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.
10
,
No
.
2
,
J
u
n
e
2
0
2
1
,
p
p
.
660
~
6
6
7
I
SS
N:
2252
-
8
8
2
2
,
DOI
: 1
0
.
1
1
5
9
1
/
ije
r
e
.
v
10
i
2
.
2
1
1
8
4
660
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
ere.
ia
esco
r
e.
co
m
Tea
cher
-
stu
dent
i
nteraction i
n ma
t
hema
tics learning
I
rm
a
Ay
uwa
nti
1
,
M
a
rsig
it
2
,
Dwi
Sis
wo
y
o
3
1,
3
De
p
a
rtme
n
t
o
f
S
c
ien
c
e
Ed
u
c
a
ti
o
n
,
U
n
iv
e
rsitas
Ne
g
e
ri
Y
o
g
y
a
k
a
rt
a
,
In
d
o
n
e
sia
2
De
p
a
rtme
n
t
o
f
M
a
t
h
e
m
a
ti
c
s E
d
u
c
a
ti
o
n
,
U
n
iv
e
rsitas
Ne
g
e
ri
Yo
g
y
a
k
a
rta,
In
d
o
n
e
sia
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
No
v
6
,
2
0
20
R
ev
is
ed
Mar
29
,
2
0
21
Acc
ep
ted
Ap
r
19
,
2
0
21
Tea
c
h
e
r
-
stu
d
e
n
ts
i
n
tera
c
ti
o
n
is
o
n
e
o
f
th
e
m
o
st
im
p
o
rta
n
t
in
tera
c
ti
o
n
s
in
lea
rn
in
g
.
Tea
c
h
e
r
-
stu
d
e
n
ts
in
t
e
ra
c
ti
o
n
a
ffe
c
ts
stu
d
e
n
t
u
n
d
e
rsta
n
d
in
g
.
Ho
we
v
e
r,
in
p
ra
c
ti
c
e
,
th
e
re
a
re
stil
l
m
a
n
y
les
so
n
s
t
h
a
t
h
a
v
e
n
o
t
a
p
p
li
e
d
tea
c
h
e
r
-
stu
d
e
n
ts
in
tera
c
ti
o
n
p
r
o
p
e
rly
.
Th
is
st
u
d
y
a
im
ed
to
re
v
e
a
l
tea
c
h
e
r
-
stu
d
e
n
t
in
tera
c
ti
o
n
in
th
e
m
a
th
e
m
a
ti
c
s
lea
rn
in
g
p
r
o
c
e
ss
th
a
t
a
ffe
c
ts
stu
d
e
n
ts’
m
a
th
e
m
a
ti
c
a
l
u
n
d
e
rsta
n
d
in
g
.
Th
i
s
stu
d
y
u
se
d
a
q
u
a
li
tati
v
e
m
e
th
o
d
with
a
p
h
e
n
o
m
e
n
o
l
o
g
ica
l
a
p
p
r
o
a
c
h
.
T
h
e
re
se
a
rc
h
su
b
jec
ts
we
re
e
ig
h
t
h
-
g
r
a
d
e
ju
n
io
r
h
ig
h
sc
h
o
o
l
stu
d
e
n
ts.
Re
se
a
rc
h
d
a
ta
we
re
o
b
tain
e
d
t
h
ro
u
g
h
o
b
se
rv
a
ti
o
n
,
in
terv
iew
s,
a
n
d
d
o
c
u
m
e
n
tatio
n
.
Ob
se
rv
a
ti
o
n
s
we
re
c
o
n
d
u
c
ted
i
n
th
e
e
ig
h
t
h
g
ra
d
e
a
n
d
in
ter
v
iew
s
we
re
c
o
n
d
u
c
ted
with
six
st
u
d
e
n
ts
fro
m
t
h
e
c
las
s.
Th
e
stu
d
e
n
ts
we
re
in
terv
iew
e
d
to
e
x
p
re
ss
th
e
ir
o
p
i
n
io
n
s
c
o
n
c
e
rn
i
n
g
lea
rn
in
g
p
ro
c
e
ss
in
tera
c
ti
o
n
s.
Th
e
re
su
l
ts
o
f
th
is
stu
d
y
sh
o
w
ed
t
h
a
t
tea
c
h
e
r
-
stu
d
e
n
t
in
tera
c
ti
o
n
h
a
s
a
ffe
c
ted
stu
d
e
n
ts’
m
a
th
e
m
a
ti
c
a
l
u
n
d
e
rsta
n
d
i
n
g
c
o
n
sists
o
f
:
1
)
Th
e
tea
c
h
e
r
tran
sfe
rs
th
e
m
a
teria
l
-
th
e
stu
d
e
n
ts
a
tt
e
n
d
to
th
e
m
a
teria
l
;
2
)
Qu
e
stio
n
-
a
n
sw
e
r
a
m
id
tea
c
h
e
r
-
stu
d
e
n
ts
;
3
)
T
h
e
tea
c
h
e
r
m
a
k
e
s
in
tere
stin
g
lea
rn
in
g
stra
teg
ies
-
stu
d
e
n
ts
a
re
a
c
ti
v
e
ly
i
n
v
o
l
v
e
d
in
lea
rn
i
n
g
;
4
)
Tea
c
h
e
rs
g
iv
e
a
wa
rd
s
-
stu
d
e
n
ts r
e
c
e
iv
e
a
wa
rd
s.
K
ey
w
o
r
d
s
:
Activ
e
lear
n
in
g
L
ea
r
n
in
g
i
n
ter
ac
tio
n
L
ea
r
n
in
g
s
tr
ateg
ies
Ma
th
em
atic
al
u
n
d
er
s
tan
d
i
n
g
T
ea
ch
er
-
s
tu
d
en
t i
n
ter
ac
tio
n
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
:
I
r
m
a
Ay
u
wan
ti
Dep
ar
tm
en
t o
f
Scien
ce
E
d
u
ca
t
io
n
Un
iv
er
s
itas
Neg
er
i Y
o
g
y
ak
ar
t
a
C
atu
r
tu
n
g
g
al,
Dep
o
k
,
Slem
an
,
D.
I
.
Yo
g
y
ak
ar
ta,
I
n
d
o
n
esia
E
m
ail:
ir
m
a.
ay
u
wan
ti2
0
1
6
@
s
tu
d
en
t.u
n
y
.
ac
.
i
d
1.
I
NT
RO
D
UCT
I
O
N
E
d
u
ca
tio
n
is
an
ef
f
o
r
t
co
n
d
u
ct
ed
b
y
h
u
m
a
n
s
to
im
p
r
o
v
e
th
e
m
s
elv
es.
I
m
p
r
o
v
em
en
ts
ar
e
c
o
n
d
u
cted
i
n
th
e
em
o
tio
n
al
in
tellig
en
ce
f
ield
,
in
tellectu
al
in
tellig
en
ce
,
s
elf
-
co
n
tr
o
l,
an
d
r
elig
io
u
s
s
p
ir
itu
ality
.
Qu
ality
ed
u
ca
tio
n
p
lay
s
an
im
p
o
r
tan
t
r
o
le
in
th
e
n
atio
n
’
s
p
r
o
g
r
ess
.
An
in
d
icato
r
o
f
a
d
ev
elo
p
ed
c
o
u
n
tr
y
is
s
h
o
wn
b
y
th
e
p
r
o
g
r
ess
o
f
th
e
e
d
u
ca
tio
n
s
ec
to
r
.
E
d
u
ca
tio
n
ch
a
n
g
es
in
to
im
p
o
r
tan
t
alo
n
g
with
t
h
e
d
ev
el
o
p
m
en
t
o
f
k
n
o
wled
g
e
a
n
d
tech
n
o
lo
g
y
,
t
h
er
ef
o
r
e
e
d
u
ca
tio
n
p
lay
s
a
b
ig
r
o
le
in
co
u
n
tr
y
p
r
o
g
r
ess
.
C
o
n
s
eq
u
en
tly
,
th
e
p
r
o
g
r
ess
o
f
ed
u
ca
tio
n
q
u
ality
i
s
a
to
p
p
r
io
r
ity
f
o
r
ev
er
y
co
u
n
t
r
y
[
1
]
.
Ma
th
em
atics
is
o
n
e
o
f
t
h
e
im
p
o
r
tan
t
s
u
b
jects
in
h
u
m
a
n
lif
e
[
2
]
-
[
4
]
.
Ma
th
em
atics
is
co
n
s
id
er
ed
as
o
n
e
o
f
th
e
b
asic
s
u
b
jects
g
iv
e
n
to
s
tu
d
en
ts
f
o
r
all
le
v
els
o
f
ed
u
ca
tio
n
.
Star
tin
g
f
r
o
m
elem
en
tar
y
s
ch
o
o
l
a
n
d
ev
en
k
in
d
e
r
g
ar
ten
t
o
co
lleg
e.
T
h
e
m
ath
em
atics
lear
n
in
g
p
r
o
ce
s
s
s
tar
ts
f
r
o
m
r
ec
o
g
n
izin
g
n
u
m
b
er
s
to
co
m
p
le
x
m
ath
em
atics.
Ma
th
em
atics
is
a
co
m
p
u
ls
o
r
y
s
u
b
ject
f
o
r
s
tu
d
en
ts
at
ev
er
y
p
r
im
ar
y
a
n
d
s
ec
o
n
d
ar
y
ed
u
ca
tio
n
lev
el.
Ma
th
em
atics
is
also
n
ee
d
ed
in
a
wo
r
ld
t
h
at
is
ch
a
n
g
in
g
with
g
lo
b
aliza
tio
n
.
Ma
th
em
atics
p
lay
s
an
im
p
o
r
tan
t
r
o
le
in
tech
n
o
lo
g
ic
al
ad
v
an
ce
s
at
th
is
t
im
e.
T
h
e
ex
am
p
les
o
f
m
ath
em
atics
u
s
ed
in
tech
n
o
lo
g
ical
ad
v
an
ce
s
co
n
s
is
t
o
f
th
e
tech
n
o
lo
g
y
d
e
v
elo
p
m
e
n
t
us
e
in
v
ar
io
u
s
f
ield
s
s
u
ch
as
ar
tific
ial
in
te
llig
en
ce
,
co
m
p
u
ter
s
cien
ce
,
m
ed
icin
e,
co
n
t
r
o
l
en
g
in
ee
r
in
g
,
d
ec
is
io
n
th
eo
r
y
,
ex
p
er
t
s
y
s
tem
s
,
ass
o
ciatio
n
s
,
m
an
ag
em
en
t
s
cien
ce
,
o
p
er
atio
n
s
r
esear
ch
,
p
atter
n
r
e
co
g
n
itio
n
,
an
d
r
o
b
o
tics
[
5
]
-
[
7
]
.
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
Tea
ch
er
-
s
tu
d
en
t in
tera
ctio
n
in
ma
th
ema
tics
lea
r
n
in
g
(
I
r
ma
A
yu
w
a
n
ti
)
661
T
h
e
r
o
le
o
f
m
at
h
em
atics
in
li
f
e
is
ex
tr
em
el
y
im
p
o
r
tan
t,
esp
ec
ially
in
tech
n
o
lo
g
ical
ad
v
an
ce
s
in
th
e
g
lo
b
aliza
tio
n
er
a.
Ho
wev
er
,
to
ad
ju
s
t
f
o
r
th
is
p
r
o
g
r
ess
,
t
h
e
u
n
d
er
s
tan
d
in
g
,
m
aster
y
,
a
n
d
s
k
ills
o
f
m
ath
e
m
atics
h
av
e
n
o
t
b
ee
n
f
o
llo
wed
,
esp
ec
ially
i
n
I
n
d
o
n
esia.
T
h
er
e
a
r
e
s
till
m
an
y
o
b
s
tacle
s
in
th
e
ef
f
o
r
t
to
im
p
r
o
v
e
s
tu
d
en
ts
’
u
n
d
er
s
tan
d
in
g
,
m
as
ter
y
,
an
d
m
at
h
s
k
ills
.
T
h
ese
co
n
s
tr
ain
ts
ca
u
s
e
m
at
h
em
at
ics
q
u
ality
to
b
e
r
elativ
ely
lo
w.
T
h
is
is
in
d
icate
d
b
y
th
e
r
esu
lts
o
f
lear
n
in
g
m
ath
em
atics
an
d
th
e
m
at
h
e
m
ati
cs
r
an
k
in
g
o
b
tain
e
d
th
r
o
u
g
h
th
e
in
te
r
n
atio
n
al
m
at
h
em
atics a
r
en
a
wh
ich
is
s
till
q
u
ite
lo
w.
T
h
e
m
ath
em
atic
q
u
ality
o
f
I
n
d
o
n
esian
s
tu
d
en
ts
,
wh
en
v
iewe
d
f
r
o
m
th
e
Pr
o
g
r
am
r
esu
lts
f
o
r
I
n
ter
n
atio
n
al
Stu
d
en
ts
Ass
ess
m
en
t (
PISA)
in
2
0
1
5
,
s
h
o
ws th
at
I
n
d
o
n
esia is
in
6
2
p
o
s
itio
n
s
o
u
t o
f
7
0
co
u
n
tr
ies
[
8
]
.
I
n
ad
d
itio
n
,
s
ee
n
f
r
o
m
t
h
e
r
esu
lts
o
f
th
e
T
r
en
d
s
I
n
ter
n
atio
n
al
Ma
th
em
atics
an
d
Scien
ce
Stu
d
y
(
T
I
MSS)
in
2
0
1
5
,
I
n
d
o
n
esia r
an
k
e
d
4
4
o
u
t
o
f
4
9
c
o
u
n
tr
ies [
9
]
.
T
h
is
r
esu
l
t is st
i
ll v
er
y
co
n
ce
r
n
i
n
g
,
ev
e
n
I
n
d
o
n
esia is lo
we
r
th
an
in
o
t
h
er
So
u
th
ea
s
t A
s
ian
co
u
n
tr
ies.
T
h
e
r
esu
lts
o
f
th
e
PISA
an
d
T
I
MSS
n
ee
d
atten
tio
n
.
Su
f
f
e
r
in
g
in
m
in
d
th
at
I
n
d
o
n
esia
’
s
o
b
jectiv
e
in
p
ar
ticip
atin
g
in
th
e
ev
en
t
is
t
o
o
b
tain
in
f
o
r
m
atio
n
ab
o
u
t
th
e
ab
ilit
ies
o
f
I
n
d
o
n
esian
s
tu
d
en
ts
in
th
e
f
ield
s
o
f
m
at
h
em
atics
an
d
s
cien
ce
[
8
]
,
[
1
0
]
.
C
o
n
s
id
er
in
g
k
n
o
win
g
th
ese
r
esu
lts
,
it
i
s
h
o
p
ed
th
at
it
ca
n
m
o
tiv
ate
s
tu
d
en
ts
an
d
ed
u
ca
t
o
r
s
to
im
p
r
o
v
e
t
h
eir
m
ath
em
atics
s
k
ills
in
th
e
f
o
llo
win
g
y
ea
r
s
.
T
h
e
PISA
an
d
T
I
MSS
r
esu
lts
s
h
o
w
th
at
m
ath
em
atics
in
I
n
d
o
n
esia
is
s
till
la
g
g
in
g
b
eh
in
d
o
th
er
co
u
n
tr
ies.
I
n
v
esti
g
atin
g
d
ee
p
e
r
in
to
th
e
co
g
n
itiv
e
d
o
m
ain
in
T
I
M
SS
,
n
am
ely
k
n
o
win
g
,
ap
p
l
y
in
g
an
d
r
ea
s
o
n
in
g
,
th
e
p
er
ce
n
ta
g
es
ar
e
3
5
%,
4
0
%,
an
d
2
5
% r
esp
ec
tiv
el
y
[
1
0
]
.
T
o
im
p
r
o
v
e
th
e
a
b
ilit
y
to
u
n
d
er
s
tan
d
m
at
h
em
atics
ca
n
b
e
d
o
n
e
th
r
o
u
g
h
im
p
r
o
v
i
n
g
th
e
lear
n
in
g
p
r
o
ce
s
s
,
o
n
e
o
f
wh
ic
h
is
th
e
t
ea
ch
er
in
n
o
v
atin
g
in
lear
n
in
g
[
1
1
]
,
t
h
e
teac
h
e
r
p
r
o
v
id
es
ef
f
ec
tiv
e
s
u
p
p
o
r
t
a
n
d
th
e
lear
n
in
g
p
r
o
ce
s
s
in
th
e
class
r
o
o
m
th
at
af
f
ec
ts
s
tu
d
en
ts
’
attitu
d
es
to
war
d
s
m
ath
em
atics
[
1
2
]
.
L
ea
r
n
in
g
in
n
o
v
atio
n
an
d
s
u
p
p
o
r
t
ca
n
b
e
p
r
o
v
id
e
d
th
r
o
u
g
h
p
o
s
itiv
e
in
ter
ac
tio
n
s
in
th
e
lear
n
in
g
p
r
o
ce
s
s
.
T
h
e
r
esu
lts
o
f
th
e
s
tu
d
y
s
aid
th
at
s
tu
d
en
ts
’
s
o
cial
in
ter
ac
tio
n
s
in
f
lu
en
ce
d
s
tu
d
en
t
ac
h
iev
em
en
t
in
m
ath
em
atics
[
1
3
]
,
[
1
4
]
.
W
ith
in
ter
esti
n
g
p
o
s
itiv
e
in
ter
ac
tio
n
s
,
th
e
s
tu
d
en
ts
wh
o
wer
e
in
itially
af
r
aid
o
f
m
ath
em
atics g
r
ad
u
ally
b
ec
am
e
f
o
n
d
o
f
m
ath
em
atics.
T
h
is
n
ee
d
s
to
b
e
d
o
n
e
co
n
tin
u
o
u
s
ly
in
th
e
lear
n
in
g
p
r
o
ce
s
s
.
T
o
im
p
r
o
v
e
s
tu
d
e
n
ts
’
m
ath
em
atica
l u
n
d
e
r
s
tan
d
in
g
s
k
ills
in
s
o
lv
in
g
m
ath
p
r
o
b
lem
s
.
T
ea
ch
er
-
s
tu
d
en
t
s
in
ter
ac
tio
n
n
ee
d
s
to
b
e
cr
ea
ted
in
lear
n
in
g
,
esp
ec
ially
in
m
ath
em
atics.
Stu
d
en
ts
n
ee
d
atten
tio
n
,
s
tim
u
latio
n
,
a
n
d
g
u
id
a
n
ce
in
lear
n
in
g
m
ath
em
atics.
Ho
wev
er
,
th
er
e
ar
e
s
till
m
an
y
teac
h
er
s
wh
o
h
av
e
n
o
t
im
p
lem
en
ted
p
o
s
itiv
e
teac
h
er
-
s
tu
d
en
t
in
ter
ac
tio
n
s
.
T
h
e
r
esu
lts
o
f
i
n
ter
v
iews
with
s
ev
er
a
l
m
ath
em
atics
teac
h
er
s
s
aid
th
a
t
th
e
teac
h
er
h
ad
n
o
t
in
ter
ac
te
d
well
with
s
tu
d
en
ts
.
T
h
er
e
ar
e
s
till
teac
h
er
s
wh
o
o
n
ly
d
eliv
er
m
ater
ial,
g
iv
e
as
s
ig
n
m
en
ts
th
en
leav
e
s
tu
d
en
ts
an
d
r
etu
r
n
to
th
e
o
f
f
ice
,
th
en
d
is
cu
s
s
q
u
esti
o
n
s
,
an
d
g
i
v
e
h
o
m
ewo
r
k
.
Acc
o
r
d
i
n
g
to
s
tu
d
en
ts
,
m
at
h
em
atics
teac
h
er
s
ten
d
to
b
e
g
r
u
m
p
y
a
n
d
an
g
r
y
wh
en
th
er
e
ar
e
s
tu
d
en
ts
wh
o
h
av
e
n
o
t
b
e
en
ab
le
to
wo
r
k
o
n
th
e
q
u
esti
o
n
s
.
T
h
is
cr
ea
tes
s
tu
d
en
ts
af
r
aid
to
ask
q
u
esti
o
n
s
an
d
in
ter
ac
t
with
th
e
teac
h
er
.
Ap
ar
t
f
r
o
m
th
is
,
th
er
e
ar
e
s
till
m
an
y
teac
h
e
r
s
w
h
o
d
o
n
o
t
k
n
o
w
h
o
w
a
n
d
wh
at
in
ter
ac
tio
n
s
teac
h
er
s
-
s
tu
d
en
ts
n
ee
d
to
b
e
ca
r
r
ied
o
u
t
in
lear
n
in
g
to
b
u
ild
a
c
o
n
d
u
civ
e
lear
n
i
n
g
atm
o
s
p
h
e
r
e
an
d
a
g
o
o
d
u
n
d
er
s
tan
d
in
g
o
f
m
ath
em
atics.
Ma
n
y
s
tu
d
ies
s
u
g
g
est
th
at
s
tu
d
en
t
in
ter
ac
tio
n
is
th
e
b
asis
f
o
r
a
d
ee
p
u
n
d
er
s
tan
d
i
n
g
o
f
s
tu
d
en
t
ac
h
iev
em
en
t.
Ho
wev
er
,
m
an
y
r
e
s
ea
r
ch
r
esu
lts
also
s
h
o
w
th
at
th
e
ap
p
licatio
n
o
f
s
tu
d
en
t
s
o
cial
in
ter
ac
tio
n
is
n
o
t
g
o
o
d
,
t
h
e
r
esu
lts
o
f
d
ata
a
n
aly
s
is
s
h
o
w
th
at
th
e
in
te
r
ac
tio
n
is
s
till
at
a
lo
w
lev
el
[
7
]
.
I
n
p
r
ac
tice,
s
tu
d
en
t i
n
ter
ac
tio
n
in
th
e
class
r
o
o
m
p
r
o
v
ed
d
i
f
f
icu
lt
[
1
5
]
.
T
h
e
teac
h
er
s
-
s
tu
d
en
ts
in
ter
ac
tio
n
is
at
th
e
ce
n
ter
o
f
teac
h
in
g
in
th
e
class
r
o
o
m
an
d
is
a
m
ajo
r
f
ac
to
r
i
n
teac
h
in
g
q
u
ality
an
d
im
p
r
o
v
in
g
s
tu
d
en
t
ac
h
iev
em
e
n
t
[
1
1
]
.
T
h
e
n
atu
r
e
an
d
q
u
ality
o
f
teac
h
er
-
s
tu
d
e
n
t
s
in
ter
ac
tio
n
is
th
e
b
asis
f
o
r
u
n
d
er
s
tan
d
in
g
s
tu
d
en
t
en
g
a
g
em
e
n
t
[
1
6
]
.
Go
o
d
teac
h
er
-
s
tu
d
en
t
s
in
ter
ac
tio
n
f
o
s
ter
s
a
co
n
d
u
civ
e
lear
n
i
n
g
atm
o
s
p
h
er
e.
A
co
n
d
u
civ
e
class
r
o
o
m
e
n
v
ir
o
n
m
en
t
em
p
h
asizes
co
o
p
e
r
atio
n
an
d
o
p
e
n
n
ess
be
twee
n
teac
h
er
an
d
s
tu
d
en
ts
[
1
7
]
,
[
1
8
]
.
T
h
er
ef
o
r
e,
in
lear
n
in
g
,
s
tu
d
en
ts
m
u
s
t
b
e
allo
wed
to
in
ter
ac
t
with
teac
h
er
s
,
class
m
ates,
an
d
th
eir
s
u
r
r
o
u
n
d
in
g
s
.
I
n
ter
ac
tio
n
with
th
e
en
v
ir
o
n
m
e
n
t
d
u
r
in
g
th
e
lear
n
in
g
p
r
o
ce
s
s
will st
im
u
late
all
s
tu
d
en
ts
’
s
en
s
es a
n
d
en
co
u
r
a
g
e
s
tu
d
en
ts
to
lear
n
cr
ea
tiv
ely
a
n
d
in
n
o
v
ativ
ely
[
1
6
]
.
T
h
e
lear
n
in
g
p
r
o
ce
s
s
in
clas
s
ca
n
n
o
t
b
e
av
o
id
e
d
b
y
th
e
in
ter
ac
tio
n
p
r
o
ce
s
s
in
it.
I
n
ter
ac
tio
n
is
p
ar
t
o
f
th
e
ef
f
o
r
t
a
p
er
s
o
n
m
ak
es
to
u
n
d
er
s
tan
d
s
o
m
eth
in
g
.
C
o
n
s
id
er
in
g
th
e
im
p
o
r
tan
ce
o
f
teac
h
er
-
s
tu
d
e
n
t
in
ter
ac
tio
n
s
in
m
ath
em
atics
le
ar
n
in
g
,
it
is
n
ec
ess
ar
y
to
r
ev
ea
l
th
e
in
ter
ac
tio
n
s
th
at
n
ee
d
t
o
b
e
b
u
ilt
b
etwe
en
teac
h
er
-
s
tu
d
en
ts
.
T
h
e
f
o
r
m
s
o
f
teac
h
er
-
s
tu
d
en
ts
p
o
s
itiv
e
in
t
er
ac
tio
n
n
ee
d
to
b
e
k
n
o
w
n
a
n
d
d
e
v
elo
p
e
d
b
y
t
h
e
teac
h
er
to
r
ea
lize
b
etter
lear
n
i
n
g
.
T
h
u
s
,
th
is
s
tu
d
y
aim
s
to
r
ev
ea
l
th
e
f
o
r
m
o
f
teac
h
er
-
s
tu
d
en
t
in
ter
ac
tio
n
th
a
t
n
ee
d
s
to
b
e
ap
p
lied
to
b
u
ild
a
co
n
d
u
civ
e
lear
n
in
g
at
m
o
s
p
h
er
e
an
d
in
cr
ea
s
e
s
tu
d
en
ts
’
m
ath
em
atica
l
k
n
o
wled
g
e.
T
h
is
s
tu
d
y
o
b
s
er
v
es
th
e
lear
n
in
g
p
r
o
ce
s
s
in
a
s
ch
o
o
l
to
s
ee
th
e
in
ter
ac
tio
n
s
th
at
o
cc
u
r
b
etwe
en
teac
h
er
-
s
tu
d
en
ts
.
T
h
e
r
esu
lts
o
f
th
e
o
b
s
er
v
atio
n
s
ar
e
co
n
s
tr
u
cted
in
to
f
o
r
m
s
o
f
in
ter
ac
tio
n
th
at
ca
n
s
er
v
e
as
a
g
u
id
e
f
o
r
o
th
er
teac
h
er
s
in
i
m
p
lem
en
tin
g
lear
n
in
g
.
T
h
e
f
o
r
m
s
o
f
in
ter
ac
tio
n
s
f
o
u
n
d
ca
n
b
e
in
clu
d
e
d
in
th
e
less
o
n
p
lan
m
a
d
e
b
y
th
e
teac
h
er
as
a
g
u
id
e
f
o
r
im
p
lem
e
n
tin
g
lear
n
in
g
i
n
class
.
C
o
n
s
eq
u
en
tly
,
th
e
r
esear
ch
q
u
esti
o
n
in
t
h
is
s
tu
d
y
is
h
o
w
th
e
f
o
r
m
s
o
f
teac
h
er
-
s
tu
d
e
n
ts
in
ter
ac
tio
n
in
m
at
h
em
atics
lear
n
in
g
n
ee
d
t
o
b
e
d
ev
elo
p
e
d
to
b
u
ild
a
g
o
o
d
lear
n
in
g
en
v
ir
o
n
m
e
n
t
th
at
ca
n
h
elp
s
tu
d
en
ts
b
u
ild
a
n
d
im
p
r
o
v
e
m
ath
em
atica
l
u
n
d
er
s
tan
d
i
n
g
.
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
202
1
:
6
6
0
-
6
6
7
662
2.
RE
S
E
ARCH
M
E
T
H
O
D
T
h
is
s
tu
d
y
aim
ed
to
r
ev
ea
l
teac
h
er
-
s
tu
d
en
t
in
ter
ac
tio
n
s
th
at
co
n
s
tr
u
ct
s
tu
d
en
ts
’
m
ath
em
atica
l
u
n
d
er
s
tan
d
i
n
g
.
T
h
is
r
esear
ch
was
co
n
d
u
cted
b
y
o
b
s
er
v
in
g
d
ir
ec
tly
th
e
p
r
o
ce
s
s
o
f
lear
n
in
g
m
ath
em
atics
in
th
e
class
r
o
o
m
to
s
ee
teac
h
er
-
s
tu
d
en
t
in
ter
ac
tio
n
s
.
R
esear
ch
er
s
ap
p
r
ec
iate
an
d
o
b
s
er
v
e
,
s
elec
t,
an
d
in
ter
p
r
et
teac
h
er
-
s
tu
d
en
t
ex
p
er
ien
ce
s
i
n
m
ath
em
atics
lear
n
in
g
in
th
e
class
r
o
o
m
.
Ob
s
er
v
atio
n
ai
m
s
to
g
ain
a
d
ee
p
u
n
d
er
s
tan
d
i
n
g
o
f
teac
h
e
r
-
s
tu
d
en
t
in
ter
ac
tio
n
s
in
m
ath
em
ati
cs
lear
n
in
g
.
T
h
is
s
tu
d
y
u
s
e
d
q
u
alitativ
e
m
eth
o
d
with
a
p
h
en
o
m
en
o
l
o
g
ical
ap
p
r
o
ac
h
.
Ph
en
o
m
en
o
lo
g
y
is
th
e
s
cien
ce
o
f
d
escr
ib
in
g
wh
at
a
p
er
s
o
n
r
ec
eiv
es,
f
ee
ls
,
an
d
k
n
o
ws
in
h
is
d
ir
ec
t
awa
r
en
ess
an
d
ex
p
er
ien
ce
.
I
n
ad
d
itio
n
to
wh
at
ar
is
es
f
r
o
m
co
n
s
cio
u
s
n
ess
is
ca
lled
a
p
h
en
o
m
en
o
n
.
Ph
en
o
m
en
o
lo
g
y
r
ev
ea
ls
wh
at
b
ec
o
m
es
r
ea
lity
an
d
a
n
e
x
p
er
ien
ce
ex
p
e
r
ien
ce
d
b
y
in
d
iv
id
u
als,
r
ev
ea
ls
,
an
d
u
n
d
e
r
s
tan
d
s
.
R
esear
ch
er
s
r
esear
ch
b
y
g
o
in
g
d
ir
ec
tly
to
th
e
class
wh
er
e
m
ath
em
atics
lear
n
in
g
o
cc
u
r
s
,
d
escr
ib
in
g
a
n
d
co
n
s
tr
u
ctin
g
ex
is
tin
g
r
ea
liti
es.
Ph
en
o
m
en
o
lo
g
y
is
u
s
ed
in
th
is
s
tu
d
y
s
o
th
at
r
esear
ch
er
s
ca
n
r
ev
ea
l
ev
er
y
m
ea
n
in
g
o
f
s
tu
d
en
t
ex
p
e
r
ien
ce
th
at
is
ca
r
r
ied
o
u
t
with
th
e
teac
h
er
in
m
ath
em
atics lea
r
n
in
g
.
2
.
1
.
P
a
rt
icipa
nt
T
h
e
p
ar
ticip
an
t
is
s
elec
t
ed
u
s
in
g
p
u
r
p
o
s
iv
e
s
am
p
lin
g
.
Par
ticip
an
t
in
th
is
s
tu
d
y
is
VI
I
I
B
g
r
ad
e
s
tu
d
en
ts
with
cr
iter
ia
as
ac
ti
v
e
class
es
an
d
tau
g
h
t
b
y
tea
ch
er
s
wh
o
h
a
d
lo
n
g
ex
p
e
r
ien
c
e
in
teac
h
in
g
.
T
h
e
teac
h
er
s
h
av
e
teac
h
i
n
g
ex
p
er
i
en
ce
f
o
r
m
o
r
e
th
an
1
5
y
ea
r
s
.
T
he
in
ter
v
iew
was
co
n
d
u
cted
b
y
s
ix
s
tu
d
en
ts
f
r
o
m
th
e
class
.
T
h
ese
s
tu
d
en
ts
we
r
e
ch
o
s
en
b
ased
o
n
th
eir
ab
ilit
y
to
ex
p
r
ess
o
p
in
io
n
s
ab
o
u
t
teac
h
er
-
s
tu
d
en
t
in
ter
ac
tio
n
s
in
th
e
m
ath
e
m
a
tics
lear
n
in
g
p
r
o
ce
s
s
.
2
.
2
.
Da
t
a
c
o
llect
io
n
Data
is
co
llec
ted
b
y
co
n
d
u
cted
o
b
s
er
v
atio
n
s
an
d
in
t
er
v
iews
with
p
ar
ticip
an
ts
a
n
d
s
tu
d
y
d
o
cu
m
e
n
tatio
n
.
T
h
e
d
ata
o
b
tain
ed
in
th
is
s
tu
d
y
wer
e
in
th
e
f
i
eld
n
o
tes
f
o
r
m
,
s
em
i
-
s
tr
u
ctu
r
e
d
in
ter
v
iews,
v
id
eo
r
ec
o
r
d
er
s
o
f
teac
h
e
r
-
s
tu
d
en
t
in
ter
ac
tio
n
s
in
th
e
lear
n
in
g
p
r
o
c
ess
an
d
s
tu
d
en
ts
’
m
ath
em
atics
lear
n
ed
o
u
tco
m
es.
T
h
e
m
ain
in
s
tr
u
m
en
t
in
t
h
is
r
esear
ch
is
th
e
r
esear
ch
er
h
er
s
elf
,
th
e
r
esear
ch
er
as
th
e
m
ain
in
s
tr
u
m
en
t
in
ex
tr
ac
tin
g
in
f
o
r
m
atio
n
f
r
o
m
o
b
s
er
v
atio
n
s
an
d
in
ter
v
iews.
Sep
ar
ately
f
r
o
m
th
e
r
esear
ch
er
s
,
th
e
in
s
tr
u
m
e
n
ts
in
th
is
s
tu
d
y
wer
e
also
in
th
e
f
o
r
m
o
f
in
ter
v
iew
s
h
ee
ts
an
d
o
b
s
er
v
ati
o
n
s
h
ee
ts
.
Data
co
llectio
n
u
s
ed
o
b
s
er
v
atio
n
s
h
ee
ts
an
d
in
ter
v
iew
g
u
i
d
es a
n
d
th
e
in
ter
v
iew
is
u
s
ed
as a
s
e
m
i
-
s
tr
u
ctu
r
ed
in
ter
v
iew
.
2
.
3
.
Da
t
a
a
na
ly
s
is
T
h
e
an
aly
s
is
o
f
th
is
s
tu
d
y
was
u
s
ed
as
a
co
m
b
in
atio
n
o
f
p
h
en
o
m
en
o
lo
g
i
d
ata
an
a
ly
s
is
f
r
o
m
Mo
u
s
tak
as
[
1
9
]
:
1
)
C
o
n
s
id
er
ea
ch
s
tatem
en
t
with
r
esp
ec
t
to
s
ig
n
if
ican
ce
f
o
r
d
escr
ip
tio
n
o
f
th
e
e
x
p
er
ie
n
ce
;
2
)
R
ec
o
r
d
all
r
elev
an
t
s
tatem
en
ts
;
3
)
L
is
t
ea
ch
n
o
n
r
ep
etitiv
e,
n
o
n
o
v
er
lap
p
i
n
g
s
tatem
en
t
;
4
)
R
elate
an
d
clu
s
ter
th
e
in
v
ar
ian
t
m
ea
n
in
g
u
n
its
in
to
th
em
es
;
5
)
Sy
n
th
esize
t
h
e
in
v
ar
ia
n
t
m
ea
n
in
g
u
n
its
an
d
th
em
es
in
t
o
a
d
escr
ip
tio
n
o
f
th
e
tex
tu
r
es
o
f
th
e
ex
p
er
ien
ce
;
6
)
R
ef
lect
o
n
y
o
u
r
o
wn
tex
tu
r
al
d
escr
ip
tio
n
;
7
)
C
o
n
s
tr
u
ct
a
tex
tu
r
al
-
s
tr
u
ctu
r
al
d
escr
ip
tio
n
o
f
th
e
m
ea
n
i
n
g
s
an
d
ess
en
ce
s
o
f
y
o
u
r
e
x
p
er
ie
n
ce
.
T
o
en
s
u
r
e
th
e
v
alid
ity
o
f
r
esear
ch
d
ata
in
th
is
s
tu
d
y
,
s
e
v
er
al
s
tep
s
to
test
th
e
v
alid
ity
o
f
th
e
d
ata
we
r
e
ca
r
r
ied
o
u
t
t
o
o
b
tai
n
v
alid
d
ata.
Acc
o
r
d
in
g
ly
,
th
e
v
alid
ity
o
f
th
e
d
ata
in
th
is
s
tu
d
y
co
n
s
is
ts
o
f
cr
ed
ib
ilit
y
o
r
in
ter
n
al
v
alid
ity
with
th
e
tr
ian
g
u
latio
n
m
eth
o
d
.
Data
tr
ian
g
u
latio
n
was
d
o
n
e
b
y
c
o
llectin
g
th
en
co
m
b
in
in
g
,
cr
o
s
s
-
ch
ec
k
in
g
t
h
e
d
ata
th
a
t
h
ad
b
ee
n
o
b
tain
e
d
th
r
o
u
g
h
o
b
s
er
v
atio
n
,
in
ter
v
iew,
an
d
d
o
cu
m
en
tatio
n
tech
n
iq
u
es.
T
r
a
n
s
f
er
ab
ilit
y
o
r
ex
ter
n
al
v
alid
ity
,
an
d
d
ep
en
d
ab
ilit
y
o
r
r
eliab
ilit
y
,
d
ep
en
d
ab
ilit
y
is
d
o
n
e
b
y
co
n
d
u
ctin
g
an
au
d
it
o
f
th
e
en
tire
r
esear
ch
p
r
o
ce
s
s
th
at
h
as b
ee
n
ca
r
r
ied
o
u
t
.
3.
RE
SU
L
T
S
AND
D
I
SCU
SS
I
O
N
T
h
e
r
esu
lts
an
d
d
is
cu
s
s
io
n
in
th
is
s
tu
d
y
ar
e
p
r
esen
ted
in
th
e
f
o
r
m
o
f
a
d
escr
ip
tio
n
.
R
esu
lts
o
f
teac
h
er
-
s
tu
d
en
ts
in
ter
ac
tio
n
i
n
th
is
s
tu
d
y
wer
e
o
b
tain
e
d
f
r
o
m
o
b
s
er
v
atio
n
,
in
ter
v
iews,
an
d
d
o
c
u
m
en
tatio
n
.
B
ased
o
n
th
e
d
ata
co
llectio
n
tech
n
iq
u
e,
th
e
r
esear
c
h
er
w
ill
s
h
o
w
th
e
o
b
s
er
v
atio
n
s
r
esu
lts
,
th
e
in
ter
v
iew
r
esu
lts
,
an
d
also
d
o
cu
m
en
tatio
n
r
esu
lt o
f
teac
h
er
-
s
tu
d
e
n
ts
in
ter
ac
tio
n
in
th
e
lear
n
in
g
p
r
o
ce
s
s
.
T
h
e
d
ata
th
at
th
e
r
esear
ch
er
p
r
esen
ts
is
d
ata
th
at
h
as
b
ee
n
r
ea
d
ca
r
e
f
u
lly
,
h
as
b
ee
n
r
ed
u
ce
d
an
d
th
e
r
esear
ch
er
h
as
cr
o
s
s
-
ch
e
ck
ed
t
h
e
r
esu
lts
o
f
o
b
s
er
v
atio
n
s
,
in
ter
v
iews,
an
d
d
o
c
u
m
en
tatio
n
.
T
h
e
in
ter
ac
tio
n
d
ata
th
at
th
e
r
esear
c
h
er
p
r
esen
ts
ar
e
th
e
in
ter
ac
tio
n
s
t
h
at
th
e
teac
h
er
c
o
n
d
u
cted
to
s
tim
u
late
lear
n
in
g
ac
tiv
ities
o
r
s
tu
d
en
t
in
ter
ac
tio
n
s
in
r
esp
o
n
d
in
g
t
o
th
e
i
n
ter
ac
tio
n
s
p
r
o
v
i
d
ed
b
y
th
e
teac
h
er
.
T
h
ese
in
ter
ac
tio
n
s
tak
e
th
e
f
o
r
m
o
f
ac
tio
n
s
tak
e
n
b
y
teac
h
er
s
o
r
s
tu
d
en
ts
.
3
.
1
.
T
ea
cher
s
t
ra
ns
f
er
ma
t
e
ria
l
-
s
t
ud
ent
s
a
t
t
end
t
o
m
a
t
er
ia
l
T
ea
ch
er
-
s
tu
d
en
t
in
ter
ac
tio
n
co
n
s
is
ts
o
f
th
e
teac
h
er
s
d
eliv
e
r
in
g
m
ater
ial
an
d
s
tu
d
e
n
ts
p
ay
in
g
atten
tio
n
is
o
n
e
f
o
r
m
o
f
in
ter
ac
tio
n
th
at
is
n
ee
d
ed
in
u
n
d
e
r
s
tan
d
in
g
m
ath
em
atics.
T
h
is
g
iv
e
an
d
tak
e
in
ter
ac
tio
n
is
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
Tea
ch
er
-
s
tu
d
en
t in
tera
ctio
n
in
ma
th
ema
tics
lea
r
n
in
g
(
I
r
ma
A
yu
w
a
n
ti
)
663
im
p
o
r
tan
t
in
lear
n
i
n
g
ac
tiv
itie
s
.
T
ea
ch
er
s
as
m
ater
ial
g
iv
er
s
an
d
s
tu
d
en
ts
as
m
ater
ial
r
ec
ip
ien
ts
c
o
llab
o
r
ate
to
ca
r
r
y
o
u
t g
o
o
d
lear
n
in
g
ac
tiv
it
ies
,
w
ith
th
e
r
esu
lt th
at
lear
n
in
g
o
b
jectiv
es
ca
n
b
e
ac
h
iev
e
d
m
ax
im
ally
.
Ma
th
em
atics
teac
h
er
s
m
u
s
t
b
e
s
k
illed
in
u
s
in
g
ap
p
r
o
p
r
iate
l
ea
r
n
in
g
s
tr
ateg
ies
in
d
eliv
er
i
n
g
m
ater
ial
in
ca
s
e
th
e
s
tu
d
en
ts
ar
e
in
ter
ested
i
n
lear
n
in
g
.
T
h
e
task
o
f
th
e
m
ath
teac
h
er
is
to
g
u
id
e
s
t
u
d
en
ts
to
u
n
d
er
s
tan
d
m
ath
em
atics,
ca
r
r
y
o
u
t
t
h
e
m
ath
em
atics
lear
n
in
g
p
r
o
ce
s
s
,
an
d
f
o
s
ter
a
s
en
s
e
o
f
p
le
asu
r
e
an
d
lo
v
e
f
o
r
m
ath
em
atics.
T
o
ac
h
iev
e
th
is
,
th
e
teac
h
er
m
u
s
t
h
av
e
th
e
k
n
o
wled
g
e,
ab
ilit
y
,
an
d
s
k
ills
r
eg
ar
d
in
g
m
ath
em
atics,
th
e
c
h
ar
ac
ter
is
tics
,
an
d
th
e
m
at
h
em
atics
lear
n
in
g
p
r
o
ce
s
s
[
2
0
]
,
[
2
1
]
.
G
o
o
d
m
aster
y
o
f
m
ater
ial
s
k
ills
,
d
eliv
er
y
s
k
ills
,
th
e
ab
ilit
y
to
s
elec
t
lear
n
in
g
s
tr
ateg
ies
to
cr
ea
te
ac
tiv
e
lear
n
i
n
g
f
o
r
s
tu
d
en
ts
.
I
n
p
r
esen
tin
g
m
ater
ial,
th
e
teac
h
er
s
h
o
u
ld
also
u
s
e
ex
am
p
les
i
n
ev
er
y
d
a
y
life
o
r
k
n
o
wn
as
r
ea
lis
ti
c
m
ath
em
atic
s
s
o
th
at
it
is
ea
s
ily
u
n
d
er
s
to
o
d
b
y
s
tu
d
en
ts
.
R
ea
lis
tic
Ma
th
em
atics
E
d
u
ca
tio
n
m
ak
es
a
s
ig
n
if
ican
t
co
n
tr
ib
u
tio
n
to
th
e
d
ev
elo
p
m
en
t
o
f
ea
r
ly
ch
ild
h
o
o
d
m
at
h
em
atics
co
m
p
eten
ce
[
2
2
]
.
B
ec
au
s
e
th
e
m
ath
em
atics
s
tag
e
f
o
r
ju
n
io
r
h
ig
h
s
ch
o
o
l
s
tu
d
en
ts
is
s
till
at
th
e
co
n
cr
ete
m
ath
em
atics
s
tag
e.
W
ith
th
ese
ab
ilit
i
es,
s
tu
d
en
ts
will
b
e
in
ter
ested
an
d
wan
t
to
p
ay
atten
tio
n
to
th
e
m
ater
ial
p
r
esen
ted
b
y
th
e
teac
h
er
.
T
h
e
s
tu
d
en
ts
ar
e
in
ter
ested
in
m
ath
em
atics
lear
n
in
g
,
s
tu
d
e
n
ts
lear
n
m
ath
em
atics
with
p
leasu
r
e
an
d
s
tu
d
en
ts
u
n
d
er
s
tan
d
th
e
m
ater
ial
p
r
esen
ted
b
y
th
e
teac
h
er
.
T
h
e
d
eliv
er
y
o
f
m
ater
ial
b
y
t
h
e
teac
h
er
is
in
f
lu
en
ce
d
b
y
th
e
m
aster
y
o
f
th
e
m
ater
ial
an
d
s
k
ills
in
s
elec
tin
g
th
e
r
ig
h
t
s
tr
ateg
y
.
B
o
th
ar
e
r
elate
d
to
ea
ch
o
th
er
,
if
m
aster
y
o
f
th
e
m
ater
ial
is
g
o
o
d
b
u
t
th
e
s
tr
ateg
y
u
s
ed
is
n
o
t r
ig
h
t th
en
th
e
s
tu
d
e
n
ts
will n
o
t b
e
in
ter
ested
.
I
f
th
e
s
tr
ateg
y
u
s
ed
is
co
r
r
ec
t b
u
t th
e
teac
h
er
d
o
es n
o
t
m
aster
th
e
m
ater
ial,
s
tu
d
e
n
ts
will
n
o
t
g
et
th
e
in
f
o
r
m
atio
n
t
h
ey
n
ee
d
.
T
h
is
is
s
u
itab
le
f
o
r
th
e
s
tatem
en
t
wh
ich
s
tates
th
a
t
wh
at
th
e
teac
h
er
d
o
es
in
lear
n
in
g
ac
tiv
ities
af
f
ec
ts
s
tu
d
en
t
ac
h
iev
em
en
t
[
1
4
]
,
[
2
3
]
.
C
o
n
s
eq
u
en
tly
,
ev
er
y
th
in
g
th
at
is
d
o
n
e
b
y
th
e
teac
h
er
will
b
e
a
n
ex
am
p
le
f
o
r
s
tu
d
e
n
ts
.
I
n
ca
s
e,
t
h
e
te
ac
h
er
m
u
s
t
alwa
y
s
co
n
s
id
er
th
e
th
i
n
g
s
th
at
m
u
s
t b
e
d
o
n
e
s
o
t
h
at
s
tu
d
en
ts
ca
n
u
n
d
er
s
tan
d
m
ath
em
atics we
ll.
T
ea
ch
er
s
’
m
ath
e
m
atica
l
k
n
o
wled
g
e
m
ad
e
s
tatis
tically
s
ig
n
if
ican
t
ch
a
n
g
es
in
th
eir
less
o
n
d
esig
n
,
th
eir
m
ath
em
atica
l
ag
e
n
d
a,
a
n
d
th
e
class
r
o
o
m
clim
ate
[
2
4
]
.
Ho
wev
er
,
s
tu
d
en
t
in
v
o
l
v
em
en
t
was
s
ig
n
if
ican
tly
r
elate
d
to
s
tu
d
en
t
g
r
ad
e
ac
q
u
is
itio
n
.
T
h
e
s
tatem
en
t
s
aid
th
at
teac
h
er
s
’
m
ath
em
atica
l
k
n
o
wled
g
e
h
a
d
an
im
p
o
r
tan
t
r
o
le
in
lear
n
in
g
d
esig
n
an
d
class
r
o
o
m
clim
ate.
T
ea
ch
er
s
w
h
o
m
aster
m
ath
em
atics
will
cr
ea
te
attr
ac
tiv
e
lear
n
in
g
d
esig
n
s
an
d
a
h
ar
m
o
n
io
u
s
class
r
o
o
m
clim
ate
in
lear
n
in
g
.
Ho
wev
e
r
,
t
h
e
v
alu
e
o
f
s
tu
d
e
n
ts
in
m
ath
em
atics
is
in
f
lu
en
ce
d
b
y
th
e
in
v
o
lv
em
e
n
t
o
f
s
tu
d
e
n
ts
in
it.
T
h
is
s
h
o
ws
th
at
t
h
e
r
e
latio
n
s
h
ip
b
etwe
en
teac
h
er
s
an
d
s
tu
d
en
ts
af
f
ec
ts
s
tu
d
en
t g
r
a
d
es.
I
n
ter
ac
tio
n
o
f
ca
r
in
g
f
o
r
ea
ch
o
th
er
a
f
f
ec
ts
s
tu
d
en
ts
’
m
ath
e
m
atica
l
u
n
d
er
s
tan
d
i
n
g
.
Pay
at
ten
tio
n
to
ea
ch
o
th
er
in
th
is
ca
s
e,
th
e
teac
h
er
is
co
n
ce
r
n
e
d
with
th
e
s
tu
d
en
ts
in
ca
s
e
th
ey
tr
y
to
p
r
o
v
id
e
an
d
co
n
v
ey
th
e
m
ater
ial
well.
Me
an
wh
ile,
s
tu
d
en
ts
’
atten
tio
n
to
teac
h
er
s
is
in
th
e
f
o
r
m
o
f
s
tu
d
en
ts
’
s
er
io
u
s
n
ess
in
ac
ce
p
tin
g
an
d
p
a
y
in
g
atte
n
tio
n
to
th
e
m
ater
ial
p
r
esen
ted
b
y
th
e
teac
h
er
.
Stu
d
en
ts
will
f
in
d
it
d
if
f
ic
u
lt
to
u
n
d
er
s
tan
d
t
h
e
m
ater
ial
if
th
ey
d
o
n
o
t
p
ay
att
en
tio
n
to
th
e
m
a
ter
ial
p
r
esen
ted
b
y
th
e
teac
h
er
.
T
h
er
e
f
o
r
e,
s
tu
d
en
ts
will
f
in
d
it
d
if
f
icu
lt
to
s
o
lv
e
p
r
o
b
lem
s
.
H
en
ce
,
th
e
teac
h
er
-
s
tu
d
en
ts
in
te
r
ac
tio
n
in
th
e
f
o
r
m
o
f
teac
h
e
r
s
d
eliv
er
in
g
m
ater
ial
an
d
s
tu
d
en
ts
p
ay
in
g
atten
tio
n
to
th
e
teac
h
er
wh
en
d
eliv
er
i
n
g
m
ater
ial
o
r
th
e
in
te
r
ac
tio
n
o
f
ca
r
in
g
f
o
r
ea
ch
o
th
er
af
f
ec
ts
s
tu
d
en
ts
’
m
at
h
e
m
atica
l u
n
d
er
s
tan
d
in
g
.
3
.
2
.
Q
ues
t
io
ns
a
nd
a
ns
wer
s
a
m
id
t
ea
cher
-
s
t
ud
ent
s
B
ased
o
n
th
e
r
esu
lts
o
f
th
e
o
b
s
er
v
atio
n
s
,
it
was
f
o
u
n
d
t
h
at
o
n
e
o
f
th
e
in
ter
ac
tio
n
s
in
t
h
e
r
esear
ch
class
was
a
q
u
esti
o
n
a
n
d
an
s
wer
s
ess
io
n
b
etwe
en
teac
h
er
s
an
d
s
tu
d
e
n
ts
.
I
n
th
e
r
esear
ch
class
,
it
ap
p
ea
r
s
th
at
th
e
teac
h
er
ask
s
q
u
esti
o
n
s
ab
o
u
t
th
e
s
tu
d
en
ts
’
in
itial
u
n
d
e
r
s
tan
d
in
g
.
T
h
e
q
u
esti
o
n
is
a
q
u
esti
o
n
ab
o
u
t
th
e
p
r
ev
io
u
s
m
ater
ial.
T
h
e
teac
h
er
also
ask
ed
q
u
esti
o
n
s
s
ev
e
r
al
tim
es
to
f
o
cu
s
o
n
s
tu
d
en
ts
’
atten
tio
n
wh
en
p
r
esen
tin
g
t
h
e
m
ate
r
ial.
I
n
a
d
d
itio
n
,
t
h
e
teac
h
e
r
also
ask
s
q
u
esti
o
n
s
at
th
e
en
d
o
f
th
e
less
o
n
,
q
u
esti
o
n
s
in
th
e
f
o
r
m
o
f
q
u
esti
o
n
s
th
at
m
u
s
t
b
e
d
o
n
e
b
y
s
tu
d
en
ts
.
Qu
esti
o
n
s
in
th
e
f
o
r
m
o
f
q
u
esti
o
n
s
ar
e
g
iv
en
to
f
in
d
o
u
t
s
tu
d
en
ts
'
u
n
d
er
s
tan
d
in
g
o
f
th
e
m
ater
ial
b
ein
g
d
is
cu
s
s
ed
.
T
h
e
teac
h
er
u
s
u
ally
g
iv
es
o
r
a
l
q
u
esti
o
n
s
wh
en
th
e
teac
h
er
is
d
eliv
er
in
g
th
e
m
ater
ial.
Oc
ca
s
io
n
ally
th
e
teac
h
er
ask
s
o
r
al
q
u
esti
o
n
s
,
f
o
r
ex
am
p
le,
“
Wh
a
t
d
o
yo
u
kn
o
w
a
b
o
u
t
n
u
mb
er
th
e
o
r
y?
a
cc
o
r
d
in
g
to
yo
u
r
la
n
g
u
a
g
e,
w
h
a
t
is
mea
n
t
b
y
n
u
mb
er
th
eo
r
y?
T
r
y
to
men
tio
n
ex
a
mp
les
o
f
n
u
mb
er
th
eo
r
y
in
ev
eryd
a
y
life?
”
.
T
h
is
k
in
d
o
f
q
u
esti
o
n
is
a
f
o
r
m
o
f
th
e
q
u
esti
o
n
th
at
th
e
teac
h
er
g
iv
es
to
g
et
s
tu
d
en
ts
’
atten
tio
n
.
Qu
esti
o
n
s
lik
e
th
is
ar
e
u
s
ed
to
lead
s
tu
d
en
ts
t
o
f
o
cu
s
m
o
r
e
o
n
th
e
m
ater
ial
b
ein
g
d
is
cu
s
s
ed
.
T
h
ese
q
u
esti
o
n
s
ar
e
also
ask
ed
to
attr
ac
t
s
tu
d
en
ts
to
th
in
k
c
r
itically
an
d
ac
tiv
ely
in
lear
n
i
n
g
.
Q
u
esti
o
n
s
h
av
e
a
b
en
ef
icial
ef
f
e
ct
o
n
wh
eth
e
r
th
e
y
ar
e
p
r
esen
ted
b
ef
o
r
e
o
r
af
te
r
th
e
r
elate
d
lear
n
in
g
m
ater
ial.
Qu
esti
o
n
s
at
th
e
b
eg
in
n
i
n
g
o
f
th
e
less
o
n
f
o
cu
s
s
tu
d
en
ts
’
atten
tio
n
o
n
co
n
ce
p
t
s
d
u
r
in
g
lear
n
in
g
,
wh
ile
q
u
esti
o
n
s
af
ter
lear
n
in
g
p
r
o
v
id
e
r
etr
iev
al
an
d
f
ee
d
b
ac
k
o
n
th
e
in
f
o
r
m
atio
n
th
at
h
as
b
ee
n
lear
n
ed
.
E
q
u
ally
ea
r
ly
lear
n
in
g
q
u
esti
o
n
s
an
d
p
o
s
t
-
lear
n
in
g
q
u
esti
o
n
s
p
r
o
v
id
e
s
u
b
s
tan
tial
p
r
o
f
it
f
r
o
m
r
ep
etitio
n
[
2
5
]
.
In
ad
d
itio
n
to
o
r
al
q
u
esti
o
n
s
,
th
e
teac
h
er
also
p
r
o
v
id
es
q
u
e
s
tio
n
s
in
th
e
f
o
r
m
o
f
p
r
ac
tice
q
u
esti
o
n
s
.
Af
ter
th
e
teac
h
e
r
ex
p
lain
s
th
e
m
ater
ial,
th
e
teac
h
er
d
is
cu
s
s
es
s
am
p
le
q
u
esti
o
n
s
b
ef
o
r
e
g
iv
in
g
e
x
er
cises
to
s
tu
d
en
ts
.
Af
ter
d
is
cu
s
s
in
g
th
e
s
am
p
le
q
u
esti
o
n
s
,
th
e
teac
h
er
p
r
o
v
id
es
s
o
m
e
q
u
esti
o
n
s
f
o
r
p
r
ac
tice.
T
h
is
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
202
1
:
6
6
0
-
6
6
7
664
q
u
esti
o
n
is
g
iv
en
to
f
in
d
o
u
t
th
e
s
tu
d
en
ts
’
u
n
d
er
s
tan
d
in
g
o
f
th
e
s
am
p
le
q
u
esti
o
n
s
th
at
h
av
e
ju
s
t
b
ee
n
d
is
cu
s
s
ed
.
Ask
in
g
h
as
an
im
p
o
r
tan
t
r
o
l
e
in
teac
h
in
g
m
ath
em
atics
[
2
6
]
.
Qu
esti
o
n
s
ar
e
a
m
ea
n
s
b
y
wh
ic
h
teac
h
er
s
lead
s
tu
d
en
ts
to
co
r
r
e
ct
m
ath
em
atica
l
co
n
ce
p
ts
an
d
p
r
o
ce
d
u
r
es
th
r
o
u
g
h
“
n
eg
o
tiati
n
g
m
ea
n
in
g
f
o
r
th
e
r
eq
u
ir
ed
lear
n
i
n
g
c
o
n
d
itio
n
s
”
[
2
7
]
.
Qu
esti
o
n
s
ar
e
o
n
e
o
f
th
e
m
o
s
t
p
o
wer
f
u
l
to
o
ls
f
o
r
co
n
s
tr
u
ctin
g
a
lear
n
i
n
g
en
v
ir
o
n
m
en
t
an
d
f
o
s
ter
in
g
s
u
c
ce
s
s
f
u
l
p
er
f
o
r
m
an
ce
[
2
8
]
.
T
h
e
p
u
r
p
o
s
e
o
f
th
e
q
u
esti
o
n
s
th
e
t
ea
ch
er
g
iv
es
is
,
th
e
teac
h
er
tr
ies
to
in
v
esti
g
ate
wh
eth
er
th
e
s
tu
d
en
t
lis
ten
s
to
an
d
th
en
u
n
d
er
s
tan
d
s
th
e
less
o
n
th
at
h
as
ju
s
t
b
ee
n
tau
g
h
t
[
2
9
]
,
[
3
0
]
Ad
d
itio
n
all
y
b
y
u
s
in
g
q
u
esti
o
n
s
,
th
e
teac
h
er
ass
es
s
es
s
tu
d
en
ts
'
k
n
o
wled
g
e,
d
eter
m
in
in
g
th
e
n
ee
d
f
o
r
f
o
c
u
s
ed
r
e
-
teac
h
in
g
,
an
d
en
c
o
u
r
ag
e
s
tu
d
en
ts
to
th
in
k
at
a
h
ig
h
er
co
g
n
itiv
e
lev
el
[
3
1
]
.
Acc
o
r
d
in
g
t
o
Veg
a
,
et
a
l.
[
3
2
]
,
s
tu
d
en
ts
’
q
u
esti
o
n
s
h
av
e
two
f
u
n
ctio
n
s
th
e
f
ir
s
t
f
u
n
cti
o
n
is
f
o
r
s
tu
d
en
ts
to
ask
th
em
s
elv
es
m
a
th
q
u
esti
o
n
s
s
o
th
at
th
e
y
lear
n
to
th
in
k
lik
e
m
ath
em
atician
s
wh
o
o
f
ten
ad
v
a
n
ce
k
n
o
wled
g
e
b
y
ask
in
g
n
ew
q
u
e
s
tio
n
s
an
d
tr
y
in
g
to
s
o
lv
e
th
em
.
T
h
e
s
ec
o
n
d
f
u
n
ctio
n
is
f
o
r
s
tu
d
e
n
ts
to
ask
th
eir
teac
h
er
lear
n
in
g
q
u
esti
o
n
s
d
u
r
in
g
less
o
n
s
wh
en
th
ey
d
o
n
o
t
u
n
d
er
s
tan
d
ce
r
tain
p
a
r
ts
o
f
th
e
less
o
n
.
B
o
th
teac
h
er
q
u
esti
o
n
s
an
d
s
tu
d
en
t
q
u
esti
o
n
s
h
av
e
a
p
u
r
p
o
s
e
an
d
f
u
n
ctio
n
i
n
lear
n
in
g
m
ath
em
at
ics.
C
o
n
s
eq
u
en
tly
,
it
ca
n
b
e
co
n
cl
u
d
ed
th
at
th
e
q
u
esti
o
n
an
d
an
s
wer
in
ter
ac
tio
n
b
etwe
en
th
e
te
ac
h
er
an
d
s
tu
d
en
ts
af
f
ec
ts
s
tu
d
en
ts
’
m
ath
em
atica
l
u
n
d
er
s
tan
d
in
g
o
f
n
u
m
b
er
p
atter
n
s
i
n
th
e
f
o
r
m
o
f
s
o
lv
in
g
th
e
g
iv
en
q
u
esti
o
n
s
b
y
o
b
tain
in
g
s
atis
f
a
cto
r
y
r
esu
lts
.
Ask
in
g
an
d
an
s
wer
in
g
q
u
esti
o
n
s
m
ak
es
s
tu
d
en
ts
m
o
r
e
f
am
iliar
with
th
e
m
ater
ial
b
ein
g
d
is
cu
s
s
ed
.
B
y
ask
in
g
an
d
an
s
wer
in
g
s
tu
d
en
ts
g
et
an
u
n
d
er
s
tan
d
in
g
o
f
th
e
m
ater
ial
b
ein
g
d
is
cu
s
s
ed
.
Stu
d
en
ts
ca
n
also
wo
r
k
o
n
p
r
o
b
lem
s
well
wh
en
th
ey
g
et
an
s
wer
s
f
r
o
m
th
e
ir
ig
n
o
r
a
n
ce
.
3
.
3
.
T
ea
cher
s
cr
ea
t
e
lea
rnin
g
s
t
ra
t
e
g
ies
t
ha
t
a
re
a
t
t
ra
ct
i
v
e
-
s
t
ud
ent
s
a
re
a
ct
iv
ely
inv
o
lv
ed
in lea
rning
An
o
th
er
in
ter
ac
tio
n
th
at
a
p
p
ea
r
s
in
th
e
o
b
s
er
v
atio
n
class
th
at
ca
n
im
p
r
o
v
e
s
tu
d
e
n
ts
’
u
n
d
er
s
tan
d
in
g
o
f
th
e
m
ater
ial
b
ein
g
d
is
cu
s
s
ed
is
th
e
lear
n
in
g
s
tr
ateg
ies
u
s
e.
L
ea
r
n
in
g
s
tr
ateg
ies
in
th
e
o
b
s
er
v
atio
n
class
is
a
lear
n
in
g
g
am
e
s
tr
ateg
y
.
T
h
e
teac
h
er
u
s
es
g
am
es
to
f
o
s
ter
m
o
tiv
atio
n
an
d
attr
ac
t
s
tu
d
en
t
s
’
atten
tio
n
in
ca
s
e
s
tu
d
en
ts
f
o
cu
s
an
d
w
o
r
k
o
n
th
e
q
u
esti
o
n
s
th
ey
r
ec
ei
v
e.
I
n
th
e
class
r
o
o
m
o
b
s
er
v
atio
n
,
th
e
teac
h
er
m
ak
es
a
g
am
e
an
d
s
tu
d
en
ts
ar
e
ac
tiv
ely
in
v
o
l
v
ed
in
th
e
g
am
e.
T
h
e
teac
h
er
co
m
p
o
s
e
s
a
g
am
e
i
n
v
o
lv
i
n
g
all
th
e
s
tu
d
en
ts
in
th
e
class
.
T
h
e
teac
h
er
co
n
tr
ib
u
tes
s
ev
er
al
q
u
esti
o
n
s
to
b
e
s
o
lv
ed
b
y
th
e
s
tu
d
en
ts
.
Ho
wev
er
,
th
e
teac
h
er
p
r
o
v
id
es a
tim
e
lim
it in
wo
r
k
in
g
o
n
th
e
p
r
o
b
lem
.
Su
b
s
eq
u
en
t
ly
,
th
e
ag
r
ee
d
tim
e
lim
it
is
f
in
is
h
ed
,
s
tu
d
e
n
ts
ar
e
in
v
ited
to
leav
e
th
eir
an
s
wer
s
o
n
th
e
ta
b
le.
Stu
d
en
ts
g
ath
er
in
f
r
o
n
t o
f
th
e
class
an
d
watc
h
th
e
teac
h
er
c
h
ec
k
th
eir
a
n
s
wer
s
.
T
h
e
teac
h
er
clo
s
es
th
e
b
o
o
k
if
th
e
s
tu
d
en
t
s’
an
s
wer
is
co
r
r
ec
t.
T
h
e
teac
h
er
le
av
es th
e
b
o
o
k
o
p
en
,
if
th
e
s
tu
d
en
t'
s
an
s
wer
i
s
s
till
wr
o
n
g
.
I
n
th
is
ac
tiv
ity
,
th
e
teac
h
er
a
n
d
s
tu
d
e
n
ts
ar
e
in
v
o
lv
ed
in
a
n
in
te
r
esti
n
g
in
ter
ac
tio
n
.
L
e
a
r
n
in
g
in
ter
ac
tio
n
s
th
at
f
o
s
ter
en
th
u
s
iasm
an
d
m
o
tiv
atio
n
in
s
tu
d
en
ts
.
L
ea
r
n
in
g
i
n
ter
ac
tio
n
s
th
at
f
o
s
ter
en
th
u
s
iasm
an
d
m
o
tiv
atio
n
h
a
v
e
an
im
p
ac
t
o
n
s
tu
d
e
n
t
u
n
d
er
s
tan
d
i
n
g
.
Stu
d
e
n
ts
wh
o
lear
n
with
f
u
n
lear
n
in
g
s
tr
ateg
ies,
ac
tiv
e
lear
n
in
g
s
itu
atio
n
s
ar
e
ea
s
ier
to
ac
ce
p
t th
e
m
ater
ial
p
r
esen
ted
.
I
n
a
s
tu
d
y
,
it
was
f
o
u
n
d
th
at
i
n
lear
n
in
g
ac
tiv
ities
u
s
in
g
ce
r
t
ain
ty
p
es
o
f
g
am
es
s
tu
d
e
n
ts
ex
p
er
ien
ce
d
im
p
r
o
v
em
e
n
ts
in
th
e
th
r
ee
p
s
y
ch
o
s
o
cial
f
ea
tu
r
es
o
f
th
e
lear
n
in
g
en
v
ir
o
n
m
e
n
t
(
teac
h
er
s
u
p
p
o
r
t,
p
er
s
o
n
al
in
v
o
lv
em
e
n
t,
an
d
r
elev
a
n
ce
)
a
s
well
a
s
ac
ad
em
ic
s
u
cc
es
s
an
d
en
jo
y
m
en
t
in
m
ath
e
m
atics
[
3
3
]
.
T
h
r
o
u
g
h
m
ath
g
am
es
an
d
ac
tiv
ities
with
o
th
er
s
tu
d
en
ts
,
s
tu
d
en
ts
b
u
ild
an
u
n
d
er
s
tan
d
i
n
g
o
f
m
ath
em
atica
l
v
alu
es
an
d
b
ased
o
n
th
at
th
ey
ac
t
b
y
co
n
s
tr
u
cti
n
g
a
n
d
m
o
d
if
y
in
g
th
eir
th
in
k
in
g
[
3
4
]
.
B
ased
o
n
t
h
is
o
p
in
i
o
n
,
it
ca
n
b
e
s
ee
n
th
at
th
e
g
am
e
s
tr
ateg
y
in
lear
n
in
g
h
as
a
g
o
o
d
im
p
ac
t
o
n
s
tu
d
en
ts
’
u
n
d
er
s
tan
d
in
g
a
b
ilit
y
.
Gen
er
ally
,
th
e
s
tu
d
en
ts
co
n
s
id
er
ed
m
at
h
em
atics
is
b
o
r
in
g
,
m
o
s
tly
ir
r
elev
an
t,
a
n
d
u
s
eless
[
3
5
]
.
T
h
er
ef
o
r
e
,
ed
u
ca
t
o
r
s
s
h
o
u
ld
s
tr
iv
e
to
u
s
e
r
eso
u
r
ce
s
a
n
d
s
tr
ateg
ies
th
at
ca
p
tu
r
e
s
tu
d
e
n
t
in
ter
est
a
n
d
m
o
tiv
atio
n
[
3
5
]
.
T
ea
ch
er
s
ar
e
ad
v
is
ed
to
u
s
e
ap
p
r
o
p
r
iate
lear
n
in
g
s
tr
at
eg
ies to
m
ee
t th
e
n
ee
d
s
o
f
s
tu
d
e
n
ts
in
d
eliv
er
in
g
m
ater
ial.
T
o
s
tr
en
g
t
h
en
t
h
e
e
d
u
ca
tio
n
al
p
r
o
ce
s
s
,
it
is
n
ec
ess
ar
y
t
o
c
o
m
b
in
e
v
ar
io
u
s
s
tr
ateg
ies
f
o
r
a
ctiv
e
an
d
co
o
p
er
ativ
e
lear
n
in
g
[
36]
.
I
n
l
ea
r
n
in
g
,
y
o
u
ca
n
n
o
t
o
n
ly
ap
p
l
y
o
n
e
lear
n
i
n
g
s
tr
ateg
y
.
T
h
er
e
n
ee
d
s
to
b
e
a
m
ix
o
f
s
tr
ateg
ies
to
cr
ea
te
ac
tiv
e,
attr
ac
tiv
e,
an
d
e
f
f
ec
tiv
e
clas
s
es
o
f
p
u
r
s
u
it.
I
n
th
e
r
esear
c
h
class
,
th
e
teac
h
er
ap
p
lies
s
ev
er
al
lear
n
in
g
s
tr
ate
g
ies
in
clu
d
in
g
lectu
r
e
s
,
p
r
o
b
le
m
-
s
o
lv
in
g
,
a
n
d
g
a
m
es.
T
h
e
p
u
r
p
o
s
e
o
f
c
o
m
b
in
i
n
g
th
ese
s
tr
ateg
ies
is
to
m
ee
t
th
e
n
ee
d
s
o
f
s
tu
d
en
ts
in
lear
n
in
g
a
ctiv
ities
.
T
o
co
n
v
ey
t
h
e
m
ater
i
al
th
e
teac
h
er
u
s
es
a
lectu
r
e
s
tr
ateg
y
,
t
o
in
c
r
ea
s
e
s
tu
d
en
t
i
n
ter
est
an
d
m
o
tiv
atio
n
,
th
e
teac
h
er
u
s
es
g
a
m
e
s
tr
ateg
ies
to
m
a
k
e
s
tu
d
en
ts
in
ter
ested
.
Me
an
w
h
ile,
to
o
b
s
er
v
e
s
tu
d
en
ts
’
a
b
ilit
y
to
s
o
lv
e
p
r
o
b
lem
s
,
th
e
teac
h
er
u
s
es
p
r
o
b
le
m
-
s
o
lv
in
g
s
tr
ateg
ies.
R
esear
ch
c
o
n
d
u
cte
d
b
y
C
lau
d
i
u
a
n
d
L
an
g
a
[
3
7
]
s
tated
th
at
o
v
e
r
all
,
th
e
m
ajo
r
ity
o
f
s
tu
d
en
ts
f
elt
th
at
b
ein
g
in
a
co
llab
o
r
ativ
e
en
v
ir
o
n
m
en
t
h
elp
ed
im
p
r
o
v
e
th
eir
m
ath
em
atics lea
r
n
in
g
.
T
h
e
s
tr
ateg
ies
u
s
ed
in
lear
n
i
n
g
ac
tiv
ities
af
f
ec
t
s
tu
d
en
ts
’
m
ath
em
atica
l
a
b
ilit
ies.
T
h
e
ch
o
ice
o
f
s
tr
ate
g
y
is
ad
ju
s
ted
to
th
e
co
n
d
itio
n
s
in
th
e
lear
n
in
g
class
r
o
o
m
.
I
t
is
im
p
o
r
tan
t
to
d
ef
in
e
a
s
tr
ateg
y
d
ir
ec
ted
at
a
s
p
ec
if
ic
g
o
al
o
r
tar
g
et
[
3
8
]
.
It
is
im
p
o
r
tan
t
to
u
s
e
s
tr
ateg
ies
in
lear
n
in
g
m
ath
em
atics.
Ma
n
y
s
tu
d
ies
h
a
v
e
s
tated
th
at
th
e
lear
n
in
g
s
tr
ateg
ies
u
s
ed
in
m
ath
em
atics
lear
n
in
g
af
f
ec
t
s
tu
d
en
ts
’
m
ath
em
at
ical
u
n
d
er
s
tan
d
in
g
,
m
ath
em
atica
l
ab
ilit
ies,
an
d
m
ath
em
atics
ac
h
iev
em
en
t.
So
m
e
o
f
th
e
b
en
ef
its
o
f
u
s
in
g
lear
n
in
g
s
tr
ateg
ies
an
d
lear
n
in
g
m
ath
em
atics
in
clu
d
e
lear
n
in
g
u
s
in
g
s
tr
ateg
ies
th
at
ar
e
ef
f
ec
tiv
e
in
s
tu
d
en
ts
’
m
ath
em
atics
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
Tea
ch
er
-
s
tu
d
en
t in
tera
ctio
n
in
ma
th
ema
tics
lea
r
n
in
g
(
I
r
ma
A
yu
w
a
n
ti
)
665
ac
h
iev
em
en
t
[
3
9
]
.
Ge
n
er
al
,
t
h
e
m
ajo
r
ity
o
f
s
tu
d
e
n
ts
f
ee
l
t
h
at
b
ein
g
in
a
n
e
n
v
ir
o
n
m
e
n
t
o
f
co
llab
o
r
ativ
e
lear
n
in
g
s
tr
ateg
ies
h
elp
s
im
p
r
o
v
e
th
eir
m
ath
e
m
atics
lear
n
in
g
[
4
0
]
.
L
ea
r
n
in
g
s
tr
ateg
ies
n
ee
d
to
b
e
u
s
ed
b
y
s
tu
d
en
ts
b
ec
au
s
e
th
ey
ca
n
en
c
o
u
r
ag
e
t
h
e
ap
p
licatio
n
o
f
t
h
eir
r
esu
lts
in
ed
u
ca
tio
n
[
4
1
]
.
3
.
4
.
T
ea
cher
g
iv
es a
w
a
rds
-
s
t
ud
ent
s
re
ce
iv
e
a
wa
rds
I
n
ter
ac
tio
n
co
n
s
is
ts
o
f
g
iv
in
g
an
d
r
ec
eiv
in
g
r
ewa
r
d
s
ar
e
p
ar
t
o
f
th
e
lear
n
in
g
ac
tiv
ities
th
at
ap
p
ea
r
in
-
class
r
o
o
m
o
b
s
er
v
atio
n
.
T
h
e
te
ac
h
er
g
iv
es r
ewa
r
d
s
to
s
tu
d
en
ts
.
Fu
r
th
er
m
o
r
e,
th
e
s
tu
d
en
ts
r
e
ce
iv
e
th
e
awa
r
d
.
I
n
th
e
o
b
s
er
v
atio
n
class
,
it
is
s
e
en
th
at
th
e
teac
h
er
ap
p
lies
an
i
n
ter
esti
n
g
lear
n
in
g
s
tr
ateg
y
b
y
m
ak
in
g
a
g
a
m
e.
T
h
e
teac
h
er
g
iv
es
th
e
q
u
esti
o
n
s
th
en
th
e
s
tu
d
en
ts
wo
r
k
at
a
ce
r
tain
tim
e.
Stu
d
e
n
ts
wh
o
an
s
wer
ed
co
r
r
ec
tly
r
ec
eiv
ed
awa
r
d
s
in
th
e
f
o
r
m
o
f
co
n
g
r
atu
latio
n
s
a
n
d
p
o
s
itiv
e
wo
r
d
s
s
u
ch
as
“
g
o
o
d
,
k
ee
p
u
p
th
e
s
p
ir
it
a
n
d
k
ee
p
it
u
p
”
.
Fu
r
th
e
r
m
o
r
e
,
th
e
teac
h
er
also
ask
s
all
s
tu
d
en
ts
to
cla
p
th
eir
h
an
d
s
as
a
s
ig
n
o
f
a
p
p
r
ec
iatio
n
f
o
r
s
tu
d
en
ts
wh
o
h
a
v
e
a
n
s
wer
ed
c
o
r
r
ec
tly
.
As
an
ap
p
r
ec
iatio
n
also
f
o
r
s
tu
d
en
ts
wh
o
ar
e
n
o
t
c
o
r
r
ec
t
b
ec
au
s
e
t
h
ey
ar
e
co
o
p
er
ativ
e
a
n
d
wan
t t
o
ac
ce
p
t th
e
p
u
n
is
h
m
e
n
t g
iv
en
.
T
h
is
ac
tiv
ity
is
a
teac
h
er
s
-
s
tu
d
en
ts
in
ter
ac
tio
n
in
lear
n
in
g
.
T
h
e
s
tu
d
en
ts
a
n
s
wer
co
r
r
ec
tly
th
e
teac
h
e
r
wan
ts
to
g
iv
e
a
p
p
r
ec
iatio
n
.
T
h
is
is
a
r
ec
ip
r
o
ca
l
in
te
r
ac
tio
n
th
at
o
cc
u
r
s
in
lear
n
in
g
ac
tiv
ities
th
at
aim
to
cr
ea
te
a
h
ar
m
o
n
io
u
s
an
d
p
leasan
t
lea
r
n
in
g
atm
o
s
p
h
er
e.
T
h
e
s
tu
d
e
n
t
s
wh
o
r
ec
eiv
e
th
e
awa
r
d
f
ee
l
h
ap
p
y
an
d
s
atis
f
ied
with
th
eir
s
u
cc
ess
in
an
s
wer
i
n
g
th
e
q
u
esti
o
n
s
g
iv
en
co
r
r
ec
tly
.
T
h
e
s
tu
d
en
ts
also
ask
ed
th
e
teac
h
er
to
r
e
p
ea
t
th
e
g
am
e
.
R
esear
ch
er
s
s
ee
s
t
u
d
en
ts
g
ettin
g
m
o
r
e
m
o
tiv
ate
d
in
p
ar
ticip
atin
g
in
th
e
n
e
x
t
g
am
e.
T
h
e
s
tu
d
e
n
ts
wh
o
p
r
e
v
io
u
s
ly
a
n
s
wer
ed
wr
o
n
g
ar
e
f
u
ll
o
f
e
n
th
u
s
iasm
an
d
o
p
tim
is
m
will
b
e
ab
le
t
o
d
o
n
ex
t.
Me
an
wh
ile,
t
h
e
s
tu
d
en
ts
wh
o
ar
e
en
t
h
u
s
iast
ic
an
d
tr
y
in
g
to
k
ee
p
s
u
cc
ee
d
i
n
g
in
wo
r
k
in
g
o
n
th
e
n
e
x
t p
r
o
b
le
m
.
T
h
e
teac
h
er
g
iv
es
awa
r
d
s
in
th
e
f
o
r
m
o
f
p
o
s
itiv
e
r
ein
f
o
r
ce
m
en
t,
u
s
in
g
wo
r
d
s
o
f
p
r
aise
to
s
tu
d
en
ts
wh
o
ca
n
wo
r
k
o
n
th
e
q
u
esti
o
n
s
.
T
h
e
teac
h
er
p
r
o
v
id
es
wo
r
d
s
o
f
co
m
f
o
r
t
an
d
en
c
o
u
r
a
g
e
m
en
t
to
s
tu
d
en
ts
wh
o
h
av
e
n
o
t
b
ee
n
ab
le
to
wo
r
k
o
n
th
e
q
u
esti
o
n
s
.
T
h
e
aim
is
to
e
n
co
u
r
a
g
e
th
em
to
b
e
m
o
r
e
m
o
tiv
ated
in
lear
n
i
n
g
.
Stu
d
en
ts
'
m
o
tiv
atio
n
to
war
d
s
lear
n
in
g
m
ath
em
atics
is
lar
g
e
ly
in
f
lu
e
n
ce
d
b
y
r
ein
f
o
r
ce
m
e
n
t
s
u
ch
as
g
r
ad
i
n
g
,
ce
r
tific
ates,
an
d
wr
itten
co
m
m
en
ts
o
n
th
eir
wo
r
k
s
am
p
le
s
.
T
h
er
e
is
a
s
ig
n
if
ican
t
d
if
f
er
en
ce
in
s
t
u
d
en
t
m
o
tiv
atio
n
to
war
d
s
lear
n
in
g
m
ath
em
atics
at
p
o
s
t
-
in
te
r
v
en
tio
n
w
h
ich
u
ltima
tely
d
eter
m
in
es
s
tu
d
en
t
ac
h
iev
em
en
t in
lea
r
n
in
g
[
4
2
]
.
I
n
a
s
tu
d
y
,
it
was
s
h
o
w
n
t
h
at
r
ea
l
r
ewa
r
d
s
d
o
h
av
e
a
n
im
p
ac
t
o
n
s
tu
d
en
ts
’
m
o
ti
v
atio
n
in
m
ath
em
atics.
R
ea
l
r
ewa
r
d
s
ca
n
b
e
u
s
ed
to
p
o
s
itiv
ely
en
co
u
r
ag
e
s
tu
d
en
ts
to
ac
h
iev
e
h
ig
h
er
s
co
r
es
o
n
test
s
an
d
ass
ig
n
m
en
ts
.
T
h
is
awa
r
d
ca
n
also
b
e
u
s
ed
to
g
et
m
o
r
e
in
v
o
lv
em
en
t
in
-
class
ac
tiv
ities
.
R
e
al
r
ewa
r
d
s
ca
n
also
b
e
u
s
ed
as
s
tep
p
in
g
s
to
n
es
t
o
f
o
s
ter
in
tr
in
s
ic
m
o
tiv
atio
n
in
a
s
m
all
p
er
ce
n
tag
e
o
f
s
tu
d
en
ts
.
E
x
p
er
im
e
n
ts
co
n
d
u
cte
d
b
y
Hu
r
lo
c
k
o
n
th
e
ef
f
ec
tiv
en
ess
o
f
r
ewa
r
d
in
g
s
h
o
wed
th
at
s
tu
d
e
n
ts
’
m
ath
em
atics
im
p
r
o
v
ed
t
h
e
m
o
s
t
wh
en
s
tu
d
e
n
ts
wer
e
g
i
v
en
p
r
aise,
t
h
en
w
h
en
t
h
ey
we
r
e
g
iv
e
n
r
e
p
r
im
an
d
s
,
an
d
at
l
ea
s
t
in
cr
ea
s
ed
wh
en
s
tu
d
en
ts
wer
e
ig
n
o
r
e
d
.
R
ewa
r
d
s
h
av
e
b
ee
n
s
h
o
wn
t
o
en
h
an
ce
v
ar
io
u
s
f
o
r
m
s
o
f
lear
n
in
g
[
4
2
]
.
I
t
is
s
u
g
g
ested
th
at
teac
h
er
s
p
r
ef
er
to
u
s
e
r
ewa
r
d
s
as
a
m
o
tiv
atio
n
al
s
tim
u
la
to
r
in
th
e
ed
u
ca
tio
n
al
p
r
o
ce
s
s
[
4
3
]
.
Awa
r
d
i
n
g
h
as
a
s
ig
n
if
ican
t
ef
f
e
ct
o
n
s
tu
d
en
ts
'
m
ath
em
atics
lear
n
in
g
o
u
tc
o
m
es
[
4
3
]
,
[
4
4
]
.
B
ased
o
n
th
ese
th
eo
r
ies,
it
is
k
n
o
wn
th
at
awa
r
d
-
g
iv
i
n
g
h
as
a
p
o
s
itiv
e
ef
f
ec
t
o
n
lear
n
in
g
m
ath
em
atics,
in
f
o
s
ter
in
g
s
tu
d
en
t
m
o
tiv
atio
n
,
o
n
s
tu
d
en
t le
ar
n
in
g
o
u
tco
m
es.
T
h
er
ef
o
r
e,
g
iv
in
g
awa
r
d
s
ca
n
im
p
r
o
v
e
s
tu
d
e
n
ts
’
m
ath
em
atica
l
u
n
d
er
s
tan
d
i
n
g
B
ase
d
o
n
th
e
d
escr
ip
tio
n
ab
o
v
e,
it
ca
n
b
e
s
ee
n
th
at
s
ev
er
al
teac
h
er
-
s
tu
d
en
t
in
ter
ac
tio
n
s
n
ee
d
to
b
e
d
ev
elo
p
e
d
in
lea
r
n
in
g
.
T
h
ese
in
ter
ac
tio
n
s
ar
e
:
1
)
T
ea
c
h
er
s
T
r
an
s
f
er
Ma
ter
ial
-
Stu
d
en
ts
Atten
d
to
Ma
ter
ial.
T
ea
ch
er
s
m
u
s
t
m
aster
m
ath
m
ater
ial
an
d
b
e
ab
le
to
co
n
v
ey
i
t
well
to
s
tu
d
en
ts
.
Stu
d
en
ts
m
u
s
t
also
r
ec
eiv
e
an
d
lis
ten
to
all
in
f
o
r
m
atio
n
f
r
o
m
t
h
e
teac
h
er
to
b
u
ild
an
d
im
p
r
o
v
e
m
ath
em
atica
l
u
n
d
er
s
tan
d
in
g
.
2
)
Qu
esti
o
n
s
a
n
d
An
s
wer
s
am
id
T
ea
ch
er
-
Stu
d
en
ts
,
q
u
esti
o
n
an
d
an
s
wer
b
et
wee
n
teac
h
er
s
an
d
s
tu
d
en
ts
ar
e
v
er
y
n
e
ce
s
s
ar
y
,
th
er
e
ar
e
s
o
m
an
y
b
e
n
ef
its
th
at
s
tu
d
en
ts
g
et
th
r
o
u
g
h
th
e
in
t
er
ac
tio
n
b
etwe
en
q
u
esti
o
n
s
an
d
an
s
wer
s
with
th
e
teac
h
er
.
3
)
T
ea
ch
e
r
s
C
r
ea
te
L
ea
r
n
in
g
Stra
teg
ies
th
at
a
r
e
Attr
ac
tiv
e
-
Stu
d
en
ts
ar
e
A
ctiv
ely
I
n
v
o
lv
ed
in
L
ea
r
n
in
g
,
lear
n
in
g
s
tr
ateg
ies
ar
e
im
p
o
r
tan
t
to
in
cr
ea
s
e
s
tu
d
en
t
ac
tiv
ity
,
th
er
ef
o
r
e
s
tu
d
e
n
ts
n
ee
d
to
ac
tiv
ely
p
ar
ticip
ate
in
t
h
e
s
tr
ateg
ies
u
s
ed
in
m
ath
em
atics
lear
n
in
g
th
at
h
av
e
b
ee
n
p
lan
n
e
d
b
y
t
h
e
t
ea
c
h
er
,
4
)
.
T
ea
ch
er
Giv
es
Awa
r
d
s
-
Stu
d
en
ts
R
ec
e
iv
e
Awa
r
d
s
,
awa
r
d
s
ar
e
a
f
o
r
m
o
f
ex
ter
n
al
m
o
tiv
atio
n
n
e
ed
ed
b
y
s
tu
d
en
ts
.
T
ea
ch
er
s
ar
e
ad
v
is
ed
n
o
t
to
b
e
s
tin
g
y
in
g
iv
in
g
awa
r
d
s
to
s
tu
d
en
ts
wh
o
h
av
e
s
u
cc
ess
f
u
l
ly
wo
r
k
ed
o
n
m
at
h
p
r
o
b
lem
s
.
T
h
is
ca
n
b
e
a
m
o
ti
v
atio
n
f
o
r
s
tu
d
e
n
ts
to
b
e
b
etter
in
th
e
f
u
tu
r
e.
T
h
ese
f
o
r
m
s
o
f
in
ter
ac
tio
n
ar
e
n
o
s
tr
an
g
er
to
lear
n
in
g
ac
tiv
ities
.
Ho
wev
er
,
g
e
n
er
ally
,
t
h
e
ap
p
li
ca
tio
n
is
s
till
n
o
t
m
ax
im
al,
o
n
l
y
a
f
ew
ar
e
ap
p
lied
an
d
o
th
e
r
s
ar
e
co
n
s
id
er
ed
n
o
t
v
er
y
im
p
o
r
tan
t.
N
o
t
all
teac
h
e
r
s
r
ec
o
g
n
ize
t
h
at
wh
at
is
co
n
s
i
d
er
ed
n
o
r
m
al
t
u
r
n
s
o
u
t
to
h
a
v
e
an
im
p
o
r
tan
t
r
o
le
in
lear
n
in
g
.
T
h
e
s
am
e
is
th
e
c
ase
with
o
th
er
f
o
r
m
s
o
f
in
ter
a
ctio
n
.
T
h
r
o
u
g
h
th
e
ex
p
lan
atio
n
s
i
n
th
is
s
tu
d
y
ab
o
u
t
th
e
b
en
e
f
its
an
d
im
p
o
r
tan
c
e
o
f
teac
h
er
-
s
tu
d
en
t
i
n
ter
ac
tio
n
s
,
it
is
h
o
p
ed
th
at
th
e
teac
h
er
will b
e
m
o
r
e
o
p
en
-
m
in
d
ed
to
s
tu
d
y
th
ese
in
ter
ac
ti
o
n
s
an
d
a
p
p
ly
th
e
m
in
m
ath
e
m
atics lea
r
n
in
g
.
T
h
e
r
esu
lts
o
f
th
e
s
tu
d
y
in
t
h
e
f
o
r
m
o
f
teac
h
er
-
s
tu
d
e
n
t
in
ter
ac
tio
n
s
in
lear
n
in
g
h
av
e
b
ee
n
d
escr
ib
ed
.
T
h
ese
r
esu
lts
h
av
e
b
ee
n
s
u
p
p
o
r
ted
b
y
p
r
ev
i
o
u
s
th
e
o
r
ies
an
d
r
esear
ch
wh
ich
s
tate
th
at
th
ese
in
ter
ac
tio
n
s
ar
e
n
ec
ess
ar
y
an
d
p
lay
a
r
o
l
e
in
l
ea
r
n
in
g
m
ath
em
atics.
W
ith
th
e
r
esu
lts
o
f
th
is
s
tu
d
y
,
it
is
h
o
p
ed
th
at
r
ea
d
er
s
ca
n
u
s
e
it,
esp
ec
ially
teac
h
er
s
o
f
m
ath
em
atics,
to
in
cr
ea
s
e
p
o
s
itiv
e
r
elatio
n
s
h
ip
s
with
s
tu
d
en
ts
th
at
ca
n
h
elp
b
u
ild
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
202
1
:
6
6
0
-
6
6
7
666
an
d
im
p
r
o
v
e
s
tu
d
e
n
ts
’
u
n
d
er
s
t
an
d
in
g
o
f
m
ath
e
m
atics.
T
ea
ch
er
s
ca
n
also
ad
d
lear
n
in
g
m
ed
ia
th
at
ca
n
s
u
p
p
o
r
t
lear
n
in
g
ac
tiv
ities
s
u
ch
as
co
m
p
u
ter
s
,
tab
lets
,
an
d
o
th
e
r
tech
n
o
lo
g
ies
Acc
o
r
d
in
g
to
r
esear
ch
o
n
co
m
p
u
ter
u
s
e
,
tab
lets
ca
n
also
im
p
r
o
v
e
s
tu
d
e
n
ts
'
m
ath
em
atica
l u
n
d
er
s
tan
d
in
g
[
4
5
]
,
[
4
6
]
.
4.
CO
NCLU
SI
O
N
T
h
e
r
esu
lts
o
f
th
is
s
tu
d
y
ar
e
f
o
r
m
s
o
f
teac
h
e
r
-
s
tu
d
en
t
i
n
ter
ac
tio
n
in
m
ath
em
atics
lear
n
in
g
th
at
ca
n
h
elp
s
tu
d
en
ts
b
u
ild
an
d
im
p
r
o
v
e
m
ath
em
atica
l
u
n
d
er
s
tan
d
in
g
.
T
h
ese
r
esu
lts
ca
n
b
e
u
s
ed
b
y
m
ath
em
atics
teac
h
er
s
in
class
r
o
o
m
lear
n
in
g
to
h
el
p
to
lear
n
ac
tiv
ities
b
ec
o
m
e
b
etter
.
T
h
e
f
o
r
m
s
o
f
i
n
ter
ac
tio
n
b
etwe
en
teac
h
er
-
s
tu
d
en
ts
th
at
n
ee
d
to
b
e
k
n
o
wn
b
ased
o
n
th
e
r
esu
lts
o
f
th
is
s
tu
d
y
ar
e
:
1
)
T
h
e
te
ac
h
er
tr
an
s
f
er
s
t
h
e
m
ater
ial
-
s
tu
d
en
ts
p
ay
atten
tio
n
to
th
e
m
ater
ial
;
2
)
Q
u
esti
o
n
s
an
d
an
s
wer
s
in
th
e
m
id
d
le
o
f
th
e
teac
h
e
r
-
s
tu
d
en
ts
;
3
)
T
h
e
teac
h
er
m
ak
e
s
lear
n
in
g
s
tr
ateg
ies
th
at
attr
a
ct
s
tu
d
en
ts
to
b
e
a
ctiv
ely
in
v
o
lv
ed
in
lear
n
i
n
g
;
4
)
T
h
e
teac
h
er
g
iv
es a
n
awa
r
d
-
t
h
e
s
tu
d
en
t r
ec
eiv
es a
n
awa
r
d
.
T
h
e
r
esu
lts
o
f
th
is
s
tu
d
y
g
u
id
e
m
ath
em
atics
teac
h
er
s
in
p
la
n
n
in
g
th
e
im
p
le
m
en
tatio
n
o
f
l
ea
r
n
in
g
in
th
e
class
r
o
o
m
.
I
n
a
d
d
itio
n
t
o
im
p
lem
en
tin
g
ac
tiv
ities
th
at
ar
e
f
u
ll
o
f
i
n
ter
ac
tio
n
s
b
e
twee
n
teac
h
er
s
an
d
s
tu
d
en
ts
,
teac
h
er
s
ca
n
also
a
d
d
lear
n
in
g
m
ed
ia
th
at
ca
n
s
u
p
p
o
r
t
lear
n
in
g
ac
tiv
ities
s
u
ch
a
s
co
m
p
u
ter
s
,
tab
lets
,
an
d
o
th
er
tec
h
n
o
lo
g
ies.
Fo
r
th
e
n
ex
t
r
esear
ch
,
it
is
h
o
p
ed
th
at
th
e
r
esear
ch
er
ca
n
d
escr
ib
e
m
o
r
e
clea
r
ly
ea
ch
in
ter
ac
tio
n
an
d
its
im
p
ac
t
o
n
lear
n
in
g
m
ath
em
atics.
Fu
r
t
h
er
m
o
r
e
,
r
esear
ch
e
r
s
ar
e
ex
p
ec
ted
to
s
h
o
w
t
h
e
wea
k
n
ess
es a
n
d
s
tr
en
g
th
s
o
f
e
ac
h
o
f
th
e
ex
is
tin
g
in
ter
ac
ti
o
n
s
.
RE
F
E
R
E
NC
E
S
[1
]
S
.
D.
Du
T
o
it
a
n
d
G
.
Du
T
o
it
,
“
Lea
rn
e
r
m
e
tac
o
g
n
it
i
o
n
a
n
d
m
a
th
e
m
a
ti
c
s
a
c
h
iev
e
m
e
n
t
d
u
r
in
g
p
ro
b
lem
-
so
lv
in
g
in
a
m
a
th
e
m
a
ti
c
s
c
las
sro
o
m
,
”
J
.
T
r
a
n
sd
isc
i
p
l.
Res
.
S
o
u
t
h
e
rn
Af
ri
c
a
,
v
o
l
.
9
,
n
o
.
3
,
p
p
.
5
0
5
-
5
1
8
,
2
0
1
3
,
d
o
i:
1
0
.
4
1
0
2
/
td
.
v
9
i
3
.
1
9
4
.
[2
]
J.
Ho
d
a
ň
o
v
á
a
n
d
D.
N
o
c
a
r,
“
M
a
t
h
e
m
a
ti
c
s
Im
p
o
rtan
c
e
in
Ou
r
Li
fe
,
”
in
IN
T
ED2
0
1
6
Pro
c
e
e
d
i
n
g
s
,
v
o
l.
1
,
M
a
r
.
2
0
1
6
,
p
p
.
3
0
8
6
-
3
0
9
2
,
d
o
i:
1
0
.
2
1
1
2
5
/
in
t
e
d
.
2
0
1
6
.
0
1
7
2
.
[3
]
B.
Ra
j
Ac
h
a
ry
a
,
“
F
a
c
to
rs
Affe
c
ti
n
g
Difficu
lt
ies
in
Lea
rn
i
n
g
M
a
th
e
m
a
ti
c
s
b
y
M
a
th
e
m
a
ti
c
s
Lea
rn
e
r
s,”
In
t.
J
.
El
e
m
.
Ed
u
c
.
,
v
o
l.
6
,
n
o
.
2
,
p
.
8
,
2
0
1
7
,
d
o
i:
1
0
.
1
1
6
4
8
/
j.
ij
e
e
d
u
.
2
0
1
7
0
6
0
2
.
1
1
.
[4
]
I
.
Ku
sm
a
ry
o
n
o
,
“
Th
e
Im
p
o
rtan
c
e
o
f
M
a
t
h
e
m
a
ti
c
a
l
P
o
we
r
i
n
M
a
th
e
m
a
ti
c
s
Lea
rn
in
g
,
”
in
In
ter
n
a
ti
o
n
a
l
C
o
n
fer
e
n
c
e
o
n
M
a
t
h
e
ma
ti
c
s,
S
c
ien
c
e
,
a
n
d
Ed
u
c
a
ti
o
n
(IC
M
S
E
2
0
1
4
)
,
2
0
1
4
,
p
p
.
M
3
5
-
M
4
0
.
[5
]
I.
Ay
u
wa
n
ti
,
M
a
rsig
i
t,
a
n
d
D.
S
i
sw
o
y
o
,
“
Th
e
d
e
v
e
l
o
p
m
e
n
t
o
f
fu
z
z
y
se
t
t
h
e
o
ry
in
t
h
e
field
o
f
h
e
a
l
th
,
”
I
n
t.
J
.
S
c
i
.
T
e
c
h
n
o
l
.
Res
.
,
v
o
l
.
9
,
n
o
.
4
,
p
p
.
1
0
7
0
-
1
0
7
4
,
2
0
2
0
.
[6
]
A.
Ha
sh
m
i
a
n
d
M
.
S
a
lee
m
,
“
Dia
g
n
o
sis
Bl
o
o
d
Tes
t
fo
r
Li
v
e
r
Dise
a
se
u
sin
g
F
u
z
z
y
L
o
g
ic,”
I
n
t.
J
.
S
c
i.
Ba
sic
Ap
p
l
.
Res
.
,
v
o
l.
2
0
,
n
o
.
1
,
p
p
.
1
5
1
-
1
8
3
,
2
0
1
5
.
[7
]
D.
Ka
rti
k
a
,
R.
L.
G
e
m
a
,
a
n
d
M
.
P
ra
ti
wi
,
“
E
x
p
e
rt
S
y
ste
m
s
f
o
r
I
d
e
n
ti
f
y
in
g
C
h
il
d
re
n
’s
S
e
v
e
re
M
a
ln
u
tri
t
io
n
,
”
J
.
Co
mp
u
t
.
S
c
i
.
In
f
.
T
e
c
h
n
o
l
.
,
v
o
l
.
2
,
p
p
.
2
0
-
2
9
,
Oc
t.
2
0
1
6
.
[8
]
A.
R.
Ra
z
a
k
,
“
Eff
e
c
ti
v
e
Lea
rn
in
g
I
n
tera
c
ti
o
n
s
fo
r
Ac
h
iev
e
m
e
n
t
,”
(in
Ba
h
a
sa
),
J
u
rn
a
l
PIL
AR
,
v
o
l.
5
,
n
o
.
2
,
p
p
.
6
3
-
7
9
,
2
0
1
3
.
[9
]
I.
V.
S
.
M
u
ll
is,
M
.
O.
M
a
rti
n
,
P
.
F
o
y
,
a
n
d
M
.
Ho
o
p
e
r
,
T
IM
S
S
2
0
1
5
I
n
ter
n
a
ti
o
n
a
l
Res
u
lt
in
M
a
th
e
ma
ti
c
s
.
Bo
st
o
n
Co
ll
e
g
e
,
TIM
S
S
&
P
I
RLS
I
n
tern
a
ti
o
n
a
l
S
t
u
d
y
Ce
n
ter
,
2
0
1
6
.
[On
li
n
e
].
A
v
a
il
a
b
le:
h
tt
p
:
//
ti
m
ss
a
n
d
p
irl
s.
b
c
.
e
d
u
/t
ims
s2
0
1
5
/i
n
ter
n
a
ti
o
n
a
l
-
re
su
lt
s
.
[1
0
]
R.
Ro
sn
a
wa
ti
,
“
M
a
th
e
m
a
ti
c
a
l
Re
a
so
n
in
g
Ab
i
li
ti
e
s
o
f
I
n
d
o
n
e
sia
n
Ju
n
io
r
H
o
g
h
S
c
h
o
o
l
S
tu
d
e
n
ts
o
n
TI
M
S
S
2
0
1
1
,”
(i
n
Ba
h
a
sa
)
in
Pro
si
d
in
g
S
e
mi
n
a
r N
a
sio
n
a
l
Pen
e
li
t
ia
n
,
Pen
d
i
d
ika
n
d
a
n
Pen
e
ra
p
a
n
M
IPA
,
2
0
1
3
,
p
p
.
M
1
–
M
6.
[1
1
]
R.
S
id
a
b
u
tar,
“
T
h
e
Eff
o
rts
t
o
I
m
p
ro
v
e
M
a
t
h
e
m
a
ti
c
s
Lea
rn
in
g
Ac
h
iev
e
m
e
n
t
Re
su
lt
s
o
f
Hi
g
h
S
c
h
o
o
l
S
tu
d
e
n
ts
a
s
Re
q
u
ired
b
y
Co
m
p
e
ten
c
y
-
Ba
se
d
Cu
rricu
l
u
m
a
n
d
Les
so
n
Le
v
e
l
-
Ba
se
d
Cu
rricu
lu
m
,
”
J
.
E
d
u
c
.
Pra
c
t
.
,
v
o
l.
7
,
n
o
.
1
5
,
pp
.
1
0
-
1
5
,
2
0
1
6
.
[1
2
]
S
.
D.
Da
v
a
d
a
s
a
n
d
Y.
F
.
Lay
,
“
F
a
c
to
rs
a
ffe
c
ti
n
g
stu
d
e
n
ts’
a
tt
it
u
d
e
to
wa
rd
m
a
th
e
m
a
ti
c
s:
A
stru
c
tu
ra
l
e
q
u
a
ti
o
n
m
o
d
e
li
n
g
a
p
p
r
o
a
c
h
,
”
E
u
ra
sia
J
.
M
a
t
h
.
S
c
i.
T
e
c
h
n
o
l.
Ed
u
c
.
,
v
o
l.
1
4
,
n
o
.
1
,
p
p
.
5
1
7
-
5
2
9
,
2
0
1
8
,
d
o
i:
1
0
.
1
2
9
7
3
/ejm
ste
/8
0
3
5
6
.
[1
3
]
B
.
Ap
ri
li
y
a
n
to
,
D.
R.
S
.
S
a
p
u
tr
o
,
a
n
d
Ri
y
a
d
i,
“
S
t
u
d
e
n
t’s
s
o
c
ial
i
n
t
e
ra
c
ti
o
n
i
n
m
a
th
e
m
a
ti
c
s
lea
rn
in
g
,
”
in
J
o
u
rn
a
l
o
f
Ph
y
sic
s: Co
n
fer
e
n
c
e
S
e
rie
s
,
v
o
l.
9
8
3
,
n
o
.
1
,
2
0
1
8
,
d
o
i:
1
0
.
1
0
8
8
/1
7
4
2
-
6
5
9
6
/
9
8
3
/1
/
0
1
2
1
3
0
.
[1
4
]
P
.
M
c
c
a
rth
y
,
A.
S
i
th
o
le,
P
.
M
c
c
a
rth
y
,
J.
-
P
.
Ch
o
,
a
n
d
E.
G
y
a
n
,
“
Tea
c
h
e
r
Qu
e
stio
n
in
g
S
trate
g
ies
i
n
M
a
th
e
m
a
ti
c
a
l
Clas
sro
o
m
Disc
o
u
rse
:
A
Ca
se
S
tu
d
y
o
f
Two
G
ra
d
e
Ei
g
h
t
Tea
c
h
e
rs
in
Ten
n
e
ss
e
e
,
USA,
”
J
.
Ed
u
c
.
Pra
c
t.
,
v
o
l.
7
,
n
o
.
2
1
,
p
p
.
8
0
-
8
9
,
2
0
1
6
.
[1
5
]
C.
D.
Bru
c
e
,
“
S
t
u
d
e
n
t
In
tera
c
ti
o
n
in
t
h
e
M
a
th
C
las
sro
o
m
:
S
tea
li
n
g
Id
e
a
s
o
r
Bu
il
d
i
n
g
U
n
d
e
rsta
n
d
in
g
,
”
W
h
a
t
W
o
rk
s?
Res
e
a
rc
h
in
to
Pra
c
ti
c
e
,
T
h
e
Li
ter
a
c
y
a
n
d
Nu
m
e
ra
c
y
S
e
c
re
taria
t
,
O
n
tario
,
p
p
.
1
-
4
,
Ja
n
.
2
0
0
7
.
[1
6
]
R.
C.
P
ian
ta,
“
Tea
c
h
e
r
–
S
t
u
d
e
n
t
In
tera
c
ti
o
n
s,”
Po
l
icy
In
si
g
h
ts
fro
m
Beh
a
v
.
Bra
in
S
c
i.
,
v
o
l
.
3
,
n
o
.
1
,
p
p
.
9
8
-
1
0
5
,
2
0
1
6
,
d
o
i:
1
0
.
1
1
7
7
/
2
3
7
2
7
3
2
2
1
5
6
2
2
4
5
7
.
[1
7
]
G
.
Bru
ti
a
n
,
“
M
e
tap
h
il
o
s
o
p
h
y
i
n
t
h
e
sy
ste
m
s o
f
m
e
tath
e
o
ries
,
”
M
e
t
a
p
h
il
o
s
o
p
h
y
,
v
o
l.
4
3
,
n
o
.
3
,
p
p
.
2
9
4
-
3
0
5
,
2
0
1
2
.
[1
8
]
R.
Wi
k
a
n
d
a
ru
,
“
M
e
tap
h
y
sic
s o
f
i
n
fo
rm
a
ti
o
n
in
Je
a
n
Ba
u
d
ril
lard
'
s
t
h
o
u
g
h
t
:
Th
e
c
o
n
tex
t
u
a
li
z
a
ti
o
n
wi
t
h
th
e
li
n
k
a
g
e
o
f
m
e
d
ia an
d
p
o
li
t
ics
in
I
n
d
o
n
e
sia
,”
(in
Ba
h
a
sa
),
J
.
Fi
lsa
f
a
t
,
v
o
l
.
2
7
,
n
o
.
2
,
p
p
.
2
6
4
-
2
8
9
,
2
0
1
8
,
d
o
i:
1
0
.
2
2
1
4
6
/j
f
.
3
2
8
0
4
.
[1
9
]
C.
M
o
u
sta
k
a
s,
P
h
e
n
o
me
n
o
l
o
g
ica
l
Res
e
a
rc
h
M
e
t
h
ods
.
S
AG
E
P
u
b
l
ica
ti
o
n
s,
I
n
c
,
1
9
9
4
.
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
Tea
ch
er
-
s
tu
d
en
t in
tera
ctio
n
in
ma
th
ema
tics
lea
r
n
in
g
(
I
r
ma
A
yu
w
a
n
ti
)
667
[2
0
]
Y.
C.
G
e
n
c
tu
rk
,
“
Tea
c
h
e
rs’
m
a
th
e
m
a
ti
c
a
l
k
n
o
wle
d
g
e
f
o
r
tea
c
h
in
g
,
in
stru
c
ti
o
n
a
l
p
ra
c
ti
c
e
s,
a
n
d
st
u
d
e
n
t
o
u
tco
m
e
s
,
”
Diss
e
rtatio
n
,
Un
iv
e
rsity
o
f
I
ll
in
o
i
s a
t
Urb
a
n
a
-
Ch
a
m
p
a
ig
n
,
Ur
b
a
n
a
,
Ill
in
o
is,
2
0
1
2
.
[2
1
]
M
.
S
h
a
h
ril
l,
“
Re
v
iew
o
f
tea
c
h
e
r
q
u
e
stio
n
in
g
i
n
m
a
th
e
m
a
ti
c
s
c
las
s
ro
o
m
s,”
Arti
c
.
I
n
t.
J
.
H
u
ma
n
it
.
S
o
c
.
S
c
i.
,
v
o
l.
3
,
n
o
.
1
7
,
p
p
.
2
2
4
-
2
3
1
,
2
0
1
3
.
[2
2
]
S
.
P
a
p
a
d
a
k
i
s
,
M
.
K
a
l
o
g
i
a
n
n
a
k
i
s
,
a
n
d
N
.
Z
a
r
a
n
i
s
,
“
Im
p
r
o
v
i
n
g
M
a
t
h
e
m
a
t
ic
s
Te
a
c
h
i
n
g
i
n
K
i
n
d
e
r
g
a
r
t
e
n
w
i
t
h
R
e
a
l
i
s
t
i
c
M
a
t
h
e
m
a
t
ic
a
l
E
d
u
c
a
t
i
o
n
,
”
E
a
r
ly
Ch
i
l
d
.
E
d
u
c
.
J
.
,
v
o
l
.
4
5
,
n
o
.
3
,
p
p
.
3
6
9
-
3
7
8
,
2
0
1
7
,
d
o
i
:
1
0
.
1
0
0
7
/
s
1
0
6
4
3
-
015
-
0
7
6
8
-
4.
[2
3
]
M
.
Ak
i
b
a
a
n
d
G
.
Li
a
n
g
,
“
Eff
e
c
ts
o
f
tea
c
h
e
r
p
r
o
fe
ss
io
n
a
l
lea
rn
in
g
a
c
ti
v
it
ies
o
n
stu
d
e
n
t
a
c
h
iev
e
m
e
n
t
g
r
o
wth
,
”
J
.
Ed
u
c
.
Res
.
,
v
o
l.
1
0
9
,
n
o
.
1
,
p
p
.
9
9
-
1
1
0
,
2
0
1
6
,
d
o
i:
1
0
.
1
0
8
0
/
0
0
2
2
0
6
7
1
.
2
0
1
4
.
9
2
4
4
7
0
.
[2
4
]
Y.
Co
p
u
r
-
G
e
n
c
tu
rk
,
“
Th
e
Eff
e
c
ts
o
f
Ch
a
n
g
e
s
in
M
a
th
e
m
a
ti
c
a
l
Kn
o
wle
d
g
e
o
n
Tea
c
h
i
n
g
:
A
Lo
n
g
i
tu
d
in
a
l
S
tu
d
y
o
f
Tea
c
h
e
rs’ Kn
o
wle
d
g
e
a
n
d
I
n
stru
c
ti
o
n
Ya
se
m
in
,
”
J
.
Res
.
M
a
th
.
Ed
u
c
.
,
v
o
l.
4
6
,
n
o
.
3
,
p
p
.
2
8
0
-
3
3
0
,
2
0
1
5
.
[2
5
]
W.
Th
a
l
h
e
ime
r,
“
Th
e
Lea
rn
i
n
g
Be
n
e
fit
s
o
f
Q
u
e
stio
n
s,”
Wo
r
k
-
le
a
rn
in
g
Re
se
a
rc
h
,
No
v
.
2
0
1
4
.
[O
n
li
n
e
].
Av
a
il
a
b
le
:
ww
w.wo
rk
lea
rn
in
g
.
c
o
m
/ca
talo
g
.
h
tml
.
[2
6
]
Z.
F
.
Ko
ç
a
k
,
R
.
Bo
z
a
n
,
a
n
d
Ö.
I
şik
,
“
Th
e
imp
o
rta
n
c
e
o
f
g
ro
u
p
wo
rk
i
n
m
a
th
e
m
a
ti
c
s,”
in
Pr
o
c
e
d
ia
-
S
o
c
ia
l
a
n
d
Beh
a
v
io
r
a
l
S
c
ie
n
c
e
s
,
v
o
l
.
1
,
n
o
.
1
,
2
0
0
9
,
p
p
.
2
3
6
3
-
2
3
6
5
,
d
o
i:
1
0
.
1
0
1
6
/j
.
sb
sp
r
o
.
2
0
0
9
.
0
1
.
4
1
4
.
[2
7
]
L.
Do
n
g
,
W.
T
.
S
e
a
h
,
a
n
d
D.
Cl
a
rk
e
,
“
P
e
d
a
g
o
g
ica
l
ten
si
o
n
s
i
n
te
a
c
h
e
r’s
q
u
e
stio
n
in
g
p
ra
c
ti
c
e
s
in
t
h
e
m
a
th
e
m
a
ti
c
s
c
las
sro
o
m
:
A
c
a
se
in
m
a
in
lan
d
C
h
in
a
,
”
E
u
ra
si
a
J
.
M
a
th
.
S
c
i.
T
e
c
h
n
o
l.
Ed
u
c
.
,
v
o
l.
1
4
,
n
o
.
1
,
p
p
.
1
6
7
-
1
8
1
,
2
0
1
8
,
d
o
i
:
1
0
.
1
2
9
7
3
/ejm
ste
/7
9
6
3
0
.
[2
8
]
E.
Afa
ri,
“
Tea
c
h
in
g
m
a
th
e
m
a
ti
c
s
in
g
a
m
e
lea
rn
in
g
e
n
v
iro
n
m
e
n
t,
”
In
t.
Rev
.
Co
n
tem
p
.
L
e
a
rn
.
Res
.
,
v
o
l.
1
,
n
o
.
1
,
p
p
.
3
3
-
4
5
,
S
e
p
.
2
0
1
2
,
d
o
i:
1
0
.
1
2
7
8
5
/i
rc
lr/
0
1
0
1
0
4
.
[2
9
]
L.
Co
l
g
a
n
,
“
M
a
k
in
g
M
a
t
h
Ch
il
d
r
e
n
Wi
ll
L
o
v
e
:
Bu
il
d
in
g
P
o
siti
v
e
M
a
th
it
u
d
e
s
to
Im
p
ro
v
e
S
t
u
d
e
n
t
Ac
h
iev
e
m
e
n
t
in
M
a
th
e
m
a
ti
c
s,”
W
h
a
t
W
o
rk
s?
Res
e
a
rc
h
in
t
o
Pr
a
c
ti
c
e
,
S
tu
d
e
n
t
Ac
h
i
e
v
e
m
e
n
t
Div
isio
n
,
O
n
tario
,
Au
g
.
2
0
1
4
.
[3
0
]
E.
S
in
a
y
a
n
d
A.
Na
h
o
r
n
ick
,
“
Tea
c
h
in
g
a
n
d
lea
rn
i
n
g
m
a
th
e
m
a
ti
c
s
re
se
a
r
c
h
se
ries
I
:
Eff
e
c
ti
v
e
in
stru
c
ti
o
n
a
l
stra
teg
ies
,
”
(Re
se
a
rc
h
Re
p
o
rt
No
.
1
6
/
1
7
-
08)
,
T
o
ro
n
to
,
On
tari
o
,
Ca
n
a
d
a
:
To
r
o
n
t
o
District
S
c
h
o
o
l
B
o
a
rd
,
2
0
1
6
.
[3
1
]
M
.
Co
n
sta
n
ti
n
e
,
C.
M
u
sin
g
a
fi,
a
n
d
K.
E.
M
u
ra
n
d
a
,
“
S
t
u
d
e
n
ts
a
n
d
Qu
e
stio
n
in
g
:
A
Re
v
iew
o
f
th
e
Ro
le
P
lay
e
d
b
y
S
tu
d
e
n
ts
G
e
n
e
ra
ted
Qu
e
stio
n
s
i
n
th
e
Tea
c
h
in
g
a
n
d
Lea
rn
in
g
P
ro
c
e
ss
,
”
S
tu
d
.
S
o
c
.
S
c
i.
Hu
m
a
n
it
.
,
v
o
l.
1
,
n
o
.
3
,
p
p
.
1
0
1
-
1
0
7
,
2
0
1
4
.
[3
2
]
J.
A
.
S
u
y
o
Ve
g
a
e
t
a
l
.
,
“
Lea
rn
in
g
S
trate
g
ies
i
n
M
a
t
h
e
m
a
ti
c
s
F
o
r
T
h
e
P
a
rti
c
ip
a
n
ts
o
f
a
n
Altern
a
ti
v
e
Ba
sic
Ed
u
c
a
ti
o
n
Ce
n
tre,”
In
t.
J
.
S
c
i.
T
e
c
h
n
o
l.
Res
.
,
v
o
l
.
8
,
n
o
.
1
1
,
p
p
.
8
2
-
8
5
,
2
0
1
9
.
[3
3]
J.
Di
F
a
tt
a
,
S
.
G
a
rc
ia,
a
n
d
S
.
G
o
r
m
a
n
,
“
In
c
re
a
sin
g
S
tu
d
e
n
t
Lea
rn
i
n
g
I
n
M
a
t
h
e
m
a
ti
c
s
Wi
th
Th
e
Us
e
o
f
C
o
ll
a
b
o
ra
ti
v
e
Tea
c
h
in
g
S
trate
g
ies
,
”
M
a
ste
r
Th
e
sis,
S
a
in
t
Xa
v
ier Un
i
v
e
rsity
,
C
h
ic
a
g
o
,
Il
li
n
o
is,
2
0
0
9
.
[3
4
]
C.
Weg
n
e
r,
L.
M
in
n
a
e
rt,
a
n
d
F
.
S
treh
lk
e
,
“
T
h
e
imp
o
rtan
c
e
o
f
lea
rn
in
g
stra
teg
ies
a
n
d
h
o
w
th
e
p
r
o
j
e
c
t
‘Ko
lu
m
b
u
s
-
Kid
s’
p
ro
m
o
tes
th
e
m
su
c
c
e
ss
fu
ll
y
,
”
Eu
ro
p
e
a
n
J
o
u
r
n
a
l
o
f
S
c
ien
c
e
a
n
d
M
a
th
e
ma
ti
c
s
Ed
u
c
a
ti
o
n
,
v
o
l.
1
,
n
o
.
3
,
p
p
.
1
3
7
-
1
4
3
2
0
1
3
.
[3
5
]
O.
Isa
iah
a
n
d
O.
O.
M
a
b
e
l,
“
E
ffe
c
ts
o
f
Co
r
p
o
ra
l
P
u
n
ish
m
e
n
t
o
n
Ac
a
d
e
m
ic
Attain
m
e
n
t
o
f
S
e
c
o
n
d
a
ry
S
c
h
o
o
l
S
tu
d
e
n
ts,”
I
n
ter
n
a
ti
o
n
a
l
J
.
I
n
n
o
v
.
Ed
u
c
.
,
v
o
l.
6
,
n
o
.
2
,
p
p
.
1
2
5
-
1
3
4
,
2
0
1
8
.
[3
6
]
I.
Ah
m
a
d
,
H.
S
a
i
d
,
a
n
d
F
.
Kh
a
n
,
“
Eff
e
c
t
o
f
c
o
rp
o
ra
l
p
u
n
ish
m
e
n
t
o
n
stu
d
e
n
t
s’
m
o
ti
v
a
ti
o
n
a
n
d
c
las
sro
o
m
lea
rn
i
n
g
,
”
Rev
.
Eu
r.
S
tu
d
.
,
v
o
l.
5
,
n
o
.
4
,
p
p
.
1
3
0
-
1
3
4
,
2
0
1
3
,
d
o
i:
1
0
.
5
5
3
9
/res
.
v
5
n
4
p
1
3
0
.
[3
7
]
L.
Clau
d
iu
a
n
d
C.
Lan
g
a
,
“
Re
wa
rd
s
An
d
P
u
n
is
h
m
e
n
ts
R
o
le
In
Te
a
c
h
e
r
-
S
tu
d
e
n
t
Re
latio
n
sh
i
p
F
ro
m
Th
e
M
e
n
to
r
’s
P
e
rsp
e
c
ti
v
e
,
”
Acta
Di
d
a
c
t.
Na
p
o
c
e
n
sa
,
v
o
l.
7
,
n
o
.
4
,
p
p
.
7
-
1
2
,
2
0
1
4
.
[3
8
]
M
.
I.
Ileg
b
u
si,
“
An
a
n
a
ly
sis
o
f
t
h
e
ro
le
o
f
re
wa
rd
s
a
n
d
p
u
n
ish
m
e
n
t
i
n
m
o
ti
v
a
ti
n
g
sc
h
o
o
l
lea
rn
in
g
,
”
In
f.
S
y
st.
De
v
.
In
fo
rm
a
t
ics
,
v
o
l.
4
,
n
o
.
1
,
p
p
.
3
5
-
3
8
,
2
0
1
3
.
[3
9
]
M
.
S
h
a
h
b
a
z
Arif
a
n
d
M
.
S
h
a
b
a
n
Ra
fi,
“
Eğ
it
imd
e
Ku
ra
m
v
e
Uy
g
u
l
a
m
a
,
”
J
o
u
rn
a
l
T
h
e
o
ry
Pra
c
t.
Ed
u
c
.
,
v
o
l.
3
,
n
o
.
2
,
p
p
.
1
7
1
-
1
8
0
,
2
0
0
7
.
[4
0
]
S
.
I
.
Ak
h
ta
r
a
n
d
A.
G
.
Aw
a
n
,
“
Th
e
imp
a
c
t
o
f
c
o
rp
o
ra
l
p
u
n
is
h
m
e
n
t
o
n
stu
d
e
n
ts’
p
e
rfo
rm
a
n
c
e
in
p
u
b
li
c
sc
h
o
o
ls
,”
Glo
b
a
l
J
o
u
rn
a
l
o
f
M
a
n
a
g
e
me
n
t,
S
o
c
ia
l
S
c
ien
c
e
s a
n
d
Hu
m
a
n
i
ti
e
s,
v
o
l
4
,
n
o
.
3
,
p
p
.
6
0
6
-
6
2
1
,
2
0
1
8
.
[4
1
]
G
.
S
.
C
h
in
g
,
“
Lo
o
k
i
n
g
i
n
to
t
h
e
i
ss
u
e
s
o
f
re
wa
rd
s
a
n
d
p
u
n
ish
m
e
n
t
in
st
u
d
e
n
ts,”
In
t.
J
.
Res
.
S
tu
d
.
P
sy
c
h
o
l.
,
v
o
l.
1
,
n
o
.
2
,
p
p
.
2
9
-
3
8
,
Ja
n
.
2
0
1
2
,
d
o
i:
1
0
.
5
8
6
1
/i
jrs
p
.
2
0
1
2
.
v
1
i
2
.
4
4
.
[4
2
]
E.
S
tan
,
“
Ab
o
u
t
Ru
les
,
P
u
n
is
h
m
e
n
ts
a
n
d
Re
wa
rd
s
in
Ed
u
c
a
ti
o
n
,
”
Pro
c
e
d
ia
-
S
o
c
.
Beh
a
v
.
S
c
i
.
,
v
o
l.
1
1
2
,
p
p
.
1
1
6
0
-
1
1
6
6
,
F
e
b
.
2
0
1
4
,
d
o
i:
1
0
.
1
0
1
6
/j
.
s
b
sp
ro
.
2
0
1
4
.
0
1
.
1
2
8
0
.
[4
3
]
M
.
M
o
sle
h
a
n
d
M
.
S
a
p
i
y
a
n
Ba
b
a
,
“
Ov
e
rv
iew
o
f
Tra
d
it
i
o
n
a
l
N
o
te
T
a
k
in
g
,
”
Ed
u
c
.
Psy
c
h
o
l.
Rev
.
,
p
p
.
1
-
2
8
,
2
0
1
3
.
[4
4
]
E.
S
u
ry
a
a
n
d
E.
No
v
ira
Rizk
in
ta,
“
Eff
e
c
t
o
f
G
ra
n
ti
n
g
Re
wa
rd
o
n
L
e
a
rn
in
g
Ou
tco
m
e
s o
f
M
a
th
e
m
a
ti
c
s
in
Clas
s
IV o
f
P
u
b
l
ic P
rima
ry
S
c
h
o
o
l
0
1
4
6
8
0
o
f
Bu
n
t
u
P
a
n
e
,
”
I
n
t.
J
.
S
c
i.
Ba
sic
A
p
p
l.
Res
.
,
v
o
l.
3
4
,
n
o
.
1
,
p
p
.
1
0
1
-
1
1
0
,
2
0
1
7
.
[4
5
]
S
.
P
a
p
a
d
a
k
is,
M
.
Ka
lo
g
ian
n
a
k
is
,
a
n
d
N.
Zara
n
is,
“
Th
e
e
ffe
c
ti
v
e
n
e
s
s
o
f
c
o
m
p
u
ter
a
n
d
tab
let
a
ss
isted
in
terv
e
n
t
io
n
i
n
e
a
rly
c
h
il
d
h
o
o
d
stu
d
e
n
ts’
u
n
d
e
rst
a
n
d
in
g
o
f
n
u
m
b
e
rs.
An
e
m
p
iri
c
a
l
stu
d
y
c
o
n
d
u
c
ted
in
G
re
e
c
e
,
”
Ed
u
c
.
In
f.
T
e
c
h
n
o
l.
,
v
o
l.
2
3
,
n
o
.
5
,
p
p
.
1
8
4
9
-
1
8
7
1
,
2
0
1
8
,
d
o
i:
1
0
.
1
0
0
7
/s1
0
6
3
9
-
0
1
8
-
9
6
9
3
-
7.
[4
6
]
S
.
P
a
p
a
d
a
k
is
,
M
.
Ka
lo
g
ian
n
a
k
is
,
a
n
d
N.
Zara
n
is,
“
Co
m
p
a
ri
n
g
Tab
lets
a
n
d
P
Cs
in
tea
c
h
i
n
g
M
a
th
e
m
a
ti
c
s:
An
a
tt
e
m
p
t
to
imp
r
o
v
e
M
a
th
e
m
a
ti
c
s
Co
m
p
e
ten
c
e
in
Early
C
h
il
d
h
o
o
d
Ed
u
c
a
ti
o
n
,
”
Pre
sc
h
.
Prim.
E
d
u
c
.
,
v
o
l.
4
,
n
o
.
2
,
p
.
2
4
1
,
2
0
1
6
,
d
o
i:
1
0
.
1
2
6
8
1
/p
p
e
j.
8
7
7
9
.
Evaluation Warning : The document was created with Spire.PDF for Python.