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[
1
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[
3
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,
p
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[
4
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[
6
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[
7
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[
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[
9
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1
4
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I
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Ph
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r
o
g
r
am
s
d
o
n
o
t
h
elp
s
tu
d
en
ts
attain
th
eir
ac
ad
em
ic
g
o
als
[
9
]
,
[
2
3
]
–
[
2
5
]
.
As
n
o
ted
,
s
tu
d
en
ts
co
n
tin
u
e
u
s
in
g
m
alad
ap
tiv
e
lear
n
in
g
m
eth
o
d
s
d
u
e
to
a
f
ailu
r
e
to
r
ec
o
g
n
ize
t
h
e
co
n
s
tr
u
ctiv
e
p
o
ten
tial
o
f
th
e
f
ee
d
b
ac
k
th
e
y
r
ec
eiv
e.
I
n
co
r
p
o
r
atin
g
th
e
c
o
r
r
ec
t
u
s
e
o
f
f
ee
d
b
ac
k
in
to
class
r
o
o
m
i
n
s
tr
u
ctio
n
in
v
o
l
v
es
th
e
u
s
e
o
f
c
o
g
n
itiv
e
an
d
m
et
ac
o
g
n
itiv
e
lea
r
n
in
g
s
tr
ateg
ies [
2
6
]
,
[
2
7
]
.
Sev
er
al
liter
atu
r
e
a
n
d
s
tu
d
ies
h
av
e
r
ev
ea
led
th
at
e
f
f
ec
tiv
e
lear
n
in
g
is
d
ep
e
n
d
en
t
u
p
o
n
ef
f
ec
tiv
e
in
f
o
r
m
atio
n
p
r
o
ce
s
s
in
g
ce
n
ter
ed
u
p
o
n
co
g
n
itiv
e
a
n
d
m
etac
o
g
n
itiv
e
s
k
ills
[
2
8
]
–
[
3
1
]
.
As
s
u
ch
s
tu
d
en
ts
’
u
s
e
o
f
lear
n
in
g
s
tr
ateg
ies
f
o
r
s
elf
-
r
eg
u
latio
n
ten
d
s
to
in
cr
ea
s
e
th
eir
ac
ad
em
ic
s
u
cc
ess
.
C
o
g
n
itiv
e
s
tr
ateg
ies,
s
u
ch
as
co
n
tr
o
l,
elab
o
r
atio
n
,
o
r
g
an
iz
atio
n
,
an
d
r
eh
ea
r
s
al
f
ac
ilit
ate
in
f
o
r
m
atio
n
p
r
o
ce
s
s
in
g
an
d
r
eten
tio
n
[
3
2
]
.
C
o
n
v
er
s
ely
,
m
etac
o
g
n
itiv
e
s
tr
ateg
ies
in
clu
d
in
g
p
lan
n
in
g
,
m
o
n
ito
r
in
g
an
d
ev
al
u
atio
n
e
m
p
o
wer
lear
n
e
r
s
to
r
eg
u
late
th
eir
o
wn
lear
n
in
g
[
3
3
],
[
3
4
]
.
W
h
ile
th
e
b
en
ef
its
o
f
co
g
n
itiv
e
an
d
m
etac
o
g
n
itiv
e
s
tr
ateg
ies
ar
e
well
-
estab
li
s
h
ed
i
n
v
ar
io
u
s
ac
ad
em
ic
d
o
m
ain
s
,
th
ei
r
s
p
ec
i
f
ic
im
p
ac
t
o
n
m
ath
em
atics
p
e
r
f
o
r
m
an
ce
r
e
q
u
ir
es
f
u
r
th
er
in
v
esti
g
atio
n
.
T
o
d
ate,
lim
ited
r
esear
ch
h
as
ex
p
lo
r
ed
h
o
w
th
ese
s
tr
ateg
ies
c
o
n
tr
ib
u
te
t
o
s
tu
d
e
n
ts
'
m
ath
em
atica
l
p
r
o
f
icien
cy
,
p
ar
ticu
lar
ly
am
o
n
g
u
n
iv
er
s
ity
s
tu
d
en
ts
.
T
h
is
s
tu
d
y
aim
ed
t
o
b
r
id
g
e
th
is
k
n
o
wled
g
e
g
a
p
b
y
e
x
am
in
in
g
th
e
r
elatio
n
s
h
ip
b
etwe
en
co
g
n
itiv
e
an
d
m
etac
o
g
n
itiv
e
lear
n
in
g
s
tr
ateg
ies
an
d
m
ath
em
atics
ac
h
iev
em
en
t
in
th
is
p
o
p
u
latio
n
.
Sp
ec
if
ically
,
it a
i
m
ed
to
an
s
wer
th
e
f
o
llo
win
g
r
esear
ch
q
u
esti
o
n
s
:
−
W
h
at
ar
e
th
e
s
tu
d
en
ts
’
lev
els
o
f
co
g
n
itiv
e
lear
n
in
g
s
tr
ateg
ies
in
ter
m
s
o
f
c
o
n
tr
o
l,
elab
o
r
atio
n
,
o
r
g
an
izatio
n
,
an
d
r
eh
ea
r
s
al?
−
W
h
at
ar
e
th
e
s
tu
d
en
ts
’
lev
els
o
f
m
etac
o
g
n
itiv
e
lear
n
in
g
s
tr
ateg
ies
in
ter
m
s
o
f
p
lan
n
in
g
,
m
o
n
ito
r
in
g
,
an
d
ev
alu
atio
n
?
−
W
h
at
is
th
e
lev
el
o
f
s
tu
d
en
ts
’
m
ath
em
atics p
r
o
f
icien
c
y
?
−
I
s
th
er
e
a
s
ig
n
if
ican
t r
elatio
n
s
h
ip
b
etwe
en
c
o
g
n
itiv
e
lear
n
in
g
s
tr
ateg
ies an
d
m
ath
em
atics p
r
o
f
icien
cy
?
−
I
s
th
er
e
a
s
ig
n
if
ican
t r
elatio
n
s
h
ip
b
etwe
en
m
etac
o
g
n
itiv
e
lea
r
n
in
g
s
tr
ateg
ies an
d
m
ath
em
at
ics p
r
o
f
icien
cy
?
B
ased
o
n
th
e
r
esear
ch
q
u
esti
o
n
s
,
th
e
f
o
llo
win
g
n
u
ll
h
y
p
o
th
eses
wer
e
test
ed
:
i)
H
0
1
:
t
h
er
e
is
n
o
s
ig
n
if
ican
t
r
elatio
n
s
h
ip
b
etwe
en
co
g
n
itiv
e
lear
n
in
g
s
tr
ateg
ies
an
d
m
ath
em
atics
p
r
o
f
icien
cy
;
an
d
ii)
H
0
2
:
t
h
er
e
is
n
o
s
ig
n
if
ican
t r
elatio
n
s
h
ip
b
etwe
e
n
m
etac
o
g
n
itiv
e
lear
n
in
g
s
tr
ateg
ies an
d
m
ath
em
atics p
r
o
f
ici
en
cy
.
2.
M
E
T
H
O
D
2
.
1
.
Resea
rc
h
d
esig
n
T
h
is
s
tu
d
y
em
p
lo
y
ed
a
d
escr
ip
tiv
e
-
co
r
r
elatio
n
al
r
esear
ch
d
esig
n
to
ad
d
r
ess
th
e
r
esear
c
h
in
q
u
ir
y
t
o
in
v
esti
g
ate
th
e
r
elatio
n
s
h
ip
b
etwe
en
co
g
n
itiv
e
an
d
m
eta
co
g
n
itiv
e
lear
n
in
g
s
tr
ateg
ies
an
d
m
ath
em
atics
p
r
o
f
icien
c
y
am
o
n
g
u
n
i
v
er
s
ity
f
r
esh
m
en
s
tu
d
en
ts
.
Descr
ip
tiv
e
d
esig
n
was u
s
ed
to
ch
ar
ac
ter
ize
th
e
r
esp
o
n
d
e
n
ts
'
lev
el
o
f
co
g
n
itiv
e
a
n
d
m
etac
o
g
n
itiv
e
lear
n
in
g
s
tr
ateg
ies
a
s
well
as
th
eir
m
ath
em
atics
p
r
o
f
icien
c
y
,
wh
ile
co
r
r
elatio
n
al
d
esig
n
was
u
s
ed
to
d
eter
m
in
e
th
e
ass
o
ciatio
n
b
etwe
en
th
ese
lear
n
in
g
s
tr
ateg
i
es
an
d
m
at
h
em
atics
p
r
o
f
icien
c
y
.
2
.
2
.
P
a
rt
icipa
nts a
nd
s
a
m
pli
ng
t
ec
hn
iqu
e
Prio
r
to
th
e
d
ata
co
llectio
n
,
wr
itten
in
f
o
r
m
ed
co
n
s
en
t
was
o
b
tain
ed
f
r
o
m
th
e
p
ar
ticip
a
n
ts
wh
ich
o
u
tlin
es
th
e
s
tu
d
y
’
s
o
b
jectiv
es,
p
r
o
ce
d
u
r
es,
v
o
l
u
n
tar
y
p
a
r
ticip
atio
n
,
an
d
d
ata
co
n
f
id
e
n
tiality
m
ea
s
u
r
es.
Mo
r
eo
v
er
,
s
tr
atif
ied
r
an
d
o
m
s
am
p
lin
g
was
em
p
l
o
y
ed
to
e
n
s
u
r
e
ad
e
q
u
ate
a
n
d
b
alan
ce
d
r
ep
r
esen
tatio
n
o
f
s
tu
d
en
ts
ac
r
o
s
s
th
e
v
ar
io
u
s
ac
ad
em
ic
p
r
o
g
r
am
s
in
th
e
u
n
iv
e
r
s
ity
.
I
n
th
is
p
r
o
ce
d
u
r
e,
th
e
e
n
tire
p
o
p
u
latio
n
o
f
f
r
esh
m
en
was
f
ir
s
t
d
iv
id
e
d
i
n
to
d
is
tin
ct
s
tr
ata
b
ased
o
n
th
eir
en
r
o
lled
co
lleg
e
o
r
d
eg
r
ee
p
r
o
g
r
am
.
E
ac
h
s
tr
atu
m
th
er
ef
o
r
e
r
ep
r
esen
ted
a
h
o
m
o
g
e
n
eo
u
s
s
u
b
g
r
o
u
p
wit
h
s
im
ilar
ac
ad
em
ic
af
f
iliatio
n
s
.
Af
ter
estab
lis
h
in
g
th
e
s
tr
ata,
th
e
r
esear
ch
e
r
s
d
eter
m
in
ed
t
h
e
p
r
o
p
o
r
tio
n
al
a
llo
ca
tio
n
f
o
r
ea
ch
s
u
b
g
r
o
u
p
b
y
co
m
p
u
tin
g
th
e
p
er
ce
n
tag
e
o
f
s
tu
d
en
ts
b
elo
n
g
in
g
to
th
at
co
lleg
e
o
r
p
r
o
g
r
am
r
elativ
e
to
th
e
to
tal
f
r
esh
m
an
p
o
p
u
latio
n
.
Usi
n
g
th
ese
p
r
o
p
o
r
tio
n
s
,
a
c
o
r
r
esp
o
n
d
in
g
n
u
m
b
er
o
f
p
a
r
ticip
an
ts
was
th
en
r
an
d
o
m
ly
s
elec
ted
f
r
o
m
ea
c
h
s
tr
atu
m
.
T
h
is
m
eth
o
d
en
s
u
r
e
d
th
at
th
e
f
in
al
s
am
p
le
clo
s
ely
r
ef
lecte
d
th
e
ac
tu
al
d
is
tr
ib
u
tio
n
o
f
f
r
esh
m
en
ac
r
o
s
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
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:
2
2
5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
15
,
No
.
3
,
J
u
n
e
20
2
6
:
2
3
3
8
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2
3
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7
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ac
ad
em
ic
p
r
o
g
r
am
s
,
th
er
e
b
y
en
h
an
cin
g
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ep
r
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tativ
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g
en
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aliza
b
ilit
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in
g
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r
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h
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ized
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ias
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u
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v
a
r
iatio
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in
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ath
em
atics
p
r
o
f
ic
ien
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d
lear
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n
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ateg
ies am
o
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ic
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cip
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iately
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ed
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ticip
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esh
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en
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o
h
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v
e
tak
en
m
ath
em
atics
g
e
n
er
al
ed
u
ca
tio
n
co
u
r
s
e
(
m
ath
em
atics
in
th
e
m
o
d
er
n
wo
r
l
d
)
in
th
e
p
r
e
v
io
u
s
s
em
ester
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r
o
m
a
p
ar
ticu
lar
u
n
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v
er
s
ity
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Min
d
o
r
o
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Ph
ilip
p
in
es.
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h
is
s
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p
le
s
ize
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p
r
im
ar
ily
co
n
s
tr
ain
ed
b
y
th
e
n
u
m
b
e
r
o
f
s
tu
d
en
ts
en
r
o
lled
in
th
e
tar
g
eted
m
ath
em
atics
co
u
r
s
e
d
u
r
in
g
th
e
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em
ester
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ata
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llectio
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y
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tic
co
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er
atio
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ch
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r
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lete
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er
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ic
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atif
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m
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lin
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elp
e
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m
ax
im
ize
t
h
e
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ep
r
esen
tativ
en
ess
o
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e
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p
le
b
y
e
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u
r
in
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r
o
p
o
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tio
n
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s
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n
o
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d
en
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r
o
m
d
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ic
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ilit
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e
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o
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en
s
am
p
le
s
ize
r
e
m
ain
s
s
u
f
f
icien
t
f
o
r
d
etec
tin
g
m
ea
n
in
g
f
u
l c
o
r
r
elati
o
n
s
an
d
p
r
o
v
i
d
in
g
r
eliab
le
in
s
ig
h
ts
with
in
th
e
co
n
te
x
t o
f
t
h
e
s
tu
d
y
.
2
.
3
.
Resea
rc
h
ins
t
rum
ent
s
A
r
esear
ch
er
-
m
ad
e
q
u
esti
o
n
n
air
e
u
s
in
g
a
f
iv
e
-
p
o
in
t
L
ik
e
r
t
s
ca
le
wa
s
d
ev
elo
p
ed
to
g
ath
er
d
ata
o
n
p
ar
ticip
an
ts
'
d
em
o
g
r
ap
h
ic
p
r
o
f
ile,
co
g
n
itiv
e
lear
n
in
g
s
tr
ateg
ies,
an
d
m
etac
o
g
n
itiv
e
lear
n
in
g
s
tr
ateg
ies.
T
h
e
co
g
n
itiv
e
lear
n
in
g
s
tr
ateg
ies
co
m
p
o
n
en
t
(
2
0
item
s
)
ass
ess
ed
co
n
tr
o
l,
elab
o
r
atio
n
,
o
r
g
an
iza
tio
n
,
an
d
r
e
h
ea
r
s
al
s
tr
ateg
ies,
wh
ile
th
e
m
etac
o
g
n
itiv
e
lear
n
in
g
s
tr
ateg
ies
co
m
p
o
n
en
t
(
1
5
item
s
)
f
o
cu
s
ed
o
n
p
lan
n
i
n
g
,
m
o
n
ito
r
in
g
,
a
n
d
e
v
alu
atio
n
s
tr
ateg
ies.
T
h
e
in
itial
p
o
o
l
o
f
ite
m
s
was
g
en
er
ated
b
ased
o
n
a
n
ex
ten
s
iv
e
r
ev
iew
o
f
r
elev
a
n
t
liter
atu
r
e
an
d
ex
is
t
in
g
v
alid
ated
in
s
tr
u
m
en
ts
o
n
l
ea
r
n
in
g
s
tr
ateg
ies.
T
o
estab
lis
h
co
n
ten
t
v
alid
ity
,
th
e
d
r
af
t
q
u
esti
o
n
n
air
e
was
ev
alu
ated
b
y
a
p
an
el
o
f
f
iv
e
ex
p
er
ts
in
ed
u
ca
tio
n
al
p
s
y
ch
o
lo
g
y
,
m
ath
em
atics
ed
u
ca
tio
n
,
an
d
r
esear
ch
m
eth
o
d
o
lo
g
y
,
w
h
o
ass
ess
ed
ea
ch
it
em
f
o
r
r
elev
a
n
ce
,
clar
it
y
,
an
d
alig
n
m
en
t
with
t
h
e
co
n
s
tr
u
cts
b
ein
g
m
ea
s
u
r
ed
.
T
h
eir
f
ee
d
b
ac
k
g
u
id
e
d
th
e
r
ev
i
s
io
n
an
d
r
ef
in
em
e
n
t
o
f
s
ev
er
a
l
item
s
to
en
h
an
ce
wo
r
d
in
g
p
r
ec
is
io
n
an
d
c
o
n
ce
p
tu
al
co
v
er
ag
e.
A
p
ilo
t
test
in
v
o
lv
in
g
3
0
s
tu
d
en
ts
with
s
im
ilar
ch
ar
ac
ter
is
tics
to
th
e
tar
g
et
p
o
p
u
latio
n
was
co
n
d
u
cted
to
ch
ec
k
t
h
e
clar
ity
an
d
co
m
p
r
e
h
en
s
ib
ilit
y
o
f
th
e
ite
m
s
.
R
eliab
ilit
y
wa
s
th
en
d
eter
m
in
e
d
u
s
in
g
C
r
o
n
b
a
ch
’
s
alp
h
a
co
ef
f
icie
n
t,
y
ield
in
g
h
ig
h
in
ter
n
al
co
n
s
is
ten
cy
f
o
r
b
o
th
th
e
co
g
n
itiv
e
(
α
=0
.
8
8
2
)
an
d
m
etac
o
g
n
itiv
e
(
α
=0
.
9
1
2
)
s
ca
les.
Ho
wev
e
r
,
co
n
f
ir
m
ato
r
y
f
ac
to
r
an
al
y
s
is
was
n
o
t
c
o
n
d
u
cted
d
u
e
to
lim
itatio
n
s
in
th
e
s
am
p
le
s
ize.
Mo
r
eo
v
er
,
r
ec
o
r
d
an
al
y
s
is
was
u
s
ed
to
o
b
tain
th
e
p
r
o
f
icien
cy
o
f
th
e
s
tu
d
en
ts
i
n
th
ei
r
m
a
th
em
atics
co
u
r
s
e.
A
s
in
g
le
c
o
u
r
s
e
g
r
ad
e
was
u
tili
ze
d
as
a
p
r
o
x
y
f
o
r
m
ath
em
atics
p
r
o
f
icie
n
cy
b
ec
au
s
e
it
p
r
o
v
i
d
es
an
o
b
jectiv
e,
s
tan
d
ar
d
ized
,
a
n
d
r
ea
d
ily
av
ailab
le
m
ea
s
u
r
e
o
f
s
tu
d
en
ts
’
ac
tu
al
p
er
f
o
r
m
an
ce
i
n
a
f
o
r
m
al
ac
ad
em
ic
s
ettin
g
.
C
o
u
r
s
e
g
r
a
d
es
r
ef
lect
s
tu
d
en
ts
’
m
aster
y
o
f
th
e
p
r
esc
r
ib
ed
lear
n
in
g
co
m
p
ete
n
cies,
as
th
ey
ar
e
d
er
i
v
ed
f
r
o
m
m
u
ltip
le
ass
ess
m
en
ts
s
u
ch
as
q
u
izze
s
,
e
x
am
in
atio
n
s
,
p
r
o
b
lem
-
s
o
lv
in
g
task
s
,
a
n
d
cl
ass
ac
tiv
ities
.
Us
in
g
an
o
f
f
icial
g
r
a
d
e
also
m
in
i
m
izes
r
esp
o
n
d
en
t
b
ias
an
d
en
s
u
r
es
co
n
s
is
ten
cy
ac
r
o
s
s
th
e
s
am
p
le,
m
ak
in
g
it
a
p
r
ac
tical
a
n
d
v
alid
in
d
icat
o
r
o
f
s
tu
d
e
n
ts
’
o
v
er
all
m
ath
em
atics
p
r
o
f
icien
c
y
with
in
t
h
e
co
n
tex
t
o
f
th
e
u
n
iv
er
s
ity
cu
r
r
icu
lu
m
.
2.
4
.
Da
t
a
c
o
llect
io
n
Data
co
llectio
n
was
ca
r
r
ied
o
u
t
af
ter
s
ec
u
r
in
g
a
p
p
r
o
v
a
l
f
r
o
m
th
e
u
n
i
v
er
s
ity
r
esear
ch
eth
ics
co
m
m
ittee
an
d
th
e
p
a
r
ticip
atin
g
ac
ad
em
ic
d
ep
a
r
tm
en
ts
.
T
h
e
r
esear
ch
er
co
o
r
d
in
ated
with
c
o
u
r
s
e
in
s
tr
u
cto
r
s
to
s
ch
ed
u
le
th
e
ad
m
in
is
tr
atio
n
o
f
th
e
q
u
esti
o
n
n
air
e
d
u
r
in
g
r
eg
u
lar
class
h
o
u
r
s
to
en
s
u
r
e
m
ax
i
m
u
m
p
ar
ticip
atio
n
an
d
m
in
im
al
d
is
r
u
p
tio
n
to
ac
a
d
em
ic
ac
tiv
ities
.
At
th
e
s
tar
t
o
f
th
e
s
ess
io
n
,
th
e
r
esear
ch
er
s
b
r
ief
ly
in
tr
o
d
u
ce
d
th
e
s
tu
d
y
,
r
eiter
ated
its
p
u
r
p
o
s
e,
an
d
ex
p
lain
ed
th
e
v
o
lu
n
tar
y
n
atu
r
e
o
f
p
ar
ticip
atio
n
.
Par
tic
ip
an
ts
th
en
s
ig
n
ed
in
f
o
r
m
e
d
co
n
s
en
t
f
o
r
m
s
b
e
f
o
r
e
co
m
p
letin
g
t
h
e
p
a
p
er
-
an
d
-
p
e
n
cil
s
u
r
v
ey
,
wh
ich
t
o
o
k
a
p
p
r
o
x
im
ately
3
0
m
in
u
tes.
Af
ter
th
e
r
etr
iev
al
o
f
th
e
co
m
p
leted
q
u
esti
o
n
n
air
es,
th
e
r
esear
ch
er
s
r
eq
u
e
s
ted
o
f
f
icial
class
r
ec
o
r
d
s
f
r
o
m
th
e
r
eg
is
tr
ar
a
n
d
co
n
ce
r
n
e
d
in
s
tr
u
cto
r
s
to
o
b
tain
s
tu
d
en
ts
’
f
in
al
m
ath
em
atics
co
u
r
s
e
g
r
ad
es.
All
co
llected
d
ata
wer
e
k
e
p
t c
o
n
f
id
en
tial,
o
r
g
a
n
ized
,
a
n
d
en
co
d
e
d
f
o
r
s
u
b
s
eq
u
en
t statis
tical
an
aly
s
is
.
2.
5
.
Da
t
a
a
na
ly
s
is
Descr
ip
tiv
e
s
tatis
t
ics
s
u
ch
as
f
r
eq
u
e
n
cy
,
m
ea
n
,
a
n
d
r
a
n
k
w
er
e
u
s
ed
to
c
h
ar
ac
ter
ize
th
e
r
e
s
p
o
n
d
en
ts
'
d
em
o
g
r
a
p
h
ic
p
r
o
f
ile
a
n
d
t
h
e
l
ev
el
o
f
c
o
g
n
itiv
e
an
d
m
etac
o
g
n
itiv
e
lear
n
in
g
s
tr
ateg
ies.
T
h
e
ca
lcu
lated
m
ea
n
s
f
o
r
co
g
n
itiv
e
an
d
m
etac
o
g
n
itiv
e
lear
n
in
g
s
tr
ateg
ies
wer
e
d
escr
ib
ed
in
ter
m
s
o
f
th
e
f
o
llo
win
g
r
an
g
e
an
d
v
er
b
al
d
escr
ip
tio
n
u
s
ed
in
th
e
u
n
iv
er
s
ity
:
v
er
y
h
ig
h
(
4
.
5
0
-
5
.
0
0
)
,
h
ig
h
(
3
.
5
0
-
4
.
4
9
)
,
m
o
d
er
ate
(
2
.
5
0
-
3
.
4
9
)
,
lo
w
(
1
.
5
0
-
2
.
4
9
)
,
an
d
v
e
r
y
lo
w
(
1
.
0
0
-
1
.
4
9
)
.
On
t
h
e
o
th
er
h
a
n
d
,
th
e
f
o
llo
win
g
r
an
g
e
an
d
d
e
s
cr
ip
tio
n
was
u
s
ed
to
ca
teg
o
r
ize
th
e
m
ath
em
atic
s
p
r
o
f
icien
cy
o
f
th
e
p
ar
ticip
an
ts
:
p
r
o
f
icien
t
(
9
0
a
n
d
ab
o
v
e)
,
a
b
o
v
e
av
er
a
g
e
(
8
5
-
8
9
)
,
d
ev
elo
p
in
g
p
r
o
f
icie
n
cy
(
8
0
-
8
4
)
,
b
elo
w
av
er
ag
e
(
7
5
-
7
9
)
,
f
ail
ed
(
7
4
a
n
d
b
elo
w)
.
Pear
s
o
n
p
r
o
d
u
ct
-
m
o
m
en
t
co
r
r
elatio
n
co
e
f
f
icien
t
w
as
em
p
lo
y
ed
to
d
ete
r
m
in
e
th
e
r
elatio
n
s
h
ip
b
etwe
en
s
tu
d
en
ts
’
co
g
n
itiv
e
an
d
m
etac
o
g
n
itiv
e
lear
n
in
g
s
tr
ateg
ies an
d
th
eir
m
ath
em
atics p
r
o
f
icien
cy
.
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
C
o
g
n
itive
a
n
d
meta
c
o
g
n
itive
l
ea
r
n
in
g
s
tr
a
teg
ies a
s
co
r
r
ela
tes o
f u
n
ivers
ity
s
tu
d
en
ts
’
…
(
P
o
leme
r
M.
C
u
a
r
to
)
2341
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
is
s
tu
d
y
in
v
esti
g
ated
th
e
in
f
lu
en
ce
o
f
th
e
c
o
g
n
itiv
e
a
n
d
m
etac
o
g
n
itiv
e
lear
n
i
n
g
s
tr
ateg
ies
to
th
e
m
ath
em
atics
p
r
o
f
icien
cy
o
f
th
e
u
n
iv
er
s
ity
f
r
esh
m
e
n
.
Desp
ite
n
u
m
er
o
u
s
liter
atu
r
es
o
n
th
e
p
o
ten
tial
b
en
ef
its
o
f
th
ese
lear
n
in
g
s
tr
ateg
ies
to
v
ar
io
u
s
ac
ad
em
ic
d
o
m
ain
s
,
its
in
f
lu
en
ce
o
n
m
ath
em
atics
h
as
n
o
t
b
ee
n
f
u
lly
ex
p
lo
r
ed
.
Utilizin
g
v
alid
ated
,
r
esear
ch
er
-
m
ad
e
q
u
esti
o
n
n
air
e
s
,
co
g
n
itiv
e
lear
n
in
g
s
tr
ateg
ies
wer
e
m
ea
s
u
r
ed
in
ter
m
s
o
f
f
o
u
r
co
m
p
o
n
e
n
ts
:
co
n
tr
o
l,
elab
o
r
atio
n
,
o
r
g
an
izati
o
n
an
d
r
e
h
ea
r
s
al
s
tr
ateg
ies
wh
ile
m
etac
o
g
n
itiv
e
lear
n
in
g
s
tr
ateg
ies we
r
e
m
ea
s
u
r
ed
in
te
r
m
s
o
f
p
lan
n
in
g
,
m
o
n
ito
r
in
g
a
n
d
ev
al
u
atio
n
s
tr
ateg
ies.
3
.
1
.
Co
g
nitiv
e
lea
rning
s
t
ra
t
eg
ies
As
p
r
esen
ted
in
T
a
b
le
1
,
r
esp
o
n
d
en
ts
ex
h
ib
ited
a
h
ig
h
lev
el
o
f
c
o
n
tr
o
l
s
tr
ateg
y
,
as
ev
id
en
ce
d
b
y
th
e
o
v
er
all
m
ea
n
o
f
3
.
6
7
.
T
h
is
s
u
g
g
ests
a
s
tr
o
n
g
ap
titu
d
e
f
o
r
id
en
tify
in
g
ess
en
tial
lear
n
in
g
o
b
jectiv
es
with
in
th
e
m
ath
em
atics
cu
r
r
icu
l
u
m
.
R
esp
o
n
d
e
n
ts
ar
e
c
o
n
s
cio
u
s
o
f
t
h
eir
lear
n
in
g
p
r
o
ce
s
s
an
d
ca
n
ef
f
ec
tiv
ely
id
e
n
tify
wh
at
is
im
p
o
r
tan
t
to
f
o
cu
s
o
n
.
B
u
ild
in
g
u
p
o
n
th
is
s
k
ill
ca
n
lead
t
o
m
o
r
e
f
o
c
u
s
ed
an
d
e
f
f
icien
t
s
tu
d
y
h
ab
its
[
3
5
]
,
[
3
6
]
.
T
h
e
em
p
h
asis
o
n
p
in
p
o
in
tin
g
im
p
o
r
tan
t
co
n
ten
t
ar
ea
s
is
p
ar
ticu
lar
ly
n
o
te
wo
r
th
y
,
as
it
alig
n
s
with
m
etac
o
g
n
itiv
e
th
eo
r
ies
o
f
ef
f
ec
tiv
e
lear
n
in
g
[
3
7
]
.
Ho
wev
er
,
th
e
ab
ilit
y
to
s
ee
k
ad
d
itio
n
al
in
f
o
r
m
atio
n
wh
en
en
co
u
n
ter
in
g
d
if
f
icu
lties
is
cr
u
cial
f
o
r
in
d
ep
en
d
en
t
lear
n
in
g
[
3
8
]
,
[
3
9
]
.
T
o
a
d
d
r
ess
th
e
id
en
tifie
d
wea
k
n
ess
,
it
i
s
es
s
en
tial
to
d
e
v
elo
p
s
tu
d
en
ts
'
in
f
o
r
m
atio
n
-
s
e
ek
in
g
s
k
ills
b
y
p
r
o
v
id
in
g
ex
p
licit
in
s
tr
u
ctio
n
o
n
ef
f
ec
tiv
e
r
esear
ch
s
tr
ateg
ies,
teac
h
in
g
s
tu
d
e
n
ts
h
o
w
to
u
s
e
lib
r
ar
y
r
eso
u
r
ce
s
an
d
o
n
l
in
e
d
atab
ases
,
an
d
en
co
u
r
a
g
in
g
th
e
m
to
s
ee
k
h
elp
f
r
o
m
teac
h
er
s
,
p
ee
r
s
,
o
r
o
th
e
r
av
ailab
le
r
eso
u
r
ce
s
wh
en
f
ac
i
n
g
ch
allen
g
es.
T
ab
le
1
.
Stu
d
e
n
ts
’
lev
el
o
f
c
o
g
n
itiv
e
lear
n
in
g
s
tr
ateg
ies
C
o
m
p
o
n
e
n
t
s
M
e
a
n
D
e
scri
p
t
i
o
n
C
o
n
t
r
o
l
3
.
6
7
H
i
g
h
El
a
b
o
r
a
t
i
o
n
3
.
3
1
M
o
d
e
r
a
t
e
O
r
g
a
n
i
z
a
t
i
o
n
3
.
2
8
M
o
d
e
r
a
t
e
R
e
h
e
a
r
s
a
l
3
.
9
6
H
i
g
h
On
t
h
e
o
t
h
e
r
h
an
d
,
r
esp
o
n
d
e
n
t
s
d
e
m
o
n
s
t
r
a
te
d
a
m
o
d
e
r
a
te
le
v
el
o
f
el
ab
o
r
a
ti
o
n
s
t
r
a
te
g
y
,
wi
th
a
n
o
v
er
all
m
ea
n
s
c
o
r
e
o
f
3
.
3
1
.
W
h
il
e
s
t
u
d
e
n
ts
d
is
p
l
a
y
e
d
a
te
n
d
e
n
c
y
to
ex
p
l
o
r
e
alt
er
n
ati
v
e
p
r
o
b
le
m
-
s
o
l
v
i
n
g
a
p
p
r
o
a
c
h
es
,
th
e
ir
a
b
il
it
y
t
o
c
o
n
n
ec
t
m
at
h
e
m
at
ica
l
c
o
n
c
e
p
ts
t
o
r
ea
l
-
w
o
r
l
d
a
p
p
lic
ati
o
n
s
a
n
d
in
te
g
r
at
e
k
n
o
wl
ed
g
e
f
r
o
m
o
t
h
e
r
s
u
b
je
cts
w
as
l
ess
p
r
o
n
o
u
n
c
e
d
.
T
h
is
s
u
g
g
ests
th
at
wh
ile
s
tu
d
en
ts
m
ay
p
o
s
s
ess
s
o
m
e
p
r
o
b
lem
-
s
o
lv
i
n
g
f
lex
ib
ilit
y
,
th
eir
ca
p
ac
ity
to
co
n
s
tr
u
ct
d
ee
p
er
m
ea
n
i
n
g
th
r
o
u
g
h
co
n
n
ec
tio
n
s
is
lim
ited
[
4
0
]
.
T
h
is
h
as
im
p
licatio
n
s
f
o
r
th
ei
r
o
v
e
r
all
m
ath
em
atica
l
lear
n
in
g
a
n
d
p
r
o
b
lem
-
s
o
lv
in
g
ab
ilit
ies
[
4
1
]
.
T
o
en
h
a
n
ce
s
tu
d
en
ts
’
elab
o
r
atio
n
s
tr
ateg
ies,
in
s
tr
u
ctio
n
al
p
r
ac
tices
s
h
o
u
ld
f
o
cu
s
o
n
f
o
s
ter
in
g
co
n
n
ec
tio
n
s
b
et
wee
n
m
ath
em
atica
l
co
n
ce
p
ts
an
d
r
ea
l
-
wo
r
ld
a
p
p
licatio
n
s
,
as
well
as
in
teg
r
atin
g
m
ath
em
atics
with
o
th
er
d
is
cip
lin
es
[
4
2
]
.
Sp
ec
if
ically
,
teac
h
er
s
ca
n
in
co
r
p
o
r
ate
m
o
r
e
r
ea
l
-
w
o
r
ld
p
r
o
b
lem
-
s
o
lv
i
n
g
s
ce
n
ar
io
s
in
to
th
eir
less
o
n
s
,
en
co
u
r
a
g
in
g
s
tu
d
en
ts
to
a
p
p
l
y
m
ath
em
atica
l
k
n
o
wled
g
e
to
au
th
en
tic
s
itu
atio
n
s
.
M
o
r
eo
v
er
,
in
ter
d
is
cip
lin
ar
y
p
r
o
jects
th
at
co
n
n
ec
t
m
ath
em
atics
with
o
th
er
s
u
b
jects
ca
n
h
elp
d
ev
elo
p
a
b
r
o
ad
e
r
p
er
s
p
ec
tiv
es
an
d
d
ee
p
er
u
n
d
er
s
tan
d
i
n
g
o
f
th
e
in
ter
c
o
n
n
ec
ted
n
ess
o
f
k
n
o
wled
g
e.
Similar
ly
,
r
esp
o
n
d
en
ts
d
em
o
n
s
tr
ated
a
m
o
d
er
ate
lev
el
o
f
o
r
g
an
izatio
n
s
tr
ateg
y
,
with
an
o
v
er
all
m
ea
n
o
f
3
.
2
8
.
W
h
ile
s
tu
d
en
ts
ap
p
ea
r
ed
to
v
alu
e
th
e
cr
ea
tio
n
o
f
s
u
m
m
ar
ies
an
d
r
ev
iew
m
ater
ials
,
th
eir
u
tili
za
tio
n
o
f
g
r
ap
h
ic
o
r
g
a
n
izer
s
was
n
o
ta
b
ly
lo
w.
T
h
is
s
u
g
g
ests
a
p
o
ten
tial
g
ap
in
s
tu
d
en
ts
'
o
r
g
an
izatio
n
al
s
k
ills
,
p
ar
ticu
lar
ly
in
v
is
u
ally
r
e
p
r
e
s
en
tin
g
in
f
o
r
m
atio
n
.
T
h
e
m
o
d
er
ate
u
s
e
o
f
o
u
tlin
es
an
d
m
n
em
o
n
ic
d
e
v
ices
in
d
icate
s
a
m
ix
ed
p
ictu
r
e
o
f
s
tu
d
en
ts
'
ab
ilit
y
to
s
tr
u
ctu
r
e
an
d
r
em
em
b
e
r
in
f
o
r
m
atio
n
ef
f
ec
ti
v
ely
.
T
h
is
f
in
d
in
g
im
p
lies
th
e
n
ee
d
f
o
r
im
p
r
o
v
ed
o
r
g
an
izatio
n
al
s
k
ills
,
p
ar
ticu
lar
ly
in
v
is
u
al
r
ep
r
esen
tati
o
n
an
d
in
f
o
r
m
atio
n
s
tr
u
ctu
r
in
g
.
T
o
en
h
a
n
ce
s
tu
d
e
n
ts
'
o
r
g
an
izatio
n
al
s
k
ills
,
teac
h
er
s
s
h
o
u
ld
p
r
io
r
itize
in
c
o
r
p
o
r
atin
g
a
v
ar
iety
o
f
o
r
g
an
izatio
n
al
to
o
ls
a
n
d
s
tr
ate
g
ies
in
to
th
eir
in
s
tr
u
ctio
n
.
E
m
p
h
asizin
g
th
e
u
s
e
o
f
g
r
ap
h
ic
o
r
g
an
izer
s
,
s
u
ch
as
m
in
d
m
ap
s
,
c
o
n
ce
p
t
m
ap
s
,
a
n
d
f
lo
wch
a
r
ts
ca
n
h
elp
s
tu
d
e
n
ts
v
is
u
ally
r
ep
r
esen
t
in
f
o
r
m
atio
n
[
4
3
]
,
id
e
n
tify
r
elatio
n
s
h
ip
s
b
etwe
en
co
n
ce
p
t
s
[
4
4
]
a
n
d
im
p
r
o
v
e
s
tu
d
e
n
ts
'
a
b
il
it
y
t
o
s
t
r
u
ct
u
r
e
a
n
d
r
e
m
e
m
b
er
i
n
f
o
r
m
ati
o
n
[
4
5
]
.
On
th
e
o
th
er
h
a
n
d
,
r
esp
o
n
d
en
ts
ex
h
ib
ited
a
h
ig
h
lev
el
o
f
r
eh
ea
r
s
al
s
tr
ateg
y
,
with
an
o
v
er
all
m
ea
n
s
co
r
e
o
f
3
.
9
6
.
T
h
is
s
u
g
g
ests
th
at
s
tu
d
en
ts
r
ely
h
ea
v
ily
o
n
r
o
te
m
em
o
r
izatio
n
an
d
p
r
ac
tic
e
ex
er
cises
to
lear
n
m
ath
em
atics.
T
h
is
in
d
icate
s
th
at
s
tu
d
en
ts
m
ay
b
e
p
r
io
r
itizin
g
p
r
o
ce
d
u
r
al
k
n
o
wled
g
e
o
v
er
c
o
n
ce
p
t
u
al
u
n
d
er
s
tan
d
i
n
g
in
m
ath
e
m
atics.
Stu
d
ies
r
ev
ea
led
th
at
wh
ile
p
r
ac
tice
is
ess
en
tial
f
o
r
s
k
i
ll
d
ev
elo
p
m
en
t,
a
n
o
v
er
em
p
h
asis
o
n
th
is
ap
p
r
o
ac
h
ca
n
lim
it
s
tu
d
e
n
ts
'
ab
ilit
y
to
th
in
k
c
r
itically
,
s
o
lv
e
co
m
p
lex
p
r
o
b
lem
s
,
a
n
d
ap
p
ly
m
at
h
em
atics
to
r
ea
l
-
wo
r
ld
s
itu
atio
n
s
[
4
2
]
,
[
4
6
]
,
[
4
7
]
.
T
h
e
s
tr
o
n
g
p
r
ef
er
en
ce
f
o
r
n
o
tetak
in
g
in
d
icate
s
a
r
elian
ce
o
n
ex
ter
n
al
cu
es f
o
r
r
ec
all,
wh
ich
m
ay
h
in
d
er
lo
n
g
-
t
er
m
r
eten
tio
n
.
T
o
f
o
s
ter
d
ee
p
e
r
lear
n
in
g
,
teac
h
er
s
s
h
o
u
ld
s
h
if
t
th
e
f
o
cu
s
f
r
o
m
r
o
te
m
em
o
r
izatio
n
t
o
m
ea
n
in
g
f
u
l
u
n
d
er
s
tan
d
in
g
.
I
n
co
r
p
o
r
atin
g
p
r
o
b
lem
-
s
o
lv
in
g
ac
tiv
ities
,
co
llab
o
r
ativ
e
lear
n
i
n
g
,
an
d
r
ea
l
-
wo
r
ld
ap
p
licatio
n
s
ca
n
h
elp
s
tu
d
en
ts
d
e
v
elo
p
a
d
ee
p
er
ap
p
r
ec
iatio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
15
,
No
.
3
,
J
u
n
e
20
2
6
:
2
3
3
8
-
2
3
4
7
2342
f
o
r
m
ath
e
m
atics.
Fu
r
th
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m
o
r
e,
teac
h
in
g
s
tu
d
e
n
ts
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f
ec
tiv
e
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o
te
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tak
in
g
s
tr
ateg
ies
th
at
en
co
u
r
a
g
e
ac
tiv
e
en
g
ag
em
e
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t
with
th
e
m
ater
ia
l,
s
u
ch
as
s
u
m
m
ar
izin
g
k
ey
i
d
ea
s
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co
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n
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ts
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n
im
p
r
o
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e
th
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r
ab
ilit
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etain
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o
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m
atio
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I
t
is
ess
en
tial
to
b
alan
ce
r
eh
ea
r
s
al
s
tr
ateg
ies
with
h
ig
h
er
-
o
r
d
er
t
h
in
k
in
g
s
k
ills
to
en
s
u
r
e
th
at
s
tu
d
en
ts
d
ev
elo
p
a
well
-
r
o
u
n
d
ed
m
at
h
em
atica
l
f
o
u
n
d
atio
n
.
3
.
2
.
M
et
a
c
o
g
nitiv
e
lea
rning
s
t
ra
t
eg
ies
As
s
h
o
wn
in
T
a
b
le
2
,
r
esp
o
n
d
en
ts
ex
h
ib
ited
a
m
o
d
er
ate
le
v
el
o
f
p
lan
n
i
n
g
s
tr
ateg
y
,
with
an
o
v
er
all
m
ea
n
s
co
r
e
o
f
3
.
3
0
.
W
h
ile
s
tu
d
en
ts
ap
p
ea
r
ed
to
r
ec
o
g
n
ize
th
e
im
p
o
r
tan
ce
o
f
s
ettin
g
g
o
als,
th
eir
ab
ilit
y
to
tr
an
s
late
th
ese
g
o
als
in
to
c
o
n
c
r
ete
ac
tio
n
p
la
n
s
was
less
ev
id
en
t.
T
h
is
s
u
g
g
ests
th
at
wh
ile
s
tu
d
en
ts
m
ay
h
av
e
a
g
en
er
al
awa
r
en
ess
o
f
th
e
b
en
e
f
its
o
f
p
lan
n
in
g
,
th
e
y
m
ay
lack
s
p
ec
if
ic
s
k
ills
in
d
ev
elo
p
in
g
an
d
im
p
lem
en
tin
g
ef
f
ec
tiv
e
s
tu
d
y
s
tr
ateg
ies.
T
o
ad
d
r
ess
th
is
,
teac
h
er
s
s
h
o
u
ld
f
o
cu
s
o
n
teac
h
in
g
s
tu
d
en
ts
h
o
w
to
b
r
ea
k
d
o
w
n
lar
g
e
g
o
als
in
t
o
s
m
aller
,
ac
h
iev
ab
le
s
tep
s
[
4
8
]
,
[
4
9
]
.
T
ea
c
h
in
g
th
e
m
h
o
w
to
m
an
ag
e
th
eir
tim
e
ef
f
ec
tiv
ely
,
s
u
ch
as
cr
ea
tin
g
s
ch
ed
u
les
an
d
p
r
io
r
itizin
g
task
s
,
ca
n
als
o
b
e
b
en
ef
icial
[
5
0
]
.
Ad
d
itio
n
ally
,
in
co
r
p
o
r
atin
g
o
p
p
o
r
tu
n
ities
f
o
r
s
tu
d
e
n
ts
to
p
r
ac
tice
p
lan
n
in
g
an
d
g
o
al
s
et
tin
g
with
in
th
e
class
r
o
o
m
ca
n
h
elp
th
em
d
ev
elo
p
th
ese
ess
en
tial sk
ill
s
s
o
th
at
th
ey
ca
n
b
ec
o
m
e
m
o
r
e
in
d
e
p
en
d
en
t a
n
d
ef
f
icien
t le
ar
n
er
s
.
T
ab
le
2
.
Stu
d
e
n
ts
’
lev
el
o
f
m
e
taco
g
n
itiv
e
lear
n
i
n
g
s
tr
ateg
ies
C
o
m
p
o
n
e
n
t
s
M
e
a
n
D
e
scri
p
t
i
o
n
P
l
a
n
n
i
n
g
3
.
3
0
M
o
d
e
r
a
t
e
M
o
n
i
t
o
r
i
n
g
3
.
6
3
H
i
g
h
Ev
a
l
u
a
t
i
o
n
3
.
4
5
M
o
d
e
r
a
t
e
On
th
e
o
th
er
h
an
d
,
r
esp
o
n
d
e
n
ts
d
em
o
n
s
tr
ated
a
h
ig
h
lev
el
o
f
m
o
n
ito
r
in
g
s
tr
ateg
y
,
with
an
o
v
e
r
all
m
ea
n
s
co
r
e
o
f
3
.
6
3
.
T
h
is
s
u
g
g
ests
th
at
s
tu
d
en
ts
a
r
e
r
elativ
ely
ad
ep
t
at
tr
a
ck
in
g
th
eir
p
r
o
g
r
ess
a
n
d
u
n
d
er
s
tan
d
i
n
g
th
eir
lear
n
in
g
p
r
o
ce
s
s
es.
Ho
wev
er
,
th
e
d
is
p
ar
ity
b
etwe
en
th
e
h
ig
h
s
co
r
es
r
e
lated
to
awa
r
en
ess
o
f
ac
tio
n
s
an
d
s
tr
ateg
ies
an
d
t
h
e
lo
wer
s
co
r
e
f
o
r
a
d
h
er
e
n
ce
to
s
tu
d
y
s
ch
ed
u
les
is
n
o
tewo
r
t
h
y
.
T
h
is
in
d
icate
s
a
p
o
ten
tial
d
is
co
n
n
ec
t
b
etwe
en
s
tu
d
en
ts
'
s
elf
-
awa
r
en
ess
an
d
th
eir
ab
ilit
y
to
r
eg
u
late
th
e
ir
s
tu
d
y
b
eh
av
i
o
r
s
ef
f
ec
tiv
ely
.
Sev
e
r
al
s
tu
d
ies
s
u
g
g
ested
th
at
teac
h
er
s
s
h
o
u
l
d
f
o
cu
s
o
n
d
e
v
elo
p
in
g
s
tu
d
en
ts
'
s
elf
-
r
eg
u
latio
n
s
k
ills
[
5
1
]
–
[
5
3
]
.
T
h
is
ca
n
b
e
a
ch
i
ev
ed
th
r
o
u
g
h
teac
h
in
g
tim
e
m
an
ag
em
en
t,
g
o
al
s
ettin
g
,
a
n
d
s
elf
-
m
o
n
ito
r
in
g
tech
n
iq
u
es
as
well
as
p
r
o
v
id
i
n
g
o
p
p
o
r
t
u
n
ities
f
o
r
s
tu
d
en
ts
to
p
r
ac
tice
th
ese
s
k
ills
in
a
s
u
p
p
o
r
tiv
e
en
v
ir
o
n
m
en
t
ca
n
also
b
e
b
e
n
ef
icial.
M
o
r
eo
v
er
,
h
elp
in
g
s
tu
d
en
ts
to
id
en
ti
f
y
p
e
r
s
o
n
al
f
ac
to
r
s
th
at
m
ay
i
n
ter
f
er
e
with
th
eir
s
tu
d
y
h
ab
its
ca
n
em
p
o
wer
th
e
m
to
d
ev
el
o
p
s
tr
ateg
ies to
o
v
e
r
co
m
e
th
ese
ch
allen
g
es.
R
esp
o
n
d
en
ts
d
e
m
o
n
s
t
r
a
te
d
a
m
o
d
er
ate
le
v
e
l
o
f
ev
al
u
a
ti
o
n
s
tr
a
te
g
y
,
w
it
h
a
n
o
v
e
r
al
l
m
ea
n
s
c
o
r
e
o
f
3
.
4
5
.
S
tu
d
en
ts
a
p
p
ea
r
e
d
t
o
r
el
y
h
ea
v
i
ly
o
n
s
u
m
m
at
iv
e
ass
es
s
m
e
n
ts
p
r
o
v
i
d
e
d
b
y
te
ac
h
e
r
s
an
d
t
h
e
ir
ab
ilit
y
t
o
en
g
a
g
e
in
s
el
f
-
ev
al
u
a
ti
o
n
an
d
g
o
al
r
e
f
le
cti
o
n
was
less
p
r
o
n
o
u
n
ce
d
.
T
h
is
i
m
p
lies
a
p
o
t
en
t
ial
o
v
er
r
elia
n
ce
o
n
ex
ter
n
al
v
alid
atio
n
a
n
d
a
lim
it
ed
ca
p
ac
ity
f
o
r
s
elf
-
ass
ess
m
en
t.
Stu
d
ies r
ec
o
m
m
en
d
e
d
th
at
d
ev
elo
p
in
g
s
tu
d
e
n
ts
'
s
elf
-
ass
es
s
m
en
t
an
d
g
o
al
-
s
et
tin
g
ab
ilit
ies
am
o
n
g
s
tu
d
e
n
t
s
s
h
o
u
ld
b
e
p
r
io
r
itized
[
5
4
]
,
[
5
5
]
.
Pro
v
id
in
g
o
p
p
o
r
t
u
n
iti
es
f
o
r
s
t
u
d
en
ts
t
o
r
ef
l
ec
t
o
n
t
h
ei
r
le
ar
n
i
n
g
p
r
o
ce
s
s
es
a
n
d
esta
b
l
is
h
p
e
r
s
o
n
a
l
l
ea
r
n
i
n
g
g
o
als
ca
n
h
el
p
th
e
m
g
ai
n
a
b
ett
er
aw
a
r
e
n
ess
o
f
t
h
ei
r
o
w
n
s
tr
e
n
g
th
s
a
n
d
w
e
ak
n
ess
es.
M
o
r
e
o
v
er
,
tea
c
h
i
n
g
s
tu
d
e
n
ts
o
n
h
o
w
to
ev
al
u
at
e
th
e
e
f
f
ec
t
iv
e
n
ess
o
f
d
if
f
e
r
en
t
s
t
u
d
y
s
tr
ate
g
i
es
ca
n
em
p
o
w
er
t
h
e
m
t
o
b
e
c
o
m
e
m
o
r
e
i
n
d
e
p
e
n
d
e
n
t
lea
r
n
e
r
s
an
d
t
o
h
e
lp
t
h
e
m
ta
k
e
o
w
n
e
r
s
h
i
p
o
f
t
h
eir
l
ea
r
n
i
n
g
a
n
d
d
ev
el
o
p
t
h
e
s
k
il
ls
n
e
ce
s
s
ar
y
f
o
r
li
f
e
lo
n
g
s
u
cc
ess
.
3
.
3
.
M
a
t
hema
t
ics
p
ro
f
iciency
T
ab
le
3
p
r
esen
ts
th
e
s
tu
d
e
n
ts
’
lev
el
o
f
m
ath
em
atics
p
r
o
f
icie
n
cy
as
m
ea
s
u
r
e
d
b
y
th
ei
r
g
r
a
d
es
in
th
e
co
u
r
s
e:
m
ath
em
atics
in
t
h
e
m
o
d
er
n
wo
r
ld
.
T
h
e
clu
s
ter
ed
d
i
s
tr
ib
u
tio
n
o
f
g
r
a
d
es
p
r
im
a
r
ily
with
in
th
e
7
5
–
8
4
r
an
g
e,
with
a
weig
h
ted
m
ea
n
o
f
8
1
.
4
6
,
in
d
icate
s
th
at
th
e
s
tu
d
en
ts
’
m
at
h
em
atics
p
er
f
o
r
m
a
n
ce
f
alls
with
in
t
h
e
d
ev
elo
p
in
g
p
r
o
f
icien
cy
lev
el
.
T
h
is
s
u
g
g
ests
th
at
wh
ile
s
tu
d
en
ts
d
em
o
n
s
tr
ate
p
ar
tial
u
n
d
er
s
tan
d
in
g
o
f
f
u
n
d
am
e
n
tal
m
ath
e
m
atica
l
co
n
ce
p
ts
,
th
eir
s
k
ills
r
em
ain
b
e
lo
w
th
e
lev
el
ex
p
ec
ted
f
o
r
f
u
ll
p
r
o
f
icien
cy
an
d
r
eq
u
ir
e
f
u
r
t
h
er
s
tr
en
g
th
en
i
n
g
.
T
h
is
im
p
lies
th
at
w
h
ile
m
o
s
t
s
tu
d
en
ts
h
a
v
e
a
f
o
u
n
d
atio
n
al
u
n
d
er
s
tan
d
in
g
o
f
t
h
e
s
u
b
ject
m
atter
,
th
er
e
is
a
lac
k
o
f
s
u
b
ject
p
r
o
f
icien
cy
an
d
th
er
e
ar
e
p
o
ten
tial
ar
ea
s
o
f
s
i
g
n
if
ican
t
wea
k
n
ess
with
in
th
e
s
tu
d
en
t
p
o
p
u
latio
n
.
T
h
is
m
ay
b
e
attr
ib
u
ted
to
s
ev
er
al
f
ac
to
r
s
s
u
ch
as
teac
h
er
ef
f
ec
tiv
en
ess
[
5
6
]
,
[
5
7
]
,
c
u
r
r
icu
lu
m
d
esig
n
[
5
8
]
,
s
o
cio
-
ec
o
n
o
m
ic
f
ac
to
r
s
[
5
9
]
,
[
6
0
]
,
s
tu
d
en
t
ch
ar
ac
ter
is
tic
s
[
6
1
]
,
an
d
o
th
er
in
ter
n
al
an
d
ex
ter
n
al
f
ac
to
r
s
[
6
2
]
.
Fu
r
th
e
r
m
o
r
e,
th
e
clu
s
ter
e
d
d
is
tr
ib
u
tio
n
s
u
g
g
ests
a
h
o
m
o
g
en
eo
u
s
g
r
o
u
p
in
ter
m
s
o
f
ac
h
iev
em
e
n
t,
i
n
d
icat
in
g
th
e
n
ee
d
f
o
r
v
ar
ie
d
in
s
tr
u
ctio
n
al
ap
p
r
o
ac
h
es
to
ca
ter
t
o
d
if
f
e
r
en
t
lea
r
n
in
g
s
ty
les
an
d
p
ac
es.
Mo
r
e
o
v
er
,
a
n
in
-
d
e
p
th
ass
ess
m
en
t
to
id
en
t
if
y
s
p
ec
if
ic
ar
ea
s
o
f
wea
k
n
ess
with
in
th
e
s
tu
d
en
t
p
o
p
u
latio
n
s
o
th
at
a
ca
r
ef
u
lly
-
d
esig
n
ed
in
ter
v
en
tio
n
m
ay
b
e
p
r
o
v
i
d
ed
to
th
e
s
tu
d
en
ts
m
o
s
t
esp
ec
ially
th
o
s
e
wh
o
ar
e
s
tr
u
g
g
lin
g
with
s
p
ec
if
ic
co
n
ce
p
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
C
o
g
n
itive
a
n
d
meta
c
o
g
n
itive
l
ea
r
n
in
g
s
tr
a
teg
ies a
s
co
r
r
ela
tes o
f u
n
ivers
ity
s
tu
d
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ts
’
…
(
P
o
leme
r
M.
C
u
a
r
to
)
2343
T
ab
le
3
.
Stu
d
e
n
ts
’
lev
el
o
f
p
r
o
f
icien
cy
in
m
ath
em
atics
P
e
r
f
o
r
ma
n
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e
F
r
e
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e
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r
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n
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–
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5
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–
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p
t
i
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n
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d
e
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l
o
p
i
n
g
p
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o
f
i
c
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n
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y
3
.
4
.
Rela
t
io
ns
hip
bet
wee
n c
o
g
nitiv
e
lea
rning
s
t
ra
t
eg
ies a
nd
m
a
t
hem
a
t
ics pro
f
iciency
C
o
r
r
elatio
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al
an
aly
s
is
was
co
n
d
u
cted
to
ex
a
m
in
e
th
e
r
elati
o
n
s
h
ip
b
etwe
en
lear
n
in
g
s
tr
ateg
ies
an
d
m
ath
em
atics
p
r
o
f
icien
c
y
,
as
p
r
esen
ted
in
T
ab
le
4
.
R
esu
lts
in
d
icate
d
s
ig
n
if
ican
t
p
o
s
itiv
e
c
o
r
r
elatio
n
s
b
etwe
en
all
th
r
ee
lear
n
in
g
s
tr
ateg
ies
a
n
d
m
ath
em
atics
p
r
o
f
icien
cy
(
T
ab
le
1
)
.
Stu
d
en
ts
wh
o
r
ep
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ted
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ig
h
er
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els
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f
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n
tr
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l
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9
9
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elab
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7
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7
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al
(
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3
4
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p
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s
tr
ateg
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ten
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ed
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ex
h
i
b
it
h
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er
lev
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s
o
f
m
ath
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atica
l
co
m
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eten
c
e.
T
h
e
f
in
d
in
g
s
o
f
th
e
p
r
esen
t
s
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d
y
s
u
p
p
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r
t
th
e
n
o
tio
n
th
at
ef
f
ec
tiv
e
lear
n
in
g
s
tr
ateg
ies
ar
e
as
s
o
ciate
d
wit
h
en
h
an
ce
d
m
ath
em
atics
p
r
o
f
icien
cy
[
2
8
]
–
[
3
1
]
.
Sp
ec
if
ically
,
th
e
r
esu
lts
d
em
o
n
s
tr
ate
th
at
co
n
tr
o
l,
elab
o
r
atio
n
,
an
d
r
e
h
ea
r
s
al
s
tr
ateg
ies
ar
e
p
o
s
itiv
ely
r
elate
d
t
o
s
tu
d
en
ts
'
m
ath
em
atica
l
p
er
f
o
r
m
an
ce
.
T
h
ese
f
in
d
in
g
s
alig
n
with
p
r
ev
io
u
s
r
esear
ch
em
p
h
asizin
g
th
e
im
p
o
r
tan
ce
o
f
co
g
n
itiv
e
s
k
ills
,
d
ee
p
p
r
o
ce
s
s
in
g
,
an
d
p
r
ac
tice
in
ac
ad
em
i
c
ac
h
iev
em
en
t [
3
2
]
.
T
ab
le
4
.
C
o
r
r
elatio
n
al
an
aly
s
is
b
etwe
en
r
esp
o
n
d
en
ts
’
lev
el
o
f
co
g
n
itiv
e
lear
n
in
g
s
tr
ateg
ies a
n
d
m
ath
em
atics
p
r
o
f
icien
c
y
V
a
r
i
a
b
l
e
s
r
p
R
e
s
u
l
t
Le
v
e
l
o
f
c
o
n
t
r
o
l
st
r
a
t
e
g
y
v
s.
ma
t
h
e
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t
i
c
s
p
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f
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e
n
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y
0
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2
9
9
0
.
0
4
1
S
i
g
n
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f
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c
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n
t
Le
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l
o
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e
l
a
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t
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o
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st
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t
e
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s.
mat
h
e
mat
i
c
s
p
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n
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y
0
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4
7
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1
7
S
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f
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c
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t
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S
i
g
n
i
f
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c
a
n
t
T
h
e
p
o
s
itiv
e
co
r
r
elatio
n
b
et
wee
n
co
n
tr
o
l
s
tr
ateg
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an
d
m
ath
em
atics
p
r
o
f
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cy
s
u
g
g
ests
th
at
s
tu
d
en
ts
wh
o
ef
f
ec
tiv
ely
m
a
n
ag
e
th
eir
lear
n
in
g
tim
e,
s
et
g
o
als,
an
d
m
o
n
ito
r
th
eir
p
r
o
g
r
ess
ten
d
to
ac
h
iev
e
h
ig
h
er
lev
els
o
f
m
at
h
em
atica
l
co
m
p
eten
ce
.
T
h
is
f
in
d
in
g
e
m
p
h
asizes
th
e
s
ig
n
if
ican
ce
o
f
s
elf
-
r
eg
u
latio
n
in
ac
ad
em
ic
s
u
cc
ess
[
5
1
]
–
[
5
3
]
.
Fu
r
th
er
m
o
r
e
,
th
e
s
tr
o
n
g
p
o
s
itiv
e
co
r
r
elatio
n
b
etwe
e
n
elab
o
r
atio
n
an
d
m
ath
em
atics
p
r
o
f
icien
cy
in
d
icate
s
th
e
im
p
o
r
tan
ce
o
f
co
n
n
ec
tin
g
n
ew
in
f
o
r
m
atio
n
to
p
r
io
r
k
n
o
wled
g
e
.
Stu
d
en
ts
ar
e
b
etter
ab
le
to
co
n
s
tr
u
ct
a
d
ee
p
er
u
n
d
er
s
tan
d
in
g
o
f
th
e
s
u
b
ject
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atter
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en
elab
o
r
atin
g
o
n
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ew
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n
ce
p
ts
an
d
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em
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k
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wled
g
e.
Fin
al
ly
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th
e
p
o
s
itiv
e
r
elatio
n
s
h
ip
b
etwe
en
r
eh
ea
r
s
al
s
tr
ateg
ies
an
d
m
ath
em
atics
p
r
o
f
icien
cy
em
p
h
asizes
th
e
r
o
le
o
f
p
r
ac
tice
an
d
m
em
o
r
izatio
n
in
m
ath
e
m
atica
l
s
k
ill
d
ev
elo
p
m
en
t.
C
o
n
s
is
ten
t
p
r
ac
tice
r
ein
f
o
r
ce
s
lear
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n
g
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d
f
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th
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r
etr
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o
f
in
f
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m
atio
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f
r
o
m
m
em
o
r
y
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wh
ich
is
n
ec
ess
ar
y
f
o
r
p
r
o
b
lem
-
s
o
lv
i
n
g
an
d
m
ath
e
m
atica
l c
o
m
p
u
tatio
n
s
.
T
h
e
ab
s
en
ce
o
f
a
s
ig
n
if
ican
t
c
o
r
r
elatio
n
b
etwe
en
o
r
g
an
izati
o
n
s
tr
ateg
y
an
d
m
ath
em
atics
p
r
o
f
icien
c
y
(
r
=0
.
2
0
7
,
p
=
0
.
0
6
2
)
is
u
n
ex
p
ec
ted
,
as
p
r
io
r
liter
atu
r
e
g
en
er
ally
s
u
p
p
o
r
ts
th
e
p
o
s
itiv
e
in
f
lu
en
ce
o
f
o
r
g
an
izatio
n
al
s
k
ills
o
n
ac
a
d
em
ic
p
er
f
o
r
m
a
n
ce
.
T
h
is
f
i
n
d
in
g
war
r
an
ts
f
u
r
th
er
in
v
es
tig
atio
n
to
i
d
en
tify
p
o
ten
tial
co
n
f
o
u
n
d
in
g
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ar
iab
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r
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ativ
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ex
p
lan
atio
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s
.
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e
p
o
s
s
ib
le
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ter
p
r
etatio
n
is
th
at
wh
ile
o
r
g
an
izatio
n
is
a
v
alu
ab
le
s
tu
d
y
s
k
ill,
its
d
ir
ec
t
im
p
ac
t
o
n
m
ath
em
atics
ac
h
iev
em
en
t
m
ay
b
e
m
ed
iated
b
y
o
th
er
f
a
cto
r
s
s
u
ch
as
th
e
n
at
u
r
e
o
f
th
e
m
ath
em
atics
cu
r
r
i
cu
lu
m
,
i
n
s
tr
u
ctio
n
al
a
p
p
r
o
ac
h
es,
o
r
ass
ess
m
en
t
p
r
ac
tices.
I
n
m
a
n
y
Ph
ilip
p
in
e
h
ig
h
er
ed
u
ca
tio
n
i
n
s
titu
tio
n
s
,
m
ath
em
atics
in
s
tr
u
ctio
n
r
em
ain
s
lar
g
ely
p
r
o
ce
d
u
r
al,
em
p
h
asizin
g
f
o
r
m
u
laic
p
r
o
b
lem
-
s
o
lv
in
g
an
d
co
m
p
u
tatio
n
al
ac
c
u
r
ac
y
o
v
er
co
n
ce
p
tu
al
in
teg
r
atio
n
.
C
o
n
s
eq
u
en
tly
,
s
tu
d
en
ts
m
ay
r
ely
m
o
r
e
o
n
r
eh
ea
r
s
al
an
d
co
n
tr
o
l
s
tr
ateg
ies
th
an
o
n
o
r
g
a
n
izatio
n
al
tech
n
iq
u
es
wh
en
s
tu
d
y
in
g
.
An
o
t
h
er
p
o
s
s
ib
le
ex
p
lan
atio
n
is
th
at
s
tu
d
en
t
s
’
o
r
g
a
n
izatio
n
al
b
eh
av
i
o
r
s
—
s
u
ch
as
s
tr
u
ctu
r
in
g
n
o
tes
o
r
ar
r
an
g
in
g
s
tu
d
y
s
ch
e
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u
les
—
m
ay
n
o
t
d
ir
ec
tly
tr
an
s
late
to
d
ee
p
er
m
at
h
em
atica
l
u
n
d
er
s
tan
d
in
g
u
n
less
co
u
p
led
with
m
etac
o
g
n
itiv
e
s
tr
ateg
ies
lik
e
p
lan
n
i
n
g
a
n
d
m
o
n
ito
r
in
g
.
Fu
tu
r
e
r
esear
ch
c
o
u
l
d
th
er
ef
o
r
e
e
x
am
in
e
h
o
w
th
e
e
f
f
ec
tiv
en
ess
o
f
o
r
g
an
izatio
n
al
s
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ateg
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in
ter
ac
ts
with
teac
h
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g
m
eth
o
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r
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en
t m
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o
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n
d
er
s
tan
d
th
eir
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o
le
in
s
u
p
p
o
r
ti
n
g
m
ath
em
atics p
r
o
f
icien
cy
.
3
.
5
.
Rela
t
io
ns
hip
bet
wee
n m
et
a
co
g
nitiv
e
le
a
rning
s
t
ra
t
eg
ies a
nd
m
a
t
hem
a
t
ics pro
f
icie
ncy
T
ab
le
5
p
r
esen
ts
th
e
co
r
r
e
latio
n
al
an
aly
s
is
b
etwe
en
m
etac
o
g
n
itiv
e
lear
n
in
g
s
tr
at
eg
ies
an
d
m
ath
em
atics
p
r
o
f
icien
cy
.
R
e
s
u
lts
in
d
icate
s
ig
n
if
ican
t
p
o
s
itiv
e
co
r
r
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n
s
b
etwe
en
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lan
n
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g
(
r
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2
9
9
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.
0
4
1
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,
m
o
n
ito
r
in
g
(
r
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.
3
3
7
,
p
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0
3
8
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,
a
n
d
e
v
alu
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n
(
r
=0
.
3
6
0
,
p
=0
.
0
2
5
)
an
d
m
ath
e
m
atics
p
r
o
f
icien
cy
.
T
h
ese
f
in
d
in
g
s
s
u
g
g
est
a
p
o
s
itiv
e
r
elatio
n
s
h
ip
b
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e
u
s
e
o
f
m
etac
o
g
n
itiv
e
lear
n
in
g
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tr
ateg
ies
an
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
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:
2
2
5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
15
,
No
.
3
,
J
u
n
e
20
2
6
:
2
3
3
8
-
2
3
4
7
2344
s
tu
d
en
ts
’
m
ath
em
atica
l
p
er
f
o
r
m
an
ce
.
T
h
e
f
i
n
d
in
g
s
o
f
t
h
e
p
r
esen
t
s
tu
d
y
in
d
icate
th
e
cr
itical
r
o
le
o
f
m
etac
o
g
n
itiv
e
lear
n
in
g
s
tr
ateg
ies in
en
h
an
cin
g
m
ath
em
atics
p
r
o
f
icien
c
y
[
3
3
]
,
[
3
4
]
,
[
6
3
]
.
T
ab
le
5
.
C
o
r
r
elatio
n
al
an
aly
s
is
b
etwe
en
r
esp
o
n
d
en
ts
’
lev
el
o
f
m
etac
o
g
n
itiv
e
lear
n
in
g
s
tr
ate
g
ies an
d
m
ath
em
atics p
r
o
f
icien
c
y
V
a
r
i
a
b
l
e
s
r
p
R
e
s
u
l
t
Le
v
e
l
o
f
p
l
a
n
n
i
n
g
s
t
r
a
t
e
g
y
v
s
.
m
a
t
h
e
mat
i
c
s
p
r
o
f
i
c
i
e
n
c
y
0
.
2
9
9
0
.
0
4
1
S
i
g
n
i
f
i
c
a
n
t
Le
v
e
l
o
f
m
o
n
i
t
o
r
i
n
g
s
t
r
a
t
e
g
y
v
s
.
m
a
t
h
e
mat
i
c
s
p
r
o
f
i
c
i
e
n
c
y
0
.
3
3
7
0
.
0
3
8
S
i
g
n
i
f
i
c
a
n
t
Le
v
e
l
o
f
e
v
a
l
u
a
t
i
o
n
s
t
r
a
t
e
g
y
v
s.
ma
t
h
e
mat
i
c
s
p
r
o
f
i
c
i
e
n
c
y
0
.
3
6
0
0
.
0
2
5
S
i
g
n
i
f
i
c
a
n
t
Stu
d
en
ts
wh
o
ef
f
ec
tiv
ely
en
g
ag
e
in
p
lan
n
in
g
,
s
ettin
g
g
o
als,
an
d
o
r
g
a
n
izin
g
th
eir
lear
n
in
g
ar
e
m
o
r
e
lik
ely
to
ap
p
r
o
ac
h
m
ath
em
atic
s
task
s
with
a
clea
r
p
u
r
p
o
s
e
a
n
d
d
ir
ec
tio
n
.
T
h
is
p
r
o
ac
tiv
e
a
p
p
r
o
ac
h
co
n
tr
ib
u
tes
to
im
p
r
o
v
ed
p
er
f
o
r
m
an
ce
b
y
f
ac
ilit
atin
g
ef
f
icien
t
tim
e
m
an
ag
em
en
t
an
d
r
eso
u
r
ce
allo
ca
tio
n
.
Mo
r
eo
v
er
,
th
e
p
o
s
itiv
e
ass
o
ciatio
n
b
etwe
en
m
o
n
ito
r
in
g
s
tr
ateg
ies
an
d
m
at
h
em
atics
p
r
o
f
icien
c
y
em
p
h
asi
ze
s
th
e
s
ig
n
if
ican
ce
o
f
s
elf
-
awa
r
e
n
ess
an
d
s
elf
-
ass
ess
m
en
t
[
5
4
]
,
[
5
5
]
.
Stu
d
en
ts
wh
o
ef
f
ec
tiv
ely
t
r
ac
k
t
h
eir
p
r
o
g
r
ess
,
id
en
tif
y
ar
ea
s
o
f
s
tr
en
g
t
h
a
n
d
wea
k
n
ess
,
an
d
ad
ju
s
t
th
eir
lear
n
in
g
s
tr
ateg
ie
s
ac
co
r
d
in
g
ly
d
em
o
n
s
tr
ate
g
r
e
ater
au
to
n
o
m
y
an
d
co
n
tr
o
l
o
v
er
th
eir
lear
n
in
g
.
Fin
ally
,
th
e
p
o
s
itiv
e
r
elatio
n
s
h
i
p
b
etwe
en
ev
al
u
atio
n
s
tr
ateg
i
es
an
d
m
ath
em
atics
p
r
o
f
icien
c
y
r
e
v
ea
ls
th
e
im
p
o
r
tan
ce
o
f
r
e
f
lectiv
e
th
i
n
k
in
g
[
6
4
]
,
[
6
5
]
.
T
h
r
o
u
g
h
r
ef
lectin
g
o
n
th
eir
lear
n
in
g
ex
p
er
ien
ce
s
,
s
tu
d
e
n
ts
g
ain
v
al
u
ab
le
in
s
ig
h
ts
in
t
o
th
eir
p
r
o
b
le
m
-
s
o
lv
in
g
p
r
o
ce
s
s
es,
id
en
tif
y
er
r
o
r
s
,
a
n
d
d
ev
elo
p
ef
f
ec
tiv
e
s
tr
ateg
ies
f
o
r
f
u
tu
r
e
task
s
.
W
h
ile
th
e
cu
r
r
en
t
s
tu
d
y
p
r
o
v
id
es
ev
id
e
n
ce
f
o
r
th
e
p
o
s
itiv
e
im
p
ac
t
o
f
m
etac
o
g
n
itiv
e
lear
n
in
g
s
tr
ate
g
ies
o
n
m
ath
e
m
atics
p
r
o
f
icie
n
cy
,
f
u
r
th
er
r
esear
ch
is
n
ee
d
ed
to
ex
a
m
in
e
th
e
ef
f
ec
tiv
en
ess
o
f
s
p
ec
if
ic
m
eta
co
g
n
itiv
e
in
ter
v
en
tio
n
s
.
4.
CO
NCLU
SI
O
N
T
h
e
f
in
d
in
g
s
o
f
th
is
s
tu
d
y
p
r
o
v
id
e
em
p
ir
ical
ev
id
en
ce
f
o
r
th
e
s
ig
n
if
ican
t
r
o
le
o
f
b
o
th
co
g
n
itiv
e
an
d
m
etac
o
g
n
itiv
e
lear
n
in
g
s
tr
at
eg
ies
in
en
h
an
cin
g
m
ath
em
atics
p
r
o
f
icien
cy
.
T
h
e
s
tu
d
y
d
em
o
n
s
tr
ates
th
at
f
r
esh
m
en
wh
o
co
n
s
is
ten
tly
ap
p
ly
co
g
n
itiv
e
s
tr
ateg
ies
s
u
ch
as
co
n
tr
o
l,
elab
o
r
atio
n
,
a
n
d
r
e
h
ea
r
s
al,
alo
n
g
with
m
etac
o
g
n
itiv
e
p
r
o
ce
s
s
es
in
cl
u
d
in
g
p
lan
n
in
g
,
m
o
n
ito
r
in
g
,
an
d
ev
alu
ati
n
g
t
h
eir
lea
r
n
i
n
g
,
e
x
h
ib
it
h
ig
h
e
r
m
ath
em
atics
p
r
o
f
icie
n
cy
.
T
h
e
s
e
f
in
d
in
g
s
h
ig
h
lig
h
t
th
e
n
ee
d
f
o
r
m
at
h
em
atics
in
s
tr
u
ctio
n
to
e
x
p
licitly
teac
h
an
d
em
b
ed
lear
n
in
g
s
tr
ateg
ies
in
th
e
c
u
r
r
icu
lu
m
th
r
o
u
g
h
a
ctiv
ities
lik
e
r
ef
lectiv
e
lear
n
i
n
g
jo
u
r
n
als,
g
u
id
ed
p
r
o
b
lem
-
s
o
lv
in
g
ch
ec
k
lis
ts
,
an
d
s
elf
-
ass
ess
m
en
t
task
s
r
eq
u
ir
in
g
s
tu
d
en
ts
to
ex
p
lain
a
n
d
j
u
s
tify
th
eir
s
o
lu
tio
n
p
r
o
ce
s
s
es.
Sch
o
o
ls
s
h
o
u
ld
also
s
tr
en
g
t
h
en
s
tu
d
en
t
s
u
p
p
o
r
t
b
y
o
f
f
e
r
in
g
s
tr
u
ctu
r
e
d
p
r
o
g
r
am
s
s
u
ch
as
p
ee
r
tu
to
r
in
g
,
r
em
e
d
ial
m
ath
em
at
ics
s
ess
io
n
s
,
an
d
s
k
ills
-
f
o
cu
s
ed
wo
r
k
s
h
o
p
s
,
wh
ile
teac
h
er
s
s
h
o
u
ld
r
ec
eiv
e
p
r
o
f
ess
io
n
al
d
ev
elo
p
m
en
t
th
at
eq
u
ip
s
th
em
to
m
o
d
el
th
in
k
-
alo
u
d
s
tr
ateg
ies,
s
ca
f
f
o
ld
m
etac
o
g
n
itiv
e
q
u
esti
o
n
in
g
,
an
d
d
esig
n
less
o
n
s
th
at
p
r
o
m
o
te
r
ea
s
o
n
in
g
an
d
r
e
f
lectio
n
.
T
ec
h
n
o
lo
g
y
-
e
n
h
an
ce
d
p
latf
o
r
m
s
,
in
clu
d
in
g
ad
ap
tiv
e
lear
n
in
g
s
y
s
tem
s
an
d
in
ter
ac
tiv
e
s
im
u
lati
o
n
s
,
m
ay
f
u
r
t
h
er
in
d
iv
id
u
alize
s
k
ill
d
ev
elo
p
m
e
n
t
an
d
tr
ac
k
s
tr
ateg
ic
lea
r
n
in
g
p
r
o
g
r
ess
.
W
h
ile
th
e
s
tu
d
y
’
s
cr
o
s
s
-
s
ec
tio
n
al
n
atu
r
e
an
d
lim
ited
p
o
p
u
latio
n
r
estrict
ca
u
s
al
in
ter
p
r
etatio
n
an
d
g
e
n
er
aliza
b
ilit
y
,
f
u
tu
r
e
r
esear
c
h
s
h
o
u
ld
ex
am
in
e
th
e
l
o
n
g
-
ter
m
ef
f
ec
ts
o
f
s
tr
ateg
y
u
s
e
o
n
ac
ad
em
ic
g
r
o
wth
,
in
v
esti
g
ate
h
o
w
m
o
tiv
atio
n
a
n
d
s
elf
-
ef
f
icac
y
m
e
d
iate
th
ese
r
elatio
n
s
h
ip
s
,
an
d
co
m
p
ar
e
th
e
ef
f
ec
tiv
e
n
ess
o
f
d
if
f
er
en
t
in
s
tr
u
ctio
n
al
in
ter
v
en
tio
n
s
f
o
r
im
p
r
o
v
in
g
s
tu
d
e
n
ts
’
co
g
n
itiv
e
an
d
m
etac
o
g
n
itiv
e
lear
n
in
g
s
k
ills
.
ACK
NO
WL
E
DG
M
E
N
T
S
Au
th
o
r
s
ac
k
n
o
wled
g
e
Min
d
o
r
o
State
Un
iv
er
s
ity
f
o
r
t
h
e
s
u
p
p
o
r
t g
iv
en
in
th
e
c
o
n
d
u
ct
o
f
t
h
is
s
tu
d
y
.
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
t
r
ib
u
to
r
R
o
les
T
a
x
o
n
o
m
y
(
C
R
ed
iT)
to
r
ec
o
g
n
ize
in
d
iv
i
d
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
ate
co
llab
o
r
atio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
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v
al
&
R
es E
d
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c
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N:
2252
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8
8
2
2
C
o
g
n
itive
a
n
d
meta
c
o
g
n
itive
l
ea
r
n
in
g
s
tr
a
teg
ies a
s
co
r
r
ela
tes o
f u
n
ivers
ity
s
tu
d
en
ts
’
…
(
P
o
leme
r
M.
C
u
a
r
to
)
2345
Na
m
e
o
f
Aut
ho
r
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C
u
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✓
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E
n
y
a
Ma
r
ie
D.
Ap
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s
to
l
✓
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C
:
C
o
n
c
e
p
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t
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h
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e
o
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f
o
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c
o
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en
t f
r
o
m
all
in
d
iv
id
u
als in
c
lu
d
ed
in
t
h
is
s
tu
d
y
.
E
T
H
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CAL AP
P
RO
V
AL
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h
is
s
tu
d
y
is
class
if
ied
as
ex
em
p
t
f
r
o
m
eth
ics
r
e
v
iew
as
p
er
p
o
licy
o
f
th
e
Un
iv
er
s
ity
E
th
i
cs
R
ev
iew
C
o
m
m
ittee.
DATA AV
AI
L
AB
I
L
I
T
Y
Der
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it
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c
a
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b
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c
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tac
ted
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:
p
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d
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p
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tab
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p
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g
(P
r
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A
CT)
fo
r
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d
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c
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to
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tern
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ig
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Un
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-
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tern
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Aw
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tst
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Ac
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P
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r.
S
h
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c
a
n
b
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c
o
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tac
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m
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:
e
n
y
a
.
a
p
o
st
o
l@m
in
su
.
e
d
u
.
p
h
.
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