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Ma
th
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Mo
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Ph
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Scien
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I
t
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two
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ter
twin
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ield
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[
1
]
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New
to
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[
2
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in
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k
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asize
d
t
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s
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d
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d
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o
lv
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a
s
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in
p
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[
3
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.
Ho
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lear
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[
4
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,
[
5
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.
T
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[
6
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.
On
th
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R
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h
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Ku
o
[
7
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s
tate
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cu
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o
b
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p
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o
m
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a
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T
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im
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ed
u
ca
tio
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co
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
2
5
2
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I
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t
J
E
v
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&
R
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d
u
c
,
Vo
l
.
14
,
No
.
5
,
Octo
b
er
20
25
:
4
1
1
9
-
412
8
4120
tau
g
h
t
in
p
h
y
s
ics
an
d
m
ath
em
atics
co
u
r
s
es
ar
e
f
u
n
d
am
en
tally
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cu
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in
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8
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p
r
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in
d
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in
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th
at
1
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-
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tu
d
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in
E
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g
lan
d
p
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p
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m
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as
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ep
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n
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elate
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ip
s
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etwe
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ity
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o
n
g
s
cien
tific
d
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cip
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[
4
]
,
[
9
]
,
[
1
0
]
.
T
h
is
m
ea
n
s
th
at
th
ese
two
s
u
b
jects,
p
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s
d
ef
in
ed
ac
c
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d
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g
to
R
ev
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d
y
[
1
1
]
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a
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o
r
k
n
o
wled
g
e
f
r
o
m
d
if
f
er
en
t
s
u
b
jects
.
”
I
n
o
th
er
wo
r
d
s
,
in
ter
d
is
cip
lin
a
r
ity
in
v
o
lv
es
g
e
n
u
in
e
co
llab
o
r
atio
n
an
d
in
te
r
ac
tio
n
b
etwe
en
f
ield
s
o
f
s
tu
d
y
th
at
ar
e
tr
ad
itio
n
ally
d
is
tin
ct.
I
n
ter
d
is
cip
lin
ar
ity
also
em
b
o
d
ies
a
co
m
p
lem
en
tar
y
ap
p
r
o
ac
h
,
co
m
b
in
in
g
v
ar
io
u
s
m
eth
o
d
s
an
d
teac
h
in
g
s
tr
ate
g
ies
with
in
a
s
p
ec
if
ic
d
is
cip
lin
e.
T
h
is
ca
n
lead
to
a
m
o
r
e
co
m
p
r
eh
en
s
iv
e
u
n
d
er
s
tan
d
i
n
g
o
f
a
s
u
b
ject.
I
n
g
e
n
er
al,
Kab
il
[
1
2
]
s
tate
d
th
at
n
o
a
r
ea
o
f
p
h
y
s
ics
d
o
es
n
o
t
in
v
o
lv
e
m
ath
em
atica
l
f
o
r
m
u
las,
eq
u
atio
n
s
,
a
n
d
m
a
n
ip
u
latio
n
s
in
s
o
m
e
f
o
r
m
.
T
h
e
in
v
o
l
v
em
e
n
t
o
f
m
ath
em
atics
in
p
h
y
s
ics
is
an
in
ter
ac
tio
n
th
at
ca
n
r
an
g
e
f
r
o
m
s
im
p
le
co
m
m
u
n
icatio
n
o
f
id
ea
s
t
o
th
e
to
tal
in
teg
r
atio
n
o
f
p
u
r
ely
m
at
h
em
atica
l
co
n
ce
p
ts
an
d
n
o
tio
n
s
[
1
3
]
.
T
o
u
n
d
er
s
tan
d
an
d
s
o
lv
e
a
s
itu
atio
n
in
p
h
y
s
ics,
teac
h
er
s
as
well
as
s
tu
d
en
ts
m
u
s
t
u
s
e
th
ei
r
m
ath
em
atica
l
k
n
o
wled
g
e
an
d
s
k
ills
[
1
4
]
–
[
1
6
]
.
T
h
is
s
tate
o
f
af
f
air
s
r
eq
u
ir
es
a
clea
r
cu
r
r
icu
lu
m
r
elatio
n
s
h
ip
b
etwe
en
p
h
y
s
ics an
d
m
ath
em
a
tics
[
1
7
]
,
[
18
]
.
I
n
th
e
Mo
r
o
cc
a
n
ed
u
ca
tio
n
al
co
n
tex
t,
wh
ile
th
er
e
is
a
r
is
in
g
in
ter
est
am
o
n
g
r
esear
ch
er
s
in
ex
p
lo
r
in
g
th
e
p
h
en
o
m
en
o
n
o
f
m
ath
em
at
izatio
n
in
p
h
y
s
ics,
th
er
e
ap
p
e
ar
s
to
b
e
a
s
ig
n
if
ican
t
s
h
o
r
tf
a
ll
in
th
e
n
u
m
b
e
r
o
f
teac
h
er
s
an
d
s
tu
d
en
ts
wh
o
ef
f
ec
tiv
ely
en
g
a
g
e
with
th
is
co
n
ce
p
t.
T
h
is
d
is
p
ar
ity
in
r
esea
r
ch
en
th
u
s
iasm
an
d
teac
h
er
s
’
in
v
o
l
v
em
en
t
s
er
v
es
as
th
e
p
r
im
ar
y
m
o
tiv
atio
n
f
o
r
th
e
wo
r
k
u
n
d
e
r
tak
en
i
n
th
is
s
tu
d
y
,
w
h
ich
s
ee
k
s
to
in
v
esti
g
ate
th
e
r
ea
s
o
n
s
b
eh
in
d
th
e
lim
ited
ad
o
p
tio
n
o
f
m
ath
e
m
atiza
tio
n
in
p
h
y
s
ics
b
y
Mo
r
o
cc
an
s
tu
d
en
ts
an
d
its
im
p
licatio
n
s
f
o
r
th
eir
lear
n
in
g
ex
p
e
r
ien
ce
s
.
T
h
e
g
en
e
r
al
q
u
esti
o
n
o
f
th
is
r
esear
ch
:
I
s
t
h
e
in
ter
d
is
cip
lin
ar
ity
o
f
m
ath
em
atics a
n
d
p
h
y
s
ics tak
en
in
to
c
o
n
s
id
er
atio
n
in
th
e
Mo
r
o
cc
an
e
d
u
ca
tio
n
al
s
y
s
tem
?
B
ased
o
n
th
e
p
r
em
is
e
th
at
th
e
teac
h
er
p
lay
s
a
p
iv
o
tal
r
o
le
i
n
d
eter
m
in
i
n
g
th
e
o
u
tco
m
e
o
f
teac
h
in
g
an
d
lear
n
in
g
en
d
ea
v
o
r
s
,
it
s
ee
m
ed
p
r
u
d
e
n
t
to
d
ir
ec
t
o
u
r
atte
n
tio
n
to
wa
r
d
th
is
f
ac
to
r
.
T
h
is
m
eth
o
d
allo
ws
u
s
to
s
im
u
ltan
eo
u
s
ly
s
h
ed
lig
h
t
o
n
t
h
e
af
o
r
em
en
tio
n
ed
o
v
er
a
r
ch
in
g
q
u
esti
o
n
an
d
th
e
s
p
ec
if
ic
in
q
u
ir
y
ce
n
tr
al
t
o
th
is
s
tu
d
y
:
Ho
w
th
e
Mo
r
o
cc
an
tea
ch
er
s
p
er
ce
iv
e
th
e
m
ath
em
ati
ca
l
im
p
licatio
n
s
in
p
h
y
s
ics
le
ar
n
in
g
?
T
o
a
d
d
r
ess
th
e
r
esear
ch
q
u
esti
o
n
,
we
id
en
tifie
d
th
e
s
p
ec
if
ic
s
ec
tio
n
s
o
f
t
h
e
2
n
d
b
ac
ca
lau
r
ea
te
p
h
y
s
ics
p
r
o
g
r
am
th
at
r
eq
u
ir
e
m
ath
em
atica
l
k
n
o
wle
d
g
e
an
d
o
u
tlin
ed
t
h
e
n
at
u
r
e
o
f
t
h
is
r
eq
u
ir
e
d
k
n
o
wled
g
e.
Su
b
s
eq
u
en
tly
,
we
an
aly
ze
d
th
e
ex
is
tin
g
s
cien
tific
liter
atu
r
e
o
n
p
h
y
s
ics
m
ath
em
atiza
tio
n
,
f
o
cu
s
in
g
o
n
eig
h
t
r
ec
en
t
ar
ticles
th
at
h
ig
h
lig
h
ted
ch
allen
g
es
in
im
p
lem
en
tin
g
m
ath
em
ati
za
tio
n
,
s
p
ec
if
ically
in
p
r
o
b
lem
-
s
o
lv
in
g
an
d
m
ath
em
atiza
tio
n
p
r
ac
tices.
W
e
th
en
d
ev
elo
p
ed
a
p
ap
er
-
an
d
-
p
e
n
cil
q
u
esti
o
n
n
air
e
co
n
s
is
tin
g
o
f
s
ix
item
s
,
d
r
awin
g
f
r
o
m
o
u
r
an
aly
s
is
o
f
2
n
d
b
ac
ca
la
u
r
ea
te
te
x
tb
o
o
k
s
an
d
th
e
s
cien
tific
liter
atu
r
e.
T
h
e
q
u
esti
o
n
n
air
e
aim
ed
to
p
r
o
v
id
e
in
s
ig
h
ts
in
t
o
v
ar
io
u
s
asp
ec
ts
o
f
p
h
y
s
ics
teac
h
in
g
an
d
lear
n
in
g
,
p
ar
ticu
lar
ly
r
eg
ar
d
in
g
th
e
in
ter
s
ec
tio
n
o
f
m
ath
e
m
atics a
n
d
p
h
y
s
ics.
2.
M
E
T
H
O
D
2
.
1
.
T
ex
t
bo
o
k
a
na
ly
s
is
T
o
s
ee
th
e
d
eg
r
ee
o
f
m
ath
e
m
atiza
tio
n
in
2
n
d
b
ac
ca
la
u
r
e
ate
p
h
y
s
ics
p
r
o
g
r
am
s
,
we
co
n
d
u
cted
a
q
u
alitativ
e
an
aly
s
is
o
f
two
p
h
y
s
ics
tex
tb
o
o
k
s
cu
r
r
en
tly
u
s
ed
in
h
ig
h
s
ch
o
o
ls
an
d
p
u
b
lis
h
ed
in
2
0
0
7
:
Al
W
ad
h
ih
/l
Ma
s
s
ar
T
ex
tb
o
o
k
(
SVT
o
p
tio
n
)
an
d
Al
W
ad
h
ih
/Al
Ma
s
s
ar
T
ex
tb
o
o
k
(
PC
o
p
tio
n
)
.
T
h
e
f
ir
s
t
p
o
in
t
n
o
ted
f
r
o
m
th
is
th
o
r
o
u
g
h
r
ea
d
in
g
o
f
t
h
e
two
tex
tb
o
o
k
s
is
th
at
ea
ch
p
ar
t
ca
lls
f
o
r
s
k
ills
an
d
/o
r
m
ath
em
atica
l
co
n
ce
p
ts
,
as
s
h
o
wn
in
T
ab
le
1
.
All
p
ar
ts
o
f
th
e
p
h
y
s
ics
p
r
o
g
r
am
in
v
o
lv
e
m
ath
em
atica
l
k
n
o
wled
g
e,
wh
ic
h
co
n
f
ir
m
s
th
e
im
p
o
r
tan
t
p
lace
o
f
m
ath
em
atiza
tio
n
in
th
e
Mo
r
o
cc
an
2
n
d
b
ac
ca
lau
r
e
ate
p
r
o
g
r
a
m
.
2
.
2
.
T
he
s
cient
if
ic
lite
ra
t
ure
T
h
e
im
p
o
r
tan
ce
o
f
p
h
y
s
ics
m
ath
em
atiza
tio
n
is
in
cr
ea
s
in
g
ly
ch
allen
g
in
g
ed
u
ca
tio
n
al
r
ese
ar
ch
er
s
.
I
n
th
e
last
two
d
ec
ad
es,
r
esear
ch
er
s
h
av
e
f
o
c
u
s
ed
eith
er
o
n
t
h
e
p
r
ac
tice
o
f
m
ath
e
m
atiza
tio
n
o
r
o
n
t
h
e
u
s
e
o
f
m
ath
em
atics
in
p
h
y
s
ics
p
r
o
b
lem
-
s
o
lv
in
g
,
as
s
h
o
wn
i
n
T
ab
le
2
.
T
h
e
liter
atu
r
e
r
esear
ch
es
af
f
ir
m
th
e
o
b
s
er
v
atio
n
th
at
m
ath
em
atics
an
d
p
h
y
s
ics
ar
e
in
ter
r
elate
d
an
d
th
at
to
u
n
d
er
s
tan
d
p
h
y
s
i
cs
p
h
en
o
m
en
a
o
n
e
ca
n
n
o
t
b
y
p
ass
m
ath
em
atics.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
P
h
ysics
ma
th
ema
tiz
a
tio
n
fr
o
m
a
tea
ch
in
g
p
ers
p
ec
tive:
s
ec
o
n
d
a
r
y
s
ch
o
o
l
…
(
A
b
d
elw
a
h
a
b
E
l A
z
z
o
u
z
i
)
4121
T
ab
le
1
.
Dif
f
e
r
en
t p
ar
ts
o
f
p
h
y
s
ics in
v
o
lv
e
m
ath
em
atics
P
r
o
g
r
a
m
p
a
r
t
s
M
a
t
h
e
ma
t
i
c
a
l
k
n
o
w
l
e
d
g
e
r
e
q
u
i
r
e
d
N
u
c
l
e
a
r
t
r
a
n
sf
o
r
m
a
t
i
o
n
(
N
T)
N
a
t
u
r
a
l
e
x
p
o
n
e
n
t
i
a
l
f
u
n
c
t
i
o
n
N
a
t
u
r
a
l
l
o
g
a
r
i
t
h
m
i
c
f
u
n
c
t
i
o
n
El
e
c
t
r
i
c
i
t
y
(
E)
D
i
f
f
e
r
e
n
t
i
a
l
e
q
u
a
t
i
o
n
s
M
e
c
h
a
n
i
c
s
(
M
)
I
n
t
e
g
r
a
l
s
a
n
d
p
r
i
m
i
t
i
v
e
s
O
t
h
e
r
s
W
a
v
e
s
C
h
e
mi
s
t
r
y
Li
n
e
a
r
f
u
n
c
t
i
o
n
A
f
f
i
n
e
f
u
n
c
t
i
o
n
D
e
r
i
v
a
b
i
l
i
t
y
T
ab
le
2
.
E
x
am
p
les o
f
s
tu
d
ies
o
n
p
h
y
s
ics m
ath
em
atiza
tio
n
D
i
sci
p
l
i
n
e
A
r
t
i
c
l
e
s
Th
e
m
a
t
i
c
P
h
y
s
i
c
s
[
18
]
–
[
20
]
P
r
o
b
l
e
m
-
s
o
l
v
i
n
g
[
6
]
,
[
1
2
]
,
[
21
]
M
a
t
h
e
ma
t
i
z
a
t
i
o
n
p
r
a
c
t
i
c
e
C
h
e
mi
s
t
r
y
[
1
4
]
P
r
o
b
l
e
m
-
s
o
l
v
i
n
g
[
1
5
]
M
a
t
h
e
ma
t
i
z
a
t
i
o
n
p
r
a
c
t
i
c
e
2
.
3
.
Q
ues
t
io
nn
a
ire
dev
elo
p
m
ent
T
h
r
o
u
g
h
th
e
ex
am
i
n
atio
n
o
f
r
e
lev
an
t
tex
tb
o
o
k
s
an
d
an
ex
ten
s
iv
e
r
ev
iew
o
f
th
e
ex
is
tin
g
liter
atu
r
e,
we
u
n
d
er
to
o
k
a
m
et
h
o
d
ical
a
p
p
r
o
ac
h
to
g
ath
e
r
p
er
tin
en
t
in
s
ig
h
ts
th
at
wo
u
l
d
ad
d
r
ess
th
e
r
e
s
ea
r
ch
in
q
u
ir
ies
at
h
an
d
.
T
o
s
y
s
tem
atica
lly
o
r
g
a
n
ize
an
d
elicit
r
esp
o
n
s
es
f
o
r
o
u
r
r
esear
ch
q
u
esti
o
n
s
,
a
s
tr
u
ctu
r
ed
p
ap
e
r
an
d
p
en
cil
q
u
esti
o
n
n
air
e
was
c
r
af
t
ed
,
en
c
o
m
p
ass
in
g
s
ix
d
is
tin
ct
item
s
.
T
h
e
in
tr
icac
ies
o
f
ea
c
h
r
esear
ch
q
u
esti
o
n
an
d
th
e
s
p
ec
if
ic
o
b
jectiv
es
ass
o
ciate
d
with
ea
c
h
item
ar
e
co
m
p
r
eh
en
s
iv
ely
d
elin
ea
te
d
in
T
ab
le
3
p
r
o
v
id
in
g
a
s
u
cc
in
ct
an
d
o
r
g
an
ized
o
v
er
v
i
ew
o
f
th
e
r
esear
c
h
f
r
am
ew
o
r
k
.
T
ab
le
3
.
Ob
jectiv
es a
n
d
e
lab
o
r
atio
n
o
f
th
e
d
if
f
e
r
en
t r
esear
ch
q
u
esti
o
n
s
Q
u
e
st
i
o
n
Q
u
e
st
i
o
n
o
b
j
e
c
t
i
v
e
Q1
W
h
a
t
p
a
r
t
(
s)
o
f
t
h
e
c
o
u
r
s
e
d
o
y
o
u
t
h
i
n
k
r
e
q
u
i
r
e
s
m
o
r
e
mat
h
e
m
a
t
i
z
a
t
i
o
n
i
n
t
h
e
t
e
r
m
i
n
a
l
p
r
o
g
r
a
m?
I
d
e
n
t
i
f
y
t
e
a
c
h
e
r
s
’
p
e
r
c
e
p
t
i
o
n
s
o
f
t
h
e
p
a
r
t
s
o
f
t
h
e
p
h
y
si
c
s
c
u
r
r
i
c
u
l
u
m
i
n
t
h
e
s
e
n
i
o
r
y
e
a
r
.
Q2
A
c
c
o
r
d
i
n
g
t
o
y
o
u
,
t
h
e
m
o
s
t
c
o
mm
o
n
p
r
o
b
l
e
ms
e
n
c
o
u
n
t
e
r
e
d
i
n
t
h
e
t
e
a
c
h
i
n
g
o
f
p
h
y
s
i
c
s i
n
t
h
e
t
e
r
mi
n
a
l
a
r
e
?
I
d
e
n
t
i
f
y
t
e
a
c
h
e
r
s
’
p
e
r
c
e
p
t
i
o
n
s
o
f
t
h
e
mo
st
e
n
c
o
u
n
t
e
r
e
d
p
r
o
b
l
e
ms
i
n
p
h
y
si
c
s
.
Q3
M
a
t
h
e
ma
t
i
c
s
a
n
d
p
h
y
si
c
s
a
r
e
c
o
m
p
l
e
men
t
a
r
y
i
n
a
l
a
s
t
i
n
g
a
n
d
c
o
n
t
i
n
u
o
u
s
w
a
y
.
I
d
e
n
t
i
f
y
t
e
a
c
h
e
r
s
’
p
e
r
c
e
p
t
i
o
n
s
o
f
t
h
e
r
e
l
a
t
i
o
n
s
h
i
p
b
e
t
w
e
e
n
p
h
y
s
i
c
s
a
n
d
mat
h
e
ma
t
i
c
s
.
Q4
To
s
t
u
d
y
a
p
h
y
s
i
c
a
l
p
h
e
n
o
m
e
n
o
n
,
o
n
e
a
l
w
a
y
s
r
e
s
o
r
t
s
t
o
t
h
e
i
n
t
e
g
r
a
t
i
o
n
o
f
m
a
t
h
e
m
a
t
i
c
s
.
I
d
e
n
t
i
f
y
t
e
a
c
h
e
r
s
’
p
e
r
c
e
p
t
i
o
n
s
o
f
t
h
e
i
n
t
e
g
r
a
t
i
o
n
o
f
m
a
t
h
e
m
a
t
i
c
s
i
n
t
o
t
h
e
e
x
p
l
a
n
a
t
i
o
n
o
f
p
h
y
si
c
a
l
o
r
c
h
e
mi
c
a
l
p
h
e
n
o
m
e
n
a
.
Q5
M
a
t
h
e
ma
t
i
z
a
t
i
o
n
i
s
a
d
i
f
f
i
c
u
l
t
y
i
n
t
e
a
c
h
i
n
g
a
n
d
l
e
a
r
n
i
n
g
p
h
y
s
i
c
s.
I
d
e
n
t
i
f
y
t
e
a
c
h
e
r
s
’
p
e
r
c
e
p
t
i
o
n
s
o
f
t
h
e
d
i
f
f
i
c
u
l
t
y
o
f
m
a
t
h
e
m
a
t
i
z
i
n
g
p
h
y
s
i
c
s
i
n
t
h
e
t
e
r
mi
n
a
l
.
Q6
D
o
y
o
u
r
st
u
d
e
n
t
s
f
i
n
d
d
i
f
f
i
c
u
l
t
i
e
s
i
n
m
a
t
h
e
mat
i
z
i
n
g
p
h
y
s
i
c
s
p
r
o
b
l
e
ms
?
I
d
e
n
t
i
f
y
t
e
a
c
h
e
r
s
’
p
e
r
c
e
p
t
i
o
n
s
o
f
t
h
e
t
y
p
e
s
o
f
d
i
f
f
i
c
u
l
t
i
e
s
a
sso
c
i
a
t
e
d
w
i
t
h
p
h
y
s
i
c
s
mat
h
e
ma
t
i
z
a
t
i
o
n
.
2
.
4
.
P
a
rt
icipa
nts
I
n
th
e
cu
r
r
en
t
in
v
esti
g
atio
n
,
we
co
n
d
u
cte
d
an
em
p
ir
ical
s
tu
d
y
in
v
o
lv
i
n
g
p
h
y
s
ics
teac
h
er
s
in
Mo
r
o
cc
an
h
ig
h
s
ch
o
o
ls
,
f
o
cu
s
in
g
o
n
th
e
ass
ess
m
en
t
o
f
th
ei
r
p
er
ce
p
tio
n
s
c
o
n
ce
r
n
i
n
g
p
h
y
s
ic
s
m
ath
em
atiza
tio
n
.
T
h
e
s
u
r
v
ey
tar
g
eted
teac
h
er
s
en
g
a
g
ed
in
h
ig
h
s
ec
o
n
d
ar
y
ed
u
ca
tio
n
with
in
t
h
e
Fez
-
Me
k
n
es
R
eg
io
n
.
T
h
e
s
elec
ted
p
o
p
u
latio
n
co
m
p
r
is
e
d
1
4
1
p
h
y
s
ics
teac
h
er
s
,
r
ep
r
es
en
tin
g
1
7
.
1
1
%
o
f
th
e
t
o
tal
tea
ch
in
g
c
o
h
o
r
t
in
th
e
r
eg
io
n
(
8
2
4
p
h
y
s
ics
teac
h
er
s
)
,
as
p
er
d
ata
o
b
tain
e
d
f
r
o
m
th
e
R
eg
io
n
al
Aca
d
e
m
y
f
o
r
E
d
u
ca
tio
n
an
d
T
r
ai
n
in
g
o
f
th
e
Fez
-
Me
k
n
es.
T
o
en
s
u
r
e
a
r
ep
r
esen
tativ
e
s
am
p
le,
th
e
s
tu
d
y
en
c
o
m
p
ass
ed
a
d
iv
er
s
e
g
r
o
u
p
o
f
teac
h
e
r
s
with
in
th
e
s
p
ec
if
ied
g
e
o
g
r
ap
h
i
ca
l a
r
ea
.
T
h
e
r
eliab
ilit
y
an
d
v
alid
ity
o
f
th
e
q
u
esti
o
n
n
air
e,
as
a
r
esear
ch
in
s
tr
u
m
en
t,
wer
e
m
eticu
lo
u
s
ly
co
n
s
id
er
ed
.
T
h
e
q
u
esti
o
n
n
air
e
d
em
o
n
s
tr
ated
h
i
g
h
f
ac
e
v
alid
ity
,
as
its
item
s
wer
e
ex
p
er
tly
d
esig
n
ed
to
alig
n
with
th
e
s
p
ec
if
ic
f
o
cu
s
o
f
th
e
s
tu
d
y
,
n
a
m
ely
th
e
p
er
ce
p
tio
n
s
o
f
p
h
y
s
ics
teac
h
er
s
r
eg
ar
d
in
g
th
e
in
teg
r
atio
n
o
f
m
ath
em
atics
in
th
eir
teac
h
in
g
p
r
ac
tices.
C
o
n
ten
t
v
alid
ity
was
en
s
u
r
ed
th
r
o
u
g
h
a
r
ig
o
r
o
u
s
r
ev
iew
p
r
o
ce
s
s
,
in
v
o
lv
in
g
ex
p
er
ts
in
b
o
th
p
h
y
s
ics
an
d
ed
u
ca
tio
n
,
to
g
u
ar
an
tee
th
e
r
elev
an
ce
an
d
ap
p
r
o
p
r
iaten
ess
o
f
th
e
q
u
esti
o
n
n
air
e
item
s
.
Fu
r
th
er
m
o
r
e,
th
e
in
s
tr
u
m
en
t
’
s
r
eliab
ilit
y
was
ass
ess
ed
th
r
o
u
g
h
a
p
ilo
t
s
tu
d
y
in
v
o
lv
in
g
a
s
u
b
s
et
o
f
th
e
tar
g
et
p
o
p
u
lat
io
n
.
I
n
ter
n
al
co
n
s
is
ten
cy
wa
s
ev
alu
ated
u
s
in
g
s
tatis
tical
m
ea
s
u
r
es
s
u
ch
as
C
r
o
n
b
ac
h
’
s
alp
h
a,
r
esu
ltin
g
i
n
a
co
e
f
f
icien
t
in
d
icativ
e
o
f
t
h
e
q
u
esti
o
n
n
air
e
’
s
r
eliab
ilit
y
.
T
h
e
r
esp
o
n
d
en
ts
,
in
th
is
ca
s
e,
wer
e
n
o
t
in
clu
d
ed
in
th
e
m
ain
s
tu
d
y
,
en
s
u
r
i
n
g
th
at
th
e
d
ata
o
b
tain
e
d
d
u
r
in
g
th
e
p
ilo
t
p
h
ase
d
id
n
o
t
in
f
lu
en
ce
th
e
s
u
b
s
eq
u
en
t a
n
aly
s
is
.
Ad
d
itio
n
ally
,
th
e
eth
ical
co
n
s
id
er
atio
n
s
s
u
r
r
o
u
n
d
in
g
th
e
a
d
m
in
is
tr
atio
n
o
f
th
e
q
u
esti
o
n
n
air
e
wer
e
ad
d
r
ess
ed
.
T
h
e
ass
u
r
an
ce
o
f
an
o
n
y
m
ity
was
co
m
m
u
n
ica
ted
tr
an
s
p
ar
en
tly
to
th
e
p
a
r
ticip
atin
g
teac
h
er
s
,
Evaluation Warning : The document was created with Spire.PDF for Python.
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t
J
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v
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&
R
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u
c
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Vo
l
.
14
,
No
.
5
,
Octo
b
er
20
25
:
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1
1
9
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412
8
4122
em
p
h
asizin
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at
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tial
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ited
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ity
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ata
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r
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ef
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d
in
th
e
co
m
p
letio
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tim
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o
f
1
0
to
2
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m
i
n
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tes,
f
u
r
th
er
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u
p
p
o
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ts
th
e
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u
esti
o
n
n
air
e
’
s
ac
ce
p
tab
ilit
y
an
d
p
r
ac
ticality
in
th
e
r
esear
ch
co
n
tex
t.
2
.
5
.
Da
t
a
t
re
a
t
m
ent
s
T
h
e
r
esu
lts
o
f
th
e
co
llected
d
ata
wer
e
p
r
o
ce
s
s
ed
b
y
Mic
r
o
s
o
f
t
E
x
ce
l.
Mo
r
eo
v
er
,
we
u
s
ed
C
r
o
n
b
ac
h
’
s
a
lp
h
a
test
to
v
e
r
if
y
t
h
e
in
ter
n
a
l
co
n
s
is
ten
cy
an
d
th
u
s
g
u
ar
an
t
ee
th
e
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eliab
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y
o
f
th
e
m
ea
s
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r
em
en
t
to
o
l
,
wh
ich
is
th
e
q
u
esti
o
n
n
air
e.
T
h
e
v
al
u
e
o
b
tain
ed
is
0
.
8
5
.
I
t
s
h
o
u
ld
b
e
n
o
ted
th
at
th
is
v
alu
e
is
h
ig
h
er
th
an
th
e
r
ec
o
m
m
en
d
ed
th
r
esh
o
ld
[2
2
]
.
I
n
d
ee
d
,
a
C
r
o
n
b
ac
h
’
s
alp
h
a
v
alu
e
b
etwe
en
0
.
7
3
an
d
0
.
9
4
in
d
icate
s
th
e
v
alid
ity
o
f
a
q
u
esti
o
n
n
air
e
[2
3
]
–
[2
5
]
.
Simp
s
o
n
[2
6
]
in
h
is
f
am
o
u
s
p
ar
ad
o
x
a
p
p
lies
an
in
d
ex
th
at
i
s
ca
lled
Simp
s
o
n
’
s
in
d
ex
.
T
h
is
in
d
ex
r
e
p
r
esen
ts
th
e
d
o
m
in
a
n
ce
o
r
d
iv
er
s
ity
o
f
a
s
am
p
le
wh
en
th
e
ch
o
ices
o
f
s
elec
ted
p
ar
ticip
an
ts
ar
e
co
m
b
in
e
d
.
Simp
s
o
n
’
s
o
r
ig
i
n
al
f
o
r
m
u
la
is
:
C=
∑
(
)
2
W
h
er
e,
f
is
th
e
r
elativ
e
f
r
e
q
u
e
n
cy
f
o
r
ea
ch
c
h
o
ice.
Als
o
,
th
e
s
cien
tific
liter
atu
r
e
f
r
eq
u
e
n
tly
u
s
es
a
s
ec
o
n
d
in
d
e
x
,
wh
ich
is
th
e
d
iv
e
r
s
ity
in
d
e
x
,
co
r
r
esp
o
n
d
in
g
t
o
th
e
Simp
s
o
n
in
d
e
x
[2
5
]
,
[
27
]
.
T
h
is
d
iv
er
s
ity
in
d
ex
is
f
ir
s
t o
f
all
m
o
r
e
in
tu
itiv
e
to
r
ea
d
th
a
n
th
e
Simp
s
o
n
in
d
e
x
.
I
ts
f
o
r
m
u
la
c
o
r
r
esp
o
n
d
s
to
:
D=
1
-
∑
.
(
−
1
)
.
(
−
1
)
W
h
er
e,
f
is
th
e
f
r
eq
u
en
cy
o
f
e
ac
h
ch
o
ice
;
n
th
e
to
tal
n
u
m
b
er
o
f
p
ar
ticip
a
n
ts
(
1
4
1
teac
h
er
s
)
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
3
.
1
.
Q
ues
t
io
n 1
T
h
e
f
ir
s
t
q
u
esti
o
n
was
ask
ed
s
o
th
at
teac
h
er
s
co
u
ld
ch
o
o
s
e
o
n
e
o
r
m
o
r
e
an
s
wer
s
at
th
e
s
am
e
tim
e.
Acc
o
r
d
in
g
to
T
ab
le
4
,
th
e
t
h
r
e
e
p
ar
ts
:
n
u
clea
r
tr
an
s
f
o
r
m
atio
n
s
(
NT
)
,
elec
tr
icity
(
E
)
,
an
d
m
ec
h
an
ics
(
M)
wer
e
ch
o
s
en
b
y
m
o
r
e
t
h
an
8
0
% o
f
t
h
e
p
o
p
u
latio
n
s
u
r
v
ey
ed
.
W
e
ca
n
th
er
ef
o
r
e
s
ay
th
at
m
o
r
e
th
a
n
4
/5
o
f
th
e
teac
h
e
r
s
in
th
e
Fez
-
Me
k
n
es
r
eg
io
n
co
n
s
id
er
th
at
th
ese
th
r
ee
p
ar
ts
o
f
p
h
y
s
ics
r
eq
u
ir
e
m
ath
em
ati
za
tio
n
.
I
t
s
h
o
u
ld
b
e
n
o
ted
t
h
at
th
e
NT
p
ar
t
is
th
e
o
n
e
th
at
u
s
es
th
e
m
o
s
t
m
ath
e
m
atics
s
in
ce
th
e
p
er
ce
n
tag
e
o
f
teac
h
er
s
wh
o
h
av
e
ch
o
s
en
it is
clo
s
e
to
1
0
0
%.
T
ab
le
4
.
Per
ce
n
ta
g
es o
f
r
esp
o
n
s
es g
iv
en
b
y
teac
h
er
s
r
eg
a
r
d
i
n
g
th
e
p
ar
ts
o
f
th
e
c
o
u
r
s
e
th
at
r
eq
u
ir
e
m
o
r
e
m
ath
em
atiza
tio
n
NT
E
M
O
t
h
e
r
1
3
7
1
1
3
1
3
1
35
97
.
1
6
%
80
.
1
4
%
92
.
9
0
%
24
.
8
2
%
T
o
s
ee
if
o
th
er
p
ar
ts
o
f
p
h
y
s
ic
s
ar
e
n
o
t m
en
tio
n
ed
in
t
h
e
p
r
o
p
o
s
itio
n
s
m
en
tio
n
ed
in
th
e
q
u
esti
o
n
n
air
e,
we
ad
d
ed
th
e
p
r
o
p
o
s
itio
n
“
o
th
er
s
”.
T
h
e
p
er
ce
n
tag
e
o
f
th
e
te
ac
h
er
s
wh
o
f
illed
in
th
is
an
s
wer
m
o
d
ality
d
id
n
o
t
ex
ce
ed
2
4
%.
T
h
ey
m
en
tio
n
e
d
two
n
ew
th
em
es: wa
v
es (
1
3
%)
an
d
ch
e
m
ical
k
in
etics (
1
1
%).
I
t
ca
n
b
e
n
o
ted
th
at
th
e
teac
h
e
r
s
’
an
s
wer
s
to
q
u
esti
o
n
Q1
ar
e
in
lin
e
with
th
e
d
ata
f
r
o
m
th
e
an
aly
s
is
o
f
s
ch
o
o
l
tex
tb
o
o
k
s
a
n
d
th
o
s
e
r
ep
o
r
ted
i
n
th
e
liter
atu
r
e,
n
a
m
ely
th
at
p
h
y
s
ics
d
e
p
en
d
s
o
n
m
ath
em
atics.
T
h
u
s
,
f
o
r
e
x
am
p
le,
in
t
h
e
ca
s
e
o
f
NT
,
th
e
E
x
p
er
ia
n
f
u
n
ctio
n
a
n
d
th
e
ex
p
o
n
e
n
tial
f
u
n
ctio
n
ar
e
n
ee
d
e
d
t
o
s
o
lv
e
p
r
o
b
lem
s
ab
o
u
t
n
u
clea
r
p
h
y
s
ics
p
h
en
o
m
en
a.
B
ain
et
a
l.
[
1
5
]
ar
g
u
es
th
at
n
u
clea
r
s
y
s
tem
s
p
r
o
v
id
e
in
te
r
esti
n
g
o
p
p
o
r
tu
n
ities
f
o
r
s
tu
d
e
n
ts
an
d
teac
h
er
s
to
in
teg
r
ate
m
ath
em
atica
l
k
n
o
wled
g
e
in
th
e
co
n
tex
t
o
f
h
al
f
-
life
tim
e
ca
lcu
latio
n
s
.
As
f
o
r
p
ar
t
(
E
)
,
it
ca
n
n
o
t
b
e
u
n
d
er
s
to
o
d
with
o
u
t
p
ass
in
g
th
e
d
if
f
er
en
tial
eq
u
atio
n
s
an
d
th
ei
r
s
o
lu
tio
n
s
.
I
n
d
ee
d
,
th
e
e
q
u
atio
n
s
o
f
elec
tr
ic
d
ip
o
les r
eq
u
ir
e
a
m
aster
y
o
f
th
e
in
teg
r
al
an
d
th
e
p
r
im
itiv
e,
th
ey
ar
e
m
an
d
ato
r
y
to
s
o
lv
e
a
s
itu
atio
n
in
elec
tr
icity
.
T
h
is
ca
n
ad
d
d
if
f
icu
lty
as
s
tated
b
y
L
eo
n
e
[
28
]
wh
o
s
tated
th
at
elec
tr
ical
cir
cu
its
ar
e
alr
ea
d
y
a
co
n
ce
p
tu
al
d
if
f
icu
lty
f
o
r
h
ig
h
s
ch
o
o
l
s
tu
d
e
n
ts
,
an
d
th
i
s
r
elatio
n
s
h
ip
with
m
ath
em
atics m
ak
es th
e
s
itu
atio
n
ev
e
n
m
o
r
e
d
if
f
icu
lt
(
Q5
)
.
T
h
e
in
teg
r
al
an
d
p
r
im
itiv
e
ar
e
also
ess
en
tial f
o
r
s
o
lv
in
g
p
r
o
b
lem
s
r
elate
d
to
m
o
tio
n
tim
e
eq
u
atio
n
s
o
f
a
m
ec
h
a
n
ical
s
y
s
tem
(
M)
lik
e
th
e
p
r
o
jectile.
I
n
th
is
co
n
tex
t,
Kim
et
a
l
.
[
6
]
s
h
o
wed
th
at
th
e
p
h
y
s
ics
eq
u
atio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
P
h
ysics
ma
th
ema
tiz
a
tio
n
fr
o
m
a
tea
ch
in
g
p
ers
p
ec
tive:
s
ec
o
n
d
a
r
y
s
ch
o
o
l
…
(
A
b
d
elw
a
h
a
b
E
l A
z
z
o
u
z
i
)
4123
r
ep
r
esen
ts
s
y
m
b
o
ls
th
at
m
ath
em
atica
lly
m
o
d
el
th
e
c
o
n
ce
p
t
u
al
k
n
o
wled
g
e
o
f
p
h
y
s
ics.
On
th
e
co
n
tr
ar
y
,
th
e
an
aly
s
is
o
f
th
e
s
elec
ted
tex
t
b
o
o
k
s
s
h
o
wed
u
s
th
at
li
n
ea
r
an
d
af
f
in
e
f
u
n
ctio
n
s
ar
e
ess
en
tial
m
ath
em
atica
l
k
n
o
wled
g
e
f
o
r
th
e
g
r
ap
h
ical
r
ea
d
in
g
o
f
s
o
m
e
to
p
ics
in
p
h
y
s
ics
s
u
ch
as
wav
es.
I
n
a
d
d
itio
n
,
d
er
iv
a
b
ilit
y
s
ee
m
s
to
b
e
im
p
o
r
tan
t
k
n
o
wled
g
e
in
th
e
ca
lcu
latio
n
o
f
t
h
e
s
p
ee
d
o
f
c
h
em
ical
r
ea
ctio
n
s
.
I
n
th
e
s
am
e
s
en
s
e,
R
o
d
r
ig
u
ez
et
a
l
.
[
29
]
co
n
clu
d
ed
th
at
th
e
u
n
d
er
s
tan
d
in
g
o
f
p
r
o
b
lem
s
in
ch
em
ical
k
in
etics
r
eq
u
ir
es
two
m
ain
f
ea
tu
r
es a
s
s
o
ciate
d
with
m
ath
em
atica
l e
q
u
atio
n
s
(
s
y
m
b
o
lic
f
o
r
m
s
)
an
d
g
r
ap
h
s
(
g
r
a
p
h
ic
f
o
r
m
s
)
.
3
.
2
.
Q
u
es
t
i
o
n
2
F
o
r
q
u
esti
o
n
Q2
,
th
e
s
u
r
v
e
y
e
d
p
o
p
u
latio
n
h
ad
th
e
ch
o
ice
t
o
s
elec
t
o
n
e
o
r
m
o
r
e
p
r
o
p
o
s
itio
n
s
am
o
n
g
th
e
f
o
u
r
p
r
o
p
o
s
ed
.
T
h
ese
d
if
f
e
r
en
t
p
r
o
p
o
s
als
wer
e
d
ed
u
ce
d
f
r
o
m
th
e
b
ib
lio
g
r
ap
h
ic
r
esear
ch
.
I
n
d
ee
d
,
we
b
ase
d
o
u
r
s
elv
es
-
am
o
n
g
o
th
er
s
-
o
n
th
e
wo
r
k
o
f
J
en
s
en
et
a
l
.
[2
0
]
.
T
h
e
d
ata
o
b
tain
ed
ar
e
p
r
esen
te
d
in
T
ab
le
5
.
W
ith
th
is
q
u
esti
o
n
,
we
aim
to
k
n
o
w
th
e
n
atu
r
e
o
f
th
e
m
o
s
t c
o
m
m
o
n
p
r
o
b
lem
s
en
co
u
n
te
r
ed
in
p
h
y
s
ics
teac
h
in
g
in
th
e
ter
m
in
al
v
ia
teac
h
er
s
’
p
er
ce
p
tio
n
s
.
Acc
o
r
d
in
g
to
th
e
d
ata
o
b
tain
ed
,
it
s
ee
m
s
th
at
ea
ch
o
f
th
e
p
r
o
p
o
s
als
ex
p
r
ess
es
th
e
o
p
in
i
o
n
o
f
ab
o
u
t
a
q
u
a
r
ter
o
f
th
e
p
o
p
u
latio
n
o
f
th
e
teac
h
er
s
s
u
r
v
ey
e
d
.
T
o
v
e
r
if
y
wh
eth
er
o
r
n
o
t
th
er
e
is
a
p
ar
ticu
lar
d
o
m
in
a
n
ce
o
f
th
e
d
if
f
er
en
t
teac
h
er
s
’
ch
o
ices,
we
u
s
e
d
Simp
s
o
n
’
s
in
d
ex
,
wh
ich
ex
p
r
ess
es d
o
m
in
a
n
ce
o
r
d
iv
er
s
ity
.
T
h
e
clo
s
er
t
h
is
in
d
ex
is
to
1
(
C
m
ax
)
,
th
e
m
o
r
e
h
o
m
o
g
e
n
eo
u
s
th
e
ch
o
ices
ar
e;
o
n
t
h
e
o
t
h
er
h
an
d
,
t
h
e
clo
s
er
it
is
to
0
(
C
m
in
)
,
th
e
m
o
r
e
d
iv
er
s
if
ied
t
h
e
ch
o
ices
ar
e
.
I
n
th
e
p
r
esen
t
wo
r
k
,
we
h
ad
0
.
2
5
0
8
as
a
v
alu
e
o
f
Simp
s
o
n
’
s
in
d
ex
s
o
we
ca
n
d
ed
u
ce
th
at
th
e
c
h
o
ices
o
f
q
u
esti
o
n
Q2
ar
e
d
iv
e
r
s
if
ied
.
Als
o
,
th
e
v
alu
e
o
f
d
iv
er
s
ity
in
d
ex
(
D
)
v
a
r
ies
in
an
o
p
p
o
s
ite
way
to
th
e
v
alu
e
o
f
h
o
m
o
g
en
eity
in
d
ex
(
C
)
.
W
h
en
D
is
clo
s
e
to
1
,
th
e
m
o
r
e
d
iv
er
s
if
ied
th
e
c
h
o
i
ce
s
ar
e.
T
h
e
clo
s
er
D
is
to
0
,
th
e
m
o
r
e
h
o
m
o
g
en
e
o
u
s
th
e
ch
o
ices
ar
e.
I
n
th
is
s
tu
d
y
,
we
h
ad
0
.
6
8
3
6
as
an
in
d
ex
o
f
d
iv
er
s
ity
wh
ich
m
ea
n
s
th
at
th
e
c
h
o
ices
in
q
u
esti
o
n
Q2
ar
e
d
iv
er
s
e.
T
h
is
f
in
d
in
g
c
o
n
f
ir
m
s
th
e
r
esu
lts
o
f
th
e
h
o
m
o
g
en
eity
in
d
ex
[
3
0
]
.
Acc
o
r
d
in
g
to
th
e
v
alu
es o
f
th
e
d
o
m
in
an
ce
an
d
th
e
d
iv
e
r
s
ity
in
d
ex
,
we
ca
n
s
ay
th
at
th
er
e
is
n
o
teac
h
er
co
n
s
en
s
u
s
.
Star
tin
g
f
r
o
m
th
e
f
ac
t
th
at
th
e
ch
o
ice
o
f
a
p
r
o
p
o
s
al
b
y
a
teac
h
er
r
ef
lects
h
is
w
ay
o
f
ap
p
r
o
ac
h
in
g
p
r
o
b
lem
s
in
p
h
y
s
ics,
we
ca
n
s
tip
u
late
th
at
-
ev
en
if
th
e
m
ajo
r
ity
o
f
th
e
q
u
esti
o
n
ed
teac
h
er
s
ad
m
it
th
at
all
2
n
d
b
ac
ca
lau
r
ea
te
to
p
ics
o
f
p
h
y
s
ics
s
tu
d
ied
r
e
q
u
ir
e
m
ath
em
atiza
tio
n
,
th
e
r
e
is
n
o
u
n
if
ied
an
d
s
t
an
d
ar
d
ized
m
eth
o
d
o
f
d
ea
lin
g
with
p
r
o
b
lem
s
in
p
h
y
s
ics am
o
n
g
th
e
q
u
esti
o
n
ed
teac
h
er
s
[
3
1
]
.
T
ab
le
5
.
Per
ce
n
ta
g
es o
f
r
esp
o
n
s
es g
iv
en
b
y
teac
h
er
s
r
eg
a
r
d
i
n
g
th
e
m
o
s
t c
o
m
m
o
n
p
r
o
b
lem
s
en
co
u
n
ter
e
d
in
p
h
y
s
ics tea
ch
in
g
P
r
o
b
l
e
m
d
e
scri
p
t
i
o
n
F
r
e
q
u
e
n
c
y
P
e
r
c
e
n
t
a
g
e
(
%)
P
r
o
b
l
e
ms
t
h
a
t
r
e
q
u
i
r
e
l
i
t
t
l
e
p
h
y
si
c
s
a
n
d
t
h
e
w
o
r
k
c
o
n
si
st
s
mai
n
l
y
o
f
m
a
t
h
e
m
a
t
i
z
i
n
g
t
h
e
si
t
u
a
t
i
o
n
.
84
2
2
.
9
5
P
r
o
b
l
e
ms
t
h
a
t
r
e
q
u
i
r
e
i
n
-
d
e
p
t
h
p
h
y
s
i
c
s
a
n
a
l
y
s
i
s
b
e
f
o
r
e
y
o
u
c
a
n
t
h
i
n
k
a
b
o
u
t
m
a
t
h
e
m
a
t
i
z
i
n
g
t
h
e
s
i
t
u
a
t
i
o
n
.
97
2
6
.
5
0
P
r
o
b
l
e
ms
t
h
a
t
r
e
q
u
i
r
e
mat
h
e
mat
i
c
s
b
e
f
o
r
e
p
h
y
s
i
c
s
t
o
s
o
l
v
e
t
h
e
p
r
o
b
l
e
m.
89
2
4
.
3
1
P
r
o
b
l
e
ms
t
h
a
t
r
e
q
u
i
r
e
p
h
y
s
i
c
s
a
n
d
ma
t
h
e
m
a
t
i
c
s
t
o
b
e
i
n
v
o
l
v
e
d
s
i
m
u
l
t
a
n
e
o
u
s
l
y
r
a
t
h
e
r
t
h
a
n
s
e
p
a
r
a
t
e
l
y
.
96
2
6
.
2
2
3
.
3
.
Q
ues
t
io
n 3
T
h
e
r
esu
lts
o
f
r
esp
o
n
s
es
b
y
teac
h
er
s
r
eg
ar
d
in
g
t
h
e
co
m
p
lem
en
tar
ity
o
f
p
h
y
s
ics
an
d
m
ath
e
m
atics
ar
e
s
h
o
wn
in
Fig
u
r
e
1
.
B
ased
o
n
t
h
ese
d
ata,
it
ap
p
ea
r
s
th
at
o
n
ly
1
4
%
o
f
th
e
s
u
r
v
e
y
p
o
p
u
latio
n
d
o
es
n
o
t
ag
r
ee
th
at
p
h
y
s
ics
an
d
m
ath
em
atics
ar
e
c
o
m
p
lem
en
tar
y
.
On
th
e
o
th
er
h
an
d
,
m
o
r
e
t
h
an
3
/4
o
f
th
e
teac
h
er
s
(
8
6
%)
s
u
b
ject
to
th
e
s
u
r
v
e
y
ex
p
r
ess
ed
th
eir
a
g
r
ee
m
en
t.
Fig
u
r
e
1
.
T
h
e
p
er
ce
n
tag
es o
f
r
esp
o
n
s
es g
iv
en
b
y
teac
h
er
s
r
e
g
ar
d
in
g
th
e
co
m
p
lem
en
tar
ity
o
f
p
h
y
s
ics an
d
m
ath
em
atics
0%
20%
40%
60%
80%
SD
D
A
SA
4%
10%
67%
19%
Pe
r
ce
n
tag
e
o
f T
e
ach
e
r
s
(%
)
R
e
s
p
o
n
s
e
O
p
ti
o
n
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
14
,
No
.
5
,
Octo
b
er
20
25
:
4
1
1
9
-
412
8
4124
3
.
4
.
Q
ues
t
io
n 4
T
h
e
d
ata
o
b
tain
ed
r
eg
a
r
d
in
g
t
h
e
r
esp
o
n
s
es
g
iv
en
b
y
teac
h
e
r
s
to
th
e
in
teg
r
atio
n
o
f
m
at
h
em
atics
in
th
e
in
ter
p
r
etatio
n
o
f
p
h
y
s
ics
p
h
en
o
m
en
a
ar
e
illu
s
tr
ated
i
n
Fig
u
r
e
2
.
As
in
th
e
p
r
ev
io
u
s
q
u
esti
o
n
s
,
th
ese
d
ata
ar
e
in
lin
e
with
th
o
s
e
p
r
o
v
i
d
ed
b
y
th
e
liter
atu
r
e
th
at
p
h
y
s
ics
h
as
d
ee
p
m
ath
e
m
atica
l
im
p
lica
tio
n
s
.
W
h
en
ev
er
a
teac
h
er
wan
ts
to
ex
p
lain
a
p
h
y
s
ical
p
h
en
o
m
en
o
n
to
s
tu
d
e
n
ts
(
Q4
)
o
r
h
e/sh
e
s
o
lv
es
a
p
r
o
b
lem
in
p
h
y
s
ics,
h
e/sh
e
ca
lls
u
p
o
n
m
at
h
em
atics
[
19
]
,
[
20
]
.
Fig
u
r
e
2
.
T
h
e
p
er
ce
n
tag
es o
f
r
esp
o
n
s
es g
iv
en
b
y
teac
h
er
s
to
th
e
in
teg
r
atio
n
o
f
m
at
h
em
atics in
th
e
in
ter
p
r
etatio
n
o
f
p
h
y
s
ics p
h
en
o
m
en
a
3
.
5
.
Q
ues
t
io
n 5
T
h
e
p
er
ce
n
tag
es
o
f
r
esp
o
n
s
es
f
o
r
q
u
esti
o
n
(
Q
5
)
ar
e
p
r
esen
te
d
in
Fig
u
r
e
3
.
T
h
e
r
esu
lts
o
f
q
u
esti
o
n
Q5
teac
h
er
s
r
ep
o
r
t
d
if
f
icu
lty
in
teac
h
in
g
p
h
y
s
ics b
ased
m
ain
ly
o
n
m
ath
em
atics.
T
h
ese
d
ata
ar
e
co
n
s
is
ten
t w
ith
th
e
s
tu
d
y
co
n
d
u
cted
b
y
H
u
an
d
R
eb
ello
[3
2
]
wh
ich
s
h
o
ws
t
h
e
co
m
p
lex
ity
o
f
ex
p
lai
n
in
g
an
d
u
n
d
er
s
tan
d
in
g
m
ath
em
atica
l e
q
u
atio
n
s
in
p
h
y
s
ics co
u
r
s
es.
I
n
d
ee
d
,
th
is
s
itu
atio
n
ac
co
r
d
in
g
to
Hu
an
d
R
eb
ello
[3
2
]
is
d
if
f
icu
lt
to
teac
h
th
e
d
is
cip
lin
e
b
e
ca
u
s
e
th
e
in
ter
ac
tio
n
b
etwe
en
m
at
h
em
atics
an
d
p
h
y
s
ics
b
ec
o
m
e
s
an
u
n
p
r
o
d
u
ctiv
e
m
ix
tu
r
e
ed
u
ca
tio
n
ally
.
T
h
e
d
a
ta
f
r
o
m
th
is
q
u
esti
o
n
is
p
er
f
ec
tly
co
n
s
is
ten
t
with
th
e
r
esp
o
n
s
es
to
q
u
esti
o
n
Q4
wh
er
e
1
8
% o
f
th
e
s
u
r
v
ey
ed
te
ac
h
er
s
s
ay
th
ey
d
o
n
o
t
n
ee
d
m
ath
em
atics to
u
n
d
er
s
tan
d
p
h
y
s
ics.
Fig
u
r
e
3
.
T
h
e
p
er
ce
n
tag
es o
f
t
ea
ch
er
s
’
r
esp
o
n
s
es to
th
e
d
if
f
i
cu
lty
o
f
m
at
h
em
atiza
tio
n
in
le
ar
n
in
g
p
h
y
s
ics
0%
10%
20%
30%
40%
50%
60%
SD
D
A
SA
9%
9%
59%
23%
Per
c
e
n
tag
e
o
f T
e
ac
h
e
rs
(
%
)
R
e
s
p
o
n
s
e
O
p
ti
o
n
s
0%
10%
20%
30%
40%
50%
SD
D
A
SA
4%
16%
32%
48%
Per
c
e
n
tag
e
o
f T
e
ac
h
e
rs
(
%
)
R
e
s
p
o
n
s
e
O
p
ti
o
n
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
P
h
ysics
ma
th
ema
tiz
a
tio
n
fr
o
m
a
tea
ch
in
g
p
ers
p
ec
tive:
s
ec
o
n
d
a
r
y
s
ch
o
o
l
…
(
A
b
d
elw
a
h
a
b
E
l A
z
z
o
u
z
i
)
4125
3
.
6
.
Q
ues
t
io
n 6
Fig
u
r
e
4
is
d
is
ju
n
ctiv
e
an
d
th
er
ef
o
r
e
th
e
ch
o
ice
ca
n
o
n
ly
b
e
y
es
o
r
n
o
.
Acc
o
r
d
i
n
g
to
Fig
u
r
e
4
,
alm
o
s
t
all
th
e
teac
h
e
r
s
s
ee
m
to
af
f
i
r
m
th
at
t
h
eir
s
tu
d
e
n
ts
f
in
d
d
i
f
f
icu
lty
with
p
h
y
s
ics
m
ath
em
ati
za
tio
n
.
T
h
e
9
2
%
o
f
th
e
teac
h
er
s
an
s
wer
ed
“
Yes
”
an
d
o
n
l
y
8
%
o
f
th
e
s
u
r
v
ey
ed
p
o
p
u
latio
n
o
p
ted
f
o
r
th
e
a
n
s
wer
m
o
d
ality
“
No
”
.
W
e
th
en
ask
ed
th
e
teac
h
er
s
wh
o
an
s
wer
ed
“
Yes
”
to
s
p
ec
if
y
th
e
ca
u
s
es
o
f
th
e
d
if
f
icu
lties
.
Sev
er
al
an
s
wer
s
wer
e
g
iv
en
:
-
Stu
d
en
ts
ca
n
n
o
t u
n
d
er
s
tan
d
th
e
p
h
y
s
ical
m
ea
n
in
g
s
o
f
m
ath
e
m
atica
l sy
m
b
o
ls
an
d
/o
r
f
o
r
m
u
las;
-
Stu
d
en
ts
ca
n
n
o
t p
h
y
s
ically
in
t
er
p
r
et
m
ath
em
atica
l e
q
u
atio
n
s
;
-
T
ea
ch
er
s
also
cited
th
at
th
eir
s
tu
d
en
ts
f
in
d
d
i
f
f
icu
lties
with
m
ath
em
atica
l
p
r
o
ce
s
s
es
in
s
o
lv
in
g
p
h
y
s
ical
p
r
o
b
lem
s
.
Fig
u
r
e
4
.
T
h
e
p
er
ce
n
tag
es o
f
t
ea
ch
er
s
’
r
esp
o
n
s
es to
d
if
f
icu
lties
with
s
tu
d
en
ts
’
m
ath
em
atiza
tio
n
o
f
p
h
y
s
ics
T
h
e
teac
h
e
r
s
q
u
esti
o
n
e
d
in
th
i
s
q
u
esti
o
n
(
Q6
)
cited
s
o
m
e
d
i
f
f
icu
lties
with
p
h
y
s
ics
m
ath
e
m
atiza
tio
n
.
T
h
ese
d
if
f
icu
lties
ar
e
alr
ea
d
y
r
ep
r
esen
ted
in
th
e
s
cien
tific
liter
atu
r
e.
Hu
an
d
R
eb
ello
[3
2
]
co
n
clu
d
ed
th
at
m
an
y
s
tu
d
e
n
ts
f
ail
to
co
m
b
in
e
th
eir
m
at
h
em
atica
l
k
n
o
wled
g
e
with
p
h
y
s
ics
in
a
p
r
o
d
u
ctiv
e
way
,
alth
o
u
g
h
th
ey
h
av
e
th
e
r
eq
u
ir
ed
m
ath
em
atic
al
k
n
o
wled
g
e.
I
n
th
is
s
en
s
e,
R
ed
is
h
an
d
Ku
o
[
7
]
p
o
in
ted
o
u
t
th
at
teac
h
er
s
ar
e
o
f
ten
s
u
r
p
r
is
ed
b
y
t
h
eir
s
tu
d
en
ts
wh
o
m
ay
ex
ce
l
i
n
m
ath
em
atics
co
u
r
s
es
b
u
t
m
ay
f
in
d
d
if
f
ic
u
lties
in
m
ath
em
atizin
g
p
h
y
s
ics.
Als
o
,
Kab
il
[
1
2
]
p
o
in
ted
o
u
t th
at
tea
ch
er
s
s
h
o
wed
th
at
s
tu
d
en
ts
f
ail
to
ad
ap
t f
o
r
m
u
las,
eq
u
atio
n
s
,
an
d
/o
r
m
ath
em
atic
al
m
an
ip
u
latio
n
s
to
th
e
p
r
o
b
le
m
atize
d
s
itu
atio
n
.
I
n
th
is
co
n
t
ex
t,
Z
eid
m
an
e
[3
3
]
s
h
o
wed
th
at
th
e
d
ev
elo
p
m
e
n
t
o
f
s
k
ills
o
f
a
s
tu
d
en
t
is
e
s
s
en
tially
r
elate
d
to
th
e
g
o
o
d
a
ttach
m
en
t
b
etwe
en
p
h
y
s
ician
p
r
ac
tices
an
d
m
at
h
em
atica
l
m
an
ip
u
latio
n
s
[
34
]
.
T
h
en
,
th
e
an
aly
s
is
o
f
t
h
e
p
er
ce
p
tio
n
s
o
f
th
e
q
u
esti
o
n
ed
teac
h
er
s
s
h
o
wed
u
s
th
at
Mo
r
o
cc
an
s
tu
d
en
ts
h
av
e
d
if
f
icu
lty
in
p
h
y
s
ics
m
ath
em
atiza
tio
n
.
T
h
is
co
n
f
ir
m
s
th
e
f
in
d
in
g
s
o
f
W
est
et
a
l
.
[
1
3
]
wh
o
s
h
o
wed
th
at
m
an
y
p
h
y
s
ics
teac
h
er
s
in
s
e
co
n
d
ar
y
ed
u
ca
tio
n
in
s
is
t o
n
th
e
d
if
f
icu
lties
o
f
s
tu
d
en
ts
in
th
eir
lack
o
f
m
ath
em
a
tical
k
n
o
wled
g
e
[
3
1
]
,
[
3
5
]
.
T
h
e
s
u
r
v
ey
o
f
p
h
y
s
ics
teac
h
er
s
in
Mo
r
o
cc
an
h
i
g
h
s
ch
o
o
ls
y
ield
ed
cr
u
cial
in
s
ig
h
ts
with
p
r
ac
tical
im
p
licatio
n
s
f
o
r
ed
u
ca
tio
n
al
p
o
licy
an
d
p
r
ac
tice.
T
ea
ch
er
s
o
v
er
wh
elm
in
g
ly
i
d
en
tifie
d
NT
,
E
,
an
d
M
as
ar
ea
s
r
eq
u
ir
in
g
h
eig
h
ten
ed
m
ath
e
m
atiza
tio
n
,
alig
n
in
g
with
lit
er
atu
r
e
em
p
h
asizin
g
th
e
in
d
is
p
en
s
ab
le
r
o
le
o
f
m
ath
em
atics
in
th
ese
p
h
y
s
ics’
d
o
m
ain
s
.
Div
e
r
s
e
ch
allen
g
e
s
in
p
h
y
s
ics
teac
h
in
g
wer
e
id
en
tifie
d
,
r
ef
lectin
g
v
ar
ied
ap
p
r
o
ac
h
es
am
o
n
g
ed
u
ca
to
r
s
.
T
h
e
s
u
r
v
ey
u
n
d
er
s
co
r
ed
th
e
en
d
u
r
i
n
g
co
m
p
lem
en
ta
r
ity
o
f
p
h
y
s
ics
an
d
m
ath
em
atics,
em
p
h
asizin
g
th
eir
co
n
tin
u
o
u
s
i
n
ter
d
ep
e
n
d
en
ce
.
W
h
ile
teac
h
er
s
r
ec
o
g
n
ize
d
th
e
n
ec
ess
ity
o
f
m
ath
em
atiza
tio
n
,
th
e
y
also
a
ck
n
o
wled
g
e
d
its
in
s
tr
u
ctio
n
al
co
m
p
lex
ities
,
r
eso
n
atin
g
wit
h
ex
is
tin
g
r
esear
ch
.
T
h
ese
f
in
d
i
n
g
s
co
llectiv
ely
i
n
f
o
r
m
th
e
n
ee
d
f
o
r
f
lex
ib
le
ed
u
ca
tio
n
al
s
tr
ateg
ies,
tailo
r
e
d
in
ter
v
en
tio
n
s
,
an
d
p
r
o
f
ess
io
n
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d
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v
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p
m
e
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t
in
i
tiativ
es
to
en
h
an
ce
t
h
e
in
teg
r
atio
n
o
f
m
ath
em
atics
in
p
h
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s
ics
ed
u
ca
tio
n
in
Mo
r
o
cc
an
h
ig
h
s
ch
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o
ls
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4.
CO
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4126
wh
o
s
e
co
n
te
n
ts
ar
e
p
u
r
el
y
m
a
th
em
atize
d
to
o
v
er
co
m
e
th
e
d
if
f
icu
lty
o
f
p
h
y
s
ics
m
ath
e
m
atiza
tio
n
.
T
h
is
w
o
r
k
em
p
h
asizes
th
e
n
ee
d
f
o
r
well
-
s
tr
u
ctu
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p
ed
ag
o
g
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in
s
tr
u
c
tio
n
s
f
o
cu
s
ed
o
n
p
h
y
s
ics
m
ath
em
atiza
tio
n
.
T
h
ese
in
s
tr
u
ctio
n
s
aim
to
p
r
o
v
id
e
cl
ea
r
g
u
id
an
ce
t
o
p
h
y
s
ics
teac
h
er
s
r
eg
ar
d
in
g
th
e
in
co
r
p
o
r
atio
n
o
f
m
ath
em
atica
l
co
n
ce
p
ts
in
to
th
eir
teac
h
in
g
p
r
ac
tices.
Ad
d
itio
n
ally
,
th
is
s
tu
d
y
s
u
g
g
ests
im
p
lem
en
tin
g
p
r
o
g
r
a
m
s
th
at
ca
n
s
tim
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late
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d
in
s
p
ir
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p
h
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ics
ed
u
ca
to
r
s
to
in
teg
r
ate
th
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ca
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g
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f
m
at
h
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atiza
tio
n
in
to
th
eir
p
h
y
s
ics
co
u
r
s
es
s
ea
m
less
ly
.
T
h
e
u
ltima
te
g
o
al
is
to
f
o
s
ter
a
m
o
r
e
ef
f
ec
tiv
e
s
cien
tific
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u
c
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n
th
at
p
r
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m
o
tes
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d
r
ei
n
f
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ce
s
p
h
y
s
ics
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ath
em
atiza
tio
n
am
o
n
g
s
tu
d
e
n
ts
.
I
n
ess
en
ce
,
it
u
n
d
er
s
co
r
es
th
e
im
p
o
r
tan
ce
o
f
p
r
o
v
id
i
n
g
teac
h
e
r
s
with
th
e
t
o
o
ls
an
d
r
eso
u
r
ce
s
n
ec
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ar
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to
im
p
r
o
v
e
th
e
u
n
d
er
s
tan
d
in
g
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d
ap
p
licatio
n
o
f
m
ath
em
atica
l p
r
in
cip
les in
th
e
co
n
tex
t o
f
p
h
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s
ics ed
u
ca
tio
n
.
W
e
h
o
p
e
th
at
th
is
r
esear
ch
wi
ll
p
r
o
v
id
e
a
n
ex
p
e
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im
en
tal
f
r
a
m
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k
f
o
r
th
e
f
o
u
n
d
atio
n
o
f
q
u
alif
ied
lear
n
in
g
an
d
teac
h
in
g
o
f
p
h
y
s
ics
in
th
e
Mo
r
o
cc
an
cu
r
r
icu
l
u
m
.
T
h
u
s
,
teac
h
er
s
wis
h
to
u
s
e
in
ter
d
is
cip
lin
ar
y
s
tu
d
ies
in
p
h
y
s
ics.
C
u
r
r
icu
lu
m
d
esig
n
er
s
ca
n
also
u
s
e
th
ese
to
p
ics
to
p
r
ep
ar
e
in
te
r
d
is
cip
lin
ar
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cu
r
r
icu
lar
ac
tiv
ities
.
I
n
g
e
n
er
al,
th
e
teac
h
er
s
in
ter
v
iewe
d
th
in
k
th
at
in
t
er
d
is
cip
lin
ar
y
s
tu
d
ies
a
r
e
u
s
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u
l,
b
u
t
th
ey
d
o
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h
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clea
r
id
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s
o
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h
o
w
to
im
p
lem
en
t th
em
in
th
e
Mo
r
o
cc
an
d
is
cip
lin
ar
y
cu
r
r
icu
lu
m
.
F
UNDING
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NF
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au
th
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r
s
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p
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t f
r
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a
n
y
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r
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an
izatio
n
f
o
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th
e
s
u
b
m
itted
wo
r
k
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u
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C
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[
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o
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ica
l
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n
d
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tu
d
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n
t
Affa
irs
a
t
th
e
F
a
c
u
lt
y
o
f
S
c
ien
c
e
s
Dh
a
r
El
M
a
h
ra
z
,
a
p
o
siti
o
n
h
e
h
e
l
d
u
n
ti
l
2
0
1
9
;
In
it
iato
r
a
n
d
c
o
o
r
d
in
a
t
o
r
o
f
v
a
ri
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u
s
p
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d
a
g
o
g
ica
l
in
n
o
v
a
ti
o
n
p
r
o
j
e
c
ts
(M
OO
Cs,
e
-
lea
rn
in
g
,
v
irt
u
a
l
lab
,
a
n
d
sim
u
lati
o
n
p
ro
jec
ts)
;
M
e
m
b
e
r
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d
c
o
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rd
i
n
a
to
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a
t
USM
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lev
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l
o
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se
v
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ra
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Eu
ro
p
e
a
n
Tem
p
u
s a
n
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m
u
s+
p
ro
jec
ts.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
a
e
lac
h
q
a
r@y
a
h
o
o
.
fr
.
Fa
tih
a
K
a
d
d
a
r
i
jo
i
n
e
d
t
h
e
De
p
a
rtme
n
t
o
f
C
h
e
m
istry
o
f
th
e
Dh
a
r
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M
a
h
ra
z
F
a
c
u
lt
y
o
f
S
c
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c
e
a
t
th
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Un
iv
e
rsity
o
f
S
id
i
M
o
h
a
m
e
d
Be
n
Ab
d
e
ll
a
h
in
F
e
z
,
M
o
r
o
c
c
o
,
in
1
9
8
8
.
He
r
first
tea
c
h
i
n
g
a
c
ti
v
it
ies
we
re
in
t
h
e
first
y
e
a
r
o
f
u
n
d
e
rg
ra
d
u
a
te
st
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d
ies
,
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ic
h
m
a
d
e
h
e
r
a
wa
re
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f
th
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d
iffi
c
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c
e
d
b
y
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ice
stu
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ts
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wa
s
p
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rtl
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sp
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si
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h
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g
t
o
re
se
a
rc
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sc
ien
c
e
d
i
d
a
c
ti
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s.
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is
re
se
a
rc
h
led
to
a
sta
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o
c
to
ra
te
th
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sis,
d
e
fe
n
d
e
d
in
2
0
0
5
.
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in
c
e
th
e
n
,
s
h
e
h
a
s
b
r
o
a
d
e
n
e
d
h
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r
in
tere
sts
t
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ro
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g
h
th
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Lab
o
ra
to
ire
d
e
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a
c
ti
q
u
e
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n
o
v
a
ti
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P
é
d
a
g
o
g
i
q
u
e
e
t
C
u
rri
c
u
laire
(LADIP
EC),
wh
ich
sh
e
d
irec
ted
fro
m
2
0
1
1
t
o
2
0
1
7
.
S
h
e
is
c
u
rre
n
tl
y
in
c
h
a
r
g
e
o
f
th
e
e
d
u
c
a
ti
o
n
a
l
tec
h
n
o
l
o
g
y
tea
m
a
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th
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Lab
o
ra
to
r
y
o
f
C
o
m
p
u
ter
S
c
ien
c
e
,
S
ig
n
a
ls,
Au
t
o
m
a
ti
o
n
,
a
n
d
Co
g
n
i
ti
v
ism
.
Dh
a
r
El
M
a
h
ra
z
F
a
c
u
lt
y
o
f
S
c
ien
c
e
s,
S
id
i
M
o
h
a
m
e
d
Be
n
Ab
d
e
ll
a
h
Un
i
v
e
rsi
ty
,
F
e
z
.
S
h
e
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
k
a
d
d
a
ri@
y
a
h
o
o
.
fr
.
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