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20
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Fos
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stu
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ts
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o
m
ly
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e
d
t
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it
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t
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e
x
p
e
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tal
o
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h
e
c
o
n
tr
o
l
g
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p
.
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e
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x
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(TI
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u
se
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ts
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tere
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ts:
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ly
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OV
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ti
m
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twe
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n
g
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o
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p
s.
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e
fin
d
in
g
s
re
v
e
a
led
two
k
e
y
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n
d
i
n
g
s:
i)
g
a
m
e
-
b
a
se
d
lea
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in
g
si
g
n
ifi
c
a
n
t
ly
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ts
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tere
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tr
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a
n
d
ii
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g
e
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d
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r
,
a
g
e
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a
n
d
lo
c
a
ti
o
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d
id
n
o
t
si
g
n
ifi
c
a
n
t
ly
a
ffe
c
t
th
e
e
ffe
c
ti
v
e
n
e
ss
o
f
t
h
e
g
a
m
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b
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se
d
lea
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g
a
p
p
ro
a
c
h
in
f
o
ste
rin
g
stu
d
e
n
ts
’
in
tere
st
in
tri
g
o
n
o
m
e
try
.
Th
e
st
u
d
y
c
o
n
c
lu
d
e
s
th
a
t
g
a
m
e
-
b
a
se
d
lea
rn
in
g
e
ffe
c
ti
v
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ly
e
n
h
a
n
c
e
s
stu
d
e
n
ts
’
i
n
tere
st
in
tri
g
o
n
o
m
e
try
,
o
ffe
rin
g
imp
li
c
a
ti
o
n
s
fo
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e
d
u
c
a
to
rs
t
o
imp
ro
v
e
m
a
th
e
m
a
ti
c
s
tea
c
h
in
g
p
ra
c
ti
c
e
s th
ro
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g
h
in
tera
c
ti
v
e
a
n
d
e
n
g
a
g
in
g
stra
teg
ies
.
K
ey
w
o
r
d
s
:
Ag
e
Gam
e
-
b
ased
lear
n
in
g
Gen
d
er
L
o
ca
tio
n
Stu
d
en
ts
’
r
eten
tio
n
in
m
ath
s
T
h
is i
s
a
n
o
p
e
n
a
c
c
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ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Felix
Or
o
m
en
a
E
g
a
r
a
Dep
ar
tm
en
t o
f
Ma
th
em
atics,
Natu
r
al
Scien
ce
s
an
d
T
ec
h
n
o
l
o
g
y
E
d
u
ca
tio
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,
Facu
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o
f
E
d
u
ca
tio
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Un
iv
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s
ity
o
f
th
e
Fre
e
State
2
0
5
Nelso
n
Ma
n
d
ela
Dr
iv
e,
P
ar
k
W
est,
B
lo
em
f
o
n
tein
,
So
u
t
h
Af
r
ica
E
m
ail: f
elix
.
eg
ar
a@
u
n
n
.
e
d
u
.
n
g
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
p
u
r
s
u
it
o
f
s
cien
tific
k
n
o
w
led
g
e
h
as
led
t
o
m
a
n
y
d
is
co
v
er
ies
an
d
in
n
o
v
atio
n
s
,
s
u
c
h
as
ad
v
a
n
ce
d
co
m
m
u
n
icatio
n
an
d
tr
a
n
s
p
o
r
tatio
n
s
y
s
tem
s
,
tr
an
s
f
o
r
m
i
n
g
th
e
wo
r
ld
in
t
o
a
g
lo
b
al
v
illag
e
[
1
]
.
T
h
ese
tech
n
o
lo
g
ical
a
d
v
an
ce
m
en
ts
a
r
e
m
ad
e
p
o
s
s
ib
le
b
y
a
s
o
lid
f
o
u
n
d
atio
n
in
m
ath
em
atics.
W
ith
o
u
t
m
ath
e
m
atics,
s
cien
tific
k
n
o
wled
g
e
wo
u
ld
l
ac
k
th
e
n
ec
ess
ar
y
s
tr
u
ctu
r
e
an
d
co
h
er
e
n
ce
,
ak
in
to
a
g
h
o
s
t
with
o
u
t
s
u
b
s
tan
ce
.
C
o
n
s
eq
u
en
tly
,
f
o
r
d
elib
e
r
ate
a
n
d
f
r
u
itfu
l
p
r
o
g
r
ess
to
o
c
cu
r
g
lo
b
ally
,
a
s
o
lid
b
asis
in
s
cien
ce
an
d
m
ath
e
m
atics
is
ess
en
tial.
Ma
th
em
atics
h
as
v
ar
io
u
s
in
ter
p
r
etatio
n
s
in
m
o
d
er
n
tim
es.
m
ath
em
atics
r
ef
lects
a
p
er
s
o
n
’
s
s
u
b
co
n
s
cio
u
s
an
d
m
e
n
tal
p
r
o
ce
s
s
es,
em
p
lo
y
in
g
p
r
ec
is
e,
lo
g
ical,
an
d
s
im
p
le
m
en
tal
p
r
o
ce
d
u
r
es
to
en
h
a
n
ce
h
u
m
an
c
o
m
p
r
e
h
en
s
io
n
o
f
o
n
eself
an
d
th
e
im
m
ed
iate
s
u
r
r
o
u
n
d
in
g
s
[
2
]
.
A
n
atio
n
’
s
we
alth
an
d
ec
o
n
o
m
ic
au
to
n
o
m
y
ar
e
in
tr
in
s
ically
lin
k
ed
to
its
p
r
o
f
icien
cy
in
m
ath
em
atics,
as
s
cien
ce
an
d
tech
n
o
lo
g
y
ar
e
b
u
ilt
u
p
o
n
th
is
s
u
b
ject
[
3
]
.
I
n
g
en
er
al,
m
ath
em
atics
s
er
v
es
as
a
b
r
id
g
e
b
etwe
en
m
ath
em
atica
l
an
d
n
o
n
-
m
ath
em
atica
l
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
.
5
,
Octo
b
er
20
25
:
3
9
7
3
-
3982
3974
in
f
o
r
m
atio
n
.
Du
e
to
its
s
ig
n
if
i
ca
n
ce
,
m
ath
em
atics
is
in
teg
r
at
ed
in
to
th
e
c
u
r
r
icu
la
o
f
elem
e
n
tar
y
an
d
s
ec
o
n
d
ar
y
s
ch
o
o
ls
an
d
p
r
er
eq
u
is
ite
f
o
r
ad
m
is
s
io
n
to
v
ar
io
u
s
p
r
o
g
r
a
m
s
an
d
co
u
r
s
es in
h
ig
h
er
ed
u
ca
tio
n
in
s
titu
tio
n
s
[
4
].
T
h
e
Natio
n
al
Po
licy
o
n
E
d
u
c
atio
n
in
Nig
er
ia
u
n
d
er
s
co
r
es
th
e
im
p
o
r
ta
n
ce
o
f
in
s
till
in
g
p
er
m
an
en
t
liter
ac
y
an
d
n
u
m
e
r
ac
y
in
s
tu
d
en
ts
.
T
h
is
p
o
licy
o
u
tlin
es
th
e
g
en
er
al
g
o
als
o
f
p
r
im
ar
y
an
d
s
ec
o
n
d
ar
y
ed
u
ca
tio
n
,
in
clu
d
in
g
th
e
d
ev
elo
p
m
en
t
o
f
life
lo
n
g
r
ea
d
in
g
,
wr
itin
g
,
an
d
n
u
m
er
ac
y
s
k
ills
,
ex
ce
lle
n
t
co
m
m
u
n
icatio
n
ab
ilit
ies,
an
d
a
s
tr
o
n
g
f
o
u
n
d
ati
o
n
f
o
r
cr
itical
an
d
an
al
y
tical
th
in
k
in
g
[
5
]
.
Ma
th
em
atics
is
cr
u
cial
f
o
r
ac
h
iev
in
g
wid
esp
r
ea
d
n
u
m
er
ac
y
an
d
s
cie
n
tific
th
in
k
in
g
,
wh
ic
h
ar
e
n
ec
e
s
s
ar
y
f
o
r
an
y
co
u
n
tr
y
’
s
ad
v
an
ce
m
en
t.
Desp
ite
its
im
p
o
r
tan
ce
,
m
an
y
s
tu
d
en
ts
f
a
ce
d
if
f
icu
lties
with
in
ter
n
al
a
n
d
ex
te
r
n
al
e
x
am
in
atio
n
s
in
m
ath
em
atics.
T
h
ese
ex
am
s
ar
e
o
f
ten
cr
itical
f
o
r
a
ca
d
em
ic
p
r
o
g
r
ess
io
n
an
d
f
u
tu
r
e
o
p
p
o
r
tu
n
ities
,
m
ak
in
g
t
h
is
is
s
u
e
p
ar
ticu
lar
ly
co
n
ce
r
n
in
g
.
Sev
er
al
f
ac
to
r
s
co
n
tr
ib
u
te
to
s
tu
d
en
ts
’
s
tr
u
g
g
les,
in
clu
d
in
g
i
n
ad
eq
u
ate
s
tu
d
y
h
ab
its
,
lac
k
o
f
co
n
f
id
en
ce
,
an
d
in
s
u
f
f
icien
t
u
n
d
er
s
tan
d
in
g
o
f
f
u
n
d
am
e
n
tal
co
n
ce
p
ts
.
Ad
d
r
ess
in
g
th
ese
ch
allen
g
es
is
ess
en
tial
to
h
elp
s
tu
d
en
ts
ac
h
ie
v
e
b
etter
r
esu
lts
an
d
d
ev
elo
p
a
p
o
s
itiv
e
attitu
d
e
to
war
d
m
ath
em
atics.
R
esear
ch
er
s
h
av
e
id
e
n
tifie
d
s
ev
er
al
f
ac
to
r
s
af
f
ec
tin
g
s
tu
d
e
n
ts
’
p
o
o
r
ac
h
iev
em
en
t
an
d
r
e
ten
tio
n
i
n
m
ath
em
atics.
So
m
e
o
f
th
ese
f
ac
to
r
s
in
clu
d
e
in
s
u
f
f
icien
t
m
ath
em
atics
in
s
tr
u
ctio
n
in
p
r
im
ar
y
s
ch
o
o
l
[
6
]
;
cr
o
wd
ed
m
ath
class
es
an
d
o
u
td
ated
m
ath
r
eso
u
r
ce
s
[
7
]
;
an
x
iety
to
war
d
s
m
ath
em
atics
[
8
]
;
h
ar
s
h
teac
h
i
n
g
m
eth
o
d
s
[
9
]
;
lack
o
f
s
tu
d
en
t
in
ter
est
[
10
]
;
s
tu
d
en
t
lazin
ess
[
11
]
;
an
d
p
o
o
r
teac
h
in
g
ap
p
r
o
ac
h
es
ad
o
p
ted
b
y
m
ath
teac
h
er
s
[
12
]
.
Am
o
n
g
th
ese
f
ac
to
r
s
,
th
e
p
o
o
r
ap
p
r
o
ac
h
to
teac
h
in
g
m
ath
em
atic
s
,
wh
ich
lead
s
to
s
tu
d
en
ts
’
lack
o
f
in
ter
est
in
th
e
s
u
b
ject,
is
o
f
p
ar
ticu
lar
in
ter
est
to
th
is
r
esear
ch
.
Ov
er
th
e
y
ea
r
s
,
m
ath
em
atics
r
esear
ch
er
s
h
av
e
s
o
u
g
h
t
ap
p
r
o
p
r
iate
m
eth
o
d
s
o
f
teac
h
in
g
m
a
th
em
atics
co
n
ce
p
ts
th
at
wo
u
ld
in
cr
ea
s
e
s
tu
d
en
ts
’
p
er
f
o
r
m
an
ce
an
d
b
o
o
s
t
th
eir
i
n
ter
est
in
th
e
s
u
b
ject.
Gam
e
-
b
ased
lear
n
in
g
is
o
n
e
s
u
ch
r
ec
o
m
m
en
d
ed
a
p
p
r
o
ac
h
to
teac
h
in
g
m
at
h
em
atics [
1
3
]
–
[1
5
].
Gam
e
-
b
ased
lear
n
in
g
u
tili
ze
s
th
e
en
g
ag
i
n
g
n
at
u
r
e
o
f
g
a
m
es
to
ac
h
iev
e
ed
u
c
atio
n
al
o
b
jectiv
es.
I
t
em
p
h
asizes
“
lear
n
in
g
th
r
o
u
g
h
g
am
es
r
ath
er
t
h
an
lear
n
i
n
g
to
p
lay
”
[
16
]
.
T
h
is
ap
p
r
o
ac
h
in
v
o
lv
es
cr
af
tin
g
ed
u
ca
tio
n
al
ac
tiv
ities
th
at
g
r
ad
u
ally
in
tr
o
d
u
ce
n
ew
co
n
c
ep
ts
an
d
g
u
id
e
lear
n
er
s
t
o
war
d
s
a
f
i
n
al
g
o
al,
in
co
r
p
o
r
atin
g
elem
en
ts
s
u
ch
as
en
g
ag
em
e
n
t,
im
m
ed
iate
r
e
war
d
s
,
an
d
f
r
ien
d
ly
co
m
p
etitio
n
.
T
h
is
ap
p
r
o
ac
h
m
ain
tain
s
lear
n
er
s
’
ac
ad
em
i
c
m
o
tiv
atio
n
[
16
]
.
B
y
in
te
g
r
atin
g
g
a
m
e
elem
en
ts
s
u
c
h
as
r
ewa
r
d
s
an
d
co
m
p
etitio
n
,
g
am
e
-
b
ased
lear
n
in
g
aim
s
t
o
k
ee
p
s
tu
d
e
n
ts
en
g
ag
ed
a
n
d
in
ter
ested
in
th
eir
s
tu
d
ies.
T
h
is
m
eth
o
d
n
o
t
o
n
l
y
m
ak
es
lear
n
i
n
g
m
o
r
e
en
jo
y
ab
le
b
u
t
also
h
el
p
s
r
e
in
f
o
r
ce
c
o
n
ce
p
ts
th
r
o
u
g
h
r
ep
etitiv
e
p
r
ac
tice
an
d
in
s
tan
t
f
ee
d
b
ac
k
.
As
a
r
esu
lt,
s
tu
d
en
ts
ar
e
m
o
r
e
lik
ely
to
s
tay
m
o
tiv
ated
an
d
co
m
m
itted
to
th
eir
ac
ad
em
i
c
g
o
als.
Gam
e
-
b
ased
lear
n
in
g
b
en
ef
its
s
tu
d
en
ts
ac
r
o
s
s
all
ed
u
ca
tio
n
al
lev
els,
f
r
o
m
p
r
e
-
s
ch
o
o
l
to
p
o
s
t
-
s
ec
o
n
d
ar
y
ed
u
ca
tio
n
,
m
a
k
in
g
it
a
h
ig
h
ly
in
clu
s
iv
e
ap
p
r
o
ac
h
.
T
h
is
in
clu
s
iv
e
s
tr
ateg
y
ca
ter
s
to
d
iv
er
s
e
lear
n
in
g
n
ee
d
s
an
d
p
r
ef
er
en
ce
s
,
m
ak
in
g
e
d
u
ca
ti
o
n
ac
ce
s
s
ib
le
an
d
e
n
jo
y
ab
le
f
o
r
ev
e
r
y
o
n
e.
I
t
h
elp
s
y
o
u
n
g
er
s
tu
d
en
ts
b
u
ild
f
o
u
n
d
atio
n
al
s
k
ills
in
a
f
u
n
a
n
d
in
ter
ac
tiv
e
way
wh
ile
p
r
o
v
id
in
g
o
ld
er
s
tu
d
e
n
ts
with
co
m
p
l
ex
p
r
o
b
lem
-
s
o
lv
i
n
g
an
d
cr
itical
th
in
k
in
g
ex
er
ci
s
es.
T
h
e
ad
ap
tab
ilit
y
o
f
g
am
e
-
b
ased
lear
n
in
g
e
n
s
u
r
es
its
r
elev
an
ce
an
d
ef
f
ec
tiv
en
ess
ac
r
o
s
s
d
if
f
er
en
t
ed
u
ca
tio
n
al
lev
els
an
d
c
o
n
te
x
ts
.
Ad
d
itio
n
ally
,
it
is
ir
r
elev
an
t
wh
er
e
o
r
h
o
w
s
tu
d
en
ts
lear
n
; th
ey
ca
n
d
o
s
o
in
d
iv
id
u
ally
o
r
in
g
r
o
u
p
s
,
u
s
in
g
p
h
y
s
ical
item
s
o
r
o
n
lin
e
g
a
m
es [
17
].
Dim
itra
et
a
l.
[
17
]
lis
ts
s
ev
er
al
co
m
m
o
n
ex
am
p
les
o
f
g
a
m
e
-
b
ased
lear
n
in
g
,
s
u
ch
as
c
ar
d
g
am
es,
wh
ich
u
s
e
a
s
tan
d
ar
d
o
r
g
am
e
-
s
p
ec
if
ic
d
ec
k
o
f
ca
r
d
s
;
b
o
ar
d
g
am
es,
wh
ich
in
v
o
l
v
e
m
o
v
i
n
g
co
m
p
o
n
e
n
ts
o
r
p
iece
s
,
ar
e
f
r
eq
u
en
tly
u
s
ed
;
c
h
ess
an
d
ch
ec
k
er
s
ar
e
th
e
two
m
o
s
t
well
-
k
n
o
wn
b
o
ar
d
g
am
es,
b
u
t
s
tu
d
en
ts
ca
n
ex
p
lo
r
e
h
u
n
d
r
ed
s
,
if
n
o
t
th
o
u
s
an
d
s
,
o
f
o
th
er
s
(
t
h
is
s
tu
d
y
u
tili
ze
d
b
o
ar
d
g
am
es).
Simu
latio
n
g
am
es
cl
o
s
ely
r
ep
licate
r
ea
l
-
wo
r
ld
ac
tio
n
s
,
with
o
n
e
o
f
th
e
m
o
s
t
well
-
k
n
o
wn
life
s
im
u
latio
n
g
am
e
f
r
an
ch
is
es
b
ein
g
“
T
h
e
Sims
”
,
wh
ich
d
eb
u
ted
in
2
0
0
0
.
W
o
r
d
g
am
es
a
r
e
in
ter
ac
tiv
e
m
ed
ia
u
s
ed
to
in
v
esti
g
ate
lin
g
u
is
tic
p
r
in
cip
les
o
r
lan
g
u
ag
e
p
r
o
f
icien
cy
.
C
lass
i
c
wo
r
d
g
am
es
in
clu
d
e
Scr
ab
b
le,
wh
ile
m
o
r
e
co
n
tem
p
o
r
ar
y
ex
am
p
les
ar
e
p
r
o
g
r
a
m
m
ed
lik
e
wo
r
d
s
with
f
r
ien
d
s
.
Pu
zz
le
g
a
m
es
em
p
h
asize
lo
g
ic,
wo
r
d
c
o
m
p
letio
n
,
s
eq
u
en
ce
s
o
lv
in
g
,
s
p
atial
awa
r
en
ess
,
an
d
p
atter
n
r
ec
o
g
n
itio
n
to
s
o
lv
e
p
u
zz
les.
Fo
r
in
s
tan
ce
,
m
ath
g
am
es
s
u
ch
as
Su
d
o
k
u
an
d
2
0
4
8
ar
e
well
-
lik
ed
.
Vid
eo
g
am
es
ar
e
elec
tr
o
n
ic
g
am
es
th
at
allo
w
p
lay
er
s
to
co
n
t
r
o
l
w
h
at
ap
p
ea
r
s
o
n
th
e
s
cr
ee
n
u
s
in
g
a
jo
y
s
tick
,
c
o
n
t
r
o
ller
,
a
n
d
k
ey
b
o
ar
d
.
C
lass
ic
ex
am
p
les
in
clu
d
e
Pac
-
Ma
n
o
r
,
m
o
r
e
r
ec
en
tly
,
Fo
r
tn
ite.
R
o
le
-
p
lay
in
g
g
a
m
es
in
v
o
lv
e
p
ar
ticip
a
n
ts
tak
in
g
o
n
th
e
r
o
les
o
f
f
ictio
n
al
ch
a
r
ac
ter
s
wh
o
g
o
o
n
jo
u
r
n
ey
s
.
T
h
ese
g
am
es
o
f
ten
f
ea
tu
r
e
in
tr
icate
s
to
r
y
lin
es
an
d
r
eq
u
ir
e
p
la
y
er
s
to
m
ak
e
d
ec
is
io
n
s
th
at
af
f
ec
t
th
e
g
am
e
’
s
o
u
tco
m
e.
R
o
le
-
p
lay
i
n
g
g
am
es
en
co
u
r
ag
e
cr
e
ativ
ity
,
s
tr
ateg
ic
th
in
k
in
g
,
an
d
tea
m
wo
r
k
as
p
lay
er
s
co
llab
o
r
ate
to
ac
h
iev
e
co
m
m
o
n
g
o
als.
T
h
ey
p
r
o
v
id
e
a
s
af
e
en
v
ir
o
n
m
e
n
t
f
o
r
s
tu
d
en
ts
to
ex
p
er
im
en
t
with
d
if
f
er
en
t scen
ar
i
o
s
an
d
p
r
o
b
le
m
-
s
o
lv
in
g
a
p
p
r
o
ac
h
es,
b
en
e
f
icial
f
o
r
o
v
er
all
co
g
n
itiv
e
an
d
s
o
cial
d
ev
elo
p
m
e
n
t.
Play
in
g
ed
u
ca
tio
n
al
g
am
es
al
lo
ws
s
tu
d
en
ts
to
r
e
-
ev
alu
ate
th
eir
lear
n
in
g
p
r
o
ce
s
s
es,
p
r
o
d
u
ce
th
eir
m
ater
ials
,
ex
ch
an
g
e
in
s
tr
u
cti
o
n
al
in
s
ig
h
ts
,
an
d
h
o
n
e
th
eir
ab
ilit
ies
f
o
r
r
ea
l
-
wo
r
ld
ap
p
licatio
n
[
1
4
]
.
Gam
es
en
co
u
r
a
g
e
lear
n
in
g
in
v
o
lv
em
en
t
at
co
g
n
itiv
e,
af
f
ec
tiv
e,
a
n
d
s
o
cio
cu
ltu
r
al
lev
els,
o
f
f
er
in
g
a
f
u
n
lear
n
in
g
m
eth
o
d
[
18
]
.
T
h
r
o
u
g
h
i
n
ter
a
ctio
n
s
b
etwe
en
lear
n
er
s
an
d
th
e
g
am
e,
lear
n
er
s
a
n
d
p
ee
r
s
,
an
d
lear
n
er
s
a
n
d
in
s
tr
u
cto
r
s
,
as we
ll a
s
th
r
o
u
g
h
m
ea
n
in
g
f
u
l f
ee
d
b
a
ck
,
g
a
m
e
-
b
ased
lear
n
in
g
p
r
o
m
o
tes th
e
c
o
llab
o
r
ativ
e
b
u
ild
in
g
o
f
k
n
o
wled
g
e
[
19
]
.
C
o
m
p
ar
ed
to
tr
ad
itio
n
al
in
s
tr
u
ctio
n
m
eth
o
d
s
,
s
tu
d
ies
h
av
e
s
h
o
wn
t
h
at
ed
u
ca
tio
n
al
g
am
e
s
en
h
an
ce
s
tu
d
en
ts
’
h
i
g
h
-
lev
el
t
h
in
k
in
g
s
k
ills
an
d
m
o
tiv
atio
n
[
20
]
.
Fu
r
t
h
er
m
o
r
e,
ev
id
e
n
ce
s
u
p
p
o
r
ts
th
e
id
ea
th
at
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
F
o
s
teri
n
g
s
tu
d
en
ts
’
in
teres
t in
tr
ig
o
n
o
metry
u
s
in
g
g
a
me
-
b
a
s
e
d
lea
r
n
in
g
s
tr
a
teg
y
…
(
F
elix
Oro
men
a
E
g
a
r
a
)
3975
g
am
e
-
b
ased
lear
n
in
g
ca
n
ef
f
ec
tiv
ely
p
r
esen
t
less
o
n
s
in
an
im
p
r
ess
iv
e
an
d
in
s
p
ir
in
g
m
an
n
er
,
i
n
cr
ea
s
in
g
s
tu
d
en
ts
’
in
ter
est
in
s
cien
ce
,
tech
n
o
lo
g
y
,
en
g
i
n
ee
r
in
g
,
an
d
m
ath
em
atics
(
STE
M)
s
u
b
j
ec
ts
an
d
im
p
r
o
v
in
g
ac
ad
em
ic
p
er
f
o
r
m
an
ce
[
14
].
Alth
o
u
g
h
g
am
e
-
b
ased
lear
n
i
n
g
h
as
n
u
m
er
o
u
s
b
e
n
ef
its
,
it
also
p
r
esen
ts
ce
r
tain
c
h
allen
g
es.
T
h
e
ap
p
r
o
ac
h
ca
n
b
e
tim
e
-
c
o
n
s
u
m
in
g
,
an
d
it
ca
n
b
e
d
i
f
f
icu
lt
to
ac
c
u
r
ately
p
r
e
d
ict
th
e
len
g
th
o
f
ea
c
h
g
am
in
g
s
ess
io
n
[
21
]
.
Fu
r
th
er
m
o
r
e,
s
o
m
e
s
tu
d
en
ts
m
ig
h
t
f
ee
l
u
n
ea
s
y
ab
o
u
t
th
e
c
o
m
p
etitiv
e
n
atu
r
e,
th
e
p
u
b
lic
d
is
p
lay
o
f
th
eir
p
er
f
o
r
m
an
ce
,
an
d
t
h
e
co
m
p
ar
is
o
n
with
o
th
er
s
[
22
]
.
Ad
d
itio
n
ally
,
g
am
if
ie
d
co
u
r
s
es
m
ig
h
t
b
e
p
er
ce
iv
ed
as
m
o
r
e
r
ig
o
r
o
u
s
,
c
au
s
in
g
s
o
m
e
s
tu
d
en
ts
to
p
r
ef
er
co
n
v
en
tio
n
al
lear
n
in
g
tech
n
i
q
u
es
[
23
]
.
I
m
p
r
o
p
e
r
tech
n
ical
ap
p
licatio
n
s
o
f
g
am
e
-
b
ased
lear
n
in
g
o
r
a
d
is
co
n
n
ec
t
f
r
o
m
lear
n
in
g
g
o
als
ca
n
also
f
r
u
s
tr
ate
lear
n
er
s
[
24
]
.
Ho
wev
er
,
m
ild
c
o
n
f
u
s
io
n
an
d
ir
r
itatio
n
d
u
r
in
g
g
a
m
e
-
b
ased
lear
n
in
g
s
ess
io
n
s
ca
n
p
r
o
m
o
te
lear
n
in
g
an
d
g
en
er
ate
p
o
s
itiv
e
af
f
ec
tiv
e
s
tates
lik
e
d
elig
h
t
a
n
d
e
x
h
ilar
a
tio
n
[
22
]
.
T
h
e
c
h
allen
g
es
to
im
p
lem
en
tin
g
an
d
em
b
r
ac
in
g
g
am
e
-
b
ased
lear
n
in
g
in
clu
d
e
d
i
f
f
icu
lty
s
elec
tin
g
an
d
i
n
teg
r
atin
g
ed
u
ca
tio
n
al
g
am
es,
teac
h
er
s
’
lac
k
o
f
tim
e
to
p
lan
g
am
ep
la
y
s
ess
io
n
s
,
an
d
in
a
d
eq
u
ate
tech
n
ical
ab
ilit
y
[
23
]
.
T
ea
c
h
er
s
m
ig
h
t
b
e
r
elu
cta
n
t
to
u
s
e
g
am
e
-
b
ased
lear
n
in
g
b
ec
a
u
s
e
th
ey
wo
r
r
y
ab
o
u
t
f
itti
n
g
it
in
to
th
eir
less
o
n
p
la
n
s
,
m
an
a
g
in
g
class
r
o
o
m
tim
e,
an
d
d
ea
lin
g
with
th
e
u
n
f
am
ilia
r
ity
o
f
th
ese
teac
h
in
g
m
eth
o
d
s
[
25
].
T
h
e
cu
r
r
en
t
s
tu
d
y
ap
p
lies
B
an
d
u
r
a
’
s
s
o
cial
lear
n
in
g
th
e
o
r
y
.
T
h
e
t
h
eo
r
y
’
s
ten
ets
in
clu
d
e
atten
tio
n
,
r
eten
tio
n
,
r
e
p
r
o
d
u
ctio
n
,
a
n
d
m
o
tiv
atio
n
,
wh
ich
a
r
e
ess
en
tial
f
o
r
lear
n
in
g
.
L
ea
r
n
er
s
m
u
s
t
co
n
ce
n
tr
ate
o
n
task
s
to
lear
n
(
atten
tio
n
)
,
in
ter
n
alize
k
n
o
wled
g
e
f
o
r
f
u
tu
r
e
u
s
e
(
r
eten
tio
n
)
,
r
ep
ea
t
ac
q
u
ir
ed
k
n
o
wled
g
e
o
r
b
eh
a
v
io
r
,
wh
en
n
ec
ess
ar
y
(
r
ep
r
o
d
u
ctio
n
)
,
an
d
b
e
m
o
tiv
ated
to
c
o
m
p
lete
task
s
,
o
f
ten
in
s
p
ir
ed
b
y
o
b
s
er
v
in
g
o
t
h
er
s
’
r
ewa
r
d
s
o
r
p
u
n
is
h
m
en
ts
(
m
o
tiv
atio
n
)
.
So
cial
lear
n
in
g
th
e
o
r
y
p
o
s
its
th
at
p
eo
p
le
lear
n
s
o
cial
b
eh
av
io
r
b
y
o
b
s
er
v
in
g
an
d
im
itatin
g
o
th
e
r
s
,
with
a
s
o
cial
e
n
v
ir
o
n
m
en
t
b
ein
g
c
r
u
cial
f
o
r
lear
n
in
g
.
Pl
ay
in
g
g
am
es
with
p
ee
r
s
in
a
class
r
o
o
m
s
ettin
g
ca
n
en
h
an
ce
s
tu
d
en
ts
’
in
ter
es
t
in
lear
n
in
g
th
r
o
u
g
h
o
b
s
er
v
a
tio
n
,
im
itatio
n
,
an
d
in
ter
ac
tio
n
,
u
ltima
tely
im
p
r
o
v
i
n
g
th
eir
p
er
f
o
r
m
an
ce
i
n
m
ath
e
m
atics.
Nu
m
er
o
u
s
in
ter
n
atio
n
al
a
n
d
l
o
ca
l
s
tu
d
ies
h
av
e
e
x
p
lo
r
e
d
h
o
w
g
am
e
-
b
ased
lear
n
in
g
af
f
ec
t
s
s
tu
d
en
ts
’
in
ter
est
in
m
ath
em
atics.
Fo
r
ex
am
p
le,
a
s
tu
d
y
b
y
B
h
ad
a
wk
ar
an
d
Gu
p
ta
[
26
]
u
s
ed
a
q
u
asi
-
ex
p
er
im
e
n
tal
d
esig
n
an
d
t
-
test
an
aly
s
is
to
s
h
o
w
th
at
elem
e
n
tar
y
s
tu
d
en
ts
wh
o
ex
p
er
ien
ce
d
g
am
e
-
b
ased
lear
n
in
g
wer
e
m
o
r
e
in
ter
ested
in
m
at
h
em
atics
th
a
n
th
o
s
e
i
n
a
c
o
n
tr
o
l
g
r
o
u
p
.
Si
m
ilar
ly
,
r
esear
ch
b
y
Yeh
et
a
l
.
[
27
]
,
in
v
esti
g
ated
th
is
ap
p
r
o
ac
h
in
T
aiwa
n
,
f
in
d
in
g
th
at
b
o
th
l
o
w
-
a
n
d
h
ig
h
-
a
ch
iev
in
g
elem
en
tar
y
s
tu
d
e
n
ts
in
th
e
ex
p
e
r
im
en
tal
g
r
o
u
p
s
h
o
wed
g
r
ea
te
r
in
ter
est
in
m
ath
em
atics
th
an
th
eir
p
ee
r
s
in
th
e
co
n
tr
o
l
g
r
o
u
p
.
I
n
B
ay
elsa
State,
Nig
er
ia,
Fre
d
er
ick
-
J
o
n
ah
an
d
I
g
b
o
jin
wae
k
wu
[
28
]
f
o
u
n
d
th
at
a
g
am
e
-
en
h
an
ce
d
in
s
tr
u
ctio
n
al
s
tr
ateg
y
s
ig
n
if
ican
tly
b
o
o
s
ted
p
r
im
ar
y
s
tu
d
en
ts
’
in
t
er
est
in
m
ath
em
atics.
A
s
tu
d
y
in
Ab
u
ja,
Nig
er
ia
b
y
Su
m
b
a
b
i
an
d
B
ass
ey
[
29
]
r
ev
ea
led
th
at
s
ec
o
n
d
ar
y
s
tu
d
e
n
ts
wh
o
u
s
ed
m
ath
e
m
atica
l
g
a
m
es
an
d
s
im
u
latio
n
s
d
ev
el
o
p
e
d
a
s
tr
o
n
g
e
r
in
ter
est
in
g
eo
m
et
r
y
c
o
m
p
ar
e
d
to
th
o
s
e
in
a
t
r
ad
itio
n
al
lear
n
in
g
en
v
i
r
o
n
m
en
t.
L
astl
y
,
in
R
iv
er
State,
Nig
er
ia,
r
esear
ch
b
y
E
ze
u
g
wu
et
a
l
.
[
30
]
d
em
o
n
s
tr
ated
th
at
a
g
am
e
-
b
ased
in
s
tr
u
ctio
n
al
ap
p
r
o
ac
h
in
cr
e
ased
ju
n
io
r
s
ec
o
n
d
ar
y
s
tu
d
en
ts
’
in
ter
est in
alg
eb
r
a,
with
r
esu
lts
in
d
icatin
g
th
at
g
e
n
d
er
d
id
n
o
t a
f
f
ec
t th
e
s
tr
ateg
y
’
s
ef
f
ec
tiv
en
ess
.
Acc
o
r
d
in
g
t
o
th
e
s
tu
d
ies,
g
a
m
e
-
b
ased
lear
n
in
g
is
an
ef
f
e
ctiv
e
s
tr
ateg
y
f
o
r
en
h
a
n
cin
g
s
tu
d
en
ts
’
in
ter
est
in
m
ath
em
atics.
Ho
w
ev
er
,
its
im
p
ac
t
o
n
s
tu
d
en
ts
’
in
ter
est
in
m
ath
em
atics
in
E
n
u
g
u
State,
Nig
er
ia,
r
em
ain
s
s
ca
r
ce
.
W
h
ile
p
r
ev
i
o
u
s
s
tu
d
ies
u
s
ed
a
q
u
asi
-
ex
p
er
im
en
tal
d
esig
n
,
th
is
s
tu
d
y
em
p
l
o
y
s
a
tr
u
e
ex
p
er
im
en
tal
d
esig
n
,
s
p
ec
if
i
ca
lly
a
r
e
p
ea
ted
m
ea
s
u
r
es
d
esig
n
,
k
n
o
wn
f
o
r
its
h
ig
h
s
cien
tific
v
alid
ity
.
Mo
r
eo
v
er
,
u
n
lik
e
t
h
e
r
e
v
iewe
d
s
tu
d
ies,
th
is
s
tu
d
y
c
o
n
s
id
er
s
th
e
in
f
lu
en
ce
o
f
m
o
d
er
at
o
r
v
a
r
iab
les
s
u
ch
as
g
en
d
er
,
ag
e
,
a
n
d
l
o
ca
tio
n
o
n
s
tu
d
en
ts
’
in
ter
est.
T
h
u
s
,
th
e
p
r
esen
t
s
tu
d
y
aim
s
to
e
v
alu
ate
t
h
e
ef
f
ec
ti
v
en
ess
o
f
g
am
e
-
b
ased
lea
r
n
in
g
o
n
s
tu
d
en
ts
’
in
ter
est
in
t
r
ig
o
n
o
m
e
tr
y
in
E
n
u
g
u
State,
Nig
er
i
a.
T
o
g
u
id
e
th
is
in
v
esti
g
atio
n
,
th
e
s
tu
d
y
f
o
c
u
s
es o
n
th
e
f
o
ll
o
win
g
r
esear
ch
q
u
esti
o
n
s
:
i)
W
h
at
ar
e
th
e
m
ea
n
in
ter
est
s
co
r
es
o
f
s
tu
d
en
ts
in
tr
ig
o
n
o
m
et
r
y
wh
en
ex
p
o
s
ed
to
th
e
g
am
e
-
b
ased
lear
n
in
g
ap
p
r
o
ac
h
?
ii)
W
h
at
ar
e
th
e
m
o
d
er
atin
g
i
n
f
l
u
en
ce
s
o
f
g
en
d
er
,
a
g
e,
an
d
l
o
ca
tio
n
o
n
s
tu
d
en
ts
’
in
ter
est
in
tr
ig
o
n
o
m
et
r
y
u
s
in
g
th
e
g
am
e
-
b
ased
lear
n
in
g
ap
p
r
o
ac
h
?
B
ased
o
n
th
ese
r
esear
ch
q
u
esti
o
n
s
,
th
e
s
tu
d
y
f
o
r
m
u
lates
two
h
y
p
o
th
eses
:
t
h
e
f
ir
s
t
h
y
p
o
th
esis
(
Ho
1
)
s
tates
th
at
th
e
g
am
e
-
b
ased
lea
r
n
in
g
ap
p
r
o
ac
h
d
o
es
n
o
t
s
ig
n
if
ican
tly
im
p
ac
t
s
tu
d
en
ts
’
in
ter
est
in
t
r
ig
o
n
o
m
etr
y
.
T
h
e
s
ec
o
n
d
h
y
p
o
th
esis
(
Ho
2
)
p
o
s
its
th
at
g
en
d
er
,
a
g
e,
an
d
lo
ca
tio
n
d
o
n
o
t
s
ig
n
if
ican
tly
i
n
f
lu
en
c
e
s
tu
d
en
ts
’
in
ter
est
in
tr
ig
o
n
o
m
etr
y
w
h
en
u
s
in
g
th
e
g
am
e
-
b
ased
lear
n
in
g
a
p
p
r
o
a
ch
.
2.
M
E
T
H
O
D
2
.
1
.
Desig
n
T
h
is
s
tu
d
y
em
p
lo
y
ed
a
m
ix
e
d
-
b
etwe
en
an
d
with
in
m
ea
s
u
r
es
an
aly
s
is
o
f
v
ar
ian
ce
(
ANOV
A)
d
esig
n
.
T
h
e
r
esear
ch
er
s
s
p
ec
if
ically
u
s
ed
th
is
d
esig
n
to
d
eter
m
i
n
e
wh
eth
er
th
e
g
am
e
-
b
ased
lear
n
in
g
a
p
p
r
o
ac
h
im
p
ac
ted
s
tu
d
en
ts
’
in
ter
est
in
tr
ig
o
n
o
m
et
r
y
b
o
th
with
in
th
e
g
r
o
u
p
s
(
co
m
p
a
r
in
g
p
r
e
-
a
n
d
p
o
s
t
-
test
r
esu
lts
)
an
d
b
etwe
en
th
e
ex
p
er
im
en
tal
an
d
co
n
tr
o
l
g
r
o
u
p
s
.
T
h
is
ap
p
r
o
ac
h
allo
ws
f
o
r
a
co
m
p
r
eh
en
s
iv
e
an
aly
s
is
o
f
th
e
in
ter
v
en
tio
n
’
s
ef
f
ec
tiv
en
ess
b
y
ex
am
in
in
g
th
e
ch
a
n
g
es o
v
e
r
tim
e
an
d
d
if
f
er
en
ce
s
b
etwe
en
th
e
two
g
r
o
u
p
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t J E
v
al
&
R
es E
d
u
c
,
Vo
l
.
14
,
No
.
5
,
Octo
b
er
20
25
:
3
9
7
3
-
3982
3976
2
.
2
.
P
a
rt
icipa
nts
A
to
tal
o
f
5
6
s
en
io
r
s
ec
o
n
d
ar
y
s
ch
o
o
l
two
(
SS
2
)
s
tu
d
en
ts
(
3
0
m
ales
an
d
2
6
f
em
ales)
b
e
twee
n
th
e
ag
es
o
f
1
4
a
n
d
1
7
y
ea
r
s
we
r
e
en
lis
ted
to
tak
e
p
ar
t
in
th
e
s
tu
d
y
.
T
h
e
s
am
p
le
s
ize
f
o
r
th
is
r
esear
ch
was
d
eter
m
in
ed
u
s
in
g
th
e
GPo
wer
3
.
1
s
o
f
twar
e,
a
to
o
l
th
at
h
elp
s
r
esear
ch
er
s
ca
lcu
late
th
e
n
ec
ess
ar
y
s
am
p
le
s
ize
to
en
s
u
r
e
th
eir
s
tu
d
y
h
as
en
o
u
g
h
s
tatis
tical
p
o
wer
.
Fo
r
th
is
s
tu
d
y
,
we
s
et
th
e
f
o
llo
win
g
p
ar
am
eter
s
in
GPo
wer
:
an
ef
f
ec
t
s
ize
o
f
.
2
5
,
a
s
ig
n
if
ican
ce
lev
el
o
f
.
0
5
,
a
p
o
wer
le
v
el
o
f
.
8
0
,
an
d
u
s
ed
th
e
F
test
s
f
o
r
ANOV
A
with
r
ep
ea
ted
m
ea
s
u
r
es
an
d
b
etwe
en
f
ac
to
r
s
.
B
ased
o
n
th
ese
p
ar
am
eter
s
,
GPo
wer
s
u
g
g
ested
a
s
am
p
le
s
ize
o
f
5
6
p
ar
ticip
an
ts
,
wh
ich
is
ap
p
r
o
p
r
iate
f
o
r
d
etec
tin
g
a
m
ed
i
u
m
ef
f
ec
t
s
ize
with
ad
eq
u
ate
p
o
wer
.
T
h
e
u
s
e
o
f
G*
Po
wer
f
o
r
s
am
p
le
s
ize
ca
lcu
latio
n
in
ex
p
er
im
en
tal
s
tu
d
ie
s
is
well
-
d
o
cu
m
en
ted
an
d
wid
ely
ac
ce
p
ted
in
t
h
e
r
esear
ch
co
m
m
u
n
ity
[
3
1
]
,
[3
2
]
.
So
m
e
cu
r
r
en
t
s
tu
d
ies
[
3
3
]
–
[
3
6
]
ha
d
ap
p
lied
GPo
wer
in
d
eter
m
in
in
g
s
am
p
le
s
ize
in
r
ec
en
t
tim
es.
T
wo
p
u
b
lic
s
ec
o
n
d
ar
y
s
ch
o
o
ls
(
o
n
e
in
an
u
r
b
a
n
an
d
r
u
r
al
ar
ea
)
we
r
e
s
elec
ted
r
an
d
o
m
l
y
f
r
o
m
th
e
1
6
p
u
b
lic
s
ec
o
n
d
ar
y
s
ch
o
o
ls
in
E
n
u
g
u
State
’
s
Ud
en
u
L
o
ca
l
Go
v
er
n
m
e
n
t
Ar
ea
(
L
GA)
with
SS
2
s
tu
d
en
ts
’
p
o
p
u
latio
n
o
f
3
,
8
3
1
[
37
]
.
Par
ticip
an
ts
in
th
is
cu
r
r
e
n
t
s
tu
d
y
wer
e
r
ec
r
u
ited
f
r
o
m
t
h
e
s
ch
o
o
ls
ch
o
s
en
b
ased
o
n
th
eir
tr
ig
o
n
o
m
etr
y
p
er
f
o
r
m
a
n
ce
in
m
ath
em
atic
s
ass
e
s
s
m
en
t
co
n
d
u
cted
b
y
th
eir
r
eg
u
lar
m
ath
teac
h
er
s
b
ef
o
r
e
th
e
in
v
esti
g
atio
n
.
Stu
d
en
ts
with
g
r
ad
es
≤
5
0
wer
e
en
lis
ted
to
p
ar
ticip
ate
in
th
e
s
tu
d
y
.
Usi
n
g
Sag
h
ae
i’
s
r
an
d
o
m
allo
ca
tio
n
s
o
f
twar
e
[
38
]
,
we
c
r
ea
ted
a
c
o
m
p
u
ter
-
g
en
er
ated
r
a
n
d
o
m
lis
t to
ass
ig
n
s
tu
d
en
ts
t
o
g
r
o
u
p
s
.
T
h
is
p
r
o
ce
s
s
r
esu
lted
in
2
7
s
tu
d
en
ts
b
ein
g
p
lace
d
in
th
e
ex
p
er
im
e
n
tal
g
r
o
u
p
a
n
d
2
9
in
t
h
e
co
n
tr
o
l
g
r
o
u
p
.
T
h
o
s
e
in
th
e
co
n
tr
o
l
g
r
o
u
p
wer
e
g
iv
en
th
e
ch
a
n
ce
to
ex
p
er
ien
ce
th
e
g
am
e
-
b
ased
lear
n
in
g
in
ter
v
e
n
tio
n
later
.
T
h
e
av
er
a
g
e
ag
e
o
f
s
tu
d
en
ts
in
th
e
ex
p
e
r
im
en
tal
g
r
o
u
p
(
1
.
4
8
±
.
5
1
)
was
n
o
t
s
ig
n
if
ica
n
tly
d
if
f
er
en
t
f
r
o
m
th
at
o
f
th
e
co
n
tr
o
l
g
r
o
u
p
(
1
.
7
2
±
.
4
6
;
t(
5
4
)
=1
.
8
8
3
,
p
=.
0
6
5
)
.
F
u
r
th
er
d
etails
ab
o
u
t
th
e
p
ar
ticip
an
ts
ca
n
b
e
f
o
u
n
d
in
T
ab
le
1
.
T
ab
le
1
.
Par
ticip
an
ts
’
d
e
m
o
g
r
ap
h
ic
in
f
o
r
m
atio
n
(
with
in
-
g
r
o
u
p
an
aly
s
is
)
C
h
a
r
a
c
t
e
r
i
s
t
i
c
d
i
m
e
n
si
o
n
Ex
p
e
r
i
m
e
n
t
a
l
g
r
o
u
p
,
n
(
%)
C
o
n
t
r
o
l
g
r
o
u
p
,
n
(
%)
2
S
i
g
n
i
f
i
c
a
n
c
e
G
e
n
d
e
r
M
a
l
e
1
4
(
4
5
.
2
)
1
7
(
5
4
.
8
)
.
0
5
8
.
8
0
9
F
e
mal
e
1
4
(
4
8
.
3
)
1
5
(
5
1
.
7
)
A
g
e
14
-
1
5
y
e
a
r
s
1
4
(
6
3
.
6
)
8
(
3
6
.
4
)
1
.
4
8
±
.
5
1
1
.
7
2
±
.
4
6
*
1
.
8
8
3
(
df
=
5
4
)
.
0
6
5
16
-
1
7
y
e
a
r
s
1
3
(
3
8
.
2
)
2
1
(
6
1
.
8
)
S
c
h
o
o
l
l
o
c
a
t
i
o
n
U
r
b
a
n
1
5
(
4
6
.
9
)
1
7
(
5
3
.
1
)
.
0
0
1
.
9
7
2
R
u
r
a
l
1
3
(
4
6
.
4
)
1
5
(
5
3
.
6
)
N
o
t
e
:
n
r
e
p
r
e
s
e
n
t
s
t
h
e
n
u
mb
e
r
o
f
p
a
r
t
i
c
i
p
a
n
t
s
;
χ
²
=
C
h
i
-
s
q
u
a
r
e
;
*t
-
t
e
st
v
a
l
u
e
2
.
3
.
M
ea
s
ure
T
h
e
tr
ig
o
n
o
m
etr
y
in
ter
est
in
v
en
to
r
y
(
T
I
I
)
,
wh
ich
t
h
e
r
esea
r
ch
er
s
ad
ap
te
d
f
r
o
m
Sn
o
w
[
39
]
m
ath
’s
in
ter
est
in
v
en
to
r
y
,
was
u
s
ed
t
o
g
ath
er
d
ata.
T
h
e
T
I
I
co
n
s
is
t
s
o
f
2
0
item
s
an
d
u
s
es
a
4
-
p
o
in
t
L
ik
er
t
-
ty
p
e
s
ca
le
with
r
esp
o
n
s
e
o
p
tio
n
s
:
s
tr
o
n
g
ly
ag
r
ee
(
4
)
,
a
g
r
ee
(
3
)
,
d
is
ag
r
ee
(
2
)
,
an
d
s
tr
o
n
g
ly
d
is
ag
r
ee
(
1
)
.
T
h
r
ee
r
esear
ch
p
r
o
f
ess
io
n
als
v
alid
ated
th
e
T
I
I
:
o
n
e
ex
p
er
t
in
m
ea
s
u
r
e
m
en
t
an
d
ev
alu
atio
n
an
d
two
ex
p
e
r
ts
in
m
ath
em
atics
ed
u
ca
tio
n
.
T
h
ese
ex
p
er
ts
r
ev
i
ewe
d
th
e
T
I
I
item
s
f
o
r
t
h
eir
p
h
r
asin
g
,
r
ele
v
an
ce
to
th
e
r
esear
ch
o
b
jectiv
es,
q
u
ality
,
an
d
lan
g
u
ag
e.
B
ased
o
n
th
eir
f
ee
d
b
ac
k
,
m
o
d
i
f
icatio
n
s
wer
e
m
ad
e
to
th
e
T
I
I
.
T
o
ass
ess
th
e
T
I
I
’
s
in
ter
n
al
co
n
s
is
ten
cy
r
eliab
ilit
y
,
tr
ial
test
in
g
was
co
n
d
u
cted
b
y
d
is
tr
ib
u
tin
g
c
o
p
ies
to
a
s
im
ilar
g
r
o
u
p
o
f
SS
2
s
tu
d
en
ts
in
a
d
if
f
er
en
t
a
r
ea
.
T
h
is
was
d
o
n
e
to
d
eter
m
in
e
h
o
w
r
eliab
le
th
e
item
s
wer
e.
T
h
e
d
ata
g
ath
e
r
ed
f
r
o
m
th
e
ad
m
in
is
tr
atio
n
o
f
th
e
p
ilo
t
test
in
g
was
ex
am
in
ed
u
s
in
g
C
r
o
n
b
ac
h
’
s
a
lp
h
a
m
eth
o
d
,
wh
ich
p
r
o
d
u
ce
d
an
in
ter
n
al
co
n
s
is
ten
cy
r
eliab
ilit
y
in
d
ex
o
f
.
8
5
.
2
.
4
.
P
r
o
ce
du
re
T
h
e
Po
s
t
Pr
im
ar
y
M
a
n
a
g
e
m
e
n
t
B
o
a
r
d
,
U
d
e
n
u
Z
o
n
a
l
o
f
f
ic
e
,
E
n
u
g
u
St
ate
,
g
r
a
n
te
d
a
p
p
r
o
v
al
f
o
r
th
e
s
tu
d
y
o
n
Oct
o
b
e
r
1
3
,
2
0
2
2
,
u
n
d
er
r
ef
er
e
n
ce
n
u
m
b
er
R
E
C
/PP
SMB
/2
2
/
0
0
3
5
4
.
T
h
e
r
es
ea
r
c
h
e
r
s
v
is
it
e
d
t
h
e
s
ch
o
o
ls
i
n
v
o
lv
ed
in
t
h
e
s
tu
d
y
t
o
f
o
r
m
all
y
o
b
t
ai
n
p
e
r
m
is
s
io
n
f
r
o
m
t
h
e
s
c
h
o
o
l
h
e
ad
s
b
e
f
o
r
e
s
ta
r
ti
n
g
t
h
e
in
v
est
ig
ati
o
n
.
T
h
e
s
t
u
d
y
was
ap
p
r
o
v
ed
b
y
th
e
p
r
in
ci
p
a
ls
o
f
th
e
s
c
h
o
o
ls
ch
o
s
en
.
T
h
e
p
a
r
en
ts
,
s
tu
d
e
n
ts
,
a
n
d
in
s
t
r
u
ct
o
r
s
c
o
n
s
e
n
t
e
d
t
o
p
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ti
ci
p
at
e
as t
h
e
y
we
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p
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i
d
ed
wit
h
i
n
f
o
r
m
e
d
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n
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t f
o
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m
s
t
o
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o
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l
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d
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t
o
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m
t
h
e
ir
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n
s
en
t
to
p
ar
t
ic
ip
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te
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h
e
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ea
r
c
h
ass
is
ta
n
ts
f
o
r
th
e
s
t
u
d
y
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er
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t
h
e
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o
r
m
al
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u
ct
o
r
s
at
th
e
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h
o
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n
s
c
h
o
o
ls
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On
e
w
ee
k
o
f
tr
ai
n
i
n
g
o
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a
p
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ly
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g
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d
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ea
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h
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n
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t
r
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g
o
n
o
m
e
tr
y
co
n
c
ep
ts
(
t
r
i
g
o
n
o
m
e
tr
ic
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n
cti
o
n
s
a
n
d
t
h
e
ir
v
al
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es
i
n
d
e
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r
ee
[
s
in
,
c
o
s
,
t
an
,
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t,
co
s
ec
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a
n
d
s
e
c]
)
u
s
i
n
g
t
h
e
g
a
m
e
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b
as
ed
a
p
p
r
o
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ch
was
d
el
iv
e
r
e
d
b
y
t
h
e
r
ese
a
r
c
h
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s
.
Ma
t
h
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m
at
ics
te
ac
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r
s
in
b
o
th
t
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e
e
x
p
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im
e
n
ta
l
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o
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p
s
we
r
e
p
r
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v
i
d
e
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wit
h
l
ess
o
n
p
la
n
s
a
n
d
n
o
tes
as
r
eso
u
r
c
es.
T
h
e
l
ess
o
n
p
l
an
f
o
r
th
e
e
x
p
er
im
en
tal
g
r
o
u
p
was
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esi
g
n
e
d
t
o
in
c
o
r
p
o
r
a
te
g
a
m
e
-
b
as
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lea
r
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i
n
g
a
n
d
in
cl
u
d
e
d
a
cti
v
i
ties
f
e
at
u
r
in
g
t
h
e
“
h
a
n
d
t
r
ic
k
”
g
am
e
a
n
d
t
h
e
b
o
a
r
d
g
am
e
“tr
ig
-
c
o
n
q
u
est
,
”
cr
ea
t
e
d
b
y
D
u
e
ñ
as
et
a
l
.
[
40
]
.
T
h
e
c
o
n
tr
o
l
g
r
o
u
p
’
s
less
o
n
p
la
n
a
n
d
n
o
te
was
d
e
v
el
o
p
e
d
u
s
i
n
g
th
e
c
o
n
v
en
ti
o
n
al
a
p
p
r
o
a
ch
.
P
r
i
o
r
t
o
b
e
g
i
n
n
i
n
g
th
e
ac
t
u
a
l
t
r
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a
tm
e
n
t
,
t
h
e
SS
2
l
ea
r
n
e
r
s
t
o
o
k
a
p
r
e
-
T
I
I
(
T
im
e
1
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
v
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&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
F
o
s
teri
n
g
s
tu
d
en
ts
’
in
teres
t in
tr
ig
o
n
o
metry
u
s
in
g
g
a
me
-
b
a
s
e
d
lea
r
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in
g
s
tr
a
teg
y
…
(
F
elix
Oro
men
a
E
g
a
r
a
)
3977
T
h
e
en
ti
r
e
c
o
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r
s
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at
m
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n
t
t
o
o
k
f
o
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r
w
ee
k
s
to
c
o
m
p
let
e.
T
h
e
ad
m
i
n
is
tr
ati
o
n
o
f
t
h
e
p
o
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t
-
T
I
I
t
est
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o
o
k
p
lac
e
d
u
r
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e
f
i
f
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h
w
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k
(
T
im
e
2
)
.
B
e
f
o
r
e
b
e
in
g
u
s
ed
i
n
t
h
e
p
o
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t
-
T
I
I
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e
p
r
e
-
T
I
I
i
te
m
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d
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t
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ite
m
s
a
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esh
l
o
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it
h
o
u
t
c
h
a
n
g
i
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g
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h
e
ir
c
o
n
te
n
ts
.
T
h
e
p
o
s
t
-
test
r
es
u
lts
we
r
e
n
o
te
d
a
n
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s
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d
to
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ese
n
t
in
f
o
r
m
at
io
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n
s
t
u
d
e
n
ts
’
p
e
r
f
o
r
m
an
ce
o
f
t
h
e
t
r
i
g
o
n
o
m
et
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ic
c
o
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c
ep
t
b
y
g
en
d
e
r
an
d
tr
ea
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m
e
n
t
g
r
o
u
p
.
F
o
u
r
we
e
k
s
late
r
,
t
h
e
p
o
s
t
-
T
I
I
ite
m
s
we
r
e
also
r
ea
r
r
a
n
g
e
d
i
n
p
r
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p
a
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ati
o
n
f
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r
th
e
f
o
ll
o
w
-
u
p
tes
t
(
T
i
m
e
3
)
.
Da
ta
o
n
s
t
u
d
e
n
ts
’
in
t
er
ests
,
ca
t
eg
o
r
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en
d
e
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d
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atm
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g
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p
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as
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lect
e
d
b
as
ed
o
n
t
h
e
f
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ll
o
w
-
u
p
f
in
d
i
n
g
s
.
2
.
5
.
Da
t
a
a
na
ly
s
is
T
h
e
d
ata
was
an
aly
ze
d
u
s
in
g
v
er
s
io
n
2
8
o
f
th
e
s
tatis
tical
p
ac
k
ag
e
f
o
r
th
e
s
o
cial
s
cien
ce
s
(
SP
SS
)
s
o
f
twar
e.
A
2
x
3
m
ix
ed
d
esig
n
was
em
p
lo
y
ed
f
o
r
th
e
an
al
y
s
is
,
with
g
r
o
u
p
(
ex
p
e
r
im
en
ta
l
v
s
.
co
n
tr
o
l
)
as
th
e
b
etwe
en
-
g
r
o
u
p
s
f
ac
to
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an
d
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im
e
(
p
r
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-
T
I
I
,
p
o
s
t
-
T
I
I
,
an
d
f
o
llo
w
-
up
-
T
I
I
)
as
th
e
with
in
-
g
r
o
u
p
s
f
ac
to
r
.
I
n
p
ar
ticu
lar
,
th
e
s
tu
d
y
q
u
esti
o
n
s
wer
e
an
s
wer
ed
u
s
in
g
th
e
m
ea
n
an
d
s
tan
d
a
r
d
d
e
v
iatio
n
,
a
n
d
th
e
h
y
p
o
th
esis
was
test
ed
u
s
in
g
th
e
F
-
test
o
f
r
ep
ea
ted
m
ea
s
u
r
es
ANOVA
.
Ma
u
ch
ly
’
s
test
o
f
s
p
h
er
icity
was
n
o
t
s
ig
n
if
ican
t
f
o
r
th
e
r
ep
ea
ted
m
ea
s
u
r
e
m
en
t
ass
u
m
p
tio
n
in
th
e
ANOV
A;
Ma
u
ch
ly
W
=.
8
7
3
,
p
=
.
0
7
2
.
A
r
ep
ea
te
d
-
m
ea
s
u
r
es
ANOV
A
is
p
r
ed
icate
d
o
n
t
h
e
s
p
h
er
icity
ass
u
m
p
tio
n
.
Acc
o
r
d
i
n
g
to
s
ta
n
d
ar
d
g
u
id
elin
es,
an
ef
f
ec
t
s
ize
g
r
ea
ter
th
an
.
0
1
is
co
n
s
id
er
ed
s
m
all,
g
r
ea
ter
th
an
.
0
6
is
m
ed
iu
m
,
an
d
g
r
ea
ter
t
h
a
n
.
1
4
is
lar
g
e
[
41
].
3.
RE
SU
L
T
S
T
ab
le
2
s
h
o
ws
th
at
s
tu
d
en
ts
wh
o
p
ar
ticip
ated
in
th
e
g
am
e
-
b
ased
lear
n
in
g
ap
p
r
o
ac
h
h
ad
a
p
r
e
-
test
m
ea
n
s
co
r
e
o
f
5
5
.
0
7
(
SD
=8
.
1
9
)
,
a
p
o
s
t
-
test
m
ea
n
s
co
r
e
o
f
6
2
.
1
5
(
SD
=6
.
5
6
)
,
an
d
a
f
o
llo
w
-
u
p
m
ea
n
s
co
r
e
o
f
7
0
.
8
9
(
SD
=4
.
9
3
)
.
I
n
co
n
tr
ast,
s
tu
d
en
ts
wh
o
wer
e
tau
g
h
t
u
s
in
g
th
e
co
n
v
en
tio
n
al
ap
p
r
o
ac
h
h
ad
a
p
r
e
-
test
m
ea
n
s
co
r
e
o
f
5
5
.
3
4
(
SD
=
5
.
4
3
)
,
a
p
o
s
t
-
test
m
ea
n
s
co
r
e
o
f
5
8
.
6
2
(
SD
=4
.
9
5
)
,
an
d
a
f
o
llo
w
-
u
p
m
ea
n
s
co
r
e
o
f
5
7
.
2
4
(
SD
=6
.
4
9
)
.
T
h
e
an
aly
s
is
o
f
s
ec
o
n
d
ar
y
s
ch
o
o
l
s
tu
d
en
ts
’
in
ter
est
in
tr
ig
o
n
o
m
etr
y
,
c
o
r
r
ec
ted
u
s
in
g
th
e
Gr
ee
n
h
o
u
s
e
-
Geiss
er
m
eth
o
d
,
r
ev
ea
led
s
ig
n
if
ican
t
ef
f
ec
ts
.
T
h
er
e
was
a
n
o
tab
le
im
p
ac
t
o
f
th
e
g
r
o
u
p
(
G)
[
F
(
1
,
5
4
)
=2
7
.
4
2
9
,
p
<.
0
0
1
,
η
2
p
=.
3
3
7
]
,
tim
e
(
T
)
[
F(
1
.
7
7
4
,
9
5
.
8
0
)
=7
8
.
5
3
9
,
p
<
.
0
0
1
,
η
2
p
=.
5
9
3
]
,
an
d
th
e
in
ter
ac
tio
n
b
etwe
en
tim
e
an
d
g
r
o
u
p
(
G
x
T
)
[
F
(
1
.
7
7
4
,
9
5
.
8
0
)
=4
2
.
0
8
6
,
p
<.
0
0
1
,
η
2
p
=.
4
3
8
]
,
as
p
r
esen
te
d
in
Fig
u
r
e
1
.
T
h
e
u
n
iv
ar
iate
an
aly
s
is
o
f
in
ter
est
s
co
r
es
s
h
o
wed
th
at
th
e
ef
f
ec
t
o
f
th
e
g
am
e
-
b
ased
lear
n
i
n
g
ap
p
r
o
ac
h
o
n
s
tu
d
en
ts
’
tr
ig
o
n
o
m
et
r
y
i
n
ter
est
in
t
h
e
e
x
p
er
im
en
tal
g
r
o
u
p
was
co
n
s
is
ten
tly
s
tr
o
n
g
[
F(
1
,
5
3
)
=
4
7
.
6
5
8
,
p
<
.
0
0
1
,
η
2
p
=.
4
8
5
,
∆
R
2
=.
4
6
6
]
.
T
h
er
e
f
o
r
e,
th
e
h
y
p
o
th
esis
is
r
ejec
ted
.
T
ab
le
2
.
R
esu
lts
o
f
r
ep
ea
ted
m
ea
s
u
r
es AN
OVA
f
o
r
th
e
s
tu
d
y
o
u
tco
m
es (
ef
f
ec
ts
o
f
g
r
o
u
p
,
ti
m
e,
an
d
tim
e
by
g
r
o
u
p
in
ter
ac
tio
n
)
V
a
r
i
a
b
l
e
s
(
TI
I
)
G
a
me
-
b
a
se
d
C
o
n
t
r
o
l
g
r
o
u
p
ANOVA
M
SD
M
SD
Ef
f
e
c
t
F
-
r
a
t
i
o
Df
η
p
2
9
5
%C
I
Ti
me
1
5
5
.
0
7
8
.
1
9
5
5
.
3
4
5
.
4
3
G
2
7
.
4
2
9
*
1
,
5
4
3
3
7
[
5
3
.
3
6
,
5
7
.
0
6
]
Ti
me
2
6
7
.
1
5
6
.
5
6
5
8
.
6
2
4
.
9
5
T
7
8
.
5
3
9
*
1
.
7
7
4
,
9
5
.
8
0
.
5
9
3
[
6
1
.
3
4
,
6
4
.
4
3
]
Ti
me
3
7
0
.
8
9
4
.
9
3
5
7
.
2
4
6
.
4
9
G
x
T
4
2
.
0
8
6
*
1
.
7
7
4
,
9
5
.
8
0
.
4
3
8
[
6
2
.
5
1
,
6
5
.
6
2
]
N
o
t
e
:
M
=
m
e
a
n
;
S
D
=
st
a
n
d
a
r
d
d
e
v
i
a
t
i
o
n
;
C
I
=
c
o
n
f
i
d
e
n
c
e
i
n
t
e
r
v
a
l
;
ɳ
P
2
=
e
f
f
e
c
t
si
z
e
;
*
p
<
.
0
0
1
Fig
u
r
e
1
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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
.
5
,
Octo
b
er
20
25
:
3
9
7
3
-
3982
3978
T
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T
ab
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3
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An
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4.
DIS
CU
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ased
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ter
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tr
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r
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ev
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wh
o
lear
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e
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etr
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g
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e
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ased
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d
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tio
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d
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.
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e
f
ir
s
t
h
y
p
o
th
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was
te
s
ted
,
an
d
th
e
r
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lts
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h
o
wed
th
at
s
tu
d
en
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in
th
e
ex
p
er
im
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tal
g
r
o
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ig
h
er
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ter
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th
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at
h
em
atica
l
co
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ce
p
t
t
h
an
t
h
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co
u
n
ter
p
a
r
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in
th
e
co
n
tr
o
l
g
r
o
u
p
.
T
h
is
d
e
m
o
n
s
t
r
ates
th
at
th
e
g
am
e
-
b
ased
le
ar
n
in
g
s
tr
ateg
y
e
f
f
ec
tiv
ely
in
cr
ea
s
ed
s
tu
d
en
ts
’
in
ter
est
in
tr
ig
o
n
o
m
etr
y
.
On
e
r
ea
s
o
n
f
o
r
th
e
s
u
cc
ess
o
f
g
a
m
e
-
b
ased
lear
n
in
g
co
u
ld
b
e
i
ts
ab
ilit
y
to
en
g
ag
e
s
tu
d
en
ts
ac
tiv
ely
in
th
e
lear
n
in
g
p
r
o
ce
s
s
.
Gam
es
o
f
ten
i
n
clu
d
e
elem
en
ts
s
u
ch
as
im
m
ed
iate
f
ee
d
b
ac
k
,
r
ewa
r
d
s
,
an
d
a
s
en
s
e
o
f
a
cc
o
m
p
lis
h
m
en
t,
wh
ich
ca
n
m
o
tiv
ate
s
tu
d
en
ts
an
d
m
ain
tain
th
eir
in
ter
est.
Ad
d
itio
n
ally
,
th
e
in
ter
ac
tiv
e
n
atu
r
e
o
f
g
a
m
es
en
co
u
r
a
g
es
s
tu
d
en
t
p
ar
ticip
atio
n
an
d
co
llab
o
r
atio
n
,
m
ak
in
g
lear
n
in
g
m
o
r
e
d
y
n
am
ic
a
n
d
e
n
jo
y
ab
le.
T
h
ese
elem
en
ts
lik
e
ly
co
n
tr
ib
u
ted
to
t
h
e
h
eig
h
ten
ed
in
ter
est
o
b
s
er
v
e
d
in
th
e
ex
p
er
im
e
n
tal
g
r
o
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p
.
T
h
is
f
in
d
in
g
is
co
n
s
is
ten
t
with
p
r
ev
i
o
u
s
s
tu
d
ies
[
26
]
–
[
30
]
,
wh
ich
r
ep
o
r
ted
th
at
g
am
e
-
b
ased
lear
n
in
g
is
an
e
f
f
e
ctiv
e
s
tr
ateg
y
f
o
r
in
cr
ea
s
in
g
s
t
u
d
en
ts
’
in
ter
est in
m
ath
e
m
atica
l c
o
n
ce
p
ts
.
Mo
r
eo
v
er
,
th
e
r
esu
lts
in
d
icate
d
th
at
g
en
d
er
,
a
g
e,
an
d
lo
ca
tio
n
d
id
n
o
t
s
ig
n
if
ican
tl
y
af
f
ec
t
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
g
a
m
e
-
b
a
s
ed
lear
n
in
g
ap
p
r
o
ac
h
in
f
o
s
ter
in
g
s
tu
d
en
ts
’
in
ter
est
in
tr
ig
o
n
o
m
et
r
y
.
T
h
is
s
u
g
g
ests
th
at
th
e
in
cr
ea
s
e
in
i
n
ter
est
was
u
n
if
o
r
m
l
y
d
is
tr
ib
u
ted
ac
r
o
s
s
d
if
f
er
en
t
d
em
o
g
r
a
p
h
ics.
T
h
e
lac
k
o
f
s
ig
n
if
ican
t
g
en
d
er
d
i
f
f
er
en
ce
s
co
u
ld
b
e
attr
ib
u
ted
to
th
e
p
o
s
itiv
e
in
f
lu
e
n
ce
o
f
th
e
g
am
e
ac
tiv
ities
o
n
tr
ig
o
n
o
m
et
r
y
i
n
s
tr
u
ctio
n
,
lea
d
in
g
t
o
in
c
r
ea
s
ed
in
te
r
est
am
o
n
g
b
o
th
m
ale
an
d
f
em
ale
s
tu
d
en
ts
.
T
h
e
ac
tiv
e
in
v
o
lv
em
e
n
t
an
d
p
ar
ticip
atio
n
in
g
am
e
-
b
ased
ac
tiv
ities
lik
ely
co
n
tr
ib
u
ted
to
t
h
is
o
u
tco
m
e,
co
r
r
o
b
o
r
atin
g
th
e
f
in
d
in
g
s
o
f
E
ze
u
g
wu
et
a
l
.
[
30
]
,
wh
o
r
ep
o
r
ted
n
o
d
if
f
er
e
n
c
es
in
in
ter
est
b
etwe
en
m
ale
a
n
d
f
em
ale
s
tu
d
en
ts
wh
en
u
s
in
g
g
am
e
-
b
ased
i
n
s
tr
u
ctio
n
al
s
tr
ateg
ies.
T
h
e
ef
f
ec
tiv
en
ess
o
f
g
am
e
-
b
ased
lear
n
in
g
ca
n
b
e
f
u
r
th
er
u
n
d
er
s
to
o
d
b
y
ex
am
i
n
in
g
t
h
e
s
p
ec
if
ic
m
ec
h
an
is
m
s
at
p
lay
.
C
o
g
n
iti
v
e
en
g
a
g
em
en
t
is
h
eig
h
te
n
ed
th
r
o
u
g
h
p
r
o
b
lem
-
s
o
lv
in
g
tas
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d
c
h
allen
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es
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
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2252
-
8
8
2
2
F
o
s
teri
n
g
s
tu
d
en
ts
’
in
teres
t in
tr
ig
o
n
o
metry
u
s
in
g
g
a
me
-
b
a
s
e
d
lea
r
n
in
g
s
tr
a
teg
y
…
(
F
elix
Oro
men
a
E
g
a
r
a
)
3979
with
in
g
am
es,
r
eq
u
ir
i
n
g
s
tu
d
e
n
ts
to
ap
p
ly
t
h
eir
k
n
o
wled
g
e
ac
tiv
ely
[
18
]
.
E
m
o
tio
n
al
in
v
o
lv
em
en
t
is
f
o
s
ter
ed
th
r
o
u
g
h
th
e
im
m
er
s
iv
e
an
d
en
jo
y
ab
le
n
atu
r
e
o
f
g
am
es,
wh
i
ch
ca
n
r
ed
u
ce
an
x
iety
a
n
d
m
a
k
e
lear
n
in
g
a
m
o
r
e
p
o
s
itiv
e
ex
p
er
ie
n
ce
[
42
]
.
So
cial
in
ter
ac
tio
n
with
in
g
am
es
p
r
o
m
o
tes
co
llab
o
r
atio
n
a
n
d
c
o
m
m
u
n
icatio
n
a
m
o
n
g
s
tu
d
en
ts
,
en
h
a
n
cin
g
th
eir
co
llectiv
e
lear
n
in
g
ex
p
er
ien
ce
[
43
]
.
T
h
ese
c
o
m
b
in
ed
elem
e
n
ts
cr
ea
te
a
r
ich
,
m
u
ltifa
ce
ted
lear
n
in
g
en
v
ir
o
n
m
en
t
th
at
tr
ad
itio
n
al
m
eth
o
d
s
m
ay
lack
.
Ad
d
itio
n
ally
,
g
am
es
o
f
ten
p
r
o
v
id
e
a
s
af
e
s
p
ac
e
f
o
r
t
r
ial
an
d
er
r
o
r
,
allo
win
g
s
tu
d
en
ts
t
o
e
x
p
er
im
e
n
t
with
o
u
t
th
e
f
ea
r
o
f
f
ailu
r
e
,
f
u
r
th
er
s
o
lid
if
y
in
g
th
eir
u
n
d
e
r
s
tan
d
in
g
a
n
d
in
te
r
e
s
t in
th
e
s
u
b
ject
m
atter
.
4
.
1
.
Co
m
pa
riso
n
wit
h pre
v
io
us
s
t
ud
ie
s
Ou
r
s
tu
d
y
b
u
ild
s
u
p
o
n
th
e
f
in
d
in
g
s
o
f
s
ev
er
al
r
esear
c
h
er
s
w
h
o
h
a
v
e
in
v
esti
g
ated
th
e
e
f
f
ec
tiv
en
ess
o
f
g
am
e
-
b
ased
lear
n
i
n
g
s
tr
ateg
ies
in
en
h
an
cin
g
s
tu
d
en
ts
’
in
ter
est
in
m
ath
em
atics
.
B
h
ad
awk
ar
an
d
Gu
p
ta
[
26
]
f
o
u
n
d
th
at
elem
en
tar
y
s
ch
o
o
l
s
tu
d
en
ts
in
I
n
d
ia
d
em
o
n
s
tr
ate
d
in
cr
ea
s
ed
in
ter
est
in
m
at
h
e
m
atics
wh
en
ex
p
o
s
ed
to
g
am
e
-
b
ased
lear
n
i
n
g
,
s
im
il
ar
to
o
u
r
f
in
d
in
g
s
am
o
n
g
s
ec
o
n
d
ar
y
s
ch
o
o
l
s
tu
d
en
ts
in
E
n
u
g
u
State,
Nig
e
r
ia.
Similar
ly
,
r
esear
ch
b
y
Yeh
et
a
l
.
[
27
]
,
o
b
s
er
v
ed
im
p
r
o
v
ed
m
ath
em
atics
in
ter
est
am
o
n
g
ele
m
en
tar
y
s
tu
d
e
n
ts
in
T
aiwa
n
u
s
in
g
g
am
e
-
b
ased
lea
r
n
in
g
en
v
ir
o
n
m
en
ts
,
s
u
p
p
o
r
ti
n
g
o
u
r
r
esu
lts
with
s
ec
o
n
d
ar
y
s
ch
o
o
l
s
tu
d
en
ts
in
E
n
u
g
u
State,
Nig
er
ia.
R
esear
ch
b
y
Fre
d
er
ick
-
J
o
n
ah
an
d
I
g
b
o
jin
wae
k
wu
[
28
]
r
ep
o
r
ted
s
ig
n
if
ica
n
t
im
p
r
o
v
em
e
n
ts
in
p
r
im
ar
y
s
tu
d
en
ts
’
m
ath
em
atics
in
ter
est
in
B
ay
elsa
S
tate,
Nig
er
ia,
th
r
o
u
g
h
g
am
e
-
e
n
h
an
ce
d
in
s
tr
u
ctio
n
al
s
tr
ateg
ies,
m
ir
r
o
r
in
g
o
u
r
f
in
d
in
g
s
in
a
s
ec
o
n
d
a
r
y
s
ch
o
o
l
co
n
tex
t.
I
n
A
b
u
ja
N
ig
er
ia,
r
esear
ch
b
y
Su
m
b
ab
i
a
n
d
B
ass
ey
[
29
]
,
d
is
co
v
er
ed
th
at
m
at
h
em
atica
l
g
am
es
a
n
d
s
im
u
latio
n
s
s
ig
n
if
ican
tly
b
o
o
s
ted
g
eo
m
etr
y
in
ter
est
am
o
n
g
s
ec
o
n
d
ar
y
s
ch
o
o
l
s
tu
d
e
n
ts
,
alig
n
in
g
with
o
u
r
o
b
s
er
v
atio
n
s
o
n
tr
i
g
o
n
o
m
etr
y
in
te
r
est
in
E
n
u
g
u
State.
R
esear
ch
b
y
E
ze
u
g
wu
et
a
l
.
[
30
]
h
ig
h
li
g
h
t
ed
th
e
ef
f
ec
tiv
en
ess
o
f
g
am
e
-
b
ased
in
s
tr
u
ctio
n
al
ap
p
r
o
ac
h
es
in
en
h
a
n
cin
g
al
g
e
b
r
a
in
ter
est
am
o
n
g
ju
n
io
r
s
ec
o
n
d
ar
y
s
ch
o
o
l
s
tu
d
e
n
ts
in
R
iv
er
State,
Nig
er
ia,
co
n
s
is
ten
t w
ith
o
u
r
f
in
d
in
g
s
o
n
tr
ig
o
n
o
m
etr
y
in
ter
est.
4
.
2
.
P
r
a
ct
ica
l/
em
pirica
l c
o
ntr
ibu
t
io
n
Ou
r
s
tu
d
y
p
r
o
v
id
es
em
p
ir
ical
ev
id
en
c
e
th
at
g
am
e
-
b
ased
le
ar
n
in
g
ca
n
ef
f
ec
tiv
ely
en
h
an
c
e
s
tu
d
en
ts
’
in
ter
est
in
m
ath
em
atics,
s
p
e
cif
ically
tr
ig
o
n
o
m
etr
y
,
ac
r
o
s
s
d
iv
er
s
e
ed
u
ca
tio
n
al
co
n
tex
ts
in
Nig
er
ia.
T
h
is
s
u
p
p
o
r
ts
p
r
ac
tical
im
p
licatio
n
s
f
o
r
ed
u
ca
to
r
s
aim
in
g
to
f
o
s
ter
en
g
ag
em
e
n
t
an
d
m
o
tiv
atio
n
in
m
ath
em
atics
th
r
o
u
g
h
i
n
ter
ac
tiv
e
a
n
d
im
m
er
s
iv
e
lear
n
in
g
ex
p
er
ien
ce
s
.
T
h
e
f
in
d
in
g
s
u
n
d
e
r
s
co
r
e
t
h
e
p
r
ac
tical
v
alu
e
o
f
in
teg
r
atin
g
g
am
e
-
b
ased
elem
e
n
ts
in
to
m
ath
em
atics
ed
u
ca
tio
n
,
alig
n
in
g
with
th
e
o
b
s
er
v
ed
b
en
ef
its
in
v
ar
io
u
s
d
em
o
g
r
a
p
h
ic
g
r
o
u
p
s
an
d
e
d
u
c
atio
n
al
s
ettin
g
s
.
4
.
3
.
T
heo
re
t
ica
l
c
o
ntr
ibu
t
io
n
Ou
r
r
esear
ch
co
n
tr
ib
u
tes
to
th
e
th
eo
r
etica
l
u
n
d
er
s
tan
d
in
g
o
f
g
am
e
-
b
ased
lear
n
in
g
’
s
im
p
ac
t
o
n
s
tu
d
en
t
in
ter
est
in
m
ath
em
atic
s
b
y
v
alid
atin
g
its
ef
f
ec
tiv
en
e
s
s
ac
r
o
s
s
d
if
f
er
en
t
e
d
u
ca
tio
n
al
en
v
ir
o
n
m
en
ts
a
n
d
d
em
o
g
r
a
p
h
ic
f
ac
to
r
s
in
Nig
er
ia.
T
h
is
ex
ten
d
s
th
e
th
eo
r
etica
l
f
r
am
ewo
r
k
b
y
d
em
o
n
s
tr
atin
g
co
n
s
is
ten
t
o
u
tco
m
es
in
en
h
a
n
cin
g
m
o
tiv
atio
n
an
d
en
g
a
g
em
en
t
th
r
o
u
g
h
in
ter
ac
tiv
e
lear
n
in
g
m
eth
o
d
s
.
T
h
e
s
tu
d
y
s
u
p
p
o
r
ts
s
o
cial
lear
n
in
g
t
h
eo
r
y
’
s
p
r
in
c
ip
les
o
f
atten
tio
n
,
r
eten
tio
n
,
r
ep
r
o
d
u
ctio
n
,
an
d
m
o
tiv
atio
n
b
y
illu
s
tr
atin
g
h
o
w
g
am
e
-
b
ased
s
tr
ateg
ies f
ac
ilit
ate
ac
tiv
e
lear
n
in
g
an
d
k
n
o
wled
g
e
ap
p
licatio
n
i
n
m
ath
em
atics.
4
.
4
.
M
et
ho
do
lo
g
ic
a
l
c
o
ntr
ibu
t
io
n
Me
th
o
d
o
lo
g
ically
,
o
u
r
s
tu
d
y
em
p
lo
y
s
a
r
o
b
u
s
t m
ix
ed
-
b
etwe
en
an
d
with
in
m
ea
s
u
r
es AN
OVA
d
esig
n
,
allo
win
g
f
o
r
a
c
o
m
p
r
e
h
en
s
iv
e
ass
ess
m
en
t
o
f
th
e
d
if
f
e
r
en
tial
im
p
ac
t
o
f
g
am
e
-
b
ased
le
ar
n
in
g
o
n
s
tu
d
en
t
in
ter
est
o
v
er
tim
e
a
n
d
ac
r
o
s
s
g
r
o
u
p
s
.
T
h
is
m
eth
o
d
o
lo
g
ical
ap
p
r
o
ac
h
co
n
tr
ib
u
tes
to
th
e
lit
er
atu
r
e
b
y
o
f
f
er
in
g
in
s
ig
h
ts
in
to
ef
f
ec
tiv
e
ed
u
ca
t
io
n
al
in
ter
v
en
tio
n
s
th
at
ca
n
b
e
ad
ap
ted
to
d
iv
e
r
s
e
ed
u
ca
t
io
n
al
co
n
tex
ts
an
d
s
tu
d
en
t
p
o
p
u
latio
n
s
.
T
h
e
b
o
r
d
er
im
p
licatio
n
s
o
f
th
ese
f
in
d
in
g
s
ex
ten
d
b
e
y
o
n
d
im
m
ed
iate
in
ter
est
in
tr
ig
o
n
o
m
et
r
y
.
I
n
teg
r
atin
g
g
a
m
e
-
b
ased
lear
n
in
g
in
to
v
ar
i
o
u
s
ed
u
ca
tio
n
al
co
n
tex
ts
co
u
ld
en
h
an
ce
s
tu
d
en
t
en
g
ag
em
e
n
t
ac
r
o
s
s
s
u
b
jects.
Fo
r
in
s
tan
ce
,
s
im
ilar
s
tr
ateg
ies
co
u
ld
b
e
a
p
p
lied
to
o
th
er
c
h
allen
g
in
g
s
u
b
jects,
p
o
ten
tially
im
p
r
o
v
in
g
o
v
e
r
all
ac
ad
em
ic
p
er
f
o
r
m
an
c
e,
an
d
f
o
s
ter
in
g
a
m
o
r
e
p
o
s
itiv
e
attitu
d
e
to
war
d
s
lear
n
in
g
.
T
h
is
ap
p
r
o
ac
h
is
in
lin
e
with
m
o
d
er
n
ed
u
ca
tio
n
al
p
r
ac
tice
s
th
at
f
o
cu
s
o
n
s
tu
d
en
t
-
ce
n
ter
ed
lear
n
in
g
an
d
th
e
cu
ltiv
atio
n
o
f
2
1
s
t
-
ce
n
tu
r
y
s
k
ills
lik
e
cr
itical
th
in
k
in
g
,
c
r
ea
tiv
ity
,
an
d
c
o
llab
o
r
atio
n
.
Ad
d
itio
n
ally
,
u
s
in
g
g
am
e
-
b
ased
lear
n
in
g
s
tr
ateg
i
es
ca
n
ac
co
m
m
o
d
ate
v
ar
i
o
u
s
lear
n
in
g
s
ty
les
an
d
n
ee
d
s
,
th
er
eb
y
m
ak
in
g
ed
u
ca
tio
n
m
o
r
e
in
clu
s
iv
e
a
n
d
ac
ce
s
s
ib
le
to
all
s
tu
d
en
ts
.
5.
CO
NCLU
SI
O
N
T
h
e
g
am
e
-
b
ased
lear
n
in
g
s
tr
ateg
y
h
as
d
em
o
n
s
tr
ated
e
f
f
ec
tiv
en
ess
in
f
o
s
ter
in
g
in
ter
est
in
m
ath
em
atics
ac
r
o
s
s
v
ar
io
u
s
co
n
tex
ts
,
in
clu
d
i
n
g
tr
ig
o
n
o
m
etr
y
am
o
n
g
s
en
io
r
s
ec
o
n
d
a
r
y
s
ch
o
o
l
s
tu
d
en
ts
in
E
n
u
g
u
State,
Nig
er
ia.
Ou
r
f
in
d
in
g
s
alig
n
with
s
im
ilar
p
o
s
iti
v
e
o
u
tco
m
es
o
b
s
er
v
ed
in
d
iv
e
r
s
e
s
ettin
g
s
,
s
u
ch
a
s
elem
en
tar
y
an
d
s
ec
o
n
d
ar
y
s
ch
o
o
ls
in
Nig
er
ia,
I
n
d
ia,
a
n
d
T
ai
wan
.
I
m
p
o
r
tan
tly
,
th
is
s
tu
d
y
r
ev
ea
led
th
at
g
en
d
e
r
,
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
.
5
,
Octo
b
er
20
25
:
3
9
7
3
-
3982
3980
ag
e,
an
d
lo
ca
tio
n
d
o
n
o
t
s
ig
n
if
ican
tly
in
f
lu
en
ce
th
e
ef
f
ec
tiv
en
ess
o
f
g
am
e
-
b
ased
lear
n
in
g
in
en
h
a
n
cin
g
s
tu
d
en
ts
’
in
ter
est
in
m
ath
em
at
ics.
Ho
wev
er
,
t
h
e
s
tu
d
y
h
as
li
m
itatio
n
s
,
in
clu
d
in
g
its
f
o
cu
s
o
n
a
s
p
ec
if
ic
s
am
p
le
o
f
SS
2
s
tu
d
en
ts
in
E
n
u
g
u
S
tate,
wh
ich
m
ay
lim
it
th
e
g
e
n
er
aliza
b
ilit
y
o
f
th
e
r
esu
lts
t
o
o
th
er
r
eg
io
n
s
an
d
ed
u
ca
tio
n
al
co
n
te
x
ts
.
Fu
tu
r
e
r
esear
ch
s
h
o
u
ld
in
clu
d
e
a
b
r
o
a
d
er
r
an
g
e
o
f
p
ar
ticip
a
n
ts
f
r
o
m
d
if
f
er
en
t y
ea
r
lev
els
an
d
lo
ca
tio
n
s
,
as
well
as
p
er
f
o
r
m
an
ce
m
etr
ics
to
ass
ess
th
e
im
p
ac
t
o
n
ac
ad
em
ic
ac
h
iev
e
m
en
t.
Ad
d
itio
n
ally
,
in
v
esti
g
atin
g
th
e
lo
n
g
-
ter
m
ef
f
ec
ts
o
f
g
am
e
-
b
ased
lear
n
in
g
o
n
s
u
s
tain
ed
in
ter
est
an
d
p
er
f
o
r
m
a
n
ce
i
n
m
ath
em
atics,
s
tu
d
en
ts
’
attitu
d
es
to
war
d
s
m
ath
em
atics
in
h
ig
h
er
ed
u
ca
tio
n
,
a
n
d
th
eir
ca
r
ee
r
ch
o
ices
wo
u
l
d
p
r
o
v
id
e
v
al
u
ab
le
i
n
s
ig
h
ts
.
E
x
am
in
in
g
th
e
cu
ltu
r
al
r
elev
a
n
ce
an
d
a
d
ap
tab
ilit
y
o
f
g
am
e
-
b
ased
lear
n
in
g
in
d
if
f
er
en
t e
d
u
ca
tio
n
al
s
y
s
tem
s
g
lo
b
ally
co
u
ld
en
h
an
ce
its
ap
p
licab
ilit
y
an
d
ef
f
ec
tiv
e
n
ess
.
T
h
e
s
tu
d
y
’
s
f
in
d
i
n
g
s
h
a
v
e
s
ig
n
if
ican
t
im
p
licatio
n
s
f
o
r
e
d
u
ca
to
r
s
a
n
d
p
o
licy
m
a
k
er
s
.
I
n
teg
r
atin
g
g
am
e
-
b
ased
lear
n
i
n
g
in
to
t
h
e
cu
r
r
icu
lu
m
c
o
u
ld
e
n
h
an
ce
s
t
u
d
en
t
en
g
ag
em
en
t
a
n
d
in
ter
e
s
t
in
m
ath
em
atics,
p
o
ten
tially
im
p
r
o
v
in
g
o
v
e
r
all
ac
ad
em
ic
p
er
f
o
r
m
an
ce
.
T
o
im
p
lem
en
t
th
ese
f
in
d
in
g
s
ef
f
ec
ti
v
ely
,
m
ath
em
atics
teac
h
er
s
co
u
ld
r
ec
ei
v
e
tr
ain
in
g
o
n
i
n
co
r
p
o
r
atin
g
g
am
e
-
b
ased
lear
n
in
g
a
p
p
r
o
ac
h
es
i
n
to
th
eir
less
o
n
s
,
p
ar
ticu
lar
ly
w
h
en
teac
h
in
g
tr
ig
o
n
o
m
etr
ic
f
u
n
ctio
n
s
.
E
d
u
ca
tio
n
al
p
o
licy
m
ak
er
s
c
o
u
ld
co
n
s
id
er
in
teg
r
atin
g
g
am
e
-
b
ased
lear
n
in
g
s
tr
ateg
i
es
in
to
th
e
n
atio
n
al
m
ath
em
atics
cu
r
r
icu
lu
m
to
c
r
ea
te
a
m
o
r
e
en
g
ag
in
g
an
d
in
ter
ac
tiv
e
lear
n
in
g
en
v
ir
o
n
m
en
t.
Ad
d
itio
n
ally
,
s
ch
o
o
ls
co
u
ld
allo
ca
te
r
eso
u
r
ce
s
to
d
ev
elo
p
an
d
im
p
lem
en
t
g
am
e
-
b
ased
lear
n
in
g
to
o
ls
an
d
ac
tiv
ities
in
th
eir
m
ath
em
at
ics
p
r
o
g
r
am
s
,
in
cl
u
d
in
g
in
v
esti
n
g
in
ed
u
ca
tio
n
al
s
o
f
twar
e,
teac
h
er
tr
ain
in
g
p
r
o
g
r
am
s
,
an
d
c
r
ea
tin
g
s
p
ac
es
co
n
d
u
civ
e
t
o
in
ter
ac
tiv
e
lear
n
in
g
.
I
n
s
u
m
m
ar
y
,
we
r
ec
o
m
m
en
d
th
at
m
at
h
em
atics
teac
h
er
s
in
co
r
p
o
r
ate
th
e
g
a
m
e
-
b
ased
lear
n
i
n
g
a
p
p
r
o
ac
h
i
n
th
eir
less
o
n
s
,
an
d
th
at
th
e
g
o
v
er
n
m
en
t
an
d
r
e
lev
an
t
ed
u
ca
tio
n
al
ag
e
n
cies
h
o
s
t
s
em
in
ar
s
an
d
wo
r
k
s
h
o
p
s
to
s
u
p
p
o
r
t
th
is
im
p
lem
en
tatio
n
.
Ma
th
e
m
atics
teac
h
er
s
s
h
o
u
ld
s
elec
t
an
d
in
teg
r
ate
ap
p
r
o
p
r
iate
g
am
e
a
ctiv
ities
in
to
th
eir
less
o
n
p
lan
s
to
e
n
h
an
ce
s
tu
d
en
ts
’
in
ter
est
in
m
ath
em
atics,
u
ltima
tely
im
p
r
o
v
i
n
g
t
h
eir
p
er
f
o
r
m
a
n
ce
in
th
e
s
u
b
ject.
ACK
NO
WL
E
DG
M
E
N
T
S
T
h
e
au
th
o
r
s
ex
p
r
ess
th
eir
s
in
ce
r
e
g
r
atitu
d
e
to
all
p
ar
ticip
a
n
ts
wh
o
g
en
er
o
u
s
ly
co
n
tr
ib
u
te
d
th
eir
tim
e
an
d
in
s
ig
h
ts
to
th
is
s
tu
d
y
.
W
e
also
g
r
atef
u
lly
ac
k
n
o
wled
g
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e
f
in
an
cial
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u
p
p
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p
r
o
v
i
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y
th
e
E
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DP
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SET
A
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esear
ch
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h
air
in
Ma
th
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ati
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E
d
u
ca
tio
n
at
th
e
Un
iv
er
s
ity
o
f
th
e
Fre
e
State,
wh
ich
m
ad
e
th
e
p
u
b
licatio
n
o
f
th
is
wo
r
k
p
o
s
s
ib
le.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
T
h
is
r
esear
ch
r
ec
eiv
ed
n
o
f
u
n
d
in
g
.
AUTHO
R
CO
NT
RI
B
UT
I
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NS ST
A
T
E
M
E
N
T
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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
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ed
iT)
to
r
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o
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n
ize
in
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iv
i
d
u
al
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th
o
r
co
n
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ip
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d
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llab
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Na
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Aut
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Felix
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o
m
en
a
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r
a
✓
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Mo
ek
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v
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tu
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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
F
o
s
teri
n
g
s
tu
d
en
ts
’
in
teres
t in
tr
ig
o
n
o
metry
u
s
in
g
g
a
me
-
b
a
s
e
d
lea
r
n
in
g
s
tr
a
teg
y
…
(
F
elix
Oro
men
a
E
g
a
r
a
)
3981
DATA AV
AI
L
AB
I
L
I
T
Y
T
h
e
d
ata
th
at
s
u
p
p
o
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t
t
h
e
f
in
d
in
g
s
o
f
th
is
s
tu
d
y
a
r
e
av
ailab
l
e
f
r
o
m
th
e
co
r
r
esp
o
n
d
in
g
a
u
th
o
r
[
FOE]
,
u
p
o
n
r
ea
s
o
n
ab
le
r
eq
u
est.
RE
F
E
R
E
NC
E
S
[
1
]
F
.
O
.
E
g
a
r
a
a
n
d
M
.
M
o
si
m
e
g
e
,
“
Ef
f
e
c
t
o
f
f
l
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p
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c
l
a
ssr
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m
l
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p
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t
h
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ma
t
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c
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c
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v
e
m
e
n
t
a
n
d
i
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r
e
s
t
a
m
o
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g
sec
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d
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s
c
h
o
o
l
st
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d
e
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t
s
,
”
E
d
u
c
a
t
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a
n
d
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n
f
o
rm
a
t
i
o
n
T
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h
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o
l
o
g
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e
s
,
v
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.
2
9
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n
o
.
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p
.
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/
s
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[
2
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L.
O
.
A
mi
n
u
a
n
d
O
.
O
.
A
k
i
n
m
e
j
i
,
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Ef
f
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t
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f
c
o
n
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t
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v
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st
b
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t
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y
o
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j
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n
i
o
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se
c
o
n
d
a
r
y
sc
h
o
o
l
st
u
d
e
n
t
s’
a
c
a
d
e
m
i
c
p
e
r
f
o
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m
a
n
c
e
i
n
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a
t
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m
a
t
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g
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t
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b
a
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M
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s
,
v
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.
4
7
,
n
o
.
2
,
p
p
.
5
8
–
6
6
,
2
0
2
2
.
[
3
]
Y
.
S
u
l
e
i
ma
n
a
n
d
A
.
H
a
mm
e
d
,
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P
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r
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e
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10
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11
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12
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.
[
13
]
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.
B
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ş
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[
14
]
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.
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[
15
]
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P
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[
16
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.
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.
D
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.
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f
[
17
]
K
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[
25
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.
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[
27
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[
28
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[
29
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[
30
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[
31
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3
7
5
8
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1
9
3
1
4
6
.
[
32
]
F
.
F
a
u
l
,
E.
Er
d
f
e
l
d
e
r
,
A
.
B
u
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r
,
a
n
d
A
.
-
G
.
L
a
n
g
,
“
S
t
a
t
i
s
t
i
c
a
l
p
o
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r
a
n
a
l
y
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w
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3
.
1
:
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st
s
f
o
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c
o
r
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l
a
t
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o
n
a
n
d
r
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g
r
e
ss
i
o
n
a
n
a
l
y
ses
,
”
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h
a
v
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o
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Re
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e
a
rch
Me
t
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s
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l
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7
5
8
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R
M
.
4
1
.
4
.
1
1
4
9
.
[
33
]
E.
Er
d
f
e
l
d
e
r
,
F
.
F
a
u
l
,
a
n
d
A
.
B
u
c
h
n
e
r
,
“
G
P
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ER
:
A
g
e
n
e
r
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l
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n
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l
y
s
i
s p
r
o
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m
,
”
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h
a
v
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o
r R
e
se
a
rc
h
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t
h
o
d
s
,
I
n
s
t
r
u
m
e
n
t
s,
a
n
d
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o
m
p
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t
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v
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l
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8
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o
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0
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3
7
5
8
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F
0
3
2
0
3
6
3
0
.
[
34
]
A
.
C
.
N
z
e
a
d
i
b
e
,
F
.
O
.
E
g
a
r
a
,
C
.
Es
e
a
d
i
,
a
n
d
J.
C
.
C
h
u
k
w
u
o
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j
i
,
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M
i
n
d
f
u
l
n
e
ss
-
b
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s
e
d
c
o
g
n
i
t
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a
p
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a
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m
a
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c
s
a
n
x
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e
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y
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mo
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g
s
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h
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a
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e
sce
n
t
s:
A
r
a
n
d
o
m
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se
d
t
r
i
a
l
,
”
J
o
u
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n
a
l
o
f
Psy
c
h
o
l
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i
s
t
s
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n
d
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n
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n
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l
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o
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0
5
5
6
3
6
5
2
3
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2
0
7
2
4
8
.
[
35
]
L.
N
.
O
n
u
i
g
b
o
,
C
.
E
sea
d
i
,
S
.
Eb
i
f
a
,
U
.
C
.
U
g
w
u
,
C
.
N
.
O
n
y
i
s
h
i
,
a
n
d
E.
K
.
O
y
e
o
k
u
,
“
Ef
f
e
c
t
o
f
r
a
t
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o
n
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l
e
m
o
t
i
v
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h
a
v
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n
d
e
p
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e
s
si
v
e
sy
m
p
t
o
ms
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mo
n
g
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n
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v
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t
y
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d
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t
s
w
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l
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n
e
ss
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n
N
i
g
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r
i
a
,
”
J
o
u
r
n
a
l
o
f
Ra
t
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l
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t
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d
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t
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h
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0
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-
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-
0
2
9
7
-
3.
[
36
]
T.
C
.
O
g
b
u
a
n
y
a
e
t
a
l
.
,
“
Ef
f
e
c
t
o
f
r
a
t
i
o
n
a
l
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e
m
o
t
i
v
e
b
e
h
a
v
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o
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t
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e
r
a
p
y
p
r
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m
o
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t
h
e
sy
m
p
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o
ms
o
f
b
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t
sy
n
d
r
o
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e
a
m
o
n
g
u
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d
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r
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d
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k
st
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n
t
s
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n
N
i
g
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r
i
a
,
”
Psy
c
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c
a
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Re
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rt
s
,
v
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l
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7
7
/
0
0
3
3
2
9
4
1
1
7
7
4
8
5
8
7
.
[
37
]
P
o
st
P
r
i
m
a
r
y
M
a
n
a
g
e
me
n
t
B
o
a
r
d
,
S
c
h
o
o
l
e
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r
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m
e
n
t
st
a
t
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st
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c
s
i
n
N
su
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k
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Ed
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c
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e
.
N
su
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k
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l
O
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U
d
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l
O
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c
e
,
O
b
o
l
l
o
-
A
f
o
r
,
2
0
2
2
.
[
38
]
M
.
S
a
g
h
a
e
i
,
“
R
a
n
d
o
m
a
l
l
o
c
a
t
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o
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s
o
f
t
w
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f
o
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p
a
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p
r
a
n
d
o
mi
z
e
d
t
r
i
a
l
s
,
”
B
MC
M
e
d
i
c
a
l
R
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M
e
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y
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v
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l
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1
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1
–
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8
-
4
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2
6
.
[
39
]
G
.
M
.
S
n
o
w
,
“
D
e
v
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l
o
p
m
e
n
t
o
f
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m
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t
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s
,
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.
S
.
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s
,
D
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me
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o
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c
k
y
,
U
n
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t
e
d
S
t
a
t
e
s
,
2011.
[
40
]
G
.
G
.
D
u
e
ñ
a
s,
J.
A
.
G
u
t
i
e
r
r
e
z
,
a
n
d
R
.
A
.
R
a
m
o
s,
“
Tr
i
g
-
C
o
n
q
u
e
s
t
:
A
g
a
m
e
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b
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se
d
l
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a
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ma
t
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st
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r
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met
r
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c
f
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o
n
s
,
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K
a
l
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n
a
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n
S
t
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Re
se
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o
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9
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o
.
1
,
p
p
.
1
–
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8
,
2
0
2
1
.
[
41
]
J.
C
o
h
e
n
,
S
t
a
t
i
st
i
c
a
l
p
o
w
e
r
a
n
a
l
y
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s
f
o
r
t
h
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b
e
h
a
v
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o
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a
l
sc
i
e
n
c
e
s
,
2
n
d
e
d
.
N
e
w
Y
o
r
k
:
A
c
a
d
e
mi
c
P
r
e
ss,
1
9
8
8
,
d
o
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:
1
0
.
4
3
2
4
/
9
7
8
0
2
0
3
7
7
1
5
8
7
.
[
42
]
E.
A
.
B
o
y
l
e
e
t
a
l
.
,
“
A
n
u
p
d
a
t
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st
e
ma
t
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l
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c
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i
mp
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c
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d
o
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c
o
mes
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o
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t
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g
a
m
e
s a
n
d
s
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o
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s
g
a
mes
,
”
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o
m
p
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t
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s a
n
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E
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c
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l
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u
.
2
0
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5
.
1
1
.
0
0
3
.
[
43
]
P
.
W
o
u
t
e
r
s
a
n
d
H
.
v
a
n
O
o
st
e
n
d
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p
,
“
A
me
t
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a
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v
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me
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,
”
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o
m
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t
e
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a
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d
E
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o
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,
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l
.
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2
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.
0
7
.
0
1
8
.
B
I
O
G
RAP
H
I
E
S O
F
AUTH
O
RS
Felix
O
r
o
m
e
n
a
Eg
a
r
a
is
a
n
e
x
p
e
rt
i
n
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e
f
ield
o
f
m
a
th
e
m
a
ti
c
s
e
d
u
c
a
ti
o
n
.
He
is
c
u
rre
n
tl
y
a
P
o
std
o
c
to
ra
l
F
e
ll
o
w
in
th
e
S
c
h
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o
f
M
a
th
e
m
a
ti
c
s,
Na
tu
ra
l
S
c
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c
e
s
a
n
d
Tec
h
n
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y
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d
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c
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th
e
F
a
c
u
lt
y
o
f
E
d
u
c
a
ti
o
n
a
t
t
h
e
Un
iv
e
r
sity
o
f
th
e
F
re
e
S
tate
,
S
o
u
t
h
Afric
a
.
His
re
se
a
rc
h
in
tere
st
in
c
lu
d
e
s
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th
n
o
m
a
th
e
m
a
ti
c
s,
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n
fo
r
m
a
ti
o
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a
n
d
c
o
m
m
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n
ica
ti
o
n
tec
h
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y
,
stu
d
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ts’
m
a
th
e
m
a
ti
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s
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c
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