t
r
a
t
e
g
i
e
s.
T
h
i
s
i
n
c
l
u
d
e
s
w
h
a
t
n
e
e
d
s
t
o
b
e
d
o
n
e
,
w
h
a
t
h
a
s
b
e
e
n
d
o
n
e
,
a
n
d
w
h
a
t
sh
o
u
l
d
b
e
d
o
n
e
i
n
s
o
l
v
i
n
g
p
r
o
b
l
e
m.
1.
Th
i
n
k
i
n
g
a
b
o
u
t
k
n
o
w
l
e
d
g
e
r
e
l
a
t
e
d
t
o
t
h
e
p
r
o
v
i
d
e
d
p
r
o
b
l
e
m
2.
Th
i
n
k
i
n
g
a
b
o
u
t
p
a
st
e
x
p
e
r
i
e
n
c
e
s
si
m
i
l
a
r
t
o
t
h
e
p
r
o
v
i
d
e
d
p
r
o
b
l
e
m
3.
Th
i
n
k
i
n
g
a
b
o
u
t
t
h
e
st
r
a
t
e
g
i
e
s
t
o
s
o
l
v
e
p
r
o
b
l
e
m
4.
Th
i
n
k
i
n
g
a
b
o
u
t
t
h
e
p
o
ss
i
b
l
e
a
l
t
e
r
n
a
t
i
v
e
t
o
so
l
v
e
p
r
o
b
l
e
m
A
M
1
A
M
2
A
M
3
A
M
4
M
e
t
a
c
o
g
n
i
t
i
v
e
e
v
a
l
u
a
t
i
o
n
(
EM
)
A
c
t
i
v
i
t
i
e
s re
l
a
t
e
d
t
o
i
n
d
i
v
i
d
u
a
l
j
u
d
g
m
e
n
t
s
a
b
o
u
t
t
h
e
p
r
o
c
e
ss
e
s,
c
a
p
a
c
i
t
i
e
s
,
a
n
d
l
i
m
i
t
a
t
i
o
n
s
o
f
t
h
i
n
k
i
n
g
w
h
e
n
s
o
l
v
i
n
g
p
r
o
b
l
e
m.
F
o
r
e
x
a
mp
l
e
,
j
u
d
g
me
n
t
s
a
b
o
u
t
t
h
e
e
f
f
e
c
t
i
v
e
n
e
ss
o
f
t
h
i
n
k
i
n
g
o
r
s
t
r
a
t
e
g
y
c
a
n
b
e
f
o
r
mu
l
a
t
e
d
.
1.
Th
i
n
k
i
n
g
a
b
o
u
t
t
h
e
p
o
ssi
b
l
e
st
e
p
s
t
o
so
l
v
e
p
r
o
b
l
e
m
2.
Th
i
n
k
i
n
g
a
n
d
e
x
a
mi
n
i
n
g
t
h
e
st
e
p
s
o
f
so
l
v
i
n
g
m
a
t
h
e
m
a
t
i
c
a
l
p
r
o
b
l
e
m
3.
Th
i
n
k
i
n
g
o
f
t
h
e
a
p
p
r
o
p
r
i
a
t
e
p
r
o
b
l
e
m
-
so
l
v
i
n
g
s
t
r
a
t
e
g
y
4.
Th
i
n
k
i
n
g
o
f
t
h
e
su
c
c
e
ssf
u
l
p
o
ss
i
b
i
l
i
t
y
t
o
so
l
v
e
p
r
o
b
l
e
m
EM
1
EM
2
EM
3
EM
4
M
e
t
a
c
o
g
n
i
t
i
v
e
r
e
g
u
l
a
t
i
o
n
(
R
M
)
O
c
c
u
r
s
w
h
e
n
met
a
c
o
g
n
i
t
i
o
n
is
u
se
d
i
n
d
i
r
e
c
t
i
n
g
k
n
o
w
l
e
d
g
e
a
n
d
t
h
o
u
g
h
t
s.
1.
F
o
r
mu
l
a
t
i
n
g
t
h
e
p
l
a
n
f
o
r
s
o
l
v
i
n
g
mat
h
e
m
a
t
i
c
a
l
p
r
o
b
l
e
m
2.
Th
i
n
k
i
n
g
o
f
a
d
o
p
t
i
n
g
a
d
i
f
f
e
r
e
n
t
mat
h
e
m
a
t
i
c
a
l
p
r
o
b
l
e
m
-
s
o
l
v
i
n
g
st
r
a
t
e
g
y
3.
Th
i
n
k
i
n
g
a
b
o
u
t
t
h
e
n
e
x
t
s
t
r
a
t
e
g
y
t
o
s
o
l
v
e
mat
h
e
m
a
t
i
c
a
l
p
r
o
b
l
e
m
4.
Th
i
n
k
i
n
g
o
f
a
d
o
p
t
i
n
g
d
i
f
f
e
r
e
n
t
s
t
r
a
t
e
g
i
e
s
t
o
so
l
v
e
m
a
t
h
e
m
a
t
i
c
a
l
p
r
o
b
l
e
m
R
M
1
R
M
2
R
M
3
R
M
4
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
3
.
1
.
Resul
t
s
T
h
e
d
escr
ip
tio
n
o
f
s
tu
d
e
n
ts
’
m
etac
o
g
n
itiv
e
p
r
o
ce
s
s
in
s
o
lv
in
g
co
n
tex
tu
al
m
ath
em
atica
l
p
r
o
b
lem
is
p
r
esen
ted
in
th
e
f
o
llo
win
g
s
ec
tio
n
.
T
h
r
ee
s
tu
d
e
n
ts
id
en
tifie
d
as
PK,
VP,
an
d
E
DM
wer
e
e
x
tr
ac
ted
to
d
escr
ib
e
th
e
s
tu
d
en
ts
’
m
etac
o
g
n
itiv
e
ac
tiv
ity
p
r
o
ce
s
s
.
T
h
e
d
ata
o
n
m
e
taco
g
n
itiv
e
ac
tiv
i
ties
wer
e
o
b
tain
ed
u
s
in
g
th
in
k
-
alo
u
d
m
eth
o
d
,
i
n
co
n
j
u
n
ctio
n
with
wr
itten
an
s
wer
s
an
d
in
ter
v
iew
test
r
esu
lts
.
3
.
1
.
1
.
M
et
a
co
g
nitiv
e
a
ct
iv
it
ie
s
o
f
t
he
f
irst
pa
rt
icipa
nt
(
P
K
)
T
h
e
r
esu
lts
o
f
th
e
th
in
k
-
alo
u
d
s
ess
io
n
an
d
wr
itten
test
s
o
n
co
n
tex
tu
al
m
ath
em
atica
l
p
r
o
b
lem
s
u
g
g
ested
th
at
PK
ex
h
ib
ited
m
etac
o
g
n
itiv
e
awa
r
e
n
ess
in
s
o
lv
in
g
p
r
o
b
lem
.
Me
taco
g
n
itiv
e
p
r
o
ce
s
s
in
clu
d
ed
Be
t
o
a
n
d
Bo
as
w
e
n
t
s
h
o
p
p
i
n
g
a
t
t
h
e
J
ay
a
p
u
r
a
M
al
l
,
a
n
d
w
er
e
i
n
t
er
est
ed
i
n
t
h
e
c
l
o
t
h
es
b
r
an
d
s
A
an
d
B
.
Be
t
o
b
o
u
g
h
t
t
w
o
b
r
a
n
d
A
cl
o
t
h
es
an
d
t
h
r
e
e
b
r
a
n
d
B
c
l
o
t
h
es
f
o
r
I
D
R
9
0
0
,
0
0
0
.
B
o
as
b
o
u
g
h
t
t
h
r
e
e
b
r
an
d
A
c
l
o
t
h
es
a
n
d
t
w
o
b
r
an
d
B
cl
o
t
h
es
fo
r
8
5
0
,0
0
0
.
a.
W
i
t
h
o
u
t
c
al
cu
l
a
t
i
n
g
t
h
e
a
c
t
u
al
p
r
i
ce
,
w
h
i
c
h
b
r
a
n
d
i
s
m
o
r
e
ex
p
e
n
si
v
e?
D
esc
r
i
b
e
y
o
u
r
reas
o
n
s.
b.
H
o
w
m
u
c
h
d
o
es
o
n
e
b
r
a
n
d
A
s
h
i
r
t
c
o
st?
H
o
w
d
o
y
o
u
c
al
cu
l
a
t
e
i
t
?
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
14
,
No
.
1
,
Feb
r
u
a
r
y
20
25
:
229
-
239
232
th
e
id
en
tific
atio
n
o
f
in
f
o
r
m
ati
o
n
f
r
o
m
th
e
p
r
o
v
id
e
d
p
r
o
b
le
m
(
AM
1
)
,
r
ef
lectin
g
o
n
p
ast
ex
p
er
ien
ce
s
(
AM
2
)
,
an
d
f
o
r
m
u
latin
g
a
s
tr
ateg
y
to
s
o
lv
e
p
r
o
b
lem
(
AM
3
)
.
I
n
AM
1
,
PK
r
ec
o
r
d
ed
ess
en
ti
al
in
f
o
r
m
atio
n
o
n
wo
r
k
s
h
ee
t,
s
h
o
wed
an
awa
r
en
ess
o
f
r
elev
an
t
in
f
o
r
m
atio
n
f
o
r
s
o
lv
in
g
co
n
te
x
tu
al
p
r
o
b
lem
,
an
d
was
ca
p
a
b
le
o
f
co
m
m
u
n
icatin
g
u
s
in
g
m
ath
em
atica
l
s
y
m
b
o
ls
.
Du
r
in
g
AM
2
,
PK
r
ec
alled
p
r
io
r
ex
p
er
ien
ce
s
in
s
o
lv
in
g
s
im
ilar
s
itu
atio
n
s
,
an
d
also
f
o
r
m
u
lat
ed
a
s
tr
ateg
y
,
p
ar
ticu
lar
ly
s
u
b
s
titu
tio
n
an
d
elim
in
atio
n
m
eth
o
d
s
f
o
r
AM
3
.
E
x
ce
r
p
ts
f
r
o
m
th
e
th
in
k
-
alo
u
d
p
r
o
ce
s
s
ar
e
p
r
esen
ted
in
T
ab
le
2
.
T
ab
le
2
.
Utter
an
ce
/b
e
h
av
io
r
o
f
PK in
th
e
asp
ec
t o
f
m
etac
o
g
n
i
tiv
e
awa
r
en
ess
U
t
t
e
r
a
n
c
e
/
b
e
h
a
v
i
o
r
W
r
i
t
t
e
n
a
n
sw
e
r
(
Ex
a
m
i
n
e
t
h
e
q
u
e
st
i
o
n
p
a
p
e
r
,
r
e
a
d
t
h
e
q
u
e
st
i
o
n
a
n
d
c
o
n
t
e
mp
l
a
t
e
)
O
h
h
h
…
y
e
s
,
I
r
e
memb
e
r
h
o
w
t
o
s
o
l
v
e
t
h
i
s
p
r
o
b
l
e
m
(
A
M
2
)
.
Th
i
s
s
h
o
u
l
d
b
e
e
x
e
mp
l
i
f
i
e
d
f
i
r
st
a
n
d
t
r
a
n
sf
o
r
me
d
i
n
t
o
a
n
e
q
u
a
t
i
o
n
(
A
M
3
)
.
(
Ex
a
m
i
n
e
t
h
e
q
u
e
st
i
o
n
p
a
p
e
r
a
n
d
p
r
o
v
i
d
e
a
n
a
n
sw
e
r
)
Th
e
f
i
r
st
e
q
u
a
t
i
o
n
i
s fo
r
B
e
t
o
w
h
o
b
o
u
g
h
t
t
w
o
c
l
o
t
h
e
s,
b
r
a
n
d
A
,
a
n
d
t
h
r
e
e
c
l
o
t
h
e
s,
b
r
a
n
d
B
w
i
t
h
a
p
r
i
c
e
900
.
000
,
s
h
o
u
l
d
b
e
2
+
3
=
900000
.
M
e
a
n
w
h
i
l
e
t
h
e
s
e
c
o
n
d
e
q
u
a
t
i
o
n
i
s
f
o
r
B
o
a
s
w
h
o
b
o
u
g
h
t
t
h
r
e
e
c
l
o
t
h
e
s
b
r
a
n
d
A
a
n
d
t
w
o
c
l
o
t
h
e
s
b
r
a
n
d
B
a
t
850
.
000
,
s
o
3
+
2
=
850000
(
A
M
1
)
.
(
S
o
l
v
e
a
n
d
w
r
i
t
e
a
n
sw
e
r
o
n
t
h
e
w
o
r
k
s
h
e
e
t
)
Th
e
q
u
e
s
t
i
o
n
s
a
r
e
:
(
a
)
W
h
i
c
h
i
s
mo
r
e
e
x
p
e
n
s
i
v
e
w
i
t
h
o
u
t
c
a
l
c
u
l
a
t
i
n
g
t
h
e
a
c
t
u
a
l
p
r
i
c
e
b
e
t
w
e
e
n
b
r
a
n
d
A
a
n
d
B
c
l
o
t
h
e
s?
W
r
i
t
e
d
o
w
n
y
o
u
r
r
e
a
s
o
n
s
,
a
n
d
(
b
)
h
o
w
mu
c
h
d
o
e
s
o
n
e
sh
i
r
t
f
r
o
m
b
r
a
n
d
A
c
o
st
?
H
o
w
d
o
y
o
u
c
a
l
c
u
l
a
t
e
i
t
?
(
A
M
1
)
O
r
i
g
i
n
a
l
v
e
r
s
i
o
n
Tr
a
n
s
l
a
t
e
d
v
e
r
si
o
n
Similar
d
ata
wer
e
o
b
tain
e
d
d
u
r
in
g
th
e
in
ter
v
iew,
wh
er
e
PK
em
p
h
asized
th
e
i
m
p
o
r
ta
n
ce
o
f
r
elev
a
n
t
in
f
o
r
m
atio
n
in
s
o
lv
in
g
c
o
n
tex
tu
al
p
r
o
b
lem
a
n
d
tr
an
s
cr
ib
i
n
g
in
to
wo
r
k
s
h
ee
t.
PK
f
u
r
t
h
er
s
h
o
wed
an
a
b
ilit
y
to
r
ep
r
esen
t
in
f
o
r
m
atio
n
u
s
in
g
m
ath
em
atica
l
s
y
m
b
o
ls
.
E
x
ce
r
p
ts
f
r
o
m
th
e
in
ter
v
iew,
f
o
c
u
s
in
g
o
n
m
etac
o
g
n
itiv
e
awa
r
en
ess
,
ar
e
p
r
esen
ted
:
P
:
Wh
y
d
o
yo
u
s
ea
r
ch
fo
r
yo
u
r
ex
is
tin
g
kn
o
w
led
g
e
r
elev
a
n
t to
p
r
o
b
lem?
PK
:
B
efo
r
e
s
o
lvin
g
p
r
o
b
lem,
I
h
a
ve
to
u
n
d
ers
ta
n
d
th
e
in
fo
r
ma
tio
n
p
r
o
vid
ed
i
n
th
e
q
u
esti
o
n
item
(
A
M1
)
.
F
o
r
ex
a
m
p
le,
th
e
w
a
ys
to
tr
a
n
s
fo
r
m
th
e
clo
th
i
n
g
b
r
a
n
d
s
p
u
r
ch
a
s
ed
b
y
B
eto
a
n
d
B
o
a
s
in
to
a
n
eq
u
a
tio
n
.
P
:
Wh
a
t h
a
ve
yo
u
d
o
n
e
to
u
n
d
ers
ta
n
d
th
e
q
u
esti
o
n
item?
PK
:
I
r
ewr
ite
th
e
in
fo
r
ma
tio
n
p
r
o
vid
ed
w
ith
in
th
e
q
u
esti
o
n
item
o
n
my
w
o
r
ksh
ee
t.
P
:
Wh
a
t is ma
th
ema
tica
l m
o
d
el
f
o
r
p
r
o
b
lem?
PK
:
I
eq
u
a
te
clo
t
h
es
fr
o
m
b
r
a
n
d
A
a
n
d
clo
t
h
es
fr
o
m
b
r
a
n
d
B
,
a
n
d
tr
a
n
s
fo
r
m
th
em
in
to
a
n
eq
u
a
tio
n
(
A
M3
)
B
ased
o
n
th
e
wr
itten
an
s
wer
s
an
d
th
in
k
-
alo
u
d
p
r
o
ce
s
s
,
m
et
ac
o
g
n
itiv
e
r
eg
u
latio
n
of
PK
i
n
s
o
lv
in
g
co
n
tex
tu
al
m
ath
em
atica
l
p
r
o
b
lem
in
clu
d
ed
th
e
co
n
s
tr
u
ctio
n
o
f
p
r
o
b
lem
-
s
o
lv
in
g
p
la
n
(
R
M1
)
an
d
th
e
f
o
r
m
u
latio
n
o
f
ad
d
itio
n
al
s
tr
ateg
y
(
R
M3
)
.
Du
r
i
n
g
R
M1
,
PK
u
s
ed
th
e
s
u
b
s
titu
tio
n
m
eth
o
d
to
r
eso
lv
e
p
r
o
b
lem
,
m
o
d
if
ied
th
e
o
r
ig
in
al
eq
u
atio
n
,
an
d
in
teg
r
ate
d
it
with
th
e
s
e
co
n
d
eq
u
atio
n
,
in
R
M3
.
E
x
ce
r
p
ts
f
r
o
m
th
e
t
h
in
k
-
alo
u
d
p
r
o
ce
s
s
ar
e
p
r
esen
ted
in
T
ab
le
3
.
A
s
im
ilar
co
n
clu
s
io
n
was
d
r
awn
f
r
o
m
th
e
in
ter
v
iew
r
esu
lts
with
PK,
wh
o
ex
p
licitly
m
en
tio
n
ed
th
at
th
e
q
u
esti
o
n
co
u
ld
b
e
r
eso
l
v
e
d
u
s
in
g
th
e
s
u
b
s
titu
tio
n
m
eth
o
d
as
p
ar
t
o
f
m
etac
o
g
n
itiv
e
r
e
g
u
latio
n
.
PK
alter
ed
th
e
in
itial
eq
u
atio
n
,
tr
an
s
f
o
r
m
in
g
it
in
to
a
n
ew
m
ath
em
atica
l
ex
p
r
ess
io
n
,
wh
ich
was
s
u
b
s
eq
u
en
tly
in
co
r
p
o
r
ated
in
to
th
e
s
ec
o
n
d
e
q
u
atio
n
.
T
h
e
in
ter
v
iew
ex
ce
r
p
t
is
p
r
esen
ted
:
P
:
Ho
w
d
id
yo
u
p
la
n
to
s
o
lve
th
is
p
r
o
b
lem?
PK
:
I
d
ec
id
ed
t
o
u
s
e
s
u
b
s
titu
tio
n
meth
o
d
a
fter
co
mp
r
eh
en
d
in
g
p
r
o
b
lem.
P
:
Ho
w
d
id
yo
u
s
o
lve
th
is
p
r
o
b
l
em?
PK
:
I
in
teg
r
a
ted
eq
u
a
tio
n
o
n
e
w
ith
eq
u
a
ti
o
n
tw
o
to
o
b
ta
in
A
g
r
a
d
e.
As
ke
d:
a
)
W
it
hout
c
a
lcula
ti
ng
the
a
c
tual
pr
ice
,
whic
h
br
a
nd
is
mor
e
e
xpe
ns
ive?
De
s
c
r
ibe
your
r
e
a
s
ons
.
b)
How
much
doe
s
one
br
a
nd
A
s
hir
t
c
os
t?
How
do
you
c
a
lcula
te
it
?
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
S
tu
d
en
ts
meta
co
g
n
itive
a
ctivities in
co
n
textu
a
l m
a
th
em
a
tica
l
p
r
o
b
lem
s
o
lvin
g
(
Yu
s
tin
u
s
Wa
n
g
g
u
w
a
y
)
233
T
ab
le
3
.
Utter
an
ce
/b
e
h
av
io
r
o
f
PK in
m
etac
o
g
n
itiv
e
r
e
g
u
latio
n
asp
ec
t
U
t
t
e
r
a
n
c
e
/
b
e
h
a
v
i
o
r
W
r
i
t
t
e
n
a
n
sw
e
r
(
Ex
a
m
i
n
e
t
h
e
w
o
r
k
s
h
e
e
t
)
F
r
o
m
t
h
e
k
n
o
w
n
e
q
u
a
t
i
o
n
,
t
h
i
s
c
a
n
b
e
s
o
l
v
e
d
u
s
i
n
g
t
h
e
su
b
s
t
i
t
u
t
i
o
n
m
e
t
h
o
d
(
R
M
1
)
-
(
Lo
o
k
a
t
t
h
e
w
o
r
k
sh
e
e
t
s a
n
d
w
r
i
t
e
)
Th
e
r
e
f
o
r
e
,
e
q
u
a
t
i
o
n
o
n
e
i
s
c
h
a
n
g
e
d
t
o
3
=
−
2
+
900
.
000
=
−
2
+
9
0
0
.
000
3
a
n
d
s
u
b
st
i
t
u
t
e
d
i
n
t
o
e
q
u
a
t
i
o
n
t
w
o
(
R
M
2
)
.
(
W
r
i
t
e
o
n
t
h
e
w
o
r
k
s
h
e
e
t
)
S
u
b
s
t
i
t
u
t
e
e
q
u
a
t
i
o
n
o
n
e
w
i
t
h
e
q
u
a
t
i
o
n
t
w
o
(
R
M
2
)
.
(
w
r
i
t
e
)
T
h
e
r
esu
lts
o
f
th
in
k
-
alo
u
d
s
ess
io
n
s
an
d
th
e
wr
itten
an
s
we
r
f
o
r
co
n
tex
t
u
al
m
ath
em
atica
l
p
r
o
b
lem
s
u
g
g
ested
th
at
m
etac
o
g
n
itiv
e
ev
alu
atio
n
b
y
PK
was
c
h
ar
ac
ter
ized
b
y
d
elib
er
atio
n
o
n
th
e
s
tep
s
to
s
o
l
v
e
p
r
o
b
lem
(
E
M
1
)
,
co
n
tem
p
latio
n
an
d
v
er
if
icatio
n
(
E
M
2
)
,
an
d
r
ef
lectio
n
o
n
th
e
ac
cu
r
ac
y
o
f
p
r
o
b
lem
s
o
lu
tio
n
(
EM3
)
.
Du
r
in
g
E
M1
,
PK sp
ec
u
lated
th
e
s
u
b
s
titu
tio
n
m
eth
o
d
to
s
o
lv
e
q
u
esti
o
n
(
b
)
,
an
d
ela
b
o
r
ated
q
u
esti
o
n
(
a)
b
y
ex
p
lain
in
g
wh
y
clo
th
in
g
b
r
an
d
B
was
m
o
r
e
ex
p
en
s
iv
e,
as
well
as
th
e
r
atio
n
ale
b
eh
in
d
th
e
an
s
wer
.
Du
r
in
g
b
o
th
E
M2
a
n
d
E
M3
,
PK
o
p
er
ated
an
d
i
n
teg
r
ated
th
e
n
ewly
f
o
r
m
u
lated
eq
u
atio
n
i
n
to
eq
u
atio
n
two
.
Su
b
s
eq
u
en
tly
,
PK
p
er
f
o
r
m
ed
esti
m
atio
n
s
u
n
til
v
alu
e
A
w
as
o
b
tain
ed
.
T
h
e
ex
am
p
les
o
f
th
e
u
tter
an
ce
s
o
r
b
eh
av
io
r
s
d
u
r
in
g
th
e
th
in
k
-
alo
u
d
s
ess
io
n
s
ar
e
s
u
m
m
ar
ized
in
T
ab
le
4
.
T
ab
le
4
.
Statem
en
t/b
eh
a
v
io
r
o
f
PK in
m
etac
o
g
n
itiv
e
e
v
alu
ati
o
n
asp
ec
t
S
t
a
t
e
me
n
t
/
b
e
h
a
v
i
o
r
W
r
i
t
t
e
n
a
n
sw
e
r
(
Ex
a
m
i
n
e
a
n
d
w
r
i
t
e
t
h
e
a
n
sw
e
r
)
Q
u
e
st
i
o
n
(
a
)
W
h
i
c
h
c
l
o
t
h
e
s a
r
e
m
o
r
e
e
x
p
e
n
si
v
e
…H
mh
mh
m
.
Th
e
o
n
e
s
t
h
a
t
a
r
e
m
o
r
e
e
x
p
e
n
s
i
v
e
a
r
e
c
l
o
t
h
e
s fr
o
m
b
r
a
n
d
B
.
Th
e
r
e
a
s
o
n
i
s
t
h
a
t
i
n
e
q
u
a
t
i
o
n
o
n
e
,
b
r
a
n
d
B
c
l
o
t
h
e
s
a
r
e
p
u
r
c
h
a
se
d
m
o
r
e
t
h
a
n
b
r
a
n
d
A
c
l
o
t
h
e
s
.
M
e
a
n
w
h
i
l
e
,
i
n
e
q
u
a
t
i
o
n
t
w
o
,
f
e
w
e
r
b
r
a
n
d
B
c
l
o
t
h
e
s
a
r
e
p
u
r
c
h
a
se
d
t
h
a
n
b
r
a
n
d
A
c
l
o
t
h
e
s.
T
h
e
r
e
f
o
r
e
,
t
h
e
p
r
i
c
e
o
b
t
a
i
n
e
d
i
n
e
q
u
a
t
i
o
n
t
w
o
i
s
c
h
e
a
p
e
r
t
h
a
n
i
n
e
q
u
a
t
i
o
n
o
n
e
(
E
M
1
)
.
O
r
i
g
i
n
a
l
v
e
r
s
i
o
n
Tr
a
n
s
l
a
t
e
v
e
r
s
i
o
n
(
W
r
i
t
i
n
g
o
n
t
h
e
w
o
r
k
s
h
e
e
t
)
3
+
2
=
850
.
000
3
+
2
(
−
2
+
900
.
000
3
)
=
850
.
000
3
+
(
−
4
)
+
1
.
800
.
000
3
=
850
.
000
9
3
+
(
−
4
)
+
1
.
800
.
000
3
=
850
.
000
9
−
4
+
1
.
800
.
000
3
=
850
.
000
5
+
1
.
800
.
000
3
=
850
.
000
5
+
1
.
800
.
000
=
2
.
550
.
000
5
=
2
.
550
.
000
−
1
.
800
.
000
5
=
750
.
000
=
750
.
000
5
=
150
.
000
(
EM
2
a
n
d
E
M
3
)
Similar
d
ata
wer
e
o
b
tain
ed
f
r
o
m
th
e
i
n
ter
v
iew
r
esu
lts
.
I
n
m
etac
o
g
n
itiv
e
e
v
alu
atio
n
,
PK
m
en
tio
n
e
d
re
-
ex
am
in
in
g
p
r
o
b
lem
-
s
o
lv
in
g
s
tep
s
an
d
th
e
f
in
al
o
u
tco
m
e,
wh
ile
also
v
er
if
y
in
g
th
e
an
s
wer
s
f
o
r
q
u
esti
o
n
s
(
a
)
an
d
(
b
)
.
T
h
e
in
ter
v
iew
ex
ce
r
p
t
is
p
r
esen
ted
:
a
)
T
he
one
s
that
a
r
e
mor
e
e
xpe
ns
ive
a
r
e
c
lo
thes
f
r
om
br
a
nd
B
.
T
he
r
e
a
s
on
is
that
in
e
qua
ti
on
one
,
br
a
nd
B
c
lot
he
s
a
r
e
pur
c
ha
s
e
d
mor
e
than
br
a
nd
A
c
lot
he
s
.
M
e
a
nwhile,
in
e
qua
ti
on
two,
f
e
we
r
br
a
nd
B
c
lot
he
s
a
r
e
pur
c
ha
s
e
d
than
br
a
nd
A
c
lot
he
s
,
s
o
the
pr
ice
obtaine
d
in
e
qua
ti
on
two
is
c
he
a
pe
r
than
in
e
qua
ti
on
one
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
14
,
No
.
1
,
Feb
r
u
a
r
y
20
25
:
229
-
239
234
P
:
Ho
w
d
id
yo
u
c
h
ec
k
yo
u
r
w
o
r
k?
PK
:
I
r
e
-
ex
a
min
e
d
my
p
r
o
b
lem
-
s
o
lvin
g
s
tep
s
a
n
d
t
h
e
r
esu
lts
.
I
r
ela
ted
my
a
n
s
w
er
w
ith
q
u
esti
o
n
(
a
)
a
n
d
d
ec
i
d
ed
th
a
t sh
ir
t B
w
a
s
mo
r
e
ex
p
en
s
ive
(
E
M1
)
.
P
:
Wer
e
yo
u
s
u
r
e
a
b
o
u
t y
o
u
r
a
n
s
w
er a
n
d
th
e
s
ta
g
es o
f p
r
o
b
le
m
-
s
o
lvin
g
?
PK
:
Yes
,
I
’
m
s
u
r
e
a
b
o
u
t m
y
a
n
s
w
ers
a
n
d
s
tep
s
fo
r
s
o
lvin
g
p
r
o
b
l
em
(
E
M2
,
E
M3
)
3
.
1
.
2
.
M
et
a
co
g
nitiv
e
a
ct
iv
it
ie
s
o
f
s
ec
o
nd
pa
rt
icipa
nts
(
VP
)
B
ased
o
n
th
e
r
esu
lts
o
f
th
e
th
i
n
k
-
alo
u
d
p
r
o
ce
s
s
an
d
th
e
wr
itt
en
an
s
wer
s
f
o
r
co
n
tex
tu
al
m
at
h
em
atica
l
p
r
o
b
lem
,
m
etac
o
g
n
itiv
e
awa
r
e
n
ess
b
y
VP
in
s
o
lv
in
g
co
n
tex
t
u
al
m
ath
em
atica
l
p
r
o
b
lem
wa
s
ch
ar
ac
ter
ized
b
y
r
ef
lectin
g
o
n
p
ast
ex
p
e
r
ien
ce
s
in
s
o
lv
in
g
s
im
ilar
p
r
o
b
lem
(
AM
2
)
an
d
co
n
tem
p
latin
g
th
e
n
ec
ess
ar
y
s
tep
s
t
o
ad
d
r
ess
th
e
cu
r
r
e
n
t
is
s
u
e
(
AM
3
)
.
Du
r
in
g
AM
2
,
VP
r
ec
alled
en
co
u
n
ter
i
n
g
a
s
im
ilar
ex
p
er
i
en
ce
wh
en
s
o
lv
in
g
an
alo
g
o
u
s
p
r
o
b
lem
,
w
h
ile
d
elib
er
atin
g
o
n
th
e
cu
r
r
e
n
t
co
u
r
s
e
o
f
ac
tio
n
an
d
d
ec
id
in
g
t
o
u
s
e
th
e
elim
in
atio
n
m
eth
o
d
,
d
u
r
in
g
AM
3
.
T
h
e
in
te
r
v
iew
ex
ce
r
p
t is p
r
esen
ted
:
VP
:
(
E
xa
min
e
q
u
esti
o
n
p
a
p
er
,
r
ea
d
s
th
e
q
u
esti
o
n
,
a
n
d
th
in
ks).
Hmh
(
t
h
in
kin
g
)
(
A
M2
)
,
th
is
p
r
o
b
lem
co
u
ld
b
e
s
o
lved
u
s
in
g
s
u
b
s
titu
tio
n
o
r
elimin
a
tio
n
me
th
o
d
(
A
M3
)
Similar
d
ata
wer
e
o
b
tain
ed
f
r
o
m
th
e
in
ter
v
iew
r
esu
lts
.
I
n
ter
m
s
o
f
m
etac
o
g
n
itiv
e
awa
r
en
ess
,
VP
r
ec
alled
p
ast
ex
p
er
ien
ce
s
in
s
o
lv
in
g
s
im
ilar
p
r
o
b
lem
an
d
a
ttem
p
ted
to
ap
p
ly
th
e
ac
q
u
ir
e
d
k
n
o
wled
g
e.
T
h
e
in
ter
v
iew
ex
ce
r
p
t is p
r
esen
ted
:
P
:
Wh
y
d
id
yo
u
r
u
min
a
te
o
n
p
r
o
b
lem
yo
u
a
r
e
cu
r
r
en
tly
fa
cin
g
?
VP
:
To
s
o
lve
p
r
o
b
lem
ea
s
ily
P
:
Wh
a
t d
id
yo
u
d
o
to
u
n
d
ers
ta
n
d
p
r
o
b
lem
g
iven
?
VP
:
I
r
eme
mb
er w
o
r
kin
g
o
n
a
s
imila
r
p
r
o
b
lem
u
s
in
g
elimin
a
tio
n
o
r
s
u
b
s
titu
tio
n
(
A
M2
)
.
P
:
Wh
a
t is ma
th
ema
tica
l m
o
d
el
fo
r
p
r
o
b
lem?
VP
:
I
ta
ke
,
fo
r
ex
a
mp
le,
b
r
a
n
d
A
a
n
d
b
r
a
n
d
B
cl
o
th
es,
a
n
d
tu
r
n
th
em
in
to
a
n
eq
u
a
tio
n
(
A
M3
)
.
I
n
s
o
lv
in
g
co
n
tex
tu
al
m
ath
e
m
atica
l
p
r
o
b
lem
,
m
etac
o
g
n
itiv
e
r
eg
u
latio
n
o
f
VP
in
cl
u
d
ed
f
o
r
m
u
latin
g
a
p
lan
f
o
r
s
o
lv
in
g
m
ath
em
atic
al
p
r
o
b
lem
(
R
M1
)
an
d
c
o
n
te
m
p
latin
g
th
e
s
u
b
s
eq
u
en
t
s
tep
s
in
m
ath
e
m
atica
l
p
r
o
b
lem
-
s
o
lv
in
g
p
r
o
ce
s
s
(
R
M3
)
.
Du
r
i
n
g
R
M1
,
VP
d
elib
er
ated
o
n
u
s
in
g
th
e
elim
in
atio
n
m
eth
o
d
,
a
n
d
m
u
ltip
lied
b
o
th
eq
u
atio
n
s
,
s
p
ec
if
ically
eq
u
atio
n
o
n
e
b
y
two
,
an
d
eq
u
atio
n
two
b
y
th
r
ee
,
in
R
M3
.
T
h
is
r
esu
lted
in
4
+
6
=
1800
(
eq
u
atio
n
o
n
e)
a
n
d
9
+
6
=
2550
(
eq
u
a
tio
n
two
)
.
Su
b
s
eq
u
e
n
tly
,
t
h
e
eq
u
atio
n
s
wer
e
m
an
ip
u
lated
to
id
e
n
tify
th
e
v
alu
e
o
f
x
.
I
n
s
tan
ce
s
o
f
s
u
b
jec
t
u
tter
an
ce
s
o
r
b
eh
a
v
io
r
s
th
r
o
u
g
h
th
e
th
i
n
k
-
alo
u
d
m
eth
o
d
ar
e
p
r
esen
ted
i
n
T
ab
le
5
.
T
ab
le
5
.
Statem
en
t/
b
eh
a
v
io
r
o
f
VP in
m
etac
o
g
n
itiv
e
r
eg
u
lati
o
n
S
t
a
t
e
me
n
t
/
B
e
h
a
v
i
o
r
W
r
i
t
t
e
n
a
n
sw
e
r
(
Ex
a
m
i
n
e
t
h
e
w
o
r
k
s
h
e
e
t
)
W
i
t
h
t
h
e
p
r
o
v
i
d
e
d
e
q
u
a
t
i
o
n
s,
t
h
i
s
p
r
o
b
l
e
m
c
a
n
b
e
s
o
l
v
e
d
u
s
i
n
g
e
l
i
mi
n
a
t
i
o
n
m
e
t
h
o
d
(
R
M
1
)
-
(
Ex
a
m
i
n
e
t
h
e
w
o
r
k
s
h
e
e
t
a
n
d
w
r
i
t
e
)
2
+
3
=
900
|
×
2
|
4
+
6
=
1
.
800
3
+
2
=
850
|
×
3
|
9
+
6
=
2
.
550
(
R
M
3
)
Similar
d
ata
wer
e
o
b
tain
ed
f
r
o
m
th
e
in
ter
v
iew
r
esu
lts
.
I
n
ter
m
s
o
f
m
etac
o
g
n
itiv
e
r
eg
u
latio
n
,
VP
m
en
tio
n
ed
u
s
in
g
elim
in
atio
n
m
eth
o
d
an
d
m
an
ip
u
latin
g
t
h
e
two
eq
u
atio
n
s
p
r
o
v
id
ed
.
T
h
e
i
n
ter
v
iew
ex
ce
r
p
t
is
p
r
esen
ted
:
P
:
Ho
w
d
id
yo
u
p
la
n
to
s
o
lve
th
is
p
r
o
b
lem?
VP
:
I
u
s
ed
elimin
a
tio
n
meth
o
d
a
fter
r
eme
mb
erin
g
h
o
w
to
s
o
lve
p
r
o
b
lem
(
R
M1
)
.
P
:
Ho
w
d
id
yo
u
s
o
lve
th
is
p
r
o
b
l
em?
VP
:
I
s
w
itch
ed
th
e
tw
o
eq
u
a
tio
n
s
in
o
r
d
er to
elimin
a
te
o
n
e
va
r
ia
b
le
(
R
M3
)
.
T
h
e
th
in
k
-
al
o
u
d
a
n
d
wr
itten
r
esu
lts
f
o
r
co
n
tex
tu
al
m
at
h
em
a
tical
p
r
o
b
lem
s
h
o
wed
th
at
m
et
ac
o
g
n
itiv
e
ev
alu
atio
n
o
f
VP
was
ch
ar
ac
t
er
ized
b
y
co
n
tem
p
latin
g
t
h
e
s
tep
s
f
o
r
s
o
lv
in
g
p
r
o
b
lem
(
E
M
1
)
,
co
n
s
id
er
i
n
g
an
d
r
ev
iewin
g
p
r
o
b
lem
-
s
o
lv
in
g
p
h
ases
(
EM2
)
,
a
n
d
s
p
ec
u
latin
g
t
h
e
f
ea
s
ib
ilit
y
o
f
co
m
p
letin
g
th
o
s
e
p
h
ases
(
E
M
4
)
.
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
S
tu
d
en
ts
meta
co
g
n
itive
a
ctivities in
co
n
textu
a
l m
a
th
em
a
tica
l
p
r
o
b
lem
s
o
lvin
g
(
Yu
s
tin
u
s
Wa
n
g
g
u
w
a
y
)
235
Du
r
in
g
EM1
,
VP
co
n
s
id
er
e
d
u
s
in
g
elim
in
atio
n
m
eth
o
d
to
s
o
lv
e
q
u
esti
o
n
(
b
)
,
an
d
ex
p
o
u
n
d
ed
o
n
q
u
esti
o
n
(
a)
b
y
ex
p
lai
n
in
g
wh
y
clo
th
in
g
b
r
an
d
B
was
m
o
r
e
e
x
p
en
s
iv
e,
alo
n
g
with
th
e
r
atio
n
ale
b
eh
in
d
t
h
e
an
s
wer
.
E
x
ce
r
p
ts
o
f
u
tter
an
ce
s
o
r
b
eh
av
io
r
s
d
u
r
in
g
th
e
th
i
n
k
-
alo
u
d
s
ess
io
n
ar
e
p
r
esen
ted
in
T
ab
le
6
.
VP
ac
k
n
o
wled
g
e
d
ex
p
er
ien
cin
g
h
esit
atio
n
in
p
r
o
b
le
m
-
s
o
lv
in
g
p
r
o
ce
s
s
an
d
v
er
if
y
in
g
an
s
wer
s
f
o
r
b
o
th
q
u
esti
o
n
(
a)
an
d
q
u
esti
o
n
(
b
)
.
T
h
e
ex
ce
r
p
t f
r
o
m
th
e
in
ter
v
iew
in
th
e
d
im
en
s
io
n
o
f
m
etac
o
g
n
itiv
e
e
v
alu
atio
n
is
:
P
:
Ho
w
d
id
yo
u
c
h
ec
k
yo
u
r
w
o
r
k?
VP
:
I
h
a
d
d
o
u
b
ts
a
b
o
u
t m
y
a
n
s
w
er,
b
u
t I
’
m
s
u
r
e
w
ith
th
e
s
tep
s
(
E
M1
)
.
P
:
Wer
e
yo
u
s
u
r
e
a
b
o
u
t y
o
u
r
a
n
s
w
er a
n
d
p
r
o
b
lem
-
s
o
lvin
g
p
r
o
ce
d
u
r
es?
VP
:
N
o
,
I
ju
s
t rea
liz
ed
th
a
t m
y
a
n
s
w
er
w
a
s
w
r
o
n
g
.
T
ab
le
6
.
Utter
an
ce
/b
e
h
av
io
r
o
f
VP in
m
etac
o
g
n
itiv
e
e
v
alu
atio
n
asp
ec
t
S
t
a
t
e
me
n
t
/
b
e
h
a
v
i
o
r
W
r
i
t
t
e
n
a
n
sw
e
r
(
Ex
a
m
i
n
e
t
h
e
q
u
e
st
i
o
n
i
t
e
m
a
n
d
w
r
i
t
e
)
f
o
r
(
a
)
t
h
e
c
l
o
t
h
e
s
f
r
o
m
b
r
a
n
d
B
i
s
mo
r
e
e
x
p
e
n
si
v
e
.
D
e
scr
i
p
t
i
o
n
,
w
h
e
n
b
u
y
i
n
g
3
c
l
o
t
h
e
s
f
r
o
m
b
r
a
n
d
B
,
B
e
t
o
p
a
i
d
h
i
g
h
e
r
t
h
a
n
B
o
a
s
,
w
h
o
b
o
u
g
h
t
t
w
o
c
l
o
t
h
e
s fr
o
m
t
h
e
sam
e
b
r
a
n
d
(
EM
1
)
.
O
r
i
g
i
n
a
l
v
e
r
s
i
o
n
Tr
a
n
s
l
a
t
e
v
e
r
s
i
o
n
(
W
r
i
t
e
o
n
t
h
e
w
o
r
k
s
h
e
e
t
)
2
+
3
=
900
|
×
2
|
4
+
6
=
1
.
800
3
+
2
=
850
|
×
3
|
9
+
6
=
2
.
550
−
5
=
−
1350
=
270
(
EM
2
)
(
S
e
e
ms
t
o
c
o
n
t
e
m
p
l
a
t
e
)
I
s t
h
i
s
t
h
e
r
i
g
h
t
a
n
sw
e
r
?
-
3
.
1
.
3
.
M
et
a
co
g
nitiv
e
a
ct
iv
it
ie
s
o
f
t
he
t
hird s
ub
j
ec
t
(
E
D
M
)
T
h
e
th
in
k
-
alo
u
d
an
d
th
e
wr
itt
en
an
s
wer
f
o
r
s
o
lv
in
g
co
n
tex
t
u
al
m
ath
em
atica
l
p
r
o
b
lem
s
u
g
g
ested
th
at
m
etac
o
g
n
itiv
e
awa
r
en
ess
o
f
E
DM
in
clu
d
ed
r
ec
allin
g
p
ast
ex
p
er
ien
ce
s
in
s
o
lv
in
g
s
im
ilar
p
r
o
b
lem
(
AM
2
)
an
d
co
n
tem
p
latin
g
t
h
e
n
ec
ess
ar
y
s
tep
s
to
ad
d
r
ess
th
e
cu
r
r
e
n
t
p
r
o
b
lem
(
AM
3
)
.
Du
r
in
g
AM
2
,
E
DM
r
ec
o
llected
en
co
u
n
ter
i
n
g
a
s
im
ilar
ex
p
er
i
en
ce
wh
en
s
o
lv
in
g
an
al
o
g
u
es
p
r
o
b
lem
,
a
n
d
also
co
n
s
id
er
e
d
r
eso
lv
in
g
u
s
in
g
elim
in
atio
n
m
eth
o
d
d
u
r
in
g
A
M3
.
T
h
e
in
ter
v
iew
ex
ce
r
p
t is p
r
esen
ted
:
E
DM
:
(
Lo
o
k
a
t
th
e
q
u
esti
o
n
item,
r
ea
d
th
e
q
u
esti
o
n
s
,
a
n
d
s
ee
m
s
th
in
kin
g
)
.
I
t
s
ee
ms
th
a
t
I
ca
n
u
s
e
elimin
a
tio
n
(
A
M3
)
.
I
’
ve
b
ee
n
d
o
in
g
t
h
is
b
efo
r
e…
(
A
M2
)
Similar
d
ata
wer
e
o
b
tain
ed
f
r
o
m
th
e
in
ter
v
iew
r
esu
lts
.
I
n
ter
m
s
o
f
m
etac
o
g
n
itiv
e
awa
r
e
n
ess
,
E
DM
m
en
tio
n
ed
r
ec
allin
g
ex
p
er
ien
ce
s
in
ad
d
r
ess
in
g
an
al
o
g
o
u
s
p
r
o
b
lem
an
d
attem
p
tin
g
to
a
p
p
ly
t
h
e
ac
q
u
ir
ed
k
n
o
wled
g
e.
T
h
e
in
te
r
v
iew
ex
c
er
p
t is p
r
esen
ted
:
P
:
Wh
y
d
id
yo
u
r
u
min
a
te
o
n
p
r
o
b
lem
yo
u
a
r
e
cu
r
r
en
tly
fa
cin
g
?
E
DM
:
I
h
a
d
w
o
r
ke
d
o
n
s
imila
r
q
u
esti
o
n
s
b
efo
r
e.
Wh
ile
r
ea
d
in
g
th
e
q
u
esti
o
n
s
,
I
immed
ia
tely
r
eme
mb
ered
I
co
u
ld
u
s
e
elimin
a
tio
n
o
r
s
u
b
s
titu
tio
n
(
A
M2
,
A
M3
)
.
P
:
Wh
a
t h
a
d
y
o
u
d
o
n
e
t
o
u
n
d
ers
ta
n
d
p
r
o
b
lem
g
iven
?
E
DM
:
I
immed
ia
tely
w
r
o
te
d
o
w
n
th
e
eq
u
a
tio
n
fr
o
m
p
r
o
b
lem.
P
:
Wh
a
t wa
s
ma
th
ema
tica
l m
o
d
el
o
f p
r
o
b
lem?
E
DM
:
I
ta
ke
,
fo
r
ex
a
mp
le,
b
r
a
n
d
A
a
n
d
b
r
a
n
d
B
cl
o
th
es a
n
d
tu
r
n
t
h
em
in
to
a
n
eq
u
a
tio
n
(
A
M3
)
.
T
h
e
th
in
k
-
al
o
u
d
a
n
d
wr
itten
r
esu
lts
f
o
r
co
n
tex
tu
al
m
at
h
em
a
tical
p
r
o
b
lem
s
h
o
wed
th
at
m
et
ac
o
g
n
itiv
e
r
eg
u
latio
n
o
f
E
DM
was
ch
a
r
a
cter
ized
b
y
f
o
r
m
u
latin
g
a
p
la
n
(
R
M1
)
an
d
co
n
tem
p
latin
g
s
u
b
s
eq
u
en
t
s
tep
s
in
p
r
o
b
lem
-
s
o
lv
in
g
p
r
o
ce
s
s
(
R
M
3
)
.
Du
r
in
g
R
M1
,
E
DM
co
n
s
id
er
ed
u
s
in
g
elim
in
atio
n
m
eth
o
d
,
wh
ile
m
u
ltip
ly
in
g
b
o
th
eq
u
atio
n
s
,
s
p
ec
if
ically
e
q
u
atio
n
o
n
e
b
y
two
,
an
d
e
q
u
a
tio
n
two
b
y
th
r
ee
,
d
u
r
in
g
R
M
3
.
T
h
is
r
esu
lted
in
4
+
6
=
1800
(
eq
u
atio
n
o
n
e)
an
d
9
+
6
=
2550
(
eq
u
atio
n
two
)
,
an
d
t
h
e
eq
u
atio
n
s
wer
e
s
u
b
s
eq
u
en
tly
m
an
ip
u
lated
t
o
d
e
r
iv
e
a
n
s
wer
.
T
h
e
u
tter
an
ce
s
o
r
b
eh
av
io
r
s
o
f
E
DM
d
u
r
i
n
g
th
e
th
in
k
-
alo
u
d
s
ess
io
n
s
ar
e
p
r
esen
ted
in
T
a
b
le
7
.
Ans
we
r
:
B
r
a
nd
B
c
lot
he
s
a
r
e
mor
e
e
xpe
ns
ive
E
xplana
t
ion:
whe
n
B
e
to
buys
3
s
hir
ts
of
br
a
nd
B
,
the
pr
ice
is
gr
e
a
ter
than
B
oa
s
who
buys
2
s
hir
ts
of
br
a
nd
B
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
14
,
No
.
1
,
Feb
r
u
a
r
y
20
25
:
229
-
239
236
T
ab
le
7
.
Utter
an
ce
/
b
eh
av
io
r
o
f
E
DM
in
m
etac
o
g
n
itiv
e
r
eg
u
l
atio
n
asp
ec
t
U
t
t
e
r
a
n
c
e
/
b
e
h
a
v
i
o
r
W
r
i
t
t
e
n
a
n
sw
e
r
(
S
e
e
w
o
r
k
s
h
e
e
t
)
Th
e
t
w
o
p
r
o
v
i
d
e
d
e
q
u
a
t
i
o
n
s
a
l
l
o
w
t
h
e
u
se
o
f
e
l
i
mi
n
a
t
i
o
n
me
t
h
o
d
,
m
a
k
i
n
g
i
t
a
n
e
a
s
y
t
a
s
k
(
R
M
1
)
-
(
Ex
a
m
i
n
e
t
h
e
w
o
r
k
s
h
e
e
t
a
n
d
w
r
i
t
e
)
2
+
3
=
900
|
×
2
|
4
+
6
=
1
.
800
3
+
2
=
850
|
×
3
|
9
+
6
=
2
.
550
(
R
M
3
)
C
o
n
co
r
d
an
t
d
ata
wer
e
o
b
tain
ed
f
r
o
m
th
e
in
ter
v
iew
r
esu
lts
,
wh
er
ein
E
DM
m
en
ti
o
n
ed
t
h
e
p
o
ten
tial
u
s
e
o
f
elim
in
atio
n
m
et
h
o
d
t
o
s
o
lv
e
p
r
o
b
lem
,
wh
ile
m
an
ip
u
latin
g
b
o
th
e
q
u
atio
n
s
f
o
r
m
ed
.
T
h
e
in
ter
v
iew
ex
ce
r
p
t is p
r
esen
ted
:
P
:
Ho
w
d
id
yo
u
p
la
n
to
s
o
lve
th
is
p
r
o
b
lem?
E
DM
:
I
u
s
ed
th
e
elimin
a
tio
n
meth
o
d
(
R
M1
)
.
P
:
Ho
w
d
id
yo
u
c
o
mp
lete
th
e
a
n
s
w
er?
E
DM
:
I
s
u
b
s
titu
ted
th
e
tw
o
eq
u
a
tio
n
s
to
elimin
a
te
o
n
e
v
a
r
ia
b
le
(
R
M3
)
.
T
h
e
th
in
k
-
alo
u
d
r
esu
lts
an
d
t
h
e
wr
itten
a
n
s
wer
s
f
o
r
co
n
tex
tu
al
m
ath
em
atica
l
p
r
o
b
le
m
s
h
o
wed
th
at
m
etac
o
g
n
itiv
e
e
v
alu
atio
n
b
y
E
DM
was
ch
ar
ac
ter
ized
b
y
c
o
n
tem
p
latin
g
th
e
s
tep
s
to
s
o
lv
e
p
r
o
b
lem
(
E
M1
)
,
co
n
s
id
er
in
g
an
d
r
ev
iewin
g
th
e
s
tep
s
(
E
M2
)
,
an
d
ev
alu
atin
g
th
e
v
alid
ity
o
f
th
e
s
o
l
u
tio
n
(
E
M3
)
.
Du
r
in
g
E
M1
s
tag
e,
E
DM
d
elib
er
ated
o
n
u
s
in
g
elim
in
atio
n
m
et
h
o
d
to
an
s
wer
q
u
esti
o
n
(
b
)
,
elab
o
r
ated
o
n
q
u
esti
o
n
(
a
)
,
an
d
ex
p
lain
ed
th
at
cl
o
th
in
g
b
r
an
d
B
was
m
o
r
e
ex
p
en
s
iv
e.
T
h
e
i
n
ter
v
iew
ex
ce
r
p
t
is
p
r
esen
ted
in
T
ab
le
8
.
Similar
d
ata
wer
e
o
b
tai
n
ed
f
r
o
m
t
h
e
i
n
ter
v
iew
r
esu
lts
,
wh
er
ein
E
DM
ex
p
r
ess
ed
in
s
tan
ce
s
o
f
u
n
ce
r
tain
ty
r
eg
a
r
d
in
g
th
e
p
r
o
v
id
e
d
an
s
wer
s
an
d
p
r
o
b
le
m
-
s
o
lv
in
g
s
tag
es,
wh
ile
v
er
i
f
y
in
g
th
e
an
s
wer
s
f
o
r
q
u
esti
o
n
s
(
a)
an
d
(
b
)
.
P
:
Ho
w
d
id
yo
u
c
h
ec
k
yo
u
r
w
o
r
k?
VP
:
I
w
a
s
co
n
fid
en
t in
my
w
o
r
k
a
n
d
h
a
d
ch
ec
ke
d
it (
E
M1
)
.
P
:
Wer
e
yo
u
s
u
r
e
a
b
o
u
t y
o
u
r
a
n
s
w
er a
n
d
th
e
a
ctio
n
s
yo
u
t
o
o
k
in
s
o
lvin
g
p
r
o
b
lem?
VP
:
Yes
(
E
M3
)
T
ab
le
8
.
Statem
en
t/b
eh
a
v
io
r
o
f
E
DM
in
m
etac
o
g
n
itiv
e
ev
alu
atio
n
asp
ec
t
S
t
a
t
e
me
n
t
/
b
e
h
a
v
i
o
r
W
r
i
t
t
e
n
a
n
sw
e
r
(
Ex
a
m
i
n
e
a
n
d
w
r
i
t
e
)
I
t
h
i
n
k
i
t
i
s
b
r
a
n
d
B
c
l
o
t
h
e
s
b
e
c
a
u
se
w
h
e
n
B
e
t
o
b
o
u
g
h
t
3
B
c
l
o
t
h
e
s
,
h
e
p
a
i
d
h
i
g
h
e
r
t
h
a
n
B
o
a
s,
w
h
o
b
o
u
g
h
t
2
c
l
o
t
h
e
s
f
r
o
m
t
h
e
s
a
me
b
r
a
n
d
(
EM
1
)
.
O
r
i
g
i
n
a
l
v
e
r
s
i
o
n
Tr
a
n
s
l
a
t
e
v
e
r
s
i
o
n
(
W
r
i
t
e
o
n
t
h
e
w
o
r
k
s
h
e
e
t
)
2
+
3
=
900
(
×
2
)
→
4
+
6
=
1800
3
+
2
=
800
(
×
3
)
→
9
+
6
=
2550
−
5
=
−
750
=
−
750
−
5
=
150
Th
e
r
e
f
o
r
e
,
c
l
o
t
h
f
r
o
m
b
r
a
n
d
A
=
I
D
R
1
5
0
.
0
0
0
(
E
M
2
)
3
.
2
.
Dis
cus
s
io
n
T
h
e
an
al
y
s
is
s
h
o
wed
th
at
all
p
ar
ticip
an
ts
e
n
g
ag
e
d
i
n
m
et
ac
o
g
n
itiv
e
a
ctiv
ities
,
n
am
ely
awa
r
en
ess
,
ev
alu
atio
n
,
an
d
r
eg
u
latio
n
.
m
etac
o
g
n
itiv
e
awa
r
en
ess
o
cc
u
r
r
ed
wh
e
n
s
tu
d
en
ts
r
ec
o
g
n
i
ze
d
th
at
th
eir
p
r
io
r
k
n
o
wled
g
e
c
o
u
ld
ass
is
t
in
s
o
lv
in
g
p
r
o
b
lem
.
T
h
is
was
in
lin
e
with
W
ils
o
n
[
1
2
]
,
s
tatin
g
th
at
k
n
o
wled
g
e
r
elate
d
to
p
r
o
b
lem
c
o
n
s
titu
ted
m
etac
o
g
n
itiv
e
awa
r
en
ess
.
R
o
f
ii
et
a
l.
[
2
5
]
also
d
escr
ib
e
d
th
e
r
o
le
o
f
m
etac
o
g
n
itiv
e
awa
r
en
ess
d
u
r
in
g
p
lan
n
in
g
p
r
o
ce
s
s
to
en
h
an
ce
k
n
o
wled
g
e
a
n
d
th
e
ef
f
ec
t
o
n
d
ec
is
io
n
-
m
ak
in
g
wh
e
n
s
elec
tin
g
o
r
id
en
tify
i
n
g
alter
n
ativ
e
s
tr
at
eg
ies.
Fu
r
th
er
m
o
r
e
,
Ar
u
m
et
a
l.
[
2
9
]
id
en
tifie
d
c
o
m
p
o
n
en
t
s
o
f
m
etac
o
g
n
itiv
e
awa
r
en
ess
,
in
clu
d
in
g
k
n
o
wled
g
e
ab
o
u
t
co
g
n
itio
n
a
n
d
co
g
n
itiv
e
r
eg
u
latio
n
th
at
im
p
ac
t
th
e
r
eso
lu
tio
n
o
f
m
ath
em
atica
l p
r
o
b
lem
am
o
n
g
s
tu
d
en
ts
.
I
thi
nk
it
'
s
s
hi
r
t
b
r
a
nd
B
,
be
c
a
us
e
whe
n
B
e
t
o
buys
3
B
s
hir
ts
,
he
ge
ts
a
bigger
tot
a
l
than
B
oa
s
who
buys
2
B
s
hir
ts
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
S
tu
d
en
ts
meta
co
g
n
itive
a
ctivities in
co
n
textu
a
l m
a
th
em
a
tica
l
p
r
o
b
lem
s
o
lvin
g
(
Yu
s
tin
u
s
Wa
n
g
g
u
w
a
y
)
237
T
h
e
cu
r
r
en
t
s
tu
d
y
s
h
o
wed
th
a
t
m
etac
o
g
n
itiv
e
r
eg
u
latio
n
o
c
cu
r
r
ed
wh
en
th
e
p
a
r
ticip
an
ts
d
ec
id
ed
to
r
ec
o
n
s
id
er
th
e
s
tep
s
r
e
p
ea
ted
l
y
u
s
ed
b
e
f
o
r
e
attem
p
ti
n
g
d
if
f
er
en
t
m
eth
o
d
s
.
Pu
r
n
o
m
o
et
a
l
.
[
4
5
]
ass
er
ted
th
at
th
e
r
ep
ea
ted
ch
ec
k
in
g
o
f
an
s
wer
s
b
ef
o
r
e
r
ea
ch
in
g
a
co
n
clu
s
io
n
was
a
ch
ar
ac
ter
is
ti
c
o
f
m
etac
o
g
n
itiv
e
r
eg
u
latio
n
ac
tiv
ities
.
Me
taco
g
n
itiv
e
r
eg
u
latio
n
r
ef
e
r
s
to
th
e
m
en
tal
ac
tiv
ities
u
s
ed
in
m
an
ag
in
g
c
o
g
n
itiv
e
s
tr
ateg
ies
in
p
r
o
b
lem
-
s
o
lv
in
g
[
4
6
]
.
T
h
is
is
s
p
ec
if
ically
n
o
ted
wh
en
p
ar
ticip
a
n
ts
alter
p
r
o
b
le
m
-
s
o
lv
in
g
m
eth
o
d
,
wh
ile
r
ec
o
r
d
in
g
th
is
alter
atio
n
o
n
th
e
wo
r
k
s
h
ee
t in
clu
d
es c
o
g
n
itiv
e
ac
tiv
ities
.
T
h
e
r
esu
lts
s
h
o
wed
th
at
m
eta
co
g
n
itiv
e
e
v
alu
atio
n
o
cc
u
r
r
ed
wh
en
s
tu
d
en
ts
ju
d
g
e
th
eir
an
s
wer
s
to
b
e
co
r
r
ec
t
af
ter
r
e
p
ea
ted
ch
ec
k
i
n
g
.
T
h
is
was
co
n
s
is
ten
t
with
Ma
g
ier
a
an
d
Z
awo
jewsk
i
[
4
7
]
,
s
u
g
g
esti
n
g
th
a
t
r
ep
etitiv
e
ch
ec
k
s
b
e
f
o
r
e
m
a
k
in
g
ju
d
g
m
en
ts
r
e
f
lecte
d
m
e
taco
g
n
itiv
e
ev
al
u
atio
n
.
I
t
ca
n
also
o
cc
u
r
wh
en
ju
d
g
em
en
ts
ar
e
m
ad
e
ab
o
u
t th
e
ef
f
ec
tiv
en
ess
o
f
co
g
n
itio
n
o
r
s
tr
ateg
y
u
s
ed
[
5
]
,
[
1
2
]
.
B
ased
o
n
th
e
ex
p
lan
atio
n
a
b
o
v
e,
s
tu
d
e
n
ts
en
g
ag
ed
i
n
m
etac
o
g
n
itiv
e
ac
tiv
ities
in
th
e
f
o
r
m
s
o
f
awa
r
en
ess
,
ev
alu
atio
n
an
d
r
eg
u
latio
n
wh
e
n
s
o
lv
in
g
co
n
t
ex
tu
al
m
ath
p
r
o
b
lem
.
Me
tac
o
g
n
itio
n
p
lay
s
an
im
p
o
r
tan
t
r
o
le
in
i
n
f
lu
en
cin
g
th
e
ab
ilit
y
t
o
s
o
lv
e
p
r
o
b
lem
,
h
en
ce
s
tu
d
e
n
ts
wh
o
a
r
e
awa
r
e
o
f
th
ei
r
m
etac
o
g
n
itio
n
ten
d
t
o
u
s
e
ef
f
e
ctiv
e
s
tr
ateg
ies
[
1
]
,
[
9
]
,
[
1
0
]
,
[
1
2
]
.
I
t
is
also
r
elate
d
to
th
e
a
b
ilit
y
o
f
s
tu
d
en
ts
to
o
r
g
an
ize
o
r
ev
alu
ate
th
o
u
g
h
ts
,
s
in
ce
th
ey
ca
n
co
n
tr
o
l
in
f
o
r
m
atio
n
p
r
o
ce
s
s
in
g
[
4
]
,
[
5
]
,
[
7
]
.
T
h
e
in
co
r
p
o
r
ati
o
n
o
f
m
etac
o
g
n
itiv
e
ac
tiv
ities
in
to
co
n
tex
tu
al
m
ath
em
atica
l
p
r
o
b
lem
s
o
lv
in
g
ca
n
aid
in
id
en
tif
y
in
g
a
n
d
r
ec
tify
in
g
p
r
o
b
lem
[
2
9
]
,
[
3
0
]
,
[
3
3
]
.
I
n
a
d
d
itio
n
,
th
e
in
teg
r
atio
n
o
f
m
at
h
em
atica
l
p
r
o
b
lem
-
s
o
lv
in
g
wi
th
th
e
en
v
ir
o
n
m
en
t
ca
n
en
h
an
ce
m
etac
o
g
n
itio
n
a
s
well
as
th
e
awa
r
en
ess
o
f
en
v
ir
o
n
m
en
tal
is
s
u
es
[
2
3
]
.
Me
taco
g
n
itiv
e
-
b
ase
d
co
n
tex
tu
al
lear
n
in
g
t
y
p
ically
i
m
p
r
o
v
es
p
r
o
b
lem
-
s
o
lv
in
g
an
d
m
ath
em
atica
l
co
m
m
u
n
icatio
n
s
k
ills
,
m
ak
in
g
it
a
r
ec
o
m
m
en
d
ed
m
eth
o
d
f
o
r
teac
h
in
g
m
ath
e
m
atica
l
[
1
8
]
.
4.
CO
NCLU
SI
O
N
I
n
co
n
cl
u
s
io
n
,
m
etac
o
g
n
itiv
e
ac
tiv
ities
ex
p
er
ien
ce
d
b
y
p
ar
ticip
an
ts
in
s
o
lv
i
n
g
co
n
tex
tu
al
m
ath
em
atica
l
p
r
o
b
lem
i
n
clu
d
ed
m
etac
o
g
n
itiv
e
awa
r
e
n
ess
,
ev
alu
atio
n
,
an
d
r
eg
u
latio
n
.
T
h
ese
th
r
ee
ac
tiv
ities
o
cc
u
r
r
e
d
alter
n
ately
with
v
ar
y
in
g
f
r
eq
u
en
cies.
T
h
e
r
esu
lts
s
h
o
wed
th
at
m
etac
o
g
n
itiv
e
p
r
o
ce
s
s
en
co
u
r
ag
e
d
s
tu
d
en
ts
to
en
g
ag
e
m
o
r
e
f
r
eq
u
en
tly
in
ev
alu
atin
g
p
r
o
b
lem
-
s
o
lv
in
g
p
r
o
ce
s
s
es.
T
h
is
in
d
icate
d
th
e
im
p
o
r
tan
ce
o
f
tr
ain
in
g
s
tu
d
en
ts
to
u
s
e
m
etac
o
g
n
itio
n
wh
en
s
o
lv
in
g
m
ath
e
m
atica
l p
r
o
b
lem
.
Fo
llo
win
g
th
e
c
o
n
clu
s
io
n
s
,
s
ev
er
al
r
ec
o
m
m
e
n
d
atio
n
s
we
r
e
p
r
o
p
o
s
ed
to
b
e
n
ef
it
ed
u
c
ato
r
s
an
d
ed
u
ca
tio
n
al
p
r
ac
titi
o
n
er
s
.
First
ly
,
th
e
i
n
co
r
p
o
r
atio
n
o
f
m
etac
o
g
n
itiv
e
ac
tiv
ities
in
p
r
o
b
lem
-
s
o
lv
in
g
was
cr
u
cial
as
it
in
s
till
ed
a
h
ab
it
o
f
ef
f
ec
tiv
ely
en
g
ag
in
g
an
d
m
an
a
g
in
g
k
n
o
wled
g
e.
Seco
n
d
ly
,
s
tu
d
en
t
s
wh
o
wer
e
ad
ep
t
at
m
etac
o
g
n
itio
n
d
ev
elo
p
e
d
th
in
k
in
g
p
atter
n
s
th
at
wer
e
m
o
r
e
c
r
itical,
ac
tiv
e,
cr
ea
tiv
e,
an
d
w
ell
-
co
n
tr
o
lled
wh
e
n
en
co
u
n
ter
i
n
g
p
r
o
b
lem
.
T
h
i
r
d
l
y
,
th
e
awa
r
e
n
ess
o
f
m
etac
o
g
n
itio
n
en
h
a
n
ce
d
p
r
o
b
lem
-
s
o
lv
i
n
g
s
k
ills
.
Fo
u
r
th
ly
,
th
e
d
ev
el
o
p
m
en
t
o
r
ad
ap
tatio
n
o
f
m
ath
em
atica
l
p
r
o
b
lem
in
t
o
co
n
te
x
tu
al
f
o
r
m
s
was
n
ec
es
s
ar
y
to
elev
ate
b
o
t
h
m
ath
em
atica
l p
r
o
b
lem
-
s
o
lv
in
g
ab
ilit
ies an
d
m
etac
o
g
n
itio
n
.
RE
F
E
R
E
NC
E
S
[
1
]
M
.
A
n
g
g
o
,
S
u
h
a
r
,
a
n
d
Y
.
E.
Y
.
K
a
n
s
i
l
,
“
S
t
u
d
e
n
t
’
s
M
e
t
a
c
o
g
n
i
t
i
v
e
A
c
t
i
v
i
t
i
e
s
i
n
S
o
l
v
i
n
g
M
a
t
h
e
m
a
t
i
c
s Pr
o
b
l
e
ms
,
”
i
n
Pro
c
e
e
d
i
n
g
s o
f
t
h
e
1
s
t
I
n
t
e
r
n
a
t
i
o
n
a
l
C
o
n
f
e
re
n
c
e
o
n
Ad
v
a
n
c
e
d
Mu
l
t
i
d
i
s
c
i
p
l
i
n
a
ry
Re
s
e
a
r
c
h
(
I
C
AM
R
2
0
1
8
)
,
2
0
1
9
,
v
o
l
.
2
2
7
,
p
p
.
1
6
–
2
0
,
d
o
i
:
1
0
.
2
9
9
1
/
i
c
a
mr
-
1
8
.
2
0
1
9
.
5
.
[
2
]
Y
.
W
a
n
g
g
u
w
a
y
,
S
l
a
m
i
n
,
D
a
f
i
k
,
I
.
N
.
M
a
y
l
i
sa
,
a
n
d
S
.
K
u
r
n
i
a
w
a
t
i
,
“
Th
e
a
n
a
l
y
s
i
s
o
f
r
e
se
a
r
c
h
-
b
a
se
d
l
e
a
r
n
i
n
g
i
m
p
l
e
men
t
a
t
i
o
n
a
n
d
i
t
s
a
f
f
e
c
t
t
o
t
h
e
st
u
d
e
n
t
s’
me
t
a
c
o
g
n
i
t
i
o
n
sk
i
l
l
i
n
s
o
l
v
i
n
g
a
r
e
s
o
l
v
i
n
g
d
o
m
i
n
a
t
i
o
n
n
u
m
b
e
r
o
f
a
g
r
a
p
h
,
”
J
o
u
r
n
a
l
o
f
P
h
y
si
c
s:
C
o
n
f
e
re
n
c
e
S
e
r
i
e
s
,
v
o
l
.
1
5
3
8
,
p
.
0
1
2
0
8
7
,
2
0
2
0
,
d
o
i
:
1
0
.
1
0
8
8
/
1
7
4
2
-
6
5
9
6
/
1
5
3
8
/
1
/
0
1
2
0
8
7
.
[
3
]
K
.
V
o
r
h
ö
l
t
e
r
,
A
.
K
r
ü
g
e
r
,
a
n
d
L
.
W
e
n
d
t
,
“
M
e
t
a
c
o
g
n
i
t
i
o
n
i
n
M
a
t
h
e
m
a
t
i
c
a
l
M
o
d
e
l
i
n
g
–
A
n
O
v
e
r
v
i
e
w
,
”
i
n
Af
f
e
c
t
i
n
M
a
t
h
e
m
a
t
i
c
a
l
Mo
d
e
l
i
n
g
,
A
d
v
a
n
c
e
s
i
n
M
a
t
h
e
m
a
t
i
c
s
Ed
u
c
a
t
i
o
n
,
S
.
A
.
C
h
a
m
b
e
r
l
i
n
a
n
d
B
.
S
r
i
r
a
ma
n
,
Ed
s
.
S
p
r
i
n
g
e
r
N
a
t
u
r
e
S
w
i
t
z
e
r
l
a
n
d
A
G
,
2
0
1
9
,
p
p
.
2
9
–
5
1
,
d
o
i
:
1
0
.
1
0
0
7
/
9
7
8
-
3
-
030
-
0
4
4
3
2
-
9_3
.
[
4
]
M
.
H
a
sse
l
h
o
r
n
a
n
d
A
.
S
.
La
b
u
h
n
,
“
M
e
t
a
c
o
g
n
i
t
i
o
n
a
n
d
S
e
l
f
-
r
e
g
u
l
a
t
e
d
L
e
a
r
n
i
n
g
,
”
i
n
E
n
c
y
c
l
o
p
e
d
i
a
o
f
A
d
o
l
e
s
c
e
n
c
e
,
B
.
B
.
B
r
o
w
n
a
n
d
M
.
J.
P
r
i
n
s
t
e
i
n
,
E
d
s.
El
s
e
v
i
e
r
I
n
c
.
,
2
0
1
1
,
p
p
.
2
2
3
–
2
3
0
,
d
o
i
:
1
0
.
1
0
1
6
/
B
9
7
8
-
0
-
12
-
3
7
3
9
5
1
-
3
.
0
0
0
2
6
-
0
.
[
5
]
D
.
H
o
l
t
o
n
a
n
d
D
.
C
l
a
r
k
e
,
“
S
c
a
f
f
o
l
d
i
n
g
a
n
d
me
t
a
c
o
g
n
i
t
i
o
n
,
”
I
n
t
e
r
n
a
t
i
o
n
a
l
J
o
u
rn
a
l
o
f
Ma
t
h
e
m
a
t
i
c
a
l
Ed
u
c
a
t
i
o
n
i
n
S
c
i
e
n
c
e
a
n
d
T
e
c
h
n
o
l
o
g
y
,
v
o
l
.
3
7
,
n
o
.
2
,
p
p
.
1
2
7
–
1
4
3
,
2
0
0
6
,
d
o
i
:
1
0
.
1
0
8
0
/
0
0
2
0
7
3
9
0
5
0
0
2
8
5
8
1
8
.
[
6
]
A
.
T
o
u
r
v
a
,
G
.
S
p
a
n
o
u
d
i
s,
a
n
d
A
.
D
e
met
r
i
o
u
,
“
C
o
g
n
i
t
i
v
e
c
o
r
r
e
l
a
t
e
s
o
f
d
e
v
e
l
o
p
i
n
g
i
n
t
e
l
l
i
g
e
n
c
e
:
T
h
e
c
o
n
t
r
i
b
u
t
i
o
n
o
f
w
o
r
k
i
n
g
memo
r
y
,
p
r
o
c
e
s
si
n
g
sp
e
e
d
a
n
d
a
t
t
e
n
t
i
o
n
,
”
I
n
t
e
l
l
i
g
e
n
c
e
,
v
o
l
.
5
4
,
p
p
.
1
3
6
–
1
4
6
,
2
0
1
6
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
i
n
t
e
l
l
.
2
0
1
5
.
1
2
.
0
0
1
.
[
7
]
R
.
T
.
W
a
r
d
a
n
d
D
.
L.
B
u
t
l
e
r
,
“
A
n
I
n
v
e
s
t
i
g
a
t
i
o
n
o
f
M
e
t
a
c
o
g
n
i
t
i
v
e
A
w
a
r
e
n
e
ss
a
n
d
A
c
a
d
e
m
i
c
P
e
r
f
o
r
ma
n
c
e
i
n
C
o
l
l
e
g
e
F
r
e
sh
me
n
,
”
Ed
u
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