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3
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5
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6
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1
1
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T
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[
1
2
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–
[
1
4
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.
C
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7
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a
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els
[
1
8
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–
[
2
3
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Ho
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s
[
2
4
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,
[
2
5
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.
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in
g
in
s
titu
tio
n
s
.
I
t
is
an
i
m
p
o
r
tan
t
ac
a
d
em
ic
co
u
r
s
e
d
u
e
t
o
its
wid
e
ap
p
licati
o
n
in
b
o
th
s
cien
ce
,
tech
n
o
lo
g
y
an
d
ec
o
n
o
m
ics
[
2
8
]
,
[
2
9
]
.
Stu
d
en
ts
o
f
ten
co
n
s
id
er
lin
ea
r
alg
eb
r
a
co
u
r
s
es
at
th
e
co
lleg
e
lev
el
as
d
if
f
icu
lt
m
at
h
em
atics
co
u
r
s
es
[
3
0
]
.
Fo
r
Stu
h
lm
an
n
[
3
1
]
,
m
o
s
t
s
tu
d
en
ts
h
av
e
g
r
ea
t
d
if
f
icu
lty
i
n
m
ak
in
g
s
en
s
e
o
f
alg
eb
r
aic
s
tr
u
ctu
r
es
an
d
ax
io
m
atic
al
g
eb
r
ai
c
m
eth
o
d
s
[
3
2
]
an
d
in
s
elec
tin
g
ap
p
r
o
p
r
iate
m
et
h
o
d
s
f
o
r
s
y
s
tem
o
f
lin
ea
r
eq
u
a
tio
n
s
[
3
3
]
.
R
esear
ch
b
y
Fer
r
y
an
s
y
ah
et
a
l
.
[
3
4
]
an
aly
ze
d
th
e
d
if
f
icu
lty
o
f
s
tu
d
en
ts
in
lear
n
in
g
lin
ea
r
alg
eb
r
a
in
m
ath
em
atics
ed
u
ca
tio
n
co
u
r
s
e
an
d
ac
co
r
d
in
g
to
th
eir
r
esu
lts
,
th
e
d
if
f
ic
u
lty
o
f
s
tu
d
en
ts
in
lear
n
in
g
lin
ea
r
alg
e
b
r
a
is
v
e
r
y
h
ig
h
:
8
8
.
6
3
%
o
f
s
tu
d
en
ts
ar
e
n
o
t
ab
le
to
r
ep
r
esen
t
t
h
e
s
y
m
b
o
l
o
r
n
o
ta
tio
n
,
8
8
.
1
1
%
o
f
s
tu
d
e
n
ts
h
av
e
d
if
f
icu
lties
in
u
s
in
g
m
ath
em
ati
ca
l
id
ea
s
an
d
lo
g
ical
r
ea
s
o
n
in
g
.
A
d
d
ed
t
o
th
is
,
teac
h
er
s
ar
e
also
n
o
t
o
p
tim
al
en
o
u
g
h
in
th
e
u
s
e
o
f
lear
n
i
n
g
m
e
d
ia
an
d
m
et
h
o
d
s
to
teac
h
lin
ea
r
alg
eb
r
a
in
th
e
clas
s
r
o
o
m
[
3
5
]
–
[
3
7
]
.
T
h
e
r
ef
o
r
e
,
it
s
ee
m
s
clea
r
th
at
teac
h
in
g
in
a
t
r
ad
itio
n
al
way
m
ay
n
o
t
s
ig
n
if
ican
tly
im
p
r
o
v
e
s
tu
d
en
t
lear
n
in
g
an
d
b
ec
o
m
es
a
r
elev
an
t
is
s
u
e
f
o
r
th
e
co
n
tin
u
in
g
an
d
in
itial
tr
ain
in
g
o
f
m
at
h
em
atics
teac
h
er
s
.
T
h
is
ar
ticle
is
r
elate
d
to
th
ese
asp
ec
ts
an
d
s
h
o
ws
t
h
e
e
x
p
er
ie
n
ce
with
s
tu
d
e
n
ts
wh
o
ar
e
b
ein
g
tr
ain
ed
as
f
u
t
u
r
e
m
a
th
em
atics
teac
h
er
s
in
a
s
tate
u
n
iv
er
s
ity
in
C
h
ile,
wh
e
r
e
lin
ea
r
alg
eb
r
a
is
o
n
e
o
f
th
e
r
eq
u
ir
ed
c
o
u
r
s
es,
h
o
wev
er
,
th
e
p
e
r
f
o
r
m
an
ce
o
f
s
tu
d
en
ts
i
n
th
is
s
u
b
ject,
h
as
n
o
t
b
ee
n
in
ac
co
r
d
an
ce
with
th
e
ex
p
ec
ted
ac
ad
e
m
ic
p
er
f
o
r
m
a
n
ce
.
C
o
n
s
id
er
in
g
th
e
d
izzy
in
g
ch
an
g
es
th
at
h
av
e
s
tr
ain
ed
th
e
wo
r
k
o
f
h
ig
h
er
ed
u
ca
tio
n
in
th
e
co
n
tex
t
o
f
th
e
C
OVI
D
-
1
9
p
an
d
em
ic
wh
ich
in
th
e
ca
s
e
o
f
C
h
ile
im
p
lied
th
e
tr
an
s
f
er
o
f
a
lar
g
e
p
ar
t
o
f
th
e
f
ac
e
-
to
-
f
ac
e
ed
u
ca
tio
n
al
wo
r
k
to
th
e
r
em
o
te
m
o
d
e
d
u
r
in
g
th
e
y
ea
r
2
0
2
0
,
wh
ich
h
ad
a
n
atio
n
al
im
p
ac
t
o
n
th
e
lear
n
in
g
o
f
m
o
r
e
th
an
3
.
5
m
illi
o
n
ch
ild
r
en
an
d
y
o
u
n
g
p
e
o
p
le
[
3
8
]
,
[
3
9
]
t
o
wh
ich
is
ad
d
ed
th
e
cu
r
r
en
t
e
x
p
lo
s
io
n
o
f
a
r
tific
ial
in
tellig
en
ce
to
o
ls
,
m
o
s
tly
u
s
ed
b
y
s
tu
d
en
ts
,
wh
ich
is
ch
alle
n
g
in
g
teac
h
i
n
g
p
r
ac
tices
m
ain
tain
ed
f
o
r
ce
n
t
u
r
ies
[
4
0
]
,
[
4
1
]
,
th
e
f
o
llo
win
g
q
u
e
s
tio
n
was
f
o
r
m
u
lated
an
d
s
er
v
ed
as
a
g
u
id
e
f
o
r
th
e
r
esear
ch
:
is
it
p
o
s
s
ib
le
to
s
u
cc
ess
f
u
lly
im
p
lem
en
t
a
d
id
a
ctic
s
tr
ateg
y
th
at
p
r
o
m
o
tes
th
e
d
ev
elo
p
m
en
t
o
f
m
ath
em
atica
l
co
m
p
eten
cies
an
d
s
o
f
t
co
m
p
eten
cies
th
at
a
r
e
p
a
r
t
o
f
th
e
cu
r
r
ic
u
lu
m
in
m
ath
e
m
atics
teac
h
er
tr
ain
in
g
?
T
o
a
n
s
wer
th
is
q
u
esti
o
n
,
a
d
id
ac
tic
s
tr
ateg
y
was
d
esig
n
ed
in
a
lin
ea
r
alg
e
b
r
a
c
o
u
r
s
e
o
f
th
e
f
ir
s
t
s
em
ester
,
wh
ic
h
b
eg
an
in
Ma
r
ch
an
d
co
n
clu
d
e
d
in
Au
g
u
s
t,
wh
o
s
e
g
en
er
al
o
b
jectiv
e
was
to
k
n
o
w
th
e
in
cid
en
ce
o
f
a
d
id
ac
tic
s
tr
ate
g
y
b
ased
o
n
t
h
e
ex
ec
u
tio
n
o
f
m
ath
em
atica
l
c
o
m
p
eten
cies
an
d
s
o
f
t
co
m
p
e
ten
cies
in
m
ath
em
atics
p
ed
a
g
o
g
y
s
tu
d
en
ts
.
T
h
e
s
p
ec
if
ic
o
b
jectiv
es
:
i
)
to
d
escr
i
b
e
th
e
d
id
ac
tic
s
tr
ateg
y
f
o
r
th
e
teac
h
in
g
o
f
lin
ea
r
alg
eb
r
a
ab
o
u
t
th
e
in
co
r
p
o
r
atio
n
o
f
co
llab
o
r
ativ
e
m
eth
o
d
o
lo
g
y
;
ii
)
to
elab
o
r
ate
,
v
alid
ate
an
d
ap
p
ly
an
ev
alu
atio
n
i
n
s
tr
u
m
en
t
b
ased
o
n
m
ath
em
atica
l
co
m
p
eten
cies
an
d
s
o
f
t
co
m
p
eten
cies;
an
d
iii
)
to
d
escr
ib
e
an
d
an
aly
ze
th
e
s
tu
d
en
ts
'
o
p
in
io
n
r
eg
ar
d
in
g
th
e
s
tr
en
g
th
s
an
d
we
ak
n
ess
es o
f
th
e
d
ev
el
o
p
m
en
t
o
f
th
e
d
id
ac
tic
s
tr
ateg
y
.
2.
RE
S
E
ARCH
B
ACK
G
RO
U
ND
T
o
en
r
ich
o
u
r
teac
h
in
g
,
we
u
s
ed
a
d
id
ac
tic
s
tr
ateg
y
th
at
h
as
as
its
r
esear
ch
f
r
am
ewo
r
k
t
h
e
co
m
p
eten
cies
d
ef
in
ed
in
o
u
r
u
n
iv
e
r
s
ity
'
s
o
wn
cu
r
r
icu
lu
m
as
ac
cr
ed
it
ed
in
p
ed
ag
o
g
ical
q
u
ality
,
wh
ich
in
clu
d
es
t
h
e
m
ath
em
atica
l
o
r
h
ar
d
co
m
p
et
en
cies
b
ased
o
n
th
e
“
Gu
id
in
g
Stan
d
ar
d
s
f
o
r
Ped
ag
o
g
y
C
ar
ee
r
s
in
Seco
n
d
ar
y
E
d
u
ca
tio
n
:
Ped
ag
o
g
ical
an
d
Dis
cip
lin
ar
y
Stan
d
ar
d
s
”
[
4
2
]
,
in
wh
ich
s
tan
d
ar
d
n
u
m
b
e
r
4
s
tates
th
at
th
e
f
u
tu
r
e
m
ath
em
atics
teac
h
er
m
u
s
t
d
e
m
o
n
s
tr
ate
d
is
cip
lin
ar
y
co
m
p
e
ten
cy
in
lin
ea
r
alg
eb
r
a
an
d
,
in
ad
d
itio
n
,
m
u
s
t
d
em
o
n
s
tr
ate
th
e
a
b
ilit
y
to
lead
th
e
lear
n
in
g
o
f
lin
ea
r
alg
eb
r
a
ap
p
licatio
n
s
in
s
ch
o
o
l
m
ath
em
atics.
W
ith
r
esp
ec
t
to
th
e
s
o
f
t
c
o
m
p
e
ten
cies,
th
o
s
e
d
ec
lar
ed
b
y
th
e
i
n
s
titu
tio
n
wer
e
co
n
s
id
er
ed
,
a
n
d
r
ep
r
esen
t
wh
at
is
ex
p
ec
ted
o
f
th
e
s
tu
d
e
n
t.
Acc
o
r
d
in
g
to
th
e
cu
r
r
ic
u
l
u
m
,
th
e
s
o
f
t
c
o
m
p
eten
cies
to
b
e
ac
h
iev
e
d
in
th
e
s
tu
d
en
ts
ar
e:
to
ca
r
r
y
o
u
t
ac
a
d
em
ic
ac
tiv
ities
b
y
co
n
tin
u
o
u
s
ly
s
ee
k
in
g
to
im
p
r
o
v
e
o
n
ese
lf
,
in
a
p
er
s
ev
e
r
in
g
m
an
n
er
,
co
m
p
ly
in
g
with
estab
lis
h
ed
n
o
r
m
s
an
d
s
tan
d
ar
d
s
an
d
m
ain
tain
in
g
eth
ical
an
d
co
ll
ab
o
r
ativ
e
ac
tio
n
s
in
th
e
p
r
o
ce
s
s
to
o
b
tain
o
p
tim
al
r
esu
lts
;
to
m
an
ag
e
o
n
e'
s
o
wn
le
ar
n
in
g
,
in
d
iv
id
u
ally
a
n
d
co
llab
o
r
ativ
ely
,
ac
tiv
atin
g
co
g
n
itiv
e,
m
eta
-
co
g
n
itiv
e
an
d
s
o
cio
-
af
f
ec
tiv
e
s
tr
ateg
ies
th
at
co
n
tr
ib
u
te
to
a
f
av
o
r
a
b
le
ex
p
er
ien
ce
o
f
th
e
ac
ad
em
ic
p
r
o
ce
s
s
es
an
d
p
r
o
f
e
s
s
io
n
al
life
;
to
u
n
d
er
s
tan
d
th
e
eth
ical
r
esp
o
n
s
ib
ilit
y
o
f
th
eir
f
u
n
ctio
n
s
,
b
eh
a
v
in
g
with
h
o
n
esty
a
n
d
p
er
s
o
n
al
i
n
teg
r
ity
,
ac
tin
g
with
r
esp
o
n
s
ib
ilit
y
an
d
s
o
cial
co
m
m
itm
e
n
t.
I
n
r
e
s
p
o
n
s
e
to
th
ese
s
o
f
t
co
m
p
eten
ce
s
,
c
o
llab
o
r
ativ
e
lea
r
n
in
g
was
in
clu
d
ed
as
a
p
r
io
r
it
y
in
o
u
r
r
esear
ch
.
T
h
e
u
s
e
o
f
g
r
o
u
p
s
in
in
s
tr
u
ctio
n
is
b
ased
o
n
th
e
p
r
in
cip
le
o
f
co
n
s
tr
u
ctiv
is
m
,
with
s
p
ec
ial
atten
tio
n
to
th
e
c
o
n
tr
ib
u
tio
n
th
at
s
o
cial
in
ter
ac
tio
n
ca
n
m
ak
e.
I
n
ess
en
ce
,
co
n
s
tr
u
ctiv
i
s
m
is
,
in
tu
r
n
,
b
ased
o
n
th
e
id
ea
th
at
in
d
iv
id
u
als lea
r
n
b
y
co
n
s
tr
u
ctin
g
th
eir
o
wn
k
n
o
wled
g
e,
co
n
n
ec
tin
g
n
ew
i
d
ea
s
an
d
e
x
p
er
ien
ce
s
with
ex
is
tin
g
k
n
o
wl
ed
g
e
an
d
ex
p
er
ien
ce
s
to
f
o
r
m
a
n
ew
o
r
im
p
r
o
v
e
d
u
n
d
er
s
tan
d
in
g
[
4
3
]
,
[
4
4
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
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SS
N
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2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
13
,
No
.
6
,
Dec
em
b
er
2
0
2
4
:
4
2
5
6
-
4
2
7
0
4258
2
.
1
.
T
ea
ching
lin
ea
r
a
lg
ebra
Sin
ce
lin
ea
r
al
g
eb
r
a
to
d
a
y
is
u
s
ef
u
l to
a
wid
e
v
ar
iety
o
f
s
tu
d
en
ts
,
th
e
q
u
esti
o
n
ar
is
es:
h
o
w
d
o
s
tu
d
e
n
ts
lear
n
lin
ea
r
alg
eb
r
a
an
d
wh
at
teac
h
in
g
m
eth
o
d
s
a
r
e
m
o
s
t
ef
f
e
ctiv
e?
T
h
e
a
v
ailab
ilit
y
o
f
co
m
p
u
ter
s
an
d
s
o
f
twar
e
h
as
f
o
r
ce
d
m
ath
em
atician
s
to
r
eth
in
k
th
e
way
th
ey
teac
h
m
ath
em
atics.
W
h
en
a
co
m
p
u
ter
ca
n
p
er
f
o
r
m
an
alg
o
r
ith
m
q
u
ick
ly
an
d
s
u
cc
ess
f
u
lly
,
it
b
eg
s
th
e
q
u
esti
o
n
:
w
h
at
d
o
es
a
s
tu
d
e
n
t
r
ea
lly
n
ee
d
t
o
lear
n
an
d
wh
at
is
th
e
m
o
s
t
ap
p
r
o
p
r
iate
teac
h
i
n
g
s
tr
ateg
y
f
o
r
a
f
u
tu
r
e
s
ec
o
n
d
a
r
y
s
ch
o
o
l
teac
h
er
?
R
o
u
g
h
ly
two
m
ain
tr
ad
itio
n
s
ca
n
b
e
d
is
tin
g
u
is
h
ed
in
t
h
e
teac
h
i
n
g
o
f
li
n
ea
r
alg
eb
r
a:
o
n
e
t
r
ad
i
tio
n
f
o
cu
s
es
o
n
t
h
e
s
tu
d
y
o
f
f
o
r
m
al
v
ec
to
r
s
p
ac
es,
wh
ile
th
e
o
th
er
p
r
o
p
o
s
es a
m
o
r
e
an
aly
tical
ap
p
r
o
ac
h
b
ased
o
n
th
e
s
tu
d
y
o
f
I
R
n
an
d
m
atr
ix
ca
lcu
lu
s
[
4
5
]
.
Fo
r
th
e
ap
p
r
o
ac
h
b
ased
o
n
m
a
tr
ix
ca
lcu
lu
s
,
it
h
as
b
ee
n
p
r
o
p
o
s
ed
th
e
u
s
e
o
f
s
o
f
twar
e
d
esig
n
ed
f
r
o
m
a
d
id
ac
tic
p
o
in
t
o
f
v
iew,
to
h
el
p
s
tu
d
en
ts
in
lear
n
in
g
th
e
co
n
ten
ts
,
g
iv
in
g
ex
am
p
les,
test
in
g
with
m
atr
ices
o
f
d
if
f
er
en
t
s
izes
to
s
ee
wh
at
h
ap
p
en
s
o
r
ev
e
n
to
s
o
lv
e
e
x
er
cises
.
T
h
e
latter
is
n
o
t
a
p
r
o
b
lem
,
in
th
e
s
en
s
e
th
at
n
o
m
atter
h
o
w
m
u
c
h
a
r
esu
lt
is
o
b
tain
ed
,
t
h
e
im
p
o
r
tan
t
th
in
g
is
n
o
t
to
o
b
tain
th
e
c
o
r
r
ec
t
r
esu
l
t,
b
u
t
to
u
n
d
e
r
s
tan
d
wh
y
wh
at
is
o
b
tain
ed
is
o
b
tain
ed
an
d
to
u
n
d
er
s
tan
d
th
e
in
t
er
n
al
p
r
o
ce
s
s
es
o
f
th
e
alg
o
r
ith
m
s
[
4
6
]
.
R
eg
ar
d
in
g
th
e
s
tu
d
y
f
o
cu
s
ed
o
n
v
ec
to
r
s
p
ac
es,
b
o
th
its
lear
n
in
g
an
d
teac
h
in
g
r
ep
r
esen
ts
a
ch
allen
g
e
d
u
e
to
its
h
ig
h
lev
el
o
f
ab
s
tr
ac
tio
n
an
d
,
i
n
a
d
d
itio
n
,
b
ec
au
s
e
t
h
is
co
n
ten
t
was
n
o
t
c
r
ea
ted
to
s
o
lv
e
p
r
o
b
lem
s
,
b
u
t
was
cr
ea
ted
to
u
n
if
y
an
d
g
en
er
alize
b
o
th
ex
is
tin
g
m
eth
o
d
s
an
d
co
n
ce
p
ts
[
4
7
]
.
I
n
r
ec
en
t
y
ea
r
s
,
r
esear
ch
h
as
f
o
cu
s
ed
o
n
m
ak
i
n
g
in
n
o
v
atio
n
s
f
o
r
lear
n
in
g
c
o
n
te
n
t
r
elate
d
to
v
ec
to
r
s
p
ac
es
[
4
8
]
,
[
4
9
]
,
id
en
tify
in
g
d
if
f
icu
lties
th
at
s
tu
d
en
ts
h
av
e
with
th
em
[
5
0
]
,
[
5
1
]
,
an
d
e
r
r
o
r
s
[
5
2
]
.
2
.
2
.
Co
lla
bo
ra
t
iv
e
lea
rning
B
o
th
in
s
ch
o
o
l,
ac
ad
em
ic
an
d
p
r
o
f
ess
io
n
al
ca
r
ee
r
s
,
we
ar
e
d
e
s
tin
ed
to
f
ac
e
p
r
o
b
lem
s
in
d
iv
i
d
u
ally
,
b
u
t
also
-
in
cr
ea
s
in
g
l
y
an
d
co
llab
o
r
ativ
ely
.
T
h
u
s
,
co
llab
o
r
ativ
e
p
r
o
b
lem
s
o
lv
in
g
b
ec
am
e
a
n
ew
d
o
m
ain
in
th
e
PISA
2
0
1
5
s
tu
d
y
.
C
o
llab
o
r
ativ
e
p
r
o
b
lem
s
o
lv
in
g
is
an
ad
v
an
tag
e
d
u
e
to
th
e
d
iv
is
io
n
o
f
lab
o
r
,
v
a
r
iety
o
f
k
n
o
wled
g
e,
d
if
f
er
en
t
p
e
r
s
p
ec
tiv
es
an
d
ex
p
er
ien
ce
s
,
r
ec
ip
r
o
ca
l
m
o
tiv
atio
n
,
all
aim
ed
at
a
b
etter
s
o
lu
tio
n
o
f
a
g
iv
en
p
r
o
b
le
m
o
r
ac
a
d
em
ic
wo
r
k
[
5
3
]
.
I
n
g
e
n
er
al,
c
o
llab
o
r
ativ
e
lear
n
in
g
i
s
a
co
n
s
tr
u
ct
th
at
id
en
tifie
s
a
f
ield
o
f
s
tr
o
n
g
a
n
d
g
r
o
win
g
r
elev
a
n
ce
an
d
is
p
ar
t
o
f
a
s
o
f
t
o
r
cr
o
s
s
-
cu
ttin
g
co
m
p
eten
cy
.
I
t
r
ef
er
s
to
in
s
tr
u
ctio
n
a
l
ar
r
an
g
em
en
ts
th
at
in
v
o
lv
e
a
m
in
im
u
m
o
f
two
o
r
m
o
r
e
s
tu
d
en
ts
wo
r
k
in
g
to
g
eth
er
o
n
a
s
h
a
r
ed
lear
n
in
g
o
b
jectiv
e
[
5
4
]
,
[
5
5
]
.
A
lar
g
e
n
u
m
b
e
r
o
f
s
tu
d
ies
d
e
m
o
n
s
tr
ate
th
e
p
o
s
itiv
e
ef
f
ec
ts
o
f
c
o
llab
o
r
ativ
e
lear
n
in
g
o
n
co
g
n
itiv
e,
m
etac
o
g
n
itiv
e,
af
f
ec
tiv
e
-
m
o
tiv
atio
n
al,
an
d
s
o
cial
asp
ec
ts
o
f
lear
n
in
g
[
1
5
]
,
[
1
7
]
,
[
5
6
]
,
[
5
7
]
.
Sev
er
al
p
r
ev
io
u
s
r
esear
ch
es
[
5
8
]
–
[
6
0
]
h
a
v
e
s
h
o
wn
th
at
s
tu
d
en
ts
wo
r
k
in
g
in
s
m
all
g
r
o
u
p
s
h
av
e
b
etter
lear
n
i
n
g
o
u
tc
o
m
es
th
an
s
tu
d
en
ts
wo
r
k
in
g
o
n
an
in
d
i
v
id
u
al
ass
ig
n
m
en
t,
s
u
ch
as
g
r
ea
ter
lear
n
in
g
g
ain
s
,
h
ig
h
e
r
p
er
f
o
r
m
an
ce
o
n
s
tan
d
ar
d
ized
test
s
o
r
o
n
s
elf
-
r
ep
o
r
ted
ass
ess
m
en
ts
d
u
r
in
g
th
e
co
u
r
s
e.
H
o
wev
er
,
th
ese
p
o
s
itiv
e
o
u
tco
m
es
ca
n
o
n
ly
b
e
ac
h
iev
ed
wh
en
teac
h
e
r
s
m
ak
e
ap
p
r
o
p
r
iate
p
ed
ag
o
g
i
ca
l d
ec
is
io
n
s
[
6
1
]
,
[
6
2
]
.
W
h
ile
s
tu
d
en
ts
wo
r
k
co
llab
o
r
ativ
ely
,
teac
h
er
s
s
h
o
u
ld
m
o
n
it
o
r
wh
at
p
r
o
b
lem
s
s
tu
d
en
ts
en
c
o
u
n
ter
an
d
in
ter
v
en
e
w
h
en
n
ec
ess
ar
y
[
6
3
]
.
T
h
e
r
ef
o
r
e
,
th
e
teac
h
er
'
s
r
o
le
is
cr
u
cial
in
f
o
s
ter
in
g
p
o
s
itiv
e
in
ter
ac
tio
n
am
o
n
g
lear
n
er
s
[
6
1
]
.
T
h
e
teac
h
e
r
d
ia
g
n
o
s
es
th
e
p
r
o
g
r
ess
o
f
th
e
g
r
o
u
p
an
d
i
n
ter
v
en
es
wh
en
n
ec
ess
ar
y
[
6
2
]
.
W
ith
o
u
t
p
r
o
p
er
g
u
i
d
an
ce
,
p
o
s
itiv
e
in
te
r
ac
tio
n
am
o
n
g
s
tu
d
e
n
ts
is
at
r
is
k
.
W
h
en
teac
h
er
s
f
ail
to
id
e
n
tify
p
r
o
b
lem
s
ea
r
ly
an
d
in
te
r
v
en
e
ap
p
r
o
p
r
iately
,
t
h
e
q
u
ality
o
f
t
h
e
c
o
llab
o
r
ativ
e
p
r
o
ce
s
s
an
d
th
e
r
esu
ltin
g
lea
r
n
in
g
o
u
tco
m
es
ca
n
b
e
h
i
n
d
e
r
e
d
.
G
u
i
d
i
n
g
g
r
o
u
p
s
o
f
s
t
u
d
e
n
ts
i
n
c
o
ll
a
b
o
r
a
t
i
v
e
w
o
r
k
is
a
d
e
m
a
n
d
i
n
g
t
a
s
k
f
o
r
t
e
a
c
h
e
r
s
[
6
4
]
.
Fo
r
ex
am
p
le,
it
r
eq
u
ir
es
teac
h
er
s
to
m
aster
m
u
ltip
le
ad
v
an
ce
d
co
m
p
eten
cies
[
6
5
]
.
T
h
is
is
b
ec
au
s
e,
d
u
r
in
g
t
h
e
lear
n
in
g
p
r
o
ce
s
s
in
wh
ich
it
tak
es
p
lace
,
teac
h
er
s
m
u
s
t
s
u
p
er
v
is
e
s
ev
er
al
g
r
o
u
p
s
at
th
e
s
am
e
tim
e,
p
r
o
v
id
e
s
u
p
p
o
r
t
r
e
g
ar
d
i
n
g
th
e
co
n
ten
t
o
f
th
e
task
as
well
as
s
tr
ateg
ies
f
o
r
c
o
llab
o
r
atio
n
,
a
n
d
m
u
s
t
d
ec
id
e
wh
eth
e
r
in
ter
v
en
tio
n
is
n
ec
ess
ar
y
an
d
,
if
s
o
,
wh
at
ty
p
e
o
f
in
ter
v
e
n
tio
n
is
m
o
s
t
ap
p
r
o
p
r
iate.
T
h
e
r
ef
o
r
e,
c
o
llab
o
r
ativ
e
lear
n
in
g
r
eq
u
ir
es
m
u
ch
m
o
r
e
f
r
o
m
th
e
teac
h
er
th
a
n
s
im
p
ly
p
lacin
g
s
tu
d
en
ts
in
g
r
o
u
p
s
a
n
d
i
n
s
tr
u
ctin
g
th
em
t
o
wo
r
k
to
g
et
h
er
[
2
0
]
,
[
6
1
]
.
3.
M
E
T
H
O
D
3
.
1
.
Resea
rc
h desi
g
n
Du
e
to
th
e
ex
p
lo
r
ato
r
y
n
atu
r
e
o
f
th
e
r
esear
ch
an
d
its
n
atu
r
e,
wh
er
e
b
o
th
th
e
p
r
o
ce
s
s
an
d
th
e
p
r
o
d
u
ct
ar
e
o
f
in
ter
est,
a
q
u
an
titativ
e
-
d
escr
ip
tiv
e
an
d
q
u
alitativ
e
-
in
te
r
p
r
etativ
e
m
eth
o
d
o
l
o
g
y
was
u
s
e
d
.
I
n
th
e
f
o
llo
win
g
,
we
d
escr
ib
e
th
e
d
etails
o
f
th
e
m
eth
o
d
o
l
o
g
ical
p
r
o
ce
s
s
,
f
o
c
u
s
in
g
o
n
th
e
co
n
te
x
t
in
wh
ich
t
h
e
r
esear
ch
was
ca
r
r
ied
o
u
t,
th
e
d
ata
th
at
was
co
llecte
d
an
d
h
o
w
th
e
an
aly
s
is
o
f
th
is
d
ata
was
ca
r
r
i
ed
o
u
t
in
o
r
d
e
r
to
r
esp
o
n
d
to
th
e
r
esear
ch
o
b
jectiv
es
wh
ich
a
r
e
r
elate
d
t
o
th
e
k
n
o
wled
g
e
o
f
t
h
e
im
p
ac
t
o
f
a
d
id
ac
tic
in
ter
v
en
tio
n
b
ased
o
f
th
e
ac
h
iev
em
en
t
o
f
d
is
cip
lin
ar
y
c
o
m
p
eten
ce
s
in
m
ath
em
atics
a
n
d
s
o
f
t
o
r
tr
a
n
s
v
er
s
al
co
m
p
ete
n
ce
s
an
d
ap
p
lied
to
s
tu
d
en
t
s
in
in
itial tr
ain
in
g
.
3
.
2
.
Sa
m
ple o
f
re
s
ea
rc
h
T
h
e
u
n
it
o
f
a
n
aly
s
is
o
f
th
e
r
esear
ch
c
o
r
r
esp
o
n
d
ed
to
2
5
s
tu
d
en
ts
,
o
f
wh
ich
1
0
ar
e
wo
m
e
n
an
d
1
5
ar
e
m
en
b
etwe
en
th
e
a
g
es
o
f
1
8
a
n
d
2
0
,
w
h
o
m
ad
e
u
p
th
e
to
tal
ity
o
f
th
o
s
e
wh
o
to
o
k
t
h
e
co
m
p
u
ls
o
r
y
s
u
b
ject
o
f
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2252
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8
8
2
2
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a
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p
erien
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b
a
s
ed
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ma
th
ema
tics
co
mp
eten
cies a
n
d
s
o
ft c
o
mp
eten
cies fo
r
…
(
V
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r
ó
n
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Día
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4259
lin
ea
r
alg
eb
r
a
in
th
eir
s
ec
o
n
d
y
ea
r
,
b
el
o
n
g
in
g
to
a
d
eg
r
ee
co
u
r
s
e
in
m
ath
em
atics tea
ch
in
g
at
a
u
n
iv
er
s
ity
in
th
e
s
o
u
th
o
f
C
h
ile.
I
t
s
h
o
u
ld
b
e
n
o
ted
th
at
all
p
a
r
ticip
an
ts
r
ec
eiv
ed
d
etailed
in
f
o
r
m
atio
n
o
n
th
e
o
b
jectiv
es
an
d
m
eth
o
d
o
l
o
g
ies o
f
th
e
s
tu
d
y
p
r
i
o
r
to
th
eir
p
ar
ticip
atio
n
.
3
.
3
.
Resea
rc
h pro
ce
du
re
L
in
ea
r
alg
eb
r
a
is
a
co
m
p
u
ls
o
r
y
co
u
r
s
e
(
s
em
ester
)
o
f
6
h
o
u
r
s
p
er
wee
k
an
d
is
lo
ca
ted
in
th
e
s
ec
o
n
d
s
em
ester
o
f
th
e
s
ec
o
n
d
y
ea
r
o
f
th
e
c
u
r
r
icu
l
u
m
.
T
h
e
p
r
ev
io
u
s
m
ath
em
atica
l
b
ac
k
g
r
o
u
n
d
o
f
th
e
s
tu
d
e
n
ts
o
f
th
e
lin
ea
r
alg
eb
r
a
co
u
r
s
e
is
an
alg
eb
r
a
co
u
r
s
e
an
d
a
g
e
o
m
etr
y
co
u
r
s
e.
T
h
e
m
ain
o
b
jectiv
e
o
f
th
e
lin
ea
r
alg
eb
r
a
co
u
r
s
e
is
f
o
r
s
tu
d
en
ts
to
d
e
v
elo
p
s
k
ills
s
u
ch
as
m
ath
e
m
atica
l
lo
g
ical
r
ea
s
o
n
in
g
a
n
d
p
r
o
b
lem
s
o
lv
in
g
.
I
t
is
ex
p
ec
ted
th
at
t
h
is
co
u
r
s
e
will
p
r
o
v
id
e
s
tu
d
en
ts
with
k
e
y
ele
m
en
ts
f
o
r
th
e
d
ev
el
o
p
m
en
t
o
f
s
u
b
s
eq
u
en
t
co
u
r
s
es.
I
t
is
d
iv
id
ed
in
to
f
iv
e
u
n
its
:
i
)
m
atr
ices
an
d
s
y
s
tem
s
o
f
lin
ea
r
eq
u
atio
n
s
;
ii
)
d
eter
m
in
an
ts
;
iii
)
v
ec
to
r
s
in
th
e
p
lan
e
an
d
in
s
p
ac
e
;
iv
)
v
ec
to
r
s
p
ac
es
;
an
d
v
)
lin
ea
r
tr
an
s
f
o
r
m
atio
n
s
.
T
h
e
ex
p
licit
m
at
h
em
atica
l
co
m
p
eten
cies
to
b
e
ac
h
iev
e
d
in
th
e
s
y
llab
u
s
f
o
r
th
e
f
ir
s
t
two
u
n
its
wer
e:
d
ev
elo
p
in
g
m
atr
i
x
alg
e
b
r
a;
id
e
n
tify
in
g
d
if
f
e
r
en
t
ty
p
es
o
f
m
atr
ices
an
d
th
eir
p
r
o
p
er
ties
;
o
p
er
a
tin
g
with
m
atr
ices;
r
elatin
g
s
y
s
tem
s
o
f
lin
ea
r
e
q
u
atio
n
s
to
m
a
tr
ices;
class
if
y
in
g
an
d
s
o
lv
in
g
s
y
s
tem
s
o
f
lin
ea
r
eq
u
atio
n
s
u
s
in
g
m
atr
ix
tech
n
iq
u
es;
d
ef
in
in
g
d
eter
m
in
an
t
o
f
m
at
r
ices;
id
en
tify
in
g
its
p
r
o
p
er
ties
,
an
d
u
s
in
g
it
to
ca
lcu
late
th
e
in
v
er
s
e
m
atr
ix
an
d
to
s
o
lv
e
s
y
s
tem
s
o
f
lin
ea
r
e
q
u
atio
n
s
wh
e
r
e
th
e
n
u
m
b
er
o
f
u
n
k
n
o
w
n
s
is
eq
u
al
to
t
h
e
n
u
m
b
er
o
f
eq
u
atio
n
s
.
Fo
r
th
e
teac
h
in
g
o
f
th
ese
u
n
its
,
ea
ch
s
tu
d
e
n
t
wa
s
p
r
o
v
id
ed
with
a
“
L
in
ea
r
Alg
e
b
r
a
Ma
n
u
al
”
c
r
ea
ted
b
y
th
e
teac
h
er
-
r
esear
ch
er
,
wit
h
th
e
co
n
ten
ts
o
f
b
o
th
u
n
its
,
wh
ich
b
eg
an
with
an
in
tr
o
d
u
c
tio
n
to
th
e
to
p
ic
o
f
s
tu
d
y
,
with
ex
am
p
les
o
f
p
r
o
b
l
em
s
f
r
o
m
ev
er
y
d
ay
life
,
an
d
w
ith
wo
r
k
g
u
id
es
as
th
e
u
n
its
p
r
o
g
r
ess
ed
.
All
o
f
t
h
is
was
in
co
r
p
o
r
ated
in
t
o
th
e
s
tu
d
en
t'
s
p
o
r
tf
o
lio
o
f
e
v
id
en
ce
.
At
t
h
e
en
d
o
f
ea
c
h
u
n
it,
ed
u
ca
tio
n
a
l
Yo
u
T
u
b
e
tu
to
r
ials
o
r
ien
ted
to
th
e
s
tu
d
y
o
f
m
at
h
e
m
atics
wer
e
s
u
g
g
ested
to
th
em
to
b
r
o
ad
e
n
th
eir
in
d
i
v
id
u
al
k
n
o
wled
g
e,
in
d
icatin
g
th
e
ad
d
r
ess
es o
f
th
e
web
s
ites
.
Acc
o
r
d
in
g
to
th
e
cu
r
r
icu
lu
m
,
t
h
e
s
o
f
t
co
m
p
eten
cies
to
b
e
ac
h
iev
ed
in
s
tu
d
en
ts
in
v
o
lv
e
ac
tin
g
eth
ically
,
h
o
n
estl
y
,
with
p
er
s
o
n
al
in
teg
r
i
ty
,
ac
tin
g
with
s
o
cial
co
m
m
itm
en
t a
n
d
p
e
r
s
o
n
al
in
te
g
r
ity
,
a
n
d
co
lla
b
o
r
ativ
ely
i
n
th
e
p
r
o
ce
s
s
to
o
b
tain
o
p
tim
al
r
esu
lts
.
T
ak
e
ch
ar
g
e
o
f
th
eir
o
wn
lear
n
in
g
,
b
o
t
h
in
d
iv
id
u
ally
an
d
co
llab
o
r
ativ
ely
,
ac
tiv
atin
g
n
o
t
o
n
ly
co
g
n
itiv
e
an
d
m
eta
-
co
g
n
itiv
e
s
tr
ateg
ies,
b
u
t
also
s
o
cio
-
af
f
ec
tiv
e
s
tr
ate
g
ies
th
at
co
n
tr
ib
u
te
to
a
f
a
v
o
r
a
b
le
ex
p
er
ien
ce
o
f
a
ca
d
em
ic
p
r
o
ce
s
s
es
an
d
p
r
o
f
es
s
io
n
al
life
.
As
a
r
esu
lt
o
f
th
ese
ex
p
ec
tatio
n
s
i
n
th
e
tr
ain
in
g
o
f
f
u
tu
r
e
s
ec
o
n
d
ar
y
s
ch
o
o
l
teac
h
er
s
in
m
ath
em
atics,
s
tu
d
en
ts
wer
e
ask
ed
to
f
o
r
m
wo
r
k
in
g
g
r
o
u
p
s
,
to
p
r
o
v
id
e
an
d
p
r
o
m
o
te
a
n
ac
tiv
e
lear
n
in
g
en
v
ir
o
n
m
e
n
t
b
y
in
v
o
lv
in
g
t
h
em
in
th
eir
lear
n
in
g
an
d
g
ettin
g
th
em
to
p
ar
ticip
ate
ac
tiv
ely
th
r
o
u
g
h
th
e
v
ar
io
u
s
ac
tiv
ities
cr
ea
ted
wi
th
m
ath
em
atica
l
task
s
th
at
we
r
e
d
esig
n
ed
s
o
th
at
s
tu
d
en
ts
co
u
ld
ex
p
er
ien
ce
m
at
h
em
atica
l
p
r
o
ce
s
s
es
f
o
r
th
em
s
elv
es.
Fo
r
th
is
p
u
r
p
o
s
e,
th
e
f
o
llo
win
g
th
r
ee
u
n
its
wer
e
d
is
tr
ib
u
ted
b
y
th
e
teac
h
e
r
to
th
e
th
r
ee
f
o
r
m
al
g
r
o
u
p
s
f
o
r
m
ed
b
y
th
e
s
tu
d
e
n
ts
o
n
a
v
o
l
u
n
tar
y
b
asis
.
I
n
th
is
way
,
th
e
aim
was
to
en
co
u
r
ag
e
co
o
p
er
ativ
e
lear
n
in
g
o
r
g
r
o
u
p
wo
r
k
,
wr
itten
an
d
o
r
al
m
ath
em
atica
l
co
m
m
u
n
icatio
n
th
r
o
u
g
h
d
is
cu
s
s
io
n
an
d
th
e
ex
ch
a
n
g
e
o
f
i
d
ea
s
am
o
n
g
th
e
s
tu
d
e
n
ts
,
p
r
io
r
to
th
e
in
d
i
v
id
u
al
p
r
esen
tatio
n
s
o
f
ea
c
h
m
ath
em
atica
l su
b
-
u
n
it.
3
.
3
.
1
.
Wo
rk
ing
in g
r
o
up
s
T
h
e
f
o
llo
win
g
t
h
r
ee
u
n
its
wer
e
cu
r
r
icu
lar
ly
d
ef
in
ed
m
ath
em
atica
l c
o
n
ten
t: v
ec
to
r
s
in
th
e
p
lan
e
an
d
in
s
p
ac
e,
v
ec
to
r
s
p
ac
es
,
an
d
lin
ea
r
tr
an
s
f
o
r
m
atio
n
s
.
T
h
e
e
x
p
licit
m
ath
em
atica
l
co
m
p
eten
cies
to
b
e
ac
h
iev
ed
ac
co
r
d
in
g
to
th
e
s
y
llab
u
s
wer
e:
id
en
tify
in
g
v
ec
to
r
s
in
th
e
p
lan
e
an
d
s
p
ac
e;
alg
eb
r
aic
s
tr
u
ctu
r
e
o
f
th
e
s
et
o
f
v
ec
to
r
s
,
th
eir
p
r
o
p
e
r
ties
an
d
r
ep
r
esen
tatio
n
;
id
en
tify
in
g
v
ec
to
r
s
p
ac
es,
th
eir
p
r
o
p
er
ties
an
d
elem
en
ts
;
id
en
tify
in
g
lin
ea
r
tr
an
s
f
o
r
m
atio
n
s
b
etwe
e
n
v
ec
to
r
s
p
ac
es,
th
eir
p
r
o
p
er
ti
es
an
d
elem
en
ts
,
an
d
ca
lcu
latin
g
eig
en
v
al
u
es
an
d
eig
en
v
ec
to
r
s
o
f
lin
ea
r
tr
a
n
s
f
o
r
m
atio
n
s
.
F
o
r
t
h
e
p
r
e
s
e
n
t
at
i
o
n
s
,
t
h
e
y
co
u
l
d
m
a
k
e
u
s
e
o
f
t
e
c
h
n
o
l
o
g
i
c
a
l
r
es
o
u
r
c
e
s
.
I
n
a
d
d
i
t
i
o
n
to
t
h
e
o
r
a
l
p
r
e
s
e
n
t
a
ti
o
n
s
,
e
a
c
h
g
r
o
u
p
h
a
d
t
o
c
a
r
r
y
o
u
t
g
r
o
u
p
w
o
r
k
s
h
o
p
s
.
A
t
t
h
e
e
n
d
o
f
t
h
e
l
e
a
r
n
i
n
g
u
n
i
t
,
t
h
e
y
h
a
d
t
o
w
r
i
t
e
a
s
u
m
m
a
t
i
v
e
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l
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tiv
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ted
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alize
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tiv
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ased
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an
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in
Fig
u
r
e
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
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8
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I
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J
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13
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6
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4260
T
h
e
ev
alu
ati
o
n
o
f
t
h
e
s
tu
d
e
n
ts
’
p
er
f
o
r
m
a
n
ce
in
cl
u
d
ed
s
u
m
m
ativ
e
wr
itten
test
s
,
p
o
r
t
f
o
lio
o
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ev
id
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ce
p
er
s
tu
d
en
t,
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r
al
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tatio
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s
,
co
-
ev
alu
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n
s
o
f
th
e
g
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o
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p
s
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o
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m
ed
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I
n
ad
d
itio
n
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f
o
llo
win
g
th
e
cu
r
r
icu
lar
r
eq
u
ir
em
e
n
ts
,
at
th
e
e
n
d
o
f
th
e
s
em
ester
,
th
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teac
h
er
-
r
esear
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h
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co
n
d
u
cted
a
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itten
ex
am
in
teg
r
atin
g
t
h
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f
iv
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n
its
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v
er
e
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th
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o
u
g
h
o
u
t
t
h
e
s
em
ester
.
T
h
e
u
n
i
v
er
s
ity
also
allo
ws
an
in
teg
r
ativ
e
p
r
o
f
icien
cy
ex
a
m
f
o
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th
o
s
e
wh
o
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ail
th
e
f
ir
s
t e
x
a
m
,
wh
ich
was n
o
t n
ec
ess
ar
y
.
Fig
u
r
e
1
.
Mo
m
en
t o
f
ex
p
o
s
u
r
e
an
d
in
ter
ac
tio
n
with
s
tu
d
en
ts
3
.
4
.
E
v
a
lua
t
io
n ins
t
rum
ent
3
.
4
.
1
.
O
pin
io
n ques
t
io
nn
a
ire
I
n
g
en
er
al,
o
p
i
n
io
n
q
u
esti
o
n
n
a
ir
e
ar
e
a
g
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t
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f
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in
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o
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at
p
e
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p
le
t
h
in
k
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d
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ata
an
o
p
in
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o
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s
o
n
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wid
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to
p
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n
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to
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m
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s
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ac
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th
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atica
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5
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1
.
Co
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C
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ased
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llab
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8
p
r
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f
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als
with
1
0
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s
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f
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th
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u
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ev
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in
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tr
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m
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eq
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ested
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ased
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s
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E
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p
o
s
ed
b
y
E
s
co
b
ar
-
Pér
ez
an
d
Ma
r
tín
ez
[
6
6
]
,
wh
o
s
e
r
atin
g
estab
lis
h
es
f
o
u
r
l
ev
els:
1
=d
o
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o
t
m
ee
t
th
e
cr
it
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io
n
,
2
=lo
w
le
v
el,
3
=
m
ed
iu
m
lev
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4
=h
i
g
h
le
v
el,
wh
ich
co
n
s
titu
tes th
e
b
asis
f
o
r
th
e
ch
ar
ac
ter
is
tics
to
b
e
ev
alu
ated
: c
o
h
er
en
ce
,
r
elev
a
n
ce
,
ad
eq
u
ac
y
a
n
d
clar
ity
.
T
h
e
co
llected
d
ata
wer
e
s
tatis
tically
p
r
o
ce
s
s
ed
in
STAT
A
v
er
s
io
n
1
4
.
0
.
Su
b
s
eq
u
e
n
tly
,
th
e
d
eg
r
ee
o
f
ag
r
ee
m
en
t
b
etwe
en
e
x
p
er
ts
w
as
d
eter
m
in
ed
with
th
e
Fleis
s
k
ap
p
a
co
ef
f
icien
t
as
an
an
aly
s
is
s
tatis
tic,
u
s
ed
to
ass
es
s
ag
r
ee
m
en
t
b
etwe
en
ev
al
u
ato
r
s
wh
o
in
d
ep
en
d
en
tly
ju
d
g
e
m
ea
s
u
r
em
e
n
t
cr
iter
ia,
in
a
n
u
m
b
er
o
f
ca
teg
o
r
ies
o
f
an
o
r
d
in
al
n
atu
r
e
[
6
7
]
.
T
h
e
m
in
im
u
m
v
al
u
e
ass
u
m
ed
b
y
th
e
co
ef
f
icien
t is 0
an
d
th
e
m
a
x
i
m
u
m
is
1
[
6
8
]
.
Fo
r
th
e
in
ter
p
r
etatio
n
o
f
th
is
co
ef
f
icien
t,
th
e
s
ca
le
e
s
tab
lis
h
ed
b
y
L
an
d
is
an
d
Ko
ch
[
6
9
]
was
tak
en
in
to
ac
co
u
n
t,
wh
ich
q
u
alitativ
ely
ex
p
r
ess
es th
e
d
eg
r
ee
o
f
a
g
r
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m
en
t
b
etwe
en
th
e
ev
alu
at
o
r
s
d
etailed
in
T
ab
le
1
.
I
tem
s
th
at
m
et
all
o
f
th
e
estab
lis
h
ed
r
eq
u
ir
em
en
ts
wer
e
co
n
s
i
d
er
ed
a
d
eq
u
ate,
item
s
th
at
r
eq
u
ir
ed
s
o
m
e
ch
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g
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wer
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co
n
s
id
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ed
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e
q
u
ate,
an
d
item
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th
at
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p
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tal
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n
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is
ten
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with
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e
estab
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h
ed
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iter
ia
wer
e
co
n
s
id
er
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in
ad
eq
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ate.
L
ik
ewise,
th
e
ch
a
r
ac
ter
is
tics
o
f
th
e
in
s
tr
u
m
en
t
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e
also
esti
m
ated
f
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r
th
e
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teg
o
r
ical
in
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icato
r
s
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f
co
h
e
r
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ce
,
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elev
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ce
,
s
u
f
f
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an
d
clar
ity
,
b
ased
o
n
th
e
o
r
d
in
al
m
ea
s
u
r
em
en
t
s
ca
le.
T
h
e
s
tatis
tica
l
p
er
f
o
r
m
an
ce
o
f
th
e
Fleis
s
k
ap
p
a
co
ef
f
icien
t
an
d
th
e
p
-
v
alu
e
as
th
e
m
o
s
t
in
f
o
r
m
ativ
e
v
alu
e
f
o
r
ea
ch
ch
ar
ac
ter
is
tic
is
s
h
o
wn
in
T
ab
le
2
.
T
h
e
d
e
g
r
ee
o
f
ag
r
ee
m
en
t
f
o
u
n
d
f
lu
ct
u
ates
b
etwe
en
s
u
b
s
tan
tial
an
d
alm
o
s
t
p
er
f
ec
t,
with
th
e
co
n
s
is
ten
cy
ch
ar
ac
ter
is
tic
b
ein
g
th
e
h
ig
h
e
s
t
(
0
.
8
7
)
ac
co
r
d
in
g
to
t
h
e
d
eg
r
ee
o
f
o
v
e
r
all
ag
r
ee
m
en
t
b
etw
ee
n
th
e
ju
d
g
es.
T
h
e
s
tatis
t
ical
s
ig
n
if
ican
ce
o
f
th
ese
ch
ar
ac
ter
is
tics
h
ad
a
b
eh
av
io
r
o
f
9
6
%
s
ec
u
r
ity
,
im
p
ly
in
g
a
p
<0
.
0
5
,
in
wh
ich
th
e
r
elev
an
ce
ch
ar
ac
ter
is
tic
p
=0
.
0
2
6
was
r
elev
an
t.
W
ith
th
e
r
esu
l
ts
d
escr
ib
ed
,
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30
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31
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.
Fig
u
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2
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atica
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Stu
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ates,
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d
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at
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ep
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ad
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ir
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ates
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a
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p
ly
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ev
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ativ
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t
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it
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d
with
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r
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ates.
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wo
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es f
r
o
m
th
e
s
tu
d
en
ts
ar
e
p
r
esen
ted
i
n
Fig
u
r
e
s
4
an
d
5
.
“
M
a
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m
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t
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ra
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n
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ro
n
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st
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t
s
.
T
o
b
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a
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o
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.”
Fig
u
r
e
4
.
A
s
tu
d
e
n
t
’
s
r
esp
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s
e
to
th
e
s
im
ilar
ities
o
f
th
e
teac
h
in
g
ex
p
e
r
ien
ce
“
I
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h
i
n
k
t
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t
t
h
e
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f
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o
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a
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t
a
i
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o
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e
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.
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n
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t
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re
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.
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h
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e
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e
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o
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.”
Fig
u
r
e
5
.
A
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d
e
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r
esp
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s
e
to
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ilar
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f
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0.0%
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S
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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J
E
v
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&
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Vo
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.
13
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−
Resea
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a
pa
cit
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As
s
im
ilar
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is
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th
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ca
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ac
ity
o
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g
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,
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h
e
s
tu
d
en
ts
at
th
e
m
o
m
en
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o
f
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m
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v
e
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o
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t
to
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r
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th
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m
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an
io
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s
.
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h
at
is
w
h
y
th
e
y
h
ad
to
in
v
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ate
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d
ep
t
h
th
e
co
n
ce
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t
to
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r
k
,
u
n
d
er
th
at
p
r
em
is
e
th
e
s
tu
d
en
ts
em
p
h
asized
lik
e
g
r
ea
t
s
tr
en
g
th
th
e
d
ev
elo
p
m
en
t
o
f
th
eir
o
w
n
ca
p
ac
ity
o
f
in
v
esti
g
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n
,
an
d
all
th
e
a
b
ilit
ies
th
at
en
tails
to
m
ak
e
a
tr
u
e
in
v
esti
g
atio
n
.
Fig
u
r
e
6
s
h
o
ws
o
n
e
s
tu
d
en
t'
s
r
esp
o
n
s
e
.
“
T
h
e
fa
c
t
o
f
lea
v
in
g
u
s
t
h
e
re
sp
o
n
sib
il
it
y
o
f
in
v
e
stig
a
t
in
g
th
e
n
e
c
e
ss
a
ry
k
n
o
wled
g
e
to
b
e
a
b
le
to
b
e
u
n
d
e
rs
to
o
d
,
w
it
h
o
u
t
a
d
o
u
b
t
a
p
le
a
sa
n
t
e
x
p
e
rie
n
c
e
.”
Fig
u
r
e
6
.
A
s
tu
d
e
n
t
’
s
r
esp
o
n
s
e
−
T
ea
m
wo
rk
As
a
r
esu
lt
o
f
t
h
e
a
n
aly
s
is
o
f
th
e
s
tu
d
en
ts
'
an
s
wer
s
to
th
e
q
u
esti
o
n
ab
o
u
t
th
e
s
tr
en
g
th
s
o
f
t
h
e
e
x
p
er
ien
ce
,
team
wo
r
k
em
er
g
es
as
a
s
im
ilar
ity
.
T
h
e
s
tu
d
e
n
ts
wer
e
d
iv
i
d
ed
in
to
team
s
in
t
h
eir
r
o
le
as
s
tu
d
en
t
-
teac
h
er
s
(
s
tu
d
en
ts
in
tr
ain
in
g
)
,
with
th
e
p
o
s
s
ib
ilit
y
o
f
tak
in
g
class
es
o
n
a
g
iv
en
m
ath
em
atica
l
co
n
te
n
t.
As
a
r
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lt
o
f
th
is
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r
k
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n
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its
d
e
m
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d
,
th
e
s
tu
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en
ts
wer
e
ab
le
to
v
alu
e
tea
m
wo
r
k
with
in
th
e
teac
h
in
g
p
r
o
f
ess
io
n
,
n
o
tin
g
th
e
im
p
o
r
tan
ce
o
f
th
is
in
o
r
d
er
t
o
b
e
a
g
o
o
d
teac
h
e
r
.
Fig
u
r
es 7
a
n
d
8
s
h
o
w
th
e
r
es
p
o
n
s
es o
f
two
s
tu
d
en
ts
.
−
“
S
e
lf
-
e
mp
lo
y
me
n
t
th
a
t
h
e
lp
e
d
ma
k
e
me
m
o
re
re
sp
o
n
sib
le
.
”
−
“
Ap
p
re
c
ia
ti
o
n
o
f
f
ield
w
o
rk
.
S
e
a
r
c
h
in
g
fo
r
s
o
lu
t
io
n
s
to
my
o
w
n
d
o
u
b
ts
a
mo
n
g
w
h
a
t
I
h
a
d
t
o
te
a
c
h
.
”
−
“
L
e
a
rn
to
w
o
rk
we
ll
wit
h
t
h
e
g
r
o
u
p
a
n
d
b
e
a
b
le
t
o
d
istrib
u
te t
h
e
c
o
n
ten
t
we
ll
.”
Fig
u
r
e
7
.
A
s
tu
d
e
n
t
’
s
r
esp
o
n
s
e
to
th
e
s
im
ilar
ities
o
f
th
e
teac
h
in
g
ex
p
e
r
ien
ce
“
It
h
e
lp
s
to
g
e
n
e
ra
te
k
n
o
wled
g
e
a
u
to
n
o
mo
u
sly
,
si
n
c
e
it
is
n
e
c
e
ss
a
ry
to
in
v
e
stig
a
te f
ro
m
.
-
M
a
n
y
p
a
rts
,
a
n
d
li
k
e
b
o
o
k
,
v
i
d
e
o
.
-
It
wa
s a
re
a
l
a
p
p
ro
a
c
h
t
o
o
u
r f
u
t
u
re
wo
rk
a
s tea
c
h
e
rs
.
-
It
h
e
l
p
s
t
o
a
p
p
re
c
ia
te
c
o
ll
a
b
o
r
a
ti
v
e
wo
rk
wit
h
in
g
r
o
u
p
s
.”
Fig
u
r
e
8
.
A
s
tu
d
e
n
t
’
s
r
esp
o
n
s
e
to
th
e
s
im
ilar
ities
o
f
th
e
teac
h
in
g
ex
p
e
r
ien
ce
4
.
3
.
2
.
Str
eng
t
hs
:
d
if
f
er
ence
s
−
Rea
f
f
irm
t
he
t
ea
ching
v
o
c
a
t
i
o
n
Vo
ca
tio
n
is
a
co
n
ce
p
t
th
at
in
it
s
g
en
esis
ca
r
r
ies
th
e
wo
r
d
“c
o
u
r
ag
e”
,
th
e
c
o
u
r
ag
e
t
o
g
iv
e
v
al
u
e
to
wh
at
o
n
e
ch
o
o
s
es.
T
h
r
o
u
g
h
t
h
is
ex
p
er
ien
ce
,
s
o
m
e
s
tu
d
en
ts
h
ig
h
lig
h
ted
as
a
s
tr
en
g
th
t
h
e
p
e
r
s
o
n
al
r
ea
f
f
ir
m
atio
n
t
h
at
th
is
was
th
e
r
ig
h
t
ca
r
ee
r
to
p
u
r
s
u
e
in
th
e
f
u
tu
r
e,
wh
ich
in
th
eir
o
p
in
io
n
,
th
ey
ac
h
iev
ed
th
r
o
u
g
h
f
ir
s
t
-
h
an
d
ex
p
er
ien
ce
o
f
th
e
teac
h
in
g
wo
r
k
th
ey
f
ac
ed
as
s
ee
n
in
Fig
u
r
e
9
.
“
T
h
e
se
e
x
p
e
rie
n
c
e
s
a
ll
o
we
d
me
to
c
o
n
fi
rm
th
a
t
I
re
a
l
ly wa
n
t
t
o
b
e
a
tea
c
h
e
r,
in
a
d
d
it
io
n
to
k
n
o
wi
n
g
wh
a
t
my
a
b
il
it
ies
a
re
a
t
th
e
ti
me
o
f
d
o
in
g
c
la
ss
e
s.
It
a
ll
o
we
d
me
to
lea
rn
b
e
tt
e
r
wh
a
t
g
ro
u
p
w
o
rk
is
.”
Fig
u
r
e
9
.
A
s
tu
d
e
n
t
’
s
r
esp
o
n
s
e
to
d
if
f
er
e
n
ce
s
in
teac
h
in
g
ex
p
er
ien
ce
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
Did
a
ctic
ex
p
erien
ce
b
a
s
ed
o
n
ma
th
ema
tics
co
mp
eten
cies a
n
d
s
o
ft c
o
mp
eten
cies fo
r
…
(
V
e
r
ó
n
ica
Día
z
)
4265
−
Dev
elo
p per
s
o
na
lity
a
nd
s
ec
urit
y
in f
ro
nt
o
f
t
he
co
urs
e
g
ro
up
An
im
p
o
r
ta
n
t
asp
ec
t
f
o
r
a
teac
h
er
is
to
h
av
e
t
h
e
p
e
r
s
o
n
ality
t
o
b
e
i
n
f
r
o
n
t
o
f
a
co
u
r
s
e
.
Ho
we
v
er
,
with
in
th
is
asp
ec
t
also
h
ig
h
lig
h
ts
th
e
s
ec
u
r
ity
o
f
wh
at
is
b
ein
g
d
o
n
e
as
a
teac
h
er
.
On
e
s
tu
d
e
n
t
s
tr
ess
ed
th
at
th
e
ex
p
er
ien
ce
h
elp
ed
h
im
to
s
tar
t
wo
r
k
in
g
o
n
t
h
ese
ess
en
tial sk
i
lls
f
o
r
a
teac
h
er
as
s
h
o
wn
i
n
Fig
u
r
e
1
0
.
“
On
e
o
f
th
e
m
o
st
imp
o
rt
a
n
t
stre
n
g
t
h
s
wa
s
t
h
e
f
a
c
t
th
a
t
t
h
is
typ
e
o
f
a
c
ti
v
it
y
a
ll
o
ws
u
s
to
se
e
if
we
re
a
ll
y
li
k
e
tea
c
h
in
g
,
a
s
it
is
th
e
c
lo
se
st
e
x
p
e
rie
n
c
e
to
a
re
a
l
c
la
ss
.
An
o
th
e
r
stre
n
g
t
h
i
s
th
a
t
it
a
ll
o
ws
u
s to
d
e
v
e
lo
p
p
e
rs
o
n
a
li
ty
a
n
d
g
re
a
ter
se
c
u
rity
.”
Fig
u
r
e
1
0
.
A
s
tu
d
en
t
’
s
r
esp
o
n
s
e
to
d
if
f
er
e
n
ce
s
in
teac
h
in
g
ex
p
er
ien
ce
−
P
ee
r
lea
rning
W
h
it
r
eg
ar
d
to
th
e
f
o
r
m
s
o
f
o
r
g
an
izatio
n
o
f
th
e
ac
tiv
ity
b
y
th
e
s
tu
d
en
ts
,
p
ee
r
co
llab
o
r
atio
n
was
id
en
tifie
d
in
th
e
r
esp
o
n
s
es
o
cc
u
r
s
wh
en
two
o
r
m
o
r
e
s
tu
d
en
ts
o
f
s
im
ilar
lev
els
wo
r
k
co
llab
o
r
ativ
ely
in
a
co
n
s
tan
t
way
to
war
d
s
th
e
r
eso
lu
tio
n
p
r
o
b
lem
.
Fo
r
s
o
m
e
s
tu
d
e
n
ts
,
th
e
ex
p
er
ien
ce
was
o
u
ts
tan
d
in
g
in
ter
m
s
o
f
p
ee
r
lear
n
in
g
as
s
ee
n
in
Fig
u
r
e
1
1
.
“
En
c
o
u
ra
g
i
n
g
se
lf
-
e
d
u
c
a
ti
o
n
,
k
n
o
wi
n
g
w
h
e
re
fro
m,
w
h
a
t
a
n
d
h
o
w
to
se
a
rc
h
fo
r
c
o
n
te
n
t.
T
h
e
c
o
n
ten
t
is
m
o
re
e
n
j
o
y
a
b
le
wh
e
n
p
re
se
n
ted
b
y
a
c
o
u
p
le,
i
.
e
.
wh
e
n
t
h
e
re
is
a
so
c
ia
l
a
ff
e
c
ti
v
e
re
la
ti
o
n
s
h
ip
.”
Fig
u
r
e
1
1
.
A
s
tu
d
en
t
’
s
r
esp
o
n
s
e
to
th
e
d
if
f
er
en
ce
s
in
th
e
teac
h
in
g
ex
p
er
ien
ce
4
.
3
.
3
.
Wea
k
nes
s
es:
s
im
ila
rit
ies
−
Dif
f
iculty
in m
a
t
hema
t
ica
l c
o
nte
nt
T
h
e
wea
k
n
ess
ac
co
r
d
in
g
to
th
e
o
p
en
an
s
wer
s
o
f
th
e
s
tu
d
en
t
s
,
h
as
r
elatio
n
with
th
e
wo
r
k
ed
co
n
ten
ts
,
an
d
th
e
d
if
f
icu
lty
ass
o
ciate
d
to
it,
wh
ich
was
in
cr
ea
s
ed
b
y
th
e
s
ca
r
ce
o
r
n
u
ll
ex
p
er
ien
ce
th
at
th
e
s
tu
d
en
ts
in
tr
ain
in
g
h
av
e
,
o
n
th
e
ac
c
o
m
p
li
s
h
m
en
t
o
f
class
es.
T
h
e
co
n
ten
ts
wo
r
k
ed
o
n
wer
e
n
o
t
co
m
p
le
tely
clea
r
to
s
o
m
e,
an
d
th
ey
also
m
a
d
e
m
is
tak
es
wh
en
wo
r
k
in
g
o
n
th
e
class
es,
wh
ich
,
alth
o
u
g
h
th
ey
wer
e
co
r
r
ec
ted
b
y
th
e
teac
h
er
o
f
th
e
s
u
b
ject
.
S
o
m
e
s
tu
d
en
ts
d
id
n
o
t
m
an
ag
e
t
o
m
aster
th
e
m
ath
em
atica
l c
o
n
ten
t w
o
r
k
ed
o
n
in
its
en
tire
ty
.
4
.
3
.
4
.
Wea
k
nes
s
es:
d
if
f
er
ence
s
−
E
m
o
t
io
na
l le
v
el
Stre
s
s
is
a
co
n
d
itio
n
th
at
h
u
m
an
b
ein
g
s
h
av
e
s
u
f
f
er
e
d
f
r
o
m
f
o
r
ce
n
tu
r
ies
an
d
th
at
r
ef
er
s
to
an
au
to
m
atic
r
esp
o
n
s
e
o
f
th
e
o
r
g
an
is
m
to
a
n
y
ev
e
n
t
th
at
is
im
p
o
s
ed
o
n
it,
c
au
s
in
g
th
e
n
er
v
o
u
s
s
y
s
tem
to
s
tim
u
late
an
d
r
ea
ct
b
y
p
r
o
d
u
cin
g
ch
a
n
g
es
at
al
p
s
y
ch
o
lo
g
ical
(
m
e
n
tal)
o
r
p
s
y
ch
o
lo
g
ical
(
p
h
y
s
ical)
lev
el,
a
n
d
th
at
o
cc
u
r
s
in
a
p
ar
ticu
lar
way
b
etwe
en
t
h
e
p
er
s
o
n
an
d
th
e
s
itu
atio
n
.
Fo
r
s
o
m
e
s
tu
d
en
ts
,
h
av
in
g
t
o
d
ea
l
with
a
d
if
f
er
en
t
m
o
d
ality
an
d
ass
u
m
in
g
th
e
r
o
le
o
f
teac
h
er
,
ca
u
s
ed
th
em
s
tr
ess
b
ec
au
s
e
o
f
th
e
r
esp
o
n
s
ib
ilit
ies
o
f
lear
n
in
g
o
f
th
eir
p
ee
r
s
.
An
o
th
er
was f
r
u
s
tr
ated
b
y
h
is
o
wn
ex
p
ec
tatio
n
s
as sh
o
wn
in
Fig
u
r
e
1
2
.
“
In
d
ica
te
t
h
e
we
a
k
n
e
ss
e
s
o
f
th
e
se
tea
c
h
in
g
e
x
p
e
rie
n
c
e
s:
I
c
o
n
sid
e
r
th
a
t
t
h
e
o
n
ly
we
a
k
n
e
ss
o
r
a
g
a
in
st
is
th
a
t
it
p
u
ts
in
a
sit
u
a
ti
o
n
o
f
mu
c
h
stre
ss
fo
r
th
e
stu
d
e
n
t
sin
c
e
we
l
o
o
k
fo
r
t
h
a
t
it
c
o
mp
lete
ly
g
o
e
s
we
ll
,
b
u
t
it
is
n
o
t
c
o
mp
lete
ly
b
a
d
sin
c
e
we
g
o
t
h
ro
u
g
h
mo
m
e
n
ts
li
k
e
th
is
d
u
rin
g
a
ll
o
u
r l
if
e
a
n
d
we
mu
st f
a
c
e
th
e
m
.”
Fig
u
r
e
1
2
.
A
s
tu
d
en
t
’
s
r
esp
o
n
s
e
in
r
elatio
n
to
t
h
e
em
o
tio
n
al
l
ev
el
Evaluation Warning : The document was created with Spire.PDF for Python.