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a
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ly
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n
d
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d
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re
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sh
ip
b
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n
TK
a
n
d
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TU
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with
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o
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a
n
t
m
e
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iatio
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o
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se
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rt
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r
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p
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rien
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e
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d
i
d
n
o
t
m
o
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e
ra
te
th
is
re
latio
n
sh
i
p
.
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o
we
v
e
r,
TK
wa
s
fo
u
n
d
to
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g
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ifi
c
a
n
tl
y
i
n
flu
e
n
c
e
P
CK
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th
e
re
b
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im
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a
c
ti
n
g
th
e
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u
a
li
t
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c
ti
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ro
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e
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b
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rs.
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d
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t
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icto
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h
e
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ti
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li
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s
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it
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ip
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ti
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th
a
t
G
h
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n
a
ian
m
a
th
e
m
a
ti
c
s
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h
e
rs
’
TK
is
p
e
rc
e
iv
e
d
to
e
n
a
b
le
th
e
m
to
lev
e
ra
g
e
d
i
g
it
a
l
to
o
ls
a
n
d
re
so
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rc
e
s
e
ffe
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ti
v
e
ly
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o
c
o
n
n
e
c
t
i
t
to
th
e
ir
P
CK
,
u
lt
ima
tely
to
lea
d
t
o
m
o
r
e
e
n
g
a
g
i
n
g
,
e
ffe
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ti
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e
,
a
n
d
imp
a
c
tfu
l
m
a
th
e
m
a
ti
c
s
in
str
u
c
ti
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n
d
e
li
v
e
ry
.
T
h
i
s
will
fo
ste
r
m
e
a
n
in
g
fu
l
lea
rn
in
g
e
x
p
e
rien
c
e
s
a
li
g
n
e
d
with
c
u
rricu
lu
m
g
o
a
ls
a
n
d
lea
rn
e
rs n
e
e
d
s.
K
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w
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d
s
:
Ma
th
em
atics tea
ch
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Ped
ag
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g
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co
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ten
t k
n
o
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e
Per
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u
s
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T
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T
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c
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ss
a
rticle
u
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e
CC B
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SA
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C
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p
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A
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:
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Op
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tm
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Ak
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Ap
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Dev
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AAM
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Ku
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Ash
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ti,
Gh
an
a
E
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ail:
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p
p
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co
m
1.
I
NT
RO
D
UCT
I
O
N
T
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n
o
lo
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’
s
r
is
e
h
as
s
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if
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tly
im
p
ac
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ed
u
ca
tio
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e
m
p
h
asizin
g
its
in
teg
r
atio
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in
to
cu
r
r
icu
lu
m
[
1
]
,
[
2
]
,
y
et
it
r
e
m
ain
s
u
n
d
er
u
tili
ze
d
d
esp
ite
its
p
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ti
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to
im
p
r
o
v
e
m
at
h
em
atics
in
s
tr
u
ctio
n
[
3
]
,
[
4
]
.
Me
an
wh
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th
e
2
1
s
t
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tu
r
y
d
em
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d
s
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-
k
n
o
w
tech
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o
lo
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p
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f
icien
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f
r
o
m
teac
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s
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r
eq
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ir
in
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th
e
m
to
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e
s
k
illed
in
b
o
th
tech
n
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d
teac
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m
eth
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d
s
to
h
e
lp
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th
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k
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a
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m
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icate
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wh
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s
o
lv
in
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p
r
ac
tical
wo
r
ld
p
r
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b
lem
s
[
5
]
–
[
8
]
.
W
h
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teac
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p
lay
a
k
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eg
r
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ce
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it
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u
ar
an
tee
its
u
s
e
in
less
o
n
s
[
5
]
,
[
9
]
.
T
o
ad
d
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ess
th
is
,
s
tak
eh
o
l
d
er
s
in
Gh
a
n
a,
lik
e
Natio
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al
T
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C
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cil
(
NT
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a
n
d
N
atio
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al
C
o
u
n
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f
o
r
C
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r
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m
an
d
Ass
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en
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(
NaCC
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,
ar
e
co
llab
o
r
atin
g
t
o
in
teg
r
ate
tech
n
o
lo
g
y
in
to
e
d
u
ca
tio
n
th
r
o
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g
h
t
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(
PLC)
i
n
itiativ
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[
1
0
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–
[
1
2
]
.
I
n
th
e
p
r
ev
io
u
s
s
tu
d
y
b
y
Mc
I
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et
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[
1
3
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,
d
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ch
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to
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em
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t
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b
r
ac
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tech
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lo
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ev
en
th
o
u
g
h
th
ey
h
av
e
lib
er
ty
o
v
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its
u
s
ag
e,
Gh
an
aian
teac
h
er
s
'
in
teg
r
atio
n
o
f
tech
n
o
lo
g
y
with
tr
ad
itio
n
al
p
ed
ag
o
g
ical
co
n
ten
t
k
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o
wled
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(
PC
K)
is
ess
en
tial
f
o
r
ef
f
ec
tiv
e
teac
h
in
g
[
1
4
]
,
[
1
5
]
.
T
ea
ch
er
s
’
a
cc
ep
tan
ce
an
d
ab
ilit
y
to
in
teg
r
ate
tech
n
o
lo
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y
k
n
o
wled
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e
(
T
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in
to
m
ath
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m
atics
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g
an
d
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in
g
wer
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ass
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s
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g
P
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K
f
r
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m
th
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tech
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lo
g
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ag
o
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n
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t
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tech
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el
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T
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f
r
am
ewo
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k
s
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Nu
m
er
o
u
s
r
esear
ch
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s
[
1
6
]
–
[
1
9
]
h
av
e
attem
p
ted
to
i
n
v
esti
g
ate
h
o
w
tech
n
o
lo
g
y
in
teg
r
atio
n
af
f
ec
ts
teac
h
er
s
'
ac
ce
p
tan
ce
o
f
it,
b
u
t th
ey
h
av
e
n
o
t ta
k
en
i
n
to
ac
co
u
n
t th
e
wa
y
th
at
co
n
v
en
tio
n
al
PC
K
m
ed
i
ates th
e
ac
ce
p
tan
ce
an
d
p
e
r
ce
iv
ed
u
s
e
o
f
tech
n
o
lo
g
y
.
No
n
eth
eless
,
tak
in
g
i
n
to
ac
co
u
n
t
th
e
m
o
d
er
atin
g
ef
f
ec
t
o
f
teac
h
e
r
s
’
p
r
o
f
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al
e
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p
er
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ce
(
PE)
b
etwe
en
th
eir
T
K
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n
d
t
h
eir
p
e
r
ce
iv
ed
tec
h
n
o
lo
g
y
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s
ef
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ln
ess
(
PTU)
h
as
r
ec
eiv
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litt
le
o
r
n
o
atten
tio
n
in
th
e
Gh
an
aian
m
ath
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atics
ed
u
ca
tio
n
al
r
esear
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f
ield
.
T
h
e
s
tu
d
y
ai
m
ed
to
f
ill
a
g
a
p
in
th
e
liter
atu
r
e
b
y
in
v
esti
g
atin
g
th
e
f
o
llo
win
g
h
y
p
o
t
h
eses
:
i)
t
h
er
e
is
n
o
s
ig
n
if
ican
t
ef
f
ec
t
o
f
teac
h
er
s
’
T
K
o
n
th
eir
PC
K
(H
01
)
;
ii)
t
h
e
r
e
is
n
o
s
ig
n
if
ican
t
ef
f
ec
t
o
f
teac
h
er
s
’
PC
K
o
n
th
eir
PTU
(H
02
)
;
iii)
t
h
er
e
is
n
o
s
ig
n
if
ican
t
ef
f
ec
t
o
f
teac
h
er
s
’
T
K
o
n
th
eir
PTU
(H
03
)
;
iv
)
t
h
er
e
is
n
o
s
ig
n
if
ica
n
t
m
ed
i
atio
n
r
o
le
o
f
PC
K
b
etwe
en
teac
h
er
s
’
T
K
an
d
PT
U
(H
04
)
;
an
d
v
)
t
h
er
e
is
n
o
s
ig
n
if
ican
t
m
o
d
er
atio
n
r
o
le
o
f
PE
b
etwe
en
teac
h
er
s
’
T
K
an
d
PTU
(H
05
)
.
T
h
e
s
tu
d
y
b
y
L
ee
et
a
l
.
[
2
0
]
ar
e
o
n
e
o
f
th
e
v
iew
th
at
s
o
m
e
ex
p
e
r
ien
ce
d
teac
h
er
s
m
a
y
b
e
o
p
e
n
to
in
teg
r
atin
g
tec
h
n
o
lo
g
y
in
to
th
eir
in
s
tr
u
ctio
n
al
p
r
ac
tices
af
ter
r
ec
o
g
n
izin
g
its
p
o
ten
tial
to
en
h
a
n
ce
lear
n
e
r
lear
n
in
g
o
u
tc
o
m
es,
r
eg
ar
d
less
o
f
th
eir
y
ea
r
s
o
f
ex
p
e
r
ien
ce
.
Sims
an
d
Fletch
er
-
W
o
o
d
[
2
1
]
also
in
d
icate
d
th
at
ex
p
er
ien
ce
d
teac
h
er
s
w
h
o
v
alu
e
p
r
o
f
ess
io
n
al
d
ev
el
o
p
m
e
n
t
an
d
life
lo
n
g
lear
n
in
g
m
a
y
ac
tiv
ely
s
ee
k
o
u
t
o
p
p
o
r
tu
n
ities
to
e
n
h
an
ce
th
eir
TK
an
d
s
k
ills
.
C
h
ai
et
a
l
.
[
2
2
]
h
ig
h
lig
h
t
th
e
c
h
allen
g
e
o
f
in
te
g
r
atin
g
k
n
o
wled
g
e
in
p
ed
a
g
o
g
y
,
s
u
b
ject
m
atter
,
an
d
tech
n
o
lo
g
y
.
Acc
o
r
d
in
g
to
Har
it
[
8
]
,
Sh
u
lm
an
a
d
v
o
ca
te
s
f
o
r
t
h
e
co
n
ce
p
t
o
f
PC
K
in
ed
u
ca
tio
n
,
teac
h
er
s
m
u
s
t
u
n
d
er
s
tan
d
cu
r
r
icu
lu
m
,
p
e
d
ag
o
g
y
,
m
ater
ial,
an
d
th
eir
i
n
ter
ac
tio
n
s
.
S
ev
er
al
s
tu
d
ies
[
8
]
,
[
2
2
]
–
[
2
7
]
h
a
v
e
all
ex
p
lo
r
ed
th
e
r
o
le
o
f
PC
K
in
e
d
u
ca
tio
n
.
PC
K
is
a
p
er
s
o
n
al
q
u
ality
th
at
c
o
n
n
ec
t
s
co
n
ten
t
k
n
o
wled
g
e
to
p
ed
ag
o
g
ical
k
n
o
wled
g
e;
in
f
l
u
en
cin
g
p
ed
ag
o
g
ical
r
atio
n
al
th
o
u
g
h
t
[
2
6
]
.
I
t
in
v
o
lv
es
u
n
d
er
s
tan
d
i
n
g
,
ju
s
tify
in
g
,
p
r
e
p
ar
in
g
,
an
d
im
p
lem
e
n
tin
g
teac
h
in
g
s
tr
ateg
ies
to
im
p
r
o
v
e
s
tu
d
en
t
o
u
tco
m
es
.
So
m
e
s
ch
o
lar
s
co
n
ten
d
th
at
th
er
e
is
n
o
r
ea
l
d
if
f
er
en
ce
b
etwe
en
PC
K
an
d
co
n
ten
t
k
n
o
wled
g
e,
c
o
n
ten
t
k
n
o
wled
g
e
m
ay
b
e
alter
e
d
f
o
r
in
s
tr
u
ctio
n
al
r
ea
s
o
n
s
[
2
4
]
,
[
2
8
]
,
[
2
9
]
.
I
n
an
ef
f
ec
tiv
e
an
aly
t
ic
co
u
r
s
e,
s
tu
d
y
b
y
Delg
ad
o
-
R
eb
o
lled
o
an
d
Z
ak
a
r
y
an
[
2
7
]
in
v
esti
g
ates
th
e
lin
k
b
etwe
en
a
lectu
r
er
'
s
PC
K
an
d
m
ath
em
atica
l
u
n
d
er
s
tan
d
i
n
g
.
T
h
e
s
tu
d
y
m
a
k
es
u
s
e
o
f
th
e
m
ath
teac
h
e
r
'
s
s
p
ec
ialized
k
n
o
wled
g
e
ap
p
r
o
ac
h
,
wh
ich
co
m
b
in
es
PC
K
w
ith
s
p
ec
ialized
ex
p
er
tis
e
f
o
r
m
ath
teac
h
er
s
.
T
h
eir
s
tu
d
y
s
h
o
ws
th
at
a
teac
h
er
's
u
n
d
er
s
tan
d
in
g
o
f
m
ath
em
atica
l c
o
n
ce
p
ts
af
f
ec
ts
th
eir
k
n
o
wled
g
e
o
f
in
s
tr
u
ctio
n
al
s
tr
ateg
ies,
m
etap
h
o
r
s
,
an
d
an
alo
g
ies.
PC
K
an
d
tech
n
o
lo
g
ical
r
eso
u
r
ce
s
ar
e
co
m
p
lex
a
n
d
m
u
ltifa
ce
ted
,
r
ef
lectin
g
th
e
wa
y
ev
o
lu
tio
n
h
as
r
ev
o
lv
ed
ar
o
u
n
d
cy
cles
o
f
g
r
o
wth
an
d
ac
cu
m
u
latio
n
[
3
0
]
.
O’
C
o
n
n
o
r
et
a
l
.
[
3
1
]
ex
p
l
o
r
e
d
th
e
u
s
e
o
f
d
ig
ital
tech
n
o
lo
g
y
an
d
p
ed
a
g
o
g
y
b
ef
o
r
e
an
d
a
f
ter
th
e
2
0
2
0
/
2
1
Vie
tn
am
lo
ck
d
o
wn
.
T
h
e
s
tu
d
y
r
e
v
ea
ls
th
at
teac
h
er
s
'
p
er
ce
p
tio
n
s
an
d
e
x
p
er
ien
ce
s
d
u
r
in
g
th
is
p
er
io
d
wer
e
d
iv
er
s
e
,
with
s
o
m
e
f
in
d
in
g
n
ew
p
ed
a
g
o
g
ical
tech
n
iq
u
es
ch
allen
g
in
g
,
wh
ile
o
th
er
s
e
n
jo
y
ed
th
e
o
p
p
o
r
tu
n
ity
to
e
x
p
er
im
en
t
with
d
if
f
er
e
n
t
teac
h
in
g
m
eth
o
d
s
.
Pre
v
i
o
u
s
s
tu
d
ies
[
3
2
]
,
[
3
3
]
co
n
ten
d
th
at
b
y
tak
in
g
a
l
o
o
k
at
th
e
T
PAC
K
co
n
s
tr
u
cts
teac
h
er
s
h
a
v
e,
it
is
p
o
s
s
ib
le
to
in
teg
r
ate
tech
n
o
l
o
g
y
a
n
d
PC
K
in
th
e
class
r
o
o
m
.
Ho
wev
e
r
,
Sp
an
g
en
b
er
g
a
n
d
Fre
itas
[
3
4
]
h
ig
h
lig
h
ts
h
o
w
s
h
if
ts
in
ed
u
ca
tio
n
an
d
s
o
ci
ety
h
av
e
af
f
ec
te
d
th
e
s
elec
tio
n
an
d
u
s
e
o
f
PC
K
an
d
r
elate
d
tech
n
o
lo
g
ies.
Me
an
wh
ile,
C
h
in
g
an
d
R
o
b
e
r
t
[
3
5
]
b
elief
th
at
n
o
a
m
o
u
n
t
o
f
tech
n
o
lo
g
y
a
d
v
an
ce
m
en
t
ca
n
u
n
d
e
r
m
in
e
th
e
im
p
o
r
tan
ce
o
f
PC
K.
No
twith
s
tan
d
in
g
,
h
ig
h
-
s
tag
e
T
PAC
K
teac
h
er
s
will
ea
s
e
th
eir
lear
n
er
s
'
s
tep
s
an
d
ac
tio
n
s
to
a
co
llab
o
r
ativ
e
ap
p
r
o
ac
h
a
s
th
ey
ex
p
lo
r
e
tech
n
o
lo
g
y
in
th
e
m
ath
em
atics
class
r
o
o
m
[
3
2
]
.
L
ee
et
a
l
.
[
2
0
]
d
is
co
v
er
ed
c
o
m
m
o
n
th
r
ea
d
s
i
n
p
u
b
licatio
n
s
th
at
ad
d
r
ess
ed
T
PAC
K,
teac
h
er
p
r
ep
ar
atio
n
,
tech
n
o
lo
g
ical
s
k
ills
,
an
d
p
ed
ag
o
g
y
wh
ile
also
f
o
c
u
s
in
g
o
n
PC
K,
teac
h
er
k
n
o
wled
g
e,
a
n
d
teac
h
er
ed
u
ca
tio
n
.
R
ak
es
et
a
l
.
[
3
6
]
also
ass
er
t
th
at
th
e
ab
s
en
ce
o
f
c
o
r
r
elatio
n
in
th
eir
f
in
d
in
g
s
is
ev
id
en
ce
th
at
th
e
tech
n
o
lo
g
y
in
T
PAC
K
is
an
ess
en
tial a
n
d
d
is
tin
ct
s
o
r
t o
f
k
n
o
wled
g
e
th
at
d
o
es n
o
t a
u
to
m
atica
lly
g
r
o
w
alo
n
g
s
id
e
PC
K.
Ho
n
g
a
n
d
Yu
[
3
7
]
i
n
d
icate
d
t
h
at
th
e
T
AM
p
ar
ad
ig
m
p
o
s
tu
lates
a
co
n
n
ec
tio
n
b
etwe
en
o
u
t
s
id
e
f
ac
to
r
s
an
d
b
o
th
p
e
r
ce
iv
ed
u
s
ef
u
ln
es
s
an
d
p
er
ce
i
v
ed
u
s
ab
ilit
y
.
B
y
u
s
in
g
B
an
d
u
r
a
’
s
co
n
ce
p
t
o
f
o
u
tco
m
e
j
u
d
g
m
e
n
t,
L
ewis
[
3
8
]
d
ef
in
es
p
e
r
ce
iv
ed
u
tili
ty
as
a
p
er
s
o
n
'
s
as
s
es
s
m
en
t
o
f
th
e
d
eg
r
ee
to
wh
ich
u
til
izin
g
a
tech
n
o
l
o
g
y
im
p
r
o
v
es
p
er
f
o
r
m
an
ce
.
Acc
o
r
d
in
g
to
Yan
g
et
a
l
.
[
1
9
]
,
teac
h
er
s
p
er
ce
iv
ed
u
tili
ty
o
f
tech
n
o
lo
g
y
was
s
ig
n
if
ican
tly
in
f
lu
en
ce
d
b
y
th
eir
d
eg
r
ee
o
f
T
PAC
K.
I
n
p
ar
ticu
lar
,
e
-
Sch
o
o
lb
a
g
ap
p
r
o
v
al
was
m
o
r
e
s
tr
o
n
g
ly
co
n
n
ec
ted
with
t
h
e
T
K
co
m
p
o
n
en
t th
an
with
t
h
e
PC
K
co
m
p
o
n
en
ts
.
2.
M
E
T
H
O
D
T
o
r
esear
ch
th
e
ab
o
v
e
-
m
en
ti
o
n
ed
g
ap
,
a
p
o
s
itiv
is
t
p
ar
ad
ig
m
em
p
h
asizin
g
em
p
ir
ical
in
v
esti
g
atio
n
was
cr
u
cial.
T
h
e
s
tu
d
y
em
p
lo
y
ed
a
c
o
r
r
elatio
n
al
d
esig
n
u
s
in
g
a
q
u
an
titativ
e
ap
p
r
o
a
ch
to
d
e
m
o
n
s
tr
ate
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
2
5
2
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8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
14
,
No
.
4
,
Au
g
u
s
t
2025
:
2
9
9
0
-
2
9
9
8
2992
teac
h
er
s
’
ac
ce
p
tan
ce
a
n
d
p
e
r
c
eiv
ed
u
s
ef
u
ln
ess
o
f
tec
h
n
o
lo
g
y
th
r
o
u
g
h
t
h
eir
PC
K
in
s
en
io
r
h
ig
h
s
ch
o
o
l
m
ath
in
s
tr
u
ctio
n
in
Gh
a
n
a.
2
.
1
.
Sa
m
ple a
n
d po
pu
la
t
io
n
A
PLC
wo
r
k
s
h
o
p
h
as
b
ee
n
o
n
g
o
in
g
at
g
o
v
er
n
m
e
n
t
s
en
io
r
h
ig
h
s
ch
o
o
ls
n
atio
n
wid
e
s
in
ce
J
u
n
e
2
0
2
3
,
m
ak
in
g
m
ath
em
atics
teac
h
er
s
atten
d
in
g
t
h
ese
s
ess
io
n
s
’
id
ea
l
ca
n
d
id
ates
f
o
r
th
e
s
tu
d
y
.
As
T
u
r
n
er
[
3
9
]
n
o
ted
,
a
s
am
p
le
is
a
f
r
ac
tio
n
o
f
t
h
e
w
h
o
le,
s
elec
ted
to
p
ar
ticip
ate
in
th
e
r
esear
ch
p
r
o
ject.
T
h
e
s
tu
d
y
u
s
ed
T
u
r
n
er
[
3
9
]
m
eth
o
d
to
s
elec
t
a
r
ep
r
esen
ta
tiv
e
s
am
p
le
o
f
1
,
1
0
0
m
ath
em
atics
teac
h
er
s
in
th
e
Ash
an
ti
R
eg
io
n
o
f
Gh
a
n
a,
k
n
o
wn
f
o
r
its
d
iv
er
s
e
teac
h
e
r
co
m
m
u
n
ity
an
d
h
ig
h
c
o
n
ce
n
tr
atio
n
o
f
s
en
io
r
h
ig
h
s
ch
o
o
l
m
a
th
em
atics tea
ch
er
s
.
2.
2
.
Q
ues
t
io
nn
a
ire
v
a
lid
it
y
a
nd
re
lia
bil
it
y
T
h
e
s
tu
d
y
ad
h
er
ed
to
th
e
co
d
e
o
f
et
h
ical
p
r
ac
tice
an
d
d
ec
lar
e
d
its
c
o
m
m
itm
en
t
to
et
h
ical
co
n
s
id
er
atio
n
s
b
y
s
ee
k
i
n
g
p
e
r
m
is
s
io
n
f
r
o
m
th
e
u
n
iv
er
s
ity
e
th
ics
s
elec
t
co
m
m
ittee
b
ef
o
r
e
ad
m
in
is
ter
in
g
th
e
q
u
esti
o
n
n
air
e
to
th
e
r
esp
o
n
d
en
ts
.
T
h
e
s
tr
u
ctu
r
ed
q
u
esti
o
n
n
air
e
u
n
d
er
wen
t
p
ilo
t
test
in
g
in
f
o
u
r
Ku
m
asi
m
u
n
icip
alities
to
en
s
u
r
e
clar
ity
an
d
co
n
s
is
ten
cy
.
T
h
e
Sep
te
m
b
er
2
0
2
3
p
ilo
t
s
u
r
v
ey
ass
ess
ed
th
e
d
ep
e
n
d
ab
ilit
y
o
f
th
e
d
ata
b
ased
o
n
m
u
ltip
le
r
esear
ch
er
s
'
ad
ap
tatio
n
s
[
1
1
]
,
[
1
4
]
,
[
3
8
]
.
T
h
e
r
esear
c
h
er
s
u
s
ed
a
f
iv
e
-
p
o
in
t
L
ik
er
t
s
ca
le
to
s
co
r
e
q
u
esti
o
n
s
in
th
e
s
tu
d
y
,
r
ewo
r
d
ed
u
n
cl
ea
r
wo
r
d
in
g
d
u
r
in
g
th
e
p
ilo
tin
g
.
T
h
e
p
ilo
ted
d
ata
s
h
o
wed
C
r
o
n
b
ac
h
’
s
alp
h
a
T
K
(
0
.
7
1
0
)
,
PC
K
(
.
7
6
5
)
,
an
d
PTU
(
0
.
8
6
4
)
o
n
2
6
4
s
am
p
le
s
izes,
r
esu
ltin
g
in
an
o
v
er
all
alp
h
a
o
f
0
.
8
0
8
.
2
.
3
.
Da
t
a
c
o
llect
io
n pro
ce
du
re
Af
ter
th
e
r
eliab
ilit
y
an
d
v
alid
ity
test
,
th
e
s
u
r
v
ey
was
c
o
n
d
u
cte
d
u
s
in
g
b
o
th
h
a
r
d
a
n
d
o
n
lin
e
q
u
esti
o
n
n
air
e
to
a
d
d
r
ess
g
e
o
g
r
ap
h
ical
p
ar
ticip
a
n
t
s
p
r
ea
d
,
en
s
u
r
in
g
ac
c
u
r
ate
c
o
llectio
n
o
f
r
esp
o
n
d
en
ts
’
d
em
o
g
r
a
p
h
ics
,
T
K,
PC
K,
an
d
PTU
d
ata.
Data
a
n
aly
s
is
in
v
o
lv
e
d
ac
ce
s
s
in
g
a
n
d
co
d
in
g
s
u
r
v
e
y
d
ata
u
s
in
g
Mic
r
o
s
o
f
t
Of
f
ice
E
x
ce
l
2
0
1
9
an
d
em
p
l
o
y
in
g
a
th
r
ee
-
s
tep
ap
p
r
o
ac
h
to
s
tr
u
ctu
r
al
eq
u
atio
n
m
o
d
elin
g
(
SEM
)
,
in
clu
d
in
g
ex
p
lo
r
ato
r
y
f
ac
to
r
a
n
aly
s
is
(
E
FA)
,
co
n
f
i
r
m
ato
r
y
f
ac
to
r
an
aly
s
is
(
C
FA)
,
an
d
SE
M
u
s
in
g
s
tatis
tical
p
ac
k
ag
e
f
o
r
th
e
s
o
cial
s
cien
ce
s
(
SP
S
S)
an
d
an
aly
s
is
o
f
m
o
m
en
t
s
tr
u
ctu
r
es
(
AM
OS)
s
o
f
twar
e’
s
.
Ho
wev
er
,
o
n
ly
9
7
9
o
f
th
e
q
u
esti
o
n
n
air
es
wer
e
d
ee
m
ed
s
u
itab
le
f
o
r
d
ata
an
aly
s
is
af
ter
d
ata
co
ll
ec
tio
n
,
y
ield
in
g
an
ex
tr
em
ely
h
ig
h
r
esp
o
n
s
e
r
ate
o
f
8
9
.
0
% [
(
9
7
9
/1
,
1
0
0
)
1
0
0
]
,
wh
i
ch
q
u
alif
ied
t
h
e
s
tu
d
y
f
o
r
ac
ce
p
tan
ce
.
3.
DE
SCR
I
P
T
I
V
E
ANA
L
YS
I
S
Of
th
e
to
tal
r
esp
o
n
d
e
n
ts
,
8
3
.
6
%
wer
e
m
ales
an
d
1
6
.
4
%
wer
e
f
em
ales.
T
h
e
ag
e
d
is
tr
ib
u
tio
n
,
f
r
o
m
h
ig
h
est to
lo
west,
is
3
5
-
4
4
y
ea
r
s
(
4
1
.
3
%),
2
5
–
3
4
y
ea
r
s
(
4
0
.
3
%),
4
5
–
5
4
y
ea
r
s
(
1
1
.
1
%),
b
elo
w
2
5
y
ea
r
s
(
5
.
9
%),
an
d
a
b
o
v
e
5
4
y
ea
r
s
(
1
.
2
%).
Am
o
n
g
th
e
s
am
p
le,
8
.
3
%
ar
e
n
o
t
p
r
o
f
ess
io
n
al
teac
h
er
s
,
wh
ile
o
v
e
r
9
1
.
7
%
a
r
e
.
Mo
s
t
r
esp
o
n
d
e
n
ts
h
o
ld
a
f
ir
s
t
d
eg
r
ee
(
7
6
.
9
%),
with
o
n
ly
2
3
.
1
%
h
o
ld
in
g
a
s
ec
o
n
d
d
eg
r
ee
.
T
h
eir
teac
h
in
g
ex
p
er
ien
ce
r
an
g
es f
r
o
m
6
to
1
5
y
ea
r
s
(
4
2
.
1
%),
with
2
5
-
3
5
y
ea
r
s
(
1
.
8
%)
co
n
s
titu
tin
g
th
e
m
in
o
r
ity
.
T
h
e
E
FA
,
g
u
id
ed
b
y
Hair
et
a
l
.
[
4
0
]
,
p
r
o
d
u
ce
d
a
Kaiser
-
Me
y
er
-
Olk
in
m
ea
s
u
r
e
o
f
s
am
p
lin
g
ad
eq
u
ac
y
o
f
0
.
8
2
8
,
in
d
icatin
g
8
2
.
8
%
ad
eq
u
ac
y
o
f
th
e
o
b
s
er
v
ab
le
v
ar
i
ab
les
lo
ad
in
g
co
r
r
ec
tly
o
n
to
t
h
e
laten
t
v
ar
iab
les.
B
ar
tlett
'
s
tes
t
o
f
s
p
h
e
r
icity
y
ie
ld
ed
a
s
ig
n
if
ican
t
p
-
v
al
u
e
o
f
0
.
0
0
0
,
in
d
icatin
g
a
s
u
b
s
tan
tial
co
r
r
elatio
n
s
u
itab
le
f
o
r
co
m
p
o
n
en
t
an
al
y
s
is
.
T
h
e
f
ir
s
t
th
r
ee
co
m
p
o
n
en
ts
,
ea
ch
ex
p
lain
in
g
m
o
r
e
th
an
5
%
o
f
th
e
v
ar
ian
ce
,
co
llectiv
ely
ac
co
u
n
ted
f
o
r
6
4
.
6
7
0
%
o
f
th
e
to
tal
v
ar
ian
ce
,
h
ig
h
lig
h
tin
g
th
eir
s
ig
n
if
ican
ce
in
ex
p
lain
in
g
d
ata
v
ar
iab
ilit
y
.
T
o
m
ak
e
th
e
C
FA
m
o
d
el
b
etter
,
co
m
p
o
n
en
ts
with
f
ac
to
r
lo
ad
in
g
s
less
th
an
0
.
5
0
we
r
e
u
s
u
ally
elim
in
ated
.
Fo
llo
win
g
th
e
C
FA p
r
o
ce
d
u
r
e,
th
e
o
b
s
er
v
e
d
v
ar
iab
les m
ain
tain
all
f
iv
e
item
s
f
o
r
ea
ch
o
f
th
e
laten
t
v
ar
iab
les
u
n
d
e
r
s
tu
d
y
ex
ce
p
t
T
K
wh
ich
was
r
ed
u
ce
d
b
y
o
n
e
,
as
s
h
o
wn
in
Fig
u
r
e
1
.
Ach
iev
in
g
in
ter
n
al
co
n
s
is
ten
cy
th
r
o
u
g
h
C
r
o
n
b
ac
h
’
s
alp
h
a
(
C
A)
en
tailed
o
b
tai
n
in
g
a
s
co
r
e
o
f
at
least
0
.
7
[
4
1
]
.
As
in
d
icate
d
i
n
T
ab
le
1
,
T
K
e
x
h
ib
ited
a
C
A
o
f
0
.
8
1
4
,
PC
K
s
h
o
wed
a
C
A
o
f
0
.
8
4
2
,
an
d
PTU
d
em
o
n
s
tr
ated
a
C
A
o
f
0
.
9
0
3
.
T
h
e
m
o
d
el
f
it
in
d
ices
in
d
icate
d
a
s
ig
n
if
ican
ce
lev
el
in
all
th
e
m
ajo
r
f
itn
ess
v
alu
es.
T
h
e
g
o
o
d
n
ess
o
f
f
it
in
d
ex
(
GFI
=
0
.
9
7
6
)
,
n
o
r
m
ed
f
it
in
d
e
x
(
NFI
=
0
.
9
7
3
)
,
in
cr
em
en
t
f
it
in
d
ex
(
I
FI=
0
.
9
8
4
)
,
an
d
T
u
k
e
y
-
L
ewis
in
d
ex
(
T
L
I
=
0
.
9
7
8
)
,
wer
e
all
g
r
ea
ter
t
h
an
0
.
9
,
in
d
icatin
g
th
at
th
e
d
ata
o
f
t
h
e
th
r
ee
-
f
ac
to
r
m
o
d
el
is
v
alid
an
d
r
em
ar
k
ab
l
y
co
m
p
atib
le
,
as
ci
ted
in
Op
p
o
n
g
-
Gy
eb
i
an
d
B
o
aten
g
[
4
2
]
.
T
h
e
a
d
ju
s
ted
g
o
o
d
n
ess
o
f
f
it
in
d
ex
(
AGFI
=
0
.
9
6
3
)
was
g
r
ea
te
r
th
a
n
th
e
e
x
p
ec
ted
0
.
8
0
as d
ec
lar
e
d
b
y
Hair
et
a
l
.
[
4
0
]
.
Per
th
e
r
ec
o
m
m
en
d
atio
n
s
o
f
Ma
r
s
h
et
a
l
.
[
4
3
]
an
d
Me
y
er
s
et
a
l
.
[
4
4
]
,
as
d
is
cu
s
s
ed
b
y
Af
th
an
o
r
h
a
n
et
a
l
.
[4
5
]
,
wh
ich
e
x
p
ec
t
all
th
e
laten
t
v
ar
iab
les
to
h
av
e
a
d
ev
iatio
n
o
f
th
e
h
y
p
o
th
esized
m
o
d
el
f
r
o
m
a
b
etter
m
atch
,
th
e
r
o
o
t
m
e
an
s
s
q
u
ar
e
r
esid
u
al
(
R
MSE
A)
also
s
h
o
wed
a
g
o
o
d
m
atch
o
f
0
.
0
4
0
less
th
an
0
.
0
8
,
co
n
f
ir
m
in
g
th
e
leg
itima
cy
a
n
d
ac
ce
p
tab
ilit
y
o
f
th
e
ess
en
tial f
ac
to
r
s
(
T
ab
le
1
)
.
B
e
f
o
r
e
es
t
i
m
at
i
n
g
t
h
e
p
r
i
m
ar
y
p
a
t
h
,
a
s
s
e
s
s
i
n
g
t
h
e
v
al
i
d
i
t
y
a
n
d
r
e
l
i
a
b
i
l
it
y
o
f
t
h
e
d
a
t
a
s
et
a
n
d
m
e
a
s
u
r
e
m
e
n
t
i
t
e
m
s
wa
s
e
s
s
e
n
ti
a
l
,
as
c
u
s
t
o
m
a
r
y
i
n
e
m
p
i
r
i
ca
l
s
t
u
d
i
es
.
C
FA
w
as
c
o
n
d
u
c
t
e
d
u
s
i
n
g
AM
O
S
(
v
.
2
3
)
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,
p
r
e
s
e
n
t
e
d
i
n
T
a
b
l
e
1
a
n
d
F
i
g
u
r
e
1
,
w
e
r
e
e
v
a
l
u
a
t
e
d
u
s
i
n
g
co
m
p
o
s
i
t
e
r
el
i
a
b
il
i
t
y
(
C
R
)
a
n
d
a
v
e
r
a
g
e
v
a
r
i
a
n
c
e
e
x
t
r
a
c
t
e
d
(
A
V
E
)
t
o
e
n
s
u
r
e
c
o
n
v
e
r
g
e
n
t
v
a
l
i
d
i
t
y
.
A
c
c
o
r
d
i
n
g
t
o
A
f
t
h
a
n
o
r
h
a
n
e
t
a
l
.
[4
5
]
,
a
m
in
im
u
m
AVE
s
co
r
e
o
f
0
.
5
an
d
a
m
in
im
u
m
C
R
s
co
r
e
o
f
0
.
7
a
r
e
n
ec
ess
ar
y
f
o
r
co
n
v
er
g
en
t
v
alid
ity
.
T
h
e
lo
west AV
E
v
alu
e,
o
b
s
er
v
ed
f
o
r
PC
K
,
was 0
.
5
2
8
,
wh
ile
t
h
e
lo
west C
R
v
alu
e,
n
o
ted
f
o
r
TK
,
was 0
.
8
3
5
.
Fig
u
r
e
1
.
C
FA
T
ab
le
1
.
C
o
n
v
er
g
en
t
v
alid
ity
a
n
d
CR
I
t
e
ms
FL
CR
AVE
M
S
V
I
t
e
ms
FL
CR
AVE
M
S
V
TK
0
.
8
3
5
0
.
5
6
1
0
.
0
1
5
0
.
8
1
4
P
C
K
0
.
8
4
8
0
.
5
2
8
0
.
0
1
5
0
.
8
4
2
TK
2
0
.
8
0
4
P
C
K
1
0
.
7
2
8
TK
3
0
.
9
6
3
P
C
K
2
0
.
7
5
7
TK
4
0
.
8
2
3
P
C
K
3
0
.
7
1
8
TK
5
0
.
6
6
4
P
C
K
4
0
.
7
2
8
P
C
K
5
0
.
7
0
0
P
TU
0
.
9
0
1
0
.
6
4
7
0
.
0
0
3
0
.
9
0
3
M
o
d
e
l
f
i
t
i
n
d
i
c
e
s
P
TU
1
0
.
6
8
8
C
M
I
N
=
4
6
3
.
5
1
9
R
M
R
=
0
.
0
6
3
P
TU
2
0
.
8
0
9
D
F
=
1
5
7
.
0
0
0
A
G
F
I
=
0
.
9
6
3
P
TU
3
0
.
7
8
1
C
M
I
N
/
D
F
=
2
.
9
5
2
N
F
I
=
0
.
9
7
3
P
TU
4
0
.
8
8
9
I
F
I
=
0
.
9
8
4
P
TU
5
0
.
8
4
1
TLI
=
0
.
9
7
8
R
M
S
EA
=
0
.
0
4
0
FL
=
f
a
c
t
o
r
l
o
a
d
i
n
g
s,
α
=
C
r
o
n
b
a
c
h
’
s
a
l
p
h
a
,
SE
=
s
e
l
f
-
e
f
f
i
c
a
c
y
,
PU
=
p
e
r
c
e
i
v
e
d
u
sef
u
l
n
e
ss
,
TU
I
=
t
e
c
h
n
o
l
o
g
y
u
sa
g
e
i
n
t
e
n
t
i
o
n
,
M
I
D
=
S
TEM
-
mat
h
e
m
a
t
i
c
s
i
n
st
r
u
c
t
i
o
n
a
l
d
e
l
i
v
e
r
y
.
4.
RE
SU
L
T
S
T
o
ex
am
in
e
ea
ch
o
f
th
e
h
y
p
o
th
eses
,
th
e
SEM
was
u
s
ed
f
o
r
th
e
an
aly
s
is
u
s
in
g
SP
SS
(
ad
d
-
in
PR
O
C
E
SS
_
v
4
.
2
_
b
eta)
.
Ho
we
v
er
,
AM
OS (
v
2
4
)
s
o
f
twar
e
wa
s
u
s
ed
to
d
r
aw
an
d
ev
alu
ate
v
a
r
io
u
s
h
y
p
o
th
esized
r
o
u
tes,
with
a
d
iag
r
am
m
atic
r
ep
r
esen
tatio
n
o
f
th
e
s
tr
u
ctu
r
al
m
o
d
el
,
as
p
r
esen
ted
in
Fig
u
r
e
2
.
T
h
e
s
tu
d
y
th
en
ap
p
lied
th
e
b
ias
-
co
r
r
ec
ted
(
B
C
)
p
er
ce
n
tile
b
o
o
ts
tr
ap
p
i
n
g
a
p
p
r
o
ac
h
to
5
,
0
0
0
b
o
o
ts
tr
ap
s
am
p
les
with
a
9
5
%
co
n
f
id
en
ce
le
v
el,
r
esu
ltin
g
in
a
s
tr
u
ctu
r
al
m
o
d
el
th
at
s
atis
f
ied
all
f
it
in
d
icato
r
s
s
u
g
g
ested
b
y
Hair
et
a
l
.
[
4
0
]
,
an
d
Go
r
etzk
o
et
a
l
.
[
4
1
]
,
ju
s
t l
ik
e
th
e
C
FA d
id
.
F
o
r
t
h
e
h
y
p
o
t
h
e
s
i
z
e
d
p
a
t
h
s
,
i
t
w
a
s
i
d
e
n
t
i
f
i
e
d
t
h
at
t
e
a
c
h
e
r
s
’
TK
h
a
d
a
s
t
at
i
s
t
i
c
al
l
y
s
i
g
n
i
f
i
c
a
n
t
e
f
f
e
c
t
o
n
t
h
e
i
r
P
C
K
(
a
1
=
0
.
1
4
5
;
p
<
0
.
0
5
)
.
H
y
p
o
t
h
e
s
i
s
H
01
:
“
t
h
e
r
e
is
n
o
s
i
g
n
i
f
i
c
a
n
t
e
f
f
e
c
t
o
f
t
e
a
c
h
e
r
s
’
T
K
o
n
t
h
e
i
r
P
C
K
”
,
w
a
s
t
h
e
r
e
f
o
r
e
r
e
j
e
c
te
d
b
y
t
h
i
s
s
t
u
d
y
.
T
e
a
c
h
e
r
s
’
PC
K
,
o
n
t
h
e
o
t
h
e
r
h
a
n
d
,
h
a
d
a
s
i
g
n
i
f
i
c
a
n
t
e
f
f
e
c
t
o
n
t
h
e
i
r
P
T
U
(a
2
=
-
0
.
1
0
4
;
p
=
0
.
0
2
3
)
.
S
u
g
g
e
s
t
in
g
t
h
a
t
,
a
s
t
e
a
c
h
e
r
s
u
s
e
d
P
C
K
,
t
h
e
i
r
P
T
U
is
l
i
k
el
y
t
o
d
e
c
l
i
n
e
b
y
a
b
o
u
t
1
0
.
4
%
,
a
n
d
v
i
c
e
v
e
r
s
a
.
H
y
p
o
t
h
es
is
H
02
:
“
t
h
e
r
e
i
s
n
o
s
i
g
n
i
f
i
c
a
n
t
e
f
f
e
ct
o
f
t
e
a
c
h
e
r
s
’
PC
K
o
n
t
h
e
i
r
PT
U
”
,
w
as
t
h
e
r
e
f
o
r
e
r
e
j
e
c
t
e
d
b
y
t
h
is
s
t
u
d
y
.
T
e
a
c
h
er
s
'
T
K
h
a
d
a
s
t
a
t
is
ti
c
a
ll
y
s
i
g
n
if
i
c
a
n
t
e
f
f
e
c
t
o
n
t
h
e
i
r
P
T
U
(
b
3
=
-
0
.
1
1
5
;
p
=
0
.
0
1
2
)
.
H
y
p
o
t
h
e
s
is
H
03
:
“
t
h
e
r
e
is
n
o
s
i
g
n
i
f
i
c
a
n
t
e
f
f
e
c
t
o
f
t
e
ac
h
e
r
s
’
TK
o
n
t
h
e
i
r
P
T
U
”
,
f
a
il
e
d
to
s
u
p
p
o
r
t
t
h
e
n
u
l
l
h
y
p
o
t
h
e
s
i
s
,
as
s
h
o
w
n
i
n
T
a
b
l
e
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
14
,
No
.
4
,
Au
g
u
s
t
2025
:
2
9
9
0
-
2
9
9
8
2994
Fig
u
r
e
2
.
Stru
ctu
r
al
p
ath
T
ab
le
2
.
Su
m
m
a
r
y
o
f
th
e
h
y
p
o
th
etica
l a
n
aly
s
is
r
esu
lts
H
y
p
o
t
h
e
s
e
s
A
n
t
e
c
e
d
e
n
t
P
a
t
h
C
o
e
f
f
.
SE
C.R
P
R
e
mar
k
Y
(
P
C
K
)
H
01
TK
(
x
)
a
1
0
.
1
4
5
0
.
0
3
2
4
.
5
3
0
.
0
0
0
S
i
g
n
i
f
i
c
a
n
t
Y
(
P
TU
)
H
02
P
C
K
(
x
)
a
2
-
0
.
1
0
4
0
.
0
4
6
-
2
.
2
6
0
.
0
2
3
S
i
g
n
i
f
i
c
a
n
t
H
03
TK
(
x
)
b
3
-
0
.
1
1
5
0
.
0
4
6
-
2
.
5
0
0
.
0
1
2
S
i
g
n
i
f
i
c
a
n
t
N
o
t
e
.
D
e
p
e
n
d
e
n
t
v
a
r
i
a
b
l
e
(
Y
)
,
p
r
e
d
i
c
t
o
r
(
X
)
,
C
.
R
:
c
r
i
t
i
c
a
l
r
a
t
i
o
n
;
S
E:
st
a
n
d
a
r
d
e
r
r
o
r
.
Fin
ally
,
th
e
m
ed
iatin
g
e
f
f
ec
t
o
f
teac
h
er
s
’
PC
K
in
th
e
r
elatio
n
s
h
ip
b
etwe
en
th
ei
r
T
K
an
d
PTU
an
d
th
eir
PE
in
ter
ac
tin
g
b
etwe
en
T
K
an
d
PTU
was
ascer
tain
ed
.
Firstl
y
,
th
e
ef
f
ec
t
o
f
teac
h
er
s
’
T
K
o
n
th
eir
PTU
was
ascer
tain
ed
an
d
f
o
u
n
d
to
b
e
s
ig
n
if
ican
tly
p
o
s
itiv
e
(
a
1
=0
.
1
4
5
; p
<0
.
0
5
)
,
as
s
ee
n
i
n
T
ab
l
e
3
T
h
at
is
,
teac
h
e
r
s
k
n
o
wled
g
ea
b
le
in
tech
n
o
lo
g
i
ca
l
s
k
ills
ar
e
lik
ely
to
h
a
v
e
a
g
r
ea
ter
p
o
s
itiv
e
k
n
o
wled
g
e
o
f
m
ath
em
atics
p
ed
ag
o
g
y
a
n
d
co
n
ten
t u
s
ed
in
in
s
tr
u
ctio
n
al
d
eliv
er
y
,
b
y
a
m
a
g
n
itu
d
e
o
f
1
4
.
5
%,
an
d
v
ice
v
e
r
s
a.
T
h
e
ef
f
ec
t
o
f
teac
h
er
s
’
T
K
o
n
th
eir
PTU
h
as
al
s
o
b
ee
n
id
en
tifie
d
as
s
ig
n
if
ican
tly
p
o
s
itiv
e.
Ho
wev
er
,
PE
(
c
1
=
-
0
.
0
0
9
;
p
>0
.
0
5
)
an
d
th
e
in
ter
ac
tio
n
o
f
PE
an
d
T
K
(
d
1
=0
.
0
2
8
;
p
>0
.
0
5
)
,
r
esp
ec
tiv
ely
,
o
n
PTU
f
ailed
to
b
e
s
ig
n
if
ican
t.
T
h
is
in
d
icate
s
t
h
at
th
e
m
o
d
er
atin
g
r
o
le
o
f
PE
h
as
litt
le
o
r
n
o
s
ig
n
if
ican
t
im
p
ac
t
o
n
th
e
m
o
d
el
.
T
h
e
co
ef
f
icien
t o
f
th
e
in
d
ir
ec
t e
f
f
ec
t w
as
-
0
.
0
1
3
,
wh
ich
was statis
t
ically
in
s
ig
n
if
ican
t (
b
ec
au
s
e
ze
r
o
(
0
)
ca
n
b
e
f
o
u
n
d
b
etwe
en
th
e
lo
wer
a
n
d
u
p
p
er
lim
its
)
,
w
h
ile
th
e
d
ir
e
ct
ef
f
ec
t
was
s
tatis
tically
s
ig
n
if
ican
t.
Hy
p
o
th
esis
H
04
:
“th
er
e
is
n
o
s
ig
n
if
ican
t
m
ed
iatio
n
r
o
le
o
f
PC
K
b
etwe
en
teac
h
er
s
’
T
K
a
n
d
PTU”
s
h
o
wed
n
o
m
ed
iatio
n
r
o
le
b
u
t r
ath
er
r
e
v
ea
led
a
d
ir
e
ct
r
elatio
n
s
h
ip
am
o
n
g
th
e
co
n
s
tr
u
cts.
B
ased
o
n
th
e
s
tatis
ticall
y
in
s
ig
n
if
ican
t
r
o
le
o
f
th
e
m
o
d
er
ato
r
,
h
y
p
o
th
esis
H
05
:
“th
er
e
is
n
o
s
ig
n
if
ican
t
m
o
d
er
atio
n
r
o
le
o
f
PE
b
etwe
en
teac
h
er
s
’
T
K
a
n
d
PTU”
f
ailed
to
b
e
r
ejec
ted
.
T
ab
le
3
.
Me
d
iatin
g
r
o
le
o
f
PC
K
b
etwe
en
T
K
an
d
PTU
A
n
t
e
c
e
d
e
n
t
M
e
d
i
a
t
o
r
(
P
C
K
)
D
e
p
e
n
d
e
n
t
(
P
TU
)
P
a
t
h
C
o
e
f
f
.
SE
CR
P
P
a
t
h
C
o
e
f
f
SE
CR
P
H
04
a
n
d
H
05
M
(
S
E)
Y
(
P
TU
)
C
o
n
st
a
n
t
β
P
CK
2
.
6
1
9
0
.
0
2
9
9
0
.
6
2
0
.
0
0
0
β
P
T
U
3
.
0
6
5
0
.
1
2
8
2
3
.
9
5
0
.
0
0
0
TK
(
x
)
a
1
0
.
1
4
5
0
.
0
3
2
4
.
5
3
0
.
0
0
0
b
3
-
0
.
1
0
2
0
.
0
4
6
-
2
.
2
2
0
.
0
2
7
P
C
K
(
M
)
a
2
-
0
.
0
8
9
0
.
0
4
6
-
1
.
9
3
0
.
0
5
5
PE
c
1
-
0
.
0
0
9
0
.
0
4
1
-
0
.
2
2
0
.
8
3
7
TK
(
P
E)
d
1
0
.
0
2
8
0
.
0
4
6
0
.
6
1
0
.
5
4
6
A
n
t
e
c
e
d
e
n
t
P
a
t
h
Ef
f
e
c
t
SE
P
LL
UL
R
e
mar
k
I
n
d
i
r
e
c
t
1
.
1
-
0
.
0
1
3
0
.
0
0
7
-
0
.
0
2
9
0
.
0
0
0
D
i
r
e
c
t
r
e
l
a
t
i
o
n
s
h
i
p
D
i
r
e
c
t
1
-
0
.
1
0
2
0
.
0
4
6
0
.
0
2
7
-
0
.
1
9
3
-
0
.
0
1
1
N
o
t
e
:
D
e
p
e
n
d
e
n
t
v
a
r
i
a
b
l
e
(
P
TU
)
,
P
r
e
d
i
c
t
o
r
(
T
K
)
,
M
e
d
i
a
t
o
r
(
P
C
K
)
,
M
o
d
e
r
a
t
o
r
(
P
E)
,
C
.
R
=
C
r
i
t
i
c
a
l
r
a
t
i
o
n
;
LL
=
Lo
w
e
r
l
i
m
i
t
;
U
L
=
U
p
p
e
r
l
i
m
i
t
5.
DIS
CU
SS
I
O
N
T
h
e
s
tu
d
y
r
ev
ea
led
a
s
tatis
tically
s
ig
n
if
ican
t e
f
f
ec
t o
f
teac
h
e
r
s
’
T
K
o
n
th
eir
PC
K.
I
t in
d
icate
s
th
at
th
e
r
ec
en
t
co
llab
o
r
ativ
e
ef
f
o
r
t
b
y
th
e
Gh
a
n
a’
s
ed
u
ca
tio
n
s
er
v
ice
an
d
o
t
h
er
s
tak
eh
o
ld
er
s
in
p
r
o
v
id
in
g
tech
n
o
lo
g
ical
to
o
ls
an
d
o
r
g
a
n
ize
p
r
o
f
ess
io
n
al
wo
r
k
s
h
o
p
s
ar
e
em
p
o
wer
in
g
m
ath
em
atics
teac
h
er
s
to
in
clu
d
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
P
ed
a
g
o
g
ica
l c
o
n
ten
t
kn
o
w
led
g
e:
b
r
id
g
in
g
ma
th
tea
ch
ers
'
tech
n
o
lo
g
y
…
(
E
mma
n
u
el
Op
p
o
n
g
-
Gye
b
i
)
2995
tech
n
o
lo
g
y
in
to
th
eir
in
s
tr
u
ct
io
n
al
d
eliv
er
y
[
1
0
]
,
[
1
2
]
.
T
h
i
s
is
in
s
u
p
p
o
r
t
o
f
Sp
an
g
en
b
e
r
g
an
d
Fre
itas
[
3
4
]
f
in
d
in
g
s
th
at
s
ee
ed
u
ca
tio
n
al
ad
v
an
ce
m
e
n
t
an
d
s
o
ciety
h
av
i
n
g
a
p
o
s
itiv
e
im
p
ac
t
o
n
th
e
s
elec
tio
n
an
d
u
s
e
o
f
tech
n
o
lo
g
y
i
n
r
elate
d
PC
K
to
im
p
ac
t
q
u
ality
in
s
tr
u
ctio
n
.
I
n
s
u
p
p
o
r
tin
g
th
e
f
in
d
i
n
g
s
b
y
Y
an
u
ar
to
et
a
l
.
[
3
2
]
,
tak
in
g
a
lo
o
k
at
teac
h
er
s
’
k
n
o
wled
g
e
in
tech
n
o
lo
g
y
,
it
is
p
o
s
s
ib
le
to
f
o
r
t
h
em
t
o
p
o
s
s
ess
a
s
tr
o
n
g
u
n
d
er
s
tan
d
i
n
g
o
f
h
o
w
to
ef
f
ec
tiv
ely
in
teg
r
ate
tech
n
o
l
o
g
y
in
t
o
th
eir
class
r
o
o
m
s
to
en
h
an
ce
th
eir
PC
K
d
eliv
er
y
.
C
o
n
tr
ar
y
to
p
r
ev
io
u
s
b
elief
s
as
in
d
icate
d
b
y
C
h
in
g
a
n
d
R
o
b
er
t
[
3
5
]
th
at
ir
r
esp
ec
tiv
e
o
f
h
o
w
tech
n
o
lo
g
y
ad
v
an
ce
s
,
PC
K
will
b
e
d
o
m
in
an
t
o
v
er
T
K.
T
h
u
s
,
th
e
r
esu
lt
is
co
n
s
is
ten
t
with
s
ev
er
al
p
r
io
r
s
tu
d
ies
[
1
7
]
,
[
1
9
]
th
at
in
d
icate
d
a
s
ig
n
if
ican
t im
p
ac
t o
f
teac
h
e
r
s
’
k
n
o
wled
g
e
a
n
d
ch
o
ice
o
f
tech
n
o
lo
g
ical
s
k
ills
o
n
th
eir
PC
K.
I
t is in
ter
esti
n
g
to
n
o
te
f
r
o
m
th
e
f
in
d
in
g
s
th
at
m
ath
em
atics tea
ch
er
s
’
PC
K
h
as a
s
ig
n
if
ican
t
im
p
ac
t o
n
h
o
w
th
ey
p
er
ce
iv
ed
th
e
u
s
ef
u
ln
ess
o
f
tech
n
o
l
o
g
y
,
s
h
ap
in
g
th
eir
attitu
d
es
an
d
b
elief
s
ab
o
u
t
th
e
v
alu
e
o
f
tech
n
o
lo
g
y
in
t
h
e
class
r
o
o
m
.
I
n
s
u
p
p
o
r
t
o
f
th
e
f
in
d
in
g
,
L
e
e
et
a
l
.
[
2
0
]
s
ee
a
well
-
p
r
ep
a
r
ed
teac
h
er
ab
r
ea
s
t
with
PC
K
alwa
y
s
h
av
e
th
e
d
esire
to
in
teg
r
ate
tech
n
o
lo
g
y
in
to
th
eir
in
s
tr
u
ctio
n
al
d
eliv
er
y
.
As
in
d
icate
d
b
y
p
r
ev
io
u
s
s
tu
d
ies
[
2
8
]
,
[
2
9
]
,
d
ev
elo
p
in
g
th
e
PC
K
o
f
in
-
s
er
v
ice
m
ath
em
atics
teac
h
er
s
em
p
o
wer
s
th
em
t
o
u
s
e
an
y
f
o
r
m
o
f
tech
n
o
lo
g
y
to
en
h
an
ce
t
h
eir
class
r
o
o
m
in
s
t
r
u
ctio
n
al
d
eliv
e
r
y
.
Su
p
p
o
r
tin
g
th
e
s
tu
d
y
r
esu
lt,
teac
h
er
s
’
d
ee
p
u
n
d
er
s
tan
d
in
g
o
f
PC
K
en
ab
les
th
em
to
id
en
tify
h
o
w
tech
n
o
lo
g
y
ca
n
e
n
h
a
n
ce
th
eir
teac
h
in
g
p
r
ac
tices
an
d
s
u
p
p
o
r
t
s
tu
d
en
t
lear
n
in
g
o
u
tco
m
es
[
3
0
]
,
[
3
5
]
–
[
3
7
]
.
L
ewis
[
3
8
]
also
s
h
ar
e
s
th
e
v
iew
o
f
th
is
s
tu
d
y
’
s
f
in
d
in
g
wh
er
e
T
K
s
h
o
ws
s
ig
n
if
ican
t
ef
f
ec
t
o
n
PTU
t
h
at
teac
h
er
s
wh
o
f
ee
l
co
n
f
id
e
n
t
in
t
h
eir
a
b
ilit
y
to
u
s
e
tech
n
o
lo
g
y
a
r
e
m
o
r
e
lik
ely
to
p
er
ce
iv
e
it
as
a
v
alu
ab
le
to
o
l
f
o
r
en
h
an
cin
g
teac
h
in
g
an
d
lear
n
in
g
ex
p
er
ien
ce
s
,
r
ath
e
r
th
an
a
s
o
u
r
ce
o
f
f
r
u
s
tr
atio
n
o
r
in
co
n
v
en
ie
n
ce
.
PE
d
o
es
n
o
t
m
o
d
er
ate
th
e
r
elatio
n
s
h
ip
b
etwe
en
teac
h
er
s
’
T
K
an
d
th
eir
PTU.
T
h
e
f
in
d
in
g
g
o
es
co
n
tr
ar
y
to
o
th
er
s
tu
d
ies
[
2
0
]
,
[
2
1
]
th
at
ex
p
r
ess
ed
h
o
w
teac
h
er
s
ex
p
er
ien
ce
ig
n
ite
th
eir
ze
s
t
to
u
s
e
tech
n
o
lo
g
y
in
th
eir
class
r
o
o
m
s
.
I
n
s
tead
,
in
d
iv
id
u
al
p
e
r
ce
p
tio
n
s
an
d
atti
tu
d
es
to
war
d
tech
n
o
lo
g
y
in
te
g
r
atio
n
p
lay
a
m
o
r
e
s
ig
n
if
ican
t
r
o
le.
W
h
ile
ex
p
e
r
ien
ce
d
teac
h
er
s
m
a
y
h
av
e
m
o
r
e
teac
h
in
g
ex
p
e
r
ien
ce
,
t
h
eir
p
er
ce
p
tio
n
s
o
f
tech
n
o
lo
g
y
u
s
ef
u
ln
ess
m
ay
s
till
v
ar
y
d
ep
en
d
in
g
o
n
f
ac
t
o
r
s
s
u
ch
as
e
x
p
o
s
u
r
e
to
tech
n
o
lo
g
y
in
teg
r
atio
n
in
itiativ
es
an
d
p
er
s
o
n
al
attitu
d
es
to
war
d
tech
n
o
lo
g
y
ad
o
p
tio
n
.
T
h
e
s
tu
d
y
f
o
u
n
d
th
at
PC
K
d
o
es
n
o
t
s
er
v
e
as
a
cr
u
cial
m
ed
iato
r
b
etwe
en
tea
ch
er
s
’
T
K
an
d
th
eir
PTU.
C
o
n
tr
ar
y
to
Sp
an
g
e
n
b
er
g
a
n
d
Fre
itas
[
3
4
]
,
wh
o
id
en
tifie
d
ef
f
ec
tiv
e
u
s
e
o
f
tec
h
n
o
lo
g
y
i
n
teac
h
er
s
’
PC
K
an
d
p
e
d
ag
o
g
ical
b
elief
s
ab
o
u
t
t
ec
h
n
o
lo
g
y
as
s
o
m
e
o
b
s
tacle
s
in
m
ath
em
atics c
lass
r
o
o
m
s
.
B
ased
o
n
th
e
f
in
d
in
g
s
o
f
th
e
s
tu
d
y
,
it
is
an
ticip
ated
th
at
Gh
an
aian
m
ath
em
atics
teac
h
er
s
’
T
K
is
p
er
ce
iv
ed
to
en
ab
le
th
em
to
le
v
er
ag
e
d
ig
ital
to
o
ls
an
d
r
eso
u
r
ce
s
ef
f
ec
tiv
ely
to
en
h
an
ce
th
eir
PC
K,
u
ltima
te
ly
lead
in
g
t
o
m
o
r
e
en
g
a
g
in
g
,
ef
f
ec
tiv
e,
an
d
im
p
ac
tf
u
l
m
ath
em
atics
in
s
tr
u
ctio
n
d
eliv
e
r
y
.
I
n
t
h
e
s
am
e
i
n
s
tan
ce
,
m
ath
em
atics
teac
h
er
s
’
PC
K
d
o
es
n
o
t
p
r
o
f
o
u
n
d
ly
in
f
lu
e
n
ce
s
th
eir
TK
an
d
s
u
b
s
eq
u
en
tly
i
m
p
ac
ts
th
eir
PTU
to
u
s
e
it
in
th
eir
class
r
o
o
m
s
,
a
s
r
ev
ea
led
b
y
s
ev
er
al
s
tu
d
ies
[
3
1
]
,
[
3
4
]
,
[
3
5
]
.
M
o
r
eo
v
e
r
,
as
em
p
h
asized
b
y
L
ee
et
a
l
.
[
2
0
]
,
PC
K
co
n
tin
u
es
to
b
e
a
g
u
id
an
ce
f
o
r
teac
h
e
r
s
in
ch
o
o
s
in
g
r
elev
a
n
t
tech
n
o
l
o
g
y
r
eso
u
r
ce
s
an
d
to
o
ls
th
at
co
m
p
lem
en
t
lear
n
er
s
’
n
ee
d
s
an
d
in
s
tr
u
ctio
n
al
o
b
j
ec
tiv
es.
I
t
wo
u
ld
b
e
p
o
in
tles
s
to
u
s
e
tech
n
o
lo
g
y
with
o
u
t
p
ed
a
g
o
g
y
an
d
co
n
te
n
t
ex
p
er
tis
e.
Hen
ce
,
tech
n
o
l
o
g
y
ca
n
n
o
t
b
e
in
is
o
latio
n
with
o
u
t
in
teg
r
atin
g
th
r
o
u
g
h
PC
K
to
en
h
an
ce
in
s
tr
u
ctio
n
al
d
eliv
er
y
q
u
ality
.
An
a
ly
zin
g
th
ese
co
n
s
id
er
atio
n
s
le
ad
s
th
e
r
esear
ch
er
s
to
th
e
co
n
clu
s
io
n
th
at
s
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tin
g
TK
in
d
ep
en
d
en
tly
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with
o
u
t
en
lis
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g
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lay
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m
ed
iatin
g
r
o
le
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f
u
tu
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e
tech
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o
lo
g
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atio
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u
l
d
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ativ
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af
f
ec
t
th
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q
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ality
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e
f
f
ec
tiv
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2
1
s
t
ce
n
tu
r
y
i
n
s
tr
u
ctio
n
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eliv
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in
Gh
an
aian
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en
io
r
h
ig
h
s
ch
o
o
ls
.
As
in
d
icate
d
b
y
Ye
h
et
a
l
.
[
3
3
]
,
tech
n
o
lo
g
y
m
ed
iatin
g
th
r
o
u
g
h
PC
K
em
p
o
wer
s
teac
h
er
s
to
d
esig
n
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d
im
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t
tech
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e
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h
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ce
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lear
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g
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x
p
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ce
s
.
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h
e
way
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o
r
war
d
to
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g
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atin
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tech
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o
lo
g
y
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r
o
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g
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m
ath
em
at
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teac
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er
s
’
PC
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ld
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r
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m
ea
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in
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l
lear
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o
p
p
o
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tu
n
ity
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at
m
ig
h
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en
h
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ce
th
eir
PTU
as st
r
ess
ed
b
y
B
ay
r
am
‐
J
ac
o
b
s
et
a
l
.
[
2
6
]
.
T
h
e
m
ath
em
atics
teac
h
er
s
’
r
elu
ctan
ce
to
r
esp
o
n
d
to
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u
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air
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o
cc
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p
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ar
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r
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W
est
Af
r
ica
Seco
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C
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E
x
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ath
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atics,
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air
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6.
CO
NCLU
SI
O
N
T
h
e
s
tu
d
y
in
v
esti
g
ated
h
o
w
P
C
K
m
ed
iates
th
e
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ce
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tan
ce
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d
p
e
r
ce
iv
ed
u
s
e
o
f
tech
n
o
lo
g
y
am
o
n
g
9
7
9
m
ath
em
atics
teac
h
er
s
in
s
en
io
r
h
ig
h
s
ch
o
o
ls
in
th
e
Ash
an
ti
R
eg
io
n
o
f
Gh
an
a.
A
f
ter
u
s
in
g
SEM
to
esti
m
ate
th
e
m
o
d
el,
th
e
r
esu
lts
s
h
o
w
n
o
m
ed
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g
r
o
le
o
f
PC
K
b
u
t
a
d
ir
ec
t
r
elatio
n
s
h
ip
b
etwe
en
TK
,
PC
K
,
an
d
p
er
ce
iv
ed
u
s
ef
u
l
n
ess
in
m
ath
em
atics
ed
u
ca
tio
n
.
PE
d
id
n
o
t
m
o
d
er
ate
t
h
is
r
elatio
n
s
h
ip
.
Ho
wev
er
,
TK
s
ig
n
if
ican
tly
in
f
l
u
en
ce
s
PC
K
,
wh
ich
in
t
u
r
n
im
p
ac
ts
th
e
q
u
ality
o
f
i
n
s
tr
u
ctio
n
p
r
o
v
id
ed
.
T
h
e
s
tu
d
y
also
r
ev
ea
ls
th
at
teac
h
er
s
’
TK
s
ig
n
if
ican
tly
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f
lu
en
ce
s
th
eir
p
er
ce
iv
ed
u
s
ef
u
ln
ess
,
in
f
lu
en
cin
g
th
eir
attitu
d
es
an
d
b
elief
s
ab
o
u
t
th
e
v
alu
e
an
d
ef
f
ec
tiv
en
ess
o
f
tech
n
o
l
o
g
y
i
n
th
e
class
r
o
o
m
.
T
h
e
f
in
d
in
g
s
also
h
ig
h
lig
h
ted
t
h
e
im
p
o
r
tan
ce
o
f
PC
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in
p
r
o
m
o
ti
n
g
ef
f
ec
tiv
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tech
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o
l
o
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s
e
in
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u
ca
tio
n
.
T
h
e
v
alu
e
o
f
t
h
is
s
tu
d
y
em
b
e
d
s
in
h
o
w
Gh
an
aian
m
ath
e
m
atics
teac
h
er
s
’
PC
K
h
as
r
ev
ea
led
n
o
t
to
p
lay
a
cr
u
cial
r
o
le
in
lin
k
i
n
g
th
eir
TK
with
PTU
.
T
o
p
r
e
v
e
n
t
th
is
co
n
s
tr
ain
t,
e
d
u
ca
tio
n
s
tak
eh
o
ld
er
s
s
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[
E
OG
]
.
RE
F
E
R
E
NC
E
S
[
1
]
E.
B
a
h
c
i
v
a
n
,
M
.
D
.
G
u
r
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,
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.
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v
u
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a
l
p
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a
n
d
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.
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k
a
y
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g
l
u
,
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g
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t
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o
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p
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c
i
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s:
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st
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t
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2
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[
2
]
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.
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N
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,
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n
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.
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:
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n
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m
,
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o
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1
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2
4
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Evaluation Warning : The document was created with Spire.PDF for Python.