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M
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kills in ru
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s,
RM
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c
a
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re
c
o
m
m
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n
d
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d
in
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ts'
m
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a
so
n
in
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d
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o
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in
th
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islan
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-
b
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d
r
u
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o
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tex
t
.
K
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s
:
C
u
ltu
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Ma
th
em
atica
l c
o
m
m
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R
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R
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T
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c
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ss
a
rticle
u
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CC B
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li
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.
C
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p
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A
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:
An
d
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s
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L
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Palin
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s
s
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Ma
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em
atics E
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Stu
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Pro
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Pattimu
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a
Un
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s
ity
J
ln
.
I
r
M.
Pu
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C
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p
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s
P
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a,
Am
b
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I
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d
o
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E
m
ail:
p
alin
u
s
s
aa
n
d
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s
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l@
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m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
im
p
o
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tan
ce
o
f
ed
u
ca
tio
n
f
o
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v
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o
f
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atio
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ca
u
s
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tr
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u
tio
n
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f
ed
u
ca
tio
n
th
at
m
u
s
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e
d
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e.
Ho
wev
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r
,
a
g
ap
ca
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s
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p
licatio
n
s
f
o
r
th
e
q
u
ality
o
f
ed
u
ca
tio
n
.
T
h
e
ea
s
ter
n
r
eg
io
n
h
as a
lway
s
b
ee
n
th
e
f
o
c
u
s
,
esp
ec
ially
Ma
l
u
k
u
,
wh
ich
is
a
p
r
o
v
in
ce
o
f
a
t
h
o
u
s
an
d
is
lan
d
s
with
ed
u
ca
tio
n
q
u
ality
th
at
is
s
till
f
ar
f
r
o
m
ex
p
ec
tatio
n
s
w
h
en
c
o
m
p
ar
ed
to
o
th
er
r
eg
io
n
s
in
I
n
d
o
n
esia
[
1
]
.
Qu
ality
m
ath
em
ati
cs
lear
n
in
g
is
m
o
r
e
d
o
m
in
an
t
f
o
r
s
tu
d
en
ts
i
n
u
r
b
a
n
ar
ea
s
c
o
m
p
ar
e
d
to
s
tu
d
en
ts
in
r
u
r
al
ar
ea
s
[
2
]
.
Su
r
v
e
y
s
in
d
ev
elo
p
e
d
co
u
n
tr
ies
lik
e
th
e
Un
ited
States
s
h
o
w
th
at
th
e
th
r
ee
m
ain
c
h
allen
g
es
th
at
ca
u
s
e
lo
w
q
u
ality
ed
u
ca
tio
n
in
r
u
r
al
ar
ea
s
ar
e
lo
w
teac
h
er
s
alar
ies,
s
o
cial
is
o
latio
n
an
d
g
eo
g
r
a
p
h
ic
is
o
latio
n
[
3
]
.
T
h
e
m
ain
ch
allen
g
e
also
m
ak
es
th
e
p
r
o
b
lem
o
f
d
if
f
icu
lty
in
lear
n
in
g
m
ath
em
atics,
s
o
th
at
it
h
as
a
n
im
p
ac
t
o
n
s
tu
d
en
ts
'
m
ath
em
atica
l
r
ea
s
o
n
in
g
s
k
ills
[
4
]
.
Ma
th
e
m
atica
l
r
ea
s
o
n
in
g
is
m
o
r
e
d
ir
e
cted
at
th
e
attitu
d
e
to
th
in
k
s
y
s
tem
atica
lly
,
lo
g
ica
lly
an
d
p
r
o
d
u
ce
a
n
ew
c
o
n
clu
s
io
n
b
ased
o
n
f
ac
ts
an
d
m
o
r
e
r
elev
an
t
s
o
u
r
ce
s
[
5
]
.
Stu
d
en
ts
m
o
r
e
ea
s
ily
u
n
d
er
s
tan
d
m
ath
em
atics
wh
en
t
h
eir
r
e
aso
n
in
g
s
k
ills
ar
e
g
o
o
d
an
d
a
b
le
to
co
m
m
u
n
icate
m
ath
em
atica
lly
s
o
th
at
m
at
h
em
atica
l
s
y
m
b
o
ls
will
b
e
m
o
r
e
m
ea
n
in
g
f
u
l
[
6
]
.
Scien
tific
r
ea
s
o
n
in
g
an
d
m
ath
em
atica
l
co
m
m
u
n
icatio
n
s
k
ills
h
av
e
a
v
er
y
clo
s
e
r
elatio
n
s
h
ip
.
C
o
m
m
u
n
icatio
n
s
k
il
ls
ar
e
an
im
p
o
r
tan
t
asp
ec
t
s
o
th
at
s
tu
d
en
ts
h
av
e
th
e
s
k
ill
to
s
o
lv
e
m
ath
em
atica
l
p
r
o
b
lem
s
,
esp
ec
ially
m
ath
e
m
atica
l
s
o
lu
tio
n
s
r
elate
d
to
s
tu
d
en
ts
'
r
ea
l
life
[
7
]
,
[
8
]
.
T
h
e
r
esu
lts
o
f
s
tu
d
ies
in
s
ev
er
al
co
u
n
tr
ie
s
in
clu
d
in
g
T
u
r
k
ey
p
r
o
v
e
th
at
th
e
s
cien
tific
r
ea
s
o
n
in
g
o
f
s
tu
d
en
ts
f
o
r
g
r
ad
e
8
s
tu
d
en
ts
is
s
till
v
er
y
lo
w
[
9
]
.
B
esid
es
th
at,
in
th
e
USA
t
h
e
s
am
e
th
in
g
s
h
o
ws
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
R
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2252
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8
8
2
2
R
ea
lis
tic
ma
th
ema
tics
ed
u
ca
tio
n
:
M
a
th
ema
tica
l rea
s
o
n
i
n
g
a
n
d
…
(
A
n
d
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o
n
Leo
n
a
r
d
o
P
a
lin
u
s
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a
)
523
th
at
s
cien
tific
r
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s
o
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in
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f
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tu
d
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is
s
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lo
w
s
o
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at
it
d
i
s
r
u
p
ts
th
e
lear
n
in
g
p
r
o
ce
s
s
o
f
STE
M
[
1
0
]
.
T
h
e
r
esu
lts
o
f
o
th
e
r
s
tu
d
ies
ab
o
u
t
co
m
m
u
n
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s
k
ills
f
o
r
s
tu
d
e
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in
I
n
d
o
n
esia
ar
e
also
s
till
lo
w
in
ter
m
s
o
f
I
MO
a
n
d
PISA
[
1
1
]
.
On
e
o
f
th
e
r
ec
o
m
m
e
n
d
ed
lear
n
in
g
m
o
d
els
is
r
e
alis
tic
m
ath
e
m
atics
lear
n
in
g
(
R
ME
)
s
in
ce
it
u
tili
ze
s
r
ea
l
-
wo
r
ld
s
itu
atio
n
s
f
o
r
s
tu
d
e
n
ts
to
co
n
s
tr
u
ct
th
ei
r
u
n
d
er
s
ta
n
d
in
g
a
n
d
k
n
o
wled
g
e.
R
ME
i
s
b
ased
o
n
t
h
e
id
ea
s
o
f
Han
s
Fre
u
d
e
n
th
al
in
th
e
1
9
7
0
s
with
h
is
f
r
ien
d
s
at
t
h
e
Fre
u
d
en
th
al
I
n
s
titu
te
[
1
2
]
.
E
x
p
er
t
s
s
ee
m
ath
em
atics
as
o
n
e
o
f
th
e
tr
a
n
s
m
is
s
io
n
s
o
f
k
n
o
wled
g
e
[
1
3
]
.
R
ME
d
e
v
elo
p
s
i
n
th
e
Neth
er
lan
d
s
f
o
r
elem
en
ta
r
y
s
ch
o
o
l
s
tu
d
en
ts
,
b
u
t
it
p
r
o
g
r
ess
es
to
ju
n
io
r
h
i
g
h
s
ch
o
o
l
lev
el
an
d
is
k
n
o
w
n
a
s
th
e
I
n
d
o
n
esian
R
ea
lis
tic
Ma
t
h
em
atics
E
d
u
ca
tio
n
(
PMR
I
)
in
I
n
d
o
n
esia
[
1
4
]
.
R
ME
v
iews
m
ath
em
atics
as
a
h
u
m
an
ac
tiv
ity
,
n
o
t
as
m
er
e
k
n
o
wled
g
e
r
ea
d
y
t
o
u
s
e
[
1
5
]
.
I
t
u
tili
ze
s
th
e
s
u
r
r
o
u
n
d
i
n
g
en
v
ir
o
n
m
e
n
t
to
b
r
i
n
g
th
o
u
g
h
ts
an
d
p
r
o
v
i
d
e
th
e
b
r
o
ad
e
s
t
o
p
p
o
r
tu
n
ities
f
o
r
s
tu
d
en
ts
in
u
n
d
e
r
s
tan
d
in
g
m
at
h
em
atica
l m
ater
ial.
Pro
v
id
in
g
th
e
b
r
o
ad
est
o
p
p
o
r
t
u
n
ities
f
o
r
s
tu
d
e
n
ts
to
lear
n
m
ath
em
atics in
a
r
ea
l
-
w
o
r
ld
c
o
n
tex
t is v
er
y
im
p
o
r
tan
t
to
p
r
o
v
id
e
a
s
o
lid
f
o
u
n
d
atio
n
o
n
a
m
ath
em
atica
l
to
p
ic
[
1
6
]
.
T
h
e
r
elev
an
t
to
p
ic
is
g
eo
m
etr
y
,
esp
ec
ially
in
th
e
f
o
r
m
o
f
a
f
lat
s
tr
u
ctu
r
e
u
s
in
g
s
tu
d
en
ts
'
d
aily
liv
es,
es
p
ec
ially
f
o
r
s
tu
d
e
n
ts
in
r
u
r
al
ar
ea
s
th
at
ar
e
lim
ited
b
y
f
ac
ilit
ies.
B
y
u
tili
zin
g
th
e
e
x
is
tin
g
d
aily
co
n
tex
t,
th
e
b
r
ain
'
s
ab
ili
ty
to
u
n
d
e
r
s
tan
d
a
p
r
o
b
l
em
in
m
ath
em
atics
will
b
e
f
o
r
m
ed
a
n
d
co
m
m
u
n
i
ca
tio
n
b
etwe
en
s
tu
d
en
ts
will
b
e
b
u
ilt
p
r
o
p
er
ly
with
o
u
t
an
y
r
e
s
tr
ictio
n
s
[
1
7
]
.
Ap
p
r
o
p
r
iate
lear
n
in
g
to
o
ls
wi
ll
b
r
in
g
s
tu
d
en
ts
in
to
th
eir
n
at
u
r
al
th
in
k
in
g
o
r
p
lay
in
g
en
v
ir
o
n
m
en
t
[
1
8
]
,
[
1
9
]
.
L
ea
r
n
in
g
t
o
o
ls
ca
n
h
elp
teac
h
e
r
s
to
m
ak
e
class
r
o
o
m
s
as a
p
la
ce
to
lear
n
an
d
s
o
lv
e
m
at
h
em
a
tical
[
2
0
]
,
[
2
1
]
.
R
ME
is
a
lear
n
in
g
ap
p
r
o
ac
h
th
at
is
co
n
s
id
er
ed
ap
p
r
o
p
r
iate
in
d
ev
elo
p
in
g
m
ath
em
atics
in
a
r
u
r
a
l
co
n
tex
t
[
1
2
]
.
R
ME
ex
p
er
ts
ex
p
lain
th
at
lear
n
i
n
g
m
ath
e
m
atics
m
u
s
t
b
e
lin
k
ed
to
r
ea
lity
[
2
2
]
,
[
2
3
]
.
T
h
is
m
ea
n
s
th
at
m
ath
em
atics
m
u
s
t
b
e
clo
s
e
to
th
e
ch
ild
an
d
r
elev
an
t
to
t
h
e
ch
ild
'
s
d
aily
s
itu
atio
n
,
esp
e
cially
s
tu
d
en
t
life
.
On
e
m
ater
ial
th
at
is
co
n
s
id
er
e
d
r
elev
an
t
is
g
e
o
m
etr
y
m
ater
ial
i
n
ju
n
io
r
h
ig
h
s
ch
o
o
l
s
tu
d
en
ts
.
T
h
e
r
esear
ch
r
ep
o
r
t
in
f
o
r
m
s
u
s
th
at
th
e
lear
n
i
n
g
o
u
tco
m
es
o
f
s
tu
d
e
n
ts
in
Ken
d
ar
i,
o
n
g
eo
m
etr
y
m
ater
ial
ar
e
s
till
l
o
w
[
2
4
]
.
I
n
ad
d
itio
n
,
th
e
m
ath
em
atics
lear
n
in
g
o
u
tco
m
es
o
f
v
o
ca
tio
n
al
s
tu
d
en
ts
in
th
e
Neth
er
lan
d
s
ar
e
s
till
lo
w,
wh
er
e
s
tu
d
en
ts
s
till
h
av
e
d
if
f
icu
lty
s
o
lv
in
g
m
ath
em
atica
l p
r
o
b
lem
s
[
2
5
]
.
On
e
o
f
m
ath
em
atics
lear
n
in
g
th
at
is
in
ac
c
o
r
d
a
n
ce
with
t
h
e
r
u
r
al
co
n
te
x
t
is
R
ME
[
2
6
]
.
Un
til
n
o
w,
th
er
e
h
as
b
ee
n
a
lack
o
f
atten
ti
o
n
f
r
o
m
th
e
g
o
v
er
n
m
e
n
t
in
Ma
lu
k
u
,
esp
ec
ially
s
ch
o
o
ls
in
r
u
r
al
ar
ea
s
[
2
7
]
.
R
u
r
al
s
ch
o
o
ls
ten
d
to
b
e
s
m
aller
an
d
f
ac
ilit
ies
ar
e
in
ad
eq
u
ate
in
ter
m
s
o
f
teac
h
in
g
s
taf
f
an
d
in
f
r
astru
ctu
r
e
[
2
8
]
.
T
h
er
ef
o
r
e,
th
is
r
esear
ch
was
m
o
r
e
f
o
cu
s
ed
o
n
s
ch
o
o
ls
an
d
s
tu
d
en
ts
in
r
u
r
al
ar
ea
s
th
at
a
r
e
lack
in
g
i
n
ter
m
s
o
f
teac
h
in
g
s
taf
f
an
d
f
ac
ilit
ies
b
y
p
r
io
r
itizin
g
ev
er
y
d
ay
co
n
te
x
ts
s
u
ch
as
th
e
lea
r
n
in
g
en
v
ir
o
n
m
en
t
an
d
th
e
p
lay
in
g
en
v
ir
o
n
m
en
t.
B
ased
o
n
th
e
ex
i
s
tin
g
p
r
o
b
lem
s
,
th
is
s
tu
d
y
aim
ed
to
an
aly
ze
th
e
ef
f
ec
t o
f
R
M
E
o
n
m
ath
em
atica
l
r
ea
s
o
n
in
g
a
n
d
co
m
m
u
n
icatio
n
s
k
ills
in
a
r
u
r
al
co
n
te
x
t.
2.
RE
S
E
ARCH
M
E
T
H
O
D
2
.
1
.
Resea
rc
h desi
g
n
T
h
is
s
tu
d
y
u
s
ed
a
q
u
asi
-
ex
p
er
i
m
en
tal
d
esig
n
with
th
e
d
esig
n
o
f
th
r
ee
p
r
e
-
test
-
p
o
s
t
-
test
co
n
t
r
o
l
class
es
an
d
th
r
ee
e
x
p
er
im
e
n
tal
class
es
f
r
o
m
th
r
ee
d
i
f
f
er
en
t
s
ch
o
o
ls
t
h
at
wer
e
u
s
ed
as
r
esear
ch
s
am
p
les.
T
h
e
g
r
o
u
p
in
g
o
f
s
tu
d
en
ts
was
d
eter
m
in
ed
b
ased
o
n
th
e
lev
el
o
f
th
e
s
ch
o
o
l
ac
co
r
d
in
g
to
th
e
r
esu
lts
o
f
ac
cr
ed
itatio
n
f
r
o
m
s
ch
o
o
ls
with
ac
cr
ed
itatio
n
cr
it
e
r
ia
ty
p
e
A,
B
,
C
,
an
d
ca
teg
o
r
ies
o
f
lev
els
o
f
m
ath
em
atica
l
s
k
ills
with
lear
n
in
g
u
s
in
g
th
e
R
ME
ap
p
r
o
ac
h
in
th
e
r
u
r
al
co
n
tex
t a
n
d
co
n
v
en
tio
n
al
lear
n
in
g
.
2
.
2
.
P
o
pu
la
t
io
n a
nd
re
s
ea
rc
h sa
m
ple
T
h
e
s
tu
d
y
was
co
n
d
u
cted
in
C
en
tr
al
Ma
lu
k
u
R
eg
en
cy
,
I
n
d
o
n
esia
on
s
ev
e
r
al
ju
n
i
o
r
h
ig
h
s
ch
o
o
ls
in
clu
d
in
g
Pu
b
lic
J
u
n
io
r
Hig
h
Sch
o
o
l
1
Ma
s
o
h
i
with
ac
cr
ed
it
atio
n
A,
Pu
b
lic
J
u
n
io
r
Hig
h
Sch
o
o
l
1
Am
a
h
ai
with
ac
cr
ed
itatio
n
B
an
d
C
h
r
is
tian
J
u
n
io
r
Hig
h
Sch
o
o
l
o
f
Ma
s
o
h
i
with
ac
cr
ed
itatio
n
C
.
T
h
e
s
a
m
p
le
s
ize
was
1
3
0
s
tu
d
en
ts
at
g
r
ad
e
V
I
I
.
Div
is
io
n
o
f
s
tu
d
en
ts
b
ased
o
n
th
e
lev
el
o
f
k
n
o
wled
g
e
,
am
o
n
g
o
th
er
s
,
lo
w,
m
ed
iu
m
an
d
h
ig
h
.
2
.
3
.
Resea
rc
h ins
t
rum
ent
s
T
h
e
in
s
tr
u
m
en
ts
wer
e
ess
ay
test
s
co
n
s
is
tin
g
o
f
f
iv
e
m
ath
em
atica
l
r
ea
s
o
n
in
g
q
u
e
s
tio
n
s
an
d
co
m
m
u
n
icatio
n
s
k
ills
te
s
ts
.
Pre
v
io
u
s
ly
,
th
e
f
iv
e
q
u
esti
o
n
s
h
a
v
e
b
ee
n
v
alid
ated
b
y
ex
p
er
ts
s
o
th
at
th
ey
m
ee
t
th
e
cr
iter
ia
p
r
o
p
er
ly
an
d
ca
n
b
e
u
s
ed
.
I
n
ad
d
itio
n
,
v
alid
atio
n
w
as
ca
r
r
ied
o
u
t
o
n
a
n
u
m
b
er
o
f
ju
n
io
r
h
ig
h
s
ch
o
o
l
m
ath
em
atics
teac
h
er
s
in
Ma
s
o
h
i
R
eg
en
cy
wh
o
wer
e
f
a
m
iliar
with
an
d
u
n
d
er
s
tan
d
th
e
m
ath
em
atics
n
ee
d
s
o
f
s
tu
d
en
ts
.
B
ef
o
r
e
co
n
d
u
ctin
g
s
tu
d
en
t
lear
n
in
g
in
ter
v
e
n
tio
n
s
,
a
p
r
e
-
test
was
co
n
d
u
cte
d
to
test
s
tu
d
en
ts
'
m
ath
em
atica
l
ab
ilit
ies.
T
h
e
p
r
e
-
test
q
u
esti
o
n
s
co
n
s
is
t
o
f
f
iv
e
q
u
esti
o
n
s
wh
ich
ar
e
s
im
il
ar
to
th
e
p
o
s
t
-
test
q
u
esti
o
n
s
.
T
h
e
d
etails
o
f
th
e
c
ateg
o
r
ies
o
f
s
tu
d
en
ts
'
m
ath
em
atics
lear
n
in
g
o
u
tco
m
es
ar
e
p
r
esen
ted
in
T
ab
le
1
.
On
e
ex
am
p
le
o
f
a
test
in
s
tr
u
m
en
t
d
ev
el
o
p
ed
as
s
h
o
w
n
in
Fig
u
r
e
1
,
“
I
f
y
o
u
lo
o
k
at
th
e
r
o
o
f
o
f
th
e
h
o
u
s
e
o
n
t
h
e
s
id
e,
it
lo
o
k
s
lik
e
an
eq
u
ilate
r
al
tr
ian
g
le.
I
f
th
e
s
id
e
len
g
t
h
is
2
x
+
4
cm
an
d
th
e
cir
cu
m
f
er
en
ce
is
1
5
0
cm
,
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
.
10
,
No
.
2
,
J
u
n
e
2
0
2
1
:
5
2
2
-
5
3
4
524
d
eter
m
in
e
th
e
v
alu
e
o
f
x
”
.
T
h
e
ea
r
ly
m
ath
em
atica
l
s
k
ills
test
,
th
e
cr
iter
ia
f
o
r
g
r
o
u
p
in
g
a
r
e
b
ased
o
n
s
tu
d
en
ts
'
m
ath
em
atica
l sk
ills
s
co
r
es b
as
ed
o
n
b
en
ch
m
ar
k
r
ef
er
en
ce
ass
ess
m
en
ts
a
s
s
h
o
wn
in
T
ab
le
1
.
Fig
u
r
e
1
.
T
est in
s
tr
u
m
e
n
t d
ev
e
lo
p
ed
T
ab
le
1
.
C
r
iter
ia
f
o
r
ea
r
ly
m
ath
em
atica
l
s
tu
d
en
ts
s
k
ill
(
E
MSS)
ca
teg
o
r
ies
Ea
r
l
y
m
a
t
h
e
m
a
t
i
c
a
l
s
t
u
d
e
n
t
s
k
i
l
l
s
(
E
M
S
)
C
a
t
e
g
o
r
y
E
MS
S
≥
7
5
%
i
d
e
a
l
sc
o
r
e
=
7
5
H
i
g
h
5
5
%
i
d
e
a
l
sc
o
r
e
=
5
5
<
E
MS
S
<
7
5
%
i
d
e
a
l
s
c
o
r
e
=
7
4
M
e
d
i
u
m
E
M
S
S
≤
5
5
%
i
d
e
a
l
sc
o
r
e
=
5
4
Lo
w
2
.
4
.
Da
t
a
co
llect
io
n t
ec
hn
iqu
e
Data
co
llectio
n
tech
n
iq
u
es
wer
e
in
ter
v
iew
g
u
id
elin
es,
q
u
esti
o
n
n
air
es
an
d
d
o
c
u
m
en
tatio
n
.
I
n
ter
v
iew
g
u
id
elin
es
wer
e
in
th
e
f
o
r
m
o
f
q
u
esti
o
n
s
co
m
p
iled
s
y
s
tem
atica
lly
in
th
e
f
o
r
m
o
f
q
u
esti
o
n
s
o
f
m
ath
em
atica
l
r
ea
s
o
n
in
g
an
d
co
m
m
u
n
icatio
n
s
k
ills
to
r
e
-
ch
ec
k
th
e
d
if
f
icu
lties
o
f
s
tu
d
en
ts
in
s
o
lv
in
g
p
r
o
b
lem
s
.
T
h
e
q
u
est
io
n
n
air
e
in
s
tr
u
m
en
t
was in
th
e
f
o
r
m
o
f
s
tu
d
en
t
a
n
d
tea
ch
er
r
esp
o
n
s
es
to
th
e
lear
n
in
g
ca
r
r
ied
o
u
t
an
d
t
h
e
p
r
o
v
is
io
n
o
f
s
o
lu
tio
n
s
f
o
r
f
u
tu
r
e
lear
n
in
g
d
ev
elo
p
m
en
t.
T
h
e
r
esu
lts
o
f
th
e
d
o
c
u
m
en
tatio
n
wer
e
in
th
e
f
o
r
m
o
f
s
tu
d
en
ts
’
an
s
wer
s
d
u
r
in
g
th
e
p
r
e
-
test
,
p
r
o
ce
s
s
an
d
p
o
s
t
-
test
u
n
til
th
e
ac
tiv
ity
d
u
r
in
g
th
e
p
r
o
ce
s
s
o
f
co
llectin
g
lear
n
in
g
o
u
tco
m
es d
ata
.
2
.
5
.
Da
t
a
a
na
ly
s
i
s
t
ec
h
ni
q
ue
Data
an
aly
ze
d
in
th
is
s
tu
d
y
wer
e
o
b
tain
ed
f
r
o
m
test
s
o
f
s
tu
d
en
ts
'
m
ath
em
atica
l
r
ea
s
o
n
in
g
an
d
co
m
m
u
n
icatio
n
s
k
ills
.
T
h
e
test
was
d
o
n
e
at
th
e
b
eg
in
n
in
g
o
f
lear
n
in
g
an
d
at
th
e
en
d
o
f
lea
r
n
in
g
.
B
ased
o
n
t
h
e
p
r
e
-
test
an
d
p
o
s
t
-
test
s
co
r
es o
f
th
e
two
s
k
ills
,
th
e
N
-
Gain
Sco
r
e
was c
alcu
lated
an
d
p
r
o
ce
s
s
ed
ac
co
r
d
in
g
to
th
e
p
r
o
b
lem
a
n
d
th
e
p
r
o
p
o
s
ed
h
y
p
o
th
esis
.
Data
p
r
o
ce
s
s
in
g
in
th
is
r
esear
c
h
was
ca
r
r
ied
o
u
t
as:
1
)
Pre
r
eq
u
is
ite
te
s
t;
2
)
I
f
th
e
d
ata
wer
e
n
o
r
m
al
,
th
e
T
-
test
was
u
s
ed
to
test
th
e
d
if
f
er
en
ce
o
f
two
a
v
er
ag
es
a
n
d
th
e
An
o
v
a
test
to
test
th
e
d
if
f
e
r
e
n
ce
o
f
m
o
r
e
th
an
two
av
er
ag
es;
3
)
I
f
th
e
d
ata
wer
e
k
n
o
wn
to
b
e
n
o
t
n
o
r
m
ally
d
is
tr
ib
u
ted
,
n
o
n
-
p
ar
a
m
etr
ic
s
tatis
tical
r
u
les
u
s
ed
W
ilco
y
o
n
test
o
r
Ma
n
n
-
W
h
itn
ey
test
to
te
s
t
th
e
d
if
f
er
en
ce
o
f
two
s
am
p
les
an
d
Kr
u
r
s
k
al
w
a
lls
te
s
t
to
te
s
t
th
e
d
if
f
er
en
ce
o
f
m
o
r
e
th
a
n
two
li
n
es.
I
n
a
d
d
itio
n
to
q
u
a
n
titativ
e
an
al
y
s
is
,
a
q
u
alitativ
e
an
aly
s
is
o
f
t
h
e
an
s
wer
s
to
ea
ch
item
was c
ar
r
ied
o
u
t,
o
b
s
er
v
atio
n
al
d
ata,
in
ter
v
iew
d
ata,
an
d
s
tu
d
en
t
r
esp
o
n
s
e
d
at
a.
I
t
aim
ed
t
o
ex
am
i
n
e
f
u
r
th
er
ab
o
u
t
m
ath
e
m
atica
l
r
ea
s
o
n
in
g
a
n
d
c
o
m
m
u
n
icatio
n
s
k
ills
,
an
d
to
f
in
d
o
u
t
wh
eth
er
th
e
im
p
le
m
en
tatio
n
o
f
lear
n
in
g
in
ac
co
r
d
an
ce
with
th
e
p
r
o
v
is
io
n
s
o
f
lear
n
i
n
g
s
et
in
b
o
th
lear
n
in
g
.
3.
RE
SU
L
T
S
A
ND
D
I
SCU
SS
I
O
N
Qu
an
titativ
e
d
ata
o
b
tain
ed
f
r
o
m
th
e
r
esu
lts
o
f
test
s
o
f
m
ath
e
m
atica
l sk
ill an
d
m
ath
em
atica
l r
ea
s
o
n
in
g
s
k
ill test
s
.
T
h
e
d
is
tr
ib
u
tio
n
o
f
t
h
e
r
esear
ch
s
am
p
le
is
p
r
esen
te
d
in
T
ab
le
2
.
T
ab
le
2
.
Dis
tr
ib
u
tio
n
o
f
r
esear
ch
s
am
p
les
Ea
r
l
y
m
a
t
h
e
m
a
t
i
c
a
l
st
u
d
e
n
t
sk
i
l
l
s
Ex
p
e
r
i
m
e
n
t
a
l
g
r
o
u
p
(
R
M
E)
C
o
n
t
r
o
l
c
l
a
ss
(
C
o
n
v
e
n
t
i
o
n
a
l
)
H
i
g
h
M
e
d
i
u
m
Lo
w
To
t
a
l
H
i
g
h
M
e
d
i
u
m
Lo
w
To
t
a
l
Lo
w
7
2
10
19
12
6
10
28
M
e
d
i
u
m
10
9
10
29
10
9
9
28
H
i
g
h
11
8
1
20
4
1
1
6
To
t
a
l
28
19
21
68
26
16
20
62
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
v
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&
R
es E
d
u
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SS
N:
2252
-
8
8
2
2
R
ea
lis
tic
ma
th
ema
tics
ed
u
ca
tio
n
:
M
a
th
ema
tica
l rea
s
o
n
i
n
g
a
n
d
…
(
A
n
d
ers
o
n
Leo
n
a
r
d
o
P
a
lin
u
s
s
a
)
525
3
.
1
.
E
a
rly
m
a
t
hema
t
ica
l
s
t
ud
ent
s
k
ills
T
h
e
cr
iter
ia
f
o
r
ea
r
ly
m
ath
em
atica
l
s
tu
d
en
ts
s
k
ill
ac
co
r
d
in
g
to
th
e
s
tu
d
en
t'
s
ea
r
ly
m
ath
em
a
tical
s
k
ill
s
d
ata
ar
e
lo
w,
m
e
d
iu
m
an
d
h
ig
h
as sh
o
wn
in
T
a
b
le
3
.
T
ab
le
3
.
Dis
tr
ib
u
tio
n
o
f
ea
r
l
y
m
ath
em
atica
l
s
tu
d
en
t
s
k
ills
(
E
MSS)
EM
S
S
C
l
a
s
sess
Ex
p
e
r
i
m
e
n
t
C
o
n
t
r
o
l
To
t
a
l
Lo
w
19
28
47
M
e
d
i
u
m
29
28
57
H
i
g
h
20
6
26
To
t
a
l
68
62
1
3
0
3
.
2
.
M
a
t
hem
a
t
ica
l r
ea
s
o
nin
g
s
k
il
l
T
h
e
f
o
l
l
o
w
i
n
g
i
s
a
d
es
c
r
i
p
ti
o
n
o
f
t
h
e
r
e
s
u
l
ts
o
f
t
h
e
p
r
e
-
t
e
s
t
,
p
o
s
t
-
t
es
t
a
n
d
i
m
p
r
o
v
e
m
e
n
t
o
f
m
at
h
e
m
a
t
i
c
al
r
e
a
s
o
n
i
n
g
s
k
il
l
b
a
s
e
d
o
n
s
c
h
o
o
l
l
e
v
e
l
,
l
e
a
r
n
i
n
g
a
n
d
e
a
r
l
y
m
a
t
h
e
m
a
t
i
c
al
s
k
il
l
p
r
e
s
e
n
t
e
d
i
n
T
a
b
le
4
.
T
ab
le
4
.
Descr
ip
tio
n
o
f
a
v
er
ag
e
m
ath
em
atica
l r
ea
s
o
n
in
g
s
k
ills
b
ased
o
n
ea
r
ly
m
ath
em
atics
s
tu
d
en
t sk
ill
(
E
MSS)
S
c
h
o
o
l
EM
S
S
̅
&
SD
R
e
a
s
o
n
i
n
g
s
k
i
l
l
C
o
n
v
e
n
t
i
o
n
a
l
R
M
E
Pre
-
t
e
st
P
o
st
-
t
e
st
<
g
>
N
Pre
-
t
e
st
P
o
st
-
t
e
st
<
g
>
N
L
o
w
Lo
w
̅
1
3
.
1
4
2
2
.
2
0
0
.
1
0
40
1
4
.
3
4
2
5
.
1
0
0
.
1
2
32
SD
5
.
2
9
6
.
7
2
0
.
0
1
1
0
.
0
6
1
1
.
3
3
0
.
0
1
M
e
d
i
u
m
̅
-
-
-
-
5
2
.
0
8
6
3
.
7
4
0
.
2
4
4
SD
-
-
-
-
6
.
0
7
-
H
i
g
h
̅
-
-
-
-
-
8
6
.
2
8
-
6
SD
-
-
-
-
9
.
8
9
-
S
u
b
-
t
o
t
a
l
̅
1
3
.
1
4
2
4
.
2
0
0
.
1
3
40
6
6
.
4
2
7
5
.
1
2
0
.
2
5
42
SD
5
.
2
9
6
.
7
2
0
.
0
1
1
0
.
0
5
5
2
7
.
2
9
0
.
1
9
M
e
d
i
u
m
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w
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3
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9
3
3
5
.
1
0
0
.
2
4
30
2
8
.
3
6
3
8
.
4
9
0
.
1
4
30
SD
8
.
4
9
1
0
.
5
6
0
.
0
2
1
2
.
6
6
1
5
.
9
9
0
.
0
3
M
e
d
i
u
m
̅
-
5
7
.
6
3
-
2
6
1
.
4
6
6
7
.
3
7
0
.
1
5
5
SD
-
.
0
0
0
0
0
-
-
6
.
4
0
-
H
i
g
h
̅
-
-
-
-
-
8
4
.
1
8
-
3
SD
-
-
-
-
4
.
8
9
-
S
u
b
-
t
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t
a
l
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1
3
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1
4
4
6
.
3
6
0.
38
32
8
9
.
8
2
9
0
.
0
4
0
.
0
2
38
SD
8
.
4
9
1
0
.
5
6
0
.
0
2
1
2
.
6
6
2
7
.
2
8
0
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1
6
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g
h
Lo
w
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1
3
.
3
3
2
7
.
6
3
0
.
1
2
41
1
7
.
3
4
3
1
.
6
2
0
.
2
1
32
SD
9
.
5
9
1
3
.
7
9
0
.
0
4
8
.
2
4
1
1
.
3
4
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0
3
M
e
d
i
u
m
̅
6
5
.
1
4
0
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2
2
12
-
6
7
.
1
3
-
9
SD
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5
.
6
3
-
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7
.
9
3
-
H
i
g
h
̅
-
8
0
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2
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9
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0
8
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9
SD
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-
7
.
7
2
-
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u
b
-
t
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t
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3
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5
7
.
5
9
0.
51
55
7
2
.
5
4
8
7
.
8
5
0.
55
50
SD
9
.
5
9
1
9
.
4
2
0
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1
0
8
.
2
3
2
6
.
9
8
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2
0
Ov
e
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a
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w
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4
4
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5
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7
8
1
2
1
5
6
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2
9
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.
2
1
0
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8
9
92
SD
1
8
.
0
8
3
1
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7
0
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5
3
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9
5
3
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d
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.
7
7
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14
1
3
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1
8
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2
5
0
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0
5
18
SD
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5
.
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3
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H
i
g
h
̅
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8
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SD
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2
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9
-
To
t
a
l
̅
4
4
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4
0
6
0
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2
3
0.
28
6
9
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5
6
6
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3
0.
0
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2
SD
1
8
.
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3
6
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2
2
3
0
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9
5
8
1
.
5
5
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7
3
T
ab
le
4
s
h
o
ws
th
e
d
escr
ip
ti
o
n
o
f
th
e
av
er
ag
e
v
alu
e
o
f
p
r
e
-
test
,
p
o
s
t
-
test
an
d
im
p
r
o
v
em
en
t
in
m
ath
em
atica
l r
ea
s
o
n
in
g
s
k
ill
.
A.
Pre
-
test
m
ath
em
atica
l r
ea
s
o
n
in
g
s
k
ill
B
ased
o
n
th
e
r
esu
lts
o
f
th
e
Pre
-
test
to
tal
o
f
m
ath
em
atica
l
r
ea
s
o
n
in
g
s
k
ill,
R
ME
is
b
etter
th
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co
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v
en
tio
n
al
lear
n
in
g
,
wh
ich
s
h
o
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th
at
th
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m
ath
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atica
l
r
ea
s
o
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in
g
s
k
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ll
o
f
s
tu
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e
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ts
with
R
ME
is
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etter
th
an
t
h
e
m
ath
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atica
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o
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k
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o
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with
co
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le
ar
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g
at
lo
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m
e
d
iu
m
an
d
h
ig
h
s
ch
o
o
l
lev
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d
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ts
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Ho
wev
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,
in
b
o
th
lear
n
in
g
,
t
h
e
s
k
ill
o
f
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tu
d
en
ts
in
t
h
e
lo
w
ca
teg
o
r
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is
o
n
ly
in
th
e
class
tau
g
h
t
b
y
co
n
v
en
tio
n
al
lear
n
in
g
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
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I
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t
J
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Vo
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10
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No
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2
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J
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2
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2
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-
5
3
4
526
B.
Po
s
t m
ath
em
atica
l r
ea
s
o
n
in
g
s
k
ill test
B
ased
o
n
th
e
r
esu
lts
o
f
th
e
p
o
s
t
-
test
to
tal
o
f
s
tu
d
en
ts
'
m
ath
em
a
tical
r
ea
s
o
n
in
g
s
k
ills
as
o
v
er
all
an
d
s
tu
d
en
ts
'
ea
r
ly
m
a
th
em
atica
l
s
k
ills
,
it
s
h
o
wed
th
at
t
h
e
s
k
ills
o
f
s
tu
d
e
n
ts
'
m
ath
em
atica
l
r
ea
s
o
n
in
g
with
R
ME
is
b
etter
th
an
s
tu
d
en
ts
'
m
ath
em
atica
l
r
ea
s
o
n
in
g
s
k
ills
with
co
n
v
en
tio
n
al
lear
n
in
g
.
Ho
we
v
er
,
in
b
o
th
lear
n
in
g
,
s
tu
d
en
ts
'
s
k
il
ls
ar
e
s
till
in
th
e
m
ed
iu
m
ca
teg
o
r
y
.
C.
I
n
cr
e
ased
m
ath
em
atica
l r
ea
s
o
n
in
g
s
k
ill
B
ased
o
n
th
e
to
tal
r
esu
lts
o
f
t
h
e
in
cr
ea
s
e
in
s
tu
d
en
ts
'
m
ath
e
m
atica
l
r
ea
s
o
n
in
g
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k
ills
as
o
v
er
all
an
d
th
e
s
tu
d
en
ts
'
ea
r
ly
m
ath
em
atica
l
s
k
ills
,
it
s
h
o
ws
th
at
th
e
in
cr
ea
s
e
in
s
tu
d
en
ts
'
m
ath
em
atica
l
r
e
aso
n
in
g
s
k
ill
with
R
ME
is
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etter
th
an
in
cr
e
ased
s
tu
d
en
ts
'
m
ath
em
atica
l
r
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aso
n
in
g
s
k
ill
with
c
o
n
v
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n
tio
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lear
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n
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th
lear
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i
n
g
,
th
e
in
cr
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s
ed
s
k
ill o
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s
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ed
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m
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teg
o
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H
y
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t
hes
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esting
1
re
s
ea
rc
h into
m
a
t
hema
t
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hes
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est
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a
.
1
T
h
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h
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ased
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ata.
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0
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tain
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d
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atica
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n
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th
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ll
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(
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atica
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ased
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t
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c
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R
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4
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6
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c
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6
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h
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atica
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test
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ased
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v
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Pre
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6
s
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ased
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s
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test
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e
S
k
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f
m
at
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atica
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ased
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t
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ea
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atica
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ills
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ased
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p
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test
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ag
e
v
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o
f
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tu
d
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ts
'
m
ath
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atica
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s
o
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in
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k
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tau
g
h
t
b
y
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er
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m
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o
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o
f
s
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d
en
ts
'
r
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s
o
n
in
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s
k
ill tau
g
h
t c
o
n
v
en
t
io
n
ally
th
at
was 1
8
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04
.
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ab
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.
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h
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p
r
e
-
test
test
o
n
m
ath
em
atica
l r
ea
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o
n
in
g
s
k
ill b
a
s
ed
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n
lear
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n
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.
(
2
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t
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d
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P
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ased
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t
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test
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ata:
H
0
:
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h
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if
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d
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ath
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atica
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k
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e
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et
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1
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ar
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d
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d
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ath
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atica
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ab
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b
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9
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h
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a
t
th
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test
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lts
ar
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n
o
r
m
ally
d
is
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ib
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ted
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d
th
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d
ata
is
h
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en
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s
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ar
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ce
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en
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th
e
T
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test
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iter
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ll
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ted
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h
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m
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g
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ity
test
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f
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ath
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atica
l
r
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k
ill
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t
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test
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ased
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n
lear
n
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a
r
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s
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wn
in
T
ab
le
9
.
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h
e
r
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lts
o
f
p
o
s
t
-
test
T
-
test
ca
lcu
lat
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f
r
ea
s
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n
in
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s
k
ill
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ased
o
n
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ab
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1
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s
h
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at
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e
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f
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T
-
test
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n
m
ath
e
m
a
tical
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ased
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ted
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I
t
m
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n
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th
at
th
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e
ar
e
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
R
ea
lis
tic
ma
th
ema
tics
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u
ca
tio
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:
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ased
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ath
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ill p
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ased
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ased
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ased
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T
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in
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ab
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1
8
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T
ab
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1
8
s
h
o
ws
a
d
escr
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tio
n
o
f
th
e
av
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a
g
e
v
alu
e
o
f
p
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-
tes
t
,
p
o
s
t
-
test
an
d
im
p
r
o
v
em
en
t
in
th
e
s
k
ill
(
g
ain
)
o
f
m
ath
em
atica
l c
o
m
m
u
n
icatio
n
as
:
A.
Pre
-
test
o
f
m
ath
em
atica
l c
o
m
m
u
n
icatio
n
s
k
ills
.
B
ass
ed
o
n
th
e
to
tal
p
r
e
test
r
esu
lts
o
f
s
tu
d
en
ts
'
o
v
er
all
m
a
th
em
atica
l
co
m
m
u
n
icatio
n
s
k
ills
an
d
ea
r
l
y
m
ath
em
atica
l
s
tu
d
en
t
s
k
ills
,
it
s
h
o
ws
th
at
th
e
p
r
e
test
o
f
s
tu
d
e
n
ts
'
m
ath
em
atica
l
co
m
m
u
n
icat
io
n
s
k
ills
with
R
ME
is
b
etter
th
an
th
e
p
r
e
test
s
o
f
s
tu
d
en
ts
'
m
ath
em
atica
l
co
m
m
u
n
icatio
n
s
k
ills
with
co
n
v
en
tio
n
al.
Ho
wev
er
,
in
b
o
th
lear
n
in
g
,
s
tu
d
en
ts
'
s
k
ill
s
ar
e
s
till
in
th
e
m
ed
iu
m
ca
teg
o
r
y
.
B.
Po
s
t
-
test
o
f
m
ath
em
atica
l c
o
m
m
u
n
icatio
n
s
k
ills
.
B
ased
o
n
th
e
to
tal
p
o
s
t
-
test
r
esu
lts
o
f
s
tu
d
en
ts
'
o
v
er
all
m
ath
em
atica
l
co
m
m
u
n
icatio
n
s
k
ills
an
d
ea
r
ly
m
ath
em
atica
l
s
tu
d
en
t
s
k
ills
,
it
s
h
o
ws th
at
th
e
p
o
s
t
-
test
s
tu
d
en
ts
'
m
ath
em
atic
al
co
m
m
u
n
icatio
n
s
k
ills
with
R
ME
wer
e
b
etter
th
an
t
h
e
s
tu
d
en
ts
'
m
ath
em
atica
l
co
m
m
u
n
icatio
n
s
k
ill
p
o
s
t
-
test
with
co
n
v
e
n
tio
n
al.
Ho
wev
er
,
in
b
o
th
lear
n
in
g
,
s
tu
d
en
ts
'
s
k
ill
s
ar
e
s
till
in
th
e
m
ed
iu
m
ca
teg
o
r
y
.
C.
I
m
p
r
o
v
in
g
t
h
e
s
k
ill (
Gain
)
o
f
m
ath
em
atica
l c
o
m
m
u
n
ica
tio
n
B
ased
o
n
th
e
to
tal
r
esu
lts
o
f
a
n
in
cr
ea
s
e
in
o
v
er
all
s
tu
d
en
ts
’
m
ath
em
atica
l
co
m
m
u
n
icatio
n
s
k
ills
an
d
ea
r
ly
m
ath
em
atica
l
s
tu
d
en
t
s
k
ills
,
it
s
h
o
ws
th
at
in
cr
ea
s
in
g
s
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ased
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I
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ased
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ased
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ased
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ased
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ased
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ased
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ased
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ased
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ased
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ase
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
R
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d
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I
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2252
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ased
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ased
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j
e
c
t
e
d
T
ab
le
2
5
s
h
o
ws
th
at
th
e
r
esu
lts
o
f
th
e
Ma
n
n
-
W
h
itn
ey
test
o
n
m
ath
em
atica
l
co
m
m
u
n
icatio
n
s
k
ills
p
o
s
t
-
test
ar
e
b
ased
o
n
ea
r
ly
m
ath
e
m
atica
l
s
tu
d
en
t
s
k
ills
,
b
ec
au
s
e
o
f
th
e
s
ig
.
less
th
an
0
.
0
5
,
th
e
n
u
ll
h
y
p
o
th
esis
is
r
ejec
ted
.
I
t
m
ea
n
s
th
at
th
er
e
ar
e
d
if
f
er
e
n
ce
s
in
s
tu
d
en
t
co
m
m
u
n
icatio
n
s
k
ills
b
ased
o
n
e
ar
ly
m
ath
em
atica
l
s
tu
d
en
t
s
k
ills
.
B
ased
o
n
t
h
e
d
ata
a
b
o
u
t
th
e
a
v
er
ag
e
v
al
u
e
o
f
m
ath
em
atica
l
co
m
m
u
n
icatio
n
s
k
ills
an
d
m
ath
em
atica
l
ea
r
ly
s
k
ill
an
d
a
cc
o
r
d
in
g
to
th
e
r
esu
lts
o
f
th
e
p
re
-
test
,
it
it
i
s
k
n
o
wn
th
at
th
er
e
ar
e
s
ig
n
if
ican
t
d
if
f
er
e
n
ce
s
.
T
ab
le
2
6
s
h
o
ws
th
at
th
e
test
r
esu
lt
s
o
f
th
e
d
if
f
er
en
ce
test
o
n
m
ath
em
atica
l
co
m
m
u
n
icatio
n
s
k
ills
Pre
-
test
b
ased
o
n
s
tu
d
en
ts
'
e
ar
ly
m
ath
em
atica
l
s
k
ills
ar
e
s
ig
n
if
ican
tly
d
if
f
er
en
t
s
o
th
at
th
e
d
ata
ar
e
also
s
ig
n
if
ican
tly
d
if
f
er
e
n
t.
T
ab
le
2
6
.
T
h
e
d
if
f
er
en
ce
test
o
n
m
ath
em
atica
l c
o
m
m
u
n
icatio
n
s
k
ills
p
r
e
-
test
b
ased
o
n
e
ar
l
y
m
ath
em
atica
l
s
tu
d
en
t
s
k
ills
(
E
MSS)
(
J)
G
r
o
u
p
M
e
a
n
d
i
f
f
e
r
e
n
c
e
(I
-
J)
S
t
d
.
Er
r
o
r
S
i
g
.
I
n
t
e
r
p
r
e
t
a
t
i
o
n
Lo
w
M
e
d
i
u
m
-
1
3
.
9
8
4
8
2
*
1
.
8
2
7
4
0
.
0
0
0
Th
e
r
e
i
s
a
d
i
f
f
e
r
e
n
c
e
H
i
g
h
-
3
6
.
7
9
1
2
1
*
2
.
1
9
0
5
7
.
0
0
0
Th
e
r
e
i
s
a
d
i
f
f
e
r
e
n
c
e
M
e
d
i
u
m
Lo
w
1
3
.
9
8
4
8
2
*
1
.
8
2
7
4
0
.
0
0
0
Th
e
r
e
i
s
a
d
i
f
f
e
r
e
n
c
e
H
i
g
h
-
2
2
.
8
0
6
3
9
*
1
.
7
7
8
1
0
.
0
0
0
Th
e
r
e
i
s
a
d
i
f
f
e
r
e
n
c
e
H
i
g
h
Lo
w
3
6
.
7
9
1
2
1
*
2
.
1
9
0
5
7
.
0
0
0
Th
e
r
e
i
s
a
d
i
f
f
e
r
e
n
c
e
M
e
d
i
u
m
2
2
.
8
0
6
3
9
*
1
.
7
7
8
1
0
.
0
0
0
Th
e
r
e
i
s
a
d
i
f
f
e
r
e
n
c
e
Su
bm
is
s
io
n o
f
h
y
po
t
hes
es 2
.
b.2
H
0
∶
µ
1
=
µ
2
=
µ
3
H
1
∶
T
h
er
e
is
at
least o
n
e
m
ath
em
a
tical
co
m
m
u
n
icatio
n
s
k
ill b
ase
d
o
n
d
if
f
er
e
n
t e
ar
ly
m
at
h
em
atica
l sk
ills
No
te
:
µ
1
=
Ma
th
em
atica
l c
o
m
m
u
n
icatio
n
s
k
ills
o
f
lo
w
g
r
o
u
p
s
tu
d
en
ts
µ
2
=
Ma
th
em
atica
l c
o
m
m
u
n
icatio
n
s
k
ills
o
f
m
ed
iu
m
g
r
o
u
p
s
tu
d
en
ts
µ
3
=
Ma
th
em
atica
l c
o
m
m
u
n
icat
io
n
s
k
ills
o
f
h
ig
h
g
r
o
u
p
s
tu
d
en
ts
T
ab
le
2
7
s
h
o
ws
t
h
at
d
ata
ar
e
n
o
r
m
ally
d
is
tr
ib
u
ted
.
I
n
ad
d
itio
n
,
T
a
b
le
2
8
s
h
o
ws
th
at
th
e
Ma
n
n
-
W
h
itn
ey
test
r
esu
lts
o
n
th
e
p
o
s
t
-
test
m
ath
em
atica
l
co
m
m
u
n
icatio
n
s
k
ills
th
at
ar
e
b
ased
o
n
ea
r
ly
m
ath
em
atica
l
s
tu
d
en
t
s
k
ills
h
av
e
a
s
ig
.
s
m
aller
th
a
n
0
.
0
5
.
T
h
u
s
,
th
e
n
u
ll
h
y
p
o
th
e
s
is
is
r
ejec
ted
.
I
t
m
ea
n
s
th
at
th
er
e
ar
e
s
ig
n
if
ican
t
d
if
f
er
en
ce
s
in
m
ath
em
atica
l
c
o
m
m
u
n
icatio
n
s
k
ills
b
ased
o
n
e
ar
ly
m
ath
em
atica
l
s
tu
d
e
n
t
s
k
ills
.
Af
ter
co
n
d
u
ctin
g
th
e
Ma
n
n
-
W
h
itn
ey
test
,
it
was
f
o
llo
wed
b
y
th
e
T
u
k
e
y
test
to
co
m
p
ar
e
th
e
c
o
m
m
u
n
i
ca
tio
n
s
k
ills
o
f
lo
w
g
r
o
u
p
s
tu
d
en
ts
with
m
ed
iu
m
g
r
o
u
p
s
tu
d
en
ts
an
d
lo
w
g
r
o
u
p
s
tu
d
en
t
s
with
h
ig
h
g
r
o
u
p
s
tu
d
en
ts
.
T
h
en
,
it
p
r
o
ce
e
d
s
with
th
e
T
-
test
to
c
o
m
p
a
r
e
m
e
d
iu
m
g
r
o
u
p
s
tu
d
en
ts
with
h
ig
h
g
r
o
u
p
s
tu
d
e
n
ts
.
T
h
e
r
esu
lts
o
f
wh
ich
ar
e
p
r
esen
ted
in
T
ab
le
2
9
.
T
ab
le
2
9
s
h
o
ws
th
e
test
r
e
s
u
lts
o
f
th
e
d
if
f
er
en
ce
s
test
o
n
m
ath
em
atica
l
co
m
m
u
n
icatio
n
s
k
il
ls
p
o
s
t
-
tes
t
ar
e
b
ased
o
n
ea
r
ly
m
ath
em
atic
al
s
tu
d
en
t
s
k
ills
.
S
in
ce
th
e
s
ig
n
if
ican
ce
is
s
m
aller
th
a
n
0
.
0
5
,
i
t
m
ea
n
s
th
at
th
er
e
ar
e
d
if
f
e
r
en
ce
s
in
t
h
e
d
ata.
T
h
u
s
,
th
e
m
ath
em
atica
l
co
m
m
u
n
icatio
n
s
k
ills
test
s
b
ased
o
n
s
tu
d
e
n
ts
'
ea
r
ly
m
ath
em
atica
l sk
ills
(
lo
w,
m
ed
iu
m
an
d
h
ig
h
)
d
if
f
e
r
s
ig
n
if
ican
tly
.
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