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P
re
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se
rv
ice
tea
c
h
e
rs
’
(P
S
Ts)
tertiary
trai
n
in
g
is
e
ss
e
n
ti
a
l
to
t
h
e
ir
d
e
v
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lo
p
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s
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d
u
c
a
to
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a
n
d
to
th
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ir
p
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ss
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a
l
re
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ss
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m
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c
q
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ire
th
e
a
b
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to
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m
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m
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m
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teria
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a
v
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Tea
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x
c
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ll
e
n
c
e
m
u
st
b
e
p
ro
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n
t
i
n
t
h
e
re
lev
a
n
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m
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th
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m
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ti
c
s
c
o
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ten
t
k
n
o
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g
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CK)
a
n
d
p
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g
fo
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ti
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tera
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ti
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g
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2
5
P
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p
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m
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n
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a
n
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th
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n
d
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m
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n
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m
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m
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m
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c
s.
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imp
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sig
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ifi
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re
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d
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n
d
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lf
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n
d
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m
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d
fo
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d
m
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m
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m
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Mid
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Pre
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A
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J
am
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Ah
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Dep
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f
Ma
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C
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p
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E
NS)
Sid
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B
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Un
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s
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NS Ben
So
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Ah
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Ou
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B
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m
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jam
al.
ah
m
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an
e@
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s
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b
a.
ac
.
m
a
1.
I
NT
RO
D
UCT
I
O
N
C
o
n
ten
t
k
n
o
wled
g
e
(
C
K)
in
cl
u
d
es
k
n
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g
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r
elate
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to
a
s
u
b
ject
an
d
its
o
r
g
an
izatio
n
al
s
tr
u
ctu
r
e
[
1
]
an
d
r
ef
er
s
to
f
ac
ts
,
co
n
ce
p
ts
,
th
eo
r
ies,
an
d
p
r
in
cip
les
[
2
]
.
A
s
ig
n
o
f
C
K
m
a
s
ter
y
is
b
ei
n
g
ab
le
to
d
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p
en
p
ar
ticu
lar
elem
e
n
ts
th
r
o
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g
h
s
cien
tific
m
aster
y
.
A
p
o
s
s
ib
le
in
d
icatio
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is
th
at
p
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-
s
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v
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t
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ch
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s
’
(
PS
T
s
)
ar
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p
r
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f
icien
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in
s
cien
tific
co
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te
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to
in
cr
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d
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o
f
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tain
t
o
p
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f
s
tu
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.
Ma
th
em
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k
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f
teac
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s
s
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tly
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wh
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r
s
teac
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J
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Vo
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15
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No
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3
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s
tu
d
en
ts
lear
n
[
3
]
.
T
h
e
ab
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y
o
f
PS
T
s
to
ass
ess
s
tu
d
en
ts
’
th
in
k
in
g
an
d
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a
g
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in
t
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tim
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tan
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C
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[
4
]
.
Ho
wev
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,
m
aster
in
g
C
K
alo
n
e
is
in
s
u
f
f
icien
t
f
o
r
ef
f
icien
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lea
r
n
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.
T
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s
also
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is
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ed
to
as
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d
ag
o
g
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co
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ten
t
k
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wled
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e
(
PC
K)
.
Un
s
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r
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ly
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th
e
PC
K
co
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ce
p
tu
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f
r
am
ewo
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k
h
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en
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p
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ch
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s
o
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a
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ts
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ca
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to
el
u
cid
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th
e
r
ea
s
o
n
s
b
eh
in
d
th
e
ch
allen
g
es
f
ac
ed
b
y
n
u
m
er
o
u
s
k
in
d
e
r
g
ar
ten
teac
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wh
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teac
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in
g
v
is
u
al
ar
ts
to
y
o
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g
ch
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r
en
[
5
]
.
Acc
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r
d
in
g
to
ce
r
tain
ea
r
lier
r
esear
ch
,
teac
h
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s
,
p
ar
ticu
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ly
th
o
s
e
in
elem
en
tar
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s
ch
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o
ls
,
d
o
n
o
t
f
u
lly
co
m
p
r
eh
e
n
d
m
ath
em
atics
[
6
]
.
Fu
r
th
er
m
o
r
e,
s
tu
d
ies
h
a
v
e
d
em
o
n
s
tr
ated
a
c
o
r
r
elatio
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b
et
wee
n
p
ed
ag
o
g
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s
k
ills
an
d
m
ath
em
atics c
o
n
ten
t k
n
o
wled
g
e
(
MCK)
[
7
]
,
[
8
]
.
Als
o
,
p
r
io
r
r
esear
ch
h
as sh
o
wn
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d
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o
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r
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o
g
ical
k
n
o
wled
g
e
(
PK)
o
f
m
ath
em
atics a
n
d
MCK [
1
]
,
[
9
]
.
W
h
er
ea
s
PC
K
co
m
p
r
is
es
u
n
d
e
r
s
tan
d
in
g
o
f
h
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w
s
tu
d
e
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ts
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th
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s
u
b
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atter
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v
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lear
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p
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c
ess
[
1
0
]
,
MCK
in
clu
d
es
th
e
k
n
o
wled
g
e
th
at
m
u
s
t
b
e
ac
q
u
ir
ed
an
d
m
aster
ed
in
o
r
d
er
to
teac
h
m
ath
em
atics.
I
t
is
in
d
is
p
u
tab
le
th
at
lea
r
n
in
g
m
ath
em
atics,
p
ar
ticu
lar
ly
in
e
lem
en
tar
y
s
ch
o
o
ls
,
p
r
esen
ts
ch
allen
g
es
f
o
r
b
o
th
t
ea
ch
er
s
an
d
th
eir
teac
h
in
g
r
es
o
u
r
ce
s
.
Fo
r
ex
am
p
le,
W
aswa
an
d
Al
-
Kass
ab
[
1
1
]
estab
lis
h
ed
th
at
in
s
tr
u
cto
r
s
an
d
in
s
tr
u
ctio
n
al
m
ater
ials
ar
e
a
n
o
th
er
f
ac
t
o
r
af
f
ec
tin
g
s
tu
d
en
t
s
’
u
n
d
er
s
tan
d
in
g
o
f
m
ath
em
atics in
th
e
Ku
r
d
is
tan
r
eg
io
n
,
a
n
d
th
e
f
ew
av
ailab
le
t
ea
ch
er
s
ar
e
ill
-
tr
ain
ed
an
d
ill
-
e
q
u
ip
p
e
d
to
d
o
th
eir
jo
b
.
T
h
e
p
r
o
p
o
s
ed
r
esear
ch
q
u
esti
o
n
was:
h
o
w
d
o
PS
T
s
f
e
el
ab
o
u
t
th
eir
MCK,
PC
K,
an
d
th
eir
r
ea
d
in
ess
to
teac
h
m
ath
em
atics in
m
id
d
le
s
ch
o
o
ls
?
T
h
is
s
tu
d
y
s
ee
k
s
to
ac
co
m
p
li
s
h
two
o
b
jectiv
es.
T
h
e
f
i
r
s
t
is
to
lo
o
k
i
n
to
h
o
w
s
ec
o
n
d
ar
y
PS
T
s
wh
o
tak
e
p
ar
t
in
a
m
ath
em
atics
teac
h
in
g
u
n
it
v
iew
th
em
s
elv
e
s
as
th
ey
in
ter
ac
t
with
an
d
s
o
lid
if
y
th
eir
MCK.
T
h
e
s
ec
o
n
d
is
to
in
v
esti
g
ate,
co
n
s
id
er
in
g
th
eir
latest
h
ig
h
e
r
ed
u
ca
tio
n
,
h
o
w
th
ese
PS
T
s
v
iew
an
d
u
n
d
er
s
tan
d
th
eir
“
r
ea
d
in
ess
”
to
tak
e
o
n
s
u
ch
a
task
.
B
o
th
o
b
jectiv
es
w
ill
b
e
ex
am
in
ed
th
r
o
u
g
h
o
u
t
th
e
s
tu
d
y
p
r
o
ject
’
s
two
p
h
ases
.
T
h
e
r
elev
an
ce
o
f
th
is
s
tu
d
y
co
m
es
f
r
o
m
th
e
co
n
v
ictio
n
th
at
th
e
u
n
it
m
at
h
em
atics
teac
h
in
g
f
o
r
ea
r
ly
ad
o
lescen
ts
ef
f
ec
tiv
ely
b
u
ild
s
s
tu
d
en
ts
’
MCK
an
d
PC
K,
a
n
d
th
at
f
u
r
th
er
r
esear
ch
in
th
i
s
f
ield
ca
n
s
u
p
p
o
r
t
ef
f
o
r
ts
to
p
r
ep
ar
e
PS
T
s
in
th
e
f
u
tu
r
e.
T
h
e
u
n
it
m
ay
s
p
ec
if
ically
af
f
ec
t
h
o
w
PS
T
s
o
f
m
ath
e
m
atics
ar
e
p
r
o
p
er
ly
q
u
alif
ied
to
teac
h
m
at
h
em
atic
s
in
th
e
class
r
o
o
m
.
T
h
is
s
tu
d
y
d
if
f
e
r
en
tiates
its
elf
f
r
o
m
ex
is
tin
g
r
esear
ch
b
y
ex
p
licitly
lin
k
in
g
PS
T
s
’
s
elf
-
v
iew
to
co
n
ten
t
en
g
ag
e
m
en
t,
s
u
g
g
esti
n
g
h
o
lis
tic
r
ec
o
m
m
en
d
atio
n
s
f
o
r
teac
h
er
tr
ain
in
g
,
a
n
d
f
o
c
u
s
in
g
o
n
p
er
c
eiv
ed
r
ea
d
in
ess
.
T
h
e
m
ajo
r
asp
ec
ts
o
f
n
o
v
elty
in
th
is
s
tu
d
y
ar
e
th
e
n
ew
c
o
n
tex
t
(
i.e
.
,
Mo
r
o
cc
o
)
an
d
h
o
w
th
is
co
n
tex
t
p
r
o
v
id
es
an
o
p
p
o
r
t
u
n
ity
to
ex
p
lo
r
e
PS
T
s
’
p
er
ce
p
ti
o
n
s
th
r
o
u
g
h
an
in
-
d
ep
th
q
u
alitativ
e
ap
p
r
o
ac
h
r
e
g
ar
d
in
g
s
p
ec
if
ic
a
r
ea
s
o
f
g
e
o
m
e
tr
y
with
in
a
cu
r
r
icu
lu
m
.
2.
L
I
T
E
R
AT
U
RE
R
E
VI
E
W
2
.
1
.
M
a
t
hema
t
ica
l
c
o
nte
nt
kn
o
wledg
e
MCK
is
a
f
u
ll,
b
r
o
ad
,
c
o
n
n
ec
ted
,
an
d
co
m
p
r
eh
e
n
s
iv
e
u
n
d
er
s
tan
d
in
g
o
f
m
ath
e
m
atics
[
6
]
.
MCK
h
as
b
ee
n
ch
ar
ac
ter
ize
d
b
y
a
n
u
m
b
er
o
f
co
n
ce
p
ts
,
s
u
ch
as
m
ath
em
atica
l
liter
ac
y
[
1
2
]
,
co
m
p
u
ta
tio
n
al
f
lu
en
cy
[
1
3
]
,
an
d
q
u
an
titativ
e
liter
ac
y
[
1
4
]
.
I
t
in
clu
d
es
m
ath
em
atica
l
r
ea
s
o
n
in
g
an
d
th
e
ab
ilit
y
to
u
s
e
m
ath
e
m
atica
l
co
n
ce
p
ts
,
p
r
o
ce
d
u
r
es,
f
ac
ts
,
an
d
f
u
n
ctio
n
s
to
d
escr
ib
e
,
ex
p
lain
,
an
d
p
r
ed
ict
p
h
e
n
o
m
e
n
a
[
1
5
]
.
Fo
c
u
s
in
g
o
n
PS
T
s
’
C
K
is
e
s
s
en
tial
to
p
r
o
p
er
ly
ed
u
ca
tin
g
teac
h
e
r
s
.
No
n
e
th
eless
,
th
er
e
is
d
is
ag
r
ee
m
en
t
o
v
er
wh
at
MCK
is
r
eq
u
ir
ed
f
o
r
s
u
cc
ess
f
u
l
teac
h
in
g
[
1
6
]
.
I
t
is
p
o
s
s
ib
le
to
s
tr
en
g
th
en
th
e
h
ig
h
C
K
am
o
n
g
ele
m
en
tar
y
tu
t
o
r
s
[
6
]
.
R
esear
ch
h
ig
h
lig
h
ts
th
at
p
r
e
s
er
v
ice
teac
h
er
s
o
f
ten
en
ter
teac
h
er
ed
u
ca
tio
n
p
r
o
g
r
am
s
with
g
ap
s
in
th
eir
m
ath
em
atica
l
k
n
o
wled
g
e,
wh
i
ch
ca
n
im
p
ac
t
th
eir
ab
ilit
y
t
o
teac
h
m
ath
em
atics
ef
f
ec
tiv
ely
[
1
7
]
.
T
o
ad
d
r
ess
th
ese
is
s
u
es,
ed
u
ca
to
r
s
an
d
r
e
s
ea
r
ch
er
s
em
p
h
asize
th
e
im
p
o
r
tan
ce
o
f
d
ev
elo
p
i
n
g
C
K
an
d
s
p
ec
ialized
co
n
ten
t
k
n
o
wled
g
e
(
SC
K)
f
o
r
teac
h
in
g
.
Fo
r
ex
am
p
le,
Do
g
b
ey
[
1
8
]
d
ev
elo
p
e
d
a
p
r
o
f
ess
io
n
al
d
ev
e
lo
p
m
en
t
p
r
o
g
r
am
t
o
h
elp
teac
h
er
s
in
elem
en
tar
y
s
ch
o
o
ls
to
im
p
r
o
v
e
th
ei
r
teac
h
in
g
o
f
m
ath
em
atics
u
s
in
g
class
r
o
o
m
d
is
co
u
r
s
e
an
d
ca
m
e
u
p
with
n
ew
m
eth
o
d
s
with
wh
o
le
f
r
ac
tio
n
an
d
n
u
m
b
er
co
m
p
u
tatio
n
s
.
T
h
e
2
1
Am
er
ican
elem
en
tar
y
s
ch
o
o
l
teac
h
er
s
p
a
r
ticip
ated
in
th
is
in
itiativ
e.
T
h
e
s
tu
d
y
’
s
f
in
d
in
g
s
s
h
o
wed
t
h
at
alth
o
u
g
h
p
a
r
ticip
an
ts
r
ep
o
r
te
d
s
o
m
e
d
if
f
icu
lties
im
p
lem
en
tin
g
th
e
k
n
o
wled
g
e
th
ey
g
ain
ed
f
r
o
m
th
e
p
r
o
f
ess
io
n
al
d
e
v
elo
p
m
en
t
p
r
o
g
r
am
i
n
th
eir
c
l
a
s
s
r
o
o
m
s
,
t
h
e
y
i
m
p
r
o
v
e
d
t
h
e
i
r
u
n
d
e
r
s
t
a
n
d
i
n
g
o
f
m
a
t
h
e
m
a
t
i
c
a
l
c
o
n
t
e
n
t
a
n
d
t
h
e
i
r
i
n
s
t
r
u
c
t
i
o
n
al
s
t
r
at
e
g
i
es
.
I
n
m
an
y
s
tates
in
th
e
Un
ited
States
,
b
ef
o
r
e
r
ec
eiv
in
g
th
eir
t
ea
ch
in
g
ce
r
tific
atio
n
,
p
r
o
s
p
ec
t
iv
e
s
ec
o
n
d
ar
y
m
ath
t
e
a
c
h
e
r
s
m
u
s
t
p
as
s
t
h
e
P
r
a
x
is
I
I
:
M
C
K
(
1
0
0
6
1
)
t
e
s
t
[
1
9
]
.
T
h
is
a
s
s
e
s
s
m
e
n
t
te
s
ts
t
h
e
M
C
K
o
f
PS
T
u
n
d
e
r
g
r
a
d
u
a
t
e
s
,
b
u
t
n
o
t
t
h
e
i
r
PC
K
o
r
c
o
m
p
r
e
h
en
s
i
o
n
o
f
t
h
e
m
a
t
h
e
m
a
ti
c
a
l
c
o
n
c
e
p
t
s
t
h
e
y
a
r
e
g
o
i
n
g
t
o
te
a
c
h
i
n
a
s
e
c
o
n
d
a
r
y
s
c
h
o
o
l
.
R
o
d
r
i
g
u
es
e
t
a
l
.
[
2
0
]
m
e
n
tio
n
e
d
t
h
e
i
m
p
o
r
t
a
n
ce
o
f
s
tr
u
ct
u
r
e
d
f
r
a
m
e
wo
r
k
s
f
o
r
d
ev
el
o
p
in
g
m
at
h
e
m
a
tic
al
r
e
as
o
n
in
g
p
r
o
ce
s
s
es i
n
p
r
o
s
p
e
cti
v
e
te
ac
h
e
r
s
.
I
t
ca
n
b
e
s
ee
n
f
r
o
m
t
h
e
d
ata
t
h
at
th
e
s
ta
r
t
in
g
p
o
i
n
t
o
f
th
e
p
r
ese
r
v
ic
e
te
ac
h
er
’
s
m
at
h
em
a
tic
al
s
k
i
lls
is
v
e
r
y
l
o
w.
T
h
er
ef
o
r
e
,
m
at
h
em
ati
cs
t
ea
c
h
er
tr
ai
n
i
n
g
s
h
o
u
l
d
im
p
o
s
e
th
e
n
ee
d
f
o
r
r
i
g
o
r
o
u
s
CK
d
e
v
el
o
p
m
e
n
t
[
2
1
]
.
T
h
e
lea
r
n
i
n
g
p
r
o
c
ess
in
class
r
o
o
m
s
,
p
a
r
ti
cu
la
r
l
y
th
e
in
t
er
ac
t
io
n
s
t
h
a
t
ta
k
e
p
l
ac
e
t
h
r
o
u
g
h
o
u
t
t
h
e
l
ea
r
n
i
n
g
p
r
o
ce
s
s
,
is
im
p
a
cte
d
b
y
th
e
p
r
i
m
ar
y
s
c
h
o
o
l
tea
c
h
e
r
ca
n
d
id
ates
li
m
it
e
d
MCK
.
F
o
r
in
s
ta
n
c
e,
a
p
r
o
s
p
ec
t
i
v
e
tea
c
h
er
m
ay
at
te
m
p
t
t
o
e
x
a
m
i
n
e
e
r
r
o
r
s
i
n
a
lea
r
n
i
n
g
m
at
er
ial
b
u
t
f
ai
l
t
o
r
ec
o
g
n
iz
e
t
h
e
f
l
aws
[
1
]
.
T
h
is
wi
ll
a
f
f
e
ct
h
o
w
h
e
o
r
s
h
e
c
h
o
o
s
es
a
n
d
g
e
n
e
r
a
tes
e
d
u
c
ati
o
n
al
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
A
q
u
a
lita
tive
s
tu
d
y
o
f m
a
th
em
a
tica
l c
o
n
ten
t k
n
o
w
led
g
e
a
n
d
p
ed
a
g
o
g
ica
l c
o
n
ten
t
… (
J
a
ma
l A
h
mich
a
n
e
)
2263
m
at
er
ials
f
o
r
a
less
o
n
a
n
d
o
f
f
e
r
s
cl
ar
if
ica
ti
o
n
s
in
class
.
T
h
e
p
r
o
s
p
e
cti
v
e
tea
c
h
e
r
s
’
k
n
o
wle
d
g
e
a
ls
o
af
f
ec
ts
h
o
w
th
e
y
u
s
e
s
t
u
d
en
ts
’
p
ast
k
n
o
w
le
d
g
e
as
p
ar
t
o
f
t
h
e
l
ea
r
n
i
n
g
p
r
o
c
ess
a
n
d
h
o
w
t
h
e
y
p
r
o
v
id
e
s
ti
m
u
l
u
s
to
t
h
e
p
u
p
i
ls
.
2
.
2
.
P
eda
g
o
g
ic
a
l c
o
nte
nt
k
no
wledg
e
PC
K
i
s
k
n
o
wled
g
e
r
eq
u
ir
ed
f
o
r
teac
h
er
s
to
co
m
p
r
e
h
en
d
s
t
u
d
en
t
m
is
co
n
ce
p
tio
n
s
,
co
m
p
r
eh
en
d
th
e
s
tr
u
ctu
r
e
an
d
d
eliv
er
y
o
f
th
e
m
es,
an
d
af
f
ec
t
t
h
e
ca
p
ac
ity
t
o
m
o
d
if
y
s
ess
io
n
s
to
f
it
all
lear
n
er
s
[
1
0
]
.
PC
K
is
also
a
f
u
n
d
am
en
tal
co
m
p
o
n
en
t
f
o
r
co
n
d
u
ctin
g
lear
n
in
g
ac
tiv
ities
.
I
n
ad
d
itio
n
to
d
eliv
er
in
g
m
ater
ial,
th
e
teac
h
er
’
s
task
s
also
in
clu
d
e
cr
ea
tin
g
e
d
u
ca
tio
n
al
ac
ti
v
ities
an
d
ass
is
tin
g
s
tu
d
en
ts
wh
o
s
tr
u
g
g
le
with
lear
n
in
g
[
2
2
]
.
On
e
wid
ely
ac
ce
p
ted
co
n
d
itio
n
f
o
r
d
ev
elo
p
in
g
PC
K
is
teac
h
er
s
’
CK
.
C
K
is
th
e
c
o
n
ce
p
t
u
al
u
n
d
er
s
tan
d
i
n
g
o
f
s
ch
o
o
l m
ath
em
atics a
n
d
th
e
ca
p
ac
ity
to
r
e
aso
n
an
d
ev
alu
ate
d
if
f
er
en
t m
ath
em
atica
l c
o
n
ce
p
ts
an
d
s
itu
atio
n
s
,
an
d
s
o
lv
e
m
ath
em
atics
p
r
o
b
lem
s
in
s
ch
o
o
l
cu
r
r
icu
la
[
2
3
]
.
Prio
r
s
tu
d
ies
h
av
e
n
o
ted
a
p
o
s
itiv
e
co
r
r
elatio
n
b
etwe
en
teac
h
er
s
’
C
K
an
d
PC
K
[
2
3
]
,
[
2
4
]
.
Ma
th
em
atica
l
teac
h
in
g
ex
p
er
i
en
ce
is
co
n
s
id
er
e
d
as
t
h
e
co
n
ten
t
-
s
p
ec
if
ic
k
n
o
wled
g
e
f
o
r
i
n
s
tr
u
ctio
n
,
wh
ich
en
co
m
p
ass
es
teac
h
er
s
’
PC
K,
C
K,
an
d
th
e
ca
p
ac
ity
to
r
ec
o
g
n
ize
co
n
ten
t
-
r
elate
d
p
r
o
b
lem
s
d
u
r
in
g
m
ath
em
atics
in
s
tr
u
ctio
n
[
2
3
]
.
Pre
v
io
u
s
r
esear
ch
h
as
s
h
o
wn
th
at
th
e
q
u
ality
o
f
m
ath
e
m
at
ics
in
s
tr
u
ctio
n
an
d
s
tu
d
en
ts
’
m
ath
em
atica
l
lear
n
in
g
ar
e
s
ig
n
if
ican
tly
in
f
lu
en
ce
d
b
y
th
e
c
o
n
ten
t
a
n
d
PC
K
o
f
teac
h
e
r
s
[
2
5
]
.
Ho
wev
er
,
th
er
e
is
co
n
f
lictin
g
em
p
ir
ical
ev
id
en
ce
a
b
o
u
t
th
e
d
eg
r
ee
o
f
v
ar
iab
ilit
y
am
o
n
g
th
e
co
m
p
o
n
en
ts
o
f
co
n
ten
t
-
s
p
ec
if
ic
k
n
o
wled
g
e.
R
esu
lts
f
r
o
m
p
r
ev
io
u
s
e
m
p
ir
ical
s
tu
d
ies
o
n
t
h
e
d
im
e
n
s
io
n
ality
o
f
co
n
ten
t
an
d
PK
o
f
m
ater
ial
h
a
v
e
b
ee
n
in
co
n
s
is
ten
t.
B
ec
au
s
e
n
u
m
er
o
u
s
c
o
n
c
ep
tu
aliza
tio
n
s
o
f
teac
h
e
r
s
’
k
n
o
wled
g
e
h
a
v
e
b
ee
n
ex
am
in
ed
o
n
v
ar
io
u
s
p
o
p
u
latio
n
s
,
it
is
ch
allen
g
in
g
to
id
e
n
tify
th
e
r
ea
s
o
n
s
b
eh
i
n
d
th
e
in
co
n
s
is
ten
t
d
ata.
T
h
e
co
n
te
n
t
an
d
PC
K
o
f
elem
en
tar
y
s
ch
o
o
l
teac
h
er
s
,
f
o
r
ex
am
p
le,
h
a
v
e
b
ee
n
s
h
o
wn
to
b
e
a
s
in
g
le
co
n
s
tr
u
ct
in
d
im
en
s
io
n
ality
s
tu
d
ies
[
2
4
]
.
I
n
co
n
tr
ast,
s
tu
d
ies
with
s
ec
o
n
d
ar
y
m
ath
em
atics
teac
h
e
r
s
h
av
e
f
o
u
n
d
th
at
teac
h
er
s
’
co
n
ten
t
a
n
d
PC
K
ar
e
s
ep
ar
ate
c
o
n
s
tr
u
cts.
T
ea
c
h
er
s
u
s
e
PC
K
as
a
to
o
l
to
h
elp
s
tu
d
en
ts
u
n
d
er
s
tan
d
,
co
n
n
ec
t w
ith
,
an
d
f
i
n
d
a
to
p
ic
m
o
r
e
en
g
a
g
in
g
[
2
6
]
.
T
ea
c
h
er
s
d
is
p
lay
PC
K
f
o
r
a
s
p
ec
if
ic
s
u
b
ject
wh
en
th
ey
ar
e
ab
le
to
en
g
a
g
e
s
tu
d
e
n
ts
with
a
r
an
g
e
o
f
i
n
ter
ests
an
d
s
k
ill
lev
els
b
y
co
n
n
ec
tin
g
th
e
t
o
p
i
c
co
n
ce
p
ts
to
o
th
er
to
p
ics,
em
p
lo
y
in
g
d
if
f
er
en
t
to
p
ic
r
ep
r
esen
tatio
n
s
,
o
r
c
h
an
g
i
n
g
th
ei
r
teac
h
i
n
g
s
ty
le
[
2
7
]
.
W
h
ile
th
e
s
cien
tific
co
m
m
u
n
ity
h
as
n
o
t
y
et
a
g
r
e
ed
o
n
a
co
m
m
o
n
co
n
ce
p
tu
al
izatio
n
o
f
PC
K
[
2
3
]
,
[
2
8
]
,
[
2
9
]
,
it
is
g
en
er
ally
r
ec
o
g
n
ized
th
at
it
in
clu
d
es
b
o
th
PK
an
d
CK
[
2
7
]
,
[
2
8
]
.
T
h
e
liter
atu
r
e
r
ev
iew
d
em
o
n
s
tr
ates
th
at
P
C
K
en
tail
s
p
lan
n
in
g
a
well
-
d
esig
n
ed
less
o
n
a
n
d
ad
ju
s
tin
g
it
b
ased
o
n
s
tu
d
en
ts
’
p
er
f
o
r
m
an
ce
af
ter
it
i
s
im
p
lem
en
ted
.
T
h
e
PC
K
i
s
b
o
th
s
p
ec
if
ic
to
a
p
ar
ticu
lar
to
p
ic
an
d
a
tar
g
et
g
r
o
u
p
o
f
s
tu
d
en
ts
in
ter
m
s
o
f
g
r
a
d
e
an
d
s
o
cial
co
n
tex
t
[
3
0
]
;
h
o
wev
er
,
PS
T
s
r
eq
u
ir
e
o
r
ien
tatio
n
to
war
d
a
d
ee
p
e
r
u
n
d
er
s
tan
d
in
g
o
f
s
tu
d
en
ts
’
id
ea
s
,
as
well
as
en
co
u
r
a
g
in
g
in
te
r
ac
tio
n
s
ab
o
u
t stu
d
en
t o
u
tco
m
es a
n
d
p
o
ten
ti
al
ca
u
s
es o
f
s
tu
d
en
ts
’
ch
allen
g
es.
T
h
e
s
e
a
r
c
h
i
n
a
n
u
m
b
e
r
o
f
s
c
i
en
t
i
f
i
c
d
a
t
a
b
as
es
l
i
k
e
Sc
o
p
u
s
,
W
e
b
o
f
S
c
i
e
n
ce
(
W
o
S
)
,
E
R
I
C
,
a
n
d
G
o
o
g
l
e
S
c
h
o
l
a
r
r
e
v
e
a
l
e
d
t
h
e
l
a
c
k
o
f
M
o
r
o
c
c
a
n
s
t
u
d
i
e
s
a
d
d
r
e
s
s
i
n
g
t
h
e
a
s
s
es
s
m
e
n
t
o
f
t
e
a
c
h
e
r
s
’
M
C
K
o
r
P
C
K
.
H
o
w
e
v
e
r
,
i
t
p
o
i
n
t
e
d
t
o
t
h
e
e
x
i
s
t
e
n
c
e
o
f
s
o
m
e
s
t
u
d
i
e
s
a
d
d
r
es
s
i
n
g
t
h
e
s
e
c
a
t
e
g
o
r
i
e
s
o
f
k
n
o
w
le
d
g
e
i
n
No
r
t
h
A
f
r
i
c
a
a
n
d
t
h
e
M
i
d
d
l
e
E
a
s
t
.
F
o
r
e
x
a
m
p
l
e
,
S
ay
e
d
[
3
1
]
d
i
s
c
u
s
s
e
d
t
h
e
l
e
v
e
l
o
f
m
a
t
h
e
m
a
t
i
c
a
l
k
n
o
w
l
e
d
g
e
n
e
ce
s
s
a
r
y
f
o
r
t
e
a
c
h
i
n
g
m
a
t
h
e
m
a
t
i
cs
a
n
d
t
h
e
a
t
ti
t
u
d
e
t
o
w
a
r
d
s
t
e
a
c
h
i
n
g
i
t
a
m
o
n
g
P
S
T
s
i
n
E
g
y
p
t
,
a
n
d
A
l
o
t
a
i
b
i
a
n
d
Y
o
u
s
s
e
[
3
2
]
i
d
e
n
t
i
f
i
ed
t
h
e
d
e
g
r
e
e
o
f
M
C
K
a
m
o
n
g
s
e
c
o
n
d
a
r
y
s
c
h
o
o
l
m
a
t
h
e
m
a
t
i
cs
t
e
a
c
h
e
r
s
i
n
S
a
u
d
i
A
r
a
b
ia
a
n
d
i
t
s
r
e
l
a
ti
o
n
s
h
i
p
t
o
m
a
t
h
e
m
a
t
i
ca
l
p
e
d
a
g
o
g
i
c
al
c
o
n
t
e
n
t
k
n
o
w
l
e
d
g
e
(
MPC
K
)
.
T
o
a
c
h
i
e
v
e
t
h
e
r
es
e
a
r
c
h
o
b
j
e
ct
i
v
e
,
t
h
e
r
es
e
a
r
c
h
e
r
p
r
e
p
a
r
e
d
t
w
o
i
n
s
t
r
u
m
e
n
ts
:
t
h
e
M
C
K
te
s
t
a
n
d
t
h
e
M
P
C
K
s
c
ale
f
o
r
s
e
c
o
n
d
a
r
y
m
a
t
h
e
m
a
t
i
c
s
te
a
c
h
e
r
s
.
G
i
v
e
n
t
h
is
g
a
p
,
t
h
e
p
r
e
s
e
n
t
s
t
u
d
y
a
i
m
s
t
o
a
d
a
p
t
a
s
u
r
v
e
y
i
n
s
t
r
u
m
e
n
t
q
u
e
s
t
i
o
n
n
a
i
r
e
i
n
M
o
r
o
c
c
a
n
l
o
we
r
s
e
c
o
n
d
a
r
y
s
c
h
o
o
ls
,
h
e
l
p
i
n
g
t
o
i
d
e
n
t
i
f
y
a
n
d
s
t
r
e
n
g
t
h
e
n
t
h
e
M
C
K
a
n
d
P
C
K
o
f
P
S
T
s
a
n
d
p
r
o
v
i
d
i
n
g
v
a
l
u
a
b
l
e
i
n
s
i
g
h
ts
i
n
t
o
P
S
T
s
’
m
a
t
h
e
m
a
t
i
c
k
n
o
w
le
d
g
e
,
t
h
e
r
e
b
y
c
o
n
t
r
i
b
u
t
i
n
g
t
o
t
h
e
e
n
h
a
n
c
e
m
e
n
t
o
f
t
e
a
c
h
e
r
e
d
u
c
a
t
i
o
n
p
r
o
g
r
a
m
s
.
A
c
c
o
r
d
i
n
g
l
y
,
t
h
e
s
t
e
p
s
o
f
a
r
e
s
e
a
r
c
h
m
e
t
h
o
d
u
s
i
n
g
a
t
h
e
m
a
ti
c
a
n
a
l
y
s
is
o
f
t
h
e
d
a
t
a
a
r
e
d
e
s
c
r
i
b
e
d
i
n
t
h
e
f
o
l
l
o
w
i
n
g
s
e
ct
i
o
n
.
3.
RE
S
E
ARCH
M
E
T
H
O
D
3
.
1
.
Co
nte
x
t
At
th
e
r
eg
io
n
al
ce
n
ter
f
o
r
ed
u
ca
tio
n
an
d
tr
ain
in
g
p
r
o
f
es
s
io
n
s
,
Fez
-
Me
k
n
es,
Mo
r
o
cc
o
,
th
e
u
n
it
m
ath
em
atics
teac
h
in
g
f
o
r
ea
r
ly
ad
o
lescen
ts
is
o
f
f
er
ed
to
s
tu
d
en
ts
wh
o
h
av
e
h
a
d
a
b
a
ch
elo
r
’
s
d
eg
r
ee
in
m
ath
em
atics
an
d
b
en
e
f
it
f
r
o
m
tr
ain
in
g
to
b
ec
o
m
e
m
id
d
le
s
ch
o
o
l
teac
h
er
s
o
f
m
ath
em
at
ics.
Par
ticip
an
ts
ca
n
u
s
e
th
e
u
n
it
to
p
u
r
s
u
e
a
s
p
ec
ializatio
n
o
r
m
ajo
r
in
m
at
h
e
m
atics
ed
u
ca
tio
n
.
T
h
e
u
n
it
is
ca
r
r
ied
o
u
t
o
v
er
23
wee
k
s
with
6
8
h
o
u
r
s
o
f
in
ter
a
ctio
n
tim
e
d
i
v
id
ed
in
to
two
s
em
ester
s
with
3
4
h
o
u
r
s
i
n
ea
ch
s
em
ester
.
Du
r
in
g
in
ter
ac
tio
n
h
o
u
r
s
,
PS
T
s
s
tu
d
y
im
p
o
r
ta
n
t
cu
r
r
icu
lu
m
an
d
p
o
licy
p
ap
er
s
,
en
g
a
g
e
with
th
e
m
id
d
le
s
ch
o
o
l
m
ath
s
u
b
ject,
lear
n
th
e
b
est
p
ed
ag
o
g
ical
s
tr
ateg
ies
f
o
r
teac
h
in
g
th
at
co
n
ten
t,
en
s
u
r
e
ac
tiv
e
p
ar
t
icip
atio
n
in
v
ar
io
u
s
tr
ain
in
g
ac
tiv
ities
(
lectu
r
es,
tu
to
r
ials
,
an
d
p
r
ac
tical
wo
r
k
)
,
a
n
d
a
n
aly
ze
t
h
e
s
cien
tific
a
n
d
o
f
f
icial
d
o
cu
m
e
n
ts
r
elatin
g
to
m
ath
em
atics
ed
u
c
atio
n
an
d
g
r
o
u
p
p
r
o
d
u
ctio
n
s
.
I
n
ea
ch
s
em
ester
,
s
tu
d
en
ts
c
o
m
p
lete
th
r
ee
test
s
r
elate
d
to
th
e
u
n
it:
a
f
in
al
s
u
m
m
ativ
e
ex
am
(
FS
E
)
an
d
two
m
id
-
s
em
ester
test
s
(
MST
)
.
Stu
d
en
ts
m
u
s
t
d
em
o
n
s
tr
ate
m
aster
y
o
f
th
e
m
ath
em
atica
l
m
ater
ial
p
r
esen
ted
in
th
e
f
ir
s
t
s
ev
en
wee
k
s
o
f
ea
c
h
s
em
ester
in
o
r
d
er
to
p
ass
th
e
two
-
h
o
u
r
M
ST.
T
h
e
FS
E
is
a
3
-
h
o
u
r
ass
ess
m
en
t
co
n
s
is
tin
g
o
f
d
ir
ec
t
q
u
esti
o
n
s
,
m
u
ltip
le
-
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
15
,
No
.
3
,
J
u
n
e
20
2
6
:
2
2
6
1
-
2
2
7
0
2264
ch
o
ice
q
u
esti
o
n
s
,
an
d
task
s
in
v
o
lv
in
g
th
e
p
r
o
ce
s
s
in
g
an
d
th
e
an
aly
s
is
o
f
teac
h
in
g
s
itu
atio
n
s
.
T
h
e
ex
am
co
v
er
s
s
ev
er
al
ar
ea
s
,
s
u
ch
as
co
n
ce
p
ts
an
d
ap
p
r
o
ac
h
es
in
teac
h
i
n
g
,
m
ath
em
atica
l
r
ea
s
o
n
in
g
,
an
d
th
e
th
e
o
r
y
o
f
teac
h
in
g
s
itu
atio
n
s
.
Ab
o
u
t 6
0
s
tu
d
en
ts
ar
e
en
r
o
lled
in
th
is
u
n
it e
ac
h
s
em
ester
.
3
.
2
.
I
ns
t
rum
ent
a
da
pta
t
i
o
n
T
o
lo
o
k
i
n
to
h
o
w
PS
T
s
wh
o
tak
e
p
ar
t
in
t
h
e
m
at
h
em
atics
teac
h
in
g
f
o
r
ea
r
ly
ad
o
lescen
ts
u
n
it
v
iew
th
em
s
elv
es
an
d
to
in
v
esti
g
ate
h
o
w
th
ese
PS
T
s
v
iew
an
d
u
n
d
er
s
tan
d
th
eir
r
ea
d
in
ess
to
tea
ch
m
ath
em
atics
in
m
id
d
le
s
ch
o
o
l,
an
ad
ap
te
d
v
e
r
s
io
n
o
f
th
e
s
u
r
v
ey
o
f
Hin
e
[
1
9
]
,
a
7
-
item
,
5
-
p
o
in
t
L
ik
er
t
s
ca
le
q
u
esti
o
n
,
an
d
th
r
ee
q
u
alitativ
e
q
u
esti
o
n
s
we
r
e
u
s
ed
to
co
llect
p
ar
ticip
a
n
ts
’
s
elf
-
p
er
ce
p
tio
n
s
.
T
h
e
r
esear
ch
er
em
p
l
o
y
ed
two
q
u
alitativ
e
ass
es
s
m
en
ts
to
g
at
h
er
in
f
o
r
m
atio
n
f
r
o
m
r
esear
c
h
p
ar
ticip
an
ts
.
B
ef
o
r
e
s
tar
tin
g
a
23
-
wee
k
ter
tiar
y
co
u
r
s
e
ce
n
ter
ed
o
n
m
ath
e
m
atica
l
co
n
ten
t,
p
ar
ticip
a
n
ts
wer
e
r
eq
u
ir
ed
t
o
an
s
wer
f
o
u
r
r
esear
ch
q
u
esti
o
n
s
.
T
h
e
n
in
s
tag
e
2
,
th
e
p
ar
ticip
an
ts
wi
ll
b
e
g
iv
en
ex
ac
tly
th
e
s
am
e
s
tu
d
y
q
u
esti
o
n
s
,
wh
ich
will
ta
k
e
p
lace
r
ig
h
t
af
ter
th
is
u
n
it
is
f
in
is
h
ed
.
T
h
e
p
r
im
ar
y
r
esear
c
h
m
eth
o
d
o
lo
g
y
u
s
e
d
in
th
is
in
ter
p
r
etativ
e
s
tu
d
y
was
th
e
q
u
alitativ
e
m
eth
o
d
.
So
m
e
o
f
t
h
e
elem
en
ts
wer
e
ad
ap
ted
i
n
r
esp
o
n
s
e
to
t
h
e
in
p
u
t
r
ec
eiv
ed
:
−
T
h
e
q
u
alitativ
e
q
u
esti
o
n
s
2
,
3
,
an
d
4
wer
e
r
estricte
d
to
teac
h
in
g
lo
wer
s
ec
o
n
d
ar
y
s
ch
o
o
l
s
.
T
h
ey
ar
e
th
e
s
am
e
o
f
th
o
s
e
o
f
Hin
e
[
1
9
]
.
−
T
h
e
item
s
o
f
q
u
esti
o
n
1
wer
e
r
estricte
d
to
teac
h
in
g
lo
wer
s
ec
o
n
d
ar
y
s
ch
o
o
ls
an
d
wer
e
ad
a
p
ted
ac
co
r
d
in
g
to
th
e
Mo
r
o
cc
an
ed
u
ca
tio
n
al
s
y
s
tem
.
T
h
is
ad
ap
tatio
n
is
illu
s
tr
ated
in
s
ec
tio
n
4
.
1
(
s
ev
e
n
to
p
i
cs).
3
.
3
.
Sa
m
ple
T
h
e
s
tag
es a
n
d
cr
iter
ia
f
o
r
s
ele
ctin
g
th
e
s
tu
d
y
s
am
p
le
ca
n
b
e
s
u
m
m
ar
ized
as:
−
At
th
e
r
eg
io
n
al
ce
n
ter
f
o
r
e
d
u
ca
tio
n
an
d
tr
ain
in
g
,
in
v
iti
n
g
PS
T
s
en
g
ag
ed
in
th
e
ea
r
ly
ad
o
lescen
ts
’
m
ath
em
atics
teac
h
in
g
u
n
it,
an
d
lear
n
in
g
to
teac
h
m
ath
em
ati
cs
in
lo
wer
s
ec
o
n
d
ar
y
s
ch
o
o
ls
,
to
p
ar
ticip
ate
in
th
is
s
tu
d
y
(
6
0
p
ar
ticip
an
ts
)
.
As
th
is
ce
n
ter
i
s
th
e
u
n
iq
u
e
ce
n
ter
in
th
e
r
eg
io
n
t
h
at
tr
ain
s
th
is
ca
teg
o
r
y
o
f
teac
h
er
s
.
−
R
eq
u
est to
th
e
af
o
r
em
e
n
tio
n
ed
ca
teg
o
r
y
o
f
PS
T
s
to
ex
p
r
ess
t
h
eir
in
ter
est in
p
ar
ticip
atin
g
in
co
m
p
letin
g
t
h
e
q
u
esti
o
n
n
air
e.
T
h
ir
ty
PS
T
s
s
h
o
wed
th
eir
in
ter
est an
d
ac
ce
p
t
ed
to
p
ar
ticip
ate
i
n
th
is
s
tu
d
y
.
−
T
h
e
r
esp
o
n
s
e
o
f
an
y
p
ar
ticip
an
t
th
at
was
f
o
u
n
d
to
b
e
in
c
o
m
p
lete
was
r
em
o
v
e
d
.
Fiv
e
r
esp
o
n
s
es
wer
e
r
em
o
v
ed
.
Fo
llo
win
g
th
ese
s
tag
es,
a
s
elf
-
s
elec
ted
s
am
p
le
(
2
5
p
ar
ticip
an
ts
)
f
o
r
s
tag
e
1
o
f
th
e
p
r
o
ject
was
co
n
s
titu
ted
.
Of
th
e
2
5
PS
T
s
,
1
5
PS
T
s
w
er
e
co
m
p
letin
g
a
B
ac
h
elo
r
o
f
Ma
th
em
atics
an
d
C
o
m
p
u
ter
Scien
ce
s
(
B
M
C
S)
d
eg
r
ee
,
a
n
d
1
0
a
B
ac
h
elo
r
o
f
Ma
th
em
atics
an
d
Ph
y
s
ics
(
B
MP)
d
eg
r
ee
.
Mo
r
e
d
etails ar
e
av
ailab
le
in
T
ab
le
1
.
T
ab
le
1
.
Pro
ject
p
ar
ticip
an
ts
(
Stag
e
1
)
G
e
n
d
e
r
B
M
C
S
B
M
P
To
t
a
l
M
a
l
e
9
5
14
F
e
mal
e
6
5
11
To
t
a
l
15
10
25
3
.
4
.
Da
t
a
a
na
ly
s
is
T
h
e
2
5
-
p
r
e
-
u
n
it
q
u
esti
o
n
n
air
e
s
’
d
ata
wer
e
ex
am
i
n
ed
f
o
r
c
o
m
m
o
n
th
e
m
es.
A
th
em
atic
an
aly
s
is
o
f
th
e
d
ata
was
p
er
f
o
r
m
ed
f
o
llo
win
g
th
e
f
r
am
ewo
r
k
an
d
r
ec
o
m
m
e
n
d
atio
n
s
p
r
o
v
id
ed
b
y
Miles
a
n
d
Hu
b
er
m
a
n
[
3
3
]
.
B
ased
o
n
d
if
f
er
en
ce
s
an
d
s
im
ilar
ities
b
etwe
en
s
o
cial
p
h
en
o
m
en
a,
th
is
f
r
am
ewo
r
k
h
elp
e
d
th
e
r
esear
ch
er
f
in
d
co
n
n
ec
tio
n
s
b
etwe
en
th
e
m
.
T
h
e
th
r
ee
p
r
im
a
r
y
co
m
p
o
n
e
n
ts
o
f
th
e
tech
n
iq
u
e
ar
e
d
ata
r
e
d
u
ctio
n
,
d
ata
d
is
p
lay
,
an
d
co
n
cl
u
s
io
n
d
r
awin
g
an
d
v
er
if
icatio
n
.
C
o
d
in
g
,
m
em
o
in
g
,
an
d
p
r
o
p
o
s
itio
n
d
e
v
elo
p
m
en
t
ar
e
th
e
th
r
e
e
p
r
im
ar
y
task
s
in
v
o
lv
ed
in
th
e
s
e
co
m
p
o
n
e
n
ts
.
C
o
d
es
ar
e
“
ta
g
s
o
r
lab
els
f
o
r
ass
ig
n
in
g
u
n
it
s
o
f
m
ea
n
in
g
to
th
e
d
escr
ip
tiv
e
o
r
in
f
e
r
en
tial
in
f
o
r
m
atio
n
co
m
p
iled
d
u
r
in
g
a
s
tu
d
y
,
”
ac
c
o
r
d
in
g
to
S
a
y
e
d
[
3
1
]
.
T
h
ese
co
d
es
wer
e
ch
o
s
en
b
ased
o
n
th
eir
m
ea
n
i
n
g
an
d
attac
h
ed
to
th
e
in
f
o
r
m
at
io
n
o
b
tain
ed
f
r
o
m
th
e
q
u
esti
o
n
n
air
es.
T
h
e
co
d
e
d
d
ata
wer
e
th
en
co
m
b
in
ed
b
y
th
e
r
esear
ch
er
u
s
in
g
m
em
o
i
n
g
to
c
r
ea
te
a
d
is
tin
g
u
is
h
ab
le
clu
s
ter
b
ased
o
n
a
s
in
g
le
o
v
er
ar
c
h
in
g
id
ea
.
T
h
e
r
esear
ch
e
r
’
s
co
n
tin
u
o
u
s
id
ea
s
d
u
r
in
g
th
e
co
d
in
g
p
r
o
ce
d
u
r
es
wer
e
lik
ewise
r
ec
o
r
d
e
d
b
y
t
h
e
m
e
m
o
in
g
tec
h
n
iq
u
e.
Fin
ally
,
th
e
r
eq
u
ir
e
m
e
n
t
to
“
f
o
r
m
alize
an
d
s
y
s
tem
atize
th
e
r
esear
ch
er
’
s
th
in
k
in
g
in
to
a
co
h
er
en
t
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et
o
f
ex
p
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atio
n
s
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in
cr
ea
s
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as
a
s
tu
d
y
g
o
es
o
n
S
a
y
e
d
[
3
1
]
.
Du
r
in
g
p
h
ase
1
o
f
th
is
s
tu
d
y
,
we
d
e
v
elo
p
ed
h
y
p
o
th
es
es
o
n
r
elate
d
s
ets
o
f
p
ar
ticip
a
n
t
s
tatem
en
ts
,
we
co
n
s
id
er
ed
th
e
r
esu
lts
,
an
d
we
g
en
er
ated
f
ir
s
t c
o
n
clu
s
io
n
s
.
T
h
e
v
alid
ity
o
f
th
is
s
tu
d
y
in
t
h
e
co
n
tex
t
o
f
MCK
is
f
u
n
d
a
m
en
tally
ac
ce
p
ta
b
le
b
ec
a
u
s
e
i
t
u
s
ed
th
ic
k
d
escr
ip
tio
n
s
o
f
th
e
co
n
tex
t
an
d
it
is
b
ased
o
n
th
e
p
r
in
cip
le
o
f
d
iv
er
s
if
y
in
g
th
e
way
q
u
es
tio
n
s
ar
e
ask
ed
o
r
u
s
in
g
m
u
ltip
le
d
ata
s
o
u
r
ce
s
o
r
m
eth
o
d
s
with
in
th
e
s
am
e
i
n
s
tr
u
m
en
t
to
co
n
f
ir
m
o
r
cr
o
s
s
-
v
alid
ate
f
in
d
in
g
s
.
T
h
e
s
tatis
tical
co
n
clu
s
io
n
is
en
r
ich
ed
a
n
d
m
ad
e
m
ea
n
in
g
f
u
l
b
y
th
e
s
p
ec
if
ic,
co
n
tex
tu
al
r
e
aso
n
s
d
er
iv
ed
f
r
o
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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J
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c
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2252
-
8
8
2
2
A
q
u
a
lita
tive
s
tu
d
y
o
f m
a
th
em
a
tica
l c
o
n
ten
t k
n
o
w
led
g
e
a
n
d
p
ed
a
g
o
g
ica
l c
o
n
ten
t
… (
J
a
ma
l A
h
mich
a
n
e
)
2265
th
e
d
ir
ec
t
q
u
esti
o
n
s
.
T
h
is
h
o
lis
tic
u
n
d
er
s
tan
d
in
g
g
iv
es
r
ea
d
er
s
m
o
r
e
co
n
f
id
en
ce
in
th
e
s
tu
d
y
’
s
co
n
clu
s
io
n
s
.
T
h
e
s
tu
d
y
’
s
r
eliab
ilit
y
is
m
ad
e
p
o
s
s
ib
le
b
y
th
e
f
ac
t
th
at
it
is
ca
r
r
ied
o
u
t
am
o
n
g
PS
T
s
o
b
ta
in
in
g
b
ac
h
el
o
r
’
s
o
r
m
aster
’
s
d
eg
r
ee
s
f
r
o
m
s
ev
er
al
Mo
r
o
cc
an
u
n
iv
er
s
ities
.
I
t r
em
a
in
s
to
b
e
s
ee
n
if
th
e
th
em
es d
is
co
v
er
ed
ar
e
lik
el
y
ap
p
licab
le
an
d
tr
an
s
f
er
ab
le
t
o
o
th
er
PS
T
s
co
h
o
r
ts
in
s
im
ilar
s
ce
n
ar
io
s
.
4.
RE
SU
L
T
S
4
.
1
.
Rea
din
ess
t
o
t
ea
ch
m
a
t
hem
a
t
ics
E
v
er
y
p
ar
ticip
a
n
t
(
2
5
o
u
t
o
f
2
5
)
ex
p
r
ess
ed
h
o
w
p
r
ep
ar
e
d
th
ey
wer
e
to
teac
h
lo
wer
s
ec
o
n
d
ar
y
s
tu
d
en
t
’
s
m
ath
em
atica
l
co
n
te
n
t.
R
eg
ar
d
in
g
t
h
e
s
ev
en
av
a
ilab
le
co
n
ten
t
to
p
ics
(
n
u
m
b
e
r
s
an
d
n
u
m
er
ical
ca
lcu
latio
n
s
,
alg
eb
r
a
an
d
liter
al
ca
lcu
latio
n
s
,
p
r
o
p
o
r
tio
n
alit
y
an
d
f
u
n
ctio
n
s
,
g
e
o
m
etr
y
,
m
e
asu
r
em
en
ts
,
g
r
ap
h
ic
an
d
s
tatis
tical
ac
tiv
itie
s
,
an
d
lo
g
ical
r
ea
s
o
n
in
g
an
d
p
r
o
b
lem
s
o
lv
in
g
)
,
p
a
r
ticip
an
ts
r
ated
th
e
m
s
elv
es o
n
a
L
ik
er
t
s
ca
le
f
r
o
m
1
to
5
,
wh
e
r
e
5
s
i
g
n
if
ies
th
at
th
ey
f
ee
l
e
n
tire
ly
r
ea
d
y
a
n
d
1
in
d
icate
s
th
at
th
ey
ar
e
least
r
ea
d
y
.
Ov
er
all,
p
a
r
ticip
an
ts
d
ec
lar
e
d
th
at
th
ey
f
elt
least
r
ea
d
y
to
tea
ch
g
e
o
m
etr
y
(
m
ea
n
=3
,
SD=0
.
8
6
)
an
d
m
o
s
t
r
ea
d
y
to
teac
h
n
u
m
b
er
s
an
d
n
u
m
er
ic
al
ca
lcu
latio
n
(
m
ea
n
=4
.
3
6
,
SD=0
.
7
5
)
.
Alth
o
u
g
h
n
o
t
v
er
y
m
u
ch
,
th
e
m
ea
n
s
co
r
e
f
o
r
ea
c
h
is
s
u
e
s
h
o
we
d
th
at
p
a
r
ticip
an
ts
f
elt
q
u
alif
ied
t
o
teac
h
m
ath
em
atics
i
n
m
id
d
le
s
ch
o
o
l
(
3
<
m
ea
n
<4
.
3
6
)
.
T
ab
le
2
d
is
p
lay
s
th
ese
d
ata.
T
ab
le
2
.
Self
-
p
e
r
ce
p
tio
n
s
o
n
t
ea
ch
in
g
co
n
ten
t
To
p
i
c
1
2
3
4
5
To
t
a
l
M
e
a
n
SD
N
u
mb
e
r
s a
n
d
n
u
m
e
r
i
c
a
l
c
a
l
c
u
l
a
t
i
o
n
0
1
1
11
12
25
4
.
3
6
0
.
7
5
A
l
g
e
b
r
a
a
n
d
l
i
t
e
r
a
l
c
a
l
c
u
l
a
t
i
o
n
s
0
1
1
16
7
25
4
.
1
6
0
.
7
0
P
r
o
p
o
r
t
i
o
n
a
l
i
t
y
a
n
d
f
u
n
c
t
i
o
n
s
1
3
3
14
4
25
3
.
6
8
1
.
0
2
G
e
o
me
t
r
y
1
7
10
5
2
25
3
0
.
8
6
M
e
a
su
r
e
me
n
t
s
2
2
4
12
5
25
3
.
6
1
.
1
0
G
r
a
p
h
i
c
a
n
d
st
a
t
i
st
i
c
a
l
a
c
t
i
v
i
t
i
e
s
1
4
5
9
6
25
3
.
6
1
.
1
5
Lo
g
i
c
a
l
r
e
a
s
o
n
i
n
g
a
n
d
p
r
o
b
l
e
m s
o
l
v
i
n
g
1
4
6
10
4
25
3
.
4
8
1
.
0
8
4
.
2
.
Rea
din
ess
t
o
t
ea
ch
s
t
ud
ent
s
E
v
er
y
p
ar
ticip
an
t
(
2
5
o
u
t
o
f
2
5
)
g
a
v
e
a
r
an
g
e
o
f
r
esp
o
n
s
es
ab
o
u
t
h
o
w
r
ea
d
y
th
ey
f
elt
to
t
ea
ch
lo
wer
s
ec
o
n
d
ar
y
s
tu
d
en
ts
.
T
h
e
r
esea
r
ch
er
d
is
tin
g
u
is
h
ed
b
etwe
en
th
r
ee
ca
teg
o
r
ies o
f
q
u
alitativ
e
r
e
s
p
o
n
s
es: u
n
ce
r
tain
,
co
n
f
id
en
t,
an
d
u
n
c
o
n
f
id
e
n
t.
Ou
t
o
f
25
p
a
r
ticip
an
ts
,
12
ex
p
r
ess
ed
th
at
t
h
ey
f
elt
co
n
f
id
en
t
t
o
teac
h
m
ath
em
atica
l m
ater
ial.
So
m
e
p
ar
ticip
an
t r
ep
lies
co
n
s
is
ted
o
f
:
“
C
o
n
ce
r
n
in
g
th
e
co
n
ten
t,
I
c
a
n
s
a
y
th
a
t I
’
m
r
ea
d
y
to
tea
ch
t
h
is
s
u
b
ject
.
”
“
I
th
in
k
I
a
m
q
u
a
lifi
ed
to
tea
ch
ma
th
ema
tics
w
ith
a
h
ig
h
r
eten
tio
n
r
a
te
b
ec
a
u
s
e
o
f
my
s
tr
o
n
g
a
ca
d
emic
b
a
ck
g
r
o
u
n
d
a
n
d
b
r
e
a
d
th
o
f m
a
t
h
ema
tica
l k
n
o
w
led
g
e
.
”
“
I
a
m
q
u
a
lifi
ed
to
tea
c
h
ma
t
h
ema
tics
to
s
tu
d
en
ts
o
f
ea
r
ly
s
ec
o
n
d
a
r
y
s
ch
o
o
l.
I
h
a
ve
s
u
fficien
t
s
u
b
ject
kn
o
w
led
g
e
a
n
d
p
ed
a
g
o
g
ica
l
s
kills
b
ec
a
u
s
e
I
h
a
ve
e
xp
erien
ce
in
tea
c
h
in
g
m
a
th
em
a
tics
in
p
r
iva
te
s
ch
o
o
ls
.
A
ls
o
,
I
h
a
v
e
ex
p
erien
ce
in
tech
n
o
lo
g
y
a
n
d
tea
ch
i
n
g
,
s
o
I
ca
n
u
s
e
th
ese
ex
p
erien
ce
s
to
mo
tiva
te
s
tu
d
en
ts
to
lea
r
n
.”
Of
th
e
2
5
PS
T
s
,
1
0
s
aid
th
e
y
wer
e
u
n
s
u
r
e
ab
o
u
t
teac
h
i
n
g
;
f
o
r
m
o
s
t
o
f
th
ese
r
e
p
lies
,
p
a
r
ticip
an
ts
s
aid
th
ey
n
ee
d
ed
d
if
f
er
en
t a
m
o
u
n
ts
o
f
a
d
d
itio
n
al
MCK a
n
d
PC
K.
Fo
r
ex
am
p
le,
s
o
m
e
p
ar
ticip
an
t
s
m
en
tio
n
ed
:
“
I
th
in
k
th
a
t
th
e
va
r
io
u
s
s
kills
I
h
a
ve
a
cq
u
ir
ed
d
u
r
in
g
th
e
ye
a
r
s
o
f
my
s
ch
o
o
lin
g
a
n
d
te
a
ch
in
g
ex
p
erien
ce
ca
n
b
e
h
elp
fu
l
w
h
e
n
it
co
mes
to
tea
ch
in
g
ma
t
h
ema
tics
.
Ho
w
ev
er,
it
’
s
s
till
n
o
t
e
n
o
u
g
h
,
a
n
d
in
o
r
d
er
to
ex
p
a
n
d
my
kn
o
w
led
g
e
a
n
d
a
p
p
ly
it
in
th
e
cl
a
s
s
r
o
o
m,
I
mu
s
t
g
et
a
n
e
d
u
ca
tio
n
in
tea
ch
in
g
.”
“
F
o
r
me,
I
a
m
q
u
ite
co
mp
et
en
t
co
n
ce
r
n
in
g
ma
th
ema
tic
CK
in
ea
r
ly
s
ec
o
n
d
a
r
y
s
ch
o
o
l,
ev
en
th
o
u
g
h
th
ere
a
r
e
s
o
me
is
s
u
es
a
n
d
g
a
p
s
,
b
u
t
th
e
s
erio
u
s
p
r
o
b
lem
is
h
o
w
to
co
n
ve
y
o
r
s
h
a
r
e
in
fo
r
ma
tio
n
w
ith
s
tu
d
en
ts
s
lig
h
tly
.”
On
ly
th
r
ee
o
u
t
o
f
25
p
a
r
ticip
an
ts
s
aid
th
at
th
ey
wer
e
u
n
co
n
f
i
d
en
t
in
th
eir
ab
ilit
y
to
teac
h
m
ath
em
atics.
On
e
o
f
t
h
em
s
t
ated
,
“
a
ctu
a
lly
,
w
ith
th
e
ma
th
ema
tica
l
kn
o
w
led
g
e
a
n
d
s
kill
s
th
a
t
I
h
a
ve
,
I
a
m
co
mp
letely
n
o
t
r
ea
d
y
to
tea
c
h
ma
th
ema
tics
,
b
u
t
I
h
o
p
e
to
i
mp
r
o
ve
my
p
ed
a
g
o
g
ica
l
a
n
d
co
n
ten
t
kn
o
w
led
g
e
.
”
T
h
ese
f
in
d
in
g
s
allo
w
u
s
to
p
r
o
p
o
s
e
s
o
m
e
s
u
b
-
th
e
m
es,
s
u
ch
as
th
e
r
o
le
o
f
ex
p
er
ien
ce
i
n
th
e
co
n
f
i
d
en
ce
to
teac
h
m
ath
em
atics
a
n
d
g
r
o
wt
h
m
in
d
s
et.
Fo
r
th
e
f
ir
s
t
s
u
b
-
th
em
e,
th
e
m
o
s
t
c
o
n
f
id
e
n
t
r
esp
o
n
d
en
ts
s
p
ec
if
icall
y
m
en
tio
n
ed
“
ex
p
er
ien
ce
in
tea
ch
in
g
in
p
r
iv
ate
s
ch
o
o
ls
”
o
r
“
tech
n
o
lo
g
y
ex
p
er
ie
n
ce
”
,
wh
ic
h
s
u
g
g
ests
th
at
s
elf
-
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
15
,
No
.
3
,
J
u
n
e
20
2
6
:
2
2
6
1
-
2
2
7
0
2266
co
n
f
id
en
ce
is
s
ig
n
if
ican
tly
in
f
lu
en
ce
d
b
y
p
r
io
r
class
r
o
o
m
e
x
p
er
ien
ce
.
Fo
r
th
e
s
ec
o
n
d
o
n
e,
we
s
ee
th
at
ev
en
am
o
n
g
th
e
“
u
n
c
o
n
f
i
d
en
t
”
an
d
“
u
n
ce
r
tain
”
g
r
o
u
p
s
,
th
er
e
is
a
s
tated
d
esire
to
ex
p
an
d
k
n
o
wled
g
e
an
d
g
et
an
ed
u
ca
tio
n
in
teac
h
i
n
g
;
th
ey
ar
e
p
o
in
tin
g
o
u
t
a
p
ar
ticu
la
r
n
ee
d
f
o
r
ad
d
itio
n
al
tr
ain
in
g
an
d
tech
n
o
lo
g
y
in
teg
r
atio
n
,
n
o
t
r
ejec
tin
g
t
h
e
p
r
o
f
ess
io
n
.
Ad
d
itio
n
ally
,
o
n
e
p
ar
ticip
an
t
co
n
n
ec
ted
h
is
s
el
f
-
co
n
f
i
d
en
ce
to
h
is
ca
p
ac
ity
to
m
o
tiv
ate
s
tu
d
en
t
s
th
r
o
u
g
h
tech
n
o
lo
g
y
,
in
d
ica
tin
g
th
at
co
n
tem
p
o
r
ar
y
PS
T
s
m
ay
v
iew
d
ig
ital
liter
ac
y
as a
f
u
n
d
a
m
en
tal
asp
e
ct
o
f
th
eir
id
e
n
tity
as e
d
u
ca
to
r
s
.
4
.
3
.
M
a
t
hema
t
ica
l c
o
nte
nt
kn
o
wledg
e
s
up
po
rt
needed
W
ith
a
s
tr
ik
in
g
9
6
%
o
f
PS
T
s
(
2
4
o
f
2
5
)
s
tatin
g
th
at
th
ey
n
ee
d
ed
m
o
r
e
MCK
to
ef
f
ec
ti
v
ely
teac
h
lo
wer
s
ec
o
n
d
ar
y
s
tu
d
en
ts
,
a
clea
r
ar
ea
f
o
r
atten
tio
n
em
er
g
es
with
in
Mo
r
o
cc
an
teac
h
er
tr
ai
n
in
g
.
Fu
r
th
er
m
o
r
e,
th
e
p
ar
ticip
a
n
ts
s
elec
ted
s
p
ec
if
ic
elem
en
ts
o
f
th
e
Mo
r
o
cc
a
n
cu
r
r
icu
lu
m
th
at
th
ey
b
elie
v
ed
r
eq
u
ir
e
d
m
o
r
e
MCK su
p
p
o
r
t.
I
n
p
ar
ticu
lar
,
th
e
o
v
er
wh
elm
in
g
m
ajo
r
it
y
o
f
P
STs (
1
5
o
f
2
4
)
s
tated
th
e
y
n
ee
d
ed
ass
is
tan
ce
with
th
e
g
eo
m
etr
y
co
m
p
o
n
e
n
t.
Var
i
o
u
s
p
ar
ticip
an
ts
’
co
m
m
en
ts
ab
o
u
t g
eo
m
etr
y
s
u
p
p
o
r
t in
cl
u
d
ed
:
“
I
th
in
k
th
a
t
g
e
o
metry
is
th
e
a
r
ea
w
h
ere
I
mo
s
t
n
ee
d
mo
r
e
tr
a
in
in
g
b
ec
a
u
s
e
d
u
r
in
g
my
ye
a
r
s
o
f
h
ig
h
s
ch
o
o
l,
I
co
n
ce
n
tr
a
ted
o
n
a
lg
eb
r
a
a
n
d
a
n
a
lysi
s
.”
“
I
h
a
ve
n
o
is
s
u
e
tea
c
h
in
g
ma
t
h
to
ju
n
io
r
h
ig
h
s
ch
o
o
l
s
tu
d
en
ts
,
b
u
t
I
th
in
k
I
n
ee
d
mo
r
e
tr
a
i
n
in
g
t
o
imp
r
o
ve
my
g
eo
metry
s
kills
.
”
“
E
ve
n
th
o
u
g
h
I
a
m
r
ea
d
y,
I
en
co
u
n
ter a
n
u
mb
er o
f d
iffi
cu
ltie
s
in
th
e
d
is
cip
lin
e
o
f g
e
o
metry
.”
A
s
ig
n
if
ican
tly
lo
wer
p
er
ce
n
tag
e
o
f
PS
T
s
s
tated
th
at
th
ey
r
e
q
u
ir
ed
f
u
r
t
h
er
MCK
f
r
o
m
th
e
Mo
r
o
cc
an
cu
r
r
icu
lu
m
co
m
p
o
n
e
n
ts
o
f
s
tatis
tics
(
1
o
f
2
4
)
,
an
aly
s
is
(
3
o
f
2
4
)
,
lo
g
ical
r
ea
s
o
n
in
g
a
n
d
p
r
o
b
lem
s
o
lv
in
g
(
2
o
f
2
4
)
,
an
d
all
f
ield
s
o
f
m
ath
em
atics
k
n
o
wled
g
e
(
3
o
f
2
4
)
.
Am
o
n
g
th
e
th
r
ee
o
u
t
o
f
25
wh
o
r
ep
o
r
ted
f
ee
lin
g
“
u
n
co
n
f
id
en
t
”
,
o
n
e
s
aid
“
n
o
t
ye
t;
h
o
w
ev
er,
I
h
a
ve
n
o
d
o
u
b
t
th
a
t
I
w
ill
d
is
co
ve
r
s
o
me
fiel
d
s
in
w
h
ich
I
n
ee
d
s
u
p
p
o
r
t
.
”
4
.
4
.
T
he
un
it
’
s
co
ntr
ibu
t
io
n t
o
un
dersta
nd
ing
m
a
t
hem
a
t
i
ca
l c
o
nte
nt
Acc
o
r
d
in
g
to
th
e
p
r
ed
ictio
n
s
o
f
all
p
ar
ticip
an
ts
(
2
5
o
u
t
o
f
2
5
)
,
m
aster
in
g
th
e
u
n
it
wo
u
ld
h
elp
th
em
p
r
ep
ar
e
to
teac
h
m
ath
e
m
atics.
Sp
ec
if
ically
,
th
e
o
v
er
wh
elm
i
n
g
m
ajo
r
ity
o
f
p
ar
ticip
an
ts
(
2
4
o
u
t
o
f
2
5
)
ag
r
ee
d
th
at
th
is
m
o
d
u
le
wo
u
ld
h
elp
th
em
s
tr
en
g
th
en
t
h
eir
PC
K
o
r
MCK
o
r
b
o
th
o
f
th
em
.
A
s
am
p
le
o
f
PS
T
s
’
s
tatem
en
ts
is
:
“
Th
is
co
u
r
s
e,
in
my
o
p
in
io
n
,
w
ill
p
r
o
vid
e
me
w
ith
th
e
p
r
o
p
er
meth
o
d
s
fo
r
te
a
ch
in
g
ma
th
ema
tics
a
n
d
h
a
n
d
lin
g
th
e
v
a
r
io
u
s
is
s
u
es th
a
t m
a
y
a
r
is
e
in
th
e
cla
s
s
r
o
o
m
.
”
(
S
tu
d
en
t
1
)
“
Th
is
u
n
it
w
ill
a
s
s
i
s
t
me
i
n
ex
p
a
n
d
in
g
a
n
d
co
mp
r
eh
e
n
d
in
g
my
m
a
th
ema
tica
l
kn
o
w
led
g
e,
p
a
r
ticu
la
r
ly
in
r
ela
tio
n
to
s
o
m
e
o
f m
y
d
eficien
cies in
g
eo
met
r
y
.
”
(
S
tu
d
en
t 6
)
“
Wit
h
th
e
s
u
p
p
o
r
t
o
f
th
e
e
d
u
c
a
tio
n
a
n
d
tr
a
in
i
n
g
ce
n
ter
’
s
ed
u
ca
to
r
s
,
I
th
i
n
k
th
is
tr
a
in
in
g
w
ill
h
elp
in
u
n
d
ers
ta
n
d
in
g
MC
K
.
Th
is
t
r
a
in
in
g
in
clu
d
es
effec
tive
less
o
n
p
la
n
n
in
g
a
n
d
th
e
ma
n
a
g
e
men
t
o
f
a
u
n
iq
u
e
co
n
ce
p
t.
F
u
r
th
ermo
r
e,
mid
d
le
s
ch
o
o
l
tr
a
in
in
g
cl
a
s
s
es
w
ill
a
llo
w
u
s
to
s
w
itch
fr
o
m
a
th
eo
r
etica
l
to
a
p
r
a
ctica
l
a
p
p
r
o
a
ch
a
n
d
a
s
s
ess
o
u
r
leve
l
o
f
a
s
s
imila
tio
n
o
f
th
e
co
u
r
s
es
.
”
(
Stu
d
en
t
2
1
)
Alo
n
g
with
th
ese
co
m
m
en
ts
,
a
f
ew
p
ar
ticip
an
ts
(
2
o
u
t
o
f
2
5
)
em
p
h
asized
th
at
th
is
u
n
it
will
o
f
f
er
th
em
th
e
co
n
f
id
en
ce
th
ey
n
ee
d
to
p
r
o
p
e
r
ly
teac
h
m
ath
e
m
atics.
As o
n
e
m
em
b
er
p
o
in
ted
o
u
t
:
“
I
b
eliev
e
th
a
t
th
is
u
n
it
w
ill
h
elp
s
h
a
p
e
th
e
tea
c
h
er
’
s
p
ers
o
n
a
lity
in
th
e
cla
s
s
r
o
o
m,
en
h
a
n
ce
h
is
tea
ch
in
g
s
kills
a
n
d
tech
n
iq
u
es,
a
n
d
e
n
r
ich
h
is
ma
th
ema
tica
l
kn
o
w
led
g
e
.
”
Acc
o
r
d
in
g
to
two
o
u
t
o
f
25
p
ar
ticip
an
ts
,
th
e
less
o
n
m
ig
h
t
b
e
u
s
ef
u
l
f
o
r
r
e
v
is
in
g
m
ath
em
atica
l
m
ater
ial.
Acc
o
r
d
in
g
t
o
o
n
e
p
ar
ticip
an
t
:
“
Th
is
less
o
n
w
ill
r
ef
r
esh
m
y
p
r
ev
io
u
s
ly
a
cq
u
ir
ed
mid
d
l
e
s
ch
o
o
l
u
n
d
ers
ta
n
d
in
g
w
h
il
e
a
ls
o
imp
a
r
tin
g
n
ew
co
n
ten
t
kn
o
w
le
d
g
e,
s
u
ch
a
s
fu
n
d
a
men
ta
l
terms
a
n
d
tea
c
h
in
g
tec
h
n
iq
u
es
e
xc
lu
s
ive
to
mid
d
le
s
ch
o
o
l m
a
t
h
ema
tics
.
”
5.
DIS
CU
SS
I
O
N
E
x
am
in
in
g
h
o
w
m
id
d
le
s
ch
o
o
l
PS
T
s
p
ar
ticip
atin
g
in
a
m
ath
em
atics
ed
u
ca
tio
n
c
o
u
r
s
e
s
aw
th
em
s
elv
es
as
th
ey
im
p
lem
en
t
ed
an
d
s
tr
en
g
th
en
e
d
th
eir
m
at
h
em
atica
l
k
n
o
wled
g
e
was
th
e
in
ten
t
o
f
t
h
is
s
tu
d
y
.
T
h
e
r
esear
ch
e
r
also
lo
o
k
e
d
i
n
to
th
e
PS
T
s
’
p
er
ce
p
tio
n
s
a
n
d
u
n
d
er
s
tan
d
in
g
s
o
f
t
h
eir
“
r
ea
d
in
ess
”
to
teac
h
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
A
q
u
a
lita
tive
s
tu
d
y
o
f m
a
th
em
a
tica
l c
o
n
ten
t k
n
o
w
led
g
e
a
n
d
p
ed
a
g
o
g
ica
l c
o
n
ten
t
… (
J
a
ma
l A
h
mich
a
n
e
)
2267
m
ath
em
atics.
T
h
e
d
ata
r
ev
ea
l
s
a
d
is
tin
ct
d
ich
o
to
m
y
in
th
e
r
ea
d
in
ess
o
f
PS
T
s
.
W
h
ile
th
er
e
is
a
f
o
u
n
d
atio
n
al
b
elief
in
th
eir
g
en
er
al
r
ea
d
i
n
e
s
s
to
teac
h
(
in
d
icate
d
b
y
a
u
n
iv
er
s
al
p
o
s
itiv
e
r
esp
o
n
s
e
to
r
ea
d
in
ess
)
,
th
er
e
is
a
s
ig
n
if
ican
t
g
ap
b
etwe
en
th
ei
r
MCK
with
h
ig
h
s
elf
-
r
atin
g
i
n
n
u
m
b
er
s
an
d
n
u
m
e
r
ical
ca
lcu
latio
n
an
d
alg
eb
r
a
v
er
s
u
s
s
elf
-
r
atin
g
d
ef
icit
in
g
eo
m
etr
y
wh
ich
is
s
tr
o
n
g
l
y
co
r
r
o
b
o
r
ated
b
y
th
e
q
u
alitativ
e
f
ee
d
b
ac
k
.
T
h
e
r
o
o
t
ca
u
s
e
o
f
th
is
d
ef
icit
ap
p
ea
r
s
to
b
e
s
y
s
tem
ic.
I
t
s
ee
m
s
th
at
p
ar
ticip
an
ts
’
p
r
io
r
ac
a
d
e
m
ic
tr
ain
in
g
lik
ely
co
n
ce
n
tr
ated
o
n
alg
eb
r
a
an
d
an
aly
s
is
,
leav
in
g
th
em
u
n
d
er
-
eq
u
ip
p
ed
to
teac
h
g
eo
m
et
r
ic
co
n
ce
p
ts
.
T
h
is
in
d
icate
s
th
at
th
e
PS
T
s
ar
e
n
o
t
s
tr
u
g
g
lin
g
with
m
at
h
em
atics
ca
p
ab
ilit
y
,
b
u
t
r
ath
e
r
with
a
s
p
ec
if
ic
cu
r
r
icu
lar
b
lin
d
s
p
o
t.
Fu
r
th
er
m
o
r
e,
a
“
c
o
n
f
id
en
ce
g
ap
”
ex
is
ts
wh
er
e
p
er
ce
iv
ed
s
u
b
ject
m
aster
y
d
o
es
n
o
t
au
to
m
atica
lly
tr
an
s
late
to
p
e
d
ag
o
g
ical
co
n
f
id
en
ce
.
T
h
is
co
n
f
id
en
ce
ap
p
ea
r
s
co
r
r
elate
d
with
ex
p
er
ien
ce
.
Par
ticip
an
ts
wh
o
h
ad
tau
g
h
t
in
p
r
i
v
ate
s
ch
o
o
ls
r
ep
o
r
ted
h
i
g
h
er
co
n
f
id
en
ce
.
T
h
is
s
u
g
g
ests
th
at
r
ea
d
in
ess
is
v
iewe
d
b
y
PS
T
s
a
s
a
p
r
ac
tical
s
k
ill
s
et
ac
q
u
ir
ed
th
r
o
u
g
h
d
o
i
n
g
.
T
h
e
p
a
r
ticip
an
ts
v
iew
th
e
tr
ain
in
g
u
n
it
as
a
c
r
u
cial
b
r
id
g
e
to
cr
o
s
s
th
is
g
ap
,
s
p
ec
if
ically
to
tr
a
n
s
itio
n
f
r
o
m
th
eo
r
etica
l
k
n
o
w
led
g
e
to
p
r
ac
tical
class
r
o
o
m
ap
p
licatio
n
.
T
h
e
co
llected
d
ata
was
ca
teg
o
r
ized
in
to
two
co
n
ce
p
tu
al
co
n
ce
r
n
s
.
Am
o
n
g
t
h
ese
co
n
ce
r
n
s
ar
e
t
h
e
n
ee
d
to
im
p
r
o
v
e
MCK
an
d
PC
K
an
d
m
ea
n
in
g
f
u
l
p
r
o
f
ess
io
n
al
lear
n
in
g
.
B
o
th
o
f
th
ese
c
o
n
ce
r
n
s
ar
e
n
o
w
ta
k
en
in
to
ac
co
u
n
t
in
lig
h
t o
f
th
e
r
esear
ch
o
n
th
e
d
e
v
elo
p
m
en
t
o
f
m
ath
e
m
atics PS
T
s
.
5
.
1
.
M
ea
nin
g
f
ul pro
f
ess
io
na
l le
a
rning
E
ac
h
o
f
th
e
2
5
r
esear
c
h
p
ar
tic
ip
an
ts
em
p
h
asized
th
e
s
ig
n
if
ican
ce
o
f
m
ath
em
atics
teac
h
in
g
f
o
r
ea
r
ly
ad
o
lescen
t
u
n
it
f
o
r
th
eir
p
r
o
f
e
s
s
io
n
al
g
r
o
wth
as
PS
T
s
o
f
m
a
th
em
atics
an
d
s
o
e
n
h
an
cin
g
th
eir
cu
r
r
e
n
t
lev
el
o
f
r
ea
d
in
ess
to
teac
h
s
tu
d
e
n
ts
.
Fu
r
th
er
m
o
r
e
,
a
lo
t
o
f
PS
T
s
wer
e
ab
le
to
ex
p
r
ess
h
o
w
h
elp
f
u
l
th
ey
th
o
u
g
h
t
th
e
u
n
it
wo
u
ld
b
e
f
o
r
th
eir
p
r
o
f
ess
io
n
al
liv
es.
T
h
e
m
ajo
r
ity
o
f
p
ar
tici
p
an
ts
,
f
o
r
ex
am
p
le,
h
o
p
e
th
at
th
is
u
n
it wo
u
ld
h
elp
th
em
lear
n
all
th
e
tech
n
iq
u
es
an
d
m
eth
o
d
s
o
f
teac
h
in
g
m
at
h
em
atics
an
d
m
a
k
e
th
e
m
ath
e
m
atica
l
co
n
ce
p
ts
o
f
th
is
lev
el
clea
r
,
u
n
d
er
s
tan
d
a
b
le,
an
d
ac
ce
s
s
ib
le
to
t
h
e
ea
r
l
y
s
ec
o
n
d
a
r
y
s
ch
o
o
l
class
,
an
d
th
er
ef
o
r
e
im
p
r
o
v
e
PS
T
s
’
PC
K
an
d
MCK.
Oth
er
s
r
ep
o
r
ted
th
at
th
e
u
n
it
will
g
iv
e
th
em
co
n
f
id
en
ce
in
t
h
eir
ab
ilit
y
to
teac
h
an
d
co
n
s
o
lid
ate
m
ath
em
atics,
w
h
e
r
ea
s
o
th
er
s
d
escr
ib
e
d
it
as
“
a
g
o
o
d
co
n
te
n
t
r
ef
r
esh
er
”
.
T
h
e
f
in
d
in
g
s
alig
n
with
p
r
ev
io
u
s
r
esear
ch
th
at
h
ig
h
lig
h
ts
th
e
im
p
o
r
tan
ce
o
f
m
ath
em
atics
u
n
its
f
o
r
PS
T
s
[
1
9
]
,
[
3
4
]
.
T
en
p
ar
ticip
an
ts
o
f
25
s
aid
th
e
y
wer
e
u
n
co
n
f
id
en
t
ab
o
u
t
teac
h
in
g
l
o
wer
s
ec
o
n
d
a
r
y
m
ath
em
atics,
an
d
th
r
ee
PS
T
s
r
ep
o
r
ted
f
ee
lin
g
u
n
ce
r
tain
.
Acc
o
r
d
in
g
to
th
is
cl
aim
an
d
t
h
e
f
ac
t
th
at
m
o
s
t
r
esp
o
n
d
e
n
ts
(
2
4
o
u
t
o
f
2
5
)
s
aid
t
h
ey
f
elt
t
h
ey
n
ee
d
ed
m
o
r
e
MCK
a
n
d
PC
K,
th
is
c
o
u
r
s
e
ap
p
ea
r
s
to
b
e
v
er
y
b
en
ef
i
cial
f
o
r
p
r
e
p
ar
in
g
f
u
tu
r
e
teac
h
er
s
in
m
at
h
em
atics.
T
h
e
p
ar
ticip
an
ts
in
d
icate
d
th
a
t
th
e
u
n
it
wo
u
l
d
im
p
r
o
v
e
t
h
eir
MCK,
PC
K,
o
r
b
o
th
,
e
v
en
t
h
at
p
ar
ticip
an
t
wh
o
h
ad
a
co
n
f
id
en
ce
r
atin
g
in
th
ei
r
MCK.
T
h
ese
s
elf
-
r
ep
o
r
ted
r
e
s
p
o
n
s
es
f
r
o
m
p
ar
ticip
an
ts
ab
o
u
t
th
e
u
n
it
’
s
wo
r
th
ar
e
in
lin
e
with
th
o
s
e
o
f
o
t
h
er
ac
ad
em
ics
[
1
9
]
,
[
3
5
]
.
T
h
e
d
at
a
r
ef
lects
a
h
ig
h
ly
o
p
tim
is
tic
an
d
g
r
o
wth
-
o
r
ien
ted
co
h
o
r
t.
Desp
ite
9
6
%
o
f
p
a
r
ticip
an
ts
s
tatin
g
th
ey
n
ee
d
m
o
r
e
CK
,
th
is
is
n
o
t
f
r
am
ed
as
a
f
ailu
r
e
b
u
t
as
a
r
o
ad
m
a
p
f
o
r
th
e
tr
ain
i
n
g
u
n
it.
5
.
2
.
T
he
need
t
o
im
pro
v
e
M
CK
a
nd
P
CK
I
n
lig
h
t
o
f
th
e
s
tu
d
y
p
ar
ticip
a
n
ts
’
af
f
ir
m
atio
n
s
o
f
th
e
n
ee
d
t
o
co
m
p
lete
th
is
u
n
it,
g
ath
er
ed
test
im
o
n
y
o
f
ten
em
p
h
asized
PS
T
s
’
s
elf
-
r
ep
o
r
te
d
n
ee
d
to
co
n
s
o
lid
ate
th
eir
MCK
an
d
PC
K.
A
to
tal
1
3
o
u
t
o
f
2
5
p
ar
ticip
an
ts
,
o
r
m
o
r
e
th
an
h
al
f
,
s
aid
th
ey
wer
e
u
n
co
n
f
id
en
t
o
r
u
n
ce
r
tain
in
teac
h
in
g
m
ath
em
atics.
Acc
o
r
d
in
g
to
th
e
m
ajo
r
ity
o
f
p
a
r
ticip
an
t
s
,
th
ey
n
ee
d
ed
h
elp
u
n
d
er
s
ta
n
d
in
g
h
o
w
to
teac
h
m
ath
em
a
tics
to
p
u
p
ils
af
ter
f
ee
lin
g
least
co
n
f
id
en
t
i
n
th
eir
MCK
an
d
PC
K.
T
h
ese
c
laim
s
s
u
p
p
o
r
t
th
e
id
ea
th
at
PC
K
i
s
cr
u
cial
f
o
r
m
ath
em
atics
teac
h
er
s
in
teac
h
in
g
an
d
lear
n
in
g
d
u
e
to
t
h
e
f
a
ct
th
at
m
ath
em
atics
is
an
ab
s
tr
ac
t
an
d
in
ter
r
elate
d
s
u
b
ject
r
eq
u
ir
in
g
a
d
eq
u
ate
k
n
o
wled
g
e
o
f
t
h
e
co
n
ten
t
an
d
in
s
tr
u
ctio
n
al
p
r
ac
tices
[
2
2
]
an
d
th
e
b
elief
th
at
m
ath
em
atics
teac
h
er
s
n
ee
d
tr
a
in
in
g
p
r
o
g
r
am
s
th
at
s
u
it
th
eir
s
p
ec
ialized
teac
h
in
g
n
ee
d
s
in
o
r
d
er
to
k
ee
p
p
ac
e
with
d
ev
elo
p
m
en
ts
an
d
ac
tiv
a
te
ex
p
er
ien
ce
s
a
m
o
n
g
th
em
[
3
6
]
.
Mo
r
e
th
a
n
5
0
%
o
f
th
o
s
e
w
h
o
r
ec
o
g
n
ize
d
th
at
th
ey
n
ee
d
e
d
ad
d
itio
n
al
s
u
p
p
o
r
t
to
im
p
r
o
v
e
th
eir
MCK
(
1
5
o
u
t
o
f
2
4
)
in
d
icate
d
t
h
at
g
eo
m
etr
y
was
th
e
Mo
r
o
cc
an
c
u
r
r
icu
lu
m
s
tr
a
n
d
i
n
wh
ich
th
ey
n
ee
d
ed
h
elp
th
e
m
o
s
t,
f
o
llo
wed
b
y
an
aly
s
is
an
d
lo
g
ical
r
ea
s
o
n
in
g
(
5
o
u
t
o
f
2
4
)
.
T
h
is
alig
n
s
with
m
an
y
s
tu
d
ies
th
at
s
tr
ess
ed
b
u
ild
in
g
tr
ain
in
g
p
r
o
g
r
am
s
d
esig
n
ed
to
d
ev
elo
p
an
d
s
u
p
p
o
r
t
th
e
g
r
o
wth
o
f
k
n
o
w
led
g
e
o
f
m
ath
em
atics
teac
h
e
r
s
,
as
s
o
m
e
m
ath
em
atics
tea
ch
er
s
h
av
e
lim
ited
k
n
o
wled
g
e
o
f
m
at
h
em
atics
ed
u
ca
tio
n
,
y
et
th
ey
teac
h
it
[
3
7
]
–
[
3
9
]
.
T
h
e
r
esear
ch
p
ar
ticip
an
ts
f
o
cu
s
ed
esp
ec
ially
o
n
th
e
n
ec
ess
ity
o
f
co
m
b
in
in
g
th
e
MCK
an
d
PC
K
th
ey
n
ee
d
t
o
teac
h
s
tu
d
en
ts
w
ith
co
n
f
id
e
n
ce
an
d
co
m
p
eten
ce
,
ev
e
n
th
o
u
g
h
cu
r
r
en
t
liter
atu
r
e
in
d
icate
s
th
at
m
a
th
em
atics
teac
h
er
s
s
h
o
u
ld
en
h
an
ce
th
eir
PK
,
C
K,
PC
K,
an
d
MCK
o
v
er
all.
T
h
is
f
o
cu
s
is
co
n
s
is
ten
t
with
th
e
ar
g
u
m
en
t
m
ad
e
b
y
a
n
u
m
b
er
o
f
ac
a
d
em
ics
th
at
teac
h
er
s
m
u
s
t h
av
e
a
s
o
lid
u
n
d
er
s
tan
d
in
g
o
f
MCK in
o
r
d
e
r
to
s
u
p
p
o
r
t stu
d
e
n
ts
’
lear
n
in
g
[
1
9
]
,
[
3
4
]
,
[
3
5
]
.
6.
CO
NCLU
SI
O
N
T
h
is
s
tu
d
y
ex
am
in
ed
th
e
s
elf
-
p
er
ce
p
tio
n
s
o
f
PS
T
s
in
m
id
d
l
e
s
ch
o
o
ls
p
ar
ticip
atin
g
in
a
m
ath
em
atics
teac
h
in
g
co
u
r
s
e
as
th
ey
p
r
ep
ar
ed
to
in
ter
ac
t
with
an
d
s
o
lid
if
y
th
eir
m
ath
em
atica
l
k
n
o
wled
g
e.
T
h
e
co
m
p
r
eh
e
n
s
io
n
o
f
th
eir
“
r
ea
d
in
ess
”
to
tak
e
o
n
a
task
o
f
th
is
k
in
d
was
also
ex
am
i
n
ed
.
T
h
e
r
esear
ch
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
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5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
15
,
No
.
3
,
J
u
n
e
20
2
6
:
2
2
6
1
-
2
2
7
0
2268
p
ar
ticip
an
ts
’
test
im
o
n
ies
co
n
f
ir
m
th
e
h
y
p
o
th
esis
th
at
p
ar
tic
ip
an
ts
n
ee
d
m
o
r
e
ass
is
tan
ce
in
im
p
r
o
v
in
g
th
eir
MCK
an
d
P
C
K,
wh
ich
i
s
alr
e
ad
y
s
u
p
p
o
r
te
d
b
y
a
b
o
d
y
o
f
liter
atu
r
e.
Simu
ltan
eo
u
s
ly
,
th
e
d
ata
o
b
tain
ed
d
u
r
in
g
Ph
ase
1
s
h
o
ws
h
o
w
m
u
ch
PS
T
s
th
in
k
co
m
p
letin
g
a
u
n
it
o
n
m
ath
em
atics
co
n
ten
t
will
h
elp
th
em
in
th
eir
f
u
tu
r
e
ca
r
ee
r
s
.
Acq
u
ir
in
g
MCK,
PC
K,
o
r
a
n
y
c
o
m
b
in
atio
n
o
f
th
e
s
e
k
n
o
wled
g
es
was
h
i
g
h
ly
v
a
lu
ed
.
Sp
ec
if
ically
,
all
p
ar
ticip
an
ts
s
tated
th
at
th
e
y
th
o
u
g
h
t
th
is
u
n
it
wo
u
ld
b
e
h
elp
f
u
l
i
n
s
tr
en
g
th
e
n
in
g
an
d
co
n
s
o
lid
atin
g
t
h
eir
MCK
an
d
PC
K.
T
h
e
s
tu
d
y
s
u
g
g
ests
a
m
ajo
r
is
s
u
e
with
s
elf
-
ef
f
icac
y
an
d
p
r
o
f
ess
io
n
al
r
ea
d
in
ess
an
d
p
o
i
n
ts
o
u
t
th
e
n
ee
d
f
o
r
ea
r
lier
an
d
m
o
r
e
in
ten
s
e
p
r
ac
tical
ex
p
er
ien
c
e
co
m
b
in
ed
with
s
tr
o
n
g
m
e
n
to
r
s
h
ip
.
PS
T
s
h
av
e
p
er
ce
iv
ed
s
ig
n
if
ican
t
g
a
p
s
in
th
eir
MCK
r
elate
d
to
g
eo
m
etr
y
an
d
PC
K
r
elate
d
to
teac
h
in
g
in
g
en
e
r
al.
T
h
er
ef
o
r
e,
it
wo
u
ld
b
e
b
en
ef
i
cial
f
o
r
t
h
e
teac
h
i
n
g
u
n
it
to
in
clu
d
e
s
p
ec
if
ic
c
o
n
ten
t
ar
ea
M
C
K
an
d
g
e
n
er
alize
d
teac
h
in
g
m
eth
o
d
s
in
th
e
c
o
u
r
s
e
s
tr
u
ctu
r
e.
T
r
ain
ee
s
n
ee
d
ex
p
er
ien
ce
d
p
r
o
f
ess
io
n
als
to
g
u
id
e
th
em
,
o
f
f
e
r
co
n
s
tr
u
ctiv
e
f
ee
d
b
ac
k
,
a
n
d
s
h
a
r
e
p
r
o
f
ess
io
n
al
in
s
ig
h
ts
.
Alth
o
u
g
h
t
h
is
s
tu
d
y
is
co
n
s
id
e
r
ed
an
ef
f
ec
tiv
e
a
n
d
ess
en
tial
t
o
o
l
f
o
r
r
e
d
u
cin
g
th
e
g
a
p
in
m
a
th
em
atics
ed
u
ca
tio
n
f
ield
s
in
th
e
Ar
ab
wo
r
ld
,
t
h
e
s
tu
d
y
h
as
ce
r
tain
lim
itatio
n
s
.
First,
th
e
s
tu
d
y
s
am
p
le
was
d
r
aw
n
f
r
o
m
a
s
in
g
le
r
eg
io
n
o
f
Mo
r
o
cc
o
,
with
ju
s
t
5
0
%
o
f
th
e
s
am
p
le
s
elf
-
s
elec
ted
to
p
ar
ticip
ate;
th
er
ef
o
r
e,
th
e
r
esu
lts
m
ay
o
n
l
y
b
e
a
p
p
licab
le
to
a
s
p
ec
if
ic
g
r
o
u
p
o
f
p
eo
p
le.
T
h
e
r
esu
lts
wo
u
ld
b
e
f
ar
m
o
r
e
th
o
r
o
u
g
h
an
d
g
en
er
aliza
b
le
if
th
e
s
tu
d
y
wa
s
ex
p
an
d
e
d
t
o
in
clu
d
e
a
lar
g
e
r
an
d
m
o
r
e
v
ar
ied
s
am
p
le
f
r
o
m
o
th
er
Mo
r
o
cc
an
r
eg
io
n
s
.
Seco
n
d
,
th
is
q
u
esti
o
n
n
air
e
s
h
o
u
ld
b
e
u
s
ed
in
co
n
ju
n
ctio
n
with
o
th
er
m
ea
s
u
r
em
en
ts
,
s
u
ch
as
in
ter
v
iews
o
r
class
r
o
o
m
o
b
s
e
r
v
atio
n
s
,
in
f
u
t
u
r
e
r
esear
ch
t
o
less
en
an
y
p
o
ten
tial
b
iases
.
Ad
d
itio
n
ally
,
o
n
ly
PS
T
s
in
Mo
r
o
cc
an
lo
wer
s
ec
o
n
d
ar
y
s
ch
o
o
ls
wer
e
in
clu
d
ed
in
th
is
s
tu
d
y
.
I
n
o
r
d
er
to
asc
er
tain
wh
eth
er
th
e
f
in
d
in
g
s
o
f
th
is
s
tu
d
y
ap
p
ly
t
o
o
th
e
r
s
itu
atio
n
s
,
it
is
r
ec
o
m
m
en
d
ed
th
at
d
if
f
er
e
n
ce
s
in
co
n
f
ir
m
atio
n
o
f
th
e
f
in
d
in
g
b
etwe
en
in
-
s
er
v
ice
teac
h
er
s
an
d
PS
T
s
in
lo
wer
s
ec
o
n
d
ar
y
s
ch
o
o
ls
b
e
s
tu
d
ied
.
B
ased
o
n
th
e
f
in
d
in
g
s
o
f
th
is
s
tu
d
y
,
a
n
u
m
b
e
r
o
f
im
p
licatio
n
s
f
o
r
eith
er
p
o
licy
o
r
teac
h
er
tr
ain
in
g
p
r
ac
tice
ca
n
b
e
p
r
o
p
o
s
ed
.
Fo
r
th
e
f
ir
s
t
o
n
e
,
p
o
lic
y
s
h
o
u
ld
s
h
if
t
f
r
o
m
t
r
ea
tin
g
MCK
an
d
PC
K
as
s
ep
ar
ate
en
titi
es.
I
n
s
tead
,
it
s
h
o
u
ld
m
an
d
ate
in
teg
r
ated
u
n
its
wh
er
e
PS
T
s
lear
n
ad
v
an
ce
d
m
ath
em
atics
co
n
ce
p
ts
th
r
o
u
g
h
th
e
len
s
o
f
m
id
d
le
-
s
ch
o
o
l
p
ed
a
g
o
g
y
;
also
,
g
iv
en
th
at
o
v
er
6
0
%
o
f
th
o
s
e
n
ee
d
in
g
h
elp
p
o
i
n
ted
s
p
ec
if
ically
to
g
eo
m
etr
y
,
p
o
li
cy
s
h
o
u
l
d
c
o
n
s
id
er
“
s
tr
an
d
-
s
p
ec
if
ic
”
m
icr
o
-
cr
ed
e
n
tials
o
r
in
ten
s
iv
e
m
o
d
u
les
with
in
teac
h
er
ce
r
tific
atio
n
to
en
s
u
r
e
m
aster
y
in
h
is
to
r
ically
d
if
f
icu
lt
ar
ea
s
.
Fo
r
th
e
s
ec
o
n
d
o
n
e,
tr
ain
in
g
p
r
o
g
r
a
m
s
s
h
o
u
ld
allo
ca
te
m
o
r
e
in
s
tr
u
ctio
n
al
h
o
u
r
s
to
g
eo
m
e
tr
y
,
an
aly
s
is
,
an
d
lo
g
ical
r
ea
s
o
n
in
g
,
as
th
ese
wer
e
id
en
tifie
d
as
th
e
p
r
im
ar
y
s
o
u
r
ce
s
o
f
u
n
ce
r
tain
ty
.
Als
o
,
p
r
o
g
r
am
s
s
h
o
u
ld
im
p
lem
en
t
f
r
eq
u
en
t
m
icr
o
-
teac
h
in
g
s
ess
io
n
s
wh
er
e
PS
T
s
p
r
ac
tice
ex
p
lain
in
g
a
b
s
tr
ac
t
co
n
ce
p
ts
to
p
ee
r
s
b
ef
o
r
e
e
n
ter
in
g
a
r
ea
l
class
r
o
o
m
to
ad
d
r
ess
th
e
u
n
ce
r
tain
g
r
o
u
p
(
wh
o
k
n
o
w
th
e
m
ath
b
u
t
f
ea
r
th
e
co
n
v
ey
i
n
g
)
.
Ad
d
itio
n
ally
,
th
e
tr
ain
in
g
s
h
o
u
ld
p
r
ep
ar
e
in
d
iv
i
d
u
als
f
o
r
th
e
em
o
tio
n
al
d
e
m
an
d
s
o
f
t
h
e
jo
b
(
e.
g
.
,
s
tr
ess
,
b
u
r
n
o
u
t,
m
a
n
ag
in
g
d
if
f
icu
lt
s
itu
atio
n
s
,
o
r
d
ea
lin
g
with
p
r
o
f
ess
io
n
al
s
etb
ac
k
s
)
.
T
h
e
co
u
r
s
e
co
u
ld
in
v
o
lv
e
em
o
tio
n
al
in
tellig
en
ce
t
r
ain
in
g
a
n
d
teac
h
i
n
g
tech
n
iq
u
es f
o
r
s
tr
ess
m
an
ag
e
m
en
t a
n
d
w
o
r
k
-
life
b
alan
ce
.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
T
h
e
p
u
b
licatio
n
o
f
th
is
wo
r
k
was
ac
co
m
p
lis
h
ed
with
f
in
a
n
cial
ass
is
tan
ce
o
f
Sid
i
Mo
h
am
ed
B
en
Ab
d
ellah
Un
iv
er
s
ity
,
Fez,
Mo
r
o
cc
o
.
AUTHO
R
CO
NT
RI
B
UT
I
O
NS
T
h
is
jo
u
r
n
al
u
s
es
th
e
C
o
n
t
r
ib
u
to
r
R
o
les
T
a
x
o
n
o
m
y
(
C
R
ed
iT)
to
r
ec
o
g
n
ize
in
d
iv
i
d
u
al
au
th
o
r
co
n
tr
ib
u
tio
n
s
,
r
ed
u
ce
au
th
o
r
s
h
ip
d
is
p
u
tes,
an
d
f
ac
ilit
ate
co
llab
o
r
atio
n
.
Na
m
e
o
f
Aut
ho
r
C
M
So
Va
Fo
I
R
D
O
E
Vi
Su
P
Fu
J
am
al
Ah
m
ich
an
e
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
Mo
s
taf
a
E
l
M
allah
i
✓
✓
✓
✓
✓
✓
✓
✓
✓
Yo
u
n
ess
Had
d
er
✓
✓
✓
C
:
C
o
n
c
e
p
t
u
a
l
i
z
a
t
i
o
n
M
:
M
e
t
h
o
d
o
l
o
g
y
So
:
So
f
t
w
a
r
e
Va
:
Va
l
i
d
a
t
i
o
n
Fo
:
Fo
r
mal
a
n
a
l
y
s
i
s
I
:
I
n
v
e
s
t
i
g
a
t
i
o
n
R
:
R
e
so
u
r
c
e
s
D
:
D
a
t
a
C
u
r
a
t
i
o
n
O
:
W
r
i
t
i
n
g
-
O
r
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i
n
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D
r
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f
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r
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a
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Fu
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M
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Au
th
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r
s
s
tate
n
o
co
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lict o
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in
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est.
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
A
q
u
a
lita
tive
s
tu
d
y
o
f m
a
th
em
a
tica
l c
o
n
ten
t k
n
o
w
led
g
e
a
n
d
p
ed
a
g
o
g
ica
l c
o
n
ten
t
… (
J
a
ma
l A
h
mich
a
n
e
)
2269
I
NF
O
RM
E
D
CO
NS
E
N
T
W
e
h
av
e
o
b
tain
ed
in
f
o
r
m
ed
c
o
n
s
en
t f
r
o
m
all
in
d
iv
id
u
als in
c
lu
d
ed
in
t
h
is
s
tu
d
y
.
DATA AV
AI
L
AB
I
L
I
T
Y
Data
ar
e
av
ailab
le
f
r
o
m
th
e
c
o
r
r
esp
o
n
d
i
n
g
au
t
h
o
r
,
[
J
A]
,
u
p
o
n
r
ea
s
o
n
ab
le
r
eq
u
est.
RE
F
E
R
E
NC
E
S
[
1
]
A
.
D
.
F
i
t
r
i
a
n
i
,
D
.
D
a
r
h
i
m
,
a
n
d
D
.
J
u
a
n
d
i
,
“
Ef
f
e
c
t
o
f
m
a
t
h
e
m
a
t
i
c
a
l
c
o
n
t
e
n
t
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o
r
o
c
c
o
.
Cu
rre
n
tl
y
,
h
e
is
a
d
o
c
to
ra
l
stu
d
e
n
t
p
u
rsu
in
g
a
P
h
.
D
.
i
n
m
a
th
e
m
a
ti
c
s
e
d
u
c
a
ti
o
n
a
t
S
id
i
M
o
h
a
m
e
d
Be
n
Ab
d
e
ll
a
h
U
n
iv
e
rsit
y
.
His
re
se
a
rc
h
fo
c
u
se
s
o
n
m
a
th
e
m
a
ti
c
s
e
d
u
c
a
ti
o
n
,
sc
a
ffo
ld
i
n
g
in
e
d
u
c
a
ti
o
n
,
p
ro
jec
t
-
b
a
se
d
lea
rn
in
g
,
S
TE
M
e
d
u
c
a
ti
o
n
,
a
n
d
li
tera
c
y
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
jam
a
l.
a
h
m
ich
a
n
e
@u
sm
b
a
.
a
c
.
m
a
.
Mo
sta
f
a
El
M
a
ll
a
h
i
is
a
n
a
ss
o
c
iate
p
ro
fe
ss
o
r
(M
a
it
re
d
e
Co
n
fé
re
n
c
e
s
Ha
b
il
it
é
)
a
t
th
e
Eco
le
No
rm
a
le
S
u
p
é
rieu
re
o
f
F
e
z
,
De
p
a
rtme
n
t
o
f
M
a
th
e
m
a
ti
c
s
a
n
d
Co
m
p
u
ter
S
c
ien
c
e
s,
S
id
i
M
o
h
a
m
e
d
Be
n
Ab
d
e
ll
a
h
U
n
i
v
e
rsity
,
F
e
z
,
M
o
ro
c
c
o
.
His res
e
a
r
c
h
in
tere
sts
in
c
lu
d
e
a
rti
ficia
l
in
telli
g
e
n
c
e
,
i
n
tern
e
t
o
f
t
h
in
g
s
(I
o
T),
c
y
b
e
rse
c
u
rit
y
,
c
o
m
p
u
ter
sc
ien
c
e
,
b
i
g
d
a
ta
,
a
n
d
re
se
a
rc
h
i
n
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
sta
fa
.
e
lma
ll
a
h
i@u
sm
b
a
.
a
c
.
m
a
.
Yo
u
n
e
ss
H
a
d
d
e
r
h
o
l
d
s
t
h
e
p
o
siti
o
n
o
f
As
so
c
iate
P
r
o
fe
ss
o
r
i
n
th
e
d
e
p
a
rtme
n
t
o
f
M
a
th
e
m
a
ti
c
s
a
t
Re
g
io
n
a
l
Ce
n
t
e
r
fo
r
Ed
u
c
a
ti
o
n
a
n
d
Train
in
g
P
ro
fe
ss
io
n
s,
F
e
z
-
M
e
k
n
e
s,
M
o
ro
c
c
o
.
His
re
se
a
rc
h
fo
c
u
se
s
o
n
M
a
t
h
e
m
a
ti
c
s
a
n
d
M
a
th
e
m
a
ti
c
s
Ed
u
c
a
ti
o
n
,
with
s
p
e
c
ifi
c
in
tere
sts
in
,
re
sp
e
c
ti
v
e
l
y
,
f
u
n
c
ti
o
n
a
l
a
n
a
ly
sis
a
n
d
S
h
u
lma
n
’s
t
h
e
o
ry
o
f
m
a
th
e
m
a
ti
c
s
tea
c
h
e
rs’
p
e
d
a
g
o
g
ica
l
c
o
n
ten
t
k
n
o
wle
d
g
e
(
P
CK).
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
h
a
d
d
fsm
@h
o
tma
il
.
c
o
m
.
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