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K
ey
w
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s
:
E
v
alu
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Fo
u
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in
d
u
s
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ev
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tio
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L
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Ma
th
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On
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to
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T
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CC B
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C
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p
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A
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:
Olaju
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Olay
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Dep
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t o
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Scien
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So
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Af
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ail:
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laju
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j.a
c.
za
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
f
o
u
r
th
in
d
u
s
tr
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ev
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lu
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ch
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ter
ized
b
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ap
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to
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ap
in
g
t
h
e
lan
d
s
ca
p
e
o
f
ed
u
ca
tio
n
[
1
]
.
I
n
th
is
tr
an
s
f
o
r
m
ativ
e
er
a,
m
ath
em
ati
ca
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tan
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s
at
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f
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r
ef
r
o
n
t,
task
ed
with
p
r
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a
r
in
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t
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cr
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s
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ly
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ig
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ld
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ca
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th
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p
o
ten
tial
o
f
em
er
g
in
g
tech
n
o
l
o
g
ies
[
2
]
.
T
h
is
s
ets
th
e
s
tag
e
f
o
r
ex
p
lo
r
in
g
th
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ev
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m
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ath
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atica
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ca
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n
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f
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u
r
th
in
d
u
s
tr
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ev
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lu
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n
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em
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h
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s
izin
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e
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s
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lin
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u
r
ce
s
to
im
p
r
o
v
e
ed
u
ca
tio
n
al
r
esu
lts
[
3
]
.
B
y
ex
am
in
in
g
th
e
i
n
ter
s
ec
tio
n
o
f
m
ath
em
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u
ca
tio
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an
d
d
ig
ital
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n
o
v
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,
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n
g
ain
in
s
ig
h
ts
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to
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ca
to
r
s
ar
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ap
tin
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ical
p
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ac
tices
to
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co
m
m
o
d
ate
s
tu
d
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’
c
h
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i
n
g
n
e
ed
s
in
th
e
a
g
e
o
f
tech
n
o
lo
g
y
[
4
]
,
[
5
]
.
T
h
e
in
t
eg
r
atio
n
o
f
o
n
lin
e
to
o
ls
in
to
m
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em
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l
ed
u
ca
tio
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o
f
f
er
s
u
n
p
r
ec
ed
e
n
ted
o
p
p
o
r
tu
n
ities
to
en
g
a
g
e
lear
n
er
s
,
p
e
r
s
o
n
alize
in
s
tr
u
ctio
n
,
an
d
f
o
s
ter
d
ee
p
e
r
c
o
n
ce
p
t
u
al
u
n
d
er
s
tan
d
in
g
.
I
n
ter
ac
tiv
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p
latf
o
r
m
s
,
v
ir
tu
al
s
im
u
latio
n
s
,
an
d
a
d
ap
tiv
e
lea
r
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in
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al
g
o
r
ith
m
s
p
r
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v
id
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s
tu
d
en
ts
with
d
y
n
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m
ic
p
o
s
s
ib
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o
r
ed
u
ca
tio
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ca
te
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to
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eir
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n
iq
u
e
r
eq
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ir
em
en
ts
an
d
ed
u
ca
tio
n
al
p
r
ef
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r
en
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s
[
6
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
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2
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8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
14
,
No
.
6
,
Dec
em
b
er
20
25
:
4
4
4
3
-
4
4
5
5
4444
T
h
e
in
co
r
p
o
r
atio
n
o
f
o
n
lin
e
r
eso
u
r
ce
s
h
as
co
m
p
letely
c
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an
g
ed
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ed
u
ca
tio
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al
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v
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m
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cu
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tech
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e,
p
a
r
ticu
lar
ly
in
th
e
r
ea
lm
o
f
m
ath
em
atics
[
7
]
.
I
n
ad
d
itio
n
t
o
k
ee
p
in
g
s
tu
d
e
n
ts
in
ter
ested
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r
ce
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o
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y
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ac
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latf
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s
th
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th
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m
p
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eh
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n
s
io
n
an
d
co
m
p
eten
cy
in
m
at
h
em
atica
l
id
ea
s
.
T
h
is
in
v
esti
g
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n
e
x
p
l
o
r
es
th
e
v
a
r
io
u
s
way
s
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at
o
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lin
e
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eso
u
r
ce
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a
r
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b
ein
g
u
s
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to
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h
an
ce
m
at
h
em
atics
ed
u
ca
tio
n
.
T
h
e
ca
p
a
city
o
f
o
n
lin
e
r
eso
u
r
ce
s
to
o
f
f
er
in
d
i
v
id
u
alize
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lear
n
in
g
ex
p
er
ien
ce
s
ca
ter
ed
to
ea
ch
s
tu
d
en
t
’
s
u
n
iq
u
e
r
eq
u
ir
em
en
ts
an
d
lea
r
n
in
g
p
r
ef
e
r
en
ce
s
is
o
n
e
o
f
its
m
ain
b
e
n
ef
its
.
Stu
d
en
ts
c
an
s
t
u
d
y
m
ath
em
atica
l
i
d
ea
s
at
th
e
ir
o
wn
p
ac
e
with
th
e
u
s
e
o
f
i
n
ter
ac
tiv
e
tu
to
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ials
,
v
ir
tu
al
m
an
ip
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lativ
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an
d
m
u
ltime
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ia
m
ater
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wh
ich
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tr
en
g
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en
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m
p
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eh
e
n
s
io
n
th
r
o
u
g
h
p
r
ac
tical
ap
p
licatio
n
[
8
]
.
R
ea
l
-
tim
e
ass
ess
m
en
t
an
d
f
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d
b
ac
k
ar
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m
ad
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wh
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in
p
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s
tu
d
en
ts
’
ar
ea
s
o
f
d
i
f
f
icu
lty
a
n
d
o
f
f
e
r
th
e
m
f
o
cu
s
ed
s
u
p
p
o
r
t.
T
ea
ch
er
s
ca
n
m
o
n
ito
r
s
tu
d
en
t p
r
o
g
r
ess
,
id
en
tif
y
m
is
co
n
ce
p
ti
o
n
s
,
an
d
tailo
r
in
s
tr
u
ctio
n
al
in
ter
v
en
tio
n
s
to
m
ee
t
in
d
iv
id
u
al
lear
n
in
g
n
ee
d
s
b
y
u
tili
zin
g
alg
o
r
ith
m
s
an
d
d
ata.
R
eg
ar
d
less
o
f
th
eir
g
eo
g
r
ap
h
ica
l
lo
ca
tio
n
,
s
tu
d
en
ts
ca
n
p
ar
ticip
ate
in
p
ee
r
-
to
-
p
ee
r
co
n
v
er
s
atio
n
an
d
p
r
o
b
lem
-
s
o
l
v
in
g
ac
tiv
ities
th
an
k
s
to
o
n
lin
e
to
o
ls
th
at
s
u
p
p
o
r
t
co
llab
o
r
ativ
e
lear
n
i
n
g
ex
p
er
ie
n
ce
s
[
9
]
–
[
1
1
]
.
B
ey
o
n
d
th
e
ty
p
ical
class
r
o
o
m
,
o
n
lin
e
class
es,
d
is
cu
s
s
io
n
b
o
ar
d
s
,
an
d
g
r
o
u
p
p
r
o
jects
en
h
an
ce
e
d
u
c
a
t
i
o
n
a
l
o
p
p
o
r
t
u
n
i
t
i
es
by
f
o
s
ter
in
g
a
f
ee
lin
g
o
f
c
o
m
m
u
n
ity
a
n
d
g
r
o
u
p
lear
n
in
g
.
Un
d
er
s
tan
d
in
g
im
p
o
r
ta
n
t
f
ac
to
r
s
lik
e
d
ig
ital
eq
u
ity
,
d
ata
p
r
iv
ac
y
,
an
d
teac
h
er
p
r
ep
a
r
ed
n
ess
is
ess
en
tial
wh
en
in
co
r
p
o
r
atin
g
o
n
lin
e
r
eso
u
r
ce
s
in
to
m
ath
em
atics
in
s
tr
u
ctio
n
.
T
o
p
r
e
v
en
t
l
ea
r
n
in
g
in
e
q
u
alities
,
it
is
ess
en
tia
l
to
g
u
ar
an
tee
th
at
ev
er
y
s
tu
d
en
t
h
as
eq
u
itab
le
ac
ce
s
s
to
tech
n
o
lo
g
y
an
d
a
d
ep
en
d
a
b
le
in
ter
n
et
co
n
n
ec
tio
n
[
1
2
]
.
I
n
o
r
d
er
to
s
u
cc
ess
f
u
lly
in
teg
r
ate
d
ig
ital
t
o
o
ls
in
to
th
eir
class
r
o
o
m
s
,
ed
u
ca
to
r
s
also
n
ee
d
to
r
ec
eiv
e
ad
eq
u
ate
tr
ain
in
g
.
T
o
g
iv
e
teac
h
er
s
th
e
k
n
o
w
-
h
o
w
t
o
m
ax
im
ize
o
n
lin
e
r
eso
u
r
ce
s
f
o
r
im
p
r
o
v
ed
s
tu
d
en
t
lear
n
in
g
,
p
r
o
f
ess
io
n
al
d
ev
el
o
p
m
en
t
p
r
o
g
r
am
s
em
p
h
asizin
g
d
ig
ital
liter
ac
y
,
in
s
tr
u
cti
o
n
al
tactics,
an
d
tech
n
o
lo
g
ical
a
b
ilit
ies
ar
e
ess
en
tial.
Dig
ital
r
eso
u
r
ce
s
ca
n
h
elp
s
tu
d
en
ts
b
ec
o
m
e
m
o
r
e
i
n
v
o
lv
e
d
,
cu
s
to
m
ize
th
eir
ed
u
ca
tio
n
,
an
d
d
ev
elo
p
a
d
ee
p
er
co
m
p
r
eh
e
n
s
io
n
o
f
m
ath
em
atica
l
id
ea
s
[
3
]
.
B
y
u
s
in
g
th
ese
r
eso
u
r
ce
s
,
teac
h
er
s
m
ay
p
r
o
v
id
e
in
clu
s
iv
e,
d
y
n
am
ic
lear
n
in
g
en
v
ir
o
n
m
en
ts
th
at
h
elp
s
tu
d
en
ts
th
r
iv
e
in
m
ath
an
d
o
th
er
s
u
b
jects.
I
n
itiativ
es
lik
e
th
e
n
o
ch
ild
lef
t
b
eh
in
d
ac
t
an
d
th
e
cr
ea
tio
n
o
f
ac
ad
em
ic
s
tan
d
a
r
d
s
h
av
e
r
aised
th
e
p
r
ess
u
r
e
to
r
aise
s
tu
d
en
t
s
u
cc
ess
.
Stan
d
ar
d
ized
test
in
g
is
f
r
eq
u
en
tly
u
s
ed
to
g
au
g
e
s
tu
d
en
t
p
er
f
o
r
m
a
n
ce
in
s
ch
o
o
ls
,
esp
ec
ially
in
m
ath
-
r
e
lated
co
u
r
s
es.
T
h
e
r
esu
lts
m
a
y
h
av
e
an
ef
f
ec
t
o
n
ad
m
i
n
is
tr
atio
n
,
p
e
r
s
o
n
n
el,
o
r
f
u
n
d
in
g
[
1
3
]
.
T
ea
ch
e
r
s
h
av
e
lo
o
k
ed
f
o
r
class
r
o
o
m
m
ate
r
ials
an
d
p
r
o
f
ess
io
n
al
d
ev
elo
p
m
en
t
to
im
p
r
o
v
e
ed
u
ca
tio
n
i
n
r
esp
o
n
s
e
to
th
es
e
h
ig
h
-
s
tak
es
test
in
g
c
o
n
tex
ts
.
Alth
o
u
g
h
s
tu
d
ies
in
d
icate
th
at
tech
n
o
l
o
g
y
ca
n
im
p
r
o
v
e
lear
n
in
g
an
d
ass
is
t
in
teac
h
in
g
m
ath
em
atics
[
1
4
]
,
[
1
5
]
,
n
o
t
ev
er
y
teac
h
e
r
u
s
es
th
ese
tech
n
iq
u
es
r
ig
h
t
awa
y
,
an
d
th
ey
d
o
n
o
t
alwa
y
s
lead
to
a
p
p
r
ec
iab
le
g
ain
s
in
s
tu
d
en
t
p
er
f
o
r
m
an
ce
.
T
h
e
in
ter
ac
tio
n
s
b
etwe
en
tech
n
o
lo
g
y
,
in
s
tr
u
ctio
n
al
s
tr
ateg
ies,
s
tu
d
en
t
in
v
o
lv
em
en
t,
an
d
in
s
tr
u
ctio
n
al
m
ater
ials
r
eq
u
i
r
e
f
u
r
t
h
er
r
esear
c
h
.
As
th
e
ed
u
ca
tio
n
al
s
y
s
tem
a
d
ap
ts
to
th
e
d
em
a
n
d
s
o
f
th
e
f
o
u
r
th
in
d
u
s
tr
ial
r
e
v
o
lu
tio
n
,
th
is
is
p
ar
ticu
lar
ly
cr
u
cial.
I
n
an
er
a
o
f
r
ap
id
ed
u
ca
tio
n
al
ch
a
n
g
e,
th
is
ar
ticle
ex
am
in
es
h
o
w
m
ath
teac
h
er
s
em
p
lo
y
ed
an
o
n
lin
e
alg
eb
r
a
tu
to
r
in
g
p
latf
o
r
m
a
n
d
h
o
w
it im
p
ac
ted
th
eir
s
tu
d
en
ts
’
p
er
f
o
r
m
an
ce
o
n
s
tan
d
a
r
d
ized
test
s
.
Desp
ite
th
e
f
ac
t
th
at
m
an
y
s
tu
d
en
ts
f
in
d
m
ath
em
atics
d
if
f
ic
u
lt,
it
is
s
ee
n
as
a
n
ess
en
tial
c
o
m
p
o
n
en
t
o
f
K
–
1
2
ed
u
ca
tio
n
a
n
d
a
p
r
er
eq
u
is
ite
f
o
r
s
u
cc
ess
in
p
o
s
ts
ec
o
n
d
ar
y
ed
u
ca
tio
n
[
1
6
]
.
I
n
p
ar
tic
u
lar
,
h
ig
h
er
p
r
o
f
ess
io
n
al
ea
r
n
in
g
s
,
g
r
ad
u
a
tio
n
r
ates,
an
d
co
lleg
e
ad
m
is
s
io
n
h
av
e
all
b
ee
n
ass
o
ciate
d
with
h
ig
h
s
ch
o
o
l
alg
eb
r
a
c
o
m
p
letio
n
[
1
7
]
.
Sin
c
e
m
ath
em
atics
is
a
n
ec
ess
ar
y
s
u
b
ject
f
o
r
s
u
cc
ess
in
th
e
f
u
t
u
r
e
,
s
tan
d
ar
d
ize
d
test
s
ar
e
s
ig
n
if
ican
t.
T
h
ese
ass
ess
m
en
ts
ar
e
n
o
w
a
cr
u
cial
co
m
p
o
n
en
t
o
f
th
e
m
o
d
e
r
n
e
d
u
ca
t
io
n
al
s
y
s
tem
,
b
ein
g
u
s
ed
to
co
m
p
a
r
e
n
atio
n
al
a
n
d
in
ter
n
atio
n
al
s
ch
o
o
l r
esu
lts
,
as
s
ess
th
e
ef
f
icac
y
o
f
teac
h
er
s
,
a
n
d
m
o
n
ito
r
s
tu
d
en
t
p
r
o
g
r
ess
.
C
o
n
ce
r
n
e
d
ab
o
u
t
th
eir
s
tu
d
en
ts
’
p
o
o
r
p
er
f
o
r
m
an
c
e,
m
an
y
ed
u
ca
to
r
s
ar
e
s
ea
r
ch
i
n
g
f
o
r
in
s
tr
u
cti
o
n
al
r
eso
u
r
ce
s
to
h
el
p
th
eir
p
u
p
ils
im
p
r
o
v
e
th
eir
a
b
ilit
y
to
r
ea
s
o
n
an
d
co
m
p
r
eh
en
d
m
ath
e
m
atica
l
id
ea
s
.
Stra
teg
ic
tech
n
o
lo
g
y
in
teg
r
atio
n
ca
n
g
r
ea
tly
im
p
r
o
v
e
m
ath
em
atics
in
s
tr
u
ctio
n
,
ev
e
n
th
o
u
g
h
n
o
t
all
tech
n
o
lo
g
ical
in
s
tr
u
m
en
ts
ar
e
s
u
cc
ess
f
u
lly
ac
ce
p
ted
o
r
h
av
e
s
tr
o
n
g
teac
h
er
s
u
p
p
o
r
t
[
1
8
]
,
[
1
9
]
.
I
t
p
r
o
v
id
es
s
tu
d
en
ts
with
wo
r
th
wh
ile
ch
an
ce
s
to
d
elv
e
f
u
r
th
er
in
to
m
at
h
em
atica
l
id
ea
s
[
2
0
]
.
Alth
o
u
g
h
teac
h
e
r
s
ca
n
u
s
e
a
wid
e
r
an
g
e
o
f
tech
n
o
lo
g
ies
to
aid
in
t
h
eir
in
s
tr
u
ctio
n
,
th
e
f
o
cu
s
o
f
th
is
s
tu
d
y
is
m
o
s
tly
o
n
o
n
lin
e
m
ath
r
eso
u
r
ce
s
,
wh
ich
ar
e
web
-
b
ased
to
o
ls
d
esig
n
ed
s
p
e
cif
ically
f
o
r
m
ath
in
s
tr
u
cti
o
n
in
th
e
wak
e
o
f
th
e
f
o
u
r
th
in
d
u
s
tr
ial
r
ev
o
lu
tio
n
.
W
h
ile
wo
r
d
p
r
o
ce
s
s
o
r
s
an
d
ca
lcu
lato
r
s
ar
e
ex
am
p
les
o
f
ed
u
ca
tio
n
al
tec
h
n
o
l
o
g
y
,
th
is
s
tu
d
y
f
o
cu
s
es
ex
clu
s
iv
ely
o
n
o
n
lin
e
p
latf
o
r
m
s
.
Acc
o
r
d
in
g
t
o
r
esear
ch
,
n
u
m
er
o
u
s
s
tr
ateg
ies
ar
e
em
p
lo
y
e
d
to
in
teg
r
ate
o
n
lin
e
m
ath
r
eso
u
r
ce
s
in
to
th
e
class
r
o
o
m
,
wh
ich
h
as
a
r
an
g
e
o
f
im
p
ac
ts
o
n
s
tu
d
en
ts
’
p
er
f
o
r
m
an
c
e.
An
o
v
er
v
iew
o
f
s
o
m
e
o
f
th
e
m
o
s
t
s
ig
n
if
ican
t
r
esear
ch
o
n
th
e
im
p
ac
t
o
f
tech
n
o
lo
g
y
o
n
s
tu
d
en
t
r
esu
lts
an
d
th
e
u
s
ag
e
o
f
d
ig
ital
to
o
ls
b
y
m
at
h
teac
h
er
s
in
th
e
class
r
o
o
m
is
p
r
o
v
i
d
ed
in
th
e
s
ec
tio
n
s
th
at
f
o
llo
w.
R
esear
ch
o
n
h
o
w
tech
n
o
lo
g
y
af
f
ec
ts
s
tu
d
en
ts
’
p
er
f
o
r
m
an
ce
in
s
ec
o
n
d
ar
y
m
ath
em
atics,
with
an
em
p
h
asis
o
n
th
e
wa
y
s
in
wh
ich
v
ar
io
u
s
m
eth
o
d
s
af
f
ec
t
p
e
r
f
o
r
m
an
ce
,
i
n
clu
d
es
[
2
1
]
–
[
2
5
]
.
T
h
e
s
tu
d
y
th
at
r
elate
s
to
th
e
u
s
e
o
f
tech
n
o
lo
g
y
b
y
teac
h
er
s
ca
n
b
e
f
o
u
n
d
in
C
h
iu
[
2
6
]
.
Ot
h
er
s
tu
d
ies
[
2
7
]
,
[
2
8
]
also
f
o
u
n
d
th
at
s
tu
d
en
t
-
ce
n
ter
ed
,
in
ter
ac
tiv
e
v
id
eo
less
o
n
s
,
wh
ich
en
co
u
r
ag
ed
co
llab
o
r
at
iv
e
p
r
o
b
lem
-
s
o
lv
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g
,
r
esu
lted
in
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ig
n
if
ican
tly
b
etter
m
at
h
em
atics
p
r
o
b
lem
-
s
o
lv
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g
s
k
ills
co
m
p
ar
ed
to
t
ea
ch
er
-
ce
n
ter
e
d
in
s
tr
u
ctio
n
.
S
ev
er
al
s
tu
d
ies
[
2
9
]
–
[
3
2
]
r
e
v
ea
led
th
at
s
im
p
ly
s
u
b
s
titu
tin
g
tech
n
o
lo
g
y
f
o
r
tea
ch
er
in
s
tr
u
ctio
n
d
id
n
o
t g
u
a
r
an
tee
b
etter
r
esu
lts
.
Evaluation Warning : The document was created with Spire.PDF for Python.
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T
h
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ten
t,
s
tr
u
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d
ar
tific
ial
in
tellig
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ce
(
A
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i
n
teg
r
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ac
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at
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ca
le
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th
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liter
atu
r
e.
T
h
e
n
o
v
elty
i
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th
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cu
r
r
en
t
s
tu
d
y
ca
n
b
e
s
u
m
m
ar
ized
:
i)
t
h
e
cu
r
r
en
t
s
tu
d
y
r
ef
lects
a
b
len
d
ed
l
ea
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n
in
g
i
n
n
o
v
atio
n
,
b
len
d
in
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p
ass
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d
ac
tiv
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s
tr
ateg
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in
a
s
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ten
n
o
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ac
co
m
m
o
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ated
i
n
liter
atu
r
e
;
ii)
p
r
o
v
id
es
a
r
ea
l
-
wo
r
ld
im
p
lem
en
tatio
n
o
f
ad
ap
tiv
e
teac
h
in
g
p
r
ac
tices
ai
d
ed
b
y
AI
,
a
n
d
n
o
t
ju
s
t
th
e
o
r
etica
l
;
iii)
p
r
o
v
id
es
a
p
ed
a
g
o
g
ical
s
h
if
t
to
war
d
s
s
tu
d
en
t
-
ce
n
ter
ed
class
r
o
o
m
s
,
wh
er
e
AI
is
n
o
t
ju
s
t
a
co
n
t
en
t
d
eliv
er
y
to
o
l
b
u
t
a
class
r
o
o
m
m
an
ag
e
m
en
t
s
tr
ateg
y
an
d
lea
r
n
in
g
s
u
p
p
o
r
t
;
an
d
iv
)
t
h
e
s
tu
d
y
s
h
o
wca
s
es
AI
’
s
ex
ten
d
ed
i
n
s
tr
u
ctio
n
al
r
o
le
b
e
y
o
n
d
th
e
class
r
o
o
m
,
s
o
m
eth
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g
n
o
t
wid
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o
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m
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ted
.
L
astl
y
,
th
e
s
tu
d
y
q
u
a
n
tifie
d
th
e
ef
f
ec
t
o
f
teac
h
er
-
i
n
itiated
ac
tiv
ities
o
n
s
tu
d
en
t p
er
f
o
r
m
a
n
ce
,
wh
ich
is
n
o
t
o
f
ten
e
x
am
in
ed
in
th
e
liter
atu
r
e
.
2.
T
H
E
O
R
E
T
I
CA
L
F
RAM
E
WO
RK
Un
d
er
s
tan
d
in
g
h
o
w
teac
h
e
r
s
u
s
e
tech
n
o
lo
g
y
in
th
e
class
r
o
o
m
an
d
h
o
w
it
im
p
ac
ts
s
tu
d
en
ts
’
co
m
p
r
eh
e
n
s
io
n
is
c
h
allen
g
in
g
.
Sev
er
al
th
eo
r
ies
o
f
in
s
tr
u
m
en
tatio
n
[
2
5
]
,
[
3
3
]
,
[
3
4
]
,
an
d
in
s
tr
u
m
e
n
tal
o
r
ch
estra
tio
n
[
3
5
]
h
av
e
b
ec
o
m
e
m
o
r
e
an
d
m
o
r
e
im
p
o
r
ta
n
t
in
m
ath
em
atics
ed
u
ca
tio
n
t
o
co
m
p
r
e
h
en
d
h
o
w
in
s
tr
u
cto
r
s
an
d
lear
n
er
s
en
g
ag
e
with
tech
n
o
lo
g
y
t
o
lear
n
m
ath
em
atics.
Acc
o
r
d
in
g
to
in
s
tr
u
m
en
tatio
n
th
e
o
r
y
,
f
o
r
s
tu
d
en
ts
to
lear
n
h
o
w
to
in
ter
ac
t
with
a
tech
n
o
lo
g
ical
to
o
l
o
r
ar
tifa
ct,
th
e
y
m
u
s
t
g
o
th
r
o
u
g
h
a
p
r
o
ce
s
s
ca
lled
“
in
s
tr
u
m
en
tal
g
en
esis
”
,
in
wh
ich
th
e
y
m
u
s
t
d
e
v
is
e
s
tr
ateg
ies
an
d
m
eth
o
d
s
f
o
r
u
s
in
g
th
e
to
o
l
to
tr
an
s
f
o
r
m
it in
to
an
in
s
tr
u
m
e
n
t
[
2
9
]
,
[
3
5
]
.
I
n
s
tr
u
m
en
tal
o
r
ch
estra
tio
n
,
th
e
ter
m
u
s
ed
to
d
escr
ib
e
th
e
r
o
le
o
f
th
e
in
s
tr
u
ct
o
r
in
g
u
id
in
g
th
e
u
s
ag
e
o
f
tech
n
o
lo
g
y
b
y
lear
n
e
r
s
,
h
as
em
er
g
ed
to
s
u
p
p
o
r
t
s
tu
d
e
n
ts
’
in
s
tr
u
m
en
tal
g
en
esis
.
T
e
ac
h
er
s
’
d
esig
n
s
an
d
im
p
lem
en
tatio
n
o
f
lear
n
in
g
ac
tiv
ities
ce
n
ter
ed
ar
o
u
n
d
th
ese
to
o
ls
ar
e
ess
en
tial
[
3
6
]
.
Sm
ale
-
J
ac
o
b
s
e
et
a
l.
[
3
7
]
h
ig
h
lig
h
ted
two
cr
itical
elem
en
ts
to
co
n
s
id
er
wh
en
u
s
in
g
tech
n
o
lo
g
y
in
m
ath
em
atics
in
s
tr
u
ctio
n
:
way
s
o
f
u
tili
za
tio
n
an
d
d
id
ac
tical
ar
r
a
n
g
em
en
ts
.
“
Did
ac
tical
co
n
f
ig
u
r
atio
n
”
r
ef
e
r
s
to
h
o
w
th
e
te
ac
h
in
g
en
v
i
r
o
n
m
e
n
t
an
d
to
o
ls
ar
e
ar
r
an
g
e
d
in
th
e
class
r
o
o
m
,
wh
ile
“
e
x
p
lo
itat
io
n
m
o
d
e
”
d
escr
ib
es
h
o
w
te
ac
h
er
s
u
tili
ze
th
ese
s
etu
p
s
to
m
ee
t
th
eir
ed
u
ca
tio
n
al
o
b
jectiv
es.
T
h
ese
co
n
ce
p
ts
h
elp
ex
p
lain
th
e
s
tr
ateg
ies
ed
u
ca
to
r
s
ad
o
p
t
to
f
ac
ilit
ate
s
tu
d
en
t le
ar
n
in
g
in
m
ath
em
atics.
Fo
r
in
s
tan
ce
,
Vita
et
a
l.
[
3
5
]
p
r
esen
ted
a
m
o
d
el
ca
lle
d
“
tech
n
ical
d
em
o
”
,
wh
er
e
a
teac
h
er
d
em
o
n
s
tr
ates
a
to
o
l
’
s
f
u
n
ctio
n
ality
(
ex
p
lo
itatio
n
m
o
d
e)
b
y
walk
in
g
s
tu
d
en
ts
th
r
o
u
g
h
th
e
s
tep
s
an
d
p
r
o
jectin
g
th
e
to
o
l
o
n
a
s
cr
ee
n
(
d
id
ac
tical
co
n
f
ig
u
r
atio
n
)
.
T
h
o
u
g
h
th
i
s
ap
p
r
o
ac
h
is
co
m
m
o
n
,
o
t
h
er
o
r
ch
estra
tio
n
ty
p
es
also
ex
is
t
an
d
o
f
f
er
v
ar
i
o
u
s
way
s
f
o
r
teac
h
er
s
to
in
co
r
p
o
r
ate
tech
n
o
lo
g
y
i
n
m
ath
em
atic
s
ed
u
ca
tio
n
.
I
n
th
is
co
n
tex
t,
in
s
tr
u
m
e
n
tal
o
r
ch
estr
atio
n
was
u
s
ed
as
a
f
r
am
ewo
r
k
to
in
ter
p
r
et
h
o
w
teac
h
e
r
s
in
co
r
p
o
r
ated
Alg
eb
r
a
Natio
n
(
AN)
in
m
ath
em
atic
s
class
e
s
.
T
h
is
s
tu
d
y
ex
p
lo
r
ed
d
if
f
er
e
n
t
co
n
f
i
g
u
r
atio
n
s
,
s
u
ch
as
in
d
iv
id
u
al
r
em
ed
iatio
n
o
r
g
r
o
u
p
lea
r
n
in
g
,
an
d
h
o
w
v
ar
io
u
s
o
r
ch
estra
tio
n
ty
p
es
wer
e
ap
p
lied
to
teac
h
alg
eb
r
aic
co
n
ce
p
ts
.
W
h
ile
it
i
s
u
n
d
er
s
to
o
d
th
at
ed
u
ca
to
r
s
u
s
e
d
iv
er
s
e
d
id
ac
ti
ca
l
m
eth
o
d
s
a
n
d
ex
p
lo
itatio
n
m
o
d
es
[
3
8
]
,
th
is
r
esear
ch
p
r
o
v
id
ed
an
o
v
er
v
ie
w
with
o
u
t d
elv
in
g
d
ee
p
l
y
in
to
ev
er
y
o
r
ch
estra
tio
n
’
s
n
u
an
ce
s
.
T
h
is
s
tu
d
y
f
o
cu
s
es
o
n
th
e
AN
o
n
lin
e
tu
to
r
in
g
p
latf
o
r
m
,
d
esi
g
n
ed
to
h
elp
b
o
th
teac
h
er
s
an
d
s
tu
d
en
ts
m
ee
t
th
e
Nig
er
ian
m
ath
em
atic
s
s
tate
s
tan
d
ar
d
s
,
p
ar
ticu
lar
ly
th
o
s
e
r
eq
u
ir
ed
f
o
r
p
ass
in
g
th
e
Nig
er
ia
Alg
eb
r
a
I
en
d
-
of
-
co
u
r
s
e
(
E
OC
)
ex
am
.
T
h
e
Alg
eb
r
a
I
E
OC
is
a
s
tan
d
ar
d
ized
ass
ess
m
en
t
m
an
d
ated
f
o
r
ev
er
y
s
tu
d
e
n
t
en
r
o
lled
i
n
Alg
e
b
r
a
I
in
p
u
b
li
c
s
ch
o
o
ls
,
m
ea
s
u
r
in
g
th
eir
m
a
s
ter
y
o
f
th
e
Nig
e
r
ia
Alg
eb
r
a
I
s
tan
d
ar
d
s
.
Fo
r
th
e
2022
–
2
0
2
3
ac
ad
em
ic
y
ea
r
,
s
tu
d
en
ts
wer
e
r
eq
u
ir
ed
to
c
o
m
p
lete
2
0
–
2
5
o
p
en
-
e
n
d
ed
q
u
esti
o
n
s
an
d
3
0
–
3
5
m
u
ltip
le
-
ch
o
ice
q
u
esti
o
n
s
with
in
a
6
0
-
m
in
u
te
tim
e
f
r
am
e.
At
th
e
tim
e
o
f
AN
’
s
in
t
r
o
d
u
ctio
n
,
Nig
er
ian
teac
h
er
s
h
ad
alr
ea
d
y
b
ee
n
im
p
lem
en
tin
g
t
h
e
Nig
er
ia
Stan
d
ar
d
s
,
also
k
n
o
wn
as
th
e
C
o
m
m
o
n
C
o
r
e
State
Stan
d
ar
d
s
f
o
r
Ma
t
h
em
atics,
f
o
r
at
least
3
y
ea
r
s
,
f
o
llo
win
g
th
eir
ad
o
p
tio
n
b
y
th
e
s
tate
in
2
0
2
1
.
T
h
e
o
n
lin
e
r
eso
u
r
ce
in
c
lu
d
ed
p
r
ac
tice
e
x
am
s
th
at
wer
e
m
o
d
ele
d
af
te
r
th
e
Alg
eb
r
a
I
E
OC
,
v
id
e
o
less
o
n
s
b
y
s
ea
s
o
n
ed
alg
e
b
r
a
tu
to
r
s
,
an
d
an
i
n
ter
ac
tiv
e,
s
y
n
c
h
r
o
n
o
u
s
wall
wh
er
e
s
tu
d
en
ts
m
ay
talk
ab
o
u
t
alg
eb
r
aic
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ea
s
with
teac
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o
t
h
er
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tu
d
en
ts
,
an
d
o
n
lin
e
tu
to
r
s
,
as
p
r
esen
ted
in
Fig
u
r
es
1
an
d
2
.
T
h
e
m
o
v
ies
wer
e
also
ac
co
m
p
a
n
ied
b
y
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wo
r
k
b
o
o
k
with
s
tu
d
y
tip
s
f
o
r
b
o
th
teac
h
er
s
an
d
p
u
p
ils
.
A
v
ar
iety
o
f
in
s
tr
u
m
e
n
tal
o
r
ch
estra
tio
n
ty
p
es a
r
e
s
h
o
wn
in
T
ab
le
1
.
T
h
e
f
o
ll
o
win
g
d
o
m
ain
s
a
r
r
an
g
ed
ea
c
h
o
f
th
ese
c
o
m
p
o
n
en
t
s
’
co
n
ten
t:
i)
lin
ea
r
eq
u
atio
n
s
,
f
u
n
ctio
n
s
,
an
d
in
e
q
u
alities
;
ii)
ex
p
o
n
en
tial
f
u
n
ctio
n
s
;
iii)
al
g
eb
r
aic
ex
p
r
ess
io
n
s
;
iv
)
an
i
n
tr
o
d
u
ctio
n
to
f
u
n
ctio
n
s
;
v
)
s
in
g
le
-
v
ar
iab
le
s
tatis
tics
;
v
i)
q
u
ad
r
atic
f
u
n
ctio
n
s
;
v
ii)
a
s
u
m
m
ar
y
o
f
f
u
n
ctio
n
s
;
an
d
v
iii)
2
-
v
ar
ia
b
le
s
tatis
t
ics.
T
h
e
co
n
ten
t
was
d
ev
elo
p
ed
i
n
ac
co
r
d
an
ce
with
Flo
r
id
a
’
s
alg
eb
r
a
s
tate
s
tan
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ar
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s
.
So
m
e
d
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p
ar
allels
ex
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A
N
a
n
d
o
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p
o
p
u
lar
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lin
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r
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lik
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AL
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KS,
Kh
an
Aca
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y
,
PLAT
O,
an
d
C
o
g
n
itiv
e
T
u
to
r
.
T
h
ese
in
ter
n
et
s
o
u
r
ce
s
o
f
f
er
ed
s
tate
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s
tan
d
a
r
d
-
alig
n
e
d
v
id
eo
t
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to
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o
n
m
ath
em
atics
to
p
ics
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d
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r
ie
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f
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r
m
ativ
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ess
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e
n
t
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th
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wed
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tu
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ts
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g
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eir
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g
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ess
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L
ik
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AN,
co
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g
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s
tu
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wo
r
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at
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co
r
r
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with
th
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lin
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less
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W
h
ile
all
th
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r
eso
u
r
ce
s
h
av
e
m
o
d
u
les
co
r
r
esp
o
n
d
in
g
with
th
e
n
in
e
a
lg
eb
r
aic
d
o
m
ain
s
o
f
AN,
c
alcu
lu
s
,
g
eo
m
etr
y
,
tr
ig
o
n
o
m
et
r
y
,
an
d
in
t
r
o
d
u
cto
r
y
m
ath
em
atics
ar
e
am
o
n
g
t
h
e
m
o
s
t
ex
ten
s
iv
e
to
p
ics
co
v
er
ed
b
y
C
o
g
n
itiv
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
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2
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t
J
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v
al
&
R
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d
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c
,
Vo
l
.
14
,
No
.
6
,
Dec
em
b
er
20
25
:
4
4
4
3
-
4
4
5
5
4446
T
u
to
r
,
Kh
an
Aca
d
em
y
,
PLA
T
O,
an
d
AL
E
KS.
W
h
ile
AN
d
o
es
n
o
t
h
av
e
a
d
ap
tiv
e
t
ec
h
n
o
lo
g
y
an
d
is
a
s
elf
-
p
ac
ed
p
latf
o
r
m
,
o
th
e
r
o
n
lin
e
r
eso
u
r
ce
s
u
s
e
ad
ap
ti
v
e
l
ea
r
n
in
g
en
v
ir
o
n
m
e
n
ts
to
p
r
o
v
id
e
in
d
iv
id
u
alize
d
ed
u
ca
tio
n
.
Desp
ite
th
is
,
AN
h
as
s
et
its
elf
ap
ar
t
f
o
r
a
n
u
m
b
e
r
o
f
r
ea
s
o
n
s
.
T
ea
ch
er
s
a
n
d
s
tu
d
en
ts
ca
n
u
s
e
it
f
o
r
f
r
ee
,
is
s
p
ec
if
ically
alig
n
ed
with
Nig
er
ia
’
s
n
atio
n
al
s
tan
d
ar
d
s
an
d
E
OC
ex
am
in
ati
o
n
an
d
o
f
f
er
s
o
n
-
s
ite
p
r
o
f
ess
io
n
al
d
e
v
elo
p
m
e
n
t
s
ess
io
n
s
led
b
y
ex
p
e
r
ien
ce
d
ed
u
ca
to
r
s
.
T
h
e
in
q
u
ir
y
-
b
ased
p
r
o
f
ess
io
n
al
d
ev
elo
p
m
e
n
t
en
ab
les
teac
h
er
s
to
ex
p
lo
r
e
AN’
s
f
ea
tu
r
es,
s
u
ch
as
v
id
eo
tu
to
r
ials
,
p
r
ac
tice
ex
am
s
,
in
ter
ac
tiv
e
s
tu
d
en
t
d
is
cu
s
s
io
n
f
o
r
u
m
s
,
a
n
d
wo
r
k
b
o
o
k
s
.
T
h
ese
r
eso
u
r
c
es
co
m
p
r
e
h
en
s
iv
ely
c
o
v
er
Al
g
eb
r
a
I
t
o
p
ics,
an
d
teac
h
er
s
ar
e
tr
ain
e
d
in
v
ar
io
u
s
in
s
tr
u
ctio
n
al
s
tr
ateg
ies,
s
u
ch
as
f
lip
p
in
g
t
h
e
class
r
o
o
m
b
y
a
s
s
ig
n
in
g
v
id
eo
s
f
o
r
h
o
m
ewo
r
k
,
s
eg
m
e
n
tin
g
v
id
eo
s
f
o
r
class
r
o
o
m
u
s
e,
o
r
in
co
r
p
o
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atin
g
t
h
em
as
c
o
-
teac
h
in
g
t
o
o
ls
d
u
r
i
n
g
less
o
n
s
.
As
th
ey
watc
h
th
e
v
id
eo
s
,
t
h
e
s
tu
d
en
ts
alwa
y
s
co
m
p
lete
t
h
e
wo
r
k
b
o
o
k
as
p
ar
t
o
f
t
h
ese
s
tr
ateg
ies.
Mo
r
e
th
a
n
1
0
0
,
0
0
0
s
tu
d
en
ts
s
tatewid
e
s
wif
tly
em
b
r
ac
ed
AN
af
ter
it
was
m
ad
e
av
ailab
le
to
all
Ab
u
ja
s
ch
o
o
ls
as
a
f
r
ee
r
eso
u
r
ce
d
u
r
in
g
th
e
2
0
2
2
–
2
0
2
3
ac
a
d
em
ic
y
ea
r
.
Nu
m
er
o
u
s
tr
ain
in
g
s
ess
io
n
s
an
d
p
r
o
f
es
s
io
n
al
d
ev
elo
p
m
en
t
d
ay
s
h
av
e
b
ee
n
h
eld
th
r
o
u
g
h
o
u
t
Ab
u
ja
to
p
r
o
m
o
te
ed
u
c
ato
r
s
’
u
s
e
o
f
th
is
tech
n
o
lo
g
y
.
Fu
r
th
er
m
o
r
e,
AN
r
ap
id
ly
d
ev
elo
p
s
in
to
a
r
eso
u
r
ce
f
o
r
in
s
tr
u
cto
r
s
an
d
s
tu
d
en
ts
as
well
as
a
co
o
p
e
r
ativ
e
o
n
lin
e
co
m
m
u
n
ity
o
f
ed
u
ca
to
r
s
.
A
p
r
o
f
ess
io
n
al
d
e
v
elo
p
m
en
t
p
r
o
g
r
a
m
h
as
b
ee
n
s
et
u
p
to
allo
w
ed
u
ca
to
r
s
to
s
h
ar
e
teac
h
in
g
r
eso
u
r
ce
s
,
watc
h
v
id
e
o
s
o
f
Ab
u
ja
class
r
o
o
m
teac
h
er
s
u
s
in
g
s
u
cc
ess
f
u
l
m
ath
em
atica
l
teac
h
in
g
tech
n
i
q
u
es,
an
d
h
av
e
co
n
v
er
s
atio
n
s
ab
o
u
t
tea
ch
in
g
m
ath
em
atics
an
d
g
etti
n
g
r
ea
d
y
f
o
r
th
e
Alg
eb
r
a
E
OC
.
T
h
is
in
itiat
iv
e
m
ir
r
o
r
s
th
e
in
ter
ac
tiv
e
wall
an
d
v
id
eo
tu
to
r
ial
f
ea
tu
r
es a
v
ailab
le
to
s
tu
d
en
ts
.
Fig
u
r
e
1
.
E
x
am
p
le
o
f
a
teac
h
i
n
g
v
id
e
o
f
o
r
AN
Fig
u
r
e
2
.
E
x
am
p
le
test
-
y
o
u
r
s
e
lf
wo
r
k
s
h
ee
t f
o
r
AN
T
ab
le
1
.
V
ar
io
u
s
ty
p
es o
f
i
n
s
tr
u
m
en
tal
o
r
c
h
estra
tio
n
[
3
5
]
SN
O
r
c
h
e
s
t
r
a
t
i
o
n
t
y
p
e
Ex
a
m
p
l
e
1
Te
c
h
n
i
c
a
l
d
e
mo
n
s
t
r
a
t
i
o
n
Th
e
t
e
a
c
h
e
r
p
r
o
j
e
c
t
s t
h
e
t
e
c
h
n
o
l
o
g
y
t
o
o
l
o
n
t
o
t
h
e
s
c
r
e
e
n
a
n
d
w
a
l
k
s s
t
u
d
e
n
t
s
t
h
r
o
u
g
h
i
t
s
t
e
c
h
n
i
c
a
l
s
t
e
p
s.
2
D
e
scri
b
e
t
h
e
s
c
r
e
e
n
A
t
e
a
c
h
e
r
d
e
m
o
n
st
r
a
t
e
s
a
mat
h
e
mat
i
c
a
l
c
o
n
c
e
p
t
o
n
a
scre
e
n
u
s
i
n
g
a
t
e
c
h
n
o
l
o
g
i
c
a
l
t
o
o
l
.
3
C
o
n
n
e
c
t
-
scre
e
n
-
b
o
a
r
d
Th
e
t
e
a
c
h
e
r
d
r
a
w
s
c
o
n
n
e
c
t
i
o
n
s
b
e
t
w
e
e
n
ma
t
h
a
n
d
o
t
h
e
r
o
n
-
b
o
a
r
d
r
e
p
r
e
s
e
n
t
a
t
i
o
n
s
u
s
i
n
g
a
t
o
o
l
t
o
e
x
p
l
a
i
n
m
a
t
h
e
m
a
t
i
c
a
l
c
o
n
c
e
p
t
s.
4
Ta
l
k
a
b
o
u
t
t
h
e
s
c
r
e
e
n
U
si
n
g
a
t
o
o
l
p
r
o
j
e
c
t
e
d
o
n
t
o
t
h
e
s
c
r
e
e
n
,
t
h
e
t
e
a
c
h
e
r
g
u
i
d
e
s
t
h
e
d
i
sc
u
ssi
o
n
o
f
a
ma
t
h
e
ma
t
i
c
a
l
c
o
n
c
e
p
t
.
5
S
p
o
t
-
a
n
d
-
s
h
o
w
Th
e
t
e
a
c
h
e
r
u
s
e
s
a
t
e
c
h
n
o
l
o
g
i
c
a
l
t
o
o
l
t
o
i
d
e
n
t
i
f
y
t
h
e
st
u
d
e
n
t
’
s
w
o
r
k
f
o
r
t
h
e
p
r
o
j
e
c
t
a
n
d
st
a
r
t
s
a
c
o
n
v
e
r
sa
t
i
o
n
a
b
o
u
t
a
ma
t
h
e
ma
t
i
c
a
l
c
o
n
c
e
p
t
.
6
W
o
r
k
i
n
g
a
s
a
S
h
e
r
p
a
S
t
u
d
e
n
t
s
sh
a
r
e
t
h
e
i
r
w
o
r
k
w
i
t
h
t
h
e
c
l
a
ss
u
s
i
n
g
t
e
c
h
n
o
l
o
g
y
w
h
i
l
e
t
h
e
t
e
a
c
h
e
r
g
u
i
d
e
s
t
h
e
d
i
s
c
u
ssi
o
n
o
f
mat
h
e
m
a
t
i
c
a
l
i
d
e
a
s
.
7
W
o
r
k
-
a
n
d
-
w
a
l
k
-
by
S
t
u
d
e
n
t
s
u
se
t
h
e
i
r
g
a
d
g
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t
s
f
o
r
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n
d
i
v
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d
u
a
l
t
e
c
h
n
o
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i
c
a
l
u
se
w
h
i
l
e
t
h
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t
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a
c
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mo
v
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s
a
r
o
u
n
d
a
n
d
w
o
r
k
s
o
n
e
-
on
-
o
n
e
w
i
t
h
e
a
c
h
st
u
d
e
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t
.
3.
M
E
T
H
O
D
T
h
e
g
o
als
o
f
th
is
s
tu
d
y
ar
e
to
co
m
p
r
e
h
en
d
h
o
w
ed
u
ca
to
r
s
ar
e
u
s
in
g
AN,
an
o
n
lin
e
m
ath
em
atics
r
eso
u
r
ce
,
to
en
g
ag
e
s
tu
d
en
ts
a
n
d
th
e
co
n
n
ec
tio
n
b
etwe
en
A
N
u
s
e
in
th
e
class
r
o
o
m
an
d
alg
eb
r
a
p
er
f
o
r
m
a
n
ce
.
Sp
ec
if
ically
,
th
e
f
o
llo
win
g
r
es
ea
r
ch
in
q
u
ir
ies will b
e
tack
led
:
-
W
h
at
asp
ec
ts
o
f
in
s
tr
u
ctio
n
ar
e
AN
in
co
r
p
o
r
atin
g
?
-
Do
es
in
cr
ea
s
ed
s
tu
d
en
t
p
er
f
o
r
m
an
ce
s
o
n
th
e
E
OC
f
o
r
Al
g
eb
r
a
I
c
o
r
r
elate
with
th
e
u
s
e
o
f
AN
in
th
e
class
r
o
o
m
?
-
Did
th
e
s
ch
o
o
ls
wh
er
e
teac
h
er
s
en
g
ag
ed
in
in
-
p
er
s
o
n
p
r
o
f
e
s
s
io
n
al
d
ev
elo
p
m
en
t,
u
tili
ze
d
th
e
AN
o
n
lin
e
lear
n
in
g
p
latf
o
r
m
,
an
d
o
r
d
er
e
d
wo
r
k
b
o
o
k
s
f
o
r
s
tu
d
e
n
ts
an
d
teac
h
er
s
ex
h
ib
it
d
if
f
er
e
n
t
m
ea
n
s
tu
d
en
t
s
co
r
es
an
d
p
ass
r
ates o
n
th
e
2
0
2
3
Alg
eb
r
a
I
E
OC
co
m
p
ar
ed
to
th
o
s
e
th
at
d
id
n
o
t in
co
r
p
o
r
ate
AN?
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4447
3
.
1
.
Sa
m
ple
T
h
is
s
tu
d
y
g
ath
er
ed
d
ata
f
r
o
m
f
o
u
r
p
r
im
ar
y
s
o
u
r
ce
s
:
t
h
e
Natio
n
al
C
en
ter
f
o
r
E
d
u
ca
tio
n
Statis
tics
(
NC
E
S)
web
s
ite,
th
e
Nig
er
ia
Dep
ar
tm
en
t
o
f
E
d
u
ca
tio
n
web
s
ite,
th
e
AN
s
y
s
tem
,
an
d
th
e
“h
o
w
teac
h
er
s
u
s
e
AN
”
s
u
r
v
ey
.
Du
r
in
g
th
e
2
0
2
2
–
2
0
2
3
s
ch
o
o
l
y
ea
r
,
5
9
6
Alg
eb
r
a
I
teac
h
er
s
in
Ab
u
ja
p
ar
ticip
ated
in
a
q
u
an
titativ
e
an
d
q
u
alitativ
e
s
u
r
v
ey
to
an
s
wer
r
esear
ch
q
u
e
s
tio
n
1
(
R
Q1
)
,
in
d
icatin
g
a
r
esp
o
n
s
e
r
ate
h
ig
h
er
th
an
th
e
n
o
r
m
f
o
r
o
n
lin
e
s
u
r
v
e
y
s
[
2
2
]
.
Fo
r
r
esear
ch
q
u
esti
o
n
s
2
(
R
Q2
)
an
d
3
(
R
Q3
)
,
d
ata
f
r
o
m
t
h
e
AN
s
y
s
tem
ca
p
tu
r
ed
u
s
ag
e
ac
r
o
s
s
two
ac
ad
em
ic
y
ea
r
s
,
in
clu
d
in
g
lo
g
in
an
d
v
id
eo
v
iew
co
u
n
ts
,
r
esp
o
n
s
es
to
q
u
esti
o
n
s
,
an
d
d
is
cu
s
s
io
n
f
o
r
u
m
co
n
tr
ib
u
tio
n
s
.
B
ec
au
s
e
th
e
Alg
eb
r
a
I
E
OC
ex
am
is
a
r
eq
u
ir
em
en
t
in
Nig
er
ian
e
d
u
ca
ti
o
n
,
atten
tio
n
was
f
o
cu
s
ed
o
n
m
id
d
le
an
d
h
ig
h
s
ch
o
o
l
d
ata.
Ad
d
itio
n
al
E
OC
r
esu
lts
f
o
r
2
0
2
1
-
2
0
2
3
an
d
r
elat
ed
s
ch
o
o
l
-
lev
el
d
ata
wer
e
g
ath
er
ed
f
r
o
m
th
e
Flo
r
id
a
Dep
ar
tm
en
t o
f
E
d
u
ca
tio
n
an
d
NC
E
S we
b
s
ites
.
A
q
u
asi
-
ex
p
er
im
en
tal
an
aly
s
i
s
f
o
r
R
Q3
as
s
ess
ed
s
ch
o
o
ls
’
p
er
f
o
r
m
an
ce
b
ased
o
n
Alg
eb
r
a
I
E
OC
m
ea
n
s
co
r
es a
n
d
p
ass
in
g
r
ates.
Key
f
ac
to
r
s
in
clu
d
ed
AN
s
y
s
tem
lo
g
in
,
teac
h
er
tr
ai
n
in
g
,
a
n
d
wo
r
k
b
o
o
k
ac
ce
s
s
.
T
h
e
av
er
ag
e
tr
ea
tm
en
t
ef
f
ec
t
(
AT
E
)
was
ca
lcu
lated
b
y
c
o
m
p
ar
in
g
m
atch
ed
tr
ea
tm
e
n
t
a
n
d
co
n
tr
o
l
g
r
o
u
p
s
:
C
o
m
p
ar
ed
to
7
3
s
ch
o
o
ls
with
o
u
t
teac
h
er
lo
g
in
s
,
wo
r
k
b
o
o
k
s
,
o
r
tr
ain
in
g
,
2
9
1
s
ch
o
o
ls
h
ad
teac
h
er
s
ac
tiv
ely
u
s
in
g
AN.
T
h
is
tech
n
iq
u
e
t
o
o
k
in
to
c
o
n
s
id
er
atio
n
g
r
o
u
p
d
if
f
er
en
ce
s
an
d
u
s
ed
a
q
u
asi
-
ex
p
er
im
en
tal
d
esig
n
t
o
less
en
th
e
im
p
ac
t o
f
u
n
co
n
tr
o
l
lab
le
v
ar
iab
les [
3
9
]
.
3
.
2
.
Q
ua
lit
y
m
e
a
s
ures
T
h
e
p
u
r
p
o
s
e
o
f
t
h
e
s
u
r
v
e
y
u
s
ed
to
a
n
s
wer
R
Q1
was
to
in
v
esti
g
ate
h
o
w
teac
h
er
s
an
d
s
tu
d
en
ts
u
s
e
AN
f
o
r
v
ar
io
u
s
in
s
tr
u
ctio
n
al
lev
els.
I
t a
s
k
ed
ab
o
u
t th
eir
u
s
e
o
f
th
e
wo
r
k
b
o
o
k
,
test
q
u
esti
o
n
s
,
d
is
cu
s
s
io
n
b
o
ar
d
,
an
d
AN
v
id
eo
,
in
clu
d
i
n
g
h
o
w,
w
h
er
e,
an
d
h
o
w
o
f
ten
t
h
ey
u
s
ed
t
h
em
.
T
h
er
e
wer
e
3
o
p
e
n
-
en
d
e
d
q
u
esti
o
n
s
an
d
3
9
clo
s
ed
en
d
ed
,
y
es/n
o
r
ati
n
g
s
ca
le
o
r
y
es/n
o
q
u
esti
o
n
s
in
th
e
s
u
r
v
ey
.
T
h
is
s
u
r
v
e
y
f
o
llo
wed
b
est
p
r
ac
tices
o
u
tlin
ed
b
y
Ye
d
ilb
ay
ev
et
a
l
.
[
4
0
]
to
e
n
s
u
r
e
q
u
esti
o
n
clar
ity
.
C
lo
s
ed
-
en
d
ed
q
u
esti
o
n
s
u
s
ed
p
r
ec
is
e
f
r
e
q
u
en
c
y
o
p
tio
n
s
,
s
u
c
h
as
“i
n
e
v
er
y
cl
ass
”
o
r
“
1
o
r
2
tim
es
in
ev
e
r
y
f
i
v
e
class
es,
”
to
a
v
o
id
am
b
ig
u
o
u
s
ter
m
s
lik
e
“
f
r
eq
u
e
n
tly
”
.
Op
en
-
en
d
e
d
q
u
e
s
tio
n
s
ad
d
r
ess
ed
AN
s
tr
en
g
th
s
,
wea
k
n
ess
es,
an
d
u
s
ag
e
lim
ita
tio
n
s
.
T
h
e
q
u
esti
o
n
n
air
e
was
p
r
ete
s
ted
,
in
clu
d
in
g
ex
p
e
r
t
ev
alu
atio
n
s
,
co
g
n
itiv
e
i
n
ter
v
iews,
an
d
p
ilo
t
r
esear
ch
,
g
u
id
ed
b
y
Par
k
e
t
a
l.
[
4
1
]
.
T
h
e
1
4
co
g
n
itiv
e
in
ter
v
iews,
s
p
lit
b
etwe
e
n
th
in
k
-
alo
u
d
an
d
v
er
b
al
-
p
r
o
b
in
g
s
ess
io
n
s
,
in
v
o
lv
ed
e
x
p
er
ien
c
ed
al
g
eb
r
a
t
ea
ch
er
s
.
Ad
d
itio
n
ally
,
e
x
p
er
t
f
ee
d
b
ac
k
f
r
o
m
3
m
ath
em
atics
ed
u
ca
to
r
s
an
d
A
N
co
ac
h
led
to
r
e
v
is
io
n
s
.
I
n
t
h
e
p
ilo
t
with
1
0
0
teac
h
er
s
,
a
4
2
%
r
esp
o
n
s
e
r
ate
h
elp
ed
id
e
n
tify
an
d
r
ev
is
e
u
n
c
lear
q
u
esti
o
n
s
.
RQ
2
an
d
RQ
3
ex
am
in
e
d
Alg
eb
r
a
I
E
OC
ex
am
p
ass
in
g
r
at
es
an
d
a
v
er
ag
e
s
co
r
es
f
o
r
s
p
r
in
g
2
0
2
4
.
Stan
d
ar
d
ized
p
ass
in
g
s
co
r
es
wer
e
s
et
b
y
th
e
Nig
er
ia
Dep
a
r
tm
en
t
o
f
E
d
u
ca
tio
n
.
c
o
n
tr
o
lled
co
v
ar
iates
in
clu
d
e
d
p
r
ev
io
u
s
p
ass
in
g
r
ates,
s
tu
d
en
t
-
teac
h
er
r
atio
s
,
p
er
ce
n
ta
g
es
o
f
p
u
p
ils
wh
o
q
u
alif
y
f
o
r
f
r
ee
o
r
r
ed
u
ce
d
-
p
r
ic
e
m
ea
ls
,
as
well
as
m
ar
k
er
s
f
o
r
titl
e
I
,
ch
ar
ter
,
o
r
m
a
g
n
et
s
ch
o
o
ls
.
T
h
e
NC
E
S
an
d
th
e
Nig
e
r
ian
Dep
ar
tm
en
t
o
f
E
d
u
ca
tio
n
p
r
o
v
id
ed
th
e
d
ata.
3
.
3
.
Ana
ly
s
is
T
h
e
s
tu
d
y
an
aly
ze
d
th
e
a
p
p
li
ca
tio
n
an
d
im
p
ac
t
o
f
AN
ac
r
o
s
s
v
ar
io
u
s
s
ch
o
o
l
s
ettin
g
s
.
Fo
r
RQ
1
,
f
r
eq
u
e
n
cy
co
u
n
ts
r
ev
ea
led
d
iv
er
s
e
AN
u
s
ag
e
am
o
n
g
tea
ch
er
s
,
with
in
s
tr
u
ctio
n
al
v
id
eo
s
an
d
in
d
iv
id
u
al
ass
ig
n
m
en
ts
b
ein
g
t
h
e
m
o
s
t
co
m
m
o
n
.
Op
e
n
-
en
d
e
d
r
esp
o
n
s
es
wer
e
an
aly
ze
d
to
u
n
d
e
r
s
tan
d
th
e
ty
p
es
o
f
in
s
tr
u
ctio
n
al
m
eth
o
d
s
,
c
o
n
f
ir
m
in
g
th
at
teac
h
er
s
f
r
eq
u
e
n
tly
em
p
lo
y
ed
a
“
s
cr
ee
n
-
ce
n
te
r
e
d
”
o
r
ch
estra
tio
n
t
o
r
ein
f
o
r
ce
al
g
eb
r
a
c
o
n
ce
p
ts
.
Fo
r
R
Q2
,
t
h
e
s
t
u
d
y
e
x
a
m
i
n
e
d
h
o
w
AN
u
s
e
i
n
d
ica
to
r
r
el
ate
d
to
al
g
eb
r
a
E
OC
p
ass
r
a
tes
,
in
c
o
r
p
o
r
at
in
g
a
r
eg
r
ess
io
n
a
n
al
y
s
is
wi
th
v
a
r
ia
b
l
es
s
u
c
h
as
t
ea
ch
er
u
s
ag
e,
t
r
a
in
in
g
,
a
n
d
w
o
r
k
b
o
o
k
o
r
d
e
r
s
.
A
lat
e
n
t
p
r
o
f
il
e
an
al
y
s
is
(
L
PA
)
g
r
o
u
p
ed
s
ch
o
o
ls
b
as
ed
o
n
s
i
x
AN
u
s
a
g
e
i
n
d
i
ca
t
o
r
-
s
t
u
d
e
n
t
l
o
g
i
n
s
,
v
i
d
eo
v
i
e
ws,
a
n
d
wo
r
k
b
o
o
k
r
at
io
s
,
a
m
o
n
g
o
t
h
e
r
s
—
t
o
i
d
e
n
tif
y
u
s
a
g
e
p
at
te
r
n
s
an
d
t
h
e
ir
i
m
p
ac
t
o
n
p
ass
r
ates
.
R
es
u
lts
s
h
o
we
d
t
h
at
s
ch
o
o
ls
wit
h
h
i
g
h
e
r
A
N
en
g
ag
em
e
n
t
te
n
d
e
d
to
h
a
v
e
b
ett
e
r
p
ass
r
at
es
o
n
t
h
e
A
lg
e
b
r
a
I
E
OC
ass
ess
m
en
t
.
I
n
ad
d
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an
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tm
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Ab
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4
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p
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RE
SU
L
T
S AN
D
D
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SCU
SS
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h
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s
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RQ
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in
d
icate
d
th
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u
ca
t
o
r
s
em
p
lo
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all
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ac
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o
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AI
in
d
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s
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m
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n
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to
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T
h
e
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6
%
o
f
ed
u
ca
to
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s
in
d
icate
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in
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
2
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8
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I
n
t
J
E
v
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&
R
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d
u
c
,
Vo
l
.
14
,
No
.
6
,
Dec
em
b
er
20
25
:
4
4
4
3
-
4
4
5
5
4448
class
r
o
o
m
at
least
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iwee
k
ly
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wh
ile
5
6
%
r
ep
o
r
ted
p
r
esen
tin
g
in
s
tr
u
ctiv
e
f
ilm
s
to
th
eir
s
tu
d
en
ts
at
least
wee
k
ly
.
E
d
u
ca
to
r
s
v
alu
ed
th
e
a
d
ap
tab
ilit
y
o
f
f
er
e
d
b
y
AN,
en
ab
lin
g
th
em
t
o
“
p
lay
a
v
id
e
o
a
n
d
c
ir
cu
late
with
in
th
e
class
r
o
o
m
”
o
r
“
p
a
u
s
e
it
f
o
r
m
ath
em
atica
l
d
is
cu
s
s
io
n
s
.
”
T
h
e
f
ilm
s
p
r
o
v
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d
ed
ex
p
licit
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d
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cc
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ct
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am
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les,
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d
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r
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tice
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alg
e
b
r
aic
to
p
ics.
E
d
u
ca
to
r
s
v
alu
ed
th
e
f
lex
ib
ilit
y
o
f
f
er
ed
b
y
AN,
en
ab
lin
g
th
e
m
to
“
p
lay
a
v
id
eo
an
d
cir
cu
la
te
ar
o
u
n
d
th
e
class
r
o
o
m
”
o
r
“
p
au
s
e
it
f
o
r
m
at
h
em
atica
l
d
is
cu
s
s
io
n
s
.
”
T
h
ey
ass
u
m
ed
th
e
f
ilm
s
wo
u
ld
s
er
v
e
as
a
g
o
o
d
b
eg
in
n
in
g
p
o
in
t
f
o
r
teac
h
in
g
t
h
e
co
n
ten
t
in
th
eir
o
wn
ter
m
s
.
Ma
n
y
teac
h
er
s
wer
e
s
u
r
e
th
at
v
iewin
g
th
e
f
ilm
s
wo
u
ld
s
er
v
e
as
an
ex
ce
llen
t
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eg
in
n
in
g
p
o
in
t
f
o
r
d
eliv
er
in
g
t
h
e
co
n
ten
t
in
th
eir
o
wn
ter
m
s
.
Ad
d
itio
n
ally
,
6
0
%
o
f
teac
h
er
s
r
ep
o
r
ted
p
r
o
v
i
d
in
g
h
o
m
ewo
r
k
wh
er
e
s
tu
d
en
ts
wo
r
k
ed
i
n
d
ep
e
n
d
en
tly
o
n
th
e
AN
web
s
ite
d
u
r
in
g
class
.
T
h
e
7
9
%
o
f
teac
h
e
r
s
ask
ed
s
tu
d
e
n
ts
to
lo
g
o
n
to
AN
u
s
in
g
class
r
o
o
m
PC
s
,
h
o
wev
er
o
th
er
d
ev
ices
s
u
ch
as
tab
lets
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ce
ll
p
h
o
n
es,
an
d
co
m
p
u
ter
lab
o
r
ato
r
ies
wer
e
also
em
p
lo
y
ed
.
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ea
c
h
er
s
co
m
m
en
ted
th
at
u
s
in
g
th
e
AN
p
latf
o
r
m
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elp
ed
s
u
p
p
o
r
t
s
tu
d
e
n
t
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ce
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ter
e
d
,
m
o
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ied
class
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lear
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g
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la
n
s
th
at
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etter
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it
a
wo
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k
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a
n
d
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n
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g
ap
p
r
o
ac
h
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h
ey
u
n
d
e
r
lin
ed
th
e
n
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ity
o
f
p
u
p
ils
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ab
le
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wo
r
k
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ep
en
d
en
tly
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t
h
e
in
s
tr
u
cto
r
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m
o
v
e
ar
o
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n
d
th
e
r
o
o
m
to
ch
ec
k
f
o
r
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n
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er
s
tan
d
in
g
.
”
T
h
e
3
4
%
o
f
in
s
tr
u
cto
r
s
r
e
p
o
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te
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ettin
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ter
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N,
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v
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io
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o
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th
e
wo
r
k
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b
y
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tr
ateg
y
.
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d
u
ca
to
r
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ca
n
s
ee
s
tu
d
e
n
ts
u
s
in
g
th
e
AN
p
latf
o
r
m
to
wo
r
k
alo
n
e
o
r
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s
m
all
g
r
o
u
p
s
th
a
n
k
s
to
t
h
is
s
y
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tem
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d
itio
n
ally
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ac
co
r
d
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g
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th
e
s
u
r
v
ey
,
5
6
% o
f
teac
h
er
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ass
ig
n
ed
AN
f
ilm
s
as h
o
m
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to
s
tu
d
en
ts
wh
o
wer
e
at
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g
e
r
o
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f
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eh
in
d
,
a
n
d
7
9
%
o
f
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h
er
s
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s
ed
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as
a
r
em
e
d
iatio
n
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o
o
l.
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o
th
e
r
s
u
cc
ess
f
u
l
m
eth
o
d
was a
r
r
an
g
in
g
t
u
to
r
in
g
s
ess
io
n
s
b
ef
o
r
e
o
r
af
ter
s
ch
o
o
l u
tili
zin
g
AN
as a
r
eso
u
r
ce
.
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h
e
v
ar
ia
b
les
ex
p
lain
ed
6
6
.
1
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th
e
v
ar
iatio
n
in
th
e
p
r
o
p
o
r
tio
n
o
f
s
tu
d
en
ts
wh
o
p
ass
ed
th
e
Alg
eb
r
a
I
E
OC
in
th
e
2
0
1
3
–
2
0
1
4
ac
ad
e
m
ic
y
ea
r
,
ac
co
r
d
in
g
to
th
e
s
ch
o
o
l
-
lev
el
m
u
ltip
l
e
r
eg
r
ess
io
n
r
esu
lts
f
r
o
m
t
h
e
p
r
elim
in
ar
y
a
n
aly
s
is
o
f
RQ
2
.
Sch
o
o
ls
with
alg
eb
r
a
teac
h
er
s
wh
o
b
o
u
g
h
t
w
o
r
k
b
o
o
k
s
h
a
d
a
6
.
7
8
%
g
r
ea
ter
p
ass
in
g
r
ate
th
an
th
o
s
e
with
o
u
t.
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o
v
er
v
iew
o
f
th
e
k
ey
f
ac
to
r
s
af
f
ec
tin
g
th
e
Alg
eb
r
a
I
E
OC
s
u
cc
ess
r
ates is g
iv
en
in
T
ab
le
2
.
T
ab
le
3
s
h
o
ws
th
e
k
e
y
v
ar
ia
b
les
in
f
lu
en
ci
n
g
Alg
eb
r
a
I
E
OC
p
ass
in
g
r
ates
in
th
e
s
p
r
in
g
o
f
2
0
1
4
.
Prio
r
p
ass
in
g
r
ates
h
ad
a
s
ig
n
i
f
ican
t
im
p
ac
t,
with
th
e
2
0
1
3
p
ass
in
g
r
ate
(
β=0
.
5
9
6
,
p
<0
.
0
0
1
)
b
ein
g
a
s
tr
o
n
g
e
r
p
r
ed
icto
r
t
h
an
th
e
2
0
1
2
p
ass
in
g
r
ate
(
β=0
.
1
2
8
,
p
=
0
.
0
0
2
)
.
W
o
r
k
b
o
o
k
s
ac
ce
s
s
ib
ilit
y
also
p
o
s
itiv
ely
in
f
lu
e
n
ce
d
p
ass
in
g
r
ates
(
β=5
.
8
8
4
,
p
=0
.
0
2
7
)
,
as
d
id
th
e
p
r
esen
ce
o
f
tr
ain
ed
teac
h
er
s
p
ar
ticip
atin
g
in
T
YP
ch
allen
g
es
(
β=0
.
0
0
8
,
p
=
0
.
0
3
3
)
.
Ad
d
itio
n
ally
,
AN
-
in
teg
r
ated
s
ch
o
o
ls
with
tr
ain
ed
teac
h
er
s
s
aw
a
n
o
tab
le
in
cr
ea
s
e
in
p
ass
in
g
r
ates
(
β=4
.
2
5
1
,
p
=0
.
0
1
4
)
.
Ho
wev
er
,
a
lar
g
er
s
tu
d
e
n
t
p
o
p
u
latio
n
n
eg
ativ
el
y
im
p
ac
ted
p
ass
in
g
r
ates
(
β=
-
0
.
0
1
0
,
p
=
0
.
0
2
4
)
,
s
u
g
g
esti
n
g
th
at
r
eso
u
r
ce
allo
ca
tio
n
m
i
g
h
t c
o
n
tr
i
b
u
te
to
th
e
s
u
cc
ess
o
f
s
tu
d
en
ts
.
T
h
e
an
aly
s
is
p
r
o
ce
ed
ed
in
th
r
ee
s
tep
s
.
First,
th
e
o
p
tim
al
n
u
m
b
er
o
f
laten
t
class
es
was
d
eter
m
in
ed
th
r
o
u
g
h
m
o
d
el
f
it
in
d
ices.
T
h
en
,
t
h
e
d
is
tr
ib
u
tio
n
o
f
s
ch
o
o
ls
ac
r
o
s
s
th
ese
class
es
an
d
th
e
class
if
icatio
n
p
r
o
b
a
b
ilit
ies
wer
e
ca
lcu
lated
.
Fin
ally
,
d
if
f
er
e
n
ce
s
in
r
ates
o
f
p
ass
in
g
th
e
Alg
eb
r
a
I
E
O
C
ex
am
ac
r
o
s
s
th
e
class
es
wer
e
as
s
es
s
ed
.
T
ab
le
4
d
is
p
lay
s
th
e
f
it
in
d
ices
u
s
ed
,
co
m
p
ar
in
g
2
,
3
-
,
an
d
4
-
class
m
o
d
els.
Giv
en
th
e
r
ejec
tio
n
o
f
th
e
4
-
class
m
o
d
el
b
y
th
e
L
MR
test
an
d
m
in
im
al
v
ar
iatio
n
in
f
it
in
d
ices,
t
h
e
3
-
class
m
o
d
el
was
s
elec
ted
f
o
r
d
etailed
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n
aly
s
is
.
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ab
le
2
.
A
s
u
m
m
a
r
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o
f
th
e
im
p
o
r
tan
t f
ac
t
o
r
s
af
f
ec
tin
g
th
e
A
lg
eb
r
a
I
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OC
s
u
cc
ess
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ates
V
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a
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ith
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r
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ates
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ates a
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er
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2
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ar
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d
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Alg
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Acc
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if
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t a
n
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ca
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lly
r
elev
an
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
2
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8
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I
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t
J
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Vo
l
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14
,
No
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6
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Dec
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b
er
20
25
:
4
4
4
3
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4450
Fig
u
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Me
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ates f
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iated
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ical
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h
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f
in
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s
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o
n
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ate
th
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t
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er
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o
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a
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t
in
an
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;
r
ath
er
,
it
is
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s
tr
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o
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d
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atio
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f
tech
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an
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at
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s
u
b
s
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tial le
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g
im
p
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o
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em
en
ts
.
On
e
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th
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t
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o
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en
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aid
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er
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n
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i
n
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id
u
a
lized
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g
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h
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is
s
u
p
p
o
r
ted
b
y
th
e
NC
T
M
f
r
am
e
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r
k
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h
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iews
tech
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n
ec
ess
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et
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o
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g
au
x
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e
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E
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u
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o
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ically
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le,
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o
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g
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o
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en
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ce
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r
e
d
(
e.
g
.
,
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id
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walk
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t
h
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g
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s
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d
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ce
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ter
ed
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g
.
,
ex
p
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an
d
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d
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s
ex
er
cises
)
ap
p
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ac
h
es
in
AN
i
n
teg
r
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n
.
T
h
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u
al
ap
p
r
o
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ch
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ig
h
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h
t
th
e
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ad
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e
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o
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m
ee
t d
iv
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s
e
lear
n
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g
s
ty
les an
d
s
k
ill lev
els.
T
h
e
r
esear
ch
r
esu
lts
p
er
s
is
t
in
d
em
o
n
s
tr
atin
g
th
e
w
o
r
th
o
f
s
tr
u
ctu
r
ed
tec
h
n
o
lo
g
y
u
s
e
in
m
a
th
em
atics
ed
u
ca
tio
n
.
T
h
at
AN
en
g
ag
e
m
en
t
an
d
Alg
eb
r
a
I
E
OC
s
co
r
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ar
e
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o
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itiv
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ea
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th
at
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eg
u
lar
,
g
u
id
ed
in
ter
ac
tio
n
with
th
e
p
latf
o
r
m
—
r
at
h
er
th
a
n
in
ci
d
en
tal
o
r
u
n
s
tr
u
ct
u
r
ed
u
s
ag
e
—
is
th
e
p
ath
to
m
ax
im
izin
g
lear
n
i
n
g
o
u
tco
m
e
s
.
Sch
o
o
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at
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ev
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ed
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lar
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g
ag
e
m
en
t
with
AN
th
r
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g
h
s
tu
d
e
n
t
lo
g
in
s
,
v
id
eo
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ar
ticip
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n
,
an
d
p
r
o
f
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n
al
teac
h
er
tr
ain
in
g
r
ep
o
r
ted
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ass
r
ates
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n
s
id
e
r
ab
ly
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ig
h
er
.
T
h
is
co
r
r
o
b
o
r
ates
th
e
co
n
ten
tio
n
th
at
well
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s
u
p
p
o
r
ted
,
s
u
s
tain
a
b
le
tech
n
o
lo
g
y
in
teg
r
atio
n
l
ea
d
s
to
im
p
r
o
v
ed
p
er
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o
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m
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ce
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h
o
in
g
ev
id
en
c
e
in
d
ig
ital le
ar
n
in
g
[
1
2
]
,
[
2
9
]
,
[
4
3
]
–
[
4
8
]
.
On
e
o
f
th
e
g
r
ea
test
co
n
tr
ib
u
tio
n
s
o
f
t
h
is
s
tu
d
y
is
ar
g
u
ab
l
y
its
r
ea
f
f
ir
m
ati
o
n
o
f
th
e
ir
r
e
p
lace
ab
le
v
alu
e
th
at
teac
h
er
s
b
r
in
g
to
d
ig
ital
lear
n
in
g
en
v
i
r
o
n
m
e
n
ts
.
T
h
e
r
e
s
u
lts
co
n
f
ir
m
th
at
tec
h
n
o
lo
g
y
alo
n
e
is
in
s
u
f
f
icien
t
to
s
p
u
r
s
tu
d
en
t
ac
h
iev
em
e
n
t
—
it
m
u
s
t
b
e
s
itu
ated
with
i
n
th
e
f
r
am
ew
o
r
k
o
f
o
r
g
an
iz
ed
,
r
esear
c
h
-
d
r
i
v
en
p
ed
ag
o
g
ical
p
r
ac
tice.
Sch
o
o
l
s
with
h
ig
h
teac
h
er
en
g
a
g
e
m
en
t
in
AN
r
ep
o
r
ted
b
etter
s
tu
d
en
t
o
u
tco
m
e,
em
p
h
asizin
g
th
e
im
p
o
r
tan
ce
o
f
teac
h
er
ag
en
cy
in
lear
n
in
g
.
T
h
is
is
co
r
r
o
b
o
r
ated
b
y
th
e
in
s
tr
u
m
en
tal
o
r
ch
estra
tio
n
th
eo
r
y
,
wh
ich
p
u
r
p
o
r
ts
th
at
tech
n
o
lo
g
y
is
m
o
s
t
ef
f
ec
tiv
e
wh
e
n
p
u
r
p
o
s
iv
ely
d
esi
g
n
e
d
an
d
l
e
d
b
y
ed
u
ca
to
r
s
[
4
9
]
–
[
5
2
]
.
Mo
v
in
g
b
ey
o
n
d
p
ass
iv
e
lear
n
er
in
ter
a
ctio
n
with
d
ig
ital
tech
n
o
lo
g
y
,
th
is
s
tu
d
y
s
u
g
g
ests
th
at
m
ath
em
atics
ed
u
ca
to
r
s
n
e
ed
to
b
e
d
ig
ital
lear
n
i
n
g
ar
c
h
itects,
d
esig
n
in
g
p
u
r
p
o
s
ef
u
l
an
d
d
y
n
am
ic
lear
n
in
g
ex
p
er
ien
ce
s
r
ath
e
r
th
an
m
er
el
y
o
f
f
e
r
in
g
ac
ce
s
s
to
tech
n
o
lo
g
y
.
Fu
r
th
er
m
o
r
e
,
th
e
s
tu
d
y
ex
t
en
d
s
ex
is
tin
g
tech
n
o
lo
g
y
a
cc
ep
tan
ce
m
o
d
el
(
T
AM
)
r
e
s
ea
r
ch
b
y
d
em
o
n
s
tr
atin
g
th
at
teac
h
er
b
elief
s
,
d
ig
ital
s
elf
-
ef
f
icac
y
,
an
d
p
r
o
f
ess
io
n
al
d
ev
elo
p
m
en
t
af
f
ec
t
n
o
t
o
n
ly
teac
h
er
s
’
ad
o
p
tio
n
o
f
tech
n
o
l
o
g
y
b
u
t
also
s
tu
d
en
t
lear
n
in
g
o
u
tco
m
es
an
d
en
g
ag
em
en
t.
T
h
is
f
in
d
in
g
s
u
p
p
o
r
ts
Salam
i
an
d
Sp
an
g
en
b
er
g
[
5
3
]
,
wh
o
p
r
o
p
o
s
ed
th
at
p
er
c
eiv
ed
u
s
ef
u
ln
ess
an
d
s
im
p
li
city
o
f
u
s
e
im
p
ac
t
tech
n
o
lo
g
y
ad
o
p
tio
n
.
Mo
r
e
r
e
ce
n
t
s
tu
d
ies
[
5
4
]
,
[
5
5
]
h
av
e
r
e
in
f
o
r
ce
d
th
at
teac
h
e
r
s
’
s
elf
-
ef
f
icac
y
an
d
attitu
d
es
to
war
d
tech
n
o
lo
g
y
s
ig
n
if
ican
tl
y
im
p
ac
t th
eir
willin
g
n
ess
to
in
teg
r
ate
d
ig
ital to
o
ls
in
to
class
r
o
o
m
in
s
tr
u
ctio
n
.
T
h
is
b
r
in
g
s
n
ew
o
p
p
o
r
tu
n
ities
to
in
v
esti
g
ate
th
e
im
p
ac
t
o
f
teac
h
er
s
’
attitu
d
es,
co
n
f
i
d
en
ce
,
an
d
p
r
o
f
ess
io
n
al
d
ev
el
o
p
m
en
t
e
x
p
er
ien
ce
s
o
n
th
e
e
f
f
icac
y
o
f
d
ig
ital
tech
n
o
lo
g
y
in
m
ath
e
m
atics
in
s
tr
u
ctio
n
.
Un
d
er
s
tan
d
in
g
th
ese
asp
ec
ts
ca
n
h
elp
to
d
esig
n
m
o
r
e
tar
g
et
ed
p
r
o
f
ess
io
n
al
d
ev
elo
p
m
en
t
ac
tiv
ities
,
r
esu
ltin
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
E
va
lu
a
tin
g
m
a
th
ema
tics
tea
ch
ers
’
u
s
a
g
e
o
f o
n
lin
e
t
o
o
ls
to
e
n
h
a
n
ce
lea
r
n
in
g
…
(
Ola
ju
mo
k
e
Ola
ye
mi
S
a
la
mi
)
4451
in
m
o
r
e
s
u
cc
ess
f
u
l
tech
n
o
lo
g
y
-
en
h
a
n
ce
d
p
e
d
ag
o
g
y
.
I
n
ter
m
s
o
f
eq
u
ity
,
th
is
s
tu
d
y
also
r
ec
o
g
n
izes
d
ig
ital
ac
ce
s
s
d
is
p
ar
ities
as
a
p
r
ed
icto
r
o
f
lear
n
i
n
g
o
u
tco
m
es.
Alth
o
u
g
h
tech
n
o
lo
g
y
ca
n
p
o
ten
tially
eq
u
alize
ed
u
ca
tio
n
d
is
p
ar
ities
,
v
ar
iatio
n
in
AN
u
s
e
b
etwe
en
s
ch
o
o
l
s
in
d
icate
s
th
at
d
i
g
ital
eq
u
ity
ch
allen
g
es
p
er
s
is
t.
C
o
n
ce
r
n
s
o
f
d
ev
ice
av
ailab
ilit
y
,
in
ter
n
et
ac
ce
s
s
ib
ilit
y
,
an
d
th
e
s
u
p
p
o
r
t
p
r
o
v
id
e
d
b
y
in
s
titu
tio
n
s
h
av
e
a
m
ajo
r
im
p
ac
t
o
n
h
o
w
ef
f
ec
tiv
el
y
s
t
u
d
en
ts
r
ea
ct
to
o
n
lin
e
lea
r
n
in
g
p
latf
o
r
m
s
.
Ad
d
r
ess
in
g
s
u
ch
d
is
p
ar
ities
th
r
o
u
g
h
tar
g
eted
in
ter
v
e
n
tio
n
s
—
s
u
ch
as
s
u
b
s
id
ized
ac
ce
s
s
to
tech
n
o
lo
g
y
,
d
ig
ital
liter
ac
y
tr
ain
in
g
,
an
d
p
r
o
f
ess
io
n
al
teac
h
er
d
ev
el
o
p
m
en
t
co
u
ld
e
n
s
u
r
e
th
at
all
s
tu
d
en
ts
h
a
v
e
th
e
o
p
p
o
r
tu
n
ity
to
b
en
ef
it
f
r
o
m
d
ig
ital
lear
n
i
n
g
in
n
o
v
atio
n
s
r
eg
ar
d
less
o
f
s
o
ci
o
ec
o
n
o
m
ic
s
tatu
s
.
Ov
er
all,
th
is
s
tu
d
y
n
o
t
o
n
ly
c
o
n
f
ir
m
s
th
e
p
r
o
m
is
e
o
f
b
len
d
ed
lear
n
in
g
a
p
p
r
o
ac
h
es
to
m
a
th
em
atics
ed
u
ca
tio
n
b
u
t
also
y
ield
s
n
ew
in
s
ig
h
ts
in
to
th
e
cir
c
u
m
s
tan
ce
s
u
n
d
er
wh
ich
d
i
g
ital
to
o
ls
ca
n
b
e
m
ad
e
to
ad
d
u
p
to
m
ea
s
u
r
ab
le
ac
ad
em
ic
g
ain
s
.
On
g
o
in
g
r
esear
ch
n
ee
d
s
to
co
n
tin
u
e
in
v
esti
g
atin
g
o
p
tim
u
m
d
i
g
ital
lear
n
in
g
m
eth
o
d
s
,
teac
h
er
tr
ain
in
g
m
o
d
els,
an
d
th
e
lo
n
g
-
ter
m
im
p
a
ct
o
f
p
lan
n
ed
tech
n
o
lo
g
y
in
te
g
r
atio
n
o
n
s
tu
d
e
n
t
ac
h
iev
em
en
t.
B
y
o
n
g
o
in
g
r
ef
i
n
em
en
t
o
f
th
e
p
ed
a
g
o
g
ical
m
o
d
els
f
o
r
o
n
lin
e
lear
n
in
g
,
we
ca
n
ac
h
iev
e
th
e
f
u
ll
p
o
ten
tial o
f
tech
n
o
lo
g
y
to
f
ac
i
litate
eq
u
itab
le
an
d
ef
f
ec
tiv
e
m
ath
in
s
tr
u
ctio
n
.
W
h
ile
th
e
p
r
o
m
is
in
g
f
in
d
in
g
s
,
th
is
s
tu
d
y
h
as
s
o
m
e
lim
itati
o
n
s
th
at
n
ee
d
to
b
e
ad
d
r
ess
ed
th
r
o
u
g
h
s
u
b
s
eq
u
en
t
r
esear
ch
.
First,
wh
ile
th
e
s
tu
d
y
ass
ess
ed
AN
’
s
i
m
p
ac
t
at
s
ch
o
o
l
lev
el,
th
e
s
tu
d
y
d
id
n
o
t
in
v
esti
g
ate
in
d
iv
id
u
al
lear
n
er
s
’
p
er
f
o
r
m
a
n
ce
in
d
ep
th
.
I
t
w
o
u
ld
b
e
h
elp
f
u
l
t
o
h
a
v
e
m
o
r
e
p
r
ec
is
e
an
aly
s
is
th
r
o
u
g
h
s
tu
d
en
t
-
lev
el
d
ata
to
m
ak
e
a
n
ev
e
n
s
tr
o
n
g
er
r
elatio
n
s
h
ip
b
etwe
en
th
e
u
tili
za
tio
n
o
f
AN
an
d
in
d
iv
id
u
al
lear
n
in
g
p
r
o
ce
s
s
es.
Ad
d
itio
n
ally
,
wh
ile
s
o
cio
ec
o
n
o
m
ic
f
ac
to
r
s
wer
e
co
n
s
id
er
ed
,
th
e
ex
ten
t
to
wh
ich
ec
o
n
o
m
ic
d
is
p
ar
ities
im
p
ac
t
tech
n
o
lo
g
y
u
p
tak
e
r
em
ai
n
s
o
p
e
n
t
o
q
u
e
s
tio
n
.
Mo
r
e
r
ef
in
e
d
a
n
aly
s
is
with
v
ar
iab
les
lik
e
h
o
u
s
eh
o
ld
in
c
o
m
e,
h
ig
h
-
s
p
ee
d
in
ter
n
et
ac
ce
s
s
,
an
d
p
ar
en
tal
s
u
p
p
o
r
t
wo
u
ld
b
e
m
o
r
e
co
m
p
r
eh
en
s
iv
e
r
eg
ar
d
i
n
g
d
ig
ital e
q
u
ity
is
s
u
es.
An
o
th
er
m
ain
lim
itatio
n
is
th
at
th
er
e
is
n
o
in
-
d
e
p
th
d
is
c
u
s
s
io
n
o
f
h
o
w
d
if
f
e
r
en
t
teac
h
in
g
s
ty
les
in
f
lu
en
ce
s
tu
d
en
t p
er
f
o
r
m
an
ce
in
u
s
in
g
AN.
W
h
ile
th
is
s
tu
d
y
ac
k
n
o
wled
g
es
th
e
wo
r
t
h
o
f
s
t
u
d
en
t
-
in
itiated
an
d
teac
h
er
-
in
itiated
ap
p
r
o
ac
h
es,
f
u
tu
r
e
r
esear
ch
m
u
s
t
ex
am
i
n
e
wh
at
i
n
s
tr
u
ctio
n
al
m
et
h
o
d
s
wo
r
k
b
est
with
d
if
f
er
en
t
g
r
o
u
p
s
o
f
s
tu
d
en
ts
.
Fo
r
in
s
tan
ce
,
l
o
n
g
itu
d
in
al
e
x
am
in
atio
n
s
o
f
th
e
ef
f
ec
ts
o
f
d
aily
,
wee
k
ly
,
a
n
d
last
-
m
in
u
te
AN
p
ar
ticip
atio
n
m
ay
r
e
v
ea
l
o
p
tim
al
p
atter
n
s
o
f
u
s
e.
I
n
t
u
r
n
,
co
m
p
ar
in
g
s
tu
d
en
t
ac
h
iev
em
e
n
t
in
v
ar
y
in
g
in
s
tr
u
ctio
n
f
o
r
m
ats
—
f
lip
p
ed
class
r
o
o
m
s
v
er
s
u
s
tr
ad
itio
n
al
lectu
r
e
-
b
ased
i
n
s
tr
u
ctio
n
—
wo
u
ld
h
elp
f
u
r
th
er
cla
r
if
y
b
est p
r
ac
tices f
o
r
in
teg
r
atin
g
d
ig
ital to
o
ls
in
to
m
ath
in
s
tr
u
ctio
n
.
Fu
r
th
er
m
o
r
e
,
th
e
s
tu
d
y
em
p
h
a
s
izes
th
e
im
p
o
r
tan
ce
o
f
teac
h
er
p
r
o
f
ess
io
n
al
d
ev
elo
p
m
en
t
f
o
r
ef
f
ec
tiv
e
AN
im
p
lem
en
tatio
n
.
Ad
d
itio
n
al
r
esear
ch
,
h
o
wev
er
,
is
n
ec
ess
ar
y
to
lear
n
ab
o
u
t
th
e
im
p
ac
t
o
f
v
ar
io
u
s
tr
ain
in
g
m
o
d
els
o
n
teac
h
er
s
’
s
u
s
tain
ed
u
s
e
o
f
tech
n
o
lo
g
y
in
th
e
lo
n
g
ter
m
.
E
x
p
er
im
e
n
tal
s
tu
d
ies
co
m
p
ar
in
g
d
if
f
e
r
en
t
p
r
o
f
ess
io
n
al
d
ev
elo
p
m
en
t
m
e
th
o
d
s
—
wo
r
k
s
h
o
p
s
,
p
ee
r
m
e
n
to
r
in
g
,
an
d
co
n
tin
u
o
u
s
co
ac
h
in
g
—
wo
u
ld
clar
if
y
th
e
m
eth
o
d
s
th
at
p
r
o
d
u
c
e
t
h
e
m
o
s
t
p
o
ten
t
im
p
r
o
v
e
m
en
ts
in
in
co
r
p
o
r
atin
g
d
ig
ital
t
o
o
ls
.
Ad
d
itio
n
ally
,
q
u
alitativ
e
class
r
o
o
m
o
b
s
er
v
at
io
n
an
d
teac
h
e
r
in
ter
v
iew
s
tu
d
ies
wo
u
ld
o
f
f
er
a
n
in
-
d
e
p
th
ex
am
in
atio
n
o
f
h
o
w
in
s
tr
u
cto
r
s
m
an
ag
e
tec
h
n
o
lo
g
i
ca
l im
p
lem
en
tatio
n
an
d
m
o
d
if
y
in
s
tr
u
ctio
n
with
e
x
p
er
ien
ce
.
Po
licy
-
wis
e,
th
is
s
tu
d
y
em
p
h
a
s
izes
th
e
n
ee
d
f
o
r
s
tr
ateg
ic
i
n
ter
v
en
tio
n
s
to
m
itig
ate
th
e
d
ig
i
tal
d
iv
id
e.
As
in
eq
u
ality
in
AN
u
s
e
was
o
b
s
er
v
ed
am
o
n
g
s
ch
o
o
ls
,
p
o
licy
m
ak
er
s
m
u
s
t
in
v
est
in
in
f
r
astru
ctu
r
e,
p
ar
ticu
lar
ly
i
n
u
n
d
er
p
r
iv
ileg
e
d
ar
ea
s
.
Dev
ice
an
d
h
ig
h
-
s
p
e
ed
in
ter
n
et
ac
ce
s
s
m
u
s
t
b
e
in
cr
ea
s
ed
,
b
u
t
s
o
m
u
s
t
teac
h
er
p
r
e
p
ar
atio
n
t
o
in
co
r
p
o
r
ate
th
ese
r
eso
u
r
ce
s
o
p
tim
al
ly
.
Su
b
s
eq
u
en
t
r
esear
ch
n
ee
d
s
to
ex
am
in
e
h
o
w
g
o
v
er
n
m
en
t a
n
d
d
is
tr
ict
-
lev
el
in
itiativ
es c
an
r
esp
o
n
d
to
d
ig
it
al
d
is
p
ar
ities
an
d
im
p
r
o
v
e
lear
n
in
g
o
u
tco
m
es.
At
a
th
eo
r
etica
l
le
v
el,
th
e
s
tu
d
y
co
r
r
o
b
o
r
ates
in
s
tr
u
m
en
tal
o
r
ch
estra
tio
n
th
eo
r
y
b
y
d
em
o
n
s
tr
atin
g
th
at
th
e
ef
f
ec
tiv
en
ess
o
f
tech
n
o
lo
g
y
d
ep
en
d
s
o
n
h
o
w
it
is
in
co
r
p
o
r
ate
d
in
to
lear
n
in
g
ac
tiv
ities
.
T
h
e
f
in
d
in
g
s
d
em
o
n
s
tr
ate
th
at
s
y
s
tem
atic
an
d
d
ir
ec
ted
u
s
e
o
f
co
m
p
u
ter
t
o
o
ls
,
an
d
n
o
t
p
ass
iv
e
s
tu
d
en
t
p
ar
ticip
atio
n
,
y
iel
d
th
e
b
est
r
esu
lts
.
T
h
i
s
b
ea
r
s
c
o
n
s
tr
u
ctiv
is
t
lear
n
in
g
th
eo
r
ies
im
p
licatio
n
s
in
th
at
it
illu
s
tr
ates
th
at
tech
n
o
lo
g
y
s
h
o
u
ld
b
e
e
m
p
lo
y
e
d
as a
to
o
l
f
o
r
ac
tiv
e
lear
n
i
n
g
r
at
h
er
th
an
c
o
n
ten
t tr
an
s
f
er
.
I
n
s
u
m
m
ar
y
,
alth
o
u
g
h
th
is
r
es
ea
r
ch
v
e
r
if
ies
th
e
ad
v
an
tag
eo
u
s
ef
f
ec
t
o
f
AN
o
n
s
tu
d
e
n
ts
’
p
e
r
f
o
r
m
a
n
ce
in
Alg
eb
r
a
I
,
m
o
r
e
p
r
ac
tical
im
p
licatio
n
s
ca
n
b
e
u
n
co
v
e
r
ed
th
r
o
u
g
h
d
ee
p
er
ex
p
lo
r
ati
o
n
o
f
its
f
in
d
in
g
s
.
Su
b
s
eq
u
en
t r
esear
ch
m
u
s
t a
im
at
r
ef
in
in
g
d
ig
ital in
teg
r
atio
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ap
p
r
o
ac
h
es,
in
v
esti
g
atin
g
m
o
s
t e
f
f
ec
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teac
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in
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m
o
d
els,
an
d
c
o
n
f
r
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n
tin
g
s
tr
u
ctu
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al
in
eq
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alities
th
at
af
f
ec
t
tech
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y
ad
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p
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in
s
ch
o
o
ls
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I
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th
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d
p
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licy
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ak
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ca
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tim
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web
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5.
I
M
P
L
I
CA
T
I
O
N
S O
F
F
I
NDI
NG
AND
F
UT
UR
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DI
RE
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T
h
e
f
in
d
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o
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th
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tu
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y
p
r
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id
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s
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m
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cr
u
cial
in
s
ig
h
ts
f
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m
ath
em
atics
in
s
tr
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ctio
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,
e
s
p
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in
r
elatio
n
to
th
e
in
teg
r
atio
n
o
f
tech
n
o
lo
g
y
-
b
ased
lear
n
in
g
to
o
ls
.
On
e
n
o
tab
le
im
p
licatio
n
is
th
e
n
ee
d
f
o
r
s
tr
ateg
ic
tech
n
o
lo
g
y
i
n
teg
r
ati
o
n
.
T
h
e
r
esu
lts
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f
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ce
th
at
to
o
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s
u
ch
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ld
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p
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tar
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aid
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ath
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an
as
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ep
lace
m
en
ts
f
o
r
tr
ad
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al
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n
s
tr
u
ctio
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.
E
f
f
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tiv
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in
te
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ch
to
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eq
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h
,
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s
u
r
in
g
th
at
tech
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o
lo
g
y
is
alig
n
ed
with
clea
r
p
ed
ag
o
g
ical
g
o
als.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
2
5
2
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8
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I
n
t
J
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&
R
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Vo
l
.
14
,
No
.
6
,
Dec
em
b
er
20
25
:
4
4
4
3
-
4
4
5
5
4452
Sch
o
o
ls
m
u
s
t
th
er
ef
o
r
e
b
e
d
elib
er
ate
in
em
b
ed
d
in
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th
e
s
e
to
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with
in
well
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th
o
u
g
h
t
-
o
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t
in
s
tr
u
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n
a
l
f
r
am
ewo
r
k
s
to
m
ax
im
ize
th
eir
im
p
ac
t.
An
o
th
er
m
ajo
r
im
p
licatio
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is
th
e
ess
en
tial
r
o
le
o
f
p
r
o
f
ess
io
n
al
d
ev
el
o
p
m
en
t
.
T
h
e
s
tu
d
y
u
n
d
er
s
co
r
es
th
at
teac
h
er
t
r
ain
in
g
is
cr
itical
f
o
r
th
e
o
p
tim
al
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tili
za
tio
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o
f
o
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lin
e
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ce
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ca
tio
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W
ith
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u
t
co
n
tin
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o
u
s
s
u
p
p
o
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t
an
d
s
k
ill
d
ev
elo
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m
e
n
t,
ev
e
n
th
e
m
o
s
t
ad
v
an
ce
d
to
o
ls
m
ay
f
all
s
h
o
r
t
o
f
th
eir
p
o
ten
tial.
Sch
o
o
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d
ed
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ca
tio
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al
lead
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m
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s
t
p
r
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r
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g
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in
g
p
r
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ev
elo
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m
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in
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th
at
eq
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ip
teac
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s
with
th
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co
m
p
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ed
to
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av
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ac
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b
len
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d
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,
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ch
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em
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tial
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Stu
d
en
ts
f
r
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ec
o
n
o
m
ically
d
is
ad
v
a
n
tag
ed
b
ac
k
g
r
o
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n
d
s
o
f
ten
f
ac
e
lim
ited
ac
ce
s
s
to
d
ig
ital
d
ev
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an
d
r
eliab
le
in
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er
n
et
co
n
n
ec
tiv
ity
.
T
h
is
d
ig
ital
d
iv
id
e
ca
n
h
in
d
e
r
th
e
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it
s
o
f
to
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lik
e
AN,
lead
in
g
to
d
is
p
ar
ities
in
ed
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ca
tio
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tco
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es.
Po
licy
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ak
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s
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s
ch
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o
l
ad
m
in
is
tr
ato
r
s
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d
co
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lead
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m
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k
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llab
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ativ
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s
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ap
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t
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n
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eq
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al
ac
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s
to
th
e
n
ec
ess
ar
y
tech
n
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l
o
g
ical
in
f
r
astru
ctu
r
e
an
d
s
u
p
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t ser
v
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Fu
r
th
er
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o
r
e
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y
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ates
th
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wer
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f
tech
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l
o
g
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in
cr
ea
s
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s
tu
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en
t
en
g
ag
em
en
t
an
d
en
ab
le
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r
e
d
lear
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in
g
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li
n
e
to
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ls
all
o
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lear
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e
r
s
to
p
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g
r
ess
at
th
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wn
s
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ee
d
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ev
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s
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id
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s
as
n
ee
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ed
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d
r
ec
eiv
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er
s
o
n
alize
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g
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id
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ce
.
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h
is
ca
p
ab
ilit
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ca
n
i
m
p
r
o
v
e
lear
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in
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ex
p
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ar
ticu
lar
ly
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ad
ap
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tech
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o
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e
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lo
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atch
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h
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u
n
iq
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s
o
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iv
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d
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.
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r
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im
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ate
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ty
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d
y
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in
d
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est
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m
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s
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ter
m
im
p
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o
f
co
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s
is
ten
t
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s
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f
AN
an
d
s
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m
ilar
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ls
.
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ile
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t
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ter
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im
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ts
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ay
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e
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id
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n
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it
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tain
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em
en
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s
t
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en
d
u
r
in
g
k
n
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wled
g
e
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eten
tio
n
an
d
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etter
p
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ep
ar
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o
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ad
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ath
em
atica
l stu
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o
th
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im
p
o
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tan
t
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tio
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ee
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t
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an
aly
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is
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elied
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lev
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ata,
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ich
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ay
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r
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al
d
if
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e
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tu
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ies
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ld
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ac
k
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g
t
h
e
p
er
f
o
r
m
an
ce
o
f
in
d
i
v
id
u
al
s
tu
d
en
ts
to
b
etter
u
n
d
er
s
tan
d
h
o
w
v
ar
io
u
s
s
u
b
g
r
o
u
p
s
r
esp
o
n
d
to
d
ig
ital in
ter
v
e
n
tio
n
s
an
d
wh
ich
f
ac
t
o
r
s
co
n
tr
ib
u
te
to
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eir
s
u
cc
ess
.
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d
itio
n
ally
,
th
er
e
is
v
alu
e
in
co
m
p
ar
in
g
d
if
f
er
en
t
d
i
g
ital
lear
n
in
g
m
o
d
els.
I
n
v
esti
g
atin
g
t
h
e
r
elativ
e
ef
f
ec
tiv
en
ess
o
f
teac
h
e
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ce
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te
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ed
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s
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n
t
-
ce
n
ter
ed
a
p
p
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o
ac
h
es
in
d
ig
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tex
ts
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n
y
ield
i
n
s
ig
h
ts
in
to
wh
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p
ed
a
g
o
g
ies
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e
m
o
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t
co
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civ
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lear
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in
t
ec
h
n
o
lo
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h
en
v
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n
m
en
ts
.
Su
ch
c
o
m
p
ar
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s
will in
f
o
r
m
th
e
d
esig
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f
m
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e
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tiv
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in
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tr
u
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al
s
tr
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es u
s
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g
p
latf
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m
s
lik
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AN.
L
astl
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f
u
tu
r
e
r
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l
d
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p
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m
m
u
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ities
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en
h
a
n
cin
g
th
e
im
p
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tatio
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o
f
d
ig
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to
o
ls
.
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h
e
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f
ec
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en
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o
f
c
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llab
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ativ
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s
tr
u
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u
ch
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p
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m
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in
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teac
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p
p
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r
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p
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ical
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est p
r
ac
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d
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e
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ir
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in
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er
s
ca
n
wo
r
k
to
war
d
m
ax
im
izin
g
th
e
b
e
n
ef
i
ts
o
f
d
ig
ital le
ar
n
in
g
to
o
ls
f
o
r
all
lear
n
er
s
.
6.
CO
NCLU
SI
O
N
T
h
is
s
tu
d
y
p
r
o
v
id
es
em
p
i
r
ical
d
ata
th
at
s
u
p
p
o
r
ts
in
cr
ea
s
ed
u
s
ag
e
o
f
AN
is
d
ir
ec
tly
r
elate
d
to
im
p
r
o
v
e
d
s
tu
d
en
t
p
er
f
o
r
m
an
c
e
o
n
Alg
e
b
r
a
I
E
OC
ex
am
s
.
T
h
o
s
e
s
ch
o
o
ls
with
teac
h
er
s
wh
o
m
ad
e
a
co
n
ce
r
ted
ef
f
o
r
t
to
in
co
r
p
o
r
ate
AN,
p
ar
ticu
lar
ly
th
r
o
u
g
h
wo
r
k
b
o
o
k
u
s
e
an
d
p
r
o
f
ess
io
n
al
d
ev
elo
p
m
en
t,
y
ield
ed
s
ig
n
if
ican
tly
h
ig
h
er
p
ass
in
g
r
a
tes.
T
h
e
r
esu
lts
h
ig
h
lig
h
t
t
h
e
i
m
p
o
r
tan
ce
o
f
s
y
s
tem
atic
tech
n
o
lo
g
y
in
teg
r
atio
n
,
with
teac
h
er
in
v
o
l
v
em
en
t
b
ein
g
cr
itical
to
m
ax
im
u
m
p
o
ten
tial o
f
th
e
p
latf
o
r
m
.
T
h
e
f
in
d
in
g
s
ar
e
c
o
n
s
is
ten
t
with
th
e
in
s
tr
u
m
e
n
tal
o
r
ch
estra
tio
n
th
eo
r
y
,
with
an
e
m
p
h
asis
o
n
tech
n
o
lo
g
y
s
u
p
p
lem
en
tin
g
,
r
at
h
er
th
an
r
ep
lacin
g
,
co
n
v
en
tio
n
al
in
s
tr
u
ctio
n
.
T
h
o
u
g
h
th
e
s
tu
d
y
co
r
r
o
b
o
r
ates
th
e
b
en
ef
its
o
f
AN,
a
d
d
itio
n
al
ef
f
o
r
ts
m
u
s
t
b
e
co
n
d
u
cted
to
d
et
er
m
in
e
its
lo
n
g
-
ter
m
im
p
ac
t,
p
atter
n
s
o
f
s
tu
d
en
t
en
g
ag
em
e
n
t
at
th
e
in
d
iv
id
u
al
lev
el,
an
d
d
ig
ital
eq
u
ity
as
it
p
er
tain
s
to
ac
ce
s
s
to
o
n
lin
e
in
s
t
r
u
ctio
n
al
r
eso
u
r
c
es.
Pro
m
o
tin
g
eq
u
al
ac
ce
s
s
to
d
ig
ital
r
eso
u
r
ce
s
f
o
r
all
lear
n
e
r
s
is
s
till
im
p
er
ativ
e
to
im
p
r
o
v
in
g
m
ath
em
atics
ed
u
ca
tio
n
o
u
tco
m
es.
ACK
NO
WL
E
DG
M
E
N
T
S
T
h
e
au
th
o
r
s
wo
u
l
d
lik
e
t
o
ex
p
r
ess
th
eir
h
ea
r
tf
elt
g
r
atitu
d
e
t
o
th
e
p
a
r
ticip
atin
g
s
ch
o
o
ls
an
d
in
s
tr
u
cto
r
s
f
o
r
th
eir
c
o
n
tr
ib
u
tio
n
s
to
th
is
s
tu
d
y
.
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