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s.
K
ey
w
o
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s
:
Ap
p
r
ec
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n
o
f
m
ath
em
atics
E
m
o
tio
n
al
in
tellig
en
ce
m
an
ag
em
en
t
E
m
o
tio
n
al
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e
g
u
latio
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E
m
o
tio
n
s
L
o
v
e
o
f
m
ath
em
atics
T
ea
ch
in
g
s
tr
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T
h
is i
s
a
n
o
p
e
n
a
c
c
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ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
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n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Nelso
n
C
ésar
San
tis
teb
an
Sala
za
r
Gr
ad
u
ate
Sch
o
o
l,
Un
iv
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s
id
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C
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Vallejo
L
im
a,
Per
u
E
m
ail: n
s
an
tis
teb
an
s
@
u
cv
v
ir
tu
al.
ed
u
.
p
e
1.
I
NT
RO
D
UCT
I
O
N
I
t
is
esti
m
ated
th
at
in
E
u
r
o
p
ea
n
,
Am
er
ica
n
,
a
n
d
Au
s
tr
alian
c
o
u
n
tr
ies,
2
0
%
o
f
th
e
s
tu
d
en
t
p
o
p
u
latio
n
lack
s
m
ath
em
atica
l
s
k
ills
,
b
ec
au
s
e
it
is
co
n
s
id
er
ed
a
d
if
f
i
cu
lt
[
1
]
a
n
d
b
o
r
in
g
s
u
b
ject
w
ith
litt
le
u
tili
ty
[
2
]
.
T
h
ese
p
er
ce
p
tio
n
s
ar
e
u
s
u
ally
th
e
r
esu
lt
o
f
b
elief
s
o
b
tain
ed
at
s
ch
o
o
l
o
r
f
a
m
ily
[
1
]
,
in
f
lu
en
ce
d
b
y
n
eg
ativ
e
em
o
tio
n
s
to
war
d
s
m
ath
em
atics
[
3
]
an
d
th
e
s
tr
ict
an
d
au
th
o
r
itar
ian
way
in
wh
ich
th
e
teac
h
er
teac
h
es
th
e
s
u
b
ject
[
4
]
,
b
r
i
n
g
in
g
as
co
n
s
eq
u
en
ce
s
an
in
cr
ea
s
e
in
ab
s
e
n
teeism
,
d
r
o
p
p
i
n
g
o
u
t
o
f
s
ch
o
o
l
an
d
ch
a
n
g
in
g
ca
r
ee
r
s
in
h
ig
h
er
e
d
u
ca
tio
n
[
5
]
.
Ho
we
v
er
,
r
esear
ch
in
m
ath
em
atics
ed
u
ca
tio
n
h
as
f
o
c
u
s
ed
o
n
co
g
n
itiv
e
f
ac
to
r
s
,
wh
ile
af
f
ec
tiv
e
f
ac
to
r
s
(
s
tu
d
en
ts
’
s
elf
-
b
elief
s
,
attitu
d
es a
n
d
em
o
tio
n
s
in
m
ath
em
ati
cs)
ar
e
ig
n
o
r
ed
[
6
]
.
E
m
o
tio
n
is
d
ef
in
ed
as
a
co
m
p
lex
f
ee
lin
g
th
at
r
esu
lts
in
p
h
y
s
ical
an
d
p
s
y
ch
o
lo
g
ical
c
h
an
g
es
th
at
af
f
ec
t
th
in
k
in
g
an
d
b
e
h
av
io
r
an
d
h
av
e
s
ig
n
if
ican
t
i
n
f
lu
en
c
e
o
n
lear
n
in
g
[
7
]
.
E
m
o
tio
n
s
th
at
ar
e
r
elate
d
t
o
k
n
o
wled
g
e
ac
q
u
is
itio
n
ar
e
d
e
f
in
ed
as
ep
is
tem
ic
em
o
tio
n
s
,
wh
er
ea
s
em
o
tio
n
s
th
at
a
r
e
r
elate
d
to
ac
ad
em
ic
s
u
cc
ess
o
r
f
ailu
r
e
ar
e
d
ef
in
e
d
as
ac
h
iev
em
en
t
o
r
ac
a
d
em
ic
em
o
tio
n
s
[
8
]
.
E
p
is
tem
ic
em
o
tio
n
s
ca
n
b
e
b
o
th
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
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2
2
E
ffect
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f le
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in
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tered
o
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emo
tio
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a
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ma
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th
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…
(
Wil
mer E
n
r
iq
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e
V
id
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r
r
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Ga
r
cía
)
3117
p
o
s
itiv
e
(
jo
y
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h
ap
p
i
n
ess
,
ex
citem
en
t,
cu
r
io
s
ity
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an
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est)
an
d
n
e
g
ativ
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f
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ir
r
itatio
n
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d
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is
s
atis
f
ac
tio
n
)
an
d
ac
h
iev
em
en
t
em
o
tio
n
s
ca
n
also
b
e
p
o
s
itiv
e
(
r
elief
,
p
r
id
e,
jo
y
,
o
p
tim
is
m
,
en
jo
y
m
e
n
t,
an
d
r
elax
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n
)
an
d
n
eg
ativ
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(
em
b
ar
r
ass
m
en
t,
d
esp
air
,
an
g
er
,
an
d
an
x
iety
)
[
9
]
.
Po
s
itiv
e
em
o
tio
n
s
ac
tiv
ate
in
s
tu
d
en
ts
lear
n
in
g
to
war
d
s
k
n
o
wled
g
e
ac
q
u
is
itio
n
,
w
h
er
ea
s
n
eg
ativ
e
em
o
tio
n
s
ar
e
d
etr
i
m
en
tal
to
ac
ad
em
i
c
p
er
f
o
r
m
an
ce
[
8
]
.
I
n
t
h
at
s
en
s
e,
em
o
tio
n
s
ar
e
im
p
o
r
tan
t
in
m
ath
em
atics
ed
u
ca
tio
n
,
as
s
tu
d
e
n
ts
ex
p
er
ien
ce
h
i
g
h
lev
els o
f
b
o
th
n
eg
ativ
e
a
n
d
p
o
s
itiv
e
em
o
tio
n
s
[
1
0
]
.
Ho
wev
er
,
it
is
n
ec
es
s
ar
y
to
d
esig
n
ef
f
ec
tiv
e
ed
u
ca
tio
n
al
p
r
ac
tices
th
at
f
o
s
ter
p
o
s
itiv
e
em
o
tio
n
s
to
war
d
s
m
ath
em
atics.
Sev
er
a
l
s
tu
d
ies
s
h
o
w
th
at
u
s
in
g
r
ea
l
-
life
s
ce
n
ar
io
s
in
m
at
h
em
atics
teac
h
in
g
ca
n
im
p
r
o
v
e
s
tu
d
en
ts
'
ap
p
r
ec
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n
o
f
th
e
s
u
b
ject
[
1
1
]
–
[
1
3
]
.
I
n
th
is
asp
ec
t,
Als
in
a
[
1
1
]
p
r
o
p
o
s
es
th
e
ac
tiv
atio
n
o
f
p
o
s
itiv
e
em
o
tio
n
s
th
r
o
u
g
h
an
ad
eq
u
ate
m
a
n
ag
em
e
n
t
o
f
m
ath
em
atics
teac
h
in
g
in
e
v
er
y
d
ay
life
,
wh
e
r
e
th
e
s
tu
d
en
t
s
ee
s
th
e
u
s
ef
u
ln
ess
o
f
u
s
in
g
m
ath
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atics
to
ex
p
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at
is
h
ap
p
en
in
g
in
th
eir
en
v
ir
o
n
m
en
t.
W
h
ile
th
e
th
eo
r
ies
o
f
em
o
tio
n
al
in
te
llig
en
ce
[
1
4
]
a
n
d
m
u
ltip
le
in
t
ellig
en
ce
s
[
1
5
]
,
o
f
f
er
t
h
eo
r
eti
ca
l
f
r
am
ewo
r
k
s
to
d
esig
n
n
ew
m
o
d
els
o
r
p
ed
a
g
o
g
ical
a
p
p
r
o
ac
h
es
in
m
ath
e
m
atics
ed
u
ca
tio
n
to
p
er
s
o
n
al
ize
co
g
n
itiv
e
an
d
em
o
tio
n
al
lear
n
in
g
p
r
o
ce
s
s
es.
On
th
e
o
n
e
h
an
d
,
Gar
d
n
e
r
an
d
Hatc
h
[
16
]
in
h
is
th
eo
r
y
o
f
m
u
ltip
le
in
tellig
en
ce
s
ar
g
u
ed
th
at
th
er
e
is
n
o
t
o
n
l
y
o
n
e
ty
p
e
o
f
in
tellig
en
ce
,
b
u
t
th
at
th
er
e
ar
e
eig
h
t
in
tellig
en
ce
s
:
lin
g
u
is
tic,
lo
g
ical
-
m
ath
em
atica
l,
s
p
atial,
b
o
d
ily
-
k
in
esth
etic,
m
u
s
ical,
in
te
r
p
er
s
o
n
al,
in
t
r
ap
er
s
o
n
al
an
d
n
at
u
r
a
lis
tic.
On
th
e
o
th
er
h
an
d
,
Go
lem
an
[1
7
]
p
r
o
p
o
s
ed
th
e
t
h
eo
r
y
o
f
em
o
tio
n
al
i
n
tellig
en
ce
ar
g
u
in
g
th
at
we
h
av
e
to
ef
f
ec
tiv
ely
m
an
ag
e
o
u
r
em
o
tio
n
s
.
I
n
th
i
s
s
en
s
e,
h
e
r
ec
o
g
n
izes
f
iv
e
d
o
m
ain
s
co
v
er
in
g
p
er
s
o
n
al
c
o
m
p
eten
cies
(
s
elf
-
awa
r
en
ess
,
s
elf
-
r
eg
u
latio
n
,
an
d
s
elf
-
m
o
tiv
atio
n
)
a
n
d
s
o
cial
co
m
p
eten
cies
(
s
o
cial
awa
r
e
n
e
s
s
o
r
em
p
ath
y
an
d
s
o
cial
s
k
ill
s
)
[
7
]
,
wh
ich
s
h
o
u
l
d
b
e
ev
id
en
ce
d
in
th
e
d
ev
elo
p
m
en
t
o
f
class
es.
I
t
s
h
o
u
ld
b
e
n
o
ted
th
at
b
o
th
ty
p
es
o
f
th
e
o
r
ies
ar
e
r
elate
d
wh
en
r
e
f
er
r
in
g
to
in
ter
p
er
s
o
n
al
an
d
i
n
tr
ap
er
s
o
n
al
in
tellig
en
ce
[1
7
]
,
al
s
o
ass
o
ciate
d
with
s
ch
o
o
l
s
u
cc
ess
[
1
5
]
.
Similar
ly
,
lear
n
in
g
s
tr
ateg
ies
ca
n
p
r
o
m
o
te
s
tu
d
e
n
ts
'
p
o
s
itiv
e
em
o
tio
n
s
an
d
r
ed
u
ce
n
eg
ativ
e
em
o
tio
n
s
[1
8
]
.
T
h
e
r
e
f
o
r
e,
th
e
d
id
ac
tic
th
eo
r
y
o
f
Z
a
y
as
[1
9
]
is
u
s
ef
u
l
to
wo
r
k
in
a
co
m
p
lem
en
tar
y
o
r
s
y
n
er
g
is
tic
way
th
e
co
g
n
itiv
e
an
d
af
f
ec
tiv
e
d
im
en
s
io
n
s
o
f
lear
n
in
g
in
h
ig
h
er
e
d
u
ca
tio
n
.
Mo
s
t
s
tu
d
ies
h
av
e
u
s
ed
th
e
d
if
f
er
e
n
t
th
eo
r
ies
a
n
d
m
eth
o
d
s
o
f
teac
h
in
g
a
n
d
lear
n
in
g
in
d
i
v
id
u
ally
o
r
in
co
m
b
in
atio
n
wh
e
n
ap
p
r
o
p
r
iate,
to
p
r
o
m
o
te
p
o
s
itiv
e
lear
n
in
g
ex
p
er
ien
ce
s
in
m
a
th
em
atics.
Ho
wev
er
,
th
e
r
e
ar
e
lim
ited
s
tu
d
ies
th
at
f
o
cu
s
o
n
in
teg
r
atin
g
th
eo
r
ies
o
f
in
tellig
en
ce
al
o
n
g
with
co
n
c
r
ete
lear
n
in
g
ap
p
r
o
ac
h
es
to
e
n
h
an
ce
m
at
h
em
atics
ap
p
r
ec
iatio
n
at
th
e
co
lleg
e
le
v
el,
h
ig
h
li
g
h
tin
g
t
h
e
n
ee
d
f
o
r
r
esear
ch
s
u
ch
as
th
e
p
r
esen
t
o
n
e
aim
ed
at
f
illi
n
g
th
is
g
ap
in
s
tu
d
en
ts
'
m
ath
em
atica
l le
ar
n
in
g
.
T
h
er
ef
o
r
e,
in
th
is
s
tu
d
y
we
s
ee
k
to
d
eter
m
in
e
th
e
ef
f
ec
t
o
f
a
lear
n
in
g
p
r
o
g
r
am
f
o
cu
s
ed
o
n
em
o
tio
n
al
m
an
ag
em
en
t
o
n
th
e
lev
el
o
f
ap
p
r
ec
iatio
n
to
war
d
m
ath
em
a
tics
in
co
lleg
e
s
tu
d
en
ts
an
d
p
o
s
e
th
e
f
o
llo
win
g
q
u
esti
o
n
:
wh
at
is
th
e
ef
f
ec
t
o
f
a
lear
n
in
g
p
r
o
g
r
am
f
o
cu
s
ed
o
n
em
o
tio
n
m
an
a
g
em
en
t
o
n
a
p
p
r
ec
iatio
n
to
wa
r
d
m
ath
em
atics
in
co
lleg
e
s
tu
d
e
n
ts
?
W
e
test
a
p
r
o
g
r
am
th
at
o
f
f
er
s
an
i
n
teg
r
ated
lea
r
n
in
g
f
r
am
ewo
r
k
b
ased
o
n
th
e
th
eo
r
ies
o
f
em
o
tio
n
al
in
tellig
en
ce
an
d
m
u
ltip
le
in
tellig
en
ce
s
,
d
id
ac
tic
ap
p
r
o
ac
h
es
to
ed
u
ca
tio
n
an
d
lear
n
in
g
e
x
p
er
ie
n
ce
s
at
th
e
u
n
iv
er
s
ity
lev
el,
wh
ich
p
r
o
v
id
e
a
b
r
o
ad
e
r
co
v
er
ag
e
o
f
th
e
co
g
n
itiv
e
an
d
non
-
c
o
g
n
itiv
e
asp
ec
ts
o
f
lear
n
in
g
ap
p
licab
le
to
th
e
co
n
te
x
t
o
f
m
ath
em
atics
ed
u
ca
tio
n
am
o
n
g
s
tu
d
en
ts
in
th
e
f
ir
s
t
cy
cles
o
f
p
s
y
ch
o
lo
g
y
,
in
it
ial
an
d
p
r
im
ar
y
e
d
u
ca
tio
n
at
a
p
r
iv
ate
u
n
iv
er
s
ity
i
n
n
o
r
th
ea
s
t
er
n
Per
u
.
W
ith
th
is
s
tu
d
y
we
s
ee
k
to
co
n
tr
ib
u
te
to
th
e
im
p
r
o
v
e
m
en
t
o
f
teac
h
in
g
p
r
ac
tice
b
y
p
r
o
p
o
s
in
g
an
d
ex
am
in
in
g
th
e
ef
f
ec
tiv
en
ess
o
f
a
th
eo
r
etica
l
teac
h
in
g
m
o
d
el
to
p
r
o
m
o
te
a
p
o
s
itiv
e
ef
f
ec
t
o
n
th
e
attitu
d
e
o
f
s
tu
d
en
ts
to
war
d
s
m
ath
em
atics to
im
p
r
o
v
e
th
eir
ac
ad
em
ic
p
er
f
o
r
m
an
ce
.
2.
M
E
T
H
O
D
2
.
1
.
P
r
o
g
ra
m
des
ig
n
Sin
ce
a
m
o
d
el
im
p
lies
th
e
a
d
ap
tatio
n
o
f
a
g
en
er
al
t
h
eo
r
y
t
o
a
s
p
ec
if
ic
c
o
n
tex
t,
th
is
s
tu
d
y
b
u
ilt
a
p
r
o
g
r
a
m
th
at
is
b
ased
o
n
t
h
e
d
id
ac
tic
th
eo
r
y
-
teac
h
in
g
-
l
ea
r
n
in
g
p
r
o
ce
s
s
o
f
Z
ay
as
[1
9
]
,
th
e
e
m
o
tio
n
al
in
tellig
en
ce
th
eo
r
y
o
f
Go
lem
an
[1
7
]
,
t
h
e
m
u
ltip
le
in
tellig
e
n
ce
s
th
eo
r
y
o
f
Gar
d
n
e
r
an
d
Hatc
h
[
16
]
an
d
th
e
u
n
iv
er
s
ity
ed
u
ca
tio
n
al
ex
p
er
i
en
ce
s
o
f
Als
in
a
[
1
1
]
,
wh
ich
attem
p
ts
to
b
r
in
g
to
g
eth
e
r
th
e
co
g
n
itiv
e
an
d
af
f
ec
tiv
e
d
im
e
n
s
io
n
s
o
f
lear
n
in
g
,
o
f
ten
co
n
s
id
er
e
d
s
ep
ar
atel
y
.
T
h
e
p
r
o
g
r
a
m
in
te
g
r
ates
d
id
ac
tic
s
tr
ateg
ies
s
u
ch
as
co
llab
o
r
ativ
e
wo
r
k
,
s
o
cial
n
etwo
r
k
s
,
m
o
b
ile
m
ath
em
atic
s
ap
p
licatio
n
s
an
d
m
u
ltime
d
i
a
p
r
esen
tatio
n
s
.
I
n
ad
d
itio
n
,
it
f
o
cu
s
es
o
n
cr
u
ci
al
em
o
tio
n
al
asp
ec
ts
s
u
ch
as
m
o
tiv
atio
n
,
s
elf
-
r
eg
u
latio
n
,
s
o
cial
s
k
ill
s
an
d
co
g
n
itiv
e
f
lex
i
b
ilit
y
.
I
n
th
e
s
p
ec
if
ic
f
ield
o
f
m
ath
e
m
atics
teac
h
in
g
,
a
m
eth
o
d
o
lo
g
y
f
o
cu
s
ed
o
n
teac
h
i
n
g
with
lo
v
e
an
d
jo
y
is
p
r
o
m
o
ted
,
in
c
o
r
p
o
r
atin
g
e
m
o
tio
n
al
r
ewa
r
d
s
s
u
ch
as
p
o
s
itiv
e
g
estu
r
es
an
d
ac
tio
n
s
b
y
t
h
e
teac
h
er
,
in
wh
ic
h
h
is
r
o
le
is
to
ac
t
as
a
f
ac
ilit
ato
r
an
d
e
x
tr
in
s
ic
m
o
tiv
ato
r
,
f
o
s
ter
in
g
a
p
o
s
itiv
e
an
d
s
tim
u
latin
g
ed
u
ca
tio
n
al
en
v
ir
o
n
m
en
t.
T
h
er
ef
o
r
e,
th
is
p
r
o
g
r
a
m
aim
s
to
d
e
v
elo
p
m
at
h
em
atica
l
co
m
p
eten
cies
f
o
r
p
r
ac
tical
an
d
wo
r
k
i
n
g
life
,
ac
tiv
atin
g
p
o
s
itiv
e
em
o
tio
n
s
in
s
tu
d
e
n
t
lear
n
in
g
an
d
f
u
tu
r
e
p
r
o
f
ess
io
n
al
an
d
d
o
es
n
o
t
p
r
iv
ileg
e
o
n
e
o
v
er
th
e
o
th
e
r
,
b
u
t
i
n
s
is
ts
th
at
b
o
th
ar
e
f
u
n
d
am
e
n
tal.
T
h
e
m
ath
em
atics
teac
h
in
g
p
r
o
g
r
am
b
ased
o
n
em
o
tio
n
m
an
ag
em
en
t is sh
o
wn
in
Fig
u
r
e
1
.
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
.
4
,
Au
g
u
s
t
2025
:
3
1
1
6
-
3
1
2
4
3118
Fig
u
r
e
1
.
Gr
a
p
h
ical
s
y
n
th
esis
o
f
th
e
m
ath
e
m
atics tea
ch
in
g
p
r
o
g
r
am
2
.
2
.
Study
des
ig
n a
nd
pa
rt
icipa
nts
Qu
asi
-
ex
p
er
im
en
tal
s
in
g
le
-
g
r
o
u
p
s
tu
d
y
,
b
ased
o
n
co
n
v
en
ien
ce
s
am
p
lin
g
,
in
1
0
8
s
tu
d
e
n
ts
en
r
o
lled
in
th
e
co
u
r
s
e
o
f
lo
g
ical
th
i
n
k
in
g
in
th
e
f
ir
s
t
ac
ad
em
ic
s
em
ester
o
f
2
0
1
9
,
ac
co
r
d
in
g
t
o
th
e
cu
r
r
en
t
cu
r
r
ic
u
lu
m
o
f
p
r
o
f
ess
io
n
al
s
ch
o
o
ls
,
d
is
tr
ib
u
ted
in
in
itial
ed
u
ca
tio
n
wh
ic
h
co
n
s
is
ted
o
f
two
s
ec
tio
n
s
:
A
(
2
2
)
an
d
B
(
3
3
)
,
elem
en
tar
y
e
d
u
ca
tio
n
(
2
4
)
an
d
p
s
y
ch
o
l
o
g
y
(
2
9
)
i
n
a
p
r
iv
ate
u
n
iv
er
s
ity
in
th
e
L
am
b
a
y
eq
u
e
r
eg
io
n
o
f
Per
u
.
All
s
tu
d
en
ts
with
r
eg
u
lar
atten
d
an
ce
wer
e
in
cl
u
d
ed
,
wh
ich
was
v
er
if
ied
t
h
r
o
u
g
h
th
e
co
n
tr
o
l
s
h
ee
t
p
r
o
v
id
ed
b
y
th
e
teac
h
er
o
f
t
h
e
s
u
b
ject.
Par
ticip
an
ts
wh
o
f
ailed
to
atten
d
wer
e
ex
clu
d
ed
f
r
o
m
th
e
s
tu
d
y
.
2
.
3
.
I
ns
t
rum
ent
T
h
e
in
s
tr
u
m
en
t
f
o
r
m
ea
s
u
r
in
g
th
e
v
ar
ia
b
le
ap
p
r
ec
iatio
n
o
f
m
ath
em
atics
was
d
ev
elo
p
ed
b
y
t
h
e
r
esear
ch
er
s
.
T
h
is
in
s
tr
u
m
en
t
co
n
s
is
ts
o
f
a
L
ik
er
t
-
ty
p
e
q
u
esti
o
n
n
air
e
with
3
9
item
s
g
r
o
u
p
e
d
in
to
two
d
im
en
s
io
n
s
:
teac
h
er
an
d
s
u
b
ject.
C
o
n
ten
t
v
alid
ity
was
ass
es
s
ed
b
y
th
r
ee
e
x
p
er
ts
with
p
o
s
tg
r
ad
u
ate
p
r
o
f
ess
io
n
al
tr
ain
in
g
o
f
m
aster
’
s
o
r
d
o
cto
r
al
d
eg
r
ee
,
w
h
o
ev
alu
ated
ea
ch
item
b
ased
o
n
th
e
o
b
jectiv
es,
d
im
en
s
io
n
s
o
f
th
e
v
ar
iab
le,
w
o
r
d
in
g
,
clar
ity
,
co
h
er
en
ce
an
d
m
ea
s
u
r
em
en
t
s
ca
le.
T
h
e
q
u
esti
o
n
n
air
e
o
b
tain
ed
a
h
ig
h
r
eliab
ilit
y
th
r
o
u
g
h
th
e
C
r
o
n
b
ac
h
’
s
a
lp
h
a
co
e
f
f
icien
t w
ith
a
v
alu
e
o
f
0
.
9
5
.
2
.
4
.
M
et
ho
do
lo
g
y
a
pp
lied in t
he
pro
po
s
a
l
Af
ter
h
av
i
n
g
t
h
e
e
n
d
o
r
s
em
e
n
t
o
f
th
r
ee
ex
p
er
ts
,
th
e
p
r
o
g
r
a
m
was
im
p
lem
en
ted
i
n
th
e
lo
g
ic
al
th
in
k
in
g
cu
r
r
icu
lar
ex
p
e
r
ien
ce
c
o
r
r
esp
o
n
d
in
g
to
t
h
e
f
i
r
s
t
cy
cle
o
f
s
tu
d
ies,
with
th
e
p
u
r
p
o
s
e
o
f
i
m
p
r
o
v
in
g
th
e
s
tu
d
en
ts
'
lev
el
o
f
a
p
p
r
ec
iatio
n
o
f
m
ath
em
atics.
T
h
e
s
tu
d
en
ts
o
f
all
g
r
o
u
p
s
wer
e
tau
g
h
t
d
u
r
in
g
1
5
two
-
h
o
u
r
lea
r
n
in
g
s
ess
io
n
s
in
th
eir
r
esp
ec
tiv
e
class
r
o
o
m
s
o
v
er
a
4
-
m
o
n
t
h
in
ter
v
al,
tau
g
h
t b
y
a
teac
h
er
i
n
ch
ar
g
e
o
f
th
e
s
u
b
ject.
A
to
tal
o
f
12
to
p
ics
r
elate
d
to
f
u
n
d
am
en
tals
o
f
m
ath
e
m
atica
l
th
in
k
in
g
,
m
e
n
tal
o
p
e
r
atio
n
s
o
r
d
er
o
f
in
f
o
r
m
atio
n
,
lo
g
ic,
p
r
o
p
o
r
tio
n
ality
,
r
u
le
o
f
t
h
r
ee
,
p
er
ce
n
t,
g
r
ap
h
r
ea
d
in
g
,
li
n
ea
r
f
u
n
ctio
n
an
d
q
u
ad
r
atic
f
u
n
ctio
n
,
tak
e
n
f
r
o
m
th
e
co
u
r
s
e
s
y
llab
u
s
o
f
th
e
s
tu
d
y
p
r
o
g
r
am
s
,
wer
e
d
ev
elo
p
ed
.
T
h
e
m
eth
o
d
o
l
o
g
y
ap
p
lied
in
ea
ch
s
ess
io
n
wa
s
p
ec
u
liar
an
d
in
n
o
v
ativ
e
,
f
o
cu
s
ed
o
n
d
i
d
ac
tic
r
eso
u
r
ce
s
th
at
allo
w
s
tu
d
en
ts
to
ac
q
u
ir
e
n
ew
lear
n
in
g
,
as
well
as
to
id
en
tify
a
n
d
u
n
d
e
r
s
tan
d
th
eir
e
m
o
tio
n
s
in
o
r
d
er
to
ad
eq
u
ately
m
an
a
g
e
th
eir
r
ea
ctio
n
s
in
a
s
p
ec
if
ic
co
n
tex
t.
T
h
e
ap
p
licatio
n
o
f
co
llab
o
r
ativ
e
wo
r
k
in
th
e
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
E
ffect
o
f le
a
r
n
in
g
ce
n
tered
o
n
emo
tio
n
a
l
ma
n
a
g
eme
n
t o
n
th
e
…
(
Wil
mer E
n
r
iq
u
e
V
id
a
u
r
r
e
Ga
r
cía
)
3119
class
r
o
o
m
was
th
e
d
id
ac
tic
s
tr
ateg
y
th
at
allo
wed
th
e
ac
tiv
e
an
d
co
n
s
tan
t
p
ar
ticip
atio
n
o
f
th
e
s
tu
d
e
n
t,
th
e
in
ter
ac
tio
n
with
th
e
m
e
m
b
er
s
o
f
th
e
w
o
r
k
team
h
elp
ed
g
r
ea
tly
to
s
o
cialize
th
e
em
o
tio
n
s
g
en
er
ated
b
y
th
e
lear
n
in
g
o
f
m
ath
em
atics
in
a
d
d
itio
n
to
ac
q
u
ir
in
g
c
o
m
m
itm
e
n
t
to
th
eir
lear
n
i
n
g
.
E
ac
h
lear
n
in
g
s
ess
io
n
h
a
d
its
o
wn
s
tr
ateg
y
wh
er
e
th
e
teac
h
er
,
tak
in
g
in
t
o
ac
co
u
n
t
th
e
th
em
atic
co
n
ten
t
to
b
e
d
ev
elo
p
ed
,
cr
ea
tes
th
e
ap
p
r
o
p
r
iate
en
v
ir
o
n
m
en
t
a
n
d
s
elec
ts
th
e
m
o
s
t
ap
p
r
o
p
r
iate
d
id
ac
tic
r
eso
u
r
ce
.
Am
o
n
g
th
e
d
id
ac
tic
r
eso
u
r
ce
s
u
s
ed
wer
e
m
ath
e
m
atica
l
ap
p
li
ca
tio
n
s
o
n
m
o
b
ile
d
ev
ices
(
Ge
o
Geb
r
a)
,
s
o
cial
n
etwo
r
k
s
(
Face
b
o
o
k
)
,
m
ess
ag
in
g
(
W
h
atsAp
p
)
,
m
u
ltime
d
ia
m
ate
r
ial
(
s
lid
es),
am
o
n
g
o
th
er
s
.
E
m
o
tio
n
al
m
an
ag
e
m
en
t
was
ca
r
r
ied
o
u
t
th
r
o
u
g
h
s
tr
ateg
ies
b
ased
o
n
th
eo
r
etica
l
m
o
d
els
o
f
em
o
tio
n
al
in
tellig
en
ce
an
d
ed
u
ca
tio
n
al
ex
p
er
ien
ce
s
.
T
h
e
teac
h
e
r
s
o
u
g
h
t
to
g
en
e
r
ate
p
o
s
itiv
e
em
o
tio
n
s
to
war
d
s
th
e
teac
h
in
g
o
f
m
ath
em
atics
b
y
c
r
ea
tin
g
em
o
tio
n
al
s
k
ills
th
r
o
u
g
h
d
ir
ec
t
tr
ea
tm
en
t
(
ca
llin
g
th
e
s
tu
d
en
t
b
y
n
am
e
)
,
cr
ea
tin
g
a
h
ea
lth
y
clim
ate,
co
n
s
tan
t
m
o
tiv
atio
n
th
r
o
u
g
h
v
e
r
b
al
en
co
u
r
ag
em
en
t,
clar
if
icatio
n
o
r
r
eso
lu
tio
n
o
f
d
o
u
b
ts
,
co
llab
o
r
ativ
e
wo
r
k
th
at
g
en
er
ates
em
p
ath
y
a
n
d
r
esp
ec
t
am
o
n
g
s
tu
d
en
ts
.
T
h
e
p
r
o
g
r
am
was
d
ev
elo
p
ed
tak
in
g
in
t
o
ac
c
o
u
n
t
co
g
n
itiv
e
an
d
em
o
tio
n
al
asp
ec
ts
b
as
ed
o
n
th
e
d
e
v
elo
p
m
e
n
t
o
f
p
r
ac
tical
ac
tiv
ities
,
co
llab
o
r
ativ
e
wo
r
k
an
d
th
e
u
s
e
o
f
tech
n
o
lo
g
y
.
Pre
-
an
d
p
o
s
t
-
test
s
wer
e
co
n
d
u
cted
o
n
all
g
r
o
u
p
s
.
T
h
e
p
o
s
t
-
test
was
ad
m
in
is
ter
ed
to
all
g
r
o
u
p
s
af
ter
th
ey
wer
e
tau
g
h
t
th
e
co
u
r
s
e
u
s
in
g
em
o
tio
n
m
a
n
ag
em
e
n
t
to
d
eter
m
in
e
t
h
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
g
r
am
.
T
h
e
p
r
etest a
n
d
p
o
s
ttes
t q
u
esti
o
n
s
wer
e
s
im
ilar
.
2
.
5
.
St
a
t
is
t
ica
l a
na
ly
s
is
S
tatis
t
ical
an
aly
s
is
an
d
p
r
o
ce
s
s
in
g
o
f
th
e
d
ata
was
p
e
r
f
o
r
m
ed
u
s
in
g
th
e
SP
SS
v
er
s
io
n
2
5
s
tatis
tica
l
p
ac
k
ag
e.
T
h
e
n
o
r
m
ality
o
f
th
e
d
ata
was
test
ed
u
s
in
g
th
e
Sh
ap
ir
o
-
W
ilk
test
,
r
ev
ea
lin
g
th
at
th
e
d
ata
wer
e
n
o
r
m
ally
d
is
tr
ib
u
ted
.
Fre
q
u
e
n
cy
s
tatis
tics
,
p
er
ce
n
tag
es,
av
er
ag
es
an
d
s
tan
d
ar
d
d
e
v
ia
tio
n
s
wer
e
f
o
u
n
d
.
Hy
p
o
th
esis
test
in
g
was p
er
f
o
r
m
ed
u
s
in
g
th
e
s
tu
d
en
t’
s
t
-
s
tatis
tic
f
o
r
r
elate
d
s
am
p
les with
a
p
-
v
alu
e<
0
.
0
5
.
2
.
6
.
E
t
hica
l
a
s
pect
s
T
h
e
in
ter
v
en
tio
n
was
ca
r
r
ie
d
o
u
t
o
n
ce
a
p
p
r
o
v
al
to
co
n
d
u
ct
th
e
s
tu
d
y
was
o
b
tain
ed
f
r
o
m
th
e
u
n
iv
er
s
ity
.
Par
ticip
atio
n
was
i
n
v
ited
b
y
wr
itten
in
f
o
r
m
e
d
c
o
n
s
en
t,
af
ter
in
f
o
r
m
in
g
th
e
o
b
j
ec
tiv
e
o
f
th
e
s
tu
d
y
.
I
n
ad
d
itio
n
,
p
ar
ticip
an
ts
wer
e
in
f
o
r
m
e
d
th
at
n
o
id
en
tif
iab
le
d
ata
wo
u
ld
b
e
co
llect
ed
an
d
th
at
th
eir
p
ar
ticip
atio
n
was c
o
m
p
letely
v
o
lu
n
tar
y
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
3
.
1
.
Resul
t
s
Descr
ip
tiv
e
s
tatis
tics
f
o
r
d
em
o
g
r
ap
h
ic
v
ar
iab
les
ar
e
p
r
o
v
id
ed
in
T
ab
le
1
.
T
h
e
m
ea
n
ag
e
o
f
th
e
p
ar
ticip
an
ts
was
1
9
.
0
6
y
ea
r
s
(
r
an
g
e
1
6
-
4
4
)
an
d
th
e
1
6
-
23
-
y
ea
r
ag
e
g
r
o
u
p
p
r
e
d
o
m
in
ated
(
9
3
.
5
%).
Fem
ales
co
n
s
titu
ted
7
8
.
7
%
o
f
th
e
p
ar
ti
cip
an
ts
.
T
h
e
p
er
ce
n
tag
es
in
T
ab
le
2
s
h
o
w
s
o
m
e
in
ter
esti
n
g
d
ata.
So
m
e
tr
en
d
s
id
en
tifie
d
wh
en
ex
p
lo
r
in
g
th
e
f
r
eq
u
en
c
y
o
f
r
esp
o
n
s
es
to
th
e
q
u
esti
o
n
n
air
e
in
clu
d
ed
th
e
ch
o
ice
o
f
ca
r
ee
r
to
av
o
id
th
ese
s
u
b
ject
d
if
f
icu
ltie
s
in
r
em
em
b
er
in
g
r
ec
en
t
lectu
r
es,
p
er
ce
iv
ed
lack
o
f
teac
h
er
m
o
tiv
atio
n
,
lim
ited
p
ar
ticip
atio
n
in
p
r
ac
tical
ex
er
cises
,
an
d
f
r
eq
u
en
t
n
ee
d
f
o
r
h
elp
with
h
o
m
e
ac
tiv
ities
.
Deta
il
s
o
f
th
e
q
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3121
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[
1
4
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[
20
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.
Giv
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[
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[
19
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Gar
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1
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o
t
h
av
e
to
s
tu
d
y
m
at
h
em
atics.
T
h
ese
f
in
d
in
g
s
ar
e
co
n
s
is
ten
t
with
th
e
p
r
ev
io
u
s
s
tu
d
ies
[2
4
]
,
[2
5
]
.
I
t
is
im
p
o
r
tan
t
to
n
o
te
th
at
th
is
r
ef
lects
t
h
e
s
tu
d
en
ts
'
ass
e
s
s
m
en
t
o
f
th
em
s
elv
es
r
eg
ar
d
in
g
th
eir
in
ab
ilit
y
to
s
tu
d
y
m
at
h
e
m
atics,
p
r
ef
er
r
in
g
ca
r
ee
r
s
with
lo
wer
m
ath
em
atica
l
in
ten
s
ity
,
an
d
h
ig
h
lig
h
ts
th
e
n
ee
d
to
in
ter
v
en
e
in
th
e
co
n
s
tr
u
ctio
n
o
f
ac
ad
em
ic
s
elf
-
estee
m
in
g
th
is
ar
ea
.
W
e
f
o
u
n
d
th
at
3
8
.
8
%
o
f
s
tu
d
en
ts
d
o
n
o
t
f
in
d
m
ath
em
atics
f
u
n
.
T
h
is
f
in
d
in
g
is
co
n
s
is
ten
t
with
th
e
s
tu
d
y
o
f
Sch
war
tze
et
a
l
.
[2
6
]
wh
o
s
h
o
wed
a
h
ig
h
p
er
ce
n
tag
e
o
f
b
o
r
ed
o
m
in
m
at
h
em
atics
in
s
tu
d
en
ts
in
Ger
m
an
y
.
I
t
s
h
o
u
ld
b
e
n
o
ted
t
h
at
b
o
r
ed
o
m
ca
n
h
in
d
er
ac
a
d
e
m
ic
p
er
f
o
r
m
an
ce
[2
2
]
.
T
o
co
m
b
at
th
is
s
itu
atio
n
,
I
ly
as
et
a
l.
[2
7
]
r
e
v
ea
led
th
a
t
d
esig
n
in
g
lear
n
in
g
t
o
o
ls
ef
f
ec
tiv
ely
b
y
th
e
teac
h
er
,
cr
ea
t
in
g
a
f
u
n
lear
n
in
g
en
v
ir
o
n
m
en
t
allo
ws
s
tu
d
e
n
ts
to
b
e
m
o
r
e
co
n
f
id
en
t
an
d
cr
e
ativ
e
in
s
o
lv
in
g
m
at
h
em
atica
l
ex
er
cises
.
Desp
ite
th
is
,
in
th
e
p
r
esen
t
s
tu
d
y
m
o
r
e
th
an
h
alf
o
f
t
h
e
s
tu
d
en
ts
(
5
8
.
3
%)
r
ef
e
r
r
ed
th
at
lear
n
i
n
g
m
ath
e
m
atics
is
n
ec
ess
ar
y
,
wh
ich
m
ea
n
s
th
at
s
tu
d
en
ts
ar
ea
war
e
o
f
th
e
v
al
u
e
o
f
m
ath
em
atics
in
v
o
ca
tio
n
al
tr
ain
in
g
,
alth
o
u
g
h
th
ey
d
o
n
o
t
p
er
ce
iv
e
th
e
r
elev
an
ce
o
f
m
at
h
em
atics f
o
r
th
ei
r
asp
ir
in
g
ca
r
ee
r
s
[2
8
]
.
W
e
f
o
u
n
d
th
at
1
9
.
4
%
o
f
t
h
e
s
t
u
d
en
ts
h
a
d
n
o
in
ter
est
in
m
ath
em
atics.
T
h
is
h
as
b
ee
n
co
r
r
o
b
o
r
ated
i
n
an
o
th
er
s
tu
d
y
[2
9
]
,
s
o
it
ca
n
b
e
co
n
jectu
r
ed
th
at
s
tu
d
en
ts
wh
o
ar
e
less
in
ter
ested
in
m
ath
em
atics
m
ay
b
e
m
o
r
e
r
elu
ctan
t
to
p
u
t
ef
f
o
r
t
in
t
o
lear
n
in
g
it;
alt
h
o
u
g
h
t
h
e
p
r
esen
t
s
tu
d
y
d
id
n
o
t
ex
am
in
e
th
is
d
ir
e
ctly
.
C
o
n
v
er
s
ely
,
a
s
tu
d
en
t'
s
g
r
ea
ter
in
ter
est
in
m
ath
em
atics
ten
d
s
to
p
r
ed
ict
h
i
g
h
er
lev
els
o
f
atten
tio
n
,
e
n
g
a
g
em
en
t,
p
e
r
s
is
ten
ce
,
an
d
th
e
u
s
e
o
f
lear
n
in
g
s
tr
ate
g
ies
[2
8
]
.
T
h
e
r
ea
s
o
n
f
o
r
th
is
is
th
e
lac
k
o
f
teac
h
e
r
m
o
tiv
a
tio
n
to
g
et
s
tu
d
en
ts
in
ter
ested
in
ac
q
u
ir
in
g
k
n
o
wled
g
e,
wh
ich
is
co
n
f
ir
m
ed
b
y
th
e
s
u
r
v
ey
r
esu
lts
,
o
f
wh
ich
o
n
ly
2
4
.
1
%
o
f
th
e
r
esp
o
n
d
en
ts
in
d
icate
th
at
th
e
teac
h
er
m
o
tiv
ates
th
eir
s
tu
d
en
ts
in
class
es.
I
t
is
im
p
o
r
ta
n
t
th
at
s
tu
d
en
ts
ar
e
m
o
tiv
ated
an
d
p
ar
ticip
ate
in
m
ath
em
atics
class
es.
Mo
tiv
ati
o
n
ca
n
i
n
f
lu
en
ce
t
h
e
ef
f
ec
tiv
e
n
ess
o
f
lear
n
in
g
an
d
th
e
d
esire
to
co
n
tin
u
e
atten
d
in
g
class
es
an
d
d
o
in
g
h
o
m
ew
o
r
k
[
30
]
.
R
eg
ar
d
in
g
t
h
is
,
Gó
m
ez
-
C
h
ac
ó
n
et
a
l.
[
1
3
]
r
ef
er
s
th
at
f
o
r
lea
r
n
in
g
m
ath
e
m
atics
it
is
f
u
n
d
am
en
tal
to
d
e
v
elo
p
ac
tiv
ities
r
elate
d
to
r
ea
li
ty
,
th
u
s
allo
win
g
th
e
r
ein
f
o
r
ce
m
e
n
t
o
f
in
q
u
ir
y
,
aw
ak
en
in
g
in
ter
est
an
d
m
o
tiv
ati
o
n
b
y
ac
tiv
atin
g
p
o
s
itiv
e
atti
tu
d
es
in
s
tu
d
en
ts
,
wh
ich
allo
w
in
cr
ea
s
in
g
th
e
ca
p
ac
ity
f
o
r
en
j
o
y
m
e
n
t
d
u
r
in
g
m
ath
em
atics
lear
n
in
g
.
B
u
t,
in
ad
d
itio
n
,
we
ca
n
n
o
t
ig
n
o
r
e
th
e
im
p
o
r
tan
ce
o
f
teac
h
er
tr
ai
n
in
g
o
n
m
eth
o
d
o
l
o
g
ies
an
d
p
e
d
ag
o
g
ical
s
tr
ateg
ies
to
d
ev
el
o
p
e
m
o
tio
n
a
l
s
u
p
p
o
r
t in
t
h
e
teac
h
in
g
o
f
m
ath
em
atics in
s
u
ch
a
way
as to
g
en
er
ate
m
o
tiv
atio
n
an
d
in
ter
est in
s
tu
d
en
ts
.
A
lar
g
e
m
ajo
r
ity
o
f
s
tu
d
en
ts
(
4
8
.
1
%)
r
ep
o
r
te
d
r
eq
u
ir
in
g
h
el
p
with
h
o
m
ewo
r
k
ass
ig
n
m
en
ts
in
co
lleg
e
m
ath
co
u
r
s
es.
T
h
is
ca
n
ca
u
s
e
b
o
r
e
d
o
m
with
h
o
m
ew
o
r
k
a
n
d
lear
n
in
g
.
T
o
a
d
d
r
ess
th
is
p
r
o
b
lem
,
Ng
u
y
en
et
a
l
.
[3
1
]
p
r
o
p
o
s
e
to
d
ev
elo
p
a
tu
to
r
in
g
s
y
s
tem
to
s
tr
en
g
th
en
m
ath
e
m
atics
p
r
o
b
le
m
-
s
o
lv
in
g
s
k
ills
in
s
tu
d
en
ts
.
An
o
th
er
s
ig
n
if
ican
t
f
in
d
in
g
was
th
at,
ab
o
u
t
5
0
%
o
f
th
e
s
tu
d
en
ts
’
p
r
esen
ted
d
if
f
icu
lties
in
r
ec
allin
g
th
e
class
tak
en
v
er
y
r
ec
en
tly
,
as
h
as
b
ee
n
f
o
u
n
d
in
ex
is
tin
g
r
esear
ch
[3
2
]
.
Stu
d
e
n
ts
ar
e
co
n
s
id
er
ed
to
h
av
e
s
u
cc
ess
f
u
lly
lear
n
ed
wh
en
th
ey
ca
n
r
ec
all
an
d
r
e
p
h
r
ase
f
ac
ts
o
r
u
s
e
th
em
to
an
s
wer
q
u
esti
o
n
s
o
n
test
s
.
T
h
er
ef
o
r
e,
s
tu
d
en
ts
with
in
th
e
s
am
p
le
h
av
e
litt
le
u
n
d
er
s
tan
d
i
n
g
an
d
m
aster
y
o
f
m
ath
em
atic
al
co
n
ce
p
ts
.
T
h
is
was
f
o
llo
wed
b
y
th
e
ef
f
ec
ts
o
f
s
tu
d
y
tim
e
o
n
m
ath
em
atics
ac
h
iev
em
en
t.
Mo
r
e
s
p
ec
if
ically
2
0
.
4
%
o
f
s
tu
d
en
ts
in
th
is
s
tu
d
y
d
o
n
o
t d
ev
o
te
tim
e
to
s
tu
d
y
m
ath
em
atics,
wh
ich
was
also
f
o
u
n
d
in
o
th
er
s
tu
d
y
[3
3
]
.
T
h
is
co
u
ld
i
n
f
lu
en
ce
a
p
o
o
r
r
ete
n
tio
n
o
f
th
e
lear
n
ed
in
f
o
r
m
atio
n
a
n
d
th
u
s
it is
q
u
ick
ly
f
o
r
g
o
tten
.
On
th
e
o
th
er
h
an
d
,
t
h
e
f
in
d
in
g
s
also
in
d
icate
d
t
h
at
a
r
ed
u
ce
d
p
er
ce
n
ta
g
e
o
f
s
tu
d
e
n
ts
(
1
0
.
2
%)
af
f
ir
m
th
at
wh
at
th
ey
lear
n
th
ey
ap
p
ly
in
r
ea
lity
,
alth
o
u
g
h
we
co
u
ld
s
ay
th
at
th
e
p
er
ce
p
tio
n
is
lo
wer
th
an
we
ex
p
ec
ted
,
it
leav
es
n
o
d
o
u
b
t
t
h
at
th
e
co
n
ten
ts
s
ee
n
in
h
ig
h
er
ed
u
ca
tio
n
ar
e
d
ev
el
o
p
ed
in
a
d
ec
o
n
tex
tu
alize
d
way
,
with
o
u
t
an
a
p
p
licatio
n
to
ev
er
y
d
ay
life
.
Sp
ec
if
ically
,
m
ath
em
atics
is
o
r
ien
ted
to
p
r
o
b
lem
s
o
lv
i
n
g
,
th
er
ef
o
r
e,
teac
h
e
r
s
h
av
e
to
co
n
n
ec
t
m
at
h
em
atics
with
ev
er
y
d
ay
p
r
o
b
lem
s
[3
2
]
.
T
h
er
e
f
o
r
e,
we
s
h
o
u
ld
co
n
s
id
e
r
th
e
n
ee
d
to
d
esig
n
ac
tiv
ities
th
at
co
n
n
ec
t m
ath
e
m
atics with
ev
er
y
d
a
y
r
ea
lity
[
1
1
]
–
[
1
3
]
.
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
.
4
,
Au
g
u
s
t
2025
:
3
1
1
6
-
3
1
2
4
3122
Ho
wev
er
,
th
er
e
is
a
r
elativ
ely
s
ig
n
if
ican
t
p
er
ce
n
tag
e
o
f
s
tu
d
en
ts
(
3
8
%)
wh
o
th
in
k
th
ey
ca
n
im
p
r
o
v
e
in
m
ath
.
T
h
is
in
ter
esti
n
g
ly
lin
k
s
to
th
e
lo
w
p
e
r
ce
n
tag
e
o
f
s
tu
d
en
ts
(
1
1
.
1
%)
wh
o
h
av
e
a
n
eg
ativ
e
th
o
u
g
h
t
th
at
th
ey
will
f
ail
m
ath
em
atics.
S
im
ilar
to
o
th
e
r
r
esear
ch
[
5
]
,
th
ese
f
in
d
in
g
s
s
u
g
g
est
th
at
r
ely
in
g
o
n
ef
f
o
r
t
i
n
m
ath
em
atics e
x
p
lain
s
th
e
d
ev
e
lo
p
m
en
t o
f
p
o
s
itiv
e
m
ath
e
m
atica
l a
ttit
u
d
es a
b
o
u
t a
ch
iev
e
m
e
n
t.
Ho
wev
er
,
in
f
o
r
m
atio
n
o
n
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
i
n
ter
v
en
ti
o
n
is
lim
ited
,
s
in
ce
a
co
m
p
a
r
i
s
o
n
g
r
o
u
p
was
n
o
t
in
clu
d
ed
.
I
n
ad
d
itio
n
,
it
is
s
u
g
g
ested
th
at
th
e
ev
alu
atio
n
o
f
th
e
p
r
o
g
r
am
b
e
ca
r
r
ie
d
o
u
t
b
y
ex
p
a
n
d
in
g
th
e
s
ize
an
d
o
r
ig
in
o
f
th
e
s
am
p
le
in
o
r
d
er
to
o
b
tain
co
n
cl
u
s
io
n
s
th
at
ca
n
b
e
g
en
er
alize
d
to
th
e
p
o
p
u
latio
n
.
I
t
is
s
u
g
g
ested
th
at
lo
n
g
itu
d
in
al
s
t
u
d
ies
b
e
d
e
v
elo
p
ed
in
o
r
d
er
to
m
ea
s
u
r
e
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
g
r
a
m
o
v
er
tim
e
an
d
in
d
if
f
er
e
n
t
ed
u
ca
tio
n
al
co
n
tex
ts
,
s
o
th
at
it
ca
n
b
e
v
alid
ated
an
d
also
r
ea
d
ju
s
ted
to
th
e
in
d
iv
id
u
al
n
ee
d
s
o
f
th
e
s
tu
d
en
ts
.
I
n
ad
d
it
io
n
,
th
e
u
s
e
o
f
th
is
ap
p
r
o
ac
h
s
h
o
u
ld
b
e
co
n
s
id
er
ed
in
o
th
e
r
p
r
o
f
ess
io
n
al
ca
r
ee
r
s
th
at
p
r
esen
t e
m
o
tio
n
al
ch
allen
g
es to
s
tu
d
en
ts
,
s
u
ch
as scien
ce
.
4.
CO
NCLU
SI
O
N
T
h
e
s
tu
d
y
d
em
o
n
s
tr
ates
th
e
d
esira
b
ilit
y
o
f
in
c
o
r
p
o
r
atin
g
lea
r
n
in
g
p
r
o
g
r
am
s
f
o
cu
s
ed
o
n
t
h
e
ab
ilit
y
to
m
an
ag
e
th
e
e
m
o
tio
n
s
o
f
u
n
iv
er
s
ity
s
tu
d
en
ts
th
at
ca
n
b
e
i
n
teg
r
ated
in
to
m
ath
em
atics
co
u
r
s
es,
to
b
e
tau
g
h
t
in
th
e
cu
r
r
ic
u
lu
m
u
s
in
g
a
p
ed
a
g
o
g
ical
ap
p
r
o
ac
h
o
f
co
m
p
ete
n
cies.
T
h
er
ef
o
r
e,
th
ey
s
h
o
u
ld
b
e
ap
p
lied
b
y
teac
h
e
r
s
o
n
th
e
b
asis
o
f
th
e
th
e
o
r
ies
o
f
b
o
th
em
o
tio
n
al
in
tellig
en
ce
a
n
d
m
u
ltip
le
in
tellig
en
ce
s
as
w
ell
as
d
id
ac
tics
an
d
lear
n
in
g
ex
p
er
ien
ce
s
at
th
e
u
n
iv
er
s
ity
lev
el.
I
n
t
h
is
way
,
it
is
p
o
s
s
ib
le
to
co
n
tr
ib
u
te
to
cr
ea
te
m
ea
n
in
g
f
u
l
,
co
m
p
r
eh
e
n
s
iv
e
an
d
s
u
s
tain
ab
l
e
lear
n
in
g
en
v
ir
o
n
m
e
n
ts
,
wh
er
e
m
ath
em
atics
is
p
er
ce
iv
ed
as
a
r
elev
an
t
to
o
l
f
o
r
b
o
th
ac
ad
e
m
ic
tr
ain
in
g
an
d
p
r
o
f
ess
io
n
al
life
.
T
h
e
p
r
ac
tical
im
p
licatio
n
s
th
a
t
ca
n
b
e
d
r
awn
f
r
o
m
th
is
s
tu
d
y
ar
e
th
at
u
n
iv
er
s
ity
in
s
titu
tio
n
s
s
h
o
u
ld
im
p
lem
en
t
tr
ain
i
n
g
w
o
r
k
s
h
o
p
s
o
n
em
o
tio
n
m
an
ag
e
m
en
t,
p
r
o
v
id
in
g
to
o
ls
a
n
d
s
tr
ateg
ies
th
at
co
n
tr
ib
u
te
to
th
e
cr
ea
tio
n
o
f
a
v
er
y
f
av
o
r
ab
le
l
ea
r
n
in
g
en
v
i
r
o
n
m
e
n
t.
I
t
is
als
o
ess
en
tial
to
in
co
r
p
o
r
ate
d
if
f
er
en
t
ac
tiv
ities
th
a
t
co
n
n
ec
t
m
at
h
em
atics
to
s
tu
d
e
n
ts
’
d
aily
life
c
o
n
tex
ts
,
wh
ich
will
allo
w
th
em
to
a
p
p
r
ec
iate
th
e
tr
an
s
ce
n
d
en
ce
o
f
th
is
s
u
b
ject,
f
o
s
ter
in
g
th
e
s
ig
n
if
ican
ce
o
f
lear
n
in
g
.
Similar
ly
,
a
co
n
tin
u
o
u
s
ev
alu
atio
n
s
y
s
tem
s
h
o
u
ld
b
e
im
p
lem
en
ted
in
wh
ich
,
in
a
d
d
itio
n
to
ac
ad
em
ic
p
er
f
o
r
m
an
ce
,
th
e
em
o
tio
n
al
well
-
b
ei
n
g
an
d
attitu
d
e
o
f
s
tu
d
en
ts
to
war
d
s
m
ath
em
atics
s
h
o
u
ld
b
e
co
n
s
id
er
e
d
.
Acc
o
r
d
in
g
to
th
e
r
esu
lts
o
f
th
is
s
tu
d
y
,
it is
s
u
g
g
ested
th
at
th
o
s
e
r
esp
o
n
s
ib
le
f
o
r
th
e
f
o
r
m
u
latio
n
o
f
p
u
b
lic
p
o
licies
in
u
n
iv
e
r
s
ity
ed
u
ca
tio
n
s
h
o
u
ld
co
n
s
id
er
th
e
n
ee
d
to
in
clu
d
e
em
o
tio
n
al
m
a
n
ag
em
en
t
as
an
ess
en
tial
an
d
tr
a
n
s
v
er
s
al
elem
en
t
in
all
ar
ea
s
an
d
d
is
cip
lin
es
o
f
u
n
iv
er
s
ity
ed
u
ca
tio
n
.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
Au
th
o
r
s
s
tate
n
o
f
u
n
d
in
g
in
v
o
lv
ed
.
AUTHO
R
CO
NT
RI
B
UT
I
O
NS ST
A
T
E
M
E
N
T
T
h
is
jo
u
r
n
al
u
s
es
th
e
C
o
n
tr
ib
u
to
r
R
o
les
T
ax
o
n
o
m
y
(
C
R
ed
iT)
to
r
ec
o
g
n
ize
in
d
iv
id
u
al
au
th
o
r
co
n
tr
ib
u
tio
n
s
,
r
ed
u
ce
au
th
o
r
s
h
ip
d
is
p
u
tes,
an
d
f
ac
ilit
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co
llab
o
r
atio
n
.
Na
m
e
o
f
Aut
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M
So
Va
Fo
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Vi
Su
P
Fu
W
ilm
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Vid
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Gar
cía
✓
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Mir
th
a
Yv
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San
tis
teb
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✓
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Nelso
n
C
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San
tis
teb
an
Salaza
r
✓
✓
✓
✓
✓
C
:
C
o
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c
e
p
t
u
a
l
i
z
a
t
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M
:
M
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So
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So
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Va
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Va
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Fo
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Fo
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Fu
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Au
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DATA AV
AI
L
AB
I
L
I
T
Y
T
h
e
d
ata
th
at
s
u
p
p
o
r
t
th
e
f
in
d
in
g
s
o
f
th
is
s
tu
d
y
ar
e
av
aila
b
le
o
n
r
eq
u
est
f
r
o
m
th
e
co
r
r
esp
o
n
d
in
g
au
th
o
r
[
NC
SS
]
.
RE
F
E
R
E
NC
E
S
[
1
]
K
.
M
a
a
ss,
V
.
G
e
i
g
e
r
,
M
.
R
.
A
r
i
z
a
,
a
n
d
M
.
G
o
o
s
,
“
T
h
e
r
o
l
e
o
f
ma
t
h
e
mat
i
c
s
i
n
i
n
t
e
r
d
i
sc
i
p
l
i
n
a
r
y
S
TE
M
e
d
u
c
a
t
i
o
n
,
”
Z
D
M
-
Ma
t
h
e
m
a
t
i
c
s E
d
u
c
a
t
i
o
n
,
v
o
l
.
5
1
,
n
o
.
6
,
p
p
.
8
6
9
–
8
8
4
,
N
o
v
.
2
0
1
9
,
d
o
i
:
1
0
.
1
0
0
7
/
s
1
1
8
5
8
-
0
1
9
-
0
1
1
0
0
-
5.
[
2
]
A
.
V
u
y
k
,
M
.
M
o
n
t
a
n
i
a
,
a
n
d
L
.
B
a
r
r
i
o
s
,
“
B
o
r
e
d
o
m
a
n
d
i
t
s
p
e
r
c
e
i
v
e
d
i
m
p
a
c
t
i
n
a
d
o
l
e
s
c
e
n
t
s
w
i
t
h
e
x
c
e
p
t
i
o
n
a
l
m
a
t
h
e
m
a
t
i
c
a
l
t
a
l
e
n
t
:
a
s
e
q
u
e
n
t
i
a
l
m
i
x
e
d
-
m
e
t
h
o
d
s
s
t
u
d
y
i
n
P
a
r
a
g
u
a
y
,
”
F
r
o
n
t
i
e
r
s
i
n
S
o
c
i
o
l
o
g
y
,
v
o
l
.
9
,
p
.
1
2
1
4
8
7
8
,
M
a
y
2
0
2
4
,
d
o
i
:
1
0
.
3
3
8
9
/
f
s
o
c
.
2
0
2
4
.
1
2
1
4
8
7
8
.
[
3
]
S
.
Za
m
i
r
,
Z.
Y
a
n
g
,
H
.
W
e
n
w
u
,
a
n
d
U
.
S
a
r
w
a
r
,
“
A
ss
e
ssi
n
g
t
h
e
a
t
t
i
t
u
d
e
a
n
d
p
r
o
b
l
e
m
-
b
a
se
d
l
e
a
r
n
i
n
g
i
n
mat
h
e
mat
i
c
s
t
h
r
o
u
g
h
P
LS
-
S
EM
m
o
d
e
l
i
n
g
,
”
PLo
S
O
N
E
,
v
o
l
.
1
7
,
n
o
.
5
,
p
.
e
0
2
6
6
3
6
3
,
M
a
y
2
0
2
2
,
d
o
i
:
1
0
.
1
3
7
1
/
j
o
u
r
n
a
l
.
p
o
n
e
.
0
2
6
6
3
6
3
.
[
4
]
S
.
Emam
j
o
m
e
h
a
n
d
M
.
B
a
h
r
a
m
i
,
“
Ef
f
e
c
t
o
f
a
s
u
p
p
o
r
t
i
v
e
-
e
d
u
c
a
t
i
v
e
p
r
o
g
r
a
m
i
n
t
h
e
ma
t
h
c
l
a
s
s fo
r
st
r
e
s
s,
a
n
x
i
e
t
y
,
a
n
d
d
e
p
r
e
ss
i
o
n
i
n
f
e
mal
e
s
t
u
d
e
n
t
s
i
n
t
h
e
t
h
i
r
d
l
e
v
e
l
o
f
j
u
n
i
o
r
h
i
g
h
sc
h
o
o
l
:
A
n
a
c
t
i
o
n
r
e
se
a
r
c
h
,
”
J
o
u
r
n
a
l
o
f
E
d
u
c
a
t
i
o
n
a
n
d
H
e
a
l
t
h
P
ro
m
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