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Ho
u
r
ig
an
an
d
L
ea
v
y
[
1
2
]
,
a
s
o
lid
u
n
d
er
s
tan
d
i
n
g
o
f
g
eo
m
et
r
ic
c
o
n
ce
p
ts
is
ess
en
tial
f
o
r
p
r
e
-
s
er
v
ice
p
r
im
ar
y
teac
h
er
s
to
en
h
an
ce
t
h
eir
teac
h
i
n
g
p
r
o
f
icien
c
y
an
d
en
s
u
r
e
th
eir
s
tu
d
en
ts
’
s
u
cc
ess
i
n
lear
n
in
g
g
e
o
m
etr
y
.
T
h
is
f
o
u
n
d
atio
n
al
k
n
o
wled
g
e
e
n
ab
les
teac
h
er
s
to
f
o
s
ter
a
d
ee
p
er
u
n
d
er
s
tan
d
in
g
o
f
g
eo
m
etr
y
am
o
n
g
th
eir
s
tu
d
e
n
ts
,
cu
ltiv
atin
g
th
e
a
n
aly
tic
al
s
k
ills
n
ec
ess
ar
y
f
o
r
co
m
p
lex
m
ath
em
atica
l
p
r
o
b
lem
s
[
1
3
]
,
[
1
4
]
.
T
h
e
Van
Hiele
m
o
d
el,
d
ev
el
o
p
ed
b
y
Din
a
Van
Hiele
-
Geld
o
f
an
d
Pier
r
e
Van
Hiele
,
d
elin
ea
tes
f
iv
e
h
ier
ar
ch
ical
lev
els
o
f
g
eo
m
etr
ic
th
in
k
in
g
:
v
is
u
aliza
tio
n
,
an
a
ly
s
is
,
in
f
o
r
m
al
d
ed
u
ctio
n
,
f
o
r
m
al
d
ed
u
ctio
n
,
an
d
r
ig
o
r
[
1
5
]
,
[
1
6
]
.
T
h
is
m
o
d
el
e
m
p
h
asizes
s
tr
u
ctu
r
ed
a
n
d
s
eq
u
en
tial
lear
n
in
g
ex
p
e
r
ien
ce
s
,
wh
ich
ar
e
cr
u
cial
f
o
r
p
r
o
g
r
ess
in
g
th
r
o
u
g
h
th
ese
lev
els
[
7
]
.
I
m
p
lem
e
n
tin
g
Van
H
iele
p
h
ase
-
b
ased
in
s
tr
u
ctio
n
h
as
b
ee
n
s
h
o
wn
to
s
ig
n
if
ican
tly
im
p
r
o
v
e
p
r
e
-
s
er
v
ice
teac
h
er
s
’
g
eo
m
etr
ic
th
in
k
i
n
g
s
k
ills
b
y
alig
n
in
g
in
s
tr
u
ctio
n
with
th
ese
p
h
ases
[
1
7
]
–
[
2
0
]
.
Su
ch
in
s
tr
u
ctio
n
al
s
tr
ateg
ies
p
r
o
m
o
te
ac
tiv
e
lear
n
in
g
an
d
en
co
u
r
ag
e
s
tu
d
e
n
ts
to
d
ev
elo
p
a
d
ee
p
e
r
u
n
d
er
s
tan
d
i
n
g
o
f
g
eo
m
etr
ic
co
n
ce
p
ts
th
r
o
u
g
h
h
an
d
s
-
o
n
ac
tiv
ities
an
d
r
ea
l
-
life
ap
p
licatio
n
s
[
2
1
]
,
[
2
2
]
.
Desp
ite
th
e
b
en
ef
its
o
f
th
e
Van
Hiele
m
o
d
el,
m
an
y
ed
u
ca
t
io
n
al
s
y
s
tem
s
,
p
ar
ticu
lar
ly
in
I
n
d
o
n
esia,
co
n
tin
u
e
to
r
ely
o
n
tr
ad
itio
n
al
m
eth
o
d
s
th
at
f
ail
t
o
d
e
v
elo
p
h
ig
h
er
-
o
r
d
er
g
eo
m
etr
ic
th
i
n
k
in
g
s
k
ills
.
I
n
co
n
tex
ts
s
u
ch
as
So
k
o
to
State,
Nig
er
ia,
th
ese
co
n
v
en
tio
n
al
s
tr
ateg
ies
h
av
e
b
ee
n
cr
iticized
f
o
r
th
eir
lim
ited
ef
f
ec
tiv
en
ess
in
f
o
s
ter
in
g
h
ig
h
er
-
o
r
d
er
g
e
o
m
etr
ic
th
in
k
in
g
s
k
ills
[
2
3
]
,
[
2
4
]
.
T
r
ad
itio
n
al
teac
h
in
g
m
eth
o
d
s
o
f
ten
f
ail
to
e
n
g
ag
e
s
tu
d
en
ts
in
m
ea
n
in
g
f
u
l
lear
n
i
n
g
e
x
p
e
r
ien
ce
s
,
p
r
e
v
en
tin
g
th
em
f
r
o
m
ap
p
r
ec
iatin
g
th
e
p
r
ac
tical
ap
p
licatio
n
s
o
f
g
eo
m
etr
y
in
d
aily
life
.
T
h
is
r
el
ian
ce
o
n
r
o
te
lear
n
in
g
a
n
d
l
ac
k
o
f
i
n
ter
ac
tiv
e,
s
tu
d
en
t
-
ce
n
ter
ed
ac
tiv
ities
co
n
tr
ib
u
te
to
th
e
g
a
p
in
s
tu
d
en
ts
’
g
eo
m
etr
ic
u
n
d
er
s
tan
d
i
n
g
an
d
th
eir
ab
ilit
y
t
o
ac
h
iev
e
h
ig
h
er
lev
els o
f
g
eo
m
etr
ic
th
in
k
in
g
[
2
5
]
,
[
2
6
]
.
I
n
I
n
d
o
n
esia,
co
n
v
e
n
tio
n
al
teac
h
in
g
m
eth
o
d
s
h
av
e
b
ee
n
in
ad
eq
u
ate
in
im
p
r
o
v
i
n
g
s
tu
d
en
ts
'
u
n
d
er
s
tan
d
i
n
g
o
f
g
eo
m
et
r
y
,
as
ev
id
en
ce
d
b
y
th
e
p
e
r
f
o
r
m
an
ce
o
f
p
r
e
-
s
er
v
ice
teac
h
e
r
s
in
co
lleg
e
wh
o
d
em
o
n
s
tr
ate
d
ef
icien
cies
in
g
eo
m
etr
ic
th
in
k
in
g
[
2
7
]
,
[
2
8
]
.
Ma
n
y
elem
en
tar
y
a
n
d
ju
n
i
o
r
h
ig
h
s
ch
o
o
l
s
tu
d
e
n
ts
in
I
n
d
o
n
esia
s
tr
u
g
g
le
with
b
as
ic
g
eo
m
etr
ic
co
n
ce
p
ts
s
u
ch
as sh
ap
es
an
d
p
lan
es
[
2
9
]
,
[
3
0
]
.
T
h
is
is
u
n
d
o
u
b
te
d
ly
co
n
n
ec
ted
to
th
e
p
e
r
f
o
r
m
an
ce
o
f
p
r
e
-
s
er
v
ice
teac
h
er
s
in
co
l
leg
e
wh
o
d
em
o
n
s
tr
ate
a
d
ef
ic
ien
cy
in
g
eo
m
et
r
ic
th
in
k
in
g
.
Ho
wev
er
,
co
m
p
ar
a
tiv
e
in
v
esti
g
atio
n
s
o
f
g
e
o
m
e
tr
ic
th
in
k
in
g
lev
els
am
o
n
g
u
n
iv
er
s
ities
r
em
ain
r
elativ
ely
u
n
d
e
r
s
tu
d
ied
.
On
e
o
f
th
e
p
r
im
a
r
y
i
n
s
titu
tio
n
s
f
o
r
tr
ain
i
n
g
p
r
e
-
s
er
v
ice
m
ath
em
atics
teac
h
er
s
in
I
n
d
o
n
esia
is
Un
iv
er
s
itas
Neg
er
i
Ma
k
ass
ar
(
UNM
)
an
d
Un
iv
er
s
itas
Mu
lawa
r
m
an
(
UNM
UL
)
.
B
y
ex
am
in
in
g
th
ese
tw
o
in
s
titu
tio
n
s
,
th
e
s
tu
d
y
s
ee
k
s
to
p
r
o
v
id
e
a
f
o
u
n
d
atio
n
f
o
r
r
ec
o
m
m
e
n
d
in
g
ap
p
r
o
p
r
iate
g
eo
m
etr
y
lear
n
in
g
s
tr
ateg
ies
an
d
en
h
an
cin
g
t
h
e
g
eo
m
etr
ic
th
in
k
in
g
lev
els
o
f
s
tu
d
en
ts
in
ed
u
ca
tio
n
al
in
s
titu
tio
n
s
.
T
h
is
s
tu
d
y
aim
s
to
ev
alu
ate
an
d
co
m
p
ar
e
th
e
g
eo
m
etr
ic
th
in
k
in
g
lev
els
o
f
g
en
er
atio
n
Z
p
r
e
-
s
er
v
ice
m
at
h
em
atics
teac
h
er
s
at
UNM
an
d
UNM
UL
,
p
r
o
v
id
in
g
v
alu
ab
le
i
n
s
ig
h
ts
f
o
r
e
d
u
ca
to
r
s
an
d
p
o
lic
y
m
ak
er
s
.
2.
M
E
T
H
O
D
T
h
is
s
tu
d
y
u
s
ed
a
q
u
an
titativ
e
co
m
p
ar
ativ
e
d
esig
n
to
ex
am
in
e
th
e
g
eo
m
etr
ic
th
i
n
k
in
g
lev
el
o
f
p
r
e
-
s
er
v
ice
m
ath
e
m
atics
teac
h
er
s
at
Un
iv
er
s
itas
Neg
er
i
Ma
k
ass
ar
(
UNM
)
an
d
Un
iv
e
r
s
itas
Mu
lawa
r
m
an
(
UNM
UL
)
.
T
h
e
p
o
p
u
latio
n
e
n
co
m
p
ass
ed
all
g
en
er
atio
n
Z
p
r
e
-
s
er
v
ice
m
ath
em
atics
teac
h
er
s
en
r
o
lled
at
b
o
th
in
s
titu
tio
n
s
.
A
to
tal
o
f
2
3
3
s
tu
d
en
ts
f
r
o
m
UNM
an
d
2
2
7
s
tu
d
en
ts
f
r
o
m
UNM
UL
was
s
elec
ted
u
s
in
g
p
u
r
p
o
s
iv
e
s
am
p
lin
g
,
wh
ich
in
v
o
l
v
es
d
elib
er
ately
ch
o
o
s
in
g
p
a
r
ticip
an
ts
wh
o
h
ad
s
u
cc
ess
f
u
lly
co
m
p
leted
th
e
b
asic
g
eo
m
etr
y
c
o
u
r
s
e.
T
h
e
in
s
tr
u
m
en
t
em
p
lo
y
ed
was
th
e
g
e
o
m
etr
ic
th
in
k
in
g
test
(
GT
T
)
,
b
ased
o
n
Van
Hiele
’
s
m
o
d
el,
co
n
s
is
ted
o
f
2
5
m
u
ltip
le
-
ch
o
ice
q
u
esti
o
n
s
ass
es
s
in
g
f
iv
e
lev
els
o
f
g
e
o
m
etr
ic
th
i
n
k
in
g
:
v
is
u
aliza
tio
n
,
an
aly
s
is
,
in
f
o
r
m
al
d
e
d
u
ctio
n
,
f
o
r
m
al
d
ed
u
ctio
n
,
a
n
d
r
i
g
o
r
[
3
1
]
.
E
ac
h
lev
el
h
ad
f
iv
e
q
u
esti
o
n
s
,
an
d
th
e
s
tu
d
en
ts
h
ad
to
an
s
wer
at
least
th
r
ee
q
u
esti
o
n
s
co
r
r
ec
tly
in
ea
ch
lev
el
to
b
e
ca
teg
o
r
ized
in
to
th
at
lev
el.
Ad
d
itio
n
ally
,
Usi
s
k
in
[
3
1
]
estab
lis
h
ed
a
wei
g
h
ted
g
eo
m
etr
ic
th
in
k
in
g
s
co
r
e
to
d
eter
m
in
e
th
e
th
in
k
in
g
le
v
el
o
f
s
tu
d
en
ts
.
Fo
r
ex
am
p
le,
if
a
s
tu
d
en
t a
n
s
wer
e
d
th
r
ee
q
u
esti
o
n
s
co
r
r
ec
tly
f
r
o
m
lev
els o
n
e,
th
r
ee
,
an
d
f
o
u
r
,
t
h
eir
s
co
r
e
wo
u
ld
b
e
1
3
(
1
+
4
+8
)
.
Usi
s
k
in
[
3
1
]
s
u
m
m
ar
ized
all
p
o
te
n
tial sco
r
es o
b
tain
ed
b
y
s
tu
d
e
n
ts
at
ea
ch
lev
e
l in
T
ab
le
1
.
T
h
e
d
ata
wer
e
c
o
llected
th
r
o
u
g
h
th
e
GT
T
.
Par
ticip
an
ts
f
r
o
m
b
o
t
h
u
n
i
v
er
s
ities
co
m
p
leted
th
e
test
with
in
th
e
s
am
e
tim
ef
r
am
e.
Descr
ip
tiv
e
an
d
i
n
f
er
en
tial
s
t
atis
tics
wer
e
u
s
ed
to
an
aly
ze
th
e
d
ata,
with
th
e
r
esu
lts
p
r
esen
ted
in
ta
b
les
an
d
ch
ar
ts
,
to
s
u
m
m
ar
ize
th
e
d
is
tr
ib
u
tio
n
o
f
g
eo
m
etr
ic
th
in
k
in
g
lev
els
a
n
d
to
co
m
p
ar
e
th
e
g
eo
m
etr
ic
t
h
in
k
in
g
lev
el
b
etwe
en
u
n
iv
er
s
ities
th
r
o
u
g
h
m
ea
n
r
a
n
k
s
an
d
s
u
m
o
f
s
co
r
es.
T
h
e
Ma
n
n
-
W
h
itn
ey
U
test
,
a
n
o
n
-
p
ar
am
etr
ic
test
,
was
u
s
ed
to
c
o
m
p
ar
e
d
if
f
e
r
en
ce
s
in
g
eo
m
et
r
ic
th
in
k
in
g
lev
el
s
an
d
to
tal
s
co
r
es
b
etwe
en
UNM
an
d
UNM
UL
s
tu
d
en
ts
wh
er
e
th
e
d
ata
is
in
o
r
d
in
al
[
3
2
]
.
T
h
e
lev
el
o
f
s
ig
n
if
ican
ce
was set a
t p
<0
.
0
5
.
A
s
tatis
ty
.
ap
p
was u
s
ed
to
v
i
s
u
ally
d
is
p
lay
an
d
p
r
o
ce
s
s
th
e
d
ata.
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
.
2
,
Ap
r
il
20
25
:
918
-
9
2
5
920
T
ab
le
1
.
W
eig
h
ted
s
u
m
o
f
s
co
r
e
o
f
g
eo
m
etr
ic
th
in
k
in
g
le
v
el
G
e
o
me
t
r
i
c
t
h
i
n
k
i
n
g
l
e
v
e
l
S
c
o
r
e
S
u
m
o
f
sc
o
re
0
0
0
,
2
,
4
,
8
,
1
6
,
1
8
,
2
0
,
2
4
1
1
1
,
5
,
9
,
1
7
,
2
1
,
2
5
2
2
3
,
1
1
,
1
9
,
2
7
3
4
6
,
7
,
2
2
,
2
3
4
8
1
3
,
1
4
,
1
5
,
2
9
,
3
0
5
16
31
N
o
t
f
i
t
-
1
0
,
1
2
,
2
6
,
2
8
T
h
e
GT
T
,
d
ev
el
o
p
ed
b
y
Us
is
k
in
[
3
1
]
th
r
o
u
g
h
th
e
c
o
g
n
i
tiv
e
d
ev
elo
p
m
e
n
t
an
d
ac
h
ie
v
em
en
t
in
s
ec
o
n
d
ar
y
s
ch
o
o
l
g
e
o
m
etr
y
(
C
DAS
SG)
p
r
o
ject,
h
as
a
r
ep
o
r
ted
r
eliab
ilit
y
co
ef
f
icien
t
o
f
r
=0
.
6
4
,
in
d
icatin
g
a
h
ig
h
lev
el
o
f
d
e
p
en
d
a
b
ilit
y
an
d
tr
u
s
two
r
th
in
ess
in
m
ea
s
u
r
in
g
g
eo
m
etr
ic
th
i
n
k
in
g
lev
els.
T
h
e
I
n
d
o
n
esian
v
er
s
io
n
o
f
t
h
e
GT
T
,
ad
a
p
ted
f
r
o
m
Z
ai
n
al
[
3
3
]
,
was
u
s
ed
to
elim
in
ate
an
y
p
o
te
n
tial
lan
g
u
a
g
e
b
a
r
r
ier
s
f
ac
e
d
b
y
s
tu
d
en
ts
.
E
th
ical
co
n
s
id
er
atio
n
s
wer
e
ad
d
r
ess
ed
b
y
o
b
tain
in
g
in
f
o
r
m
ed
c
o
n
s
en
t
f
r
o
m
all
p
ar
ticip
an
ts
,
en
s
u
r
in
g
th
e
co
n
f
id
e
n
tiality
an
d
a
n
o
n
y
m
ity
o
f
th
eir
r
esp
o
n
s
es,
an
d
ad
h
er
in
g
to
r
esp
o
n
s
ib
le
d
ata
u
s
ag
e
p
r
ac
tices.
3.
RE
SU
L
T
S
AND
D
I
SCU
SS
I
O
N
3
.
1
.
Ana
ly
s
is
o
f
t
he
dis
t
ributio
n o
f
s
t
ud
ent
s
’
g
eo
m
et
ric
t
hin
k
ing
lev
els
T
h
is
s
ec
tio
n
ev
alu
ates
th
e
g
e
o
m
etr
ic
th
in
k
in
g
lev
els
o
f
s
tu
d
e
n
ts
f
r
o
m
UNM
a
n
d
UNM
UL
,
f
o
llo
win
g
th
e
estab
lis
h
ed
cr
iter
ia
o
f
t
h
e
Van
Hiele
m
o
d
el.
T
h
e
Van
Hiele
m
o
d
el
ca
teg
o
r
izes
g
e
o
m
etr
ic
th
in
k
in
g
in
to
f
iv
e
d
is
tin
ct
lev
els,
ea
ch
r
ep
r
esen
tin
g
a
p
r
o
g
r
ess
iv
ely
d
ee
p
er
u
n
d
er
s
tan
d
in
g
o
f
g
e
o
m
etr
i
c
co
n
ce
p
ts
.
T
ab
le
2
an
d
Fig
u
r
e
1
p
r
o
v
id
e
an
o
v
er
v
iew
o
f
th
e
d
is
tr
ib
u
tio
n
o
f
s
tu
d
en
ts
ac
r
o
s
s
d
if
f
er
en
t le
v
els o
f
g
eo
m
etr
ic
th
in
k
in
g
.
T
ab
le
2
s
h
o
ws
th
at
b
o
th
u
n
iv
er
s
ities
h
av
e
s
tu
d
en
ts
d
is
tr
ib
u
ted
ac
r
o
s
s
v
ar
io
u
s
lev
els,
with
n
o
tab
le
d
if
f
er
en
ce
s
in
th
e
p
atter
n
s
o
b
s
er
v
ed
.
At
th
e
lo
west
lev
el
(
l
ev
el
0
)
,
2
7
s
tu
d
en
ts
f
r
o
m
UN
M
(
1
1
.
6
%)
a
n
d
2
5
s
tu
d
en
ts
f
r
o
m
UNM
UL
(
1
1
.
0
%)
s
tr
u
g
g
le
d
with
b
asic
s
h
ap
e
r
ec
o
g
n
itio
n
.
Ma
n
y
s
tu
d
e
n
ts
wer
e
at
lev
el
1
(
v
is
u
aliza
tio
n
)
,
wh
er
e
6
5
s
tu
d
en
ts
f
r
o
m
UNM
(
2
7
.
9
%)
an
d
8
7
s
tu
d
en
ts
f
r
o
m
UNM
UL
(
3
8
.
3
%)
wer
e
ab
le
to
r
ec
o
g
n
ize
s
h
ap
es
b
ased
o
n
ap
p
ea
r
an
ce
b
u
t
h
ad
n
o
t
y
et
p
r
o
g
r
ess
ed
to
u
n
d
er
s
tan
d
i
n
g
t
h
eir
p
r
o
p
er
ties
.
L
ev
el
2
(
an
aly
s
is
)
s
aw
a
s
ig
n
if
ican
t
n
u
m
b
er
o
f
s
tu
d
en
ts
,
with
8
9
f
r
o
m
UNM
(
3
8
.
2
%)
an
d
7
4
f
r
o
m
UNM
UL
(
3
2
.
6
%)
d
em
o
n
s
tr
atin
g
a
s
tr
o
n
g
er
g
r
as
p
o
f
g
eo
m
etr
ic
p
r
o
p
e
r
ties
.
T
ab
le
2
.
T
h
e
o
v
e
r
v
iew
o
f
th
e
l
ev
els o
f
g
eo
m
etr
ic
th
in
k
in
g
a
m
o
n
g
s
tu
d
e
n
ts
in
UNM
an
d
U
NM
UL
G
e
o
me
t
r
i
c
t
h
i
n
k
i
n
g
l
e
v
e
l
S
u
m
o
f
sco
r
e
C
r
i
t
e
r
i
a
o
f
t
h
r
e
e
o
u
t
o
f
f
i
v
e
c
o
r
r
e
c
t
a
n
sw
e
r
UNM
U
N
M
U
L
F
r
e
q
u
e
n
c
y
To
t
a
l
F
r
e
q
u
e
n
c
y
To
t
a
l
0
0
7
2
7
(
1
1
.
6
%)
17
2
5
(
1
1
.
0
%)
2
11
2
8
0
2
16
5
2
18
4
2
1
1
47
6
5
(
2
7
.
9
%)
64
8
7
(
3
8
.
3
%)
5
3
10
9
2
4
17
9
8
21
2
1
25
2
0
2
3
46
8
9
(
3
8
.
2
%)
53
7
4
(
3
2
.
6
%)
11
14
4
19
25
16
27
4
1
3
6
2
3
4
(
1
4
.
6
%)
2
2
7
(
1
1
.
9
%)
7
17
23
22
1
0
23
14
2
4
13
1
4
(
1
.
7
%)
0
1
0
(
4
.
4
%)
15
3
10
5
31
6
6
(
2
.
6
%)
3
3
(
1
.
3
%)
N
o
t
f
i
t
10
7
8
(
3
.
4
%)
1
1
(
0
.
4
%)
26
1
0
To
t
a
l
2
3
3
1
0
0
2
2
7
1
0
0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
E
va
lu
a
tin
g
t
h
e
g
eo
metric th
in
kin
g
leve
ls
o
f
g
en
era
tio
n
Z p
r
e
-
s
ervice
… (
Mu
h
a
mma
d
A
mma
r
N
a
u
fa
l
)
921
As
th
e
co
m
p
lex
ity
o
f
th
e
le
v
els
in
cr
ea
s
ed
,
f
ewe
r
s
tu
d
en
ts
ad
v
an
ce
d
to
h
ig
h
er
lev
els.
At
l
ev
el
3
(
in
f
o
r
m
al
d
ed
u
ctio
n
)
,
3
4
s
tu
d
en
ts
f
r
o
m
UNM
(
1
4
.
6
%)
a
n
d
2
7
s
tu
d
en
ts
f
r
o
m
UNM
UL
(
1
1
.
9
%)
u
n
d
er
s
to
o
d
r
elatio
n
s
h
ip
s
b
etwe
en
g
eo
m
et
r
ic
p
r
o
p
e
r
ties
.
L
ev
el
4
(
f
o
r
m
al
d
ed
u
ctio
n
)
h
ad
v
e
r
y
f
ew
s
tu
d
en
ts
:
f
o
u
r
f
r
o
m
UNM
(
1
.
7
%)
an
d
1
0
f
r
o
m
U
NM
UL
(
4
.
4
%),
i
n
d
icatin
g
a
lim
ited
ca
p
ac
ity
f
o
r
d
ev
elo
p
in
g
an
d
u
n
d
e
r
s
tan
d
in
g
f
o
r
m
al
p
r
o
o
f
s
.
At
l
ev
el
5
(
r
ig
o
r
)
,
o
n
ly
a
s
m
all
n
u
m
b
e
r
o
f
s
tu
d
en
ts
wer
e
p
r
esen
t,
with
s
ix
f
r
o
m
UNM
(
2
.
6
%)
an
d
th
r
ee
f
r
o
m
UNM
UL
(
1
.
3
%),
s
u
g
g
esti
n
g
th
at
r
ig
o
r
o
u
s
g
eo
m
etr
ic
th
in
k
in
g
is
r
ar
e
am
o
n
g
th
e
p
ar
ticip
a
n
ts
.
Ad
d
itio
n
ally
,
s
o
m
e
s
tu
d
en
ts
d
id
n
o
t f
it in
to
an
y
s
p
ec
if
ic
lev
el,
with
eig
h
t stu
d
en
ts
f
r
o
m
UNM
(
3
.
4
%)
an
d
o
n
e
f
r
o
m
UNM
UL
(
0
.
4
%).
Ov
er
all,
wh
ile
a
s
u
b
s
tan
tial
p
r
o
p
o
r
tio
n
o
f
s
tu
d
en
ts
p
o
s
s
ess
f
o
u
n
d
atio
n
al
g
eo
m
etr
ic
k
n
o
wled
g
e,
a
s
m
aller
n
u
m
b
er
h
av
e
ac
h
iev
e
d
h
ig
h
er
p
r
o
f
icien
cy
in
g
eo
m
etr
ic
co
g
n
itio
n
.
Fig
u
r
e
1
illu
s
tr
ates th
e
co
m
p
ar
is
o
n
o
f
g
eo
m
etr
ic
th
in
k
in
g
lev
els am
o
n
g
th
e
p
ar
ticip
a
n
ts
f
r
o
m
UNM
an
d
UNM
UL
.
Fig
u
r
e
1
.
C
o
m
p
a
r
is
o
n
o
f
s
tu
d
e
n
ts
’
g
eo
m
etr
ic
th
in
k
in
g
le
v
el
3
.
2
.
Ana
ly
s
is
o
f
t
he
s
t
ud
ent
s
’
g
eo
m
et
ric
t
hin
k
ing
lev
els
T
ab
le
3
p
r
esen
ts
th
e
m
ea
n
r
a
n
k
s
f
o
r
g
e
o
m
etr
ic
t
h
in
k
in
g
le
v
els
an
d
o
v
er
all
s
co
r
es
b
etwe
en
th
e
two
u
n
iv
er
s
ities
.
I
t
o
f
f
er
s
a
q
u
a
n
titativ
e
co
m
p
ar
is
o
n
o
f
s
tu
d
en
t
p
er
f
o
r
m
an
ce
.
T
h
e
m
ea
n
r
an
k
s
f
o
r
b
o
t
h
g
e
o
m
etr
ic
th
in
k
in
g
lev
els
an
d
s
u
m
s
co
r
es
h
ig
h
lig
h
t
a
p
er
f
o
r
m
a
n
ce
d
i
s
p
ar
ity
b
etwe
en
UNM
a
n
d
U
NM
UL
s
tu
d
en
ts
.
I
t
s
u
g
g
ests
d
if
f
er
en
ce
s
in
h
o
w
ef
f
ec
tiv
ely
ea
ch
in
s
titu
tio
n
f
o
s
ter
s
g
eo
m
etr
ic
th
in
k
in
g
.
UNM
s
tu
d
en
ts
d
em
o
n
s
tr
ated
h
ig
h
er
m
ea
n
r
a
n
k
s
in
b
o
th
g
e
o
m
etr
ic
th
in
k
i
n
g
lev
els
(
2
4
0
.
8
8
)
an
d
s
u
m
s
co
r
es
(
2
5
4
.
9
)
co
m
p
a
r
ed
to
UNM
UL
s
tu
d
en
ts
(
2
1
9
.
8
4
an
d
2
0
5
.
4
6
,
r
esp
ec
tiv
el
y
)
.
T
h
is
s
u
g
g
ests
th
at
UNM
s
tu
d
en
ts
n
o
t
o
n
ly
e
x
h
ib
it
b
etter
g
eo
m
etr
ic
th
in
k
in
g
b
u
t
also
ac
h
iev
e
h
ig
h
er
o
v
er
all
s
co
r
es
in
g
eo
m
et
r
ic
task
s
.
T
h
e
h
ig
h
e
r
s
u
m
s
co
r
es a
t U
N
M
in
d
icate
a
m
o
r
e
r
o
b
u
s
t u
n
d
e
r
s
tan
d
in
g
an
d
ap
p
licatio
n
o
f
g
eo
m
etr
ic
co
n
ce
p
ts
.
T
h
e
r
esu
lts
o
f
th
e
Ma
n
n
-
W
h
itn
ey
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test
,
as
s
h
o
wn
in
T
ab
le
4
,
p
r
o
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id
e
a
d
ee
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er
u
n
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er
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d
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o
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ese
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if
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er
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s
.
T
h
e
d
if
f
er
en
ce
in
g
eo
m
etr
ic
th
in
k
in
g
lev
els
b
etwe
en
UNM
an
d
UNM
UL
was
n
o
t
s
tatis
t
ically
s
ig
n
if
ican
t
(
U=
2
4
0
2
6
,
p
=0
.
0
9
)
,
in
d
icatin
g
s
i
m
ilar
p
er
f
o
r
m
an
ce
lev
els
in
g
eo
m
etr
ic
th
i
n
k
in
g
.
Ho
wev
er
,
t
h
e
d
i
f
f
er
en
ce
in
s
u
m
s
co
r
es
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tically
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i
g
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if
ican
t
(
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2
0
7
6
0
.
5
,
p
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0
0
1
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,
c
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ir
m
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g
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at
UNM
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ts
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u
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er
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o
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m
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h
eir
UNM
UL
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u
n
ter
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ar
ts
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er
all.
T
ab
le
3
.
Me
an
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o
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two
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n
iv
er
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ities
U
n
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v
e
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t
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3
3
2
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0
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8
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1
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2
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0
4
To
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l
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6
0
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m
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3
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9
5
9
3
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1
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5
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N
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L
2
2
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0
5
.
4
6
4
6
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3
8
.
5
To
t
a
l
4
6
0
T
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le
4
.
R
esu
lt o
f
Ma
n
n
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h
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a
n
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0
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o
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e
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6
0
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5
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4
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0
4
0
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0
0
0
0
.
0
0
0
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
.
2
,
Ap
r
il
20
25
:
918
-
9
2
5
922
3
.
3
.
Dis
cus
s
io
n
T
h
e
co
m
p
ar
ativ
e
a
n
aly
s
is
o
f
g
eo
m
etr
ic
th
in
k
in
g
am
o
n
g
g
en
e
r
atio
n
Z
p
r
e
-
s
er
v
ice
m
a
th
em
atics
teac
h
er
s
f
r
o
m
UNM
a
n
d
UNM
UL
p
r
o
v
id
es
cr
itical
in
s
ig
h
ts
in
to
th
e
ef
f
ec
tiv
e
n
ess
o
f
c
u
r
r
en
t
ed
u
ca
tio
n
al
s
tr
ateg
ies
at
th
ese
in
s
titu
tio
n
s
.
T
h
e
f
in
d
in
g
s
r
e
v
ea
l
d
is
p
a
r
ities
in
g
eo
m
etr
ic
th
in
k
in
g
lev
els
an
d
o
v
er
all
p
er
f
o
r
m
an
ce
,
with
s
ig
n
if
ica
n
t
im
p
licatio
n
s
f
o
r
im
p
r
o
v
in
g
t
ea
ch
in
g
m
eth
o
d
o
l
o
g
ies.
T
h
es
e
d
is
p
ar
ities
s
u
g
g
est
th
at
wh
ile
b
o
th
in
s
titu
tio
n
s
ar
e
d
ev
elo
p
in
g
s
tu
d
en
ts
’
g
eo
m
e
tr
ic
th
in
k
in
g
,
th
e
a
p
p
r
o
ac
h
es
an
d
o
u
tco
m
es
v
ar
y
,
in
d
icatin
g
a
n
ee
d
f
o
r
tailo
r
ed
in
s
tr
u
ctio
n
al
s
tr
ateg
ies.
UNM
s
tu
d
en
ts
g
en
er
ally
p
er
f
o
r
m
ed
b
etter
,
p
ar
ticu
lar
ly
in
in
ter
m
ed
iate
g
e
o
m
etr
ic
th
i
n
k
i
n
g
lev
els
(
an
aly
s
is
an
d
in
f
o
r
m
al
d
ed
u
ct
io
n
)
.
T
h
is
h
ig
h
e
r
p
er
f
o
r
m
a
n
ce
m
ay
b
e
attr
ib
u
te
d
to
t
h
e
in
s
tr
u
ctio
n
al
s
tr
ateg
ies
em
p
lo
y
ed
at
UNM
,
wh
ich
a
p
p
ea
r
to
b
e
m
o
r
e
ef
f
ec
tiv
e
i
n
f
o
s
ter
in
g
a
d
ee
p
er
u
n
d
e
r
s
tan
d
in
g
o
f
g
e
o
m
etr
ic
p
r
o
p
er
ties
an
d
lo
g
ical
r
elatio
n
s
h
ip
s
.
On
th
e
o
th
er
h
an
d
,
U
NM
UL
s
tu
d
en
ts
ex
h
ib
ited
a
b
r
o
ad
e
r
d
is
tr
ib
u
tio
n
ac
r
o
s
s
all
lev
els,
with
a
n
o
tab
le
p
r
esen
ce
at
b
o
th
th
e
b
a
s
ic
v
is
u
aliza
tio
n
lev
el
an
d
th
e
ad
v
an
ce
d
f
o
r
m
al
d
ed
u
ctio
n
le
v
el.
T
h
is
d
is
tr
ib
u
tio
n
in
d
icate
s
a
less
f
o
c
u
s
ed
b
u
t
b
r
o
a
d
er
r
an
g
e
o
f
g
eo
m
e
tr
ic
th
in
k
in
g
s
k
ills
am
o
n
g
UNM
UL
s
tu
d
en
ts
,
s
u
g
g
esti
n
g
th
at
wh
ile
s
o
m
e
s
tu
d
en
ts
ex
ce
l
in
b
asic
r
ec
o
g
n
itio
n
an
d
a
d
v
an
ce
d
d
ed
u
ctio
n
,
o
th
e
r
s
m
ay
s
tr
u
g
g
l
e
to
p
r
o
g
r
ess
b
ey
o
n
d
i
n
itial
lev
els.
T
h
is
d
is
cr
ep
an
cy
u
n
d
e
r
s
co
r
es
a
d
iv
er
g
en
ce
in
th
e
f
o
u
n
d
atio
n
al
a
n
d
a
d
v
a
n
ce
d
g
e
o
m
etr
ic
th
i
n
k
in
g
ab
ili
ties
b
etwe
en
th
e
two
ac
a
d
em
ic
in
s
titu
tio
n
s
.
T
h
e
p
r
ev
alen
ce
o
f
UNM
s
tu
d
en
ts
at
in
ter
m
ed
iate
lev
els
in
d
icate
s
th
e
ef
f
icac
y
o
f
p
e
d
ag
o
g
ical
ap
p
r
o
ac
h
es
th
a
t
f
ac
ilit
ate
th
e
ad
v
an
ce
m
e
n
t o
f
a
n
aly
tical
an
d
in
f
o
r
m
al
d
ed
u
cti
v
e
lev
el.
T
h
ese
r
esu
lts
alig
n
with
p
r
e
v
io
u
s
s
tu
d
ies
th
at
cr
iticize
tr
ad
itio
n
al
teac
h
er
-
ce
n
ter
ed
in
s
tr
u
ctio
n
al
ap
p
r
o
ac
h
es
f
o
r
th
eir
lim
ited
ef
f
ec
tiv
en
ess
in
d
ev
elo
p
in
g
g
eo
m
etr
ic
th
in
k
in
g
.
C
o
n
v
en
tio
n
al
teac
h
in
g
m
eth
o
d
s
,
wh
ich
ar
e
p
r
e
v
alen
t
in
m
a
n
y
ed
u
ca
tio
n
al
co
n
tex
ts
,
in
clu
d
in
g
Nig
er
ia,
h
a
v
e
b
ee
n
s
h
o
w
n
to
in
ad
e
q
u
ately
ad
d
r
ess
th
e
r
ea
l
-
life
a
p
p
lic
atio
n
o
f
g
e
o
m
etr
ic
c
o
n
ce
p
t
s
an
d
f
ail
to
en
g
a
g
e
s
tu
d
en
ts
in
h
a
n
d
s
-
o
n
,
s
tu
d
en
t
-
ce
n
ter
ed
lear
n
in
g
ac
ti
v
ities
[
2
3
]
.
Su
ch
ap
p
r
o
ac
h
es
ar
e
n
o
t
alig
n
ed
with
th
e
Van
H
iele
m
o
d
el
’
s
p
h
ases
o
f
lear
n
in
g
g
e
o
m
etr
y
,
wh
ich
e
m
p
h
asize
d
is
co
v
er
y
-
b
ased
lear
n
in
g
an
d
in
c
r
em
en
tal
d
ev
elo
p
m
en
t
o
f
g
eo
m
etr
ic
u
n
d
er
s
tan
d
i
n
g
[
1
7
]
,
[
3
4
]
,
[
3
5
]
.
T
h
is
is
also
co
n
s
is
ten
t w
ith
f
in
d
in
g
s
f
r
o
m
Hass
an
et
a
l.
[
2
3
]
wh
o
r
ep
o
r
ted
p
o
o
r
p
er
f
o
r
m
an
ce
in
g
e
o
m
etr
y
am
o
n
g
Nig
er
ian
s
ec
o
n
d
ar
y
s
ch
o
o
l
s
tu
d
en
ts
d
u
e
to
in
ad
eq
u
ate
g
eo
m
etr
ic
s
k
ills
an
d
in
ef
f
ec
tiv
e
teac
h
in
g
s
tr
ateg
ie
s
.
Mo
r
eo
v
er
,
s
tu
d
ies
h
av
e
co
n
f
ir
m
ed
t
h
at
th
e
u
s
e
o
f
tr
a
d
i
tio
n
al
in
s
tr
u
ctio
n
al
s
tr
ateg
ies
co
n
tr
ib
u
tes
to
a
s
i
g
n
if
ican
t
g
ap
in
s
tu
d
en
ts
’
g
e
o
m
etr
ic
u
n
d
er
s
tan
d
in
g
an
d
t
h
eir
ac
q
u
is
itio
n
o
f
ad
v
an
ce
d
g
eo
m
etr
ic
t
h
in
k
in
g
s
k
ills
[
36
]
–
[
38
]
.
T
h
e
p
r
e
d
o
m
in
a
n
t
u
s
e
o
f
r
o
te
l
ea
r
n
in
g
,
as
h
ig
h
lig
h
ted
i
n
th
e
f
in
d
in
g
s
,
h
in
d
e
r
s
s
tu
d
en
ts
f
r
o
m
r
ea
ch
in
g
h
ig
h
er
lev
els
o
f
g
eo
m
etr
ic
t
h
in
k
in
g
.
Ho
u
r
ig
a
n
an
d
L
ea
v
y
[
1
2
]
em
p
h
asize
th
e
n
ec
ess
ity
f
o
r
p
r
e
-
s
er
v
ice
p
r
im
ar
y
teac
h
er
s
t
o
p
o
s
s
ess
a
co
m
p
r
eh
e
n
s
iv
e
u
n
d
er
s
tan
d
i
n
g
o
f
g
e
o
m
etr
ic
c
o
n
ce
p
ts
t
o
e
n
h
an
ce
th
eir
teac
h
in
g
p
r
o
f
icien
c
y
.
T
h
e
ef
f
icac
y
o
f
Van
Hiele
p
h
ase
-
b
ased
in
s
tr
u
ctio
n
in
en
h
an
cin
g
th
e
g
eo
m
et
r
ic
th
in
k
in
g
ab
ilit
ies
o
f
p
r
e
-
s
er
v
ice
teac
h
e
r
s
h
as
b
ee
n
s
u
b
s
tan
tiated
b
y
em
p
ir
ical
ev
id
en
ce
.
Ar
m
ah
et
a
l.
[3
6
]
h
av
e
d
em
o
n
s
tr
ated
th
at
s
tr
u
ctu
r
ed
in
s
tr
u
ctio
n
al
a
p
p
r
o
ac
h
es
alig
n
ed
with
th
e
Van
Hiele
p
h
ases
ca
n
m
ar
k
ed
ly
en
h
an
ce
g
e
o
m
etr
ic
th
in
k
in
g
s
k
ills
.
T
h
e
f
in
d
in
g
s
u
n
d
er
s
co
r
e
th
e
n
ee
d
f
o
r
ed
u
ca
tio
n
al
r
ef
o
r
m
s
th
at
ad
o
p
t
m
o
r
e
ef
f
ec
tiv
e
s
tu
d
en
t
-
ce
n
ter
ed
in
s
tr
u
ctio
n
al
s
tr
ateg
ies
alig
n
e
d
with
Van
Hiele’
s
p
h
ases
o
f
lear
n
in
g
.
Van
Hiele
’
s
m
o
d
el
p
r
o
p
o
s
es
th
at
s
tu
d
en
ts
p
r
o
g
r
ess
th
r
o
u
g
h
d
i
f
f
er
en
t
lev
els
o
f
g
eo
m
etr
ic
th
in
k
in
g
,
f
r
o
m
b
asic
r
ec
o
g
n
i
tio
n
o
f
s
h
a
p
es
to
co
n
s
tr
u
ctin
g
f
o
r
m
al
p
r
o
o
f
s
[3
9
]
.
B
y
im
p
lem
en
tin
g
in
s
tr
u
ct
io
n
b
ased
o
n
Van
Hiele
’
s
p
h
ases
,
s
tu
d
en
ts
ca
n
ac
h
iev
e
a
b
etter
g
r
asp
o
f
g
e
o
m
etr
ic
co
n
ce
p
ts
co
m
p
ar
ed
t
o
tr
ad
itio
n
al
m
eth
o
d
s
[
1
8
]
,
[
3
4
]
,
[
40
]
.
T
h
e
u
s
e
o
f
Van
Hiele
’
s
p
h
ase
-
b
ased
teac
h
in
g
s
tr
ateg
ies
h
as
b
ee
n
f
o
u
n
d
to
h
elp
s
tu
d
en
ts
o
v
er
co
m
e
ch
al
len
g
es
in
g
eo
m
etr
y
lear
n
in
g
[
2
0]
.
Fu
r
t
h
er
m
o
r
e,
s
tu
d
ies
h
av
e
in
d
icate
d
th
at
in
ter
v
en
tio
n
s
b
ased
o
n
Van
Hiele
’
s
p
h
ases
ca
n
ef
f
ec
tiv
ely
ad
d
r
ess
s
tu
d
en
ts
’
d
if
f
icu
lties
in
g
eo
m
etr
y
,
lead
i
n
g
to
im
p
r
o
v
ed
ac
h
ie
v
em
en
t
an
d
attitu
d
es
to
war
d
s
th
e
s
u
b
ject
[
2
1
]
,
[
2
4
]
.
E
d
u
ca
ti
o
n
al
in
s
titu
tio
n
s
s
h
o
u
ld
f
o
c
u
s
o
n
in
te
r
ac
tiv
e
a
n
d
p
r
ac
tical
le
ar
n
in
g
ex
p
e
r
ien
ce
s
,
en
co
u
r
a
g
in
g
s
tu
d
en
ts
to
ex
p
l
o
r
e
an
d
u
n
d
e
r
s
tan
d
g
eo
m
etr
i
c
co
n
ce
p
ts
d
ee
p
ly
,
th
e
r
eb
y
p
r
ep
ar
in
g
th
em
m
o
r
e
ef
f
ec
tiv
ely
f
o
r
f
u
tu
r
e
teac
h
in
g
r
o
les.
T
h
ese
in
s
ig
h
ts
ar
e
c
r
itical
f
o
r
ed
u
ca
to
r
s
an
d
p
o
licy
m
ak
er
s
aim
in
g
to
elev
ate
th
e
q
u
ality
o
f
m
ath
e
m
atics e
d
u
ca
tio
n
an
d
g
eo
m
etr
ic
in
s
tr
u
ctio
n
in
u
n
iv
er
s
ities
.
4.
CO
NCLU
SI
O
N
T
h
e
s
tu
d
y
r
ev
ea
le
d
n
o
ta
b
le
d
i
f
f
er
en
ce
s
in
th
e
g
e
o
m
etr
ic
th
i
n
k
in
g
lev
els
b
etwe
en
s
tu
d
e
n
ts
at
UNM
an
d
UNM
UL
,
with
UNM
s
t
u
d
en
ts
g
e
n
er
ally
o
u
tp
er
f
o
r
m
i
n
g
th
eir
UNM
UL
co
u
n
ter
p
a
r
ts
,
p
ar
ticu
lar
ly
in
in
ter
m
ed
iate
lev
els o
f
g
e
o
m
etr
ic
th
in
k
in
g
.
T
h
is
s
u
g
g
ests
th
at
th
e
in
s
tr
u
ctio
n
al
s
tr
ateg
ies at
UNM
m
ay
b
e
m
o
r
e
ef
f
ec
tiv
e
in
f
o
s
ter
in
g
a
d
ee
p
er
u
n
d
er
s
tan
d
in
g
o
f
g
eo
m
et
r
ic
co
n
ce
p
ts
.
T
o
ef
f
ec
tiv
el
y
en
h
an
ce
g
eo
m
etr
ic
th
in
k
in
g
lev
els,
it
is
r
ec
o
m
m
en
d
ed
th
at
b
o
th
i
n
s
titu
tio
n
s
im
p
lem
en
t
s
p
ec
if
ic
s
tu
d
e
n
t
-
ce
n
ter
ed
lear
n
in
g
s
tr
ateg
ies.
T
h
ese
in
clu
d
e
in
co
r
p
o
r
atin
g
in
ter
ac
tiv
e
g
e
o
m
etr
y
s
o
f
twar
e
lik
e
Geo
Geb
r
a
to
f
ac
ilit
ate
h
an
d
s
-
o
n
lear
n
in
g
,
o
r
g
an
izin
g
co
llab
o
r
a
tiv
e
p
r
o
b
lem
-
s
o
lv
i
n
g
s
ess
io
n
s
to
f
o
s
ter
d
ee
p
er
u
n
d
er
s
tan
d
i
n
g
,
an
d
in
te
g
r
atin
g
p
r
o
ject
-
b
ased
lear
n
in
g
ac
tiv
ities
th
at
r
eq
u
ir
e
s
tu
d
en
ts
to
ap
p
ly
g
eo
m
etr
ic
co
n
ce
p
ts
to
r
ea
l
-
wo
r
ld
p
r
o
b
lem
s
.
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Ad
d
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,
r
eg
u
lar
ass
ess
m
en
ts
u
s
in
g
Van
Hiele’
s
p
h
as
e
-
b
ased
m
o
d
el
s
h
o
u
ld
b
e
co
n
d
u
cted
to
m
o
n
ito
r
p
r
o
g
r
ess
an
d
tailo
r
in
s
tr
u
cti
o
n
to
m
ee
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th
e
d
iv
er
s
e
lear
n
in
g
n
ee
d
s
o
f
s
tu
d
en
ts
.
Mo
r
eo
v
er
,
p
r
o
f
ess
io
n
al
d
ev
elo
p
m
e
n
t
f
o
r
in
s
tr
u
cto
r
s
is
ess
en
tial
to
en
s
u
r
e
th
ey
a
r
e
well
-
eq
u
ip
p
e
d
with
ef
f
ec
tiv
e
teac
h
in
g
s
tr
ateg
ies
th
at
alig
n
with
th
e
Van
Hie
l
e
m
o
d
el.
C
r
o
s
s
-
in
s
titu
tio
n
al
c
o
llab
o
r
atio
n
b
etwe
en
UNM
an
d
UNM
UL
co
u
ld
f
o
s
ter
th
e
ex
ch
an
g
e
o
f
b
est
p
r
ac
tices,
lead
in
g
to
im
p
r
o
v
ed
o
u
tco
m
es
in
teac
h
in
g
g
e
o
m
etr
y
.
R
ec
o
g
n
izin
g
th
e
v
ar
ied
d
is
tr
ib
u
tio
n
o
f
s
tu
d
en
ts
ac
r
o
s
s
th
e
Van
Hiele
le
v
els,
in
s
tr
u
ctio
n
s
h
o
u
ld
b
e
tai
lo
r
ed
to
in
d
i
v
id
u
al
lear
n
in
g
n
ee
d
s
,
o
f
f
er
i
n
g
ad
d
itio
n
al
s
u
p
p
o
r
t
f
o
r
th
o
s
e
s
tr
u
g
g
lin
g
an
d
ad
v
an
ce
d
c
h
allen
g
es
f
o
r
th
o
s
e
r
ea
d
y
to
p
r
o
g
r
ess
.
L
o
n
g
itu
d
in
al
s
tu
d
i
es
tr
ac
k
in
g
s
tu
d
en
ts
’
p
r
o
g
r
ess
co
u
ld
p
r
o
v
id
e
v
alu
ab
le
in
s
ig
h
ts
in
to
th
e
ef
f
ec
tiv
en
ess
o
f
th
ese
s
tr
ateg
ies
an
d
in
f
o
r
m
o
n
g
o
in
g
c
u
r
r
icu
lu
m
im
p
r
o
v
em
e
n
ts
.
T
h
ese
r
ec
o
m
m
e
n
d
atio
n
s
h
ig
h
lig
h
t
t
h
e
n
ee
d
f
o
r
ed
u
ca
tio
n
al
r
ef
o
r
m
s
th
at
p
r
io
r
it
ize
s
tu
d
en
t
-
ce
n
ter
e
d
,
p
h
ase
-
b
ased
in
s
tr
u
ctio
n
al
s
tr
ateg
ies to
elev
ate
th
e
q
u
alit
y
o
f
m
at
h
em
atics e
d
u
ca
tio
n
a
n
d
g
eo
m
etr
ic
i
n
s
tr
u
ctio
n
in
u
n
i
v
er
s
ities
.
ACK
NO
WL
E
DG
E
M
E
NT
S
T
h
e
au
th
o
r
s
co
n
v
ey
th
e
a
p
p
r
ec
iatio
n
to
t
h
e
Min
is
tr
y
o
f
E
d
u
ca
tio
n
,
C
u
ltu
r
e,
R
esear
ch
,
an
d
T
ec
h
n
o
lo
g
y
,
I
n
d
o
n
esia
f
o
r
p
r
o
v
id
in
g
f
in
an
cial
h
elp
.
T
h
e
r
e
s
ea
r
ch
r
ec
eiv
ed
f
u
n
d
in
g
f
r
o
m
th
e
Dir
ec
to
r
ate
o
f
R
esear
ch
,
T
ec
h
n
o
lo
g
y
,
an
d
C
o
m
m
u
n
ity
Ser
v
ice
Fu
n
d
am
e
n
t
al
R
esear
ch
Gr
an
t
n
o
.
0
6
5
/E5
/
PG.0
2
.
0
0
.
PL/2
0
2
4
.
I
n
ad
d
itio
n
,
g
r
atitu
d
e
is
ex
ten
d
ed
to
UNM
an
d
UNM
UL
a
s
well
as
J
u
m
ad
ila
Pu
r
n
am
a
f
o
r
th
eir
p
r
icele
s
s
h
elp
in
f
ac
ilit
atin
g
th
e
d
ata
c
o
llectio
n
p
r
o
ce
s
s
.
RE
F
E
R
E
NC
E
S
[
1
]
A
.
Z
a
m
a
n
,
A
.
G
h
a
f
a
r
,
F
.
U
.
R
a
h
m
a
n
,
a
n
d
I
.
H
u
ss
a
i
n
,
“
E
x
a
mi
n
i
n
g
p
e
r
f
o
r
m
a
n
c
e
o
f
g
e
o
m
e
t
r
i
c
a
l
t
h
i
n
k
i
n
g
i
n
m
a
t
h
e
ma
t
i
c
s
a
t
s
e
c
o
n
d
a
r
y
sc
h
o
o
l
l
e
v
e
l
i
n
P
a
k
i
s
t
a
n
,
”
P
a
k
i
s
t
a
n
J
o
u
r
n
a
l
o
f
E
d
u
c
a
t
i
o
n
,
v
o
l
.
3
5
,
n
o
.
1
,
p
p
.
3
3
–
4
2
,
S
e
p
.
2
0
1
8
,
d
o
i
:
1
0
.
3
0
9
7
1
/
p
j
e
.
v
3
5
i
1
.
5
6
0
.
[
2
]
S
.
O
b
a
r
a
a
n
d
B
.
N
i
e
,
“
M
a
t
h
e
mat
i
c
s
t
e
a
c
h
e
r
s’
g
e
o
me
t
r
i
c
t
h
i
n
k
i
n
g
:
a
c
a
se
st
u
d
y
o
f
i
n
-
ser
v
i
c
e
t
e
a
c
h
e
r
s’
c
o
n
st
r
u
c
t
i
n
g
,
c
o
n
j
e
c
t
u
r
i
n
g
,
a
n
d
e
x
p
l
o
r
i
n
g
w
i
t
h
d
y
n
a
mi
c
g
e
o
me
t
r
y
s
o
f
t
w
a
r
e
,
”
Eu
r
o
p
e
a
n
J
o
u
r
n
a
l
o
f
M
a
t
h
e
m
a
t
i
c
s
a
n
d
S
c
i
e
n
c
e
E
d
u
c
a
t
i
o
n
,
v
o
l
.
4
,
n
o
.
1
,
2
0
2
3
,
p
p
.
6
5
–
7
8
,
M
a
r
.
2
0
2
3
,
d
o
i
:
1
0
.
1
2
9
7
3
/
e
j
mse
.
4
.
1
.
6
5
.
[
3
]
Z.
La
v
i
c
z
a
,
C
.
A
.
A
.
P
.
A
b
a
r
,
a
n
d
M
.
Te
j
e
r
a
,
“
S
p
a
t
i
a
l
g
e
o
me
t
r
i
c
t
h
i
n
k
i
n
g
a
n
d
i
t
s
a
r
t
i
c
u
l
a
t
i
o
n
w
i
t
h
t
h
e
v
i
su
a
l
i
z
a
t
i
o
n
a
n
d
man
i
p
u
l
a
t
i
o
n
o
f
o
b
j
e
c
t
s
i
n
3
D
,
”
Ed
u
c
a
ç
ã
o
Ma
t
e
m
á
t
i
c
a
Pe
s
q
u
i
s
a
R
e
v
i
st
a
d
o
Pro
g
r
a
m
a
d
e
Est
u
d
o
s
P
ó
s
-
G
ra
d
u
a
d
o
s
e
m
E
d
u
c
a
ç
ã
o
Ma
t
e
m
á
t
i
c
a
,
v
o
l
.
2
5
,
n
o
.
2
,
p
p
.
2
5
8
–
2
7
7
,
A
u
g
.
2
0
2
3
,
d
o
i
:
1
0
.
2
3
9
2
5
/
1
9
8
3
-
3
1
5
6
.
2
0
2
3
v
2
5
i
2
p
2
5
8
-
2
7
7
.
[
4
]
L.
D
o
r
e
l
,
“
Th
e
r
e
l
a
t
i
o
n
s
h
i
p
b
e
t
w
e
e
n
v
i
s
u
a
l
a
n
d
a
b
s
t
r
a
c
t
c
o
m
p
r
e
h
e
n
si
o
n
i
n
sp
a
t
i
a
l
g
e
o
m
e
t
r
y
,
a
n
d
i
t
s
i
m
p
o
r
t
a
n
c
e
t
o
d
e
v
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,
h
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t
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M
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o
f
UN
M
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wa
s
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le
c
ted
a
s
th
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se
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re
tary
o
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te
rn
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ti
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l
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s
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ro
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ra
m
o
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M
IP
A
UN
M
i
n
2
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4
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His
re
se
a
rc
h
in
tere
sts
in
c
l
u
d
e
m
a
th
e
m
a
ti
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s
e
d
u
c
a
ti
o
n
,
g
e
o
m
e
tri
c
th
in
k
in
g
,
S
TE
A
M
e
d
u
c
a
ti
o
n
,
f
li
p
p
e
d
c
las
sro
o
m
,
a
n
d
e
t
h
n
o
m
a
th
e
m
a
ti
c
s.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
a
m
m
a
r.
n
a
u
fa
l@u
n
m
.
a
c
.
id
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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J
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2252
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ics
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U
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Ha
sa
n
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d
d
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(
UNHAS
),
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d
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a
n
d
m
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re
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ti
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fro
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sitas
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M
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fro
m
Un
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g
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ri
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k
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ss
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r
(UN
M
),
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n
d
o
n
e
sia
.
His
re
se
a
rc
h
in
tere
sts
a
re
m
a
th
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m
a
ti
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s
e
d
u
c
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ti
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n
,
a
p
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m
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m
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ti
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s in
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ics
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d
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ti
stics
.
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c
a
n
b
e
c
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n
tac
ted
a
t
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m
a
il
:
h
is
y
a
m
ih
sa
n
@u
n
m
.
a
c
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i
d
.
Aul
ia
u
l
Fi
tr
a
h
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a
m
sud
d
in
re
c
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iv
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d
h
e
r
m
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ste
r
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s
d
e
g
re
e
in
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a
t
h
e
m
a
ti
c
s
Ed
u
c
a
ti
o
n
fro
m
Un
i
v
e
rsitas
Ne
g
e
ri
Yo
g
y
a
k
a
rta,
In
d
o
n
e
sia
.
S
h
e
i
s
c
u
rre
n
tl
y
a
lec
tu
re
r
in
th
e
M
a
th
e
m
a
ti
c
s
Ed
u
c
a
ti
o
n
P
r
o
g
ra
m
,
F
a
c
u
lt
y
o
f
Tea
c
h
e
r
Train
i
n
g
a
n
d
E
d
u
c
a
ti
o
n
,
Un
i
v
e
rsitas
M
u
law
a
rm
a
n
,
In
d
o
n
e
sia
.
He
r
c
u
rre
n
t
re
se
a
rc
h
i
n
tere
sts
in
c
lu
d
e
m
a
th
e
m
a
ti
c
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l
li
tera
c
y
a
n
d
re
a
li
stic m
a
th
e
m
a
ti
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s e
d
u
c
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ti
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n
.
S
h
e
c
a
n
b
e
c
o
n
tac
ted
a
t
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m
a
il
:
a
u
l
iau
lfi
trah
@
u
n
m
u
l
.
a
c
.
id
.
Za
id
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i
n
a
l
re
c
e
iv
e
d
th
e
b
a
c
h
e
lo
r
a
n
d
m
a
ste
r’s
in
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a
th
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m
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ti
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s
Ed
u
c
a
ti
o
n
fr
o
m
th
e
Un
iv
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rsitas
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g
e
ri
M
a
k
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ss
a
r,
In
d
o
n
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sia
,
a
n
d
P
h
.
D.
d
e
g
re
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i
n
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th
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m
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ti
c
s
Ed
u
c
a
ti
o
n
fro
m
th
e
Un
iv
e
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n
o
l
o
g
i
M
a
lay
sia
,
M
a
lay
sia
.
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h
a
s
o
v
e
r
2
0
y
e
a
rs
o
f
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p
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rien
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Ac
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m
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n
with
th
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l
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n
d
th
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Un
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g
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ri
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k
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ss
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r,
wh
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so
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ti
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a
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lt
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c
a
ti
o
n
,
Un
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a
s
Ne
g
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ri
M
a
k
a
ss
a
r.
His
c
u
rre
n
t
re
se
a
rc
h
in
tere
st
in
c
lu
d
e
s
m
a
th
e
m
a
ti
c
s
e
d
u
c
a
ti
o
n
,
g
e
o
m
e
tri
c
th
in
k
in
g
,
a
n
d
g
e
o
m
e
try
lea
rn
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n
g
fo
r
p
rima
ry
sc
h
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l
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
z
z
a
id
@u
n
m
.
a
c
.
id
.
Nur
Wa
h
i
d
in
As
h
a
r
i
is
a
L
e
c
tu
re
r
in
M
a
th
e
m
a
ti
c
s
E
d
u
c
a
ti
o
n
P
r
o
g
ra
m
a
t
th
e
F
a
c
u
lt
y
o
f
M
a
th
e
m
a
ti
c
s
a
n
d
Na
tu
ra
l
S
c
ien
c
e
s,
Un
iv
e
rsitas
Ne
g
e
ri
M
a
k
a
ss
a
r
(UN
M
).
He
c
o
m
p
lete
d
h
is
u
n
d
e
rg
ra
d
u
a
te
s
tu
d
ies
in
M
a
th
e
m
a
ti
c
s
Ed
u
c
a
ti
o
n
a
t
Un
i
v
e
rsitas
Ne
g
e
ri
M
a
k
a
ss
a
r
a
n
d
o
b
tai
n
e
d
a
m
a
ste
r’s
d
e
g
re
e
in
M
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th
e
m
a
ti
c
s
Ed
u
c
a
ti
o
n
fro
m
Un
i
v
e
rsitas
P
e
n
d
i
d
ik
a
n
In
d
o
n
e
sia
,
a
lea
d
in
g
i
n
stit
u
t
io
n
i
n
e
d
u
c
a
ti
o
n
in
I
n
d
o
n
e
sia
.
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b
e
g
a
n
h
is
a
c
a
d
e
m
ic
c
a
re
e
r
a
t
Un
iv
e
rsitas
Co
k
ro
a
m
in
o
to
P
a
l
o
p
o
,
wh
e
re
h
e
m
a
d
e
sig
n
ifi
c
a
n
t
c
o
n
tri
b
u
ti
o
n
s
to
t
h
e
d
e
v
e
lo
p
m
e
n
t
o
f
c
u
rricu
l
u
m
a
n
d
t
e
a
c
h
in
g
m
e
th
o
d
s
i
n
m
a
th
e
m
a
ti
c
s.
Cu
rre
n
tl
y
b
a
se
d
a
t
UN
M
,
He
is
a
c
ti
v
e
ly
e
n
g
a
g
e
d
i
n
re
se
a
rc
h
fo
c
u
se
d
o
n
p
ro
b
lem
-
b
a
se
d
lea
rn
in
g
,
p
ro
jec
t
-
b
a
se
d
lea
rn
in
g
,
e
th
n
o
m
a
th
e
m
a
ti
c
s,
g
e
o
m
e
tri
c
th
in
k
in
g
,
h
i
g
h
e
r
o
rd
e
r
th
i
n
k
in
g
sk
il
ls
(HO
TS
),
S
T
EAM
lea
rn
in
g
,
a
n
d
t
h
e
a
p
p
li
c
a
ti
o
n
o
f
a
rti
ficia
l
in
telli
g
e
n
c
e
in
m
a
th
e
m
a
ti
c
s
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
n
u
r.
wa
h
i
d
i
n
.
a
sh
a
ri@u
n
m
.
a
c
.
id
.
Mu
h
a
m
m
a
d
Na
sir
u
H
a
ss
a
n
i
s
a
S
e
n
io
r
Lec
tu
re
r
a
t
t
h
e
S
o
k
o
to
S
tate
U
n
iv
e
rsit
y
,
S
o
k
o
to
,
Ni
g
e
ria.
He
wa
s
a
p
p
o
i
n
ted
a
s
a
ss
ista
n
t
lec
tu
re
r
in
t
h
e
u
n
i
v
e
rsity
in
2
0
1
5
a
n
d
p
r
o
m
o
ted
to
th
e
ra
n
k
o
f
lec
tu
re
r
1
we
n
t
o
n
to
p
u
rs
u
e
h
is
g
ra
d
u
a
te
stu
d
ies
in
M
a
t
h
e
m
a
ti
c
s
Ed
u
c
a
ti
o
n
(P
h
.
D.)
a
t
th
e
U
n
iv
e
rsiti
Te
k
n
o
lo
g
i
M
a
lay
sia
fr
o
m
2
0
1
8
to
2
0
2
1
.
Ha
ss
a
n
’s
re
se
a
rc
h
in
tere
sts
li
e
in
m
a
th
e
m
a
ti
c
s
e
d
u
c
a
ti
o
n
,
g
e
o
m
e
tri
c
th
in
k
in
g
,
tea
c
h
e
r
,
a
n
d
te
a
c
h
e
r
e
d
u
c
a
ti
o
n
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
m
o
h
a
m
m
a
d
.
n
a
siru
h
a
ss
a
n
@s
su
.
e
d
u
.
n
g
.
Evaluation Warning : The document was created with Spire.PDF for Python.