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C
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A
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1.
I
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N
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tem
p
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a
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s
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iab
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[
1
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.
T
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[
2
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T
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[
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3
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Desp
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[
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[
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Fig
u
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s
u
ch
as
“
m
ath
em
atica
l
r
ea
s
o
n
in
g
”
an
d
“
e
d
u
ca
tio
n
al
tech
n
o
lo
g
y
”
,
u
n
d
e
r
lin
in
g
th
eir
cr
u
cial
r
o
le
in
m
ath
em
at
ical
p
ed
ag
o
g
y
.
T
o
r
ef
lect
an
d
d
elv
e
d
ee
p
er
in
to
th
ese
th
em
e
s
,
a
s
ea
r
ch
s
tr
ateg
y
f
o
r
t
h
e
liter
atu
r
e
r
ev
iew
was
d
ev
elo
p
e
d
,
c
o
v
er
in
g
p
u
b
licati
o
n
s
b
etwe
en
2
0
1
8
a
n
d
2
0
2
3
,
u
s
in
g
th
e
f
o
llo
win
g
s
ea
r
ch
s
tr
in
g
:
(
“Ge
o
Geb
r
a”
)
an
d
(
“h
i
g
h
s
ch
o
o
l”
)
an
d
(
“e
x
p
er
im
e
n
tal
s
tu
d
y
”
o
r
“c
ase
s
tu
d
y
”)
an
d
(
“m
ath
em
atics
teac
h
in
g
”
o
r
“e
d
u
ca
tio
n
al
tec
h
n
o
lo
g
y
”)
.
T
h
is
s
ea
r
ch
was
m
eticu
lo
u
s
ly
d
esig
n
ed
to
ca
p
t
u
r
e
t
h
e
ess
en
ce
o
f
em
er
g
in
g
th
em
es a
n
d
d
ir
ec
t th
e
an
aly
s
is
o
f
r
elev
a
n
t liter
atu
r
e.
T
ab
le
1
p
r
esen
ts
a
s
elec
tio
n
o
f
f
u
n
d
am
e
n
tal
an
d
h
ig
h
ly
r
elev
an
t w
o
r
k
s
in
th
e
f
ield
,
id
en
tifi
ed
th
r
o
u
g
h
th
e
s
y
s
tem
atic
liter
atu
r
e
r
ev
ie
w
o
f
th
is
s
tu
d
y
.
T
h
ese
wo
r
k
s
,
r
ec
o
g
n
ized
as
k
ey
r
ef
e
r
en
ce
s
,
ca
n
p
r
o
v
id
e
a
s
o
lid
s
tar
tin
g
p
o
in
t f
o
r
f
u
t
u
r
e
s
tu
d
ie
s
in
th
is
ar
ea
[
9
]
–
[
1
5
]
.
T
h
is
s
tu
d
y
aim
s
to
o
f
f
er
in
s
ig
h
ts
in
to
h
o
w
th
e
in
teg
r
atio
n
o
f
ed
u
ca
tio
n
al
tech
n
o
l
o
g
ies
s
u
ch
as
Geo
Geb
r
a
ca
n
e
n
h
an
c
e
th
e
teac
h
in
g
o
f
tr
ig
o
n
o
m
etr
y
an
d
m
at
h
em
atica
l
co
m
p
eten
cies
in
g
en
er
al
[
5
]
.
T
h
is
co
m
p
r
eh
en
s
iv
e
ap
p
r
o
ac
h
s
ee
k
s
n
o
t
o
n
ly
to
m
ea
s
u
r
e
th
e
a
ca
d
em
ic
im
p
ac
t
o
f
Geo
Geb
r
a
b
u
t
also
to
u
n
d
e
r
s
tan
d
s
tu
d
en
ts
’
e
x
p
er
ie
n
ce
s
with
th
is
to
o
l,
t
h
er
eb
y
p
r
o
v
id
in
g
a
d
ee
p
p
er
s
p
ec
tiv
e
o
n
th
e
in
teg
r
atio
n
o
f
tech
n
o
l
o
g
y
in
m
ath
e
m
atics
ed
u
ca
tio
n
[
1
6
]
,
[
1
7
]
.
T
h
e
an
ticip
ated
f
in
d
in
g
s
o
f
th
e
s
tu
d
y
ar
e
ex
p
ec
ted
to
o
f
f
e
r
v
alu
a
b
le
in
s
ig
h
ts
f
o
r
ed
u
ca
t
o
r
s
an
d
p
o
licy
m
ak
e
r
s
in
ter
ested
in
im
p
r
o
v
i
n
g
b
o
th
th
e
teac
h
in
g
o
f
tr
ig
o
n
o
m
etr
y
an
d
g
en
er
al
m
ath
em
atica
l c
o
m
p
ete
n
cies.
Fig
u
r
e
1
.
Key
ter
m
s
co
-
o
c
cu
r
r
en
ce
m
ap
2.
M
E
T
H
O
D
T
o
in
v
esti
g
ate
h
o
w
th
e
Geo
Geb
r
a
s
o
f
twar
e
im
p
ac
ts
tr
ig
o
n
o
m
etr
y
lear
n
in
g
in
a
ten
th
-
g
r
a
d
e
m
ath
em
atics
class
,
a
ca
s
e
s
tu
d
y
in
ter
v
e
n
tio
n
was
im
p
lem
e
n
ted
in
Mo
n
ter
ía
,
C
o
lo
m
b
ia
.
T
h
e
s
tu
d
y
ad
o
p
ted
a
m
ix
ed
-
m
eth
o
d
s
d
ata
co
llectio
n
ap
p
r
o
ac
h
,
in
te
g
r
atin
g
b
o
th
q
u
an
titativ
e
an
d
q
u
alitativ
e
m
et
h
o
d
s
.
T
h
is
m
eth
o
d
allo
wed
f
o
r
a
m
o
r
e
co
m
p
r
e
h
en
s
iv
e
ass
ess
m
en
t
o
f
Geo
Geb
r
a
’
s
im
p
ac
t,
ca
p
tu
r
in
g
n
o
t
o
n
ly
c
h
an
g
es
in
ac
ad
em
ic
p
er
f
o
r
m
an
ce
b
u
t a
ls
o
s
tu
d
en
ts
’
p
er
ce
p
tio
n
s
an
d
ex
p
er
ien
ce
s
.
T
h
is
m
ix
ed
ap
p
r
o
ac
h
was
cr
u
cial
to
u
n
d
e
r
s
tan
d
in
g
Geo
G
eb
r
a
’
s
in
f
lu
en
ce
o
n
v
ar
io
u
s
asp
ec
ts
o
f
lear
n
in
g
.
I
n
ad
d
itio
n
to
m
ea
s
u
r
in
g
im
p
r
o
v
em
en
ts
in
tr
ig
o
n
o
m
etr
ic
s
k
ills
,
s
tu
d
en
ts
’
attitu
d
es
an
d
r
esp
o
n
s
es
to
th
e
u
s
e
o
f
t
h
is
tech
n
o
l
o
g
ical
to
o
l
wer
e
e
x
p
lo
r
e
d
.
T
h
is
s
ec
tio
n
o
f
th
e
s
tu
d
y
p
r
o
v
id
es
d
etails
ab
o
u
t
th
e
p
ar
ticip
an
ts
,
th
e
e
d
u
ca
tio
n
al
s
ettin
g
,
th
e
i
n
ter
v
en
tio
n
m
et
h
o
d
o
lo
g
y
,
th
e
s
tu
d
y
’
s
d
u
r
atio
n
,
t
h
e
ass
ess
m
en
t
to
o
ls
u
s
ed
,
an
d
th
e
m
et
h
o
d
s
em
p
lo
y
ed
f
o
r
a
n
aly
zin
g
t
h
e
co
llecte
d
d
ata.
B
y
co
m
b
in
i
n
g
d
if
f
er
en
t
r
esear
ch
m
eth
o
d
s
,
th
e
s
tu
d
y
o
f
f
er
ed
a
m
o
r
e
co
m
p
lete
an
d
n
u
an
ce
d
p
er
s
p
ec
t
iv
e
o
n
th
e
r
o
le
o
f
Geo
Ge
b
r
a
in
t
h
e
m
ath
em
atics
class
r
o
o
m
.
T
h
e
d
ata
co
llecte
d
th
r
o
u
g
h
th
is
m
ix
ed
m
eth
o
d
o
lo
g
y
n
o
t
o
n
ly
in
f
o
r
m
ed
a
b
o
u
t
p
er
f
o
r
m
a
n
ce
o
u
tco
m
es
b
u
t
also
p
r
o
v
id
ed
v
alu
ab
le
in
s
ig
h
ts
in
to
h
o
w
Geo
Geb
r
a
ca
n
b
e
ef
f
ec
tiv
ely
in
teg
r
ated
in
t
o
tr
ig
o
n
o
m
et
r
y
teac
h
in
g
to
e
n
h
a
n
ce
s
tu
d
en
ts
’
ed
u
ca
tio
n
al
ex
p
e
r
ien
ce
.
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
.
13
,
No
.
5
,
Octo
b
er
2
0
2
4
:
2
8
7
6
-
2889
2878
T
ab
le
1
.
C
o
m
p
a
r
ativ
e
an
aly
s
is
o
f
s
tu
d
ies o
n
t
h
e
ap
p
licatio
n
o
f
Geo
Geb
r
a
in
m
ath
em
atica
l e
d
u
ca
tio
n
S
t
u
d
y
S
t
u
d
y
p
u
r
p
o
s
e
K
e
y
d
i
s
c
o
v
e
r
i
e
s
K
e
y
c
o
n
t
r
i
b
u
t
i
o
n
s
S
t
u
d
y
si
g
n
i
f
i
c
a
n
c
e
P
r
o
sp
e
c
t
s
[
9
]
I
mp
a
c
t
o
f
t
h
e
B
-
G
e
o
M
o
d
u
l
e
o
n
p
r
o
b
l
e
m
-
so
l
v
i
n
g
i
n
r
u
r
a
l
se
c
o
n
d
a
r
y
st
u
d
e
n
t
s
I
mp
r
o
v
e
d
p
r
o
b
l
e
m
-
so
l
v
i
n
g
a
b
i
l
i
t
i
e
s
Ef
f
e
c
t
i
v
e
n
e
ss
o
f
G
e
o
G
e
b
r
a
i
n
t
a
sk
-
b
a
s
e
d
t
e
a
c
h
i
n
g
I
mp
o
r
t
a
n
c
e
o
f
d
i
g
i
t
a
l
t
o
o
l
s
i
n
m
a
t
h
e
m
a
t
i
c
a
l
sk
i
l
l
s
Ex
p
a
n
d
e
d
u
s
e
o
f
G
e
o
G
e
b
r
a
i
n
e
d
u
c
a
t
i
o
n
a
l
s
e
t
t
i
n
g
s
[
1
0
]
D
e
v
e
l
o
p
m
e
n
t
o
f
mat
h
e
m
a
t
i
c
a
l
c
o
mm
u
n
i
c
a
t
i
o
n
sk
i
l
l
s
w
i
t
h
G
e
o
G
e
b
r
a
S
i
g
n
i
f
i
c
a
n
t
i
mp
r
o
v
e
me
n
t
i
n
c
o
mm
u
n
i
c
a
t
i
o
n
sk
i
l
l
s
Ef
f
i
c
a
c
y
o
f
G
e
o
G
e
b
r
a
i
n
mat
h
e
m
a
t
i
c
a
l
c
o
mm
u
n
i
c
a
t
i
o
n
V
a
l
u
e
o
f
i
n
t
e
r
a
c
t
i
v
e
so
f
t
w
a
r
e
i
n
mat
h
e
m
a
t
i
c
a
l
u
n
d
e
r
s
t
a
n
d
i
n
g
A
d
o
p
t
i
o
n
o
f
G
e
o
G
e
b
r
a
i
n
d
i
v
e
r
se
e
d
u
c
a
t
i
o
n
a
l
e
n
v
i
r
o
n
m
e
n
t
s
[
1
1
]
I
mp
a
c
t
o
f
G
e
o
G
e
b
r
a
so
f
t
w
a
r
e
o
n
g
e
o
m
e
t
r
y
p
e
r
f
o
r
m
a
n
c
e
a
n
d
a
t
t
i
t
u
d
e
Ex
p
e
r
i
m
e
n
t
a
l
g
r
o
u
p
o
u
t
p
e
r
f
o
r
me
d
c
o
n
t
r
o
l
g
r
o
u
p
Emp
i
r
i
c
a
l
e
v
i
d
e
n
c
e
o
f
G
e
o
G
e
b
r
a
b
e
n
e
f
i
t
s
i
n
g
e
o
me
t
r
y
I
n
t
e
g
r
a
t
i
o
n
o
f
t
e
c
h
n
o
l
o
g
y
t
o
e
n
h
a
n
c
e
l
e
a
r
n
i
n
g
o
u
t
c
o
mes
R
e
se
a
r
c
h
o
n
G
e
o
G
e
b
r
a
e
f
f
e
c
t
s
a
c
r
o
ss
d
i
f
f
e
r
e
n
t
e
d
u
c
a
t
i
o
n
a
l
l
e
v
e
l
s
[
1
2
]
G
e
o
G
e
b
r
a
i
n
u
n
d
e
r
s
t
a
n
d
i
n
g
c
o
n
t
i
n
u
i
t
y
a
n
d
p
r
o
c
e
d
u
r
a
l
k
n
o
w
l
e
d
g
e
i
m
p
r
o
v
e
me
n
t
S
u
p
p
o
r
t
s
p
r
o
c
e
d
u
r
a
l
k
n
o
w
l
e
d
g
e
i
mp
r
o
v
e
me
n
t
I
mp
o
r
t
a
n
c
e
o
f
TPA
C
K
f
o
r
e
f
f
e
c
t
i
v
e
G
e
o
G
e
b
r
a
u
se
R
e
l
e
v
a
n
c
e
i
n
e
d
u
c
a
t
i
o
n
a
l
s
e
t
t
i
n
g
s
f
o
r
v
i
s
u
a
l
i
z
i
n
g
mat
h
e
m
a
t
i
c
a
l
c
o
n
c
e
p
t
s
R
e
se
a
r
c
h
o
n
TPA
C
K
a
n
d
s
o
c
i
a
l
p
r
o
x
i
m
i
t
y
f
a
c
t
o
r
s
[
1
3
]
G
e
o
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C
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g
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n
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st
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t
s
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n
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l
g
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b
r
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c
c
o
n
c
e
p
t
s
B
r
o
a
d
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r
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mp
l
e
m
e
n
t
a
t
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o
n
o
f
G
e
o
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e
b
r
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n
t
e
c
h
n
o
l
o
g
y
-
a
ss
i
st
e
d
l
e
a
r
n
i
n
g
st
r
a
t
e
g
i
e
s
[
1
4
]
Ef
f
e
c
t
i
v
e
n
e
ss
o
f
i
n
s
t
r
u
c
t
i
o
n
a
l
p
r
o
m
p
t
s
i
n
G
e
o
G
e
b
r
a
f
o
r
g
i
f
t
e
d
st
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d
e
n
t
s
i
n
m
a
t
h
e
mat
i
c
s
I
mp
r
o
v
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m
e
n
t
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n
l
e
a
r
n
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n
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a
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h
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e
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me
n
t
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o
f
g
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e
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st
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t
s
I
mp
r
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v
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d
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n
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t
r
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c
t
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o
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a
l
st
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e
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n
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e
g
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t
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p
r
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mp
t
s
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t
o
G
e
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r
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C
o
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r
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b
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t
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c
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t
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g
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f
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st
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s
En
h
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g
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t
i
o
n
t
h
r
o
u
g
h
t
e
c
h
n
o
l
o
g
y
[
1
5
]
C
o
n
t
r
i
b
u
t
i
o
n
s
,
c
h
a
l
l
e
n
g
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a
n
d
l
i
m
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t
a
t
i
o
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f
G
e
o
G
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r
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h
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m
a
t
h
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m
a
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c
s
I
mp
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v
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t
e
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e
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t
a
n
d
a
c
h
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e
v
e
me
n
t
i
n
mat
h
e
m
a
t
i
c
s
Te
c
h
n
o
l
o
g
i
c
a
l
f
l
u
e
n
c
y
a
m
o
n
g
u
sers
a
n
d
s
t
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d
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n
t
-
t
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c
h
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r
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C
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G
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t
e
x
t
s
2
.
1
.
P
a
rt
icipa
nts
T
o
co
n
d
u
ct
th
is
s
tu
d
y
,
a
ca
r
ef
u
l
s
elec
tio
n
o
f
1
2
7
ten
th
-
g
r
ad
e
s
tu
d
en
ts
f
r
o
m
a
s
ch
o
o
l
in
Mo
n
ter
ía
was
m
ad
e.
T
h
e
c
h
o
ice
o
f
th
ese
p
ar
ticip
an
ts
was
b
ased
o
n
th
ei
r
ac
ad
em
ic
p
er
f
o
r
m
a
n
ce
i
n
m
ath
em
atics
an
d
,
in
p
ar
ticu
lar
,
t
h
e
ch
allen
g
es
th
ey
f
ac
ed
in
th
e
ar
ea
o
f
t
r
ig
o
n
o
m
e
tr
y
.
T
h
is
p
u
r
p
o
s
ef
u
l
s
elec
tio
n
allo
wed
f
o
r
a
m
o
r
e
f
o
cu
s
ed
an
d
r
ele
v
an
t
an
aly
s
is
o
f
th
e
im
p
ac
t
o
f
Geo
Geb
r
a
o
n
s
tu
d
en
ts
wh
o
s
h
o
wed
s
p
e
cif
ic
n
ee
d
s
in
th
is
d
is
cip
lin
e
[
1
8
]
.
T
h
is
tar
g
eted
a
p
p
r
o
ac
h
e
n
s
u
r
e
d
th
at
th
e
s
tu
d
y
f
o
c
u
s
ed
o
n
th
o
s
e
s
tu
d
en
ts
f
o
r
wh
o
m
th
e
in
t
er
v
en
tio
n
co
u
ld
b
e
m
o
s
t
b
en
e
f
icial.
B
y
co
n
ce
n
tr
atin
g
o
n
s
tu
d
en
ts
with
p
ar
ticu
lar
d
if
f
icu
lties
in
tr
ig
o
n
o
m
etr
y
,
th
e
s
tu
d
y
aim
ed
to
ex
p
lo
r
e
n
o
t
o
n
ly
th
e
g
en
er
al
ef
f
icac
y
o
f
Geo
Geb
r
a
b
u
t
also
its
p
o
ten
tial
to
a
d
d
r
es
s
s
p
ec
if
ic
lear
n
in
g
ch
allen
g
es.
T
h
is
m
eth
o
d
o
lo
g
y
h
elp
ed
en
s
u
r
e
th
at
th
e
s
tu
d
y
’
s
r
esu
lts
wer
e
b
o
th
r
elev
an
t
a
n
d
ap
p
licab
le
t
o
a
r
ea
l e
d
u
ca
tio
n
al
c
o
n
tex
t.
2
.
2
.
Study
des
ig
n
T
h
e
d
esig
n
o
f
th
is
s
tu
d
y
in
clu
d
ed
a
q
u
asi
-
ex
p
er
im
e
n
tal
ap
p
r
o
ac
h
u
s
in
g
p
r
etest/p
o
s
ttes
t
ass
ess
m
en
ts
.
T
h
is
m
eth
o
d
allo
wed
f
o
r
th
e
o
b
s
er
v
atio
n
an
d
co
m
p
ar
is
o
n
o
f
ea
ch
s
tu
d
en
t
’
s
p
er
f
o
r
m
a
n
ce
in
tr
ig
o
n
o
m
etr
y
b
ef
o
r
e
a
n
d
af
ter
t
h
e
im
p
lem
en
tatio
n
o
f
Geo
Geb
r
a.
T
h
is
ap
p
r
o
ac
h
p
r
o
v
id
es
a
clea
r
an
d
d
ir
e
ct
ev
alu
atio
n
o
f
th
e
im
p
ac
t th
at
th
e
s
o
f
twar
e
h
ad
o
n
th
e
s
tu
d
en
ts
’
lear
n
in
g
a
n
d
u
n
d
er
s
tan
d
in
g
[
1
9
]
.
T
h
e
ad
v
an
tag
e
o
f
th
is
q
u
asi
-
ex
p
er
im
en
tal
d
esig
n
lies
in
its
ab
ilit
y
to
m
ea
s
u
r
e
th
e
s
p
ec
if
ic
ef
f
ec
ts
o
f
th
e
in
ter
v
en
tio
n
o
n
th
e
s
am
e
g
r
o
u
p
o
f
s
tu
d
en
ts
.
B
y
co
m
p
ar
in
g
t
h
e
r
esu
lts
o
f
th
e
p
r
etest
an
d
p
o
s
ttes
t
ass
es
s
m
en
ts
,
im
p
r
o
v
em
en
ts
ca
n
b
e
id
en
tifie
d
n
o
t
o
n
ly
in
tr
ig
o
n
o
m
et
r
ic
s
k
ills
b
u
t
also
in
o
th
er
asp
ec
ts
o
f
ac
ad
em
ic
p
er
f
o
r
m
an
ce
.
T
h
is
ap
p
r
o
ac
h
h
elp
s
to
d
eter
m
in
e
th
e
ef
f
ec
tiv
en
ess
o
f
Geo
Geb
r
a
in
th
e
class
r
o
o
m
,
o
f
f
er
in
g
v
alu
a
b
le
in
s
ig
h
ts
f
o
r
f
u
tu
r
e
p
e
d
ag
o
g
ical
s
tr
ateg
ies.
2
.
3
.
I
nte
rv
ent
io
n
t
o
o
l
I
n
th
e
s
tu
d
y
,
th
e
m
at
h
em
atica
l
s
im
u
lato
r
Ge
o
Geb
r
a
was
u
s
ed
as
th
e
p
r
im
a
r
y
in
ter
v
en
ti
o
n
to
o
l
t
o
co
m
p
lem
en
t
tr
a
d
itio
n
al
tr
ig
o
n
o
m
etr
y
teac
h
i
n
g
.
T
h
is
o
p
en
-
s
o
u
r
ce
ed
u
ca
tio
n
al
s
o
f
twar
e
o
f
f
er
s
an
in
ter
ac
tiv
e
p
latf
o
r
m
th
at
en
r
ich
es
th
e
lear
n
in
g
ex
p
e
r
ien
ce
in
m
ath
em
atics
[
5
]
,
[
8
]
,
[
2
0
]
.
I
ts
im
p
lem
en
tatio
n
allo
wed
s
tu
d
en
ts
to
ex
p
lo
r
e
tr
ig
o
n
o
m
e
tr
ic
co
n
ce
p
ts
in
a
m
o
r
e
d
y
n
a
m
ic
an
d
v
is
u
al
m
an
n
er
,
f
ac
ili
tatin
g
a
d
ee
p
er
an
d
m
o
r
e
ap
p
lied
u
n
d
er
s
tan
d
in
g
o
f
th
e
co
u
r
s
e
[
9
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t
J
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&
R
es E
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8
8
2
2
I
mp
r
o
vin
g
tr
ig
o
n
o
metric c
o
mp
eten
cy
w
ith
Geo
Geb
r
a
:
a
q
u
a
s
i
-
ex
p
erimen
ta
l
…
(
Yu
lieth
C
a
r
r
ia
z
o
-
R
eg
in
o
)
2879
T
h
e
in
teg
r
atio
n
o
f
Geo
Geb
r
a
in
to
th
e
cu
r
r
icu
l
u
m
aim
ed
n
o
t
o
n
ly
to
im
p
r
o
v
e
ac
ad
e
m
ic
p
e
r
f
o
r
m
a
n
ce
in
tr
ig
o
n
o
m
etr
y
b
u
t
also
to
p
r
o
m
o
te
a
m
o
r
e
in
te
r
ac
tiv
e
an
d
p
ar
ticip
ato
r
y
lear
n
in
g
ap
p
r
o
ac
h
.
T
h
e
in
tu
itiv
e
an
d
v
er
s
atile
n
atu
r
e
o
f
th
is
s
o
f
tw
ar
e
m
ak
es
it
a
v
alu
ab
le
to
o
l
f
o
r
illu
s
tr
atin
g
co
m
p
lex
m
ath
em
atica
l
co
n
ce
p
ts
,
en
ab
lin
g
s
tu
d
en
ts
to
ex
p
er
i
m
en
t
with
d
if
f
er
en
t
p
r
o
b
lem
s
an
d
s
o
lu
tio
n
s
in
r
ea
l
tim
e.
T
h
e
ad
o
p
tio
n
o
f
Geo
Geb
r
a
in
th
is
s
tu
d
y
u
n
d
e
r
s
co
r
es
th
e
g
r
o
win
g
im
p
o
r
tan
c
e
o
f
c
o
m
b
in
i
n
g
tr
a
d
itio
n
al
tea
ch
in
g
m
et
h
o
d
s
with
in
n
o
v
ativ
e
tec
h
n
o
lo
g
ies in
th
e
ed
u
ca
tio
n
al
f
ield
.
2
.
4
.
I
nte
rv
ent
io
n
pro
ce
du
re
s
T
h
e
in
ter
v
en
tio
n
in
th
is
s
tu
d
y
f
o
cu
s
ed
o
n
i
n
teg
r
atin
g
Geo
Ge
b
r
a
in
to
tr
ig
o
n
o
m
etr
y
teac
h
in
g
s
ess
io
n
s
,
s
p
an
n
in
g
a
p
er
i
o
d
o
f
s
ix
m
o
n
th
s
.
Du
r
in
g
th
is
tim
e,
s
tu
d
en
ts
ac
tiv
ely
u
s
ed
th
e
s
im
u
lato
r
u
n
d
er
th
e
s
u
p
er
v
is
io
n
an
d
g
u
i
d
an
ce
o
f
th
eir
teac
h
er
s
to
d
elv
e
in
to
v
ar
io
u
s
co
n
ce
p
ts
,
th
eo
r
em
s
,
an
d
tr
i
g
o
n
o
m
et
r
ic
p
r
o
b
lem
s
.
T
h
is
in
ter
ac
tiv
e
to
o
l
allo
wed
th
e
m
to
ex
p
lo
r
e
a
n
d
u
n
d
er
s
tan
d
tr
ig
o
n
o
m
etr
y
i
n
a
m
o
r
e
d
y
n
am
ic
an
d
e
n
g
ag
in
g
m
an
n
er
[
2
1
]
.
Fu
r
th
e
r
m
o
r
e
,
to
m
ax
im
ize
th
e
lear
n
in
g
p
o
te
n
tial,
s
p
ec
if
ic
ac
tiv
ities
an
d
ex
er
cises
in
Geo
Geb
r
a
wer
e
d
esig
n
ed
to
r
ein
f
o
r
ce
th
e
co
n
ce
p
ts
tau
g
h
t
in
class
.
T
h
es
e
ac
tiv
ities
wer
e
aim
ed
at
p
r
o
m
o
tin
g
n
o
t
ju
s
t
th
e
m
em
o
r
izatio
n
o
f
f
o
r
m
u
las
an
d
p
r
o
ce
d
u
r
es,
b
u
t
also
at
f
o
s
ter
in
g
a
d
ee
p
e
r
c
o
n
ce
p
tu
al
u
n
d
er
s
tan
d
in
g
.
T
h
e
in
clu
s
io
n
o
f
Geo
Geb
r
a
as
a
d
id
ac
tic
to
o
l
in
th
e
tr
ig
o
n
o
m
etr
y
cu
r
r
icu
l
u
m
r
ep
r
es
en
ted
a
s
ig
n
if
ican
t
ad
v
an
ce
m
e
n
t
in
teac
h
in
g
m
e
th
o
d
o
lo
g
y
,
alig
n
in
g
with
co
n
tem
p
o
r
a
r
y
t
r
en
d
s
o
f
i
n
co
r
p
o
r
atin
g
ed
u
ca
tio
n
al
tech
n
o
lo
g
ies in
th
e
class
r
o
o
m
to
en
h
an
ce
th
e
lear
n
i
n
g
p
r
o
ce
s
s
.
2
.
5
.
E
v
a
lua
t
i
o
n
m
ea
s
ures
T
o
ass
ess
th
e
im
p
ac
t
o
f
G
eo
Geb
r
a
o
n
tr
ig
o
n
o
m
et
r
y
le
ar
n
in
g
,
two
ev
alu
atio
n
m
eth
o
d
s
wer
e
im
p
lem
en
ted
[
2
2
]
.
I
n
itially
,
a
p
r
etest
was
ad
m
in
is
ter
ed
to
s
tu
d
en
ts
to
estab
lis
h
th
eir
lev
el
o
f
co
m
p
eten
ce
in
tr
ig
o
n
o
m
et
r
y
b
e
f
o
r
e
th
e
i
n
ter
v
en
tio
n
.
Su
b
s
eq
u
en
tly
,
a
p
o
s
ttes
t
was
co
n
d
u
cted
af
ter
th
e
co
m
p
letio
n
o
f
th
e
in
ter
v
en
tio
n
p
er
io
d
,
aim
in
g
to
m
ea
s
u
r
e
im
p
r
o
v
em
e
n
ts
in
s
tu
d
en
ts
’
ac
ad
em
ic
p
er
f
o
r
m
an
ce
[
2
3
]
.
T
h
ese
ass
es
s
m
en
ts
co
n
s
is
ted
o
f
tr
ig
o
n
o
m
etr
y
p
r
o
b
lem
s
d
esig
n
ed
t
o
ev
alu
ate
b
o
t
h
co
n
ce
p
tu
al
an
d
p
r
o
ce
d
u
r
al
s
k
ills
.
I
n
ad
d
itio
n
to
th
ese
q
u
a
n
titativ
e
test
s
,
q
u
alitativ
e
d
ata
wer
e
co
llected
to
en
r
ich
th
e
an
al
y
s
is
[
2
3
]
,
[
2
4
]
.
T
h
ese
in
clu
d
ed
d
etailed
class
r
o
o
m
o
b
s
er
v
atio
n
s
,
lear
n
i
n
g
jo
u
r
n
als
k
e
p
t
b
y
s
tu
d
en
ts
,
a
n
d
s
em
i
-
s
tr
u
ctu
r
e
d
in
ter
v
iews.
T
h
ese
m
eth
o
d
s
p
r
o
v
id
ed
a
d
ee
p
er
u
n
d
er
s
tan
d
i
n
g
o
f
h
o
w
s
tu
d
e
n
ts
in
ter
ac
ted
with
Geo
Geb
r
a
an
d
h
o
w
it
in
f
lu
en
c
ed
th
eir
lea
r
n
i
n
g
p
r
o
ce
s
s
.
T
h
e
co
m
b
in
ed
a
p
p
r
o
ac
h
o
f
q
u
an
titativ
e
an
d
q
u
alitativ
e
ass
e
s
s
m
en
ts
allo
wed
f
o
r
a
c
o
m
p
r
e
h
en
s
iv
e
ev
alu
atio
n
o
f
Geo
Geb
r
a
’
s
ef
f
ec
t,
o
f
f
er
in
g
a
m
o
r
e
c
o
m
p
lete
v
iew
o
f
th
e
ed
u
ca
tio
n
al
im
p
ac
t
o
f
th
e
s
o
f
t
war
e
in
tr
ig
o
n
o
m
etr
y
teac
h
in
g
.
2
.
6
.
Da
t
a
a
na
ly
s
is
T
h
e
q
u
a
n
titativ
e
d
ata
o
b
tain
ed
f
r
o
m
th
e
p
r
etest
an
d
p
o
s
ttes
t
wer
e
an
aly
ze
d
u
s
in
g
d
escr
ip
tiv
e
s
tatis
t
ics,
wh
er
e
th
e
m
ea
n
a
n
d
s
tan
d
ar
d
d
ev
iatio
n
f
o
r
ea
ch
s
et
o
f
s
co
r
es
wer
e
ca
lcu
late
d
[
2
5
]
.
T
o
id
en
tif
y
s
ig
n
if
ican
t
d
if
f
er
en
ce
s
in
s
tu
d
en
ts
’
ac
ad
em
ic
p
er
f
o
r
m
an
c
e
b
ef
o
r
e
an
d
af
ter
th
e
in
ter
v
en
tio
n
,
th
e
p
ai
r
ed
s
am
p
les t
-
test
was u
til
ized
[
2
6
]
.
T
h
e
e
q
u
atio
n
f
o
r
t
h
e
p
air
ed
s
am
p
les t
-
test
is
a
s
(
1
)
:
=
̿
−
√
(
1
)
w
h
er
e
,
t
is
th
e
t
-
test
s
tatis
tic,
̿
is
th
e
m
ea
n
o
f
th
e
d
if
f
e
r
en
ce
s
,
μD
is
th
e
p
o
p
u
latio
n
m
ea
n
d
if
f
er
en
ce
(
w
h
ich
is
g
en
er
ally
ass
u
m
ed
to
b
e
0
in
th
e
n
u
ll
h
y
p
o
t
h
esis
)
,
S
D
is
th
e
s
tan
d
ar
d
d
ev
iatio
n
o
f
th
e
d
if
f
e
r
en
ce
s
,
an
d
n
is
th
e
s
am
p
le
s
ize.
T
h
e
q
u
alitativ
e
d
ata
wer
e
an
a
ly
ze
d
th
r
o
u
g
h
th
e
m
atic
co
n
te
n
t
an
aly
s
is
,
aim
in
g
to
id
en
tif
y
r
ec
u
r
r
in
g
th
em
es
an
d
p
atter
n
s
in
s
tu
d
en
ts
’
lear
n
in
g
ex
p
er
ien
ce
s
with
Geo
Geb
r
a
[
2
7
]
.
T
o
en
s
u
r
e
th
e
r
eliab
ilit
y
o
f
th
e
co
n
ten
t
an
aly
s
is
,
C
o
h
en
’
s
Kap
p
a
co
ef
f
icien
t
was
ca
lcu
lated
,
wh
ich
m
ea
s
u
r
es
th
e
lev
el
o
f
ag
r
ee
m
en
t
b
etwe
en
two
co
d
er
s
[
2
8
]
.
T
h
e
eq
u
atio
n
(
2
)
is
f
o
r
ca
lcu
latin
g
C
o
h
e
n
’
s
Kap
p
a
co
ef
f
icien
t
.
=
0
−
ℯ
1
−
ℯ
(
2
)
w
h
er
e
,
k
is
C
o
h
en
’
s
Kap
p
a
co
ef
f
icien
t,
P
0
is
th
e
o
b
s
er
v
e
d
ag
r
ee
m
en
t p
r
o
p
o
r
tio
n
b
etwe
en
t
h
e
co
d
er
s
,
an
d
P
e
is
th
e
p
r
o
p
o
r
tio
n
o
f
a
g
r
ee
m
e
n
t th
at
wo
u
ld
b
e
e
x
p
ec
ted
b
y
c
h
an
ce
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
r
esu
lts
o
f
th
e
s
tu
d
y
in
v
o
l
v
in
g
t
h
e
u
s
e
o
f
Geo
Geb
r
a
as
a
d
id
ac
tic
to
o
l
in
a
tr
i
g
o
n
o
m
etr
y
class
f
o
r
an
ex
p
e
r
im
en
tal
g
r
o
u
p
o
f
ten
t
h
-
g
r
ad
e
s
tu
d
en
ts
in
Mo
n
ter
ía
wer
e
an
aly
ze
d
an
d
co
m
p
ar
ed
with
a
co
n
tr
o
l
g
r
o
u
p
th
at
r
ec
eiv
ed
tr
ad
itio
n
al
teac
h
in
g
.
T
h
is
an
aly
s
is
f
o
c
u
s
ed
o
n
ev
alu
atin
g
k
e
y
c
o
m
p
eten
cies
s
u
ch
as
r
ea
s
o
n
in
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es
E
d
u
c
,
Vo
l
.
13
,
No
.
5
,
Octo
b
er
2
0
2
4
:
2
8
7
6
-
2889
2880
an
d
ar
g
u
m
en
tatio
n
,
c
o
m
m
u
n
ic
atio
n
,
r
ep
r
esen
tatio
n
a
n
d
m
o
d
elin
g
,
an
d
p
r
o
b
lem
p
o
s
in
g
an
d
s
o
lv
in
g
.
Ass
ess
in
g
th
ese
co
m
p
eten
cies w
as c
r
u
cia
l to
d
eter
m
in
e
th
e
ef
f
ec
tiv
e
im
p
ac
t o
f
Geo
Geb
r
a
o
n
s
tu
d
en
t l
ea
r
n
in
g
.
T
o
ca
r
r
y
o
u
t
th
is
an
aly
s
is
,
a
s
et
o
f
s
p
ec
if
ic
item
s
d
etailed
i
n
T
ab
le
2
,
wh
ic
h
f
o
r
m
s
p
a
r
t
o
f
th
e
d
ata
co
llectio
n
in
s
tr
u
m
e
n
t,
was
u
s
ed
.
T
h
ese
item
s
wer
e
ca
r
ef
u
ll
y
s
elec
ted
to
ef
f
ec
tiv
ely
e
v
al
u
ate
th
e
m
en
tio
n
ed
co
m
p
eten
cies.
T
h
e
co
m
p
ar
is
o
n
b
etwe
en
th
e
ex
p
e
r
im
en
tal
a
n
d
co
n
tr
o
l
g
r
o
u
p
s
p
r
o
v
id
ed
v
alu
ab
le
in
s
ig
h
t
in
to
th
e
ef
f
ec
tiv
en
ess
o
f
teac
h
in
g
m
eth
o
d
o
lo
g
ies,
b
o
th
tr
a
d
itio
n
al
an
d
in
n
o
v
ativ
e,
in
i
m
p
r
o
v
i
n
g
ac
ad
em
ic
p
er
f
o
r
m
an
ce
an
d
tr
ig
o
n
o
m
etr
y
s
k
ills
o
f
s
tu
d
en
ts
.
T
h
is
co
m
p
ar
ativ
e
ap
p
r
o
ac
h
a
llo
wed
n
o
t
o
n
ly
to
m
ea
s
u
r
e
th
e
ef
f
icac
y
o
f
Geo
Geb
r
a
in
en
h
an
cin
g
s
p
ec
if
ic
co
m
p
eten
cies
b
u
t
also
to
g
ain
a
b
r
o
ad
er
u
n
d
er
s
ta
n
d
in
g
o
f
h
o
w
th
e
in
teg
r
atio
n
o
f
tech
n
o
lo
g
y
in
teac
h
in
g
ca
n
in
f
lu
en
ce
th
e
ed
u
ca
tio
n
al
p
r
o
ce
s
s
.
T
h
e
in
clu
s
io
n
o
f
a
tr
ad
itio
n
al
co
n
tr
o
l
g
r
o
u
p
p
r
o
v
id
e
d
a
s
ig
n
if
ican
t
b
en
ch
m
a
r
k
f
o
r
ass
ess
in
g
th
e
b
en
ef
its
o
f
Geo
Ge
b
r
a
-
ass
is
ted
teac
h
in
g
co
m
p
a
r
ed
to
co
n
v
en
tio
n
al
m
eth
o
d
s
.
T
h
e
f
o
llo
win
g
ar
e
th
e
r
esu
lts
o
b
tain
ed
in
th
e
p
r
etes
t.
T
ab
le
2
.
L
is
t o
f
item
s
f
o
r
th
e
i
n
f
o
r
m
atio
n
co
llectio
n
i
n
s
tr
u
m
en
t
C
o
m
p
e
t
e
n
c
y
I
n
d
i
c
a
t
o
r
s
I
t
e
ms f
r
o
m t
h
e
i
n
st
r
u
m
e
n
t
C
o
m
p
e
t
e
n
c
y
o
f
r
e
a
so
n
i
n
g
a
n
d
a
r
g
u
me
n
t
a
t
i
o
n
−
A
r
g
u
e
,
e
x
p
l
a
i
n
,
a
n
d
j
u
st
i
f
y
c
h
o
i
c
e
s i
n
p
r
o
c
e
d
u
r
e
s i
n
v
o
l
v
i
n
g
t
r
i
g
o
n
o
m
e
t
r
i
c
r
a
t
i
o
s.
−
F
o
r
mu
l
a
t
e
h
y
p
o
t
h
e
ses
a
n
d
ma
k
e
c
o
n
j
e
c
t
u
r
e
s,
u
s
i
n
g
t
r
i
g
o
n
o
me
t
r
i
c
r
a
t
i
o
s.
−
Ex
p
l
o
r
e
e
x
a
m
p
l
e
s a
n
d
c
o
u
n
t
e
r
e
x
a
mp
l
e
s rel
a
t
e
d
t
o
t
r
i
g
o
n
o
me
t
r
i
c
r
a
t
i
o
s.
−
G
e
n
e
r
a
l
i
z
e
p
r
o
p
e
r
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r
a
t
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C
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so
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o
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−
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h
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c
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f
me
t
h
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d
s a
n
d
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s
t
r
u
me
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s
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ms w
i
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h
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r
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r
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a
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3
,
15
To
t
a
l
15
3
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1
.
Rea
s
o
nin
g
a
nd
a
rg
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m
e
nta
t
io
n c
o
m
pet
ence
As
s
h
o
wn
in
Fig
u
r
e
2
an
d
Fi
g
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r
e
3
,
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em
o
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ated
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ic
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er
f
o
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m
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e
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o
m
p
eten
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ar
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ts
r
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asic
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ic
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atio
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.
Fig
u
r
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2
.
R
ea
s
o
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m
en
tatio
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m
p
eten
ce
(
c
o
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tr
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l g
r
o
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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
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8
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2
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Fig
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3
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ence
Fig
u
r
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4
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d
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em
o
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ate
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at,
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o
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e
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ter
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v
ast
m
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ity
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o
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co
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u
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ep
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n
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o
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g
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,
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8
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3
.
3
.
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blem
po
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o
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ence
As
s
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wn
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Fig
u
r
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d
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e
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h
e
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ated
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icien
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f
o
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ce
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n
th
e
co
m
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eten
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o
f
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g
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n
t
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e
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,
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asic
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th
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T
h
ese
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ed
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h
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etter
,
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th
e
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r
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teg
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T
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m
m
u
n
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,
r
e
p
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d
m
o
d
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eten
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b
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o
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g
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s
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lv
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g
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m
p
ete
n
ce
.
Fig
u
r
e
4
.
C
o
m
m
u
n
icatio
n
,
r
ep
r
esen
tatio
n
,
an
d
m
o
d
elin
g
co
m
p
eten
ce
(
co
n
tr
o
l
g
r
o
u
p
)
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
.
13
,
No
.
5
,
Octo
b
er
2
0
2
4
:
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-
2889
2882
Fig
u
r
e
5
.
C
o
m
m
u
n
icatio
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ep
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m
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d
elin
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m
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eten
ce
(
ex
p
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im
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g
r
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p
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Fig
u
r
e
6
.
Pro
b
lem
p
o
s
in
g
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d
p
r
o
b
lem
s
o
l
v
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g
c
o
m
p
eten
ce
(
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n
tr
o
l g
r
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p
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Fig
u
r
e
7
.
Pro
b
lem
p
o
s
in
g
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d
p
r
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b
lem
s
o
l
v
in
g
c
o
m
p
eten
ce
(
ex
p
er
im
en
tal
g
r
o
u
p
)
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
I
mp
r
o
vin
g
tr
ig
o
n
o
metric c
o
mp
eten
cy
w
ith
Geo
Geb
r
a
:
a
q
u
a
s
i
-
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erimen
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(
Yu
lieth
C
a
r
r
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o
-
R
eg
in
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)
2883
3
.
4
.
Di
m
ens
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f
re
a
s
o
nin
g
a
nd
a
rg
um
ent
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t
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n c
o
m
pet
e
nce
As
illu
s
tr
ated
in
Fig
u
r
es
8
a
n
d
9
,
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n
th
e
co
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l
g
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p
,
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9
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f
s
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Geo
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ce
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s
ig
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ican
tly
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f
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:
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.
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tical
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o
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:
s
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se
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d
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k
t
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B
ased
o
n
th
e
T
ab
le
4
,
th
e
r
esear
ch
h
y
p
o
th
esis
is
co
n
f
ir
m
ed
,
an
d
th
e
n
u
ll
h
y
p
o
th
esis
is
r
eje
cted
.
I
t
is
co
n
clu
d
e
d
f
r
o
m
th
e
em
p
ir
ical
f
in
d
in
g
s
p
r
esen
ted
h
er
e
th
at
th
e
u
s
e
o
f
th
e
Geo
Geb
r
a
s
im
u
lato
r
as
a
d
id
ac
tic
r
eso
u
r
ce
h
as
s
ig
n
if
ican
t
ef
f
e
cts
o
n
th
e
lev
el
o
f
co
m
p
ete
n
ce
in
lear
n
in
g
tr
ig
o
n
o
m
et
r
y
(
g
eo
m
etr
ic
-
m
etr
ic
m
ath
em
atica
l
th
in
k
in
g
)
in
te
n
th
-
g
r
a
d
e
s
tu
d
en
ts
o
f
a
s
ch
o
o
l
in
t
h
e
city
o
f
Mo
n
ter
ía.
Fu
r
th
er
m
o
r
e,
th
e
co
r
r
o
b
o
r
atio
n
o
f
th
e
h
y
p
o
th
esis
in
th
i
s
r
esear
ch
co
n
f
ir
m
s
p
r
ev
io
u
s
r
esear
ch
an
d
t
h
eo
r
ies
in
th
e
f
ield
.
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