I
nte
rna
t
io
na
l J
o
urna
l o
f
E
v
a
lua
t
io
n a
nd
Resea
rc
h in
E
du
ca
t
io
n (
I
J
E
RE
)
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2020
,
p
p
.
751
~
758
I
SS
N:
2252
-
8822
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
e
r
e
.
v
9
i
3
.
2
0
6
1
7
7
51
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
ere.
ia
esco
r
e.
co
m
Ty
pes o
f
m
a
the
ma
tical tas
k
s
used i
n seco
nda
ry
clas
sro
o
m
instruction
Va
lbo
na
B
er
is
ha
,
Ruzhdi
B
y
t
y
qi
F
a
c
u
lt
y
o
f
Ed
u
c
a
ti
o
n
,
U
n
iv
e
rsity
o
f
P
ris
h
ti
n
a
,
Ko
so
v
o
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Ma
r
2
6
,
2
0
2
0
R
ev
i
s
ed
J
u
n
2
2
,
2
0
2
0
A
cc
ep
ted
Ju
l
1
5
,
2
0
2
0
T
h
is
stu
d
y
e
x
a
m
in
e
d
th
e
q
u
a
li
ty
a
n
d
ty
p
e
s
o
f
m
a
th
e
m
a
ti
c
a
l
tas
k
s
u
se
d
f
o
r
c
las
sro
o
m
in
stru
c
ti
o
n
in
a
n
u
p
p
e
r
se
c
o
n
d
a
ry
sc
h
o
o
l
–
g
y
m
n
a
siu
m
.
A
ll
th
e
m
a
th
e
m
a
ti
c
a
l
tas
k
s
p
re
se
n
ted
in
n
in
e
d
if
f
e
re
n
t
sc
h
o
o
l
c
las
sro
o
m
s
d
u
ri
n
g
th
e
f
irst
se
m
e
ste
r
o
f
th
e
sc
h
o
o
l
y
e
a
r
2
0
1
8
/2
0
1
9
w
e
re
a
n
a
l
y
se
d
a
g
a
in
st
a
5
D
a
n
a
ly
ti
c
a
l
f
r
a
m
e
w
o
rk
.
T
h
e
d
im
e
n
sio
n
s
o
f
th
e
i
n
d
iv
id
u
a
l
tas
k
a
n
a
l
y
sis
w
e
r
e
c
o
n
tex
tu
a
l
f
e
a
tu
re
s;
th
e
a
n
sw
e
r
f
o
rm
s
re
q
u
ired
;
f
o
rm
s
o
f
p
re
se
n
tatio
n
;
ty
p
e
s
o
f
re
q
u
ired
m
a
th
e
m
a
ti
c
a
l
a
c
ti
v
it
y
a
n
d
c
o
g
n
it
iv
e
d
e
m
a
n
d
s
in
v
o
lv
e
d
.
P
e
rf
o
rm
e
d
a
n
a
ly
sis
g
i
v
e
d
p
e
rsp
e
c
ti
v
e
o
n
t
h
e
lea
rn
i
n
g
o
p
p
o
rt
u
n
i
ti
e
s
o
f
fe
re
d
i
n
c
las
sro
o
m
in
stru
c
ti
o
n
f
o
r
b
u
il
d
in
g
m
a
th
e
m
a
ti
c
a
l
c
o
m
p
e
ten
c
ies
sp
e
c
if
i
e
d
in
th
e
c
u
rre
n
t
sta
te
e
d
u
c
a
ti
o
n
c
u
rric
u
lu
m
.
T
h
e
re
su
lt
s
in
d
ica
te
th
a
t
th
e
se
lec
ti
o
n
o
f
tas
k
s
w
a
s
n
o
t
in
a
c
c
o
rd
a
n
c
e
w
it
h
th
e
c
u
rric
u
lu
m
re
q
u
irem
e
n
ts.
M
o
stly
,
tea
c
h
e
rs
u
se
d
c
lo
se
-
e
n
d
e
d
,
non
-
a
p
p
l
ica
ti
v
e
,
lo
w
e
r
-
lev
e
l
c
o
g
n
it
iv
e
tas
k
s
p
re
se
n
ted
in
sy
m
b
o
li
c
f
o
r
m
,
p
ro
m
o
ti
n
g
o
p
e
ra
ti
o
n
s
a
n
d
c
a
lcu
l
a
ti
o
n
s
a
s
a
c
e
n
tral
a
c
ti
v
it
y
.
T
h
e
s
e
t
y
p
e
s
o
f
t
a
sk
s
a
re
u
su
a
ll
y
a
s
so
c
iate
d
w
it
h
k
n
o
w
led
g
e
a
n
d
sk
il
ls
o
f
lo
w
e
r
o
rd
e
rs.
In
th
is
c
a
se
,
c
las
sro
o
m
in
stru
c
ti
o
n
h
a
d
lo
w
p
o
ten
ti
a
l
a
n
d
v
e
ry
li
tt
le
ro
o
m
lef
t
to
b
u
il
d
a
sig
n
if
ica
n
t
p
o
rti
o
n
o
f
c
o
m
p
e
ten
c
ies
a
n
d
lea
rn
in
g
o
u
tco
m
e
s o
f
h
ig
h
e
r
o
rd
e
rs.
K
ey
w
o
r
d
s
:
C
ateg
o
r
izatio
n
C
u
r
r
ic
u
lu
m
r
eq
u
ir
e
m
e
n
ts
Featu
r
es a
n
al
y
s
i
s
Ma
th
e
m
atica
l ta
s
k
s
Seco
n
d
ar
y
s
c
h
o
o
l
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Valb
o
n
a
B
er
is
h
a,
Facu
lt
y
o
f
E
d
u
ca
t
io
n
,
Un
i
v
er
s
it
y
o
f
P
r
is
h
t
in
a,
R
r
.
"
A
g
i
m
R
a
m
ad
an
i"
,
p
.
n
.
1
0
0
0
0
P
r
is
h
tin
ë,
Ko
s
o
v
o
.
E
m
ail:
v
alb
o
n
a.
b
er
is
h
a
@
u
n
i
-
p
r
.
ed
u
1.
I
NT
RO
D
UCT
I
O
N
T
h
er
e
ar
e
ef
f
o
r
ts
v
i
s
ib
le
all
ar
o
u
n
d
th
e
g
lo
b
e
ai
m
ed
at
r
ef
o
r
m
i
n
g
ed
u
ca
tio
n
s
y
s
te
m
s
.
T
h
e
o
p
er
atio
n
aliza
tio
n
o
f
th
e
k
e
y
co
m
p
eten
ce
s
f
o
r
lif
e
is
th
e
m
ai
n
o
b
j
ec
tiv
e
o
f
teac
h
in
g
an
d
lear
n
i
n
g
.
Stu
d
e
n
ts
'
r
ea
l
n
ee
d
s
a
n
d
in
ter
ests
ar
e
ad
d
r
ess
ed
,
s
o
th
e
y
ca
n
ac
q
u
ir
e
th
e
s
k
i
lls
a
n
d
h
ab
its
n
ee
d
ed
to
r
esp
o
n
d
cr
iticall
y
a
n
d
cr
ea
tiv
el
y
to
r
ea
l
lif
e
s
it
u
atio
n
s
i
n
o
r
d
er
to
h
an
d
le
an
d
s
o
l
v
e
p
r
o
b
l
e
m
s
co
n
s
tr
u
c
tiv
e
l
y
.
No
w
ad
a
y
s
,
m
at
h
e
m
a
tics
is
s
e
en
as
a
d
ev
elo
p
er
an
d
f
ac
ilit
ato
r
o
f
lo
g
ical,
s
y
s
te
m
atica
ll
y
,
c
r
itical
an
d
cr
ea
tiv
e
s
tu
d
e
n
t
'
s
th
i
n
k
i
n
g
[
1
]
.
L
a
tel
y
,
s
p
ec
ial
e
f
f
o
r
ts
h
av
e
b
ee
n
m
ad
e
f
o
r
t
h
e
ac
q
u
i
s
itio
n
o
f
m
ath
e
m
at
ical
co
m
p
ete
n
cie
s
w
ith
in
co
r
e
co
m
p
e
ten
cie
s
,
o
r
“
th
e
ab
ilit
y
to
u
n
d
er
s
ta
n
d
,
j
u
d
g
e,
d
o
,
an
d
u
s
e
m
a
th
e
m
atic
s
”
[
2
]
.
C
o
n
te
m
p
o
r
ar
y
m
at
h
e
m
a
tics
teac
h
i
n
g
an
d
as
s
ess
m
e
n
t
f
o
cu
s
e
s
o
n
co
m
p
ete
n
c
y
atta
in
m
en
t
lev
el
s
,
w
it
h
co
n
tin
u
o
u
s
f
ee
d
b
ac
k
a
n
d
f
o
ll
o
w
-
u
p
i
n
co
m
p
eten
c
y
p
er
f
o
r
m
an
ce
i
m
p
r
o
v
e
m
e
n
t.
T
h
e
m
a
j
o
r
r
esp
o
n
s
ib
ilit
y
i
n
th
is
r
e
g
ar
d
is
to
d
eter
m
i
n
e
th
e
task
s
to
b
e
u
s
ed
in
clas
s
r
o
o
m
in
s
tr
u
ctio
n
.
T
h
e
is
s
u
e
o
f
s
ele
ctin
g
m
at
h
e
m
atica
l
task
s
f
o
r
class
r
o
o
m
in
s
tr
u
ctio
n
is
o
f
g
r
ea
t
in
ter
est
f
o
r
m
at
h
e
m
atic
s
ed
u
ca
tio
n
r
ese
ar
ch
er
s
[
2
-
7
]
,
s
in
ce
task
s
ar
e
an
ess
e
n
tial p
ar
t o
f
m
at
h
e
m
a
ti
cs tea
ch
i
n
g
an
d
lear
n
i
n
g
[
8
]
.
E
f
f
ec
tiv
e
teac
h
i
n
g
an
d
co
n
s
tr
u
ctio
n
o
f
m
ath
e
m
at
ical
co
m
p
eten
ce
s
r
elate
s
m
ain
l
y
to
t
h
e
u
s
e
o
f
r
ich
,
v
ar
ied
,
m
ea
n
in
g
f
u
l
an
d
w
o
r
t
h
w
h
ile
m
at
h
e
m
atica
l
ta
s
k
s
[9
,
1
0
]
.
A
p
r
o
p
er
task
s
elec
tio
n
a
n
d
th
e
w
a
y
t
h
e
y
ar
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8822
I
n
t
.
J
.
E
v
al
.
&
R
es
.
E
d
u
c
.
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2020
:
7
5
1
-
758
752
p
r
esen
ted
an
d
p
r
o
ce
s
s
ed
w
it
h
s
tu
d
e
n
ts
ar
e
k
e
y
f
ac
to
r
s
th
at
d
eter
m
i
n
e
th
e
p
o
ten
tia
l
an
d
o
p
p
o
r
tu
n
ities
f
o
r
d
ee
p
an
d
m
ea
n
i
n
g
f
u
l
co
n
ce
p
tu
a
l
lear
n
in
g
[
1
1
]
.
So
lv
in
g
o
f
f
a
m
ili
ar
task
s
,
f
o
r
in
s
ta
n
ce
,
o
f
ten
d
o
es
n
o
t
r
eq
u
ir
e
an
y
k
in
d
o
f
co
n
ce
p
t
u
al
u
n
d
er
s
ta
n
d
in
g
[
1
2
]
,
s
o
it
d
o
es
n
o
t
b
r
i
n
g
an
y
b
e
n
ef
it
i
n
t
h
at
d
ir
ec
tio
n
.
P
r
o
p
er
s
elec
tio
n
,
a
m
o
n
g
o
t
h
er
th
i
n
g
s
,
i
m
p
lie
s
t
h
e
u
s
e
o
f
d
i
v
er
s
e
t
y
p
e
s
o
f
tas
k
s
th
at
co
v
er
a
w
id
e
r
an
g
e
o
f
lea
r
n
in
g
o
u
tco
m
e
s
.
A
n
ar
r
o
w
r
an
g
e
o
f
tas
k
t
y
p
e
s
m
a
tch
es
w
i
th
a
n
ar
r
o
w
r
an
g
e
o
f
l
ea
r
n
in
g
o
u
tco
m
es.
B
ased
o
n
r
ec
en
t r
esear
ch
,
s
u
c
h
as
[
7
,
13
-
1
5
]
th
e
u
s
e
o
f
t
e
x
tb
o
o
k
s
as
t
h
e
s
o
le
s
o
u
r
ce
f
o
r
clas
s
r
o
o
m
tas
k
s
elec
t
io
n
is
s
ca
r
ce
.
Usu
al
l
y
,
te
x
tb
o
o
k
s
d
o
n
o
t
f
ac
ilit
ate
t
h
e
d
ev
elo
p
m
e
n
t
o
f
a
f
u
ll
r
an
g
e
o
f
m
at
h
e
m
a
tical
co
m
p
ete
n
ce
s
.
T
h
er
ef
o
r
e,
teac
h
er
s
’
co
m
m
i
t
m
e
n
t
i
n
th
is
r
eg
ar
d
is
v
ital
[
1
6
]
.
T
h
e
u
s
e
o
f
v
ar
io
u
s
r
eso
u
r
ce
s
f
o
r
task
s
e
lectio
n
,
as
w
ell
a
s
f
o
r
m
u
lati
n
g
,
d
esi
g
n
in
g
an
d
m
o
d
if
y
i
n
g
o
w
n
ta
s
k
s
is
o
f
u
t
m
o
s
t
i
m
p
o
r
tan
ce
.
Selectio
n
o
f
tas
k
s
,
f
o
r
m
u
la
tin
g
an
d
ch
an
g
i
n
g
t
h
e
m
ar
e
i
m
p
o
r
tan
t a
s
p
ec
ts
o
f
les
s
o
n
p
lan
n
i
n
g
[
1
7
]
.
Mo
r
eo
v
er
,
d
if
f
er
e
n
t
t
y
p
es
o
f
task
s
h
av
e
d
if
f
er
en
t
w
ei
g
h
t,
r
o
le
an
d
p
o
ten
tial
in
m
at
h
e
m
atic
s
teac
h
in
g
an
d
lear
n
i
n
g
[
1
8
,
1
9
]
.
No
t
all
m
at
h
e
m
a
tic
al
ta
s
k
s
o
f
f
er
t
h
e
s
a
m
e
lear
n
in
g
o
p
p
o
r
tu
n
it
ies
[
2
0
]
.
A
n
a
p
p
r
o
p
r
iate
ch
o
ice
o
f
task
s
h
elp
s
s
t
u
d
en
t
s
m
o
v
e
to
h
ig
h
er
lev
el
s
o
f
m
at
h
e
m
atica
l
t
h
in
k
i
n
g
an
d
lear
n
in
g
[
2
1
]
.
T
h
e
w
eig
h
t,
r
o
le,
an
d
p
o
ten
tial
th
at
m
at
h
e
m
atica
l
ta
s
k
s
p
o
s
s
ess
i
n
ter
m
s
o
f
lear
n
in
g
m
at
h
e
m
atic
s
ar
e
d
eter
m
in
ed
m
a
in
l
y
b
y
a
n
al
y
s
i
n
g
t
h
eir
es
s
en
tia
l
f
ea
tu
r
es
an
d
t
h
e
d
e
m
an
d
s
th
e
y
p
lace
o
n
s
tu
d
e
n
ts
.
A
v
er
y
i
m
p
o
r
ta
n
t
f
ea
tu
r
e
o
f
m
at
h
e
m
a
tical
ta
s
k
s
i
s
t
h
e
le
v
e
l
o
f
co
g
n
i
tiv
e
d
e
m
a
n
d
p
lace
d
in
o
r
d
er
to
ca
r
r
y
o
n
a
tas
k
.
T
h
e
lev
el
o
f
co
g
n
i
tiv
e
d
em
a
n
d
p
lace
d
b
y
a
m
at
h
e
m
a
tical
tas
k
r
ep
r
esen
t
s
t
h
e
w
a
y
an
d
t
y
p
e
o
f
t
h
in
k
i
n
g
n
ee
d
ed
t
o
s
o
lv
e
a
ta
s
k
.
T
h
e
co
g
n
iti
v
e
lev
el
o
f
th
e
tas
k
is
u
s
u
all
y
d
e
f
in
ed
b
ased
o
n
th
e
d
ep
th
o
f
co
n
ce
p
tu
al
m
a
th
e
m
at
ical
th
in
k
i
n
g
.
T
h
er
e
ar
e
s
ev
er
al
co
m
m
o
n
l
y
u
s
ed
ta
x
o
n
o
m
ies
to
s
tr
u
ctu
r
e
a
n
d
class
i
f
y
m
at
h
e
m
atica
l
ta
s
k
s
b
ase
d
o
n
th
eir
co
g
n
i
tiv
e
r
eq
u
ir
e
m
en
ts
.
Fo
r
th
e
p
r
ese
n
t
an
al
y
s
is
,
t
h
e
L
ev
e
l
C
o
g
n
it
iv
e
De
m
a
n
d
(
L
C
D
)
f
r
a
m
e
w
o
r
k
d
ev
elo
p
ed
b
y
Ste
in
&
S
m
it
h
i
s
u
s
ed
[
2
2
]
.
T
h
e
r
ea
l
-
w
o
r
ld
co
n
tex
ts
i
n
v
o
lv
ed
w
ith
a
m
at
h
e
m
atica
l
task
r
ep
r
esen
t
a
f
ea
tu
r
e
th
at
p
la
y
s
a
s
ig
n
i
f
ica
n
t
r
o
le
in
lin
k
i
n
g
s
ch
o
o
l
m
at
h
e
m
a
tics
tas
k
s
w
it
h
s
t
u
d
en
t
s
'
r
ea
l
ex
p
er
ien
ce
s
.
T
h
er
ef
o
r
e,
th
e
c
ateg
o
r
is
atio
n
o
f
a
m
at
h
e
m
atica
l
tas
k
ac
co
r
d
in
g
to
t
h
e
t
y
p
e,
a
m
o
u
n
t
an
d
n
atu
r
e
o
f
th
e
co
n
tex
t
e
m
b
ed
d
ed
in
it
is
a
v
er
y
f
r
eq
u
e
n
t
d
i
m
e
n
s
io
n
o
f
tas
k
ch
ar
ac
ter
izat
io
n
.
T
h
er
e
ar
e
s
ev
er
al
f
r
a
m
e
w
o
r
k
s
a
n
d
m
eth
o
d
s
f
o
r
ca
teg
o
r
izin
g
m
at
h
e
m
a
tical
tas
k
s
b
ased
o
n
th
e
t
y
p
e,
ex
ten
t
an
d
n
at
u
r
e
o
f
t
h
e
co
n
tex
t
s
i
n
v
o
lv
ed
.
T
h
e
cu
r
r
en
t
ca
teg
o
r
is
atio
n
o
f
tas
k
s
b
ased
o
n
th
eir
co
n
tex
t
u
al
f
ea
t
u
r
es is
a
d
o
p
ted
ac
c
o
r
d
in
g
to
th
e
v
ie
w
s
o
f
au
t
h
o
r
s
in
[
2
3
]
.
T
r
a
d
itio
n
al
m
at
h
e
m
atics
cla
s
s
r
o
o
m
i
n
s
tr
u
ctio
n
r
elies
h
ea
v
il
y
o
n
ca
lcu
latio
n
s
a
nd
th
e
s
y
m
b
o
lic
f
o
r
m
o
f
co
m
m
u
n
icatio
n
.
T
h
e
r
ed
ef
in
itio
n
o
f
m
a
th
e
m
atica
l
co
m
p
e
ten
ce
,
o
n
th
e
o
th
er
h
an
d
,
is
ass
o
ciate
d
w
it
h
o
th
er
t
y
p
es
o
f
m
at
h
e
m
atica
l
ac
ti
v
it
y
b
esid
es
ca
lcu
latin
g
.
I
n
[
2
4
]
,
f
o
u
r
ty
p
e
s
o
f
m
at
h
e
m
atica
l
ac
ti
v
it
y
ar
e
id
en
ti
f
ied
:
r
ep
r
esen
tatio
n
an
d
m
o
d
elli
n
g
ac
ti
v
it
y
,
o
p
er
atio
n
an
d
ca
lcu
latio
n
ac
tiv
i
t
y
,
in
ter
p
r
etatio
n
ac
tiv
it
y
,
ar
g
u
m
e
n
tatio
n
a
n
d
r
ea
s
o
n
i
n
g
ac
tiv
it
y
.
I
n
[
1
0
,
24]
m
ath
e
m
at
ical
task
s
ar
e
d
if
f
er
en
tia
ted
an
d
ca
teg
o
r
is
ed
b
ased
o
n
th
e
m
ain
ac
ti
v
it
y
/
ac
ti
v
itie
s
r
eq
u
ir
ed
to
ca
r
r
y
o
n
a
ta
s
k
.
Th
is
an
al
y
tical
d
i
m
e
n
s
io
n
p
r
o
v
i
d
es
in
f
o
r
m
atio
n
o
n
class
r
o
o
m
i
n
s
tr
u
ctio
n
p
o
ten
t
ia
l f
o
r
d
ev
elo
p
in
g
t
h
e
f
u
l
l r
an
g
e
o
f
m
at
h
e
m
atica
l s
k
il
ls
.
An
o
th
er
i
m
p
o
r
ta
n
t
d
i
m
e
n
s
io
n
o
f
d
if
f
er
e
n
tiati
n
g
m
at
h
e
m
ati
ca
l
task
s
is
th
eir
f
o
r
m
o
f
p
r
esen
tat
io
n
.
T
h
e
p
r
esen
tatio
n
o
f
task
s
ca
n
b
e
d
o
n
e
in
d
if
f
er
en
t
m
o
d
es
an
d
f
o
r
m
s
-
ve
r
b
al,
s
y
m
b
o
lic,
v
i
s
u
al
an
d
co
m
b
i
n
ed
o
n
e.
T
h
e
f
o
r
m
s
o
f
co
m
m
u
n
i
ca
tio
n
i
n
m
at
h
e
m
a
tics
c
lass
r
o
o
m
s
ar
e
i
n
ter
r
elate
d
an
d
d
e
p
en
d
o
n
t
h
e
v
ar
iet
y
o
f
f
o
r
m
s
o
f
p
r
esen
tatio
n
o
f
m
at
h
e
m
a
tical
tas
k
s
.
All
th
e
m
en
tio
n
ed
f
o
r
m
s
m
u
s
t
b
e
in
clu
d
ed
in
to
d
ay
's
m
at
h
e
m
a
tics
cla
s
s
r
o
o
m
i
n
s
tr
u
ctio
n
.
Di
f
f
er
e
n
t
a
n
d
m
u
ltip
le
p
r
esen
tatio
n
a
n
d
co
m
m
u
n
ica
ti
o
n
f
o
r
m
s
f
ac
ilit
ate
th
e
d
ev
elo
p
m
en
t
o
f
r
ep
r
esen
t
atio
n
,
m
o
d
elli
n
g
an
d
co
m
m
u
n
icatio
n
s
k
ill
s
.
T
h
e
cu
r
r
en
t
ca
t
eg
o
r
is
atio
n
o
f
tas
k
s
b
ased
o
n
th
eir
f
o
r
m
o
f
p
r
esen
t
atio
n
is
ad
o
p
ted
ac
co
r
d
in
g
to
t
h
e
v
ie
w
s
o
f
a
u
t
h
o
r
s
in
[
2
3
]
.
T
h
e
an
s
w
er
t
y
p
e
r
eq
u
ir
ed
b
y
t
h
e
tas
k
s
u
s
ed
f
o
r
th
e
class
r
o
o
m
in
s
tr
u
ctio
n
in
d
icate
s
w
h
et
h
er
th
e
teac
h
in
g
ap
p
r
o
ac
h
is
o
p
en
o
r
clo
s
ed
.
A
n
o
p
en
teac
h
i
n
g
a
p
p
r
o
ac
h
cr
ea
tes
a
r
ich
en
v
ir
o
n
m
en
t
f
o
r
cr
ea
tiv
it
y
,
au
to
n
o
m
y
a
n
d
d
ee
p
er
lev
el
s
o
f
co
n
ce
p
tu
al
u
n
d
er
s
ta
n
d
in
g
.
I
t
is
co
m
m
o
n
l
y
co
n
v
e
y
ed
th
r
o
u
g
h
in
co
r
p
o
r
atin
g
ill
-
s
tr
u
ct
u
r
ed
task
s
t
h
at
h
a
v
e
m
o
r
e
th
an
o
n
e
s
o
lv
in
g
p
ath
an
d
s
ev
er
al
o
r
m
an
y
s
o
lu
tio
n
s
.
A
c
lo
s
ed
teac
h
in
g
ap
p
r
o
ac
h
r
elies
m
ai
n
l
y
o
n
f
u
ll
y
d
ef
i
n
ed
task
s
,
w
h
ic
h
u
s
u
a
ll
y
h
a
v
e
o
n
l
y
o
n
e
w
a
y
o
f
s
o
l
v
in
g
an
d
o
n
l
y
o
n
e
s
o
lu
tio
n
.
T
h
e
cu
r
r
en
t
ca
teg
o
r
is
atio
n
o
f
ta
s
k
s
b
ased
o
n
th
e
an
s
w
er
t
y
p
e
r
eq
u
ir
ed
i
s
ad
o
p
ted
ac
co
r
d
in
g
to
th
e
v
ie
w
s
o
f
a
u
t
h
o
r
s
in
[
2
3
]
.
Ko
s
o
v
a
is
th
e
y
o
u
n
g
est
s
ta
te
in
E
u
r
o
p
e.
I
t
g
ain
ed
in
d
ep
en
d
en
ce
in
2
0
0
8
,
af
ter
en
d
in
g
w
ar
ag
ai
n
s
t
Ser
b
ian
o
cc
u
p
atio
n
in
1
9
9
9
.
On
e
o
f
t
h
e
m
o
s
t
p
r
ess
i
n
g
i
s
s
u
e
s
i
n
p
o
s
t
-
w
ar
Ko
s
o
v
a
w
a
s
th
e
ad
v
a
n
ce
m
e
n
t
o
f
th
e
ed
u
ca
tio
n
s
y
s
te
m
.
T
h
e
o
ld
ed
u
ca
tio
n
s
y
s
te
m
i
n
h
er
ite
d
f
r
o
m
t
h
e
Y
u
g
o
s
la
v
er
a
an
d
Ser
b
ian
o
cc
u
p
atio
n
w
a
s
to
tall
y
d
y
s
f
u
n
ctio
n
a
l.
Ma
th
e
m
atics
cu
r
r
ic
u
lu
m
w
as
a
p
u
r
el
y
tr
ad
itio
n
al
o
n
e
with
teac
h
er
-
ce
n
ter
ed
teac
h
i
n
g
,
an
ab
s
tr
ac
t
ap
p
r
o
ac
h
to
m
ath
e
m
atica
l
co
n
ce
p
ts
,
r
o
te
lear
n
in
g
,
a
n
d
a
f
o
cu
s
o
n
d
ev
elo
p
in
g
s
t
u
d
en
ts
'
s
k
il
ls
f
o
r
au
to
m
ated
ca
lc
u
lati
o
n
s
,
o
p
er
atio
n
s
,
al
g
o
r
ith
m
s
a
n
d
p
r
o
ce
d
u
r
es
[
1
5
]
.
T
w
o
s
tate
ed
u
ca
tio
n
c
u
r
r
icu
la
h
av
e
b
ee
n
d
ev
elo
p
ed
s
i
n
ce
t
h
e
en
d
o
f
th
e
w
ar
.
T
h
e
f
ir
s
t
o
n
e
w
as
i
s
s
u
ed
in
th
e
2
0
0
3
/2
0
0
4
s
ch
o
o
l
y
ea
r
.
T
h
e
f
ir
s
t
af
ter
-
w
ar
cu
r
r
icu
lu
m
b
r
o
u
g
h
t
i
m
p
o
r
ta
n
t,
co
n
s
tr
u
cti
v
is
t
ch
a
n
g
es
to
th
e
en
tir
e
ed
u
ca
tio
n
s
y
s
te
m
.
I
t
b
r
o
u
g
h
t
a
lo
t
o
f
ch
an
g
e
in
m
at
h
e
m
a
tics
teac
h
in
g
an
d
lea
r
n
in
g
,
to
o
.
I
t
b
r
o
ad
en
ed
th
e
r
a
n
g
e
o
f
m
at
h
e
m
atics
lear
n
in
g
o
u
tco
m
e
s
,
i
n
tr
o
d
u
ce
d
th
e
co
n
ce
p
t
o
f
p
r
o
b
le
m
s
o
lv
in
g
,
e
x
p
lo
r
atio
n
a
n
d
h
ig
h
er
o
r
d
er
th
in
k
in
g
s
k
i
lls
.
B
u
t,
Ko
s
o
v
a
w
a
s
s
till
to
o
f
ar
b
eh
in
d
th
e
d
ev
elo
p
ed
p
ar
t
o
f
E
u
r
o
p
e.
T
h
e
u
n
f
u
l
f
illed
n
ee
d
to
b
u
ild
a
m
o
d
er
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
v
al
&
R
e
s
E
d
u
c
.
I
SS
N:
2252
-
8822
Typ
es o
f m
a
th
ema
tica
l ta
s
ks u
s
ed
in
s
ec
o
n
d
a
r
y
cla
s
s
r
o
o
m
in
s
tr
u
ctio
n
(
V
a
lb
o
n
a
B
eris
h
a
)
753
an
d
co
m
p
atib
le
ed
u
ca
tio
n
s
y
s
te
m
w
it
h
th
e
d
ev
elo
p
ed
p
a
r
t
o
f
th
e
w
o
r
ld
,
v
er
y
s
o
o
n
b
r
o
u
g
h
t
u
s
to
th
e
cu
r
r
en
t
p
o
s
itio
n
,
m
o
m
e
n
t
s
af
ter
t
h
e
i
m
p
le
m
en
ta
tio
n
o
f
t
h
e
s
ec
o
n
d
p
o
s
t
-
w
ar
cu
r
r
ic
u
l
u
m
.
T
h
e
clai
m
o
f
t
h
e
n
e
w
cu
r
r
icu
l
u
m
is
to
f
o
r
m
a
m
o
d
er
n
s
ch
o
o
l
s
y
s
te
m
b
ased
o
n
s
tan
d
ar
d
s
an
d
co
m
p
ete
n
cies
[
2
5
]
.
A
s
f
o
r
th
e
m
ath
e
m
at
ics
p
ar
t
o
f
it,
it
r
ese
m
b
les
m
o
s
t
co
n
te
m
p
o
r
ar
y
m
at
h
e
m
a
tics
c
u
r
r
icu
la
i
n
f
l
u
e
n
ce
d
b
y
th
e
P
I
S
A
m
at
h
e
m
a
tical
f
r
a
m
e
w
o
r
k
a
n
d
th
e
f
ac
t
t
h
at
m
at
h
e
m
atic
s
m
u
s
t
b
e
at
th
e
s
er
v
ice
o
f
s
o
ciet
y
,
o
f
d
ail
y
li
f
e
an
d
r
ap
id
tech
n
o
lo
g
ical
d
ev
e
lo
p
m
en
t.
Am
o
n
g
o
t
h
er
th
in
g
s
,
t
h
e
co
r
e
cu
r
r
icu
l
u
m
f
o
r
u
p
p
e
r
s
ec
o
n
d
ar
y
s
c
h
o
o
l
s
ets
u
p
th
e
m
ai
n
m
a
th
e
m
atic
s
co
m
p
ete
n
cies
th
at
r
el
y
h
ea
v
il
y
o
n
p
r
o
b
le
m
s
o
lv
in
g
,
w
it
h
a
p
ar
ticu
lar
f
o
cu
s
o
n
co
n
tex
t
u
al
p
r
o
b
le
m
s
;
ar
g
u
m
e
n
tatio
n
a
n
d
r
ea
s
o
n
i
n
g
;
co
m
m
u
n
icat
io
n
;
m
ak
i
n
g
co
n
n
ec
ti
o
n
s
;
r
ea
s
o
n
i
n
g
an
d
p
r
o
o
f
;
r
ep
r
esen
tatio
n
;
m
o
d
elli
n
g
a
n
d
u
s
e
o
f
I
C
T
[
2
6
]
.
Yet,
k
o
s
o
v
ar
s
t
u
d
en
t
s
h
a
v
e
p
er
f
o
r
m
ed
v
er
y
p
o
o
r
l
y
i
n
P
I
SA
2
0
1
5
an
d
PISA
2
0
1
8
,
s
in
ce
Ko
s
o
v
o
b
eg
an
to
p
ar
ticip
ate
in
th
is
in
ter
n
atio
n
al
s
t
u
d
y
.
No
t
a
lo
ca
l
s
tu
d
y
h
as
y
et
d
ea
lt
w
it
h
t
h
e
f
ac
to
r
s
ass
o
ciate
d
w
it
h
t
h
e
r
e
v
ea
led
w
ea
k
n
ess
e
s
r
elate
d
to
m
at
h
e
m
atica
l
co
m
p
eten
c
ies
an
d
s
tu
d
e
n
t
'
s
s
k
i
lls
i
n
p
r
o
b
le
m
s
o
l
v
in
g
.
T
h
o
u
g
h
t
h
e
is
s
u
an
ce
o
f
t
h
e
n
e
w
c
u
r
r
icu
l
u
m
lead
s
in
t
h
e
r
ig
h
t
d
ir
ec
tio
n
,
s
till
,
th
i
s
lar
g
e
an
d
r
elativ
el
y
f
ast
c
u
r
r
icu
lu
m
s
h
if
t
n
ee
d
s
to
b
e
a
s
s
o
ciate
d
w
it
h
n
ec
es
s
ar
y
p
r
ac
tica
l
tr
an
s
itio
n
s
,
w
h
ic
h
i
s
t
h
e
m
o
s
t
d
if
f
icu
l
t
p
ar
t
o
f
ed
u
ca
t
io
n
al
r
ef
o
r
m
.
T
h
e
ac
tu
al
s
t
u
d
y
d
ea
l
s
ex
ac
t
l
y
w
i
th
th
is
v
er
y
q
u
es
tio
n
-
if
t
h
er
e
is
an
alig
n
m
e
n
t
b
et
w
ee
n
cu
r
r
icu
l
u
m
in
te
n
tio
n
s
a
n
d
class
r
o
o
m
p
r
ac
tices.
T
h
e
is
s
u
e
in
q
u
esti
o
n
w
ill
b
e
i
n
v
esti
g
ated
th
r
o
u
g
h
th
e
a
n
al
y
s
i
s
a
n
d
ch
ar
ac
ter
izatio
n
o
f
t
h
e
ta
s
k
s
u
s
ed
f
o
r
m
at
h
e
m
a
tics
class
r
o
o
m
i
n
s
tr
u
ctio
n
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
T
h
is
s
tu
d
y
e
x
a
m
i
n
e
d
th
e
q
u
al
it
y
an
d
t
y
p
e
s
o
f
ta
s
k
s
u
s
ed
f
o
r
m
a
th
e
m
atic
s
clas
s
r
o
o
m
in
s
t
r
u
ctio
n
i
n
an
u
p
p
er
s
ec
o
n
d
ar
y
s
c
h
o
o
l
–
g
y
m
n
as
iu
m
,
lo
ca
ted
i
n
o
n
e
o
f
th
e
Ko
s
o
v
a
m
u
n
icip
alities
.
A
l
l
t
h
e
tas
k
s
u
s
ed
d
u
r
in
g
th
e
s
c
h
o
o
l
y
ea
r
2
0
1
8
/2
0
1
9
in
n
in
e
c
lass
r
o
o
m
s
o
f
t
h
i
s
s
c
h
o
o
l
(
g
r
ad
es
1
0
–
1
2
)
,
w
e
r
e
an
al
y
z
ed
a
g
ain
s
t
a
f
iv
e
-
d
i
m
en
s
io
n
al
an
a
l
y
t
ical
f
r
a
m
e
w
o
r
k
.
T
h
e
n
u
m
b
er
o
f
th
e
m
a
th
e
m
atica
l
ta
s
k
s
an
al
y
ze
d
w
a
s
2
1
3
1
.
A
ll
n
i
n
e
class
r
o
o
m
s
h
ad
d
if
f
er
e
n
t
m
a
t
h
e
m
a
tics
teac
h
er
s
.
T
h
e
task
s
w
er
e
co
llected
d
ir
ec
tl
y
f
r
o
m
t
ea
ch
er
s
an
d
s
t
u
d
en
t
class
r
o
o
m
n
o
te
s
.
T
ab
le
1
s
h
o
w
s
th
e
d
is
tr
ib
u
tio
n
o
f
tas
k
s
f
o
r
class
r
o
o
m
s
.
T
ab
le
1
.
T
h
e
d
is
tr
ib
u
tio
n
o
f
t
h
e
co
llected
task
s
ac
co
r
d
in
g
to
th
e
clas
s
r
o
o
m
s
C
l
a
ssr
o
o
ms
1
0
a
1
0
b
1
0
c
1
1
a
1
1
b
1
1
c
1
2
a
1
2
b
1
2
c
N
u
mb
e
r
o
f
t
a
sk
s
4
2
1
4
2
6
2
6
0
1
6
1
1
8
1
1
0
0
2
5
1
2
2
4
1
0
7
T
h
e
u
tili
s
ed
a
n
al
y
tical
f
r
a
m
e
w
o
r
k
r
ep
r
ese
n
t
ed
a
co
m
b
i
n
atio
n
o
f
f
i
v
e
an
al
y
tica
l
d
im
en
s
io
n
s
.
T
h
e
an
al
y
tical
d
i
m
en
s
io
n
s
in
clu
d
e
d
co
n
tex
t
u
al
f
ea
tu
r
es
;
th
e
an
s
w
er
f
o
r
m
s
r
eq
u
ir
ed
;
f
o
r
m
s
o
f
p
r
ese
n
tatio
n
;
t
y
p
es
o
f
r
eq
u
ir
ed
m
at
h
e
m
atic
al
ac
tiv
it
y
a
n
d
co
g
n
iti
v
e
d
e
m
an
d
s
in
v
o
lv
ed
.
T
h
e
f
r
a
m
e
w
o
r
k
w
a
s
b
u
ilt
h
a
v
i
n
g
in
m
i
n
d
th
e
s
p
ec
if
ic
r
an
g
e
o
f
cu
r
r
icu
lu
m
r
eq
u
ir
e
m
e
n
ts
t
h
at
d
ir
ec
t
ed
th
e
class
r
o
o
m
in
s
tr
u
ctio
n
in
th
i
s
ca
s
e.
T
ab
le
2
p
r
o
v
id
es
a
s
u
m
m
ar
y
o
f
all
f
iv
e
a
n
al
y
tical
d
i
m
e
n
s
i
o
n
s
b
y
th
e
ca
teg
o
r
ies
u
s
ed
in
th
e
s
tu
d
y
a
n
d
th
ei
r
b
r
ief
d
escr
ip
tio
n
.
T
h
e
f
ea
tu
r
es
an
al
y
s
ed
p
r
o
v
id
e
an
o
v
e
r
v
ie
w
o
f
t
h
e
lear
n
i
n
g
o
p
p
o
r
tu
n
ities
o
f
f
er
ed
in
th
e
cla
s
s
r
o
o
m
i
n
s
tr
u
ctio
n
.
T
h
e
c
u
r
r
en
t
s
tu
d
y
u
tili
ze
d
a
co
n
ten
t
an
al
y
s
is
d
esi
g
n
b
ase
d
o
n
q
u
an
titati
v
e
ap
p
r
o
ac
h
.
Fo
r
th
e
d
ata
p
r
o
ce
s
s
in
g
w
e
h
a
v
e
u
s
ed
d
escr
ip
tiv
e
s
tatis
tic
s
(
f
r
eq
u
e
n
cies a
n
d
p
er
c
en
tag
e
s
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8822
I
n
t
.
J
.
E
v
al
.
&
R
es
.
E
d
u
c
.
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2020
:
7
5
1
-
758
754
T
ab
le
2
.
T
h
e
an
al
y
tical
f
r
a
m
e
w
o
r
k
u
s
ed
i
n
th
e
s
tu
d
y
C
a
t
e
g
o
r
i
e
s
D
e
scri
p
t
i
o
n
A
n
a
l
y
t
i
c
a
l
d
i
me
n
s
i
o
n
:
C
o
n
t
e
x
t
u
a
l
f
e
a
t
u
r
e
s [2
3
]
N
o
n
-
a
p
p
l
i
c
a
t
i
v
e
t
a
sk
s
N
o
c
o
n
n
e
c
t
i
o
n
w
i
t
h
r
e
a
l
i
t
y
-
r
e
l
a
t
e
d
c
o
n
t
e
x
t
s
F
i
c
t
i
t
i
o
u
s
-
a
p
p
l
i
c
a
t
i
o
n
t
a
s
k
s
C
o
n
t
a
i
n
r
e
a
l
i
t
y
-
r
e
l
a
t
e
d
c
o
n
t
e
x
t
s
d
e
si
g
n
e
d
b
y
t
h
e
a
u
t
h
o
r
/
s
A
u
t
h
e
n
t
i
c
-
a
p
p
l
i
c
a
t
i
o
n
s
t
a
s
k
s
C
o
n
t
a
i
n
r
e
a
l
-
l
i
f
e
d
a
t
a
o
r
d
a
t
a
c
o
l
l
e
c
t
e
d
b
y
st
u
d
e
n
t
s fr
o
m
t
h
e
i
r
d
a
i
l
y
l
i
v
e
s
A
n
a
l
y
t
i
c
a
l
d
i
me
n
s
i
o
n
:
F
o
r
ms o
f
p
r
e
se
n
t
a
t
i
o
n
[
2
3
]
S
y
mb
o
l
i
c
T
a
sk
s p
r
e
se
n
t
e
d
i
n
sy
mb
o
l
i
c
f
o
r
m
T
e
x
t
u
a
l
T
a
sk
s p
r
e
se
n
t
e
d
i
n
t
e
x
t
u
a
l
f
o
r
m
V
i
su
a
l
T
a
sk
s p
r
e
se
n
t
e
d
i
n
v
i
s
u
a
l
f
o
r
m
C
o
mb
i
n
e
d
T
a
sk
s p
r
e
se
n
t
e
d
i
n
c
o
mb
i
n
e
d
mo
d
e
s o
f
t
w
o
o
r
t
h
r
e
e
p
r
e
se
n
t
a
t
i
o
n
f
o
r
ms
A
n
a
l
y
t
i
c
a
l
d
i
me
n
s
i
o
n
:
A
n
s
w
e
r
f
o
r
ms r
e
q
u
i
r
e
d
[
2
3
]
C
l
o
se
-
e
n
d
e
d
t
a
s
k
s
H
a
v
e
o
n
l
y
o
n
e
a
n
sw
e
r
O
p
e
n
-
e
n
d
e
d
t
a
s
k
s
H
a
v
e
se
v
e
r
a
l
o
r
man
y
c
o
r
r
e
c
t
a
n
sw
e
r
s
M
u
l
t
i
p
l
e
r
e
sp
o
n
se
t
a
sk
s
R
e
sp
o
n
d
e
n
t
s
se
l
e
c
t
o
n
l
y
c
o
r
r
e
c
t
a
n
sw
e
r
s fr
o
m t
h
e
c
h
o
i
c
e
s o
f
f
e
r
e
d
A
n
a
l
y
t
i
c
a
l
d
i
me
n
s
i
o
n
:
M
a
t
h
e
m
a
t
i
c
a
l
a
c
t
i
v
i
t
y
i
n
v
o
l
v
e
d
[
1
0
,
2
4
]
.
R
e
p
r
e
se
n
t
a
t
i
o
n
s
a
n
d
mo
d
e
l
l
i
n
g
t
a
s
k
s
R
e
q
u
i
r
e
t
h
e
p
r
e
se
n
t
a
t
i
o
n
o
f
mat
h
e
ma
t
i
c
a
l
d
a
t
a
i
n
d
i
f
f
e
r
e
n
t
f
o
r
ms;
t
h
e
t
r
a
n
sl
a
t
i
o
n
o
f
ma
t
h
e
ma
t
i
c
a
l
d
a
t
a
f
r
o
m
o
n
e
r
e
p
r
e
se
n
t
a
t
i
o
n
t
o
a
n
o
t
h
e
r
C
a
l
c
u
l
a
t
i
o
n
a
n
d
o
p
e
r
a
t
i
o
n
t
a
s
k
s
R
e
q
u
i
r
e
t
h
e
p
e
r
f
o
r
man
c
e
o
f
mat
h
e
ma
t
i
c
a
l
o
p
e
r
a
t
i
o
n
s
,
c
a
l
c
u
l
a
t
i
o
n
s,
t
r
a
n
sf
o
r
ma
t
i
o
n
s,
g
e
o
me
t
r
i
c
c
o
n
st
r
u
c
t
i
o
n
s e
t
c
.
I
n
t
e
r
p
r
e
t
a
t
i
o
n
t
a
s
k
s
R
e
q
u
i
r
e
t
h
e
r
e
c
o
g
n
i
t
i
o
n
,
r
e
a
d
i
n
g
a
n
d
c
o
n
t
e
x
t
u
a
l
i
n
t
e
r
p
r
e
t
a
t
i
o
n
o
f
mat
h
e
mat
i
c
a
l
r
e
l
a
t
i
o
n
s o
r
d
a
t
a
p
r
e
se
n
t
e
d
i
n
d
i
f
f
e
r
e
n
t
f
o
r
ms
A
r
g
u
me
n
t
a
t
i
o
n
a
n
d
r
e
a
so
n
i
n
g
t
a
s
k
s
R
e
q
u
i
r
e
e
l
a
b
o
r
a
t
i
o
n
s
,
d
e
scri
p
t
i
o
n
s
a
n
d
st
r
i
n
g
i
n
g
o
f
t
h
e
r
i
g
h
t
a
r
g
u
me
n
t
s
t
h
a
t
l
e
a
d
t
o
a
c
o
n
c
l
u
si
o
n
A
n
a
l
y
t
i
c
a
l
d
i
me
n
s
i
o
n
:
L
e
v
e
l
o
f
c
o
g
n
i
t
i
v
e
d
e
man
d
[
2
2
]
M
e
mo
r
i
sat
i
o
n
t
a
s
k
s
I
n
v
o
l
v
e
t
h
e
r
e
p
r
o
d
u
c
t
i
o
n
o
f
p
r
e
v
i
o
u
sl
y
l
e
a
r
n
e
d
r
u
l
e
s,
f
a
c
t
s
,
f
o
r
mu
l
a
s
o
r
d
e
f
i
n
i
t
i
o
n
s
P
r
o
c
e
d
u
r
e
s w
i
t
h
n
o
c
o
n
n
e
c
t
i
o
n
t
a
sk
s
I
n
v
o
l
v
e
t
h
e
p
e
r
f
o
r
man
c
e
o
f
g
e
n
e
r
a
l
p
r
o
c
e
d
u
r
e
s a
n
d
a
l
g
o
r
i
t
h
ms
,
w
i
t
h
o
u
t
ma
k
i
n
g
a
n
y
c
o
n
n
e
c
t
i
o
n
s t
o
t
h
e
u
n
d
e
r
l
y
i
n
g
c
o
n
c
e
p
t
s o
r
me
a
n
i
n
g
P
r
o
c
e
d
u
r
e
s w
i
t
h
c
o
n
n
e
c
t
i
o
n
t
a
sk
s
I
n
v
o
l
v
e
t
h
e
p
e
r
f
o
r
man
c
e
o
f
g
e
n
e
r
a
l
p
r
o
c
e
d
u
r
e
s a
n
d
a
l
g
o
r
i
t
h
ms
mak
i
n
g
c
o
n
n
e
c
t
i
o
n
s
t
o
t
h
e
u
n
d
e
r
l
y
i
n
g
c
o
n
c
e
p
t
s o
r
me
a
n
i
n
g
D
o
i
n
g
ma
t
h
t
a
sk
s
I
n
v
o
l
v
e
c
o
mp
l
e
x
a
n
d
n
o
n
-
a
l
g
o
r
i
t
h
m
i
c
t
h
i
n
k
i
n
g
,
e
x
p
l
o
r
a
t
i
o
n
a
n
d
u
n
d
e
r
st
a
n
d
i
n
g
o
f
mat
h
e
ma
t
i
c
s
c
o
n
c
e
p
t
s,
p
r
o
c
e
sse
s o
r
r
e
l
a
t
i
o
n
sh
i
p
s
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
Fi
g
u
r
e
1
g
i
v
es
an
o
v
er
v
ie
w
o
f
th
e
co
n
te
x
t
u
al
ch
ar
ac
t
er
i
s
t
ics
o
f
t
h
e
ta
s
k
s
a
n
al
y
z
ed
ac
co
r
d
in
g
to
th
e
class
r
o
o
m
s
.
T
h
e
g
r
ap
h
s
h
o
w
s
a
d
ee
p
i
m
b
alan
ce
in
th
e
r
ep
r
esen
tatio
n
of
e
x
is
ti
n
g
ca
teg
o
r
ies.
Vast
m
aj
o
r
it
y
of
task
s
p
r
esen
ted
in
all
n
i
n
e
class
r
o
o
m
s
ar
e
of
n
o
n
-
ap
p
lica
tiv
e
t
y
p
e.
E
x
ac
tl
y
9
9
.
3
0
%
of
t
h
e
m
b
elo
n
g
i
n
th
i
s
ca
teg
o
r
y
.
T
h
e
o
th
er
t
w
o
ca
teg
o
r
ies
ar
e
alm
o
s
t
u
n
r
ep
r
esen
te
d
.
B
o
th
co
n
tain
0
.
7
0
%
of
th
e
task
s
,
w
i
th
o
n
l
y
one
of
th
e
ta
s
k
s
b
ein
g
of
an
au
t
h
e
n
tic
-
ap
p
licativ
e
t
y
p
e.
B
u
t,
ch
a
llen
g
in
g
s
tu
d
e
n
ts
w
i
th
co
n
tex
t
u
al
p
r
o
b
lem
s
is
o
n
e
o
f
t
h
e
e
x
p
licit
r
eq
u
ir
e
m
e
n
ts
o
f
o
u
r
c
u
r
r
icu
lu
m
.
Stu
d
e
n
ts
s
h
o
u
ld
“
d
e
s
cr
ib
e
an
d
s
o
l
v
e
p
r
o
b
le
m
s
itu
a
tio
n
s
t
h
at
ar
is
e
w
i
th
i
n
m
ath
e
m
atic
s
an
d
in
co
n
tex
ts
f
r
o
m
o
t
h
er
f
ield
s
as
w
ell
as
f
r
o
m
s
h
ar
ed
ex
p
er
ien
ce
s
o
f
e
v
er
y
d
a
y
lif
e
[
2
6
]
.
W
e
m
u
s
t
r
ec
all
h
er
e
th
e
v
er
y
p
o
o
r
p
er
f
o
r
m
an
ce
o
f
Ko
s
o
v
ar
s
t
u
d
en
t
s
th
e
f
ir
s
t
t
w
o
ti
m
e
s
o
f
p
ar
ticip
atio
n
in
P
I
SA
2
0
1
5
an
d
P
I
SA
2
0
1
8
.
On
e
o
f
th
e
m
aj
o
r
f
ac
to
r
s
o
f
th
is
p
o
o
r
p
er
f
o
r
m
a
n
ce
ap
p
ea
r
s
to
b
e
o
u
r
s
tu
d
en
ts
'
n
o
n
-
e
x
p
o
s
u
r
e
to
co
n
tex
tu
al
tas
k
s
.
T
h
is
ex
tr
e
m
e
n
o
n
-
e
x
p
o
s
u
r
e
h
a
s
also
b
ee
n
d
o
cu
m
e
n
ted
in
s
ev
er
al
o
t
h
er
lo
ca
l
s
tu
d
ie
s
t
h
a
t
h
a
v
e
e
x
a
m
in
ed
t
h
e
p
r
ese
n
ce
o
f
co
n
te
x
t
s
i
n
m
at
h
e
m
atics
t
ex
tb
o
o
k
s
[
2
7
-
2
9
]
at
d
if
f
er
e
n
t sc
h
o
o
lin
g
lev
e
ls
,
an
d
class
r
o
o
m
ass
e
s
s
m
e
n
t i
n
ele
m
en
tar
y
s
c
h
o
o
l [
2
5
,
3
0
]
.
Fig
u
r
e
1
.
C
o
n
te
x
tu
al
f
ea
t
u
r
es
o
f
th
e
a
n
al
y
ze
d
tas
k
s
ac
co
r
d
in
g
to
th
e
clas
s
r
o
o
m
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
v
al
&
R
e
s
E
d
u
c
.
I
SS
N:
2252
-
8822
Typ
es o
f m
a
th
ema
tica
l ta
s
ks u
s
ed
in
s
ec
o
n
d
a
r
y
cla
s
s
r
o
o
m
in
s
tr
u
ctio
n
(
V
a
lb
o
n
a
B
eris
h
a
)
755
T
h
e
f
in
d
in
g
s
o
n
th
e
f
o
r
m
s
o
f
task
p
r
esen
tat
io
n
ac
co
r
d
in
g
to
th
e
class
r
o
o
m
s
ar
e
s
h
o
w
n
in
Fig
u
r
e
2.
Vast
m
aj
o
r
it
y
o
f
t
h
e
u
s
ed
ta
s
k
s
,
8
0
.
3
8
%,
a
r
e
p
r
esen
ted
i
n
s
y
m
b
o
lic
f
o
r
m
.
On
l
y
7
.
1
3
%
o
f
th
e
tas
k
s
ar
e
p
r
esen
ted
w
it
h
tex
t,
w
h
ile
4
.
2
2
%
o
f
th
e
task
s
h
a
v
e
a
v
is
u
al
f
o
r
m
.
T
h
e
r
em
ain
i
n
g
8
.
2
6
%
ar
e
o
f
co
m
b
in
ed
f
o
r
m
.
Mo
r
eo
v
er
,
th
e
id
en
ti
f
ied
v
is
u
al
r
ep
r
ese
n
tatio
n
s
ar
e
m
ai
n
l
y
in
th
e
f
o
r
m
o
f
n
u
m
er
ical
s
et
d
iag
r
a
m
s
.
Ot
h
er
t
y
p
es
o
f
v
i
s
u
al
r
ep
r
ese
n
tatio
n
s
s
u
c
h
as
p
ict
u
r
es
r
elate
d
w
it
h
r
ea
l
-
w
o
r
ld
co
n
tex
ts
,
g
r
ap
h
s
etc.
ar
e
n
o
t
r
ep
r
esen
ted
at
all.
Fin
d
in
g
s
in
d
icate
th
at
t
h
e
ce
n
tr
al
f
o
r
m
o
f
m
at
h
e
m
atic
s
class
r
o
o
m
co
m
m
u
n
icat
io
n
is
th
e
s
y
m
b
o
lic
o
n
e.
Mu
c
h
ad
v
an
tag
e
i
s
g
i
v
en
to
s
y
m
b
o
lic
f
o
r
m
c
o
m
p
ar
ed
to
o
th
er
f
o
r
m
s
o
f
p
r
esen
tin
g
id
ea
s
,
co
n
ce
p
ts
an
d
p
r
o
b
lem
s
.
I
n
t
h
i
s
ca
s
e,
b
o
th
tex
t
u
al
a
n
d
v
i
s
u
a
l
f
o
r
m
o
f
m
at
h
e
m
atica
l
co
m
m
u
n
ica
tio
n
i
s
h
i
g
h
l
y
n
eg
lec
ted
,
d
esp
ite
th
e
f
ac
t
t
h
e
s
e
t
w
o
f
o
r
m
s
h
a
v
e
a
n
i
m
p
o
r
tan
t
f
u
n
ctio
n
i
n
m
at
h
e
m
a
tics
tea
ch
in
g
a
n
d
lear
n
in
g
.
B
o
th
f
o
r
m
s
f
ac
ili
tate
th
e
m
o
d
ellin
g
,
r
ep
r
esen
tatio
n
an
d
p
r
o
b
l
e
m
-
s
o
lv
in
g
s
k
ill
s
.
Fig
u
r
e
2
.
Fo
r
m
s
o
f
p
r
esen
tatio
n
o
f
t
h
e
an
al
y
z
ed
tas
k
s
ac
co
r
d
in
g
to
t
h
e
clas
s
r
o
o
m
s
Fig
u
r
e
3
r
ev
ea
l
s
t
h
e
r
es
u
lts
o
n
t
h
e
a
n
s
w
er
f
o
r
m
r
eq
u
ir
ed
b
y
t
h
e
tas
k
s
.
Fi
n
d
in
g
s
in
d
icate
th
at
v
as
t
m
aj
o
r
ity
o
f
tas
k
s
,
9
5
.
2
1
%
o
f
th
e
m
,
ar
e
clo
s
e
-
e
n
d
ed
o
n
es.
E
ig
h
t
task
s
o
r
0
.
3
8
%
o
f
th
e
to
tal
n
u
m
b
er
o
f
tas
k
s
an
al
y
s
ed
ar
e
o
p
en
-
en
d
ed
o
n
es,
an
d
th
e
r
em
ai
n
i
n
g
4
.
4
1
%
ar
e
o
f
m
u
lt
ip
le
-
c
h
o
ice
t
y
p
e.
R
es
u
lts
in
d
icat
e
a
s
tr
ictl
y
clo
s
ed
ap
p
r
o
ac
h
to
m
at
h
e
m
a
tics
in
s
tr
u
c
tio
n
.
T
h
is
t
y
p
e
o
f
in
s
tr
u
ctio
n
d
o
es
n
o
t
allo
w
m
u
c
h
r
o
o
m
f
o
r
th
e
co
n
s
tr
u
ctio
n
o
f
a
w
id
e
r
an
g
e
o
f
s
k
ill
s
r
elate
d
to
cr
ea
tiv
it
y
,
p
r
o
d
u
ctio
n
an
d
au
to
n
o
m
o
u
s
s
tr
ateg
ie
s
.
C
u
r
r
en
t
f
i
n
d
in
g
s
co
m
b
in
ed
w
ith
v
er
y
s
i
m
i
lar
f
in
d
i
n
g
s
f
r
o
m
a
r
ec
en
t
lo
ca
l
s
tu
d
y
e
x
a
m
in
i
n
g
te
s
t
d
esi
g
n
as
an
ass
e
s
s
m
e
n
t
to
o
l
in
ele
m
en
t
ar
y
m
at
h
e
m
atics
cla
s
s
r
o
o
m
s
[
2
5
]
ar
g
u
e
th
at
an
o
p
en
ap
p
r
o
ac
h
to
m
at
h
e
m
atics
teac
h
i
n
g
a
n
d
lear
n
i
n
g
i
s
n
o
t a
t
all
f
a
m
iliar
to
Ko
s
o
v
ar
teac
h
er
s
.
Fig
u
r
e
3
.
T
h
e
an
s
w
er
f
o
r
m
s
r
e
q
u
ir
ed
in
th
e
a
n
al
y
s
ed
tas
k
s
ac
co
r
d
in
g
to
th
e
clas
s
r
o
o
m
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8822
I
n
t
.
J
.
E
v
al
.
&
R
es
.
E
d
u
c
.
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2020
:
7
5
1
-
758
756
Fig
u
r
e
4
g
i
v
es
a
n
in
s
ig
h
t
i
n
t
o
th
e
m
at
h
e
m
atica
l
ac
ti
v
itie
s
r
eq
u
ir
ed
o
f
s
tu
d
en
t
s
i
n
o
r
d
er
to
s
o
lv
e
th
e
task
s
.
T
h
e
co
d
in
g
o
f
task
s
w
a
s
d
o
n
e
ac
c
o
r
d
in
g
to
th
e
m
ai
n
ac
tiv
it
y
r
eq
u
ir
ed
in
th
e
task
.
T
h
er
e
ar
e
8
5
.
9
7
%
o
f
th
e
to
tal
n
u
m
b
er
o
f
tas
k
s
an
al
y
s
ed
f
all
i
n
th
e
ca
teg
o
r
y
o
f
m
at
h
e
m
a
tical
ca
lcu
latio
n
s
an
d
o
p
er
atio
n
s
.
R
ep
r
esen
tat
io
n
o
r
m
o
d
ellin
g
is
r
eq
u
ir
ed
in
1
2
.
6
2
%
o
f
task
s
as
th
e
m
ain
ac
ti
v
it
y
.
Mo
s
t
o
f
s
u
c
h
task
s
w
er
e
p
r
esen
ted
in
th
e
ten
t
h
g
r
ad
e.
A
s
m
all
p
o
r
tio
n
o
f
task
s
,
5
.
1
1
%
o
f
th
e
m
,
r
eq
u
ir
e
in
ter
p
r
etatio
n
o
f
m
a
th
e
m
atica
l
r
ep
r
esen
tatio
n
s
,
e
x
p
r
ess
io
n
s
o
r
f
o
r
m
u
la
s
an
d
o
n
l
y
4
.
7
9
%
o
f
tas
k
s
r
eq
u
ir
e
ar
g
u
m
e
n
tati
o
n
o
r
r
ea
s
o
n
in
g
a
s
a
ce
n
tr
al
ac
ti
v
it
y
.
T
h
e
r
es
u
lts
o
n
m
at
h
e
m
atica
l
ac
ti
v
itie
s
i
n
d
icate
a
r
ath
er
tr
ad
itio
n
al
wa
y
o
f
m
at
h
e
m
a
tic
s
teac
h
i
n
g
a
n
d
lear
n
i
n
g
.
S
tu
d
e
n
ts
ar
e
tr
ain
ed
m
ai
n
l
y
in
t
h
e
d
o
m
ai
n
o
f
ca
lc
u
latio
n
s
an
d
o
p
er
atio
n
s
.
I
n
ter
p
r
etin
g
s
k
il
ls
as
w
el
l a
s
ar
g
u
m
en
ta
tio
n
an
d
r
ea
s
o
n
in
g
s
k
ill
s
ar
e
al
m
o
s
t c
o
m
p
letel
y
o
v
er
lo
o
k
ed
.
Fig
u
r
e
4
.
Ma
th
e
m
a
tical
ac
ti
v
it
ies
in
v
o
lv
ed
w
it
h
t
h
e
tas
k
s
a
n
a
l
y
ze
d
ac
co
r
d
in
g
to
th
e
cla
s
s
r
o
o
m
s
Fin
d
i
n
g
s
r
elate
d
to
th
e
co
g
n
it
iv
e
d
e
m
a
n
d
s
co
n
v
e
y
ed
by
t
h
e
an
al
y
s
ed
tas
k
s
ar
e
s
h
o
w
n
in
Fig
u
r
e
5.
8
7
.
6
6
%
of
task
s
ar
e
of
lo
w
co
g
n
i
tiv
e
lev
e
l.
T
h
e
m
aj
o
r
f
r
ac
ti
o
n
of
t
h
ese
lo
w
co
g
n
iti
v
e
le
v
e
l
tas
k
s
is
p
r
o
ce
d
u
r
al
o
n
es,
w
ith
no
r
elatio
n
to
th
e
c
o
n
ce
p
ts
an
d
m
ea
n
i
n
g
s
b
eh
i
n
d
th
e
p
r
o
ce
d
u
r
es
n
ee
d
ed
f
o
r
s
o
lv
in
g
t
h
e
m
.
A
s
m
al
l
f
r
ac
tio
n
of
t
h
ese
tas
k
s
ar
e
m
e
m
o
r
izat
io
n
o
n
es.
T
h
o
s
e
ar
e
ca
r
r
ied
on
w
i
th
t
h
e
h
elp
of
m
e
m
o
r
ized
f
ac
t
s
an
d
r
u
les.
T
h
is
g
r
o
u
p
of
ta
s
k
s
i
n
cl
u
d
es
m
an
y
ca
s
e
s
w
h
er
e
s
t
u
d
en
ts
m
i
g
h
t
ca
r
r
y
out
th
e
tas
k
in
a
v
er
y
m
ea
n
i
n
g
le
s
s
an
d
al
m
o
s
t
ab
s
en
t
-
m
i
n
d
ed
w
a
y
.
On
l
y
3
.
5
2
%
of
t
h
e
to
tal
n
u
m
b
er
s
of
t
h
e
ta
s
k
s
r
ela
te
to
a
u
to
n
o
m
o
u
s
s
o
lu
tio
n
s
tr
ateg
ie
s
an
d
s
tr
ateg
ie
s
,
w
h
i
le
th
e
r
est
of
th
e
h
i
g
h
er
co
g
n
iti
v
e
le
v
el
tas
k
s
ca
n
be
s
o
l
v
ed
u
s
in
g
g
en
er
al
p
r
o
ce
d
u
r
es
ass
o
ciate
d
w
it
h
t
h
e
co
n
ce
p
ts
a
n
d
m
ea
n
i
n
g
s
b
eh
in
d
th
e
s
e
p
r
o
ce
d
u
r
es.
On
ce
a
g
ain
,
th
e
r
e
s
u
l
ts
do
n
o
t
in
d
icate
ali
g
n
m
e
n
t
w
it
h
h
ig
h
er
-
o
r
d
er
cu
r
r
icu
lu
m
r
eq
u
ir
e
m
en
ts
.
Mo
s
t
of
t
h
e
tas
k
s
an
al
y
z
ed
p
r
o
m
o
te
m
e
m
o
r
izat
io
n
an
d
au
to
m
a
ted
p
r
o
ce
d
u
r
es
ap
p
licatio
n
s
,
th
ey
do
n
o
t
d
ea
l
w
i
th
co
n
ce
p
t
u
al
an
d
m
ea
n
i
n
g
f
u
l
u
n
d
er
s
ta
n
d
in
g
at
all.
On
l
y
a
s
m
all
f
r
ac
tio
n
of
tas
k
s
h
as
t
h
e
p
o
ten
tial
to
d
ev
elo
p
cr
itical
a
n
d
cr
ea
tiv
e
th
i
n
k
i
n
g
th
r
o
u
g
h
d
ee
p
co
n
ce
p
tu
al
u
n
d
e
r
s
tan
d
in
g
.
T
h
e
ti
m
e
s
p
en
t
f
o
r
class
r
o
o
m
i
n
s
tr
u
ctio
n
is
n
o
t
well
m
a
n
ag
ed
,
g
i
v
e
n
th
e
co
g
n
iti
v
e
d
e
m
a
n
d
s
of
p
r
es
en
ted
tas
k
s
“
.
.
.
if
m
o
r
e
ti
m
e
w
er
e
s
p
e
n
t
i
n
clas
s
r
o
o
m
w
it
h
s
tu
d
e
n
ts
e
n
g
a
g
ed
i
n
wo
r
k
i
n
g
o
n
co
g
n
i
tiv
e
l
y
d
e
m
a
n
d
in
g
n
o
n
r
o
u
tin
e
ta
s
k
s
,
as
o
p
p
o
s
ed
to
ex
er
cises
in
w
h
ich
a
k
n
o
w
n
p
r
o
ce
d
u
r
e
is
p
r
ac
ticed
,
s
tu
d
en
t
’
s
o
p
p
o
r
tu
n
it
ies f
o
r
th
i
n
k
i
n
g
a
n
d
lear
n
i
n
g
w
o
u
ld
lik
el
y
b
e
en
h
an
ce
”
[
1
1
]
.
Fig
u
r
e
5
.
L
C
D
o
f
tas
k
s
a
n
al
y
z
ed
ac
co
r
d
in
g
to
th
e
class
r
o
o
m
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
v
al
&
R
e
s
E
d
u
c
.
I
SS
N:
2252
-
8822
Typ
es o
f m
a
th
ema
tica
l ta
s
ks u
s
ed
in
s
ec
o
n
d
a
r
y
cla
s
s
r
o
o
m
in
s
tr
u
ctio
n
(
V
a
lb
o
n
a
B
eris
h
a
)
757
4.
CO
NCLU
SI
O
N
T
h
e
f
in
d
i
n
g
s
in
d
icate
a
s
ig
n
i
f
ica
n
t
i
m
b
ala
n
ce
i
n
r
ep
r
esen
t
atio
n
o
f
t
h
e
d
if
f
er
en
t
ca
te
g
o
r
ies
w
it
h
i
n
ea
ch
o
f
th
e
an
al
y
tica
l
d
i
m
e
n
s
io
n
s
ex
a
m
i
n
ed
.
Gi
v
en
th
a
t
all
th
e
p
ar
ticip
atin
g
ca
te
g
o
r
ies
h
a
v
e
t
h
eir
o
w
n
i
m
p
o
r
tan
ce
an
d
d
iv
er
s
e
r
o
le
in
th
e
b
u
ild
i
n
g
o
f
in
ten
d
ed
co
m
p
eten
ce
s
an
d
lear
n
in
g
o
u
tco
m
e
s
,
all
o
f
th
e
m
m
u
s
t
h
av
e
a
b
alan
ce
d
r
ep
r
esen
tatio
n
in
class
r
o
o
m
in
s
tr
u
ctio
n
.
I
n
s
u
ch
a
ca
s
e
o
f
h
u
g
e
i
m
b
a
lan
ce
s
,
n
eg
at
iv
e
i
m
p
licatio
n
s
f
o
r
lear
n
in
g
ar
e
v
er
y
e
x
p
ec
tab
le.
T
h
e
cu
r
r
en
t
Ko
s
o
v
ar
cu
r
r
icu
lu
m
s
e
ts
o
u
t
a
w
id
e
r
an
g
e
o
f
in
te
n
d
ed
lear
n
in
g
o
u
tco
m
es
f
o
r
m
at
h
e
m
atics.
B
esid
e
s
th
e
f
ac
tu
a
l
k
n
o
w
led
g
e
a
n
d
p
r
o
ce
d
u
r
al
s
k
ills
,
its
in
ten
t
io
n
s
ar
e
attai
n
m
e
n
t
o
f
h
i
g
h
er
o
r
d
er
th
i
n
k
i
n
g
an
d
r
ea
s
o
n
in
g
s
k
ill
s
,
cr
itical
an
d
cr
ea
tiv
e
th
i
n
k
in
g
an
d
r
ea
l
-
w
o
r
ld
co
m
p
ete
n
cies.
I
n
ad
d
itio
n
to
t
h
e
n
o
ted
i
m
b
al
an
ce
s
b
et
w
ee
n
ca
te
g
o
r
ies,
t
h
e
f
i
n
d
in
g
s
s
h
o
w
th
a
t
m
o
s
t
o
f
th
e
ta
s
k
s
u
s
ed
f
o
r
cl
ass
r
o
o
m
in
s
tr
u
ctio
n
r
elate
to
ca
teg
o
r
ies
th
at
m
ai
n
l
y
co
n
tr
i
b
u
te
to
lo
w
er
o
r
d
er
lear
n
in
g
o
u
tco
m
es.
Mo
s
tl
y
,
teac
h
er
s
u
s
ed
clo
s
e
-
en
d
ed
,
n
o
n
-
ap
p
licati
v
e,
lo
wer
-
lev
el
co
g
n
iti
v
e
tas
k
s
p
r
esen
ted
in
s
y
m
b
o
lic
f
o
r
m
,
p
r
o
m
o
tin
g
o
p
er
atio
n
s
an
d
ca
lcu
latio
n
s
as
a
ce
n
tr
al
ac
tiv
it
y
.
T
h
ese
tas
k
s
t
y
p
ica
ll
y
e
m
p
h
a
s
iz
e
m
e
m
o
r
izat
io
n
a
n
d
p
r
o
m
o
te
o
p
er
atio
n
s
an
d
ca
lc
u
latio
n
s
th
r
o
u
g
h
a
u
to
m
ated
p
r
o
ce
d
u
r
es.
T
ask
s
w
h
ich
h
a
v
e
th
e
p
o
ten
tial
f
o
r
d
ev
elo
p
in
g
cr
itical
an
d
cr
ea
tiv
e
th
in
k
i
n
g
;
d
ee
p
co
n
ce
p
tu
al
u
n
d
er
s
ta
n
d
in
g
;
in
ter
p
r
etatio
n
,
ap
p
licatio
n
an
d
m
o
d
elli
n
g
s
k
il
ls
–
ar
e
v
er
y
r
ar
e
o
n
es.
As
f
ar
as
th
e
o
p
p
o
r
tu
n
i
ties
o
f
f
er
ed
b
y
th
e
s
elec
ted
t
y
p
es
o
f
task
s
ar
e
co
n
s
id
er
ed
,
th
e
class
r
o
o
m
i
n
s
tr
u
ctio
n
i
n
th
is
ca
s
e,
is
n
o
t
w
ell
ali
g
n
ed
w
it
h
th
e
cu
r
r
en
t
s
tate
cu
r
r
ic
u
lu
m
r
eq
u
ir
e
m
en
t
s
f
o
r
th
e
f
ield
o
f
m
a
th
e
m
ati
cs.
I
n
co
n
clu
s
io
n
,
it
ca
n
b
e
s
aid
th
at
b
ased
o
n
th
e
p
er
f
o
r
m
ed
a
n
al
y
s
i
s
o
n
t
h
e
t
y
p
es
o
f
ta
s
k
s
u
s
ed
f
o
r
cla
s
s
r
o
o
m
i
n
s
tr
u
ctio
n
,
th
e
i
m
p
l
e
m
en
ted
clas
s
r
o
o
m
cu
r
r
icu
l
u
m
i
s
n
o
t
in
li
n
e
w
i
th
th
e
s
tate
in
ten
d
ed
cu
r
r
icu
l
u
m
.
T
h
e
task
s
u
s
ed
en
ab
le
v
er
y
li
ttle
o
r
n
o
s
p
ac
e
f
o
r
v
id
e
r
an
g
e
o
f
in
te
n
d
ed
lear
n
i
n
g
o
u
tco
m
e
s
o
f
h
ig
h
er
o
r
d
er
s
.
RE
F
E
R
E
NC
E
S
[1
]
M
u
tm
a
in
a
h
,
e
t
a
l
,
“
Ef
f
e
c
ti
v
e
n
e
ss
o
f
e
x
p
e
rien
ti
a
l
lea
rn
in
g
-
b
a
se
d
t
e
a
c
h
in
g
m
a
teria
l
in
M
a
t
h
e
m
a
ti
c
s
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Eva
l
u
a
ti
o
n
a
n
d
Res
e
a
rc
h
in
Ed
u
c
a
ti
o
n
(
IJ
ER
E),
v
o
l
.
8
,
n
o
.
1
,
p
p
.
5
7
-
6
3
,
2
0
1
9
.
[2
]
J.
L
it
h
n
e
r,
“
P
ri
n
c
ip
les
f
o
r
d
e
sig
n
in
g
m
a
th
e
m
a
ti
c
a
l
tas
k
s
th
a
t
e
n
h
a
n
c
e
im
it
a
ti
v
e
a
n
d
c
re
a
ti
v
e
re
a
so
n
in
g
,
”
Z
DM
,
M
a
th
e
ma
ti
c
s E
d
u
c
a
t
io
n
,
v
o
l.
4
9
,
n
o
.
6
,
p
p
.
9
3
7
–
9
4
9
,
2
0
1
7
.
[3
]
P
.
S
u
ll
iv
a
n
,
e
t
a
l
,
“
Co
n
v
e
rti
n
g
m
a
th
e
m
a
ti
c
s
tas
k
s
to
lea
rn
in
g
o
p
p
o
rtu
n
it
ies
:
A
n
im
p
o
rtan
t
a
sp
e
c
t
o
f
k
n
o
w
led
g
e
f
o
r
m
a
th
e
m
a
ti
c
s tea
c
h
in
g
,
”
M
a
th
e
ma
ti
c
s E
d
u
c
a
ti
o
n
Res
e
a
rc
h
J
o
u
rn
a
l,
v
o
l.
21
,
n
o
.
1
,
p
p
.
85
-
1
0
5
,
2
0
0
9
.
[4
]
A
.
Co
les
a
n
d
L
.
Bro
w
n
,
“
M
a
k
i
n
g
d
isti
n
c
ti
o
n
s
in
ta
sk
d
e
sig
n
a
n
d
stu
d
e
n
t
a
c
ti
v
it
y
,
”
In
A
.
W
a
t
so
n
,
M
.
O
h
tan
i,
J.
A
in
le
y
,
J.
Bo
li
te
F
ra
n
t,
M
.
Do
o
rm
a
n
,
C.
Kie
ra
n
,
A
.
L
e
u
n
g
,
C.
M
a
rg
o
li
n
a
s,
P
.
S
u
ll
iv
a
n
,
D.
T
h
o
m
p
so
n
,
&
Y.
Ya
n
g
(Ed
s.)
Pr
o
c
e
e
d
in
g
s
o
f
ICM
I
S
tu
d
y
2
2
:
T
a
sk
De
sig
n
in
M
a
th
e
ma
ti
c
s
Ed
u
c
a
ti
o
n
,
p
p
.
1
8
3
–
1
9
2
,
Ox
f
o
rd
:
In
tern
a
ti
o
n
a
l
Co
m
m
issio
n
o
n
M
a
th
e
m
a
ti
c
s In
stru
c
ti
o
n
,
2
0
1
3
.
[5
]
C.
M
a
rg
o
li
n
a
s,
“
T
a
sk
d
e
sig
n
in
m
a
th
e
m
a
ti
c
s
e
d
u
c
a
ti
o
n
,
”
Pro
c
e
e
d
in
g
s
o
f
ICM
I
S
t
u
d
y
2
2
,
Ox
f
o
rd
,
Un
it
e
d
Kin
g
d
o
m
201
4
.
[6
]
D.
Clark
e
,
H.
S
trø
m
sk
a
g
,
H.
L
.
J
o
h
n
s
o
n
,
A
.
Bik
n
e
r
-
A
h
sb
a
h
s
a
n
d
K.
G
a
rd
n
e
r
,
M
a
th
e
m
a
ti
c
a
l
tas
k
s
a
n
d
t
h
e
st
u
d
e
n
t.
In
P
.
L
il
jed
a
h
l,
C.
Nic
o
l,
S
.
Oe
st
e
rle,
&
D.
A
ll
a
n
(Ed
s.)
Pro
c
e
e
d
i
n
g
s
o
f
t
h
e
3
8
t
h
C
o
n
fer
e
n
c
e
o
f
t
h
e
In
ter
n
a
t
io
n
a
l
Gr
o
u
p
fo
r
Psy
c
h
o
l
o
g
y
o
f
M
a
t
h
e
ma
ti
c
s
Ed
u
c
a
t
io
n
a
n
d
t
h
e
3
6
t
h
Co
n
fer
e
n
c
e
o
f
t
h
e
N
o
rth
Ame
ric
a
n
Ch
a
p
ter
o
f
th
e
Psy
c
h
o
lo
g
y
o
f
M
a
th
e
ma
ti
c
s E
d
u
c
a
ti
o
n
, v
ol
.
1
,
p
p
.
1
1
7
–
1
4
3
,
V
a
n
c
o
u
v
e
r,
Ca
n
a
d
a
:
P
M
E,
2
0
1
4
.
[7
]
A
.
Watso
n
a
n
d
M
.
Oh
tan
i,
“
T
h
e
m
e
s
a
n
d
issu
e
s
in
m
a
th
e
m
a
ti
c
s
e
d
u
c
a
ti
o
n
c
o
n
c
e
rn
in
g
tas
k
d
e
sig
n
,
”
In
A
.
W
a
tso
n
&
M
.
Oh
tan
i
(E
d
s.),
T
a
sk
d
e
sig
n
i
n
ma
t
h
e
ma
ti
c
s e
d
u
c
a
ti
o
n
:
An
IC
M
I
stu
d
y
,
Be
rli
n
:
S
p
rin
g
e
r,
2
0
1
5
.
[8
]
NCT
M
,
Prin
c
ip
les
a
n
d
st
a
n
d
a
r
d
s
fo
r sc
h
o
o
l
m
a
th
e
ma
ti
c
s
,
Re
sto
n
,
V
A
:
A
u
th
o
r,
2
0
0
0
.
[9
]
S.
Bre
e
n
a
n
d
A
.
O'
S
h
e
a
,
“
M
a
th
e
m
a
ti
c
a
l
th
in
k
in
g
a
n
d
tas
k
d
e
sig
n
,
”
Irish
M
a
th
e
ma
ti
c
a
l
S
o
c
iety
Bu
ll
e
ti
n
,
v
o
l
.
6
6
,
p
p
.
39
-
4
9
,
No
v
2
0
1
0
.
[1
0
]
D.
G
ra
c
in
,
“
Re
q
u
irem
e
n
ts
in
m
a
th
e
m
a
ti
c
s
te
x
tb
o
o
k
s:
a
f
i
v
e
-
d
ime
n
sio
n
a
l
a
n
a
ly
sis
o
f
te
x
tb
o
o
k
e
x
e
rc
ise
s
a
n
d
e
x
a
m
p
les
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
M
a
th
e
ma
ti
c
a
l
E
d
u
c
a
ti
o
n
i
n
S
c
ien
c
e
a
nd
T
e
c
h
n
o
lo
g
y
,
v
o
l.
49
,
n
o
.
7
,
p
p
.
1
0
0
3
-
1
0
2
4
,
2
0
1
8
.
[1
1
]
M
.
A
.
S
im
o
n
a
n
d
R.
T
z
u
r,
“
Ex
p
li
c
a
ti
n
g
th
e
r
o
le
o
f
m
a
th
e
m
a
ti
c
a
l
tas
k
s
in
c
o
n
c
e
p
tu
a
l
lea
rn
i
n
g
:
A
n
e
lab
o
ra
ti
o
n
o
f
th
e
h
y
p
o
th
e
ti
c
a
l
lea
rn
i
n
g
traje
c
to
ry
,
”
M
a
th
e
ma
ti
c
a
l
t
h
in
k
i
n
g
a
n
d
lea
rn
in
g
,
v
ol
.
6
,
n
o
.
2
,
p
p
.
91
-
1
0
4
,
2
0
0
4
.
[1
2
]
J.
Bo
e
se
n
,
J.
L
it
h
n
e
r
,
a
n
d
T
.
P
a
lm
,
“
T
h
e
re
latio
n
b
e
tw
e
e
n
t
y
p
e
s
o
f
a
ss
e
ss
m
e
n
t
tas
k
s
a
n
d
th
e
m
a
th
e
m
a
ti
c
a
l
re
a
so
n
in
g
stu
d
e
n
ts
u
se
,
”
Ed
u
c
a
ti
o
n
a
l
S
tu
d
ie
s in
M
a
t
h
e
ma
ti
c
s
,
v
o
l.
75
,
n
o
.
1
,
p
p
.
89
-
1
0
5
,
2
0
1
0
.
[1
3
]
H.
L
.
Jo
h
n
so
n
,
A
.
Co
les
,
a
n
d
D.
Clark
e
,
“
M
a
th
e
m
a
ti
c
a
l
tas
k
s
a
n
d
th
e
stu
d
e
n
t:
n
a
v
ig
a
t
in
g
"
ten
sio
n
s
o
f
in
ten
ti
o
n
s"
b
e
tw
e
e
n
d
e
sig
n
e
rs,
tea
c
h
e
rs,
a
n
d
stu
d
e
n
ts
,
”
Z
DM
,
v
o
l.
49
,
no
.
6
,
p
p
.
8
1
3
-
8
2
2
,
2
0
1
7
.
[1
4
]
K.
Jo
n
e
s
a
n
d
B.
P
e
p
in
,
“
Re
se
a
rc
h
o
n
m
a
th
e
m
a
ti
c
s
tea
c
h
e
rs
a
s
p
a
rtn
e
rs
in
tas
k
d
e
sig
n
,
”
J
o
u
rn
a
l
o
f
M
a
th
e
ma
ti
c
s
T
e
a
c
h
e
r E
d
u
c
a
ti
o
n
,
v
o
l.
19
,
n
o
.
2
-
3
,
p
p
.
1
0
5
-
1
2
1
,
2
0
1
6
.
[1
5
]
V
.
Be
rish
a
,
e
t
a
l
,
“
M
ism
a
tch
b
e
tw
e
e
n
c
u
rricu
lu
m
in
ten
ti
o
n
s
a
n
d
tex
tb
o
o
k
d
e
sig
n
:
an
a
ss
e
ss
m
e
n
t
of
m
a
th
e
m
a
ti
c
s
tex
tb
o
o
k
s
f
o
r
lo
w
e
r
se
c
o
n
d
a
ry
sc
h
o
o
l
in
Ko
so
v
o
,
”
GS
T
F
J
o
u
r
n
a
l
on
Ed
u
c
a
ti
o
n
,
v
o
l.
2
,
n
o
.
2
,
pp.
31
–
35,
2
0
1
5
.
[1
6
]
S
.
Re
z
a
t
a
n
d
R.
S
träß
e
r,
“
F
r
o
m
th
e
d
i
d
a
c
ti
c
a
l
tri
a
n
g
le
t
o
th
e
s
o
c
io
-
d
id
a
c
ti
c
a
l
tetra
h
e
d
ro
n
:
a
rti
f
a
c
ts
a
s
f
u
n
d
a
m
e
n
tal
c
o
n
stit
u
e
n
ts
o
f
th
e
d
id
a
c
ti
c
a
l
sit
u
a
ti
o
n
,
”
Z
DM
—
T
h
e
I
n
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
n
M
a
th
e
ma
ti
c
s
E
d
u
c
a
ti
o
n
,
v
o
l
.
44
,
n
o
.
5
,
p
p
.
6
4
1
–
6
5
1
,
2
0
1
2
.
[1
7
]
D.
P
imm
,
P
a
rt
III
c
o
m
m
e
n
tar
y
:
“
W
h
o
k
n
o
w
s
b
e
st?
T
a
l
e
s
o
f
o
rd
in
a
ti
o
n
,
su
b
o
rd
i
n
a
ti
o
n
,
a
n
d
i
n
su
b
o
rd
i
n
a
ti
o
n
,
”
In
M
a
th
e
ma
ti
c
s T
e
a
c
h
e
rs
a
t
W
o
rk
,
Ro
u
tl
e
d
g
e
,
p
p
.
2
1
0
-
2
1
6
,
2
0
1
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8822
I
n
t
.
J
.
E
v
al
.
&
R
es
.
E
d
u
c
.
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2020
:
7
5
1
-
758
758
[1
8
]
Y.
L
i,
“
A
c
o
m
p
a
riso
n
o
f
p
ro
b
lem
s
th
a
t
f
o
ll
o
w
se
lec
ted
c
o
n
ten
t
p
re
se
n
tatio
n
s
i
n
Am
e
rica
n
a
n
d
Ch
in
e
se
m
a
th
e
m
a
ti
c
s
tex
tb
o
o
k
s
,
”
J
o
u
r
n
a
l
fo
r R
e
se
a
rc
h
in
M
a
t
h
e
ma
ti
c
s E
d
u
c
a
ti
o
n
,
v
o
l.
3
1
,
n
o
.
2
,
p
p
.
2
3
4
-
2
4
1
,
2
0
0
0
.
[1
9
]
B.
P
e
p
i
n
a
n
d
L
.
Ha
g
g
a
rt
y
,
“
M
a
k
in
g
c
o
n
n
e
c
ti
o
n
s
a
n
d
se
e
k
in
g
u
n
d
e
rsta
n
d
in
g
:
M
a
th
e
m
a
ti
c
a
l
ta
s
k
s
in
En
g
li
sh
,
F
re
n
c
h
a
n
d
G
e
r
m
a
n
tex
tb
o
o
k
s
,
”
AERA
7
,
p
p
.
1
-
1
5
,
2
0
0
7
[2
0
]
M
.
K.
S
tei
n
,
M
.
S
.
S
m
it
h
.
,
M
.
A
.
He
n
n
in
g
se
n
,
a
n
d
E.
A
.
S
il
v
e
r
,
S
t
a
n
d
a
rd
s
-
b
a
se
d
m
a
th
i
n
stru
c
ti
o
n
:
A
c
a
se
b
o
o
k
f
o
r
p
ro
fes
sio
n
a
l
d
e
v
e
lo
p
me
n
t
,
T
e
a
c
h
e
rs Co
ll
e
g
e
P
re
ss
,
2
0
0
9
.
[2
1
]
T
.
A
d
ig
u
z
e
l
a
n
d
Y.
A
k
p
in
a
r,
“
I
m
p
ro
v
in
g
S
c
h
o
o
l
C
h
il
d
re
n
'
s
M
a
t
h
e
m
a
ti
c
a
l
W
o
rd
P
r
o
b
lem
S
o
lv
in
g
S
k
il
ls
th
ro
u
g
h
Co
m
p
u
ter
-
Ba
se
d
M
u
lt
ip
le
Re
p
re
se
n
tatio
n
s
,
”
Asso
c
ia
t
io
n
f
o
r
E
d
u
c
a
t
io
n
a
l
Co
mm
u
n
ic
a
ti
o
n
s
a
n
d
T
e
c
h
n
o
lo
g
y
,
Ch
ica
g
o
,
IL
,
Oc
to
b
e
r
1
9
-
2
3
,
p
p
.
1
-
1
0
,
2
0
0
4
.
[2
2
]
I.
Ba
y
a
z
it
,
“
Qu
a
li
t
y
o
f
th
e
tas
k
s
in
th
e
n
e
w
T
u
rk
ish
e
le
m
e
n
tar
y
m
a
th
e
m
a
ti
c
s
te
x
tb
o
o
k
s:
T
h
e
c
a
se
o
f
p
ro
p
o
rt
io
n
a
l
re
a
so
n
in
g
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
S
c
ien
c
e
a
n
d
M
a
t
h
e
ma
ti
c
s E
d
u
c
a
ti
o
n
,
v
ol
.
1
1
,
n
o
.
3
,
p
p
.
6
5
1
-
6
8
2
,
2
0
1
2
.
[2
3
]
Y.
Zh
u
a
n
d
L
.
F
a
n
,
“
F
o
c
u
s
o
n
t
h
e
re
p
re
se
n
tatio
n
o
f
p
ro
b
lem
t
y
p
e
s in
in
ten
d
e
d
c
u
rricu
l
u
m
:
A
c
o
m
p
a
ri
so
n
o
f
se
lec
ted
m
a
th
e
m
a
ti
c
s
tex
tb
o
o
k
s
f
ro
m
M
a
in
lan
d
Ch
in
a
a
n
d
th
e
Un
it
e
d
S
tate
s
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
S
c
ien
c
e
a
n
d
M
a
th
e
ma
ti
c
s E
d
u
c
a
t
io
n
,
v
o
l.
4
,
n
o
.
4
,
p
p
.
6
0
9
-
6
2
6
,
2
0
0
6
.
[2
4
]
IDM,
S
ta
n
d
a
rd
s
f
o
r
th
e
ma
t
h
e
ma
ti
c
a
l
c
o
mp
e
ten
c
ies
o
f
A
u
stria
n
st
u
d
e
n
ts
a
t
th
e
e
n
d
o
f
t
h
e
8
t
h
g
ra
d
e
,
A
lp
e
n
-
A
d
ria
Un
iv
e
rsität,
Kla
g
e
n
f
u
rt,
2
0
0
7
.
[2
5
]
M
A
S
H
T
,
Ko
rn
iza
Ku
rr
iku
l
a
re
e
Arsimit
Pa
r
a
u
n
ive
rista
r
të
K
o
so
v
ë
s,
(
e
rish
iku
a
r),
2
0
1
7
.
[
O
n
li
n
e
]
.
A
v
a
il
a
b
le:
h
tt
p
s:/
/m
a
sh
t.
rk
s
-
g
o
v
.
n
e
t/
u
p
lo
a
d
s/
2
0
1
7
/
0
3
/k
o
r
n
iza
-
k
u
rrik
u
lare
-
f
in
a
le.p
d
f
[2
6
]
M
A
S
H
T
,
Ku
rr
iku
la
Bër
th
a
më
p
ë
r
Arsimin
e
M
e
së
m
të
L
a
rtë
(
Gjimn
a
ze
t
-
k
la
s
a
X
,
XI,
XII
),
2
0
1
7
.
[
On
li
n
e
]
.
Av
a
il
a
b
le:
h
tt
p
s://
m
a
sh
t.
rk
s
-
g
o
v
.
n
e
t/
u
p
l
o
a
d
s/2
0
1
7
/
0
3
/k
o
r
n
iza
-
b
e
rth
a
m
e
-
3
-
f
in
a
l.
p
d
f
[2
7
]
R.
S
a
ll
a
,
“
Ch
a
ra
c
teristics
o
f
th
e
tas
k
s
p
re
se
n
ted
in
m
a
th
tex
tb
o
o
k
s
f
o
r
g
ra
d
e
1
0
,
”
Un
p
u
b
li
s
h
e
d
m
a
ste
r
th
e
sis
,
Un
iv
e
rsit
y
o
f
P
rish
ti
n
a
,
2
0
1
8
.
[2
8
]
N.
Ku
rtes
h
i,
“
T
h
e
re
p
re
se
n
tati
o
n
o
f
re
a
l
c
o
n
tex
ts
in
m
a
th
e
m
a
ti
c
s
tex
tb
o
o
k
s
f
o
r
lo
w
e
r
s
e
c
o
n
d
a
ry
sc
h
o
o
l
,
”
Un
p
u
b
li
sh
e
d
m
a
ste
r
th
e
sis.
Un
iv
e
rsity
o
f
P
rish
ti
n
a
,
2
0
1
7
.
[2
9
]
V
.
Be
rish
a
,
H.
Ja
sh
a
ri,
Xh
.
T
h
a
q
i
,
a
n
d
S
h
.
Kl
in
a
k
u
,
“
A
ss
e
ss
m
e
n
t
o
f
M
a
th
e
m
a
ti
c
s
Tex
tb
o
o
k
s
P
o
te
n
ti
a
l
in
T
e
r
m
s
o
f
S
tu
d
e
n
t’
s M
o
ti
v
a
ti
o
n
a
n
d
Co
m
p
re
h
e
n
sio
n
,
”
J
o
u
rn
a
l
o
f
Ed
u
c
a
ti
o
n
a
n
d
Pr
a
c
ti
c
e
,
v
o
l.
4
,
n
o
.
28
,
p
p
.
3
3
-
1
7
,
2
0
1
3
.
[3
0
]
A
.
M
u
ra
ti
,
“
T
e
st as
a
n
a
ss
e
s
s
m
e
n
t
to
o
l
in
m
a
th
e
m
a
ti
c
s
,
”
Un
p
u
b
li
sh
e
d
m
a
ste
r
th
e
sis,
Un
iv
e
rsit
y
o
f
P
rish
ti
n
a
,
2
0
1
8
.
Evaluation Warning : The document was created with Spire.PDF for Python.