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M
a
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m
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c
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se
lf
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t
(M
S
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is
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t
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o
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str
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th
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t
p
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m
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rs
m
u
st
h
a
v
e
in
m
a
th
e
m
a
ti
c
s
lea
rn
in
g
.
T
h
e
a
im
o
f
th
e
re
se
a
rc
h
wa
s
to
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ly
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p
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e
c
ti
v
e
m
a
th
e
m
a
ti
c
s
tea
c
h
e
rs.
Th
e
re
se
a
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h
wa
s
q
u
a
si
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e
x
p
e
rime
n
tal
wit
h
th
e
d
e
sig
n
o
f
o
n
e
g
ro
u
p
p
re
tes
t
-
p
o
sttes
t.
Th
e
re
su
lt
s
s
h
o
we
d
th
a
t
fo
r
p
r
o
sp
e
c
ti
v
e
tea
c
h
e
rs,
M
S
-
C
in
c
re
a
se
d
in
th
e
m
e
d
i
u
m
c
a
teg
o
r
y
wh
il
e
t
h
e
M
S
-
C
i
n
d
ica
to
rs
a
c
h
i
e
v
e
d
in
t
h
e
m
e
d
iu
m
a
n
d
lo
w
c
a
teg
o
ries
.
Th
e
in
c
re
a
se
o
f
M
S
-
C
is d
u
e
to
th
e
e
ff
e
c
ti
v
e
n
e
ss
o
f
c
o
ll
a
b
o
ra
ti
v
e
m
in
d
m
a
p
p
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n
g
(
CM
M
)
lea
rn
i
n
g
stra
teg
y
a
n
d
t
h
e
p
ro
c
e
ss
o
f
stre
n
g
th
e
n
in
g
M
S
-
C
c
a
p
a
c
it
y
o
f
p
ro
sp
e
c
ti
v
e
tea
c
h
e
rs.
T
h
e
C
M
M
fa
c
il
it
a
tes
p
ro
sp
e
c
ti
v
e
tea
c
h
e
rs
to
c
o
n
str
u
c
t
c
re
a
ti
v
e
id
e
a
s
th
ro
u
g
h
stru
c
tu
re
d
c
o
ll
e
c
ti
v
e
id
e
a
s th
a
t
su
p
p
o
rt
t
h
e
in
c
re
a
se
o
f
M
S
-
C
a
m
o
n
g
p
r
o
sp
e
c
ti
v
e
tea
c
h
e
r
.
K
ey
w
o
r
d
s
:
C
o
llab
o
r
ativ
e
m
in
d
-
m
ap
p
i
n
g
Ma
th
em
atics self
-
co
n
ce
p
t
Pro
s
p
ec
tiv
e
teac
h
er
s
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
An
d
er
s
o
n
L
e
o
n
ar
d
o
Palin
u
s
s
a
,
Dep
ar
tm
en
t o
f
Ma
th
em
atics E
d
u
ca
tio
n
,
Pattimu
r
a
Un
iv
er
s
ity
,
Po
k
a,
T
lk
.
Am
b
o
n
,
Ko
ta
Am
b
o
n
,
Ma
lu
k
u
,
I
n
d
o
n
esia
.
E
m
ail:
p
alin
u
s
s
aa
n
d
er
s
o
n
l@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
co
n
tr
o
l
r
an
g
e
o
f
th
e
Ma
lu
k
u
r
eg
io
n
is
a
p
r
o
b
lem
f
o
r
h
ig
h
s
ch
o
o
l
g
r
a
d
u
ates
in
th
e
b
o
r
d
er
ar
ea
s
to
co
n
tin
u
e
th
ei
r
s
tu
d
ies
in
h
i
g
h
e
r
ed
u
ca
tio
n
in
Am
b
o
n
city
.
T
h
is
p
r
o
b
lem
n
ee
d
s
f
o
r
a
s
o
lu
tio
n
b
y
im
p
lem
en
tin
g
lear
n
in
g
p
r
o
g
r
a
m
s
f
o
r
d
is
ad
v
a
n
tag
ed
,
o
u
ter
m
o
s
t,
an
d
lea
d
in
g
r
eg
io
n
s
in
th
e
b
o
r
d
e
r
ar
ea
s
in
Ma
lu
k
u
p
r
o
v
in
ce
.
T
h
e
g
o
al
is
to
im
p
r
o
v
e
th
e
q
u
ality
o
f
h
u
m
a
n
r
eso
u
r
ce
s
in
th
e
Ar
u
is
lan
d
d
is
tr
ict.
T
h
e
ar
ea
r
eq
u
ir
es
o
p
tim
al
teac
h
er
r
eso
u
r
ce
s
,
b
o
t
h
q
u
a
n
tity
an
d
q
u
ality
.
T
h
e
s
tu
d
y
p
r
o
g
r
a
m
o
u
ts
id
e
th
e
m
ain
ca
m
p
u
s
(
SP
OM
C
)
in
Pattimu
r
a
Un
iv
er
s
ity
is
o
n
e
o
f
alter
n
ativ
e
s
o
lu
tio
n
s
to
an
s
we
r
th
e
ed
u
ca
tio
n
al
ch
allen
g
es
f
a
ce
d
b
y
s
tu
d
en
ts
to
co
n
tin
u
e
th
eir
s
tu
d
ies in
h
ig
h
e
r
ed
u
ca
tio
n
.
Ar
u
is
lan
d
d
is
tr
ict
is
lo
ca
ted
in
th
e
b
o
r
d
er
ar
ea
with
Au
s
tr
alia.
R
ea
l
co
n
d
itio
n
s
in
th
e
f
ield
p
r
o
v
e
t
h
at
m
an
y
teac
h
er
s
an
d
s
tu
d
e
n
ts
s
p
en
d
tim
e
at
s
ea
r
ath
er
th
an
lear
n
in
g
to
d
ev
el
o
p
p
o
ten
tial
f
o
r
p
r
esen
t
a
n
d
f
u
tu
r
e
liv
es.
T
h
e
av
e
r
ag
e
co
m
m
u
n
ity
liv
es
o
n
th
e
co
ast.
R
esear
ch
r
elate
d
to
s
elf
-
co
n
ce
p
t,
esp
ec
ially
MS
-
C
in
t
h
e
b
o
r
d
er
ar
ea
s
h
as
n
o
t
b
e
en
wid
ely
d
ev
el
o
p
ed
[
1
]
.
T
h
e
p
r
o
s
p
ec
tiv
e
teac
h
er
s
i
n
lectu
r
es
co
m
e
with
d
i
f
f
er
en
t
m
in
d
s
ets
an
d
ab
ilit
ies.
T
h
e
d
i
f
f
er
en
ce
s
h
av
e
an
im
p
ac
t
o
n
s
tu
d
en
ts
’
MS
-
C
in
lear
n
in
g
.
E
a
r
ly
s
tu
d
ies
id
en
ti
f
ied
;
m
o
s
t
p
r
o
s
p
ec
tiv
e
teac
h
er
s
h
av
e
lo
w
MS
-
C
s
s
o
th
at
it
n
ee
d
s
o
p
tim
al
r
ein
f
o
r
ce
m
e
n
t.
Stu
d
en
ts
'
an
x
iety
b
ef
o
r
e
jo
in
i
n
g
m
ath
em
ati
cs
lear
n
in
g
b
ec
o
m
es
an
im
p
o
r
tan
t
p
r
o
b
lem
th
at
n
ee
d
s
s
o
lu
tio
n
.
An
o
th
er
p
r
o
b
l
em
is
th
at
s
tu
d
en
ts
h
av
e
d
if
f
ic
u
lty
co
m
p
letin
g
m
ath
em
atica
l
task
s
.
Stu
d
en
ts
ar
e
o
f
th
e
v
iew
th
at
th
e
r
e
a
r
e
li
m
itatio
n
s
to
th
eir
m
ath
e
m
atics
ab
ilit
ies.
T
h
is
v
iew
in
f
lu
en
ce
s
m
o
tiv
atio
n
,
an
d
ac
h
iev
em
en
t o
f
m
ath
em
atics l
ea
r
n
in
g
o
u
tco
m
es
[
2
]
.
Ma
th
em
atica
l
an
x
iety
an
d
s
tu
d
en
ts
'
v
iew
s
o
n
s
elf
-
lim
itatio
n
s
h
o
w
n
eg
ativ
e
s
elf
-
co
n
ce
p
t
s
[
3
]
.
Self
-
co
n
ce
p
t
is
an
im
p
o
r
ta
n
t
co
n
s
tr
u
ct
in
e
d
u
ca
tio
n
,
r
elate
d
t
o
i
n
d
iv
id
u
al
ac
ad
em
ic
ac
h
iev
em
en
t
[
4
]
.
T
h
e
v
iew
o
f
th
e
s
elf
-
in
ab
ilit
y
ab
o
u
t
th
e
h
o
p
e
o
f
ac
h
iev
in
g
s
u
cc
ess
an
d
s
elf
-
co
n
f
id
e
n
ce
in
lear
n
in
g
a
ls
o
s
h
o
ws
n
eg
ativ
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
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2
2
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I
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t
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J
.
E
v
al
.
&
R
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.
E
d
u
c
.
Vo
l.
9
,
No
.
4
,
Dec
em
b
e
r
2
0
2
0
:
7
9
9
-
8
0
6
800
s
elf
-
co
n
ce
p
t.
I
t
h
as
an
im
p
ac
t
o
n
lear
n
in
g
m
o
tiv
atio
n
an
d
ex
ce
s
s
iv
e
an
x
iety
b
ef
o
r
e
tak
in
g
less
o
n
s
[
5
]
.
Self
-
co
n
ce
p
t
is
a
m
u
lti
-
d
im
en
s
io
n
al
p
r
o
ce
s
s
th
at
r
ef
e
r
s
to
t
h
e
in
d
iv
id
u
al'
s
s
elf
-
p
er
ce
p
tio
n
s
an
d
is
r
elate
d
to
a
n
u
m
b
er
o
f
ch
ar
ac
ter
is
tics
p
o
s
s
ess
ed
b
y
o
n
eself
,
s
u
ch
as
p
h
y
s
ical
ap
p
ea
r
an
ce
,
p
er
f
o
r
m
a
n
ce
,
s
elf
-
ab
ilit
y
,
g
o
als,
v
alu
es,
an
d
s
elf
-
esteem
[
6
]
.
Self
-
co
n
ce
p
t
g
r
ea
tly
in
f
lu
en
ce
s
h
o
w
s
tu
d
en
ts
f
ee
l
ab
o
u
t
th
em
s
elv
es,
th
eir
m
ath
em
atics
a
b
ilit
y
,
an
d
d
ec
is
io
n
s
m
ad
e
r
eg
ar
d
in
g
e
d
u
ca
tio
n
th
at
ar
e
m
an
if
este
d
th
r
o
u
g
h
s
tu
d
en
ts
’
ac
ad
em
ic
ac
h
iev
em
en
t
in
lear
n
in
g
[
7
]
.
Aca
d
em
ic
s
elf
-
co
n
ce
p
ts
ar
e
r
elate
d
to
ac
ad
em
ic
ac
h
iev
em
en
t
an
d
ar
e
d
ef
in
ed
as
b
elief
s
an
d
f
ee
lin
g
s
o
r
in
d
iv
id
u
al
in
telle
ctu
al
p
er
ce
p
tio
n
s
o
f
ab
ilit
ies
p
o
s
s
ess
ed
[
8
]
.
Aca
d
em
ic
s
e
lf
-
co
n
ce
p
t
is
s
elf
-
p
er
ce
p
tio
n
an
d
lead
s
m
o
r
e
t
o
s
ch
o
last
ic
co
m
p
eten
ce
,
n
o
t
attitu
d
e
[
9
]
.
Self
-
co
n
ce
p
t
r
e
f
er
s
to
s
o
m
eo
n
e'
s
p
er
ce
p
tio
n
o
f
th
em
s
elv
es
in
r
elatio
n
to
t
h
eir
ac
a
d
em
ic
ac
h
iev
em
en
t
[
1
0
]
.
I
n
d
iv
id
u
al
ac
ad
em
ic
s
elf
-
co
n
ce
p
ts
h
av
e
a
d
ir
ec
t
an
d
in
d
ir
ec
t
ef
f
e
ct
o
n
ac
ad
em
ic
ac
h
iev
em
en
t,
an
in
cr
ea
s
e
in
ac
ad
em
ic
s
elf
-
co
n
ce
p
ts
lead
s
to
an
in
cr
ea
s
e
in
ac
ad
em
ic
ac
h
iev
em
en
t
an
d
v
ice
v
er
s
a,
h
ig
h
ac
ad
em
ic
s
elf
-
co
n
ce
p
ts
d
ir
ec
tly
in
f
lu
en
ce
ac
ad
em
i
c
ac
h
iev
em
en
t
b
etter
b
ec
au
s
e
o
f
th
e
p
o
s
itiv
e
s
elf
-
co
n
ce
p
ts
s
tu
d
en
ts
h
av
e
ca
n
tr
ig
g
e
r
t
h
em
to
b
e
ac
tiv
ely
in
v
o
lv
ed
in
co
n
s
tr
u
ctin
g
cr
ea
tiv
e
id
ea
s
in
m
ath
em
atics
lea
r
n
in
g
[
1
1
]
.
T
o
t
r
ig
g
er
an
in
c
r
ea
s
e
o
f
MS
-
C
o
n
p
r
o
s
p
ec
tiv
e
teac
h
er
s
,
s
p
ec
ial
t
r
ea
tm
en
t
is
im
p
o
r
tan
t
to
f
o
r
m
p
o
s
itiv
e
s
tu
d
e
n
ts
’
s
elf
-
co
n
ce
p
ts
in
m
ath
e
m
atics
lear
n
in
g
.
MS
-
C
r
ef
er
s
to
p
er
ce
p
tio
n
s
o
r
b
elief
s
in
ab
ilit
y
to
d
o
well
in
m
ath
em
atics
o
r
b
elief
s
in
lear
n
in
g
m
ath
em
atics
[
1
2
]
.
MS
-
C
is
a
s
tr
o
n
g
in
d
icato
r
o
f
s
ch
o
o
l
p
e
r
f
o
r
m
an
ce
,
ed
u
ca
tio
n
an
d
em
p
lo
y
m
en
t
ch
o
ices
[
1
3
]
.
MS
-
C
h
as
a
p
o
s
itiv
e
r
elatio
n
s
h
ip
with
s
tu
d
en
ts
’
m
ath
em
atics
ac
h
iev
em
en
t
[
1
4
]
.
Stu
d
e
n
ts
ar
e
m
o
r
e
co
n
f
id
en
t
ab
o
u
t
m
ath
e
m
atica
l
ab
ilit
ies
b
ec
au
s
e
th
e
y
h
av
e
h
ig
h
p
o
s
itiv
e
s
elf
-
co
n
ce
p
ts
[
1
5
]
.
So
cial
s
u
p
p
o
r
t
o
f
p
a
r
en
ts
p
lay
s
an
im
p
o
r
tan
t
r
o
le
in
p
r
ed
ictin
g
MS
-
C
[
1
6
]
.
Ma
th
em
atica
l
s
el
f
-
co
n
ce
p
ts
r
ef
er
to
s
tu
d
en
ts
'
p
er
ce
p
tio
n
s
o
f
th
eir
o
wn
ca
p
ac
it
y
an
d
le
v
el
o
f
p
er
f
o
r
m
an
ce
in
m
ath
em
atics
[
1
7
]
.
MS
-
C
ca
n
in
cr
ea
s
e
s
tu
d
en
ts
’
co
n
f
i
d
en
ce
[
1
8
]
.
T
h
e
r
esu
lts
o
f
th
e
s
tu
d
y
in
d
icate
t
h
at
MS
-
C
is
im
p
o
r
tan
t f
o
r
p
r
o
s
p
ec
tiv
e
teac
h
er
s
to
b
e
ac
tiv
ely
in
v
o
lv
ed
i
n
s
o
lv
in
g
m
ath
em
atica
l p
r
o
b
lem
s
.
Stu
d
en
ts
’
MS
-
C
ca
n
b
e
i
m
p
r
o
v
e
d
th
r
o
u
g
h
co
llab
o
r
at
iv
e
p
r
o
b
lem
-
s
o
lv
in
g
lear
n
i
n
g
m
o
d
el.
C
o
llab
o
r
ativ
e
lear
n
in
g
in
v
o
lv
es
s
tu
d
en
ts
to
d
ed
icate
th
em
s
elv
es
to
wo
r
k
in
g
r
o
u
p
s
b
y
s
ettin
g
p
r
o
jectio
n
s
o
f
wo
r
k
to
g
eth
e
r
an
d
p
r
esen
tin
g
n
ew
k
n
o
wled
g
e
th
r
o
u
g
h
co
ll
ab
o
r
atio
n
[
1
9
]
.
Stu
d
en
ts
in
co
llab
o
r
ativ
e
g
r
o
u
p
s
lear
n
to
co
n
s
tr
u
ct
k
n
o
wled
g
e
to
g
eth
er
as
a
s
tr
u
ctu
r
e
in
t
h
in
k
in
g
m
at
h
em
atica
lly
.
E
f
f
ec
ti
v
e
lear
n
in
g
o
cc
u
r
s
wh
en
in
d
iv
i
d
u
als
lea
r
n
f
r
o
m
o
th
er
s
r
ath
er
th
an
s
elf
-
s
tu
d
y
[
2
0
]
,
o
n
e
o
f
wh
ic
h
is
co
llab
o
r
ativ
e
lear
n
in
g
.
T
h
e
co
llab
o
r
ativ
e
lear
n
in
g
ap
p
r
o
a
ch
is
a
f
o
r
m
o
f
c
r
ea
tiv
e
lear
n
i
n
g
an
d
is
d
o
n
e
b
y
p
r
esen
tin
g
co
n
tex
tu
al
lear
n
in
g
m
ed
ia
th
at
ca
n
tr
ig
g
e
r
s
tu
d
e
n
ts
to
wo
r
k
ac
tiv
ely
as
a
wh
o
le
in
co
n
v
ey
in
g
cr
ea
tiv
e
i
d
ea
s
[
2
1
]
.
C
r
ea
tiv
e
lear
n
in
g
is
ch
ar
ac
ter
ized
b
y
s
u
b
m
itti
n
g
ch
allen
g
in
g
q
u
esti
o
n
s
,
m
ak
in
g
co
n
n
ec
tio
n
s
an
d
s
ee
in
g
r
elatio
n
s
h
ip
s
,
im
ag
in
in
g
wh
at
m
ig
h
t
h
a
p
p
e
n
,
ex
p
lo
r
i
n
g
cr
ea
tiv
e
id
ea
s
,
h
av
in
g
m
an
y
o
p
tio
n
s
in
s
o
lv
in
g
p
r
o
b
lem
s
,
h
a
v
in
g
cr
itical
id
ea
s
f
r
o
m
co
n
cr
ete
ac
tio
n
s
,
an
d
g
e
n
er
atin
g
id
ea
s
to
ac
h
iev
e
o
p
tim
al
r
esu
lts
[
2
2
]
.
C
o
llab
o
r
ativ
e
lear
n
in
g
m
ak
es
s
tu
d
en
ts
ac
tiv
e
in
lear
n
in
g
,
b
e
ca
u
s
e
o
f
th
e
e
m
p
h
asis
o
n
f
r
ee
in
d
iv
id
u
al
th
in
k
in
g
a
n
d
t
h
eir
ab
ilit
y
to
s
o
lv
e
p
r
o
b
lem
s
[
2
3
]
.
T
h
e
s
tag
es
in
co
llab
o
r
ativ
e
lear
n
in
g
ar
e
en
g
ag
em
e
n
t,
ex
p
lo
r
atio
n
,
tr
a
n
s
f
o
r
m
atio
n
,
p
r
esen
tatio
n
an
d
r
ef
lectio
n
[
2
4
]
.
E
x
p
l
o
r
atio
n
an
d
r
ef
lectio
n
ar
e
im
p
o
r
ta
n
t
s
tag
es
in
f
o
r
m
in
g
MS
-
C
o
f
p
r
o
s
p
ec
t
iv
e
teac
h
er
s
.
R
ef
lectio
n
is
d
o
n
e
to
e
v
alu
ate
th
e
s
tr
en
g
th
s
an
d
wea
k
n
ess
es
o
f
s
tu
d
en
ts
d
u
r
in
g
th
e
co
llab
o
r
ati
o
n
p
r
o
ce
s
s
.
T
h
e
p
r
o
ce
s
s
o
f
co
llab
o
r
atio
n
,
d
em
o
n
s
tr
atio
n
,
a
n
d
u
n
d
er
s
tan
d
in
g
o
f
th
e
m
ater
ial
lear
n
ed
ca
n
b
e
d
o
n
e
th
r
o
u
g
h
m
i
n
d
m
ap
p
i
n
g
s
tr
ateg
ies
an
d
im
p
lem
en
t
ed
th
r
o
u
g
h
g
r
o
u
p
lear
n
in
g
[
2
5
,
2
6
]
.
Min
d
m
ap
p
in
g
is
an
ap
p
licatio
n
th
at
g
iv
es
m
ea
n
in
g
to
u
n
d
e
r
s
tan
d
in
g
in
f
o
r
m
atio
n
in
a
s
im
p
le
way
[
2
7
]
.
T
h
is
r
esear
ch
co
m
b
in
es
co
llab
o
r
ativ
e
le
ar
n
in
g
with
m
in
d
m
ap
p
in
g
s
e
ttin
g
s
th
at
is
ca
lled
C
o
llab
o
r
ativ
e
Min
d
Ma
p
p
i
n
g
(
C
MM
)
.
C
MM
ca
n
tr
ig
g
er
s
tu
d
en
ts
to
co
n
s
tr
u
ct
id
ea
s
to
g
eth
er
in
s
o
lv
i
n
g
m
ath
em
atica
l
p
r
o
b
lem
s
[
2
8
]
.
L
ea
r
n
in
g
with
th
e
C
MM
s
tr
ateg
y
f
o
r
p
r
o
s
p
ec
tiv
e
p
r
im
ar
y
s
ch
o
o
l
teac
h
er
s
in
th
e
SP
OM
C
in
th
e
Ar
u
is
lan
d
d
is
tr
ict
aim
s
to
in
cr
ea
s
e
s
tu
d
en
ts
’
MS
-
C
an
d
m
in
im
ize
n
eg
ativ
e
MS
-
C
,
in
clu
d
in
g
:
m
ath
em
atica
l
an
x
iety
,
s
elf
-
p
er
ce
p
tio
n
o
f
lim
ited
m
at
h
em
atics
ab
ilit
ies,
s
en
s
itiv
ity
to
cr
itici
s
m
,
o
th
er
p
eo
p
le'
s
v
iews
o
n
ab
ilit
y
m
ath
em
atics,
a
n
eg
ativ
e
s
elf
-
v
iew
o
f
th
e
f
u
tu
r
e.
I
f
n
eg
ativ
e
MS
-
C
ca
n
b
e
m
in
im
ized
,
t
h
er
e
will
b
e
an
in
cr
ea
s
e
in
m
ath
em
atics
lear
n
in
g
o
u
tco
m
es.
Min
i
m
izin
g
th
e
n
eg
ati
v
e
MS
-
C
o
f
s
tu
d
en
ts
tak
es
tim
e
co
n
tin
u
o
u
s
ly
an
d
n
ee
d
s
co
n
c
r
ete
ac
tio
n
s
to
im
p
r
o
v
e
MS
-
C
f
o
r
p
r
o
s
p
ec
tiv
e
elem
en
tar
y
s
c
h
o
o
l
teac
h
er
s
in
t
h
e
SP
OM
C
in
Ar
u
R
eg
en
cy
,
Ma
l
u
k
u
Pro
v
in
ce
,
I
n
d
o
n
esia.
2.
RE
S
E
ARCH
M
E
T
H
O
D
T
h
e
r
esear
c
h
was
q
u
asi
-
ex
p
er
im
en
tal
em
p
lo
y
ed
d
esig
n
o
f
o
n
e
g
r
o
u
p
p
r
etest
-
p
o
s
ttes
t
an
d
in
v
o
lv
in
g
6
0
s
tu
d
en
ts
o
f
p
r
im
ar
y
s
ch
o
o
l
teac
h
er
ca
n
d
id
ates
as
r
esear
ch
s
u
b
jects.
T
h
e
r
esear
ch
d
esig
n
ca
n
b
e
s
ee
n
as
f
o
llo
ws
[
2
9
]
.
O
1
-
-
-
-
-
-
-
X
-
-
-
-
-
-
O
2
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
Ma
th
ema
tica
l self
-
co
n
ce
p
t a
m
o
n
g
p
r
o
s
p
ec
tive
tea
c
h
ers
(
Jo
h
a
n
n
is
Ta
ka
r
ia
)
801
No
te:
O
1
:
Pre
test
MS
-
C
O
2
:
Po
s
ttes
t M
S
-
C
X
:
C
MM
Stra
teg
y
an
d
Stre
n
g
t
h
en
in
g
o
f
MS
-
C
ca
p
ac
ity
T
h
e
s
tu
d
y
s
am
p
le
was
6
0
s
tu
d
en
ts
o
f
p
r
im
ar
y
s
ch
o
o
l
teac
h
er
ca
n
d
id
ates
in
th
e
f
if
th
s
em
ester
o
f
th
e
ac
ad
em
ic
y
ea
r
2
0
1
7
/
2
0
1
8
.
T
h
e
s
am
p
lin
g
tec
h
n
iq
u
e
was
d
o
n
e
th
r
o
u
g
h
p
u
r
p
o
s
iv
e
s
am
p
lin
g
.
T
h
e
ai
m
was
to
f
in
d
o
u
t
t
h
e
im
p
r
o
v
em
en
t
o
f
s
tu
d
en
ts
’
MS
-
C
with
co
n
s
i
d
er
atio
n
o
f
th
e
s
o
cial
b
ac
k
g
r
o
u
n
d
,
cu
ltu
r
e,
an
d
lo
ca
tio
n
o
f
s
tu
d
e
n
ts
in
t
h
e
o
u
t
er
m
o
s
t
ar
ea
s
,
as
well
as
th
e
ab
ilit
y
o
f
s
tu
d
en
ts
wh
o
v
a
r
ied
at
h
ig
h
,
m
e
d
iu
m
an
d
lo
w
lev
els.
T
h
e
s
tu
d
y
was c
o
n
d
u
cted
f
o
r
o
n
e
s
em
ester
(
6
m
o
n
th
s
)
in
th
e
Ma
th
em
atics E
d
u
c
atio
n
co
u
r
s
e.
T
h
e
Pre
test
Se
lf
-
C
o
n
ce
p
t
s
ca
l
e
(
Pre
test
-
MS
-
C
)
was
u
s
ed
to
m
ea
s
u
r
e
th
e
in
itial
ab
ilit
y
o
f
s
tu
d
en
ts
’
MS
-
C
b
ef
o
r
e
ap
p
ly
in
g
th
e
C
MM
s
tr
ateg
y
an
d
s
tr
en
g
th
en
in
g
MS
-
C
ca
p
ac
ity
.
An
o
th
er
g
o
al
was
to
d
is
tr
ib
u
te
s
tu
d
en
ts
in
co
llab
o
r
ativ
e
g
r
o
u
p
s
ac
co
r
d
in
g
to
th
e
r
u
les
o
f
f
o
r
m
in
g
id
ea
l
g
r
o
u
p
s
.
Af
ter
th
e
C
MM
s
tr
ateg
y
was
ap
p
lied
,
Po
s
ttes
t
s
elf
-
co
n
ce
p
t
(
Po
s
test
-
MS
-
C
)
was
im
p
lem
e
n
ted
.
T
h
e
MS
-
C
s
ca
le
b
ef
o
r
e
b
ein
g
d
is
tr
ib
u
ted
t
o
th
e
r
esp
o
n
d
e
n
t
was
f
ir
s
t
v
alid
a
ted
b
y
th
e
ex
p
er
t
a
n
d
a
s
tati
s
tical
test
wa
s
p
er
f
o
r
m
ed
to
s
ee
th
e
v
alid
ity
an
d
r
eliab
ilit
y
.
Fo
u
r
ty
f
iv
e
item
s
wer
e
d
is
tr
ib
u
ted
to
r
esp
o
n
d
en
ts
,
an
d
test
s
wer
e
co
n
d
u
cted
to
ch
ec
k
th
e
v
alid
ity
o
f
th
e
MS
-
C
s
ca
le
with
th
e
h
elp
o
f
SP
SS
v
er
-
1
9
,
id
e
n
tifie
d
th
at
4
3
item
s
wer
e
d
ec
lar
ed
v
alid
wh
ile
2
item
s
wer
e
in
v
alid
,
s
o
4
3
item
s
o
f
s
tatem
en
ts
wer
e
u
s
ed
in
th
e
MS
-
C
d
ata
co
llectio
n
p
r
o
ce
s
s
.
T
h
e
r
eliab
ilit
y
test
r
esu
lts
o
b
tain
ed
C
r
o
n
b
ac
h
'
s
A
lp
h
a
v
alu
e
o
f
0
.
9
3
in
th
e
v
er
y
h
ig
h
ca
teg
o
r
y
.
T
h
e
o
b
s
er
v
atio
n
s
h
ee
t
was
u
s
ed
t
o
ass
es
s
lear
n
in
g
ac
tiv
ities
f
o
r
b
o
th
s
tu
d
en
ts
an
d
lectu
r
er
s
.
At
th
e
en
d
o
f
th
e
less
o
n
in
ter
v
iews
wer
e
co
n
d
u
cted
with
s
tu
d
en
ts
to
ex
p
lo
r
e
m
o
r
e
d
ee
p
ly
th
e
MS
-
C
th
at
is
h
eld
b
y
p
r
o
s
p
ec
tiv
e
teac
h
er
s
.
Or
d
in
al
MS
-
C
d
ata
is
co
n
v
er
ted
to
in
ter
v
al
s
ca
le
u
s
in
g
th
e
Me
th
o
d
o
f
Su
cc
ess
iv
e
I
n
ter
v
al
(
MSI
)
.
O
r
d
in
al
d
ata
s
h
o
u
ld
b
e
co
n
v
er
ted
to
in
ter
v
al
d
ata
(
f
o
r
ex
a
m
p
le
with
MSI
)
.
T
h
e
p
u
r
p
o
s
e
o
f
wh
ich
was to
f
u
lf
ill
th
e
d
ata
an
aly
s
is
r
eq
u
ir
em
en
ts
in
p
ar
am
etr
ic
s
tatis
tic
s
[
3
0
]
.
T
h
e
co
n
v
er
s
io
n
d
ata
wer
e
an
aly
ze
d
u
s
in
g
p
air
ed
t
-
test
s
am
p
les.
T
h
e
r
esu
lts
o
f
t
h
e
an
aly
s
is
wer
e
th
en
d
escr
i
b
ed
th
r
o
u
g
h
s
tag
es
:
1
)
Descr
ib
in
g
th
e
r
esu
lts
o
f
r
esear
ch
r
elate
d
to
s
tu
d
en
ts
’
MS
-
C
o
b
tain
e
d
t
h
r
o
u
g
h
o
b
s
er
v
atio
n
an
d
in
ter
v
iews;
2
)
An
aly
zin
g
o
f
im
p
r
o
v
em
e
n
t o
f
s
tu
d
en
ts
'
m
ath
em
atica
l self
-
co
n
ce
p
ts
u
s
in
g
ce
n
tr
alize
d
N
-
g
ain
[3
1
,
3
2
]
.
3.
RE
SU
L
T
S
A
ND
D
I
SCU
SS
I
O
N
B
ef
o
r
e
th
e
im
p
lem
e
n
tatio
n
o
f
th
e
C
MM
s
tr
ateg
y
an
d
s
tr
en
g
t
h
en
in
g
MS
-
C
ca
p
ac
ity
,
it
was
n
ec
ess
ar
y
to
h
av
e
p
r
etest.
I
t
aim
ed
to
f
in
d
o
u
t
th
e
in
itial
m
ath
em
atica
l
s
elf
-
co
n
ce
p
t
o
f
s
tu
d
en
ts
.
Pre
te
s
t
-
SC
an
d
Po
s
test
-
SC
wer
e
m
ea
s
u
r
ed
u
s
in
g
a
f
o
u
r
-
g
r
a
d
e
MS
-
C
s
ca
le,
in
th
e
c
ateg
o
r
ies:
Stro
n
g
ly
Ag
r
ee
,
Ag
r
ee
,
Dis
ag
r
ee
,
an
d
Stro
n
g
ly
Dis
ag
r
ee
an
d
in
clu
d
e
two
m
ain
co
m
p
o
n
e
n
ts
,
n
am
ely
,
th
e
co
n
ce
p
tu
al
an
d
a
ttit
u
d
e
co
m
p
o
n
e
n
ts
o
u
tlin
ed
in
f
iv
e
in
d
icato
r
s
:
1
)
Views
o
f
m
ath
em
atics
ab
ilit
ies
an
d
d
is
ab
ilit
ies;
2
)
Ma
th
em
atica
l
attit
u
d
e
an
d
s
elf
-
co
n
f
id
en
ce
;
3
)
Self
-
s
en
s
itiv
e;
4
)
Ma
th
em
atics
is
im
p
o
r
t
an
t
f
o
r
th
e
f
u
t
u
r
e;
a
n
d
5
)
Oth
e
r
p
eo
p
le'
s
v
iews
o
n
m
ath
em
atics a
b
ilit
ies.
3
.
1
.
Str
eng
t
henin
g
t
he
ca
pa
cit
y
o
f
s
t
ud
ent
s
’
MS
-
C
B
ef
o
r
e
th
e
lear
n
in
g
p
r
o
ce
s
s
u
s
in
g
th
e
C
MM
s
tr
ateg
y
,
th
e
lectu
r
er
ef
f
ec
tiv
ely
i
d
en
tifi
ed
MS
-
C
p
r
o
b
lem
s
b
y
r
ef
er
r
i
n
g
to
th
e
P
r
etest
-
SC
r
esu
lts
.
I
d
en
tific
atio
n
r
esu
lts
wer
e
d
is
cu
s
s
ed
d
u
r
in
g
th
e
b
r
ain
s
to
r
m
in
g
p
r
o
ce
s
s
to
s
tr
en
g
t
h
en
MS
-
C
ca
p
ac
ity
b
ased
o
n
id
en
tific
ati
o
n
o
f
s
tr
en
g
t
h
s
an
d
wea
k
n
es
s
es.
B
ased
o
n
th
e
r
esu
lts
o
f
th
e
id
en
tific
atio
n
,
th
e
lectu
r
er
s
g
r
o
u
p
e
d
th
e
MS
-
C
p
r
o
b
lem
s
ex
p
er
ien
ce
d
b
y
s
tu
d
en
ts
to
b
e
d
is
cu
s
s
ed
in
th
e
s
h
ar
i
n
g
p
r
o
ce
s
s
b
etwe
en
s
tu
d
en
ts
an
d
lectu
r
er
s
an
d
s
tu
d
e
n
ts
an
d
p
ee
r
s
.
T
h
e
g
o
al
was
to
g
et
a
s
o
lu
tio
n
to
m
in
im
ize
th
e
n
eg
ativ
e
MS
-
C
o
f
s
tu
d
en
ts
in
lear
n
in
g
.
Fig
u
r
e
1
s
h
o
ws
th
e
s
y
s
te
m
atic
s
tr
en
g
th
en
in
g
o
f
MS
-
C
ca
p
ac
ity
.
Fig
u
r
e
1
.
Sy
s
tem
atics o
f
s
tu
d
e
n
ts
’
MS
-
C
ca
p
ac
ity
s
tr
en
g
th
en
in
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t
.
J
.
E
v
al
.
&
R
es
.
E
d
u
c
.
Vo
l.
9
,
No
.
4
,
Dec
em
b
e
r
2
0
2
0
:
7
9
9
-
8
0
6
802
3
.
2
.
CM
M
s
t
ra
t
eg
y
im
plem
ent
a
t
i
o
n
T
h
e
in
cr
ea
s
e
o
f
MS
-
C
was
m
ea
s
u
r
ed
af
ter
th
e
C
MM
s
tr
ateg
y
was
ap
p
lied
wh
ich
was
o
r
ie
n
ted
to
th
e
ef
f
ec
tiv
en
ess
o
f
s
tu
d
e
n
ts
’
in
te
r
ac
tio
n
an
d
s
tr
en
g
th
e
n
in
g
MS
-
C
ca
p
ac
ity
.
C
o
llab
o
r
ativ
e
lea
r
n
in
g
is
a
f
o
r
m
o
f
lear
n
in
g
th
at
in
v
o
lv
es
i
n
tellectu
al
ef
f
o
r
ts
to
g
eth
e
r
to
s
ee
k
m
u
tu
al
u
n
d
er
s
tan
d
in
g
,
s
o
lu
ti
o
n
s
,
m
ea
n
in
g
s
,
a
n
d
p
r
o
d
u
ce
p
r
o
d
u
cts
b
ased
o
n
m
u
tu
al
ag
r
ee
m
e
n
t
[3
3
]
.
L
ea
r
n
in
g
co
llab
o
r
ativ
e
p
r
o
b
lem
s
o
lv
i
n
g
r
eq
u
ir
es
p
r
o
b
lem
s
th
at
ar
e
s
o
lv
ed
in
g
r
o
u
p
s
an
d
n
o
t
o
n
ly
b
y
in
d
iv
i
d
u
al
ab
ilit
ies.
T
h
is
wa
s
d
u
e
to
a
lack
o
f
ex
p
er
ien
ce
f
r
o
m
d
if
f
er
en
t
in
d
i
v
id
u
als
[3
4
]
.
C
o
llab
o
r
ativ
e
lear
n
in
g
is
a
lear
n
in
g
s
tr
ateg
y
th
at
r
eq
u
ir
es
s
tu
d
en
ts
to
b
e
in
d
iv
id
u
ally
r
esp
o
n
s
ib
le,
in
ter
ac
t,
an
d
co
llab
o
r
ate
as
a
s
tr
u
ctu
r
e
in
d
ev
el
o
p
in
g
i
d
ea
s
to
g
et
h
er
.
Stu
d
en
ts
wer
e
en
co
u
r
a
g
ed
to
f
in
d
a
v
ar
iety
o
f
o
p
in
io
n
s
in
m
ath
em
atica
l
p
r
o
b
lem
s
o
lv
in
g
.
T
h
is
s
tu
d
y
u
s
ed
co
llab
o
r
ativ
e
s
tr
ateg
ies
with
f
iv
e
s
tag
es
in
l
ea
r
n
in
g
:
en
g
a
g
em
en
t,
ex
p
lo
r
a
tio
n
,
tr
a
n
s
f
o
r
m
atio
n
,
p
r
esen
tatio
n
an
d
r
ef
lectio
n
.
Fig
u
r
e
2
d
is
p
lay
s
th
e
C
MM
s
tr
ateg
y
.
Fig
u
r
e
2
.
C
MM
s
tr
ateg
y
d
esig
n
T
h
e
C
MM
lear
n
in
g
s
tr
ateg
y
in
Fig
u
r
e
2
s
h
o
ws
th
at
s
tu
d
en
ts
to
g
eth
er
c
o
u
ld
f
o
r
m
c
o
llab
o
r
ativ
e
g
r
o
u
p
s
f
r
ee
ly
b
y
r
ef
er
r
i
n
g
t
o
th
e
id
ea
l
g
r
o
u
p
f
o
r
m
atio
n
cr
iter
ia.
I
n
th
e
co
llab
o
r
atio
n
p
r
o
ce
s
s
,
s
tu
d
en
ts
in
d
iv
id
u
ally
e
x
p
lo
r
e
d
cr
ea
tiv
e
id
ea
s
b
y
m
ak
in
g
th
o
u
g
h
t
m
ap
s
o
f
m
ath
em
atica
l
id
ea
s
ex
p
r
ess
ed
in
v
ar
i
o
u
s
cr
ea
tiv
e
way
s
.
Fo
r
t
h
e
m
in
d
m
ap
p
in
g
p
r
o
ce
s
s
,
th
e
lectu
r
er
h
a
d
p
r
o
v
id
ed
an
o
v
er
v
iew
o
f
h
o
w
to
d
esig
n
a
m
in
d
m
ap
o
f
th
e
c
o
n
ce
p
ts
lear
n
e
d
.
T
h
e
r
esu
lts
o
f
th
e
e
x
p
lo
r
atio
n
o
f
id
ea
s
wer
e
th
e
n
tr
an
s
f
o
r
m
ed
in
to
g
r
o
u
p
s
to
eq
u
ate
id
ea
s
t
h
at
h
a
d
b
ee
n
co
n
ce
p
tu
alize
d
.
Af
ter
a
n
a
g
r
ee
m
en
t
o
n
id
ea
s
to
g
eth
e
r
,
th
e
g
r
o
u
p
in
ter
p
r
eted
t
h
e
r
esu
lts
o
f
th
e
co
llab
o
r
atio
n
b
y
d
is
p
lay
in
g
th
e
wo
r
k
.
E
ac
h
g
r
o
u
p
v
is
ited
ea
ch
o
th
e
r
an
d
o
b
s
er
v
ed
th
e
wo
r
k
o
f
o
th
er
g
r
o
u
p
s
an
d
ask
ed
q
u
esti
o
n
s
ab
o
u
t
th
e
r
esu
lts
o
f
co
lla
b
o
r
atio
n
.
E
ac
h
s
tu
d
e
n
t
in
th
e
g
r
o
u
p
in
d
iv
i
d
u
ally
an
d
c
o
llectiv
ely
was
r
esp
o
n
s
ib
le
f
o
r
an
s
wer
in
g
ea
ch
q
u
esti
o
n
f
r
o
m
a
n
o
th
er
g
r
o
u
p
.
At
th
e
e
n
d
o
f
th
e
co
llab
o
r
atio
n
,
r
ef
lectio
n
was
ca
r
r
ied
o
u
t
b
o
th
in
d
i
v
id
u
ally
a
n
d
in
g
r
o
u
p
s
.
I
f
t
h
er
e
wer
e
p
r
o
b
lem
s
th
at
h
ad
n
o
t
b
ee
n
r
eso
lv
ed
o
r
wer
e
n
o
t
in
l
in
e
with
th
e
ex
p
ec
tatio
n
s
o
f
t
h
e
s
tu
d
en
ts
,
th
en
b
r
ain
s
to
r
m
in
g
with
th
e
lectu
r
er
was c
ar
r
ied
o
u
t.
All c
o
llab
o
r
ativ
e
p
r
o
ce
s
s
es we
r
e
ca
r
r
ied
o
u
t
u
s
in
g
o
b
s
er
v
atio
n
s
h
ee
ts
to
o
b
s
er
v
e
th
e
ac
tiv
ities
o
f
s
tu
d
en
ts
an
d
lectu
r
er
s
in
lea
r
n
in
g
.
I
t
was
also
id
en
tifie
d
th
at
le
ctu
r
er
s
co
n
d
u
cte
d
in
ter
v
iews
with
s
ev
er
al
s
tu
d
en
ts
to
ex
p
lo
r
e
m
o
r
e
d
ee
p
ly
th
e
p
r
o
b
lem
s
f
ac
ed
b
y
s
tu
d
en
ts
.
Mo
tiv
atio
n
an
d
d
ir
ec
tio
n
wer
e
g
iv
en
b
y
lectu
r
er
s
to
s
tr
en
g
th
en
th
e
MS
-
C
o
f
s
tu
d
en
ts
.
L
ec
tu
r
er
s
p
o
s
itio
n
th
em
s
elv
es
was
as
an
ac
tiv
e
f
ac
ilit
ato
r
in
alig
n
in
g
v
ar
io
u
s
o
p
in
io
n
s
an
d
p
r
o
v
id
i
n
g
s
o
lu
tio
n
s
to
th
e
p
r
o
b
lem
s
f
ac
ed
b
y
ea
c
h
s
tu
d
en
t
wh
en
th
ey
wer
e
in
ter
a
ctin
g
,
b
ec
au
s
e
MS
-
C
ca
n
b
e
im
p
r
o
v
e
d
b
y
ac
ti
v
e
in
ter
ac
ti
o
n
s
.
Self
-
co
n
ce
p
t
is
n
o
t
in
h
er
ited
f
r
o
m
b
ir
th
,
b
u
t
is
d
e
v
elo
p
ed
o
r
b
u
ilt
b
y
in
d
iv
id
u
als
th
r
o
u
g
h
i
n
ter
ac
tio
n
with
th
e
s
o
cio
-
cu
ltu
r
al
e
n
v
ir
o
n
m
en
t
[3
5
]
.
Stu
d
en
ts
’
s
elf
-
co
n
ce
p
ts
ca
n
d
ev
elo
p
alo
n
g
with
th
e
m
atu
r
ity
o
f
s
tu
d
en
ts
in
lectu
r
es,
wh
er
e
co
g
n
i
tiv
e
lev
els
in
cr
ea
s
e
a
n
d
t
h
eir
em
o
tio
n
al
lev
el
ca
n
b
e
co
n
tr
o
lled
.
Ad
u
lt
d
ev
elo
p
m
en
t
ca
n
b
e
s
tu
d
ied
an
d
an
al
y
ze
d
th
r
o
u
g
h
a
d
y
n
am
ic,
g
o
a
ls
,
o
r
ien
tatio
n
to
b
e
ac
h
iev
ed
,
an
d
th
e
d
e
v
elo
p
m
en
t
o
f
a
v
alu
e
s
y
s
tem
,
b
ec
a
u
s
e
it
d
ea
ls
with
co
g
n
itiv
e
an
d
em
o
tio
n
al
p
r
o
ce
s
s
es
[
36
,
3
7
]
.
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
Ma
th
ema
tica
l self
-
co
n
ce
p
t a
m
o
n
g
p
r
o
s
p
ec
tive
tea
c
h
ers
(
Jo
h
a
n
n
is
Ta
ka
r
ia
)
803
3
.
3
.
T
est
t
he
diff
er
ence
in
MS
-
C
increa
s
e
B
ef
o
r
e
test
in
g
to
s
ee
wh
eth
er
th
er
e
was
a
d
if
f
er
e
n
ce
in
th
e
in
cr
ea
s
e
in
m
ath
em
atica
l
s
elf
-
c
o
n
ce
p
t
o
f
p
r
o
s
p
ec
tiv
e
teac
h
er
s
b
ef
o
r
e
an
d
af
ter
u
s
in
g
th
e
C
MM
s
tr
ateg
y
,
it
is
n
ec
ess
ar
y
to
t
e
s
t
th
e
n
o
r
m
ality
an
d
h
o
m
o
g
en
eity
o
f
th
e
d
ata.
T
ab
l
e
1
p
r
esen
ts
th
e
r
esu
lts
o
f
t
h
e
MS
-
C
d
ata
n
o
r
m
ality
an
d
h
o
m
o
g
en
eity
test
.
T
ab
le
1
.
T
est f
o
r
n
o
r
m
ality
an
d
h
o
m
o
g
en
eity
o
f
MS
-
C
d
ata
K
o
l
m
o
g
o
r
o
v
-
S
m
i
r
n
o
v
a
I
n
t
e
r
p
r
e
t
a
t
i
o
n
P
r
e
_
S
C
0.
2
0
0
N
o
r
mal
P
o
st
_
S
C
0.
1
7
0
N
o
r
mal
Le
v
e
n
e
's
t
e
s
t
f
o
r
e
q
u
a
l
i
t
y
o
f
v
a
r
i
a
n
c
e
s
P
r
e
_
P
o
s
t
_
S
C
0.
1
8
5
H
o
mo
g
e
n
R
ef
er
r
in
g
to
T
a
b
le
1
r
elate
d
t
o
th
e
n
o
r
m
al
an
d
h
o
m
o
g
e
n
eo
u
s
test
,
it
is
o
b
tain
ed
th
e
v
al
u
e
o
f
Sig
.
Pre
_
SC
an
d
Po
s
t_
SC
(
0
.
2
0
0
an
d
0
.
1
7
0
)
g
r
ea
ter
th
an
0
.
0
5
,
s
o
th
at
g
r
o
u
p
d
ata
is
n
o
r
m
ally
d
is
tr
ib
u
ted
.
Af
te
r
f
u
lf
illi
n
g
th
e
n
o
r
m
al
ass
u
m
p
ti
o
n
s
,
th
en
th
e
d
ata
h
o
m
o
g
e
n
eit
y
was te
s
ted
u
s
in
g
th
e
L
ev
en
e
test
,
wh
ich
r
esu
lte
d
in
th
e
Sig
.
(
0
.
1
8
5
)
g
r
ea
ter
th
an
0
.
0
5
,
s
o
th
e
d
ata
is
h
o
m
o
g
en
eo
u
s
.
Af
te
r
f
u
lf
illi
n
g
th
e
ass
u
m
p
tio
n
s
in
th
e
p
ar
am
etr
ic
test
,
th
e
test
in
g
wa
s
d
o
n
e
to
s
ee
th
e
d
if
f
er
e
n
ce
in
th
e
in
cr
ea
s
e
o
f
m
ath
em
atica
l
s
elf
-
co
n
ce
p
t
u
s
in
g
th
e
d
ep
en
d
en
t sam
p
le
t
-
test
with
th
e
test
in
g
h
y
p
o
th
esis
:
Statis
t
ical
Hy
p
o
th
esis
:
Ho
:
µ
−
=
µ
−
H
1:
µ
−
>
µ
−
B
y
th
e
co
n
d
itio
n
s
:
µ
−
=
Av
er
ag
e
N
-
g
a
in
p
r
e
-
M
S
-
C
µ
−
=
Av
er
ag
e
N
-
g
a
in
p
o
s
t
-
MS
-
C
R
esear
ch
Hy
p
o
th
esis
:
Ho
:
T
h
e
in
cr
ea
s
e
in
MS
-
C
o
f
s
tu
d
en
ts
b
ef
o
r
e
an
d
af
ter
u
s
in
g
th
e
C
MM
s
tr
ateg
y
is
n
o
t d
if
f
er
en
t
H
1
:
T
h
e
in
cr
ea
s
e
in
s
tu
d
e
n
ts
’
MS
-
C
af
ter
u
s
in
g
th
e
C
MM
s
tr
ateg
y
is
b
etter
th
an
b
ef
o
r
e
u
s
i
n
g
C
MM
T
ab
le
2
d
is
p
lay
s
t
h
e
r
esu
lts
o
f
th
e
test
f
o
r
th
e
d
i
f
f
er
en
ce
in
M
S
-
C
in
cr
ea
s
e
wh
ich
was
an
aly
ze
d
u
s
in
g
th
e
Pair
ed
s
am
p
le
t
-
test
o
n
th
e
N
-
g
ain
v
alu
e
o
b
tain
e
d
.
T
ab
le
2
.
T
est th
e
d
i
f
f
er
en
ce
in
MS
-
C
in
cr
ea
s
e
S
e
l
f
-
c
o
n
c
e
p
t
M
a
t
e
mat
i
s
Te
st
Ty
p
e
t
Df
si
g
I
n
t
e
r
p
r
e
t
a
t
i
o
n
N
-
g
a
i
n
<
g
>
P
a
i
r
e
d
S
a
m
p
l
e
t
-
t
e
st
-
9.
818
59
0.
0
0
0
H
1
a
c
c
e
p
t
e
d
T
h
e
r
esu
lts
o
f
th
e
Pair
ed
Sam
p
le
t
-
test
i
n
T
ab
le
2
s
h
o
w
s
th
at
th
e
Sig
.
(
0
.
0
0
0
)
less
th
an
0
.
0
5
s
o
th
at
th
e
H
1
d
ec
is
io
n
is
ac
ce
p
te
d
.
T
h
is
m
ea
n
s
th
at
th
e
in
cr
ea
s
e
in
s
tu
d
en
ts
’
MS
-
C
af
ter
u
s
in
g
th
e
C
MM
s
tr
ateg
y
is
b
etter
th
an
b
ef
o
r
e
u
s
in
g
C
MM
.
T
h
e
r
esu
lts
o
f
t
h
ese
s
tatis
tica
l
test
s
s
h
o
w
th
at
th
e
C
MM
tr
ateg
y
is
ef
f
ec
tiv
e
in
in
cr
ea
s
in
g
th
e
MS
-
C
o
f
p
r
o
s
p
e
ctiv
e
teac
h
er
s
in
th
e
b
o
r
d
e
r
ar
ea
.
3
.
4
.
I
m
pro
v
em
ent
o
f
s
t
ud
ent
s
’
MS
-
C
ind
ica
t
o
rs
T
o
an
aly
ze
th
e
in
cr
ea
s
e
o
f
s
tu
d
en
ts
’
MS
-
C
in
d
icato
r
s
,
i
t
was
u
s
ed
Po
s
t
-
SC
with
4
3
item
s
o
f
s
tatem
en
ts
b
o
th
p
o
s
itiv
e
an
d
n
eg
ativ
e
th
at
h
av
e
b
ee
n
test
ed
f
o
r
v
alid
ity
an
d
r
eliab
ilit
y
.
T
h
e
in
cr
ea
s
e
in
m
ath
em
atica
l
s
elf
-
co
n
ce
p
ts
was
an
aly
ze
d
u
s
in
g
N
-
g
ain
,
b
u
t f
o
r
th
e
p
u
r
p
o
s
es
o
f
an
aly
s
is
,
th
e
s
elf
-
co
n
ce
p
t d
ata
wh
ich
was
o
r
d
in
al
t
y
p
e
is
co
n
v
er
ted
t
o
th
e
in
ter
v
al
s
ca
le
u
s
i
n
g
th
e
Su
cc
ess
f
u
l
I
n
ter
v
al
Me
th
o
d
(
MSI
)
.
T
ab
le
3
p
r
esen
ts
an
in
cr
ea
s
e
in
MS
-
C
in
d
icato
r
s
.
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.
9
,
No
.
4
,
Dec
em
b
e
r
2
0
2
0
:
7
9
9
-
8
0
6
804
T
ab
le
3
.
T
h
e
in
cr
ea
s
e
o
f
MS
-
C
in
d
icato
r
s
I
n
d
i
c
a
t
o
r
s
S
u
b
I
n
d
i
c
a
t
o
r
s
N
-
g
a
i
n
̅
−
̅
−
(
%)
C
a
t
e
g
o
r
y
V
i
e
w
s
o
n
M
a
t
h
e
ma
t
i
c
s
C
a
p
a
b
i
l
i
t
i
e
s &
D
i
sab
i
l
i
t
i
e
s
U
n
d
e
r
st
a
n
d
i
n
g
ma
t
h
e
ma
t
i
c
s
0.
38
0.
27
2
7
%
Lo
w
M
a
t
h
e
ma
t
i
c
a
l
c
o
mm
u
n
i
c
a
t
i
o
n
s
k
i
l
l
s
0.
26
C
o
n
st
r
u
c
t
i
o
n
o
f
ma
t
h
e
ma
t
i
c
a
l
i
d
e
a
s
0.
23
M
a
t
h
e
ma
t
i
c
a
l
p
r
o
b
l
e
m
-
so
l
v
i
n
g
s
k
i
l
l
s
0.
24
U
n
d
e
r
st
a
n
d
i
n
g
ma
t
h
e
ma
t
i
c
a
l
i
n
f
o
r
mat
i
o
n
0
.
2
3
M
a
t
h
e
ma
t
i
c
s i
s
I
mp
o
r
t
a
n
t
f
o
r
t
h
e
F
u
t
u
r
e
M
a
t
h
e
ma
t
i
c
s i
s
I
mp
o
r
t
a
n
t
f
o
r
t
h
e
F
u
t
u
r
e
0.
38
0.
31
3
1
%
M
e
d
i
u
m
B
e
c
o
m
e
a
P
r
o
f
e
ss
i
o
n
a
l
M
a
t
h
e
m
a
t
i
c
s
Te
a
c
h
e
r
0.
24
A
c
t
i
v
e
l
y
i
n
v
o
l
v
e
d
i
n
t
h
e
c
o
mm
u
n
i
t
y
0.
32
M
a
t
h
e
ma
t
i
c
s At
t
i
t
u
d
e
& C
o
n
f
i
d
e
n
c
e
M
a
t
h
e
ma
t
i
c
a
l
S
e
l
f
C
o
n
f
i
d
e
n
c
e
0.
50
0.
48
4
8
%
M
e
d
i
u
m
W
o
r
k
o
n
m
a
t
h
a
ssi
g
n
me
n
t
s
i
n
d
e
p
e
n
d
e
n
t
l
y
0.
64
H
a
r
d
w
o
r
k
e
r
0.
52
R
e
s
p
o
n
s
i
b
l
e
0.
44
M
a
t
h
e
ma
t
i
c
a
l
l
y
R
e
f
l
e
c
t
i
v
e
o
p
i
n
i
o
n
s
0.
38
S
o
l
v
e
mat
h
p
r
o
b
l
e
ms
t
h
o
r
o
u
g
h
l
y
0.
46
S
e
l
f
i
s
h
0.
32
R
e
s
p
e
c
t
p
e
o
p
l
e
's
0.
58
S
e
l
f
-
S
e
n
s
i
t
i
v
i
t
y
M
a
t
h
e
ma
t
i
c
a
l
a
n
x
i
e
t
y
0.
22
0.
28
2
8
%
Lo
w
S
e
n
s
i
t
i
v
e
t
o
c
r
i
t
i
c
i
sm
0.
24
S
e
n
s
i
t
i
v
e
t
o
p
r
a
i
se
0.
29
F
e
e
l
i
g
n
o
r
e
d
b
y
t
h
e
l
e
c
t
u
r
e
r
0.
27
D
o
u
b
t
a
b
o
u
t
t
h
e
w
o
r
k
o
f
ma
t
h
e
ma
t
i
c
s
0.
38
O
t
h
e
r
p
e
o
p
l
e
's
v
i
e
w
s
o
n
ma
t
h
e
ma
t
i
c
a
l
a
b
i
l
i
t
i
e
s
H
a
v
e
ma
t
h
sk
i
l
l
s
0.
41
0.
37
3
7
%
M
e
d
i
u
m
D
o
n
'
t
h
a
v
e
c
o
mm
u
n
i
c
a
t
i
o
n
s
k
i
l
l
s
0.
34
U
n
d
i
sc
i
p
l
i
n
e
d
t
o
w
o
r
k
o
n
i
n
d
e
p
e
n
d
e
n
t
t
a
s
k
s
0.
36
To
t
a
l
0.
34
3
4
%
M
e
d
i
u
m
T
ab
le
3
s
h
o
ws
th
at
s
elf
-
co
n
f
id
en
ce
an
d
s
tu
d
en
ts
’
attitu
d
e
s
to
war
d
m
ath
em
atics
ab
ilit
i
es
ca
n
b
e
in
cr
ea
s
ed
b
y
4
8
%
in
th
e
m
ed
i
u
m
ca
teg
o
r
y
.
B
ased
o
n
th
e
r
e
s
u
lts
o
f
th
e
in
ter
v
iew,
it
was
r
ev
ea
led
th
at
d
u
r
in
g
th
e
p
r
o
ce
s
s
o
f
ex
p
l
o
r
atio
n
an
d
tr
an
s
f
o
r
m
atio
n
o
f
id
ea
s
am
o
n
g
s
tu
d
en
ts
wh
e
n
c
o
llab
o
r
ati
n
g
,
t
h
ey
ex
ch
a
n
g
ed
in
f
o
r
m
atio
n
an
d
g
a
v
e
r
ein
f
o
r
ce
m
en
t,
s
o
th
at
th
ey
co
u
ld
d
ev
elo
p
MS
-
C
p
r
o
s
p
ec
tiv
e
teac
h
er
s
.
T
h
e
C
MM
lear
n
in
g
s
tr
ateg
y
tr
ig
g
er
e
d
s
tu
d
en
ts
to
co
n
s
tr
u
ct
cr
ea
tiv
e
i
d
ea
s
th
r
o
u
g
h
th
o
u
g
h
t
m
ap
s
t
h
at
wer
e
ca
r
r
ied
o
u
t
an
d
r
ea
c
h
ed
a
n
in
cr
ea
s
e
o
f
2
4
%,
b
u
t
s
till
in
th
e
lo
w
ca
teg
o
r
y
.
T
h
e
r
esu
lts
o
f
o
b
s
er
v
atio
n
s
s
h
o
w
th
at
s
tu
d
en
ts
ca
n
p
r
o
v
i
d
e
v
ar
ied
an
s
wer
s
to
co
l
lab
o
r
ativ
e
m
ath
em
ati
cs
p
r
o
b
lem
s
.
T
h
e
p
r
o
ce
s
s
o
f
ex
p
lo
r
i
n
g
an
d
tr
an
s
f
o
r
m
in
g
id
ea
s
r
eq
u
ir
es
an
MS
-
C
th
at
is
s
tr
o
n
g
in
co
n
v
ey
i
n
g
th
e
id
ea
s
o
f
ea
ch
in
d
iv
id
u
al
wh
en
co
llab
o
r
atin
g
in
g
r
o
u
p
s
.
C
MM
lear
n
in
g
s
tr
ateg
y
in
v
o
lv
es
r
ef
lectio
n
as
an
im
p
o
r
ta
n
t
s
tep
in
th
e
c
o
llab
o
r
atio
n
p
r
o
ce
s
s
.
R
ef
lectio
n
ca
n
f
ac
ilit
ate
s
tu
d
en
ts
in
v
ar
io
u
s
lev
els
o
f
ab
ilit
y
to
k
n
o
w
th
eir
wea
k
n
ess
es
an
d
s
tr
en
g
th
s
.
B
y
r
ef
lectio
n
,
s
tu
d
en
ts
ca
n
s
h
ar
e
ex
p
er
ien
ce
s
an
d
p
r
o
v
id
e
m
u
tu
al
r
ei
n
f
o
r
ce
m
en
t,
w
h
ich
h
as
an
im
p
ac
t
o
n
t
h
e
d
ev
elo
p
m
e
n
t
o
f
s
tu
d
en
ts
’
MS
-
C
.
Ar
g
u
ed
t
h
at
r
ef
lectio
n
ca
n
co
n
s
id
er
s
tu
d
en
ts
’
m
o
tiv
atio
n
,
id
ea
s
r
aised
,
s
k
ills
n
ee
d
ed
to
lear
n
in
v
ar
io
u
s
s
itu
atio
n
s
,
an
d
ca
n
r
ef
lect
o
b
s
tacle
s
in
lear
n
in
g
th
at
will
b
e
g
ap
s
in
k
n
o
wled
g
e
an
d
s
k
ills
,
an
d
h
o
w
s
tu
d
en
ts
ca
n
m
an
ag
e
th
em
[3
8
]
.
T
h
r
o
u
g
h
th
e
o
b
s
er
v
atio
n
s
h
ee
t,
it
was
f
o
u
n
d
th
at
th
e
r
e
was
a
p
r
o
ce
s
s
o
f
tr
an
s
f
o
r
m
in
g
id
ea
s
am
o
n
g
s
tu
d
en
ts
wh
o
n
ee
d
ed
c
o
u
r
a
g
e
in
b
u
ild
in
g
ef
f
ec
tiv
e
c
o
m
m
u
n
icatio
n
a
n
d
ac
h
iev
in
g
a
n
in
cr
ea
s
e
o
f
2
6
%.
E
f
f
ec
tiv
e
co
m
m
u
n
icatio
n
was
b
u
ilt
th
r
o
u
g
h
v
a
r
io
u
s
o
p
in
io
n
s
ex
p
r
ess
ed
b
y
s
tu
d
en
ts
in
co
l
lab
o
r
ativ
e
g
r
o
u
p
s
.
C
o
u
r
ag
e
r
eq
u
ir
es
p
o
s
itiv
e
s
elf
-
co
n
ce
p
ts
in
s
tu
d
en
ts
.
Po
s
itiv
e
s
tu
d
en
ts
’
MS
-
C
m
ad
e
co
llab
o
r
atio
n
m
o
r
e
m
ea
n
in
g
f
u
l,
b
ec
au
s
e
th
e
lear
n
in
g
atm
o
s
p
h
er
e
b
ec
am
e
f
u
n
an
d
f
lex
ib
le.
T
h
is
was
s
h
o
wn
th
r
o
u
g
h
s
ev
er
al
th
in
g
s
,
n
am
ely
:
1
)
s
tu
d
e
n
ts
co
llectiv
ely
cr
ea
ted
an
atm
o
s
p
h
er
e
o
f
co
llab
o
r
atio
n
to
b
e
ef
f
ec
tiv
e
an
d
f
u
n
;
2
)
p
r
o
s
p
ec
tiv
e
teac
h
er
s
co
u
l
d
e
x
p
lo
r
e
id
ea
s
in
d
iv
i
d
u
ally
th
r
o
u
g
h
a
v
ar
iety
o
f
i
d
ea
s
co
n
ce
p
tu
alize
d
th
r
o
u
g
h
th
o
u
g
h
t
m
ap
s
;
3
)
T
h
e
C
MM
Stra
teg
y
tr
ig
g
er
e
d
s
tu
d
en
ts
to
ex
ch
an
g
e
id
ea
s
to
ac
h
iev
e
an
ag
r
ee
m
en
t;
4
)
ea
c
h
in
d
iv
id
u
al
co
u
ld
d
em
o
n
s
tr
ate
m
ath
em
atica
l
ab
ilit
y
to
wo
r
k
ef
f
ec
tiv
ely
an
d
a
p
p
r
ec
iate
d
iv
er
s
ity
in
g
r
o
u
p
s
;
5
)
s
tu
d
en
ts
b
u
ilt
cr
iticis
m
an
d
g
iv
e
ea
c
h
o
t
h
er
p
o
s
itiv
e
r
esp
o
n
s
es
f
lex
ib
ly
;
ea
ch
in
d
i
v
id
u
al
ca
r
r
ied
o
u
t
r
esp
o
n
s
ib
ilit
ies
well
in
co
m
p
letin
g
m
ath
em
atics
task
s
,
ev
en
th
o
u
g
h
th
er
e
ar
e
s
o
m
e
s
tu
d
en
ts
wh
o
h
ad
n
o
t
o
p
tim
ized
t
h
eir
th
i
n
k
in
g
ab
ili
ties
;
an
d
6
)
s
tu
d
e
n
ts
s
h
o
wed
r
esp
ec
t
f
o
r
p
ee
r
o
p
in
io
n
s
;
s
tu
d
en
ts
te
n
d
to
s
till
s
h
o
w
p
er
s
o
n
al
s
elf
is
h
n
ess
,
b
u
t
with
th
e
d
ir
ec
tio
n
o
f
th
e
l
ec
tu
r
er
,
th
e
attitu
d
e
o
f
th
e
s
t
u
d
en
t'
s
eg
o
ca
n
b
e
m
in
im
ized
.
T
h
e
C
MM
s
tr
ateg
y
co
n
tr
ib
u
ted
p
o
s
itiv
ely
to
th
e
in
cr
ea
s
e
in
s
tu
d
en
ts
’
MS
-
C
.
Ov
er
all,
s
tu
d
en
ts
ac
h
iev
ed
MS
-
C
in
cr
ea
s
e
in
th
e
m
ed
iu
m
ca
teg
o
r
y
,
wh
ile
in
c
r
ea
s
e
in
th
e
lo
w
an
d
m
ed
iu
m
ca
teg
o
r
ies
f
o
r
t
h
e
MS
-
C
p
er
-
in
d
icato
r
.
T
h
e
ac
h
iev
em
en
t
o
f
in
c
r
ea
s
in
g
MS
-
C
o
f
s
tu
d
en
ts
in
th
e
m
e
d
iu
m
a
n
d
lo
w
ca
teg
o
r
ies
in
d
icate
s
th
at
p
r
o
s
p
ec
tiv
e
teac
h
er
s
in
th
e
b
o
r
d
er
ar
ea
m
u
s
t
b
e
co
n
tin
u
o
u
s
ly
p
r
o
v
i
d
ed
ass
is
tan
ce
an
d
s
tr
en
g
th
en
in
g
o
f
th
e
MS
-
C
c
ap
ac
ity
th
ey
h
a
v
e.
T
h
e
v
iews
o
n
th
e
d
if
f
icu
lty
o
f
m
ath
e
m
atics,
an
x
iety
,
an
d
m
ath
em
atics
s
elf
-
co
n
f
id
en
ce
a
r
e
im
p
o
r
tan
t
in
d
icato
r
s
th
at
m
u
s
t
b
e
im
p
r
o
v
e
d
,
b
ec
au
s
e
th
es
e
in
d
icato
r
s
ar
e
th
e
ca
u
s
es
o
f
th
e
lo
w
in
c
r
ea
s
e
i
n
s
tu
d
en
ts
’
MS
-
C
.
Alth
o
u
g
h
M
S
-
C
in
cr
ea
s
ed
in
t
h
e
lo
w
an
d
m
ed
iu
m
ca
te
g
o
r
ies,
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
Ma
th
ema
tica
l self
-
co
n
ce
p
t a
m
o
n
g
p
r
o
s
p
ec
tive
tea
c
h
ers
(
Jo
h
a
n
n
is
Ta
ka
r
ia
)
805
th
e
C
MM
s
tr
ateg
y
an
d
th
e
s
tr
en
g
th
en
in
g
o
f
MS
-
C
ca
p
ac
ity
wer
e
ef
f
ec
tiv
e
f
o
r
u
s
e
in
m
ath
em
atics
lear
n
in
g
,
b
u
t
it
n
ee
d
ed
a
r
elativ
ely
lo
n
g
tim
e
f
o
r
o
p
tim
al
MS
-
C
d
ev
elo
p
m
en
t.
T
h
e
in
cr
e
ase
o
f
s
tu
d
en
ts
’
MS
-
C
in
lear
n
in
g
is
f
ac
ilit
ated
b
y
s
tr
en
g
th
en
in
g
MS
-
C
ca
p
ac
ity
a
n
d
th
e
u
s
e
o
f
C
MM
lear
n
i
n
g
s
tr
ateg
ies.
On
e
d
im
en
s
io
n
o
f
f
o
r
m
in
g
a
s
elf
c
o
n
ce
p
t
is
c
o
lectiv
e
s
elf
co
n
ce
p
t,
r
ef
e
r
r
in
g
to
th
e
c
o
llab
o
r
ati
v
e
p
r
o
ce
s
s
in
wh
ich
in
d
iv
id
u
als ar
e
lo
ca
t
e
d
[
39
,
4
0
]
.
I
n
d
iv
id
u
al
s
elf
-
co
n
ce
p
ts
ca
n
b
e
f
o
r
m
ed
th
r
o
u
g
h
p
r
o
ce
s
s
es in
g
r
o
u
p
s
wh
en
in
ter
ac
ti
n
g
.
Stu
d
en
ts
’
MS
-
C
ca
n
b
e
im
p
r
o
v
ed
th
r
o
u
g
h
e
f
f
ec
tiv
e
lear
n
in
g
in
ter
ac
t
io
n
s
.
L
ec
tu
r
er
s
ca
n
cr
ea
te
an
atm
o
s
p
h
er
e
an
d
ass
u
m
p
tio
n
o
f
s
tu
d
en
ts
to
w
ar
d
s
th
eir
c
o
n
ce
p
ts
,
b
o
th
p
o
s
itiv
e
an
d
n
eg
ativ
e
s
elf
-
c
o
n
ce
p
ts
.
Pro
f
ess
io
n
al
lectu
r
er
s
s
h
o
u
ld
b
e
ab
le
t
o
b
r
in
g
u
p
a
p
o
s
itiv
e
s
elf
-
c
o
n
ce
p
t
o
f
s
tu
d
en
ts
b
y
way
o
f
,
1
)
r
esp
ec
tin
g
s
tu
d
en
ts
’
o
p
in
io
n
s
,
2
)
p
r
o
v
id
in
g
o
p
p
o
r
t
u
n
ities
f
o
r
s
tu
d
en
ts
to
ask
q
u
esti
o
n
s
,
3
)
t
r
ig
g
er
in
g
c
o
g
n
it
iv
e
co
n
f
lict
am
o
n
g
s
tu
d
en
ts
,
4
)
g
i
v
in
g
p
r
aise
with
wo
r
d
s
th
at
ca
n
m
o
tiv
ate
lear
n
in
g
.
MS
-
C
o
f
p
r
o
s
p
ec
tiv
e
p
r
im
ar
y
s
ch
o
o
l
teac
h
er
s
s
h
o
u
ld
b
e
ab
le
to
a
d
ju
s
t
an
d
ch
an
g
e
with
th
e
c
u
ltu
r
e
in
wh
ich
s
tu
d
en
ts
ar
e
l
o
ca
ted
.
T
h
e
m
i
n
d
s
et
an
d
attitu
d
e
o
f
s
tu
d
en
ts
in
lear
n
in
g
m
u
s
t b
e
ad
ap
ted
to
th
e
c
o
n
tex
tu
al
p
r
o
b
lem
s
o
f
th
e
lo
ca
l c
u
ltu
r
e.
T
h
ese
ch
a
n
g
es
ca
n
af
f
ec
t
th
e
atm
o
s
p
h
er
e
a
n
d
lear
n
in
g
s
ty
les
th
at
ar
e
f
le
x
ib
le
an
d
ch
a
n
g
e
th
e
n
eg
ativ
e
p
e
r
s
p
ec
tiv
e
o
f
o
t
h
er
s
th
r
o
u
g
h
th
e
ab
ilit
ies
s
h
o
wn
wh
en
in
ter
ac
tin
g
[4
1
]
.
T
h
e
o
p
ti
m
al
im
p
lem
en
tati
o
n
o
f
t
h
e
C
MM
lear
n
in
g
s
tr
ateg
y
ca
n
im
p
r
o
v
e
th
e
MS
-
C
o
f
p
r
o
s
p
ec
tiv
e
elem
en
tar
y
s
ch
o
o
l
teac
h
er
in
th
e
b
o
r
d
er
ar
ea
s
i
n
th
e
Ar
u
I
s
lan
d
s
,
Ma
lu
k
u
p
r
o
v
in
ce
,
I
n
d
o
n
esia.
4.
CO
NCLU
SI
O
N
Ov
er
all,
p
r
o
s
p
ec
tiv
e
elem
en
tar
y
s
ch
o
o
l
teac
h
er
h
as
a
n
in
cr
ea
s
e
o
f
MS
-
C
with
a
n
a
v
er
a
g
e
ac
h
iev
em
en
t
o
f
im
p
r
o
v
em
en
t
in
t
h
e
lo
w
ca
teg
o
r
y
.
MS
-
C
p
er
in
d
icato
r
in
cr
ea
s
es
in
th
e
m
ed
iu
m
an
d
l
o
w
ca
teg
o
r
ies.
I
n
cr
ea
s
in
g
th
e
MS
-
C
o
f
p
r
o
s
p
ec
tiv
e
elem
en
tar
y
s
ch
o
o
l
teac
h
er
s
is
d
u
e
to
th
e
p
r
o
ce
s
s
o
f
s
tr
en
g
th
en
in
g
MS
-
C
ca
p
ac
ity
an
d
th
e
ef
f
ec
tiv
en
ess
o
f
cr
ea
ti
v
e
lear
n
in
g
u
s
in
g
th
e
C
MM
s
tr
ateg
y
.
T
h
e
C
MM
s
tr
ateg
y
ca
n
f
ac
ilit
ate
s
tu
d
en
ts
to
s
h
ar
e
m
ath
em
atica
l
id
ea
s
c
r
ea
tiv
ely
th
r
o
u
g
h
a
co
llab
o
r
ati
v
e
p
r
o
ce
s
s
ca
r
r
ied
o
u
t
in
s
tr
u
ctu
r
e
d
co
llectiv
ity
.
I
n
th
e
co
llab
o
r
ativ
e
p
r
o
ce
s
s
,
s
tu
d
en
ts
g
iv
e
a
p
o
s
itiv
e
r
esp
o
n
s
e
to
lear
n
in
g
with
th
e
C
MM
s
tr
ateg
y
.
T
h
is
r
es
p
o
n
s
e
h
as
im
p
licatio
n
s
o
n
t
h
e
in
cr
ea
s
in
g
MS
-
C
in
d
icat
o
r
s
o
n
p
r
o
s
p
ec
tiv
e
teac
h
er
s
.
T
o
in
cr
ea
s
e
th
e
MS
-
C
,
it
r
eq
u
ir
es
a
co
n
tin
u
o
u
s
p
r
o
ce
s
s
.
T
h
is
co
n
clu
s
io
n
r
ec
o
m
m
en
d
s
r
elev
an
t
r
esear
ch
to
b
e
ca
r
r
ied
o
u
t
b
y
u
s
in
g
o
th
er
c
r
ea
tiv
e
lear
n
in
g
s
tr
ateg
ies
in
m
ea
s
u
r
in
g
m
o
tiv
atio
n
,
s
elf
-
p
r
o
f
icien
c
y
,
an
d
o
th
er
asp
ec
ts
o
f
attitu
d
es,
as we
ll a
s
m
ath
em
atics lea
r
n
in
g
o
u
tc
o
m
es.
RE
F
E
R
E
NC
E
S
[1
]
V.
Ko
lo
ss
o
v
a
n
d
J.
S
c
o
tt
,
“
S
e
lec
ted
c
o
n
c
e
p
t
u
a
l
issu
e
s i
n
b
o
rd
e
r
st
u
d
ies
,”
Belg
e
o
,
v
o
l.
2
0
1
3
,
n
o
.
1
,
p
p
.
1
–
1
9
,
2
0
1
3
.
[2
]
Y.
Lai,
e
t
a
l
.
,
“
Eff
e
c
ts
o
f
m
a
th
e
m
a
ti
c
s
a
n
x
iety
a
n
d
m
a
th
e
m
a
ti
c
a
l
m
e
tac
o
g
n
it
i
o
n
o
n
wo
rd
p
r
o
b
lem
so
l
v
in
g
i
n
c
h
il
d
re
n
with
a
n
d
wit
h
o
u
t
m
a
th
e
m
a
ti
c
a
l
lea
rn
in
g
d
iffi
c
u
lt
ies
,”
PL
o
S
On
e
,
v
o
l.
1
0
,
n
o
.
6
,
p
p
.
1
–
1
9
,
2
0
1
5
.
[3
]
M
.
P
a
e
c
h
ter,
D.
M
a
c
h
e
r,
K.
M
a
rtsk
v
ish
v
il
i
,
S
.
Wi
m
m
e
r,
a
n
d
I
.
P
a
p
o
u
se
k
,
“
M
a
t
h
e
m
a
ti
c
s
An
x
iet
y
a
n
d
sta
ti
stics
a
n
x
iety
.
S
h
a
re
d
b
u
t
a
lso
u
n
s
h
a
re
d
c
o
m
p
o
n
e
n
ts
a
n
d
a
n
tag
o
n
isti
c
c
o
n
tri
b
u
t
io
n
s
to
p
e
rf
o
rm
a
n
c
e
in
sta
ti
stics
,”
Fro
n
t.
Ph
y
sio
l.
,
v
o
l.
8
,
n
o
.
J
u
l
y
,
p
p
.
1
–
1
3
,
2
0
1
7
.
[4
]
J.
Xu
,
“
Re
c
ip
r
o
c
a
l
e
ffe
c
ts
o
f
h
o
m
e
wo
rk
se
lf
-
c
o
n
c
e
p
t,
i
n
tere
st,
e
ffo
rt,
a
n
d
m
a
th
a
c
h
iev
e
m
e
n
t
,”
Co
n
tem
p
.
Ed
u
c
.
Psy
c
h
o
l.
,
v
o
l
.
5
5
,
p
p
.
4
2
–
5
2
,
Oc
t.
2
0
1
8
.
[5
]
A.
D.
G
o
ld
m
a
n
a
n
d
A.
M
.
P
e
n
n
e
r
,
“
Ex
p
l
o
rin
g
in
ter
n
a
ti
o
n
a
l
g
e
n
d
e
r
d
iffere
n
c
e
s
in
m
a
th
e
m
a
ti
c
s
se
lf
-
c
o
n
c
e
p
t
,”
In
t.
J
.
Ad
o
les
c
.
Y
o
u
th
,
v
o
l.
2
1
,
n
o
.
4
,
p
p
.
4
0
3
–
4
1
8
,
2
0
1
6
.
[6
]
A.
G
re
g
o
ry
,
R.
P
.
Ha
stin
g
s,
a
n
d
H.
Ko
v
sh
o
ff
,
“
Ac
a
d
e
m
ic
se
lf
-
c
o
n
c
e
p
t
a
n
d
se
n
se
o
f
sc
h
o
o
l
b
e
lo
n
g
i
n
g
o
f
a
d
o
les
c
e
n
t
sib
li
n
g
s o
f
a
u
ti
stic c
h
il
d
re
n
,”
Res
.
De
v
.
Disa
b
il
.
,
v
o
l.
9
6
,
n
o
.
Ja
n
u
a
r
y
,
p
p
.
3
7
-
45
,
2
0
2
0
.
[7
]
M
.
M
.
Ha
m
m
o
u
d
i
,
“
M
e
a
su
re
m
e
n
t
o
f
st
u
d
e
n
ts’
m
a
th
e
m
a
ti
c
s
m
o
ti
v
a
ti
o
n
a
n
d
se
lf
-
c
o
n
c
e
p
t
a
t
i
n
stit
u
ti
o
n
s
o
f
h
ig
h
e
r
e
d
u
c
a
ti
o
n
:
e
v
i
d
e
n
c
e
o
f
re
li
a
b
il
it
y
a
n
d
v
a
li
d
it
y
,”
I
n
t.
J
.
M
a
th
.
Ed
u
c
.
S
c
i.
T
e
c
h
n
o
l.
,
v
o
l.
51
,
n
o
.
1
,
p
p
.
1
–
2
4
,
2
0
1
9
.
[8
]
I.
B.
Wo
lt
e
r
a
n
d
B
.
Ha
n
n
o
v
e
r
,
“
G
e
n
d
e
r
r
o
le
se
lf
-
c
o
n
c
e
p
t
a
t
sc
h
o
o
l
sta
rt
a
n
d
it
s
imp
a
c
t
o
n
a
c
a
d
e
m
ic
se
lf
-
c
o
n
c
e
p
t
a
n
d
p
e
rfo
rm
a
n
c
e
in
m
a
th
e
m
a
ti
c
s a
n
d
re
a
d
in
g
,”
E
u
r.
J
.
De
v
.
Psy
c
h
o
l.
,
v
o
l.
1
3
,
n
o
.
6
,
p
p
.
6
8
1
–
7
0
3
,
2
0
1
6
.
[9
]
M
.
S
e
a
to
n
,
P
.
P
a
rk
e
r,
H.
W.
M
a
r
sh
,
R.
G
.
Cra
v
e
n
,
a
n
d
A.
S
.
Ye
u
n
g
,
“
Th
e
re
c
ip
r
o
c
a
l
re
latio
n
s
b
e
tw
e
e
n
se
lf
-
c
o
n
c
e
p
t,
m
o
ti
v
a
ti
o
n
a
n
d
a
c
h
iev
e
m
e
n
t:
Ju
x
t
a
p
o
sin
g
a
c
a
d
e
m
ic
se
lf
-
c
o
n
c
e
p
t
a
n
d
a
c
h
ie
v
e
m
e
n
t
g
o
a
l
o
rie
n
tatio
n
s
fo
r
m
a
th
e
m
a
ti
c
s
su
c
c
e
ss
,”
Ed
u
c
.
Psy
c
h
o
l.
,
v
o
l.
3
4
,
n
o
.
1
,
p
p
.
4
9
–
7
2
,
2
0
1
4
.
[1
0
]
J.
F
a
n
g
,
X.
H
u
a
n
g
,
M
.
Z
h
a
n
g
,
F
.
Hu
a
n
g
,
Z.
Li
,
a
n
d
Q.
Yu
an
,
“
Th
e
b
i
g
-
fish
-
li
tt
le
-
p
o
n
d
e
ffe
c
t
o
n
a
c
a
d
e
m
ic
se
lf
-
c
o
n
c
e
p
t:
A m
e
ta
-
a
n
a
ly
sis
,”
Fr
o
n
t.
Psy
c
h
o
l.
,
v
o
l.
9
,
n
o
.
A
u
g
u
st
,
p
p
.
1
–
1
1
,
2
0
1
8
.
[1
1
]
L.
Ho
l
o
p
a
i
n
e
n
,
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.
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.
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ts
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[1
3
]
G
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.
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.
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.
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.
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Trau
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Ba
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T
h
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De
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ts’
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lf
-
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t
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Re
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r:
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t
Co
u
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tri
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s,
Diffe
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n
t
Traje
c
to
ries
?
”
J
.
Res
.
A
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.
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.
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.
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J.
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in
,
“
An
a
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.
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5
]
W.
L
u
o
,
D.
Ho
g
a
n
,
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S
.
Tan
,
B
.
Ka
u
r,
P
.
T
.
N
g
,
a
n
d
M
.
C
h
a
n
,
“
S
e
lf
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c
o
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l
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ts’
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lf
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rs
,”
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n
J
.
S
o
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.
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.
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.
[1
6
]
C.
S
u
a
n
d
M
.
H
y
n
ie
,
“
Eff
e
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ts
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o
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d
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se
,
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ro
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n
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n
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d
ian
,
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n
d
C
h
in
e
se
Ca
n
a
d
ian
imm
ig
ra
n
t
m
o
th
e
rs
,”
J
.
Cro
ss
.
C
u
lt
.
Psy
c
h
o
l.
,
v
o
l
.
4
2
,
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o
.
6
,
p
p
.
9
4
4
–
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6
2
,
2
0
1
1
.
[1
7
]
H.
S
a
lmi,
M
.
P
.
Va
in
ik
a
i
n
e
n
,
a
n
d
H.
Th
u
n
e
b
e
rg
,
“
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m
a
ti
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a
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il
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se
lf
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tre
e
x
h
ib
it
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n
in
Latv
ia
a
n
d
S
we
d
e
n
,”
J
.
S
c
i.
C
o
mm
u
n
.
,
v
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l.
1
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,
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o
.
4
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p
p
.
1
–
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9
,
2
0
1
5
.
[1
8
]
R.
S
h
e
ld
ra
k
e
,
“
Diffe
re
n
ti
a
l
p
re
d
icto
rs
o
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u
n
d
e
r
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ti
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s
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n
d
sc
ien
c
e
stu
d
e
n
ts
in
E
n
g
lan
d
,”
L
e
a
rn
.
In
d
i
v
id
.
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l.
4
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p
.
3
0
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–
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1
3
,
Ju
l.
2
0
1
6
.
[1
9
]
T.
Ry
b
e
rg
,
J.
Da
v
i
d
se
n
,
a
n
d
V.
Ho
d
g
so
n
,
“
Un
d
e
rsta
n
d
i
n
g
n
o
m
a
d
ic
c
o
ll
a
b
o
ra
ti
v
e
lea
rn
in
g
g
ro
u
p
s
,”
Br.
J
.
E
d
u
c
.
T
e
c
h
n
o
l
.
,
v
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l
.
4
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p
.
2
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0
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.
[2
0
]
E.
Re
tn
o
wa
ti
,
P
.
Ay
re
s
,
a
n
d
J.
S
we
ll
e
r,
“
Co
ll
a
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ra
ti
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lea
rn
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e
ffe
c
ts
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n
st
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n
ts
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a
v
e
c
o
m
p
lete
o
r
in
c
o
m
p
lete
k
n
o
wle
d
g
e
,”
A
p
p
l
ied
C
o
g
n
it
ive
P
sy
c
h
o
lo
g
y
,
v
o
l.
3
2
,
n
o
.
6
,
p
p
.
68
1
–
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2
,
2
0
1
8
.
[2
1
]
L.
A.
F
e
n
g
e
,
“
En
h
a
n
c
in
g
t
h
e
d
o
c
to
ra
l
jo
u
rn
e
y
:
T
h
e
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o
le
o
f
g
r
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u
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su
p
e
rv
isi
o
n
in
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p
o
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n
g
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o
ll
a
b
o
ra
ti
v
e
lea
rn
in
g
a
n
d
c
re
a
ti
v
it
y
,”
S
tu
d
.
Hi
g
h
.
Ed
u
c
.
,
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l.
3
7
,
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o
.
4
,
p
p
.
4
0
1
–
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4
,
2
0
1
2
.
[2
2
]
S
.
M
.
Rit
ter
a
n
d
N.
M
o
ste
rt
,
“
En
h
a
n
c
e
m
e
n
t
o
f
Cre
a
ti
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e
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n
k
in
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k
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ll
s
Us
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g
a
C
o
g
n
it
iv
e
-
B
a
se
d
Cre
a
ti
v
it
y
Train
in
g
,”
J
.
C
o
g
n
.
E
n
h
a
n
c
.
,
v
o
l.
1
,
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o
.
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,
p
p
.
2
4
3
–
2
5
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,
2
0
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7
.
[2
3
]
C.
Ro
sé
,
e
t
a
l.
,
“
An
a
ly
z
in
g
c
o
ll
a
b
o
ra
ti
v
e
lea
rn
in
g
p
r
o
c
e
ss
e
s a
u
to
m
a
ti
c
a
ll
y
:
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p
lo
i
ti
n
g
th
e
a
d
v
a
n
c
e
s o
f
c
o
m
p
u
tatio
n
a
l
li
n
g
u
isti
c
s
i
n
c
o
m
p
u
ter
-
su
p
p
o
rted
c
o
ll
a
b
o
ra
ti
v
e
lea
rn
in
g
,”
In
t.
J
.
C
o
mp
u
t
.
C
o
ll
a
b
.
L
e
a
r
n
.
,
v
o
l.
3
,
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o
.
3
,
p
p
.
2
3
7
–
2
7
1
,
2
0
0
8
.
[2
4
]
N.
Da
v
id
so
n
a
n
d
C.
H.
M
a
jo
r
,
“
Bo
u
n
d
a
ry
Cr
o
ss
in
g
s:
C
o
o
p
e
ra
ti
v
e
Lea
rn
in
g
,
C
o
ll
a
b
o
ra
ti
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e
Lea
rn
i
n
g
,
a
n
d
P
r
o
b
lem
-
Ba
se
d
Lea
rn
in
g
,”
J
.
Exc
e
ll
.
Co
l
l.
T
e
a
c
h
.
,
v
o
l.
2
5
,
n
o
.
3
-
4
,
p
p
.
7
–
5
5
,
2
0
1
4
.
[2
5
]
A.
Ro
sc
ian
o
,
“
T
h
e
e
ffe
c
ti
v
e
n
e
ss
o
f
m
in
d
m
a
p
p
in
g
a
s
a
n
a
c
ti
v
e
l
e
a
rn
in
g
stra
teg
y
a
m
o
n
g
a
ss
o
c
iate
d
e
g
re
e
n
u
rsi
n
g
stu
d
e
n
ts
,”
T
e
a
c
h
.
L
e
a
rn
.
Nu
rs
.
,
v
o
l.
1
0
,
n
o
.
2
,
p
p
.
9
3
–
9
9
,
2
0
1
5
.
[2
6
]
J.
R.
Ba
tl
o
lo
n
a
a
n
d
H.
F
.
S
o
u
isa
,
“
P
ro
b
lem
b
a
se
d
lea
rn
in
g
:
S
t
u
d
e
n
t
s’
m
e
n
tal
m
o
d
e
ls o
n
wa
ter
c
o
n
d
u
c
ti
v
it
y
c
o
n
c
e
p
t
,”
In
t.
J
.
Eva
l.
Res
.
Ed
u
c
.
,
v
o
l
.
9
,
n
o
.
2
,
p
p
.
2
6
9
–
2
7
7
,
2
0
2
0
.
[2
7
]
E.
A.
M
c
Cre
a
a
n
d
S
.
J.
Lo
re
n
z
e
t
,
“
M
in
d
M
a
p
p
i
n
g
:
An
Ex
p
e
rien
ti
a
l
Ap
p
r
o
a
c
h
t
o
S
y
ll
a
b
u
s
Re
v
iew
,”
Or
g
a
n
.
M
a
n
a
g
.
J.
,
v
o
l.
1
5
,
n
o
.
1
,
p
p
.
3
5
–
4
3
,
2
0
1
8
.
[2
8
]
H.
S
to
k
h
o
f,
B.
d
e
Vrie
s,
T
.
Ba
sti
a
e
n
s,
a
n
d
R.
M
a
rten
s
,
“
Us
in
g
M
i
n
d
M
a
p
s
to
M
a
k
e
S
tu
d
e
n
t
Qu
e
sti
o
n
i
n
g
Eff
e
c
ti
v
e
:
Lea
rn
in
g
Ou
tco
m
e
s o
f
a
P
rin
c
i
p
le
-
Ba
se
d
S
c
e
n
a
rio
fo
r
Tea
c
h
e
r
G
u
id
a
n
c
e
,”
Res
.
S
c
i.
Ed
u
c
.
,
v
o
l.
5
0
,
p
p
.
1
–
2
3
,
2
0
1
8
.
[2
9
]
R.
Ok
a
n
o
,
e
t
a
l.
,
“
Th
e
Us
e
a
n
d
I
n
t
,”
J
Am
M
e
d
In
f.
Asso
c
.
,
v
o
l.
1
3
,
n
o
.
1
,
p
p
.
1
6
–
2
3
,
2
0
0
6
.
[3
0
]
W. L.
Ha
y
s,
Qu
a
n
ti
fi
c
a
ti
o
n
in
p
sy
c
h
o
lo
g
y
.
P
re
n
ti
c
e
Ha
ll
:
Ne
w De
lh
i
,
1
9
67
.
[3
1
]
R.
R.
Ha
k
e
,
“
In
tera
c
ti
v
e
-
e
n
g
a
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e
n
t
v
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rsu
s
tra
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it
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o
n
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l
m
e
th
o
d
s:
A
six
-
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sa
n
d
-
st
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t
su
r
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e
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o
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m
e
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h
a
n
ics
tes
t
d
a
ta fo
r
i
n
tro
d
u
c
t
o
ry
p
h
y
sic
s c
o
u
r
se
s
,”
Am.
J
.
Ph
y
s.
,
v
o
l
.
6
6
,
n
o
.
1
,
p
p
.
6
4
–
7
4
,
1
9
9
8
.
[3
2
]
D.
E.
M
e
lt
z
e
r
,
“
Th
e
re
lati
o
n
s
h
ip
b
e
twe
e
n
m
a
t
h
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m
a
ti
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s
p
re
p
a
ra
ti
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n
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n
d
c
o
n
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e
p
tu
a
l
lea
rn
i
n
g
g
a
i
n
s
in
p
h
y
sic
s:
A
p
o
ss
ib
le ‘
h
i
d
d
e
n
v
a
riab
le’ i
n
d
iag
n
o
stic
p
re
tes
t
sc
o
re
s
,”
Am.
J
.
P
h
y
s.
,
v
o
l.
7
0
,
n
o
.
1
2
,
p
p
.
1
2
5
9
–
1
2
6
8
,
2
0
0
2
.
[3
3
]
C.
N.
L
o
e
s,
K.
C
.
C
u
lv
e
r,
a
n
d
T.
L
.
Tr
o
li
a
n
,
“
Ho
w
C
o
ll
a
b
o
r
a
ti
v
e
Lea
rn
in
g
En
h
a
n
c
e
s
S
tu
d
e
n
ts’
Op
e
n
n
e
ss
t
o
Div
e
rsity
,”
J
.
Hi
g
h
e
r E
d
u
c
.
,
v
o
l.
8
9
,
n
o
.
6
,
p
p
.
9
3
5
–
9
6
0
,
2
0
1
8
.
[3
4
]
C.
N.
Lo
e
s
a
n
d
E.
T.
P
a
sc
a
re
ll
a
,
“
Co
ll
a
b
o
ra
ti
v
e
Lea
rn
in
g
a
n
d
Crit
i
c
a
l
Th
in
k
in
g
:
Tes
ti
n
g
t
h
e
Li
n
k
,”
J
.
Hig
h
e
r
Ed
u
c
.
,
v
o
l.
8
8
,
n
o
.
5
,
p
p
.
7
2
6
–
7
5
3
,
2
0
1
7
.
[3
5
]
S
.
Zh
a
o
,
S
.
G
ra
sm
u
c
k
,
a
n
d
J.
M
a
rti
n
,
“
Id
e
n
ti
t
y
c
o
n
str
u
c
ti
o
n
o
n
F
a
c
e
b
o
o
k
:
Di
g
it
a
l
e
m
p
o
we
rm
e
n
t
in
a
n
c
h
o
re
d
re
latio
n
sh
i
p
s
,”
Co
m
p
u
t
.
Hu
m
a
n
B
e
h
a
v
.
,
v
o
l
.
2
4
,
n
o
.
5
,
p
p
.
1
8
1
6
–
1
8
3
6
,
2
0
0
8
.
[3
6
]
E.
Wo
o
d
a
n
d
H.
He
d
g
e
s
,
“
Cu
rric
u
lu
m
i
n
e
a
rly
c
h
il
d
h
o
o
d
e
d
u
c
a
ti
o
n
:
c
rit
ica
l
q
u
e
stio
n
s
a
b
o
u
t
c
o
n
te
n
t
,
c
o
h
e
re
n
c
e
,
a
n
d
c
o
n
tro
l
,”
Cu
rr
ic.
J
.
,
v
o
l.
2
7
,
n
o
.
3
,
p
p
.
3
8
7
–
4
0
5
,
2
0
1
6
.
[3
7
]
M
.
Lea
sa
,
A.
D.
Co
re
b
ima
,
Ib
r
o
h
im,
a
n
d
H.
S
u
wo
n
o
,
“
Emo
t
i
o
n
a
l
i
n
telli
g
e
n
c
e
a
m
o
n
g
a
u
d
it
o
r
y
,
re
a
d
in
g
,
a
n
d
k
in
e
sth
e
ti
c
lea
rn
in
g
sty
les
o
f
e
lem
e
n
tary
sc
h
o
o
l
st
u
d
e
n
ts
i
n
Am
b
o
n
-
I
n
d
o
n
e
sia
,”
I
n
t.
El
e
c
tro
n
.
J
.
E
lem
.
E
d
u
c
.
,
v
o
l.
1
0
,
n
o
.
1
,
p
p
.
8
3
–
9
1
,
2
0
1
7
.
[3
8
]
M
.
Lea
sa
,
M
.
Tala
k
u
a
,
a
n
d
J.
R.
Ba
tl
o
l
o
n
a
,
“
T
h
e
d
e
v
e
l
o
p
m
e
n
t
o
f
a
th
e
m
a
ti
c
m
o
d
u
le
b
a
se
d
o
n
N
u
m
b
e
re
d
He
a
d
s
To
g
e
t
h
e
r
(NH
T)
c
o
o
p
e
ra
ti
v
e
lea
rn
in
g
m
o
d
e
l
f
o
r
e
lem
e
n
tary
st
u
d
e
n
ts
i
n
Am
b
o
n
,
M
o
lu
c
c
a
s
-
In
d
o
n
e
s
ia
,”
Ne
w
Ed
u
c
.
Rev
.
,
v
o
l.
4
6
,
n
o
.
4
,
p
p
.
1
7
4
–
1
8
5
,
2
0
1
6
.
[3
9
]
N.
R.
B
o
y
e
r,
P
.
A.
M
a
h
e
r,
a
n
d
S
.
Kirk
m
a
n
,
“
Tran
sf
o
r
m
a
ti
v
e
Lea
rn
i
n
g
in
On
li
n
e
S
e
tt
in
g
s:
T
h
e
Us
e
o
f
S
e
lf
-
Dire
c
ti
o
n
,
M
e
tac
o
g
n
it
io
n
,
a
n
d
Co
ll
a
b
o
ra
ti
v
e
Lea
rn
in
g
,”
J
.
T
r
a
n
sfo
rm
.
Ed
u
c
.
,
v
o
l.
4
,
n
o
.
4
,
p
p
.
3
3
5
–
3
6
1
,
2
0
0
6
.
[
40
]
K.
S
c
a
g
e
r,
J.
Bo
o
n
stra
,
T.
P
e
e
te
rs,
J.
Vu
lp
e
r
h
o
rst,
a
n
d
F
.
W
ieg
a
n
t
,
“
Co
l
lab
o
ra
ti
v
e
lea
rn
i
n
g
i
n
h
i
g
h
e
r
e
d
u
c
a
ti
o
n
:
Ev
o
k
in
g
p
o
siti
v
e
in
terd
e
p
e
n
d
e
n
c
e
,”
CBE
L
if
e
S
c
i.
E
d
u
c
.
,
v
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l.
1
5
,
n
o
.
4
,
p
p
.
1
–
9
,
2
0
1
6
.
[4
1
]
A.
A.
An
d
e
rso
n
,
e
t
a
l.
,
“
E
x
p
l
o
ri
n
g
t
h
e
ro
le
o
f
tas
k
p
e
rf
o
rm
a
n
c
e
a
n
d
lea
rn
in
g
sty
le
o
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re
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o
n
tal
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e
m
o
d
y
n
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m
ics
d
u
ri
n
g
a
w
o
rk
i
n
g
m
e
m
o
ry
tas
k
,”
PL
o
S
On
e
,
v
o
l
.
1
3
,
n
o
.
6
,
p
p
.
1
–
1
6
,
2
0
1
8
.
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