In
te
r
n
ation
a
l Jou
rn
al
o
f E
v
al
u
a
t
i
on
a
n
d
R
e
se
arc
h
in
Ed
u
c
ation
(
IJERE
)
V
o
l.7,
N
o.2,
Ju
n
e
20
1
8
,
pp. 132~
141
ISSN
: 2252-
88
22,
D
O
I
:
10.11
59
1
/ijer
e
.
v
7
.
i
2
.13
0
5
4
132
Jou
rn
a
l
h
o
me
pa
ge
: h
t
t
p
:/
/
i
a
e
s
core.
c
om
/
j
ou
rna
l
s
/in
dex
.
p
h
p
/IJERE
The R
o
le of Jour
nal
Writing in
Se
n
ior High School Students’
Attitude toward Mathematics
Ivee
K.
Guce
Mathematics
Depart
m
e
nt
,
D
e
L
a
S
al
l
e
L
i
p
a,
P
hi
li
pp
i
n
es
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
ce
i
v
e
d
May
3
, 2018
Re
vise
d Ma
y
2
1
, 201
8
Ac
ce
p
t
ed
M
a
y
2
9
,
2
018
The
stud
y
in
ve
s
t
ig
a
t
e
d
t
he
i
n
f
lu
e
n
c
e
o
f
jo
urn
a
l
wri
t
in
g
on
t
he
s
e
nio
r
h
ig
h
sc
ho
ol
s
tud
e
n
t
s’
a
tt
itud
e
to
wa
rd
m
a
t
he
ma
tic
s
.
A
m
i
xe
d
-
me
th
o
d
a
p
proach
,
part
icu
l
arly
t
h
e
c
on
vergen
t
p
a
ral
l
e
l
d
es
ig
n
,
w
as
u
sed
i
n
t
his
s
tu
dy.
Using
Scale
on
A
ttitud
e
T
oward
Mat
h
emat
i
c
s
(SA
T
M)
(
Guce
&
Tal
e
ns,
201
3),
th
e
st
udents’
at
titud
e
t
oward
t
h
e
sub
j
ect
w
as
m
easured
i
n
f
o
ur
s
ubs
c
a
l
e
s—liki
ng
or
d
is
likin
g
m
ath
e
m
a
ti
cs,
t
e
nd
e
n
cy
t
o
en
gag
e
i
n
or
a
v
o
i
d
m
ath
e
m
atical
acti
v
iti
e
s
,
b
eli
e
f
t
h
at
o
n
e
i
s
good
or
b
ad
i
n
m
a
t
h
em
ati
c
s
an
d
b
el
ie
f
t
h
a
t
mathematics
i
s
u
se
f
u
l
or
u
se
le
ss.
U
sing
f
oc
u
s
g
ro
up
d
isc
u
ssion
,
t
he
i
ns
ights
of
t
he
s
tudent
s
on
j
ourna
l
w
r
itin
g
as
a
m
athemat
i
cs
c
l
a
ss
a
ct
iv
ity
w
ere
gat
h
ered.
Res
u
lt
s
usin
g
q
u
an
titative
dat
a
r
ev
e
a
l
e
d
po
si
tiv
e
s
ig
n
i
f
i
cant
diff
erences
i
n
th
e
attitu
de
o
f
t
h
e
res
pon
den
t
s
in
t
erm
s
o
f
(i
)
lik
i
ng
m
a
th
ematics
and
(i
i)
h
avin
g
the
t
e
nden
c
y
t
o
e
ng
ag
e
i
n
m
ath
e
m
a
t
i
cal
acti
v
iti
e
s
.
T
his
ali
gned
w
i
th
t
he
r
es
ul
t
in
t
h
e
f
oc
u
s
g
ro
up
di
s
cus
s
i
o
n
wh
ich
sug
g
e
s
te
d
th
a
t
s
tu
d
e
nts
pe
rc
e
i
ve
j
o
u
r
na
l
writ
in
g
a
s
a
h
e
l
p
f
ul
t
oo
l
for
them
t
o
enj
o
y
m
a
th
em
atics
and
en
g
a
ge
i
n
i
t
.
Th
e
act
ivity,
th
us,
m
a
y
b
e
reg
a
rded
a
s
a
m
eans
to im
p
rove
s
t
uden
t
s
’
a
t
tit
u
d
e toward mat
he
matics.
K
eyw
ord
:
A
ttit
u
d
e
Jour
nal
Lea
r
ni
ng
R
e
fl
e
c
t
i
on
W
r
it
ing
Co
pyri
gh
t © 2
018 In
stitute
of
Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
Ivee K. Guce,
P
h
.
D
.
Ma
them
at
ics De
partm
e
n
t
,
D
e
L
a
S
a
l
l
e
L
ip
a
,
Pr
es
.
J
.
P
.
Laurel
Highw
ay,
Lipa
C
ity,
Bata
n
g
as,
P
h
i
l
ip
p
i
ne
s.
Em
ail:
i
v
e
e
.
g
u
c
e@d
l
s
l
.
e
du.
p
h
1.
I
N
TR
OD
U
C
TI
O
N
T
e
a
c
h
e
r
s
a
r
e
o
f
t
e
n
c
o
n
c
e
r
n
e
d
,
i
f
n
o
t
f
r
u
s
t
r
a
t
e
d
,
a
b
o
u
t
t
h
e
i
r
s
t
ude
n
t
s’
d
i
s
li
ke
o
r
fear
o
f
ma
them
at
i
c
s.
N
o
t
on
l
y
i
s
m
a
them
at
ics
o
f
te
n
view
e
d
a
s
an
i
rrele
v
a
n
t
a
n
d
u
n
p
o
p
u
l
ar
s
ub
ject
[
1]
,
bu
t
lac
k
o
f
ski
l
l
i
n
mat
h
e
m
a
t
i
c
s
i
s
s
e
l
do
m
th
ough
t
of
a
s
d
i
st
u
r
b
i
ng
[
2
]
.
Att
e
mp
t
s
h
a
ve
a
l
r
eady
be
e
n
m
a
d
e
for
t
h
e
p
u
rp
ose
of
impro
v
i
n
g e
ith
e
r
stude
nt e
n
g
a
g
em
ent [
3
]-[4]
or
att
i
t
u
de
t
ow
ard
t
h
e subject
[
5
]-[9].
Lit
e
ra
tu
re
p
ro
vi
d
e
s
evi
d
e
n
c
e
th
at
t
h
e
a
tt
itu
d
e
o
f
st
ud
en
t
t
o
wa
r
d
ma
t
h
e
m
a
t
ic
s
p
l
a
y
s
a
n
e
ssen
tia
l
ro
le
in
l
ea
rni
n
g
t
h
e
su
b
j
e
c
t.
A
tt
itu
de
t
ow
ar
d
t
h
e
s
u
bj
e
c
t
t
o
g
e
t
h
e
r
w
i
t
h
ac
a
d
em
ic
m
o
t
iva
t
io
n
a
nd
i
n
te
l
l
i
g
enc
e
qu
o
t
ie
nt
p
re
di
c
t
m
a
t
he
ma
t
i
c
s
a
chie
vem
e
n
t
[
9]
-[1
1
].
A
s
l
e
arne
rs
hav
i
ng
th
e
i
r
o
w
n
pe
rso
n
a
l
b
e
l
i
efs,
e
m
o
ti
o
n
s,
and
view
s,
s
t
u
den
t
s’
a
tt
it
u
d
e
is
p
a
r
t
a
n
d
par
cel
o
f
the
l
e
ar
ni
n
g
proc
es
s
[12].
T
h
e
i
r
m
o
tiva
t
io
n
t
o
l
e
a
rn
d
ri
ve
s
them
t
o
a
c
h
ie
v
e
.
H
e
nc
e,
a
tt
i
t
ude
c
a
n
no
t
be
s
epar
ate
d
f
r
o
m
lea
r
n
in
g
as
t
he
y
are
ac
quire
d
t
h
r
o
ug
h
the
process
of
l
e
a
rn
i
ng i
t
se
lf
[
13].
A
t
t
itu
de
t
ow
ar
d m
a
them
at
ics,
as d
e
fine
d
by Ma an
d
K
is
h
o
r [1
4],
is
a
n “
a
ggr
ega
t
e
d
m
ea
s
u
r
e
of
li
k
i
n
g
a
n
d
di
sli
k
in
g
of
m
a
t
h
e
ma
t
i
c
s,
a
t
end
e
n
c
y
to
e
ng
a
g
e
i
n
o
r
a
v
oid
m
a
t
h
em
atica
l
a
c
t
i
v
i
tie
s,
a
b
el
ie
f
t
h
a
t
one
i
s
go
o
d
o
r
ba
d
a
t
m
a
t
he
ma
ti
c
s
a
nd
a
be
lie
f
t
h
at
m
athem
a
t
i
cs
i
s
u
s
e
fu
l
or
u
se
less.”
A
c
c
o
rdi
ng
t
o
T
h
u
rl
o
w
[
8]
,
a
t
ti
t
u
d
e
i
s
e
v
en
m
o
r
e
p
r
on
ounc
ed
i
n
t
h
e
are
a
o
f
ma
th
e
m
a
t
i
c
s.
A
t
tem
p
ts t
o impr
o
v
e
a
tti
tu
de t
ow
a
r
d the
s
u
b
j
ec
t
have
l
o
n
g
bee
n
d
o
n
e
in
t
he
p
a
s
t.
T
h
e
m
o
s
t
w
i
de
ly
h
e
l
d
of
w
hi
ch
is
t
h
e
u
se
o
f
w
r
iti
ng
l
ike
ma
th
d
iar
i
e
s
,
reflect
i
o
n,
a
nd jo
urna
l
w
r
it
i
n
g
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJERE
I
S
S
N
:
2252-
88
22
T
h
e
Role
of
Jo
urn
a
l
Wri
tin
g i
n
Se
n
i
or
H
i
g
h
Sch
o
o
l S
t
ude
n
t
s’ Atti
tude
t
o
ward
M
a
the
m
a
t
i
c
s(
Ive
e
K. G
u
ce)
13
3
The
stu
dy
o
n
t
he
u
se
o
f
jo
u
r
na
ls
h
a
s
b
ec
o
m
e
a
n
i
m
porta
nt
v
i
e
w
p
o
i
n
t
i
n
a
n
effor
t
t
o
c
h
an
ge
t
he
att
itu
de
o
f
st
u
d
en
ts
t
ow
a
r
d
m
a
them
at
ics.
T
he
s
tu
die
s
o
f
V
a
n
D
e
r
M
ol
en
[
1
5
]
a
n
d
La
utu
l
i
p
pe
&
L
a
u
t
u
li
p
p
e
[1
6]
s
how
ed
t
hat
i
n
c
l
us
i
on
o
f
w
rit
i
n
g
a
c
t
i
v
i
t
ie
s
in
t
h
e
m
at
hem
a
ti
cs
c
urri
c
u
l
u
m
is
b
e
n
eficia
l
t
o
b
oth
st
ude
n
t
and
t
e
ac
h
e
r.
J
our
nal
w
r
i
t
i
n
g
cre
a
tes
a
su
pp
ort
i
ve
c
lass
a
tmos
ph
er
e
[
17]
a
nd
i
m
p
r
ove
d
the
c
l
a
ssr
oom
env
i
ro
nm
en
t
so
t
hat
a
n
x
i
e
t
y
w
a
s
less
l
i
ke
ly
t
o
in
ter
f
er
e
w
i
t
h
l
ea
rn
in
g
[
18]
.
N
a
h
r
gang
a
n
d
P
e
terson
[1
9
]
w
ere
succe
ssfu
l
i
n
u
s
ing
jour
na
l
w
r
it
i
n
g
i
n
h
e
l
pin
g
s
tu
de
nt
s
e
x
p
r
ess
a
n
x
i
e
t
i
e
s
a
b
out
t
h
e
s
ubje
c
t
whi
l
e
M
i
lle
r
a
n
d
En
gla
n
d
[
20]
u
se
d
t
h
e
a
c
t
i
vi
ty
t
o
de
ter
m
in
e
the
pro
b
lem
s
e
nco
u
n
tere
d
by
t
h
eir
stu
d
e
n
t
s
i
n
t
h
e
lear
nin
g
o
f
ma
them
at
i
c
s.
A
ccor
d
in
g
to
F
ord
[2
1],
att
itu
de
t
ow
ard
ma
t
h
e
m
a
t
i
c
s
i
m
prove
s
as
s
t
ude
n
t
s
be
c
o
m
e
l
ess
anx
i
ou
s.
J
o
u
r
n
a
l
w
ri
ti
n
g
i
n
a
m
a
them
at
ics
class
ha
s
bee
n
f
oun
d
to
r
e
duce
ma
th
a
n
x
ie
t
y
r
esu
l
tin
g
to
a
n
impro
v
e
d
a
tt
itu
de
tow
ar
d t
h
e
s
u
bjec
t [
1
7],
[21]-[
22].
The
s
t
ude
n
t
s’
o
ppor
tun
i
ty
t
o
c
o
m
m
unica
t
e
t
heir
f
eel
i
n
g
s
a
n
d
o
p
i
ni
on
s
t
o
t
he
ir
t
e
a
c
he
r
is
o
n
e
impor
ta
nt fea
tur
e
o
f jo
urna
l
w
r
itin
g.
I
t
b
u
i
l
d
s
a
c
o
n
n
ect
i
o
n be
tw
e
e
n
t
he
t
eac
her an
d the
st
ude
n
t
s [23]
-[26] a
n
d
affords
t
h
e
op
por
tun
i
t
y
t
o
c
o
mm
unica
te
m
a
t
hem
a
t
i
ca
l
i
d
e
a
s
,
w
h
i
c
h
is
o
ne
o
f
the
goals
stressed
in
N
CT
M'
s
st
a
ndard
s
[2
7].
Co
un
trym
an
[
25]
u
se
d
j
our
n
a
l
w
r
iti
ng
a
s
a
m
e
a
ns
t
o
ha
ve
c
on
t
i
n
u
i
n
g
d
i
a
log
u
e
s
w
i
t
h
s
t
u
d
e
n
t
s
and
a
s
a
v
eh
ic
l
e
f
or
s
t
u
den
t
s
elf-
ex
press
i
o
n
.
S
t
ude
n
t
s
w
h
o
fee
l
h
e
s
i
t
a
n
t
t
o
a
s
k
q
u
e
s
t
i
o
n
s
a
r
e
o
f
t
e
n
w
i
l
l
i
n
g
t
o
w
r
ite
w
ha
t
the
y
w
an
t
t
o
t
el
l
t
h
e
t
e
ac
her
[28].
Thro
u
g
h
the
j
our
na
l
e
n
trie
s,
t
ea
c
h
e
r
s
m
a
y
ga
in
i
mpor
tan
t
i
n
fo
rma
t
i
o
n
a
n
d
di
scov
e
r
p
a
t
tern
s
of
t
ho
ugh
t
o
f
t
h
e
i
r
s
t
u
d
e
nt
s
tha
t
m
i
g
h
t
o
t
h
e
r
w
i
se
b
e
o
v
e
r
lo
oke
d
[2
9]
n
ot
t
o
me
ntio
n
t
h
a
t
i
t
pro
v
i
d
es t
he
t
e
a
c
h
er
w
it
h
an a
dd
iti
o
n
al m
ea
n
s
t
o e
v
a
l
ua
te st
ude
n
t
s’
u
n
d
e
r
st
and
i
ng [1
7].
H
o
w
e
ver,
m
ost
o
f
t
h
e
s
tud
i
e
s
t
ha
t
e
x
p
l
or
ed
t
he
e
ffe
c
t
s
of
j
our
n
al
w
ri
ti
n
g
i
n
t
h
e
at
tit
u
d
e
of
s
tude
nts
tow
a
rd
t
he
m
a
t
hem
a
t
i
cs
d
ea
lt
w
i
th
s
t
ude
n
t
s
fr
om
p
rima
ry
t
o
j
u
n
i
or
h
ig
h
s
c
ho
o
l
[
6],
[8]
-[9]
an
d
c
o
lle
ge
[
5]
,
[3
0].
N
o
t
m
u
c
h
a
t
t
e
n
ti
o
n
h
as
b
ee
n
g
i
v
e
n
t
o
s
tud
i
es
w
hic
h
f
oc
us
on
t
h
e
u
s
e
of
j
o
u
rna
l
w
r
i
t
i
n
g
a
s
a
m
eans
to
cha
nge
s
e
n
i
o
r
hi
g
h
s
c
h
o
o
l
s
t
ude
n
t
s’
a
tt
i
t
u
d
e
t
ow
a
r
d
m
a
th
em
atics
.
A
w
i
de
r
ange
o
f
re
se
arc
h
c
once
r
n
i
ng
hig
h
sch
o
o
l
s
tu
de
n
t
s has t
e
nde
d to
foc
us o
n
at
t
itu
de
a
s it re
l
a
t
e
s t
o d
i
ffere
n
t
varia
b
l
e
s
l
ik
e
m
o
t
i
va
tio
n,
e
n
g
a
g
e
m
ent,
and
ac
h
i
e
v
em
e
n
t.
E
v
i
de
nce
o
n
t
he
r
ole
of
j
our
nal
w
r
i
t
i
n
g
in
i
mp
rov
i
ng
hi
g
h
s
ch
o
o
l
s
t
ude
n
t
s’
m
athe
m
a
tics
att
itu
de
r
e
m
a
i
n
s
i
nc
onc
l
u
si
ve.
I
n
D
e
La
S
all
e
L
i
p
a,
s
t
ude
n
t
s
are
tra
i
ne
d
to
b
e
i
n
n
o
v
at
ive
an
d
cri
t
ica
l
t
h
i
n
k
e
r
s
be
in
g
o
n
e
of
t
he
Exp
e
ct
e
d
L
a
s
al
li
a
n
G
ra
du
at
e
At
t
r
i
b
u
t
e
s
.
R
e
sea
r
ch
i
nd
i
c
a
t
es
t
h
a
t
t
he
u
se
o
f
j
our
na
l
im
pr
o
v
es
c
r
i
t
i
ca
l
th
i
n
k
i
ng
sk
i
l
ls
o
f
s
t
ude
nts
[31]
;
D
e
w
e
y
(19
9
1
)
a
s
c
i
t
ed
i
n
Lew
&
S
c
him
i
d
t
[3
2].
Wh
i
l
e
one
s
t
u
dy
i
n
v
o
l
v
i
ng
j
our
nal
w
r
itin
g
i
n
a
c
olle
ge
m
a
t
h
e
m
a
ti
c
s
c
la
ssro
om
[
23]
h
a
s
a
lre
a
dy
be
e
n
co
nduc
t
e
d
i
n
t
h
e
i
n
s
t
i
tu
ti
o
n
,
n
o
re
se
arc
h
us
i
n
g
j
our
na
l
w
r
i
t
i
n
g
a
s
a
n
attem
p
t
to
c
ha
nge
t
h
e
a
t
t
i
t
u
d
e
o
f
s
tu
de
nts
t
o
w
a
r
d
m
athem
a
tic
s
ap
pea
r
s
t
o
h
a
v
e
bee
n
co
n
duc
te
d th
us
f
a
r
.
Th
e
pu
rpo
s
e
of
t
hi
s
st
udy
w
as
t
o
inv
e
st
i
g
a
t
e
th
e
in
fl
ue
n
ce
o
f
j
our
nal
w
r
it
in
g
on
t
h
e
se
nior
h
ig
h
sch
o
o
l
st
ude
n
t
s’
atti
t
u
de
t
ow
ar
d m
a
them
at
ics.
T
he
f
ol
low
i
ng
que
sti
o
ns w
e
r
e
addre
s
se
d.
a)
Wha
t
i
s
t
h
e
st
u
d
en
ts’ a
tti
t
ude
t
ow
a
r
d m
a
the
m
atics
before
a
n
d
a
f
t
e
r jo
urna
l
w
r
itin
g
w
a
s uti
l
i
z
e
d
?
b)
Is
t
he
re
a
s
igni
fic
a
n
t
d
i
ffere
nc
e
in
t
he
a
t
t
itu
de
t
ow
ard
m
a
them
ati
c
s
o
f
t
h
e
s
tude
nt
s befor
e
a
nd
after
jo
ur
na
l
w
r
iti
ng
w
a
s
ut
i
lize
d
?
c)
W
h
a
t
a
re
t
he
s
t
u
d
e
n
t
s’
p
e
r
c
e
p
t
i
on
s
on
t
he
i
nfl
u
en
c
e
o
f
j
o
u
r
nal
writ
ing
in
t
h
e
i
r
a
tt
itu
d
e
tow
a
rd
m
a
t
he
ma
ti
c
s
?
Thi
s
s
tud
y
wi
ll
g
iv
e
awa
r
en
ess
to
t
ea
ch
ers
o
f
t
h
e
D
e
La
S
al
l
e
L
ipa
spe
c
ifica
l
l
y
t
h
o
se
f
rom
S
e
nior
H
i
g
h
S
c
hoo
l
Ma
them
at
ics
L
e
arni
ng
A
re
a
a
bou
t
j
ourna
l
w
r
i
t
in
g
a
s
a
me
ans
t
o
i
mpro
ve
t
h
e
s
tude
nts’
a
tti
tu
de
tow
a
rd
m
a
t
he
ma
t
i
c
s
.
In
t
h
i
s
pape
r,
t
he
a
r
g
u
m
e
n
t
i
s
t
ha
t
t
h
rou
g
h
j
o
u
rna
l
w
ritin
g,
t
he
a
tt
it
ude
o
f
the
stude
n
t
s
tow
a
rd t
he
s
ub
jec
t
w
i
l
l
impr
o
v
e
.
T
he d
isc
u
ssi
on
of
r
esu
l
ts
i
s d
iv
ide
d
i
nto tw
o
se
c
t
i
o
ns.
T
h
e
first part
i
s on
t
h
e
att
itu
des
o
f
t
he
s
tu
de
nts
t
o
w
a
rd
m
athe
ma
t
i
c
s
w
h
ile
t
he
s
e
c
o
n
d
p
art
is
o
n
the
s
t
u
d
e
n
ts’
ins
i
g
h
t
s
a
b
out
j
our
nal
w
r
itin
g
as a
c
l
a
ss
a
c
t
i
v
i
t
y.
A
use
f
u
l
f
ra
me
w
o
rk
t
o
unde
rs
tan
d
t
h
e
r
o
l
e
o
f
t
e
a
c
h
e
r
s’
q
ue
st
ion
i
n
g
a
s
a
d
r
i
v
e
r
t
o
s
t
u
d
e
n
t
r
e
f
l
e
c
t
i
o
n
is
t
ha
t
of
L
e
v
V
yg
o
t
s
ky’s
S
o
c
i
a
l
D
eve
l
o
p
m
e
n
t
The
o
ry.
Th
is
t
heor
y
po
sits
t
hat
“
s
oc
ia
l
i
n
t
e
rac
tio
n
p
l
ays
a
fu
n
d
am
enta
l
ro
le
i
n
t
h
e
proc
e
ss
of
c
o
g
n
it
i
v
e
deve
lo
pm
en
t.”
(
V
yg
otsk
y,
1
9
78
as
c
ite
d
by
Y
o
u
n
g
j
u
[3
3])
as
h
e
s
t
r
o
n
g
l
y
b
e
l
i
e
v
e
d
t
h
a
t
c
o
m
m
u
n
i
t
y
p
l
a
y
s
a
c
e
n
t
r
a
l
r
o
l
e
i
n
t
h
e
p
r
oc
es
s
of
m
ea
nin
g
-m
aki
n
g
[3
4].
W
h
ile
P
i
a
get’s
no
tio
n
tha
t
d
e
v
el
o
p
me
n
t
p
r
e
ce
d
e
s
le
arni
n
g
,
V
ygo
ts
ky
a
r
gue
d
t
h
at
d
ev
e
l
op
ment
al
p
ro
ce
ss
f
o
ll
ows
t
h
e
lear
n
i
n
g
p
roce
ss.
A
c
cordi
n
g
to
V
yg
ots
k
y
(1
9
7
8
as
c
i
t
ed
b
y
[3
4]),
t
he
l
e
a
rni
n
g
b
y
a
chi
l
d
oc
c
u
rs
t
hou
gh
s
ocia
l
in
t
e
rac
t
i
on
w
i
t
h
a
s
ki
l
l
f
u
l
t
u
tor
.
T
h
e
t
u
t
or
m
ay
e
it
her
m
odel
b
eha
v
i
o
r
s
o
r
prov
i
d
e
i
n
s
t
ruct
io
ns
f
or
t
h
e
c
hild
referr
ed
t
o
a
s
c
oo
pera
ti
ve
o
r
col
l
a
bora
t
i
v
e
d
i
al
o
gue.
T
h
e
c
h
il
d
s
ee
ks
t
o
unde
rs
tan
d
t
he
i
ns
t
r
uct
i
on
s
g
i
v
e
n
b
y
the
t
u
tor
(us
u
a
lly
t
he
t
e
a
c
h
e
r)
the
n
i
n
t
erna
lize
s
t
he
i
nf
orm
a
ti
o
n
,
us
ing
it
to
c
o
n
t
r
o
l
h
i
s
ow
n
per
f
or
m
a
nce
.
V
i
g
o
tsk
y
[
34]
m
entio
ne
d
t
h
at
a
du
lt
s
u
pp
ort
all
o
w
s
a
c
h
i
l
d
t
o
op
er
a
t
e
be
y
o
n
d
h
i
s
b
asel
i
n
e
ca
pab
ili
t
i
es
h
e
l
p
i
ng
h
i
m t
o
e
x
cee
d
wh
a
t
ca
n
b
e at
ta
i
n
ed
a
lo
ne
.
A
n
o
t
her
fra
m
e
w
ork
t
h
is
s
tud
y
i
s
a
n
ch
ored
o
n
i
s
S
chö
n
’s
[
3
6
]
Ref
lec
tio
n-i
n
-A
ction
a
n
d
Re
fl
ec
ti
on-
on-A
c
ti
on.
“
Refle
c
t
i
o
n
M
o
d
e
l
s
a
n
d
F
ra
me
w
o
rks”
[
37]
d
e
s
cri
b
es
r
e
fl
e
c
ti
on-
in-
act
io
n
as
s
ome
t
h
i
ng
t
ha
t
conc
er
ns
g
e
tti
n
g
t
o
the
bo
t
t
om
o
f
w
h
a
t
i
s
hap
p
e
n
i
n
g
i
n
t
he
s
ub
j
ec
t’s
pr
o
c
es
ses,
d
e
c
i
si
o
n
-m
akin
g,
a
nd
f
e
e
lin
gs
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2252-
8822
IJERE
V
ol
.
7,
N
o.
2,
June
2
0
1
8
:
13
2
– 14
1
13
4
at
t
he
t
im
e
of
t
he
e
ve
nt
o
f
i
n
t
e
ra
ction.
I
t
re
prese
n
t
s
a
p
roc
e
s
s
by
w
h
ich
one
c
an
l
ear
n
fro
m
expe
rienc
e
[
38].
It
is
d
esc
r
i
b
e
d
a
s
re
flec
tin
g
o
n
t
he
i
nc
id
e
n
t
w
h
i
l
e
it
ca
n
stil
l
b
e
b
e
n
e
fic
i
a
l
t
o
th
e
situ
a
tio
n
as
o
ppo
sed
to
reflect
i
n
g on h
o
w
one
w
ou
ld
do t
h
i
n
gs
d
i
f
fe
re
nt
l
y
i
n
t
h
e fu
t
u
r
e
[36].
A
lter
n
a
t
i
v
e
l
y,
r
eflect
i
o
n-on-a
c
tio
n
i
n
vo
lve
s
e
xam
i
n
i
ng
a
pr
ev
io
us
e
ven
t
t
o
take
i
nt
o
a
c
c
ou
n
t
n
ew
in
form
ation
or
p
er
spe
c
t
i
v
es
t
hat
o
p
ene
d
i
n
r
e
lat
i
o
n
t
o
the
sub
j
e
c
t
’s
p
roc
e
sses,
f
ee
lin
gs,
and
ac
t
i
o
n
s
[37]
.
A
s
S
c
hön
[
36]
p
ut
i
t,
“
w
e
r
efle
ct
o
n
a
c
tio
n,
t
hink
i
n
g
bac
k
o
n
w
h
at
w
e
ha
ve
d
one
i
n
orde
r
t
o
d
is
co
ver
h
o
w
o
u
r
kn
ow
i
ng-
in-
act
io
n
ma
y
ha
ve
c
on
tri
b
ute
d
t
o
an
une
x
p
ec
t
e
d
ou
t
c
ome
”
(p.
2
6).
It
i
s
bas
i
ca
l
l
y
refl
e
c
t
i
n
g
o
n
how
prac
t
i
c
e
can
b
e
im
prove
d
afte
r
the
even
t.
2.
METHOD
Jour
na
l
w
r
it
i
ng
w
a
s
intr
od
u
c
ed
t
o
the
s
t
u
d
en
ts
a
s
part
o
f
e
v
er
y
m
eet
in
g
a
c
t
ivi
t
y
f
o
r
the
w
h
o
l
e
d
u
r
at
ion
of
t
he
s
tu
dy
.
It
s
na
t
u
re
a
n
d
pu
rp
o
s
e
we
re
l
i
k
e
w
i
s
e
di
s
c
u
sse
d
as
p
art
o
f
t
heir
o
rie
n
ta
t
i
on.
The
part
ici
p
a
n
t
s
w
er
e
fort
y-fo
ur
G
ra
de
1
1
sen
i
or
h
ig
h
sc
ho
o
l
s
t
u
d
e
n
ts
o
f
D
e
L
a
S
a
lle
L
ipa
e
n
r
o
l
l
ed
i
n
o
n
e
o
f
t
h
e
P
r
eca
l
c
ul
u
s
c
l
a
sses
i
n
t
he
f
i
r
st
s
e
m
e
s
t
e
r
of
s
c
h
o
o
l
y
e
a
r
201
7-2
01
8.
T
he
j
o
u
rna
l
w
ritin
g
w
e
nt
on
for
eight weeks.
A
l
t
h
o
u
gh
jo
ur
nal
w
r
iti
n
g
w
a
s
i
mplem
e
n
t
e
d
a
s
a
per
m
a
n
ent
c
l
a
s
s
a
c
t
i
v
ity,
it
w
a
s
ma
de
c
lear
t
o
t
h
e
stude
n
t
s tha
t
i
t w
i
l
l
n
o
t
b
e
par
t
of the
i
r
gr
a
d
e com
p
u
t
a
tio
n. T
h
e
j
ou
rn
al
e
nt
ri
es
w
ere
u
s
e
d
s
o
l
ely
fo
r
di
agno
st
ic
pur
poses
o
f
t
h
e
t
e
ac
her.
T
h
e
n
o
tio
n
t
h
a
t
j
o
u
r
na
l
w
r
it
i
ng
is
n
o
t
g
r
a
ded
i
n
it
iate
s
m
o
st
o
f
t
h
e
be
ne
fi
t
s
o
f
j
our
nal
w
r
itin
g
[2
3].
The
tea
c
h
er
,
how
e
v
er,
ens
u
re
d
t
h
a
t
e
a
c
h
s
tu
d
e
nt
r
eg
ular
ly
w
rit
e
s
i
n
t
h
e
j
ou
r
n
a
l
b
y
a
c
tive
l
y
sup
e
rvi
s
in
g
t
h
e
a
c
tivi
t
y.
A
m
axim
um
o
f
ten
m
i
nu
t
e
s
w
a
s
all
o
tte
d
f
or
t
he
act
i
v
i
t
y,
done
a
t
t
h
e
e
nd
of
ea
ch m
ee
ting.
Jour
na
l
que
sti
ons
o
r
pr
omp
t
s
w
e
re
p
r
o
vi
de
d
b
y
t
he
t
eac
h
e
r
for
t
he
s
tu
d
e
nt
s
t
o
r
e
f
lec
t
on.
A
s
state
d
by
[
39],
j
our
na
l
pr
o
m
p
t
s
a
r
e t
h
e
m
o
s
t
m
ea
n
i
ng
ful
w
r
i
t
i
n
g ta
sks
a
s
i
t
i
n
v
o
l
v
e
s
s
o
l
ic
iti
n
g
f
r
o
m
stude
nts’
w
ritte
n
respo
n
ses
to
s
pe
ci
fic
q
u
es
tio
ns
[
20].
N
o
t
o
n
ly
d
oes
m
e
a
n
i
n
g-m
a
k
i
n
g
a
c
t
i
v
ity
e
na
ble
st
ude
n
t
s
t
o
d
e
v
e
l
o
p
a
n
aw
a
r
ene
s
s
of
t
he
s
el
f;
it
a
l
so
a
llow
s
t
he
s
tude
nts
t
o
r
e
l
ate
m
a
them
a
t
i
c
s
t
o
r
ea
l-l
i
f
e
f
ac
ts
i
mpr
o
vin
g
un
dersta
n
d
i
n
g of
t
he su
b
jec
t
[
23].
The
jo
urna
l
e
n
t
r
ies
o
f
t
he
s
t
u
d
e
nt
s
w
e
re
r
ea
d
a
n
d
re
view
e
d
r
egu
l
a
rly
and
we
re
u
s
e
d
by
t
h
e
t
ea
ch
er
t
o
dia
g
no
se
p
r
o
b
l
e
m
s
or
c
once
r
ns
t
ha
t
the
st
ude
n
t
s
ha
d.
I
t
served
as
a
n
ope
n
l
i
n
e
of
c
omm
unica
t
i
on
be
tw
e
e
n
t
h
e
m
.
Gu
c
e
[
23
]
po
int
e
d
out
t
h
a
t
j
o
u
r
n
a
l
i
ng
o
f
t
h
e
s
t
ud
en
ts
p
ro
v
i
de
s
t
h
e
teac
her
wi
t
h
a
no
the
r
s
t
r
at
egy
for
targe
t
s
t
ude
n
t
s
to
c
om
mun
i
ca
t
e
t
heir
t
h
o
u
g
h
t
s.
B
es
ides,
it
a
l
l
o
w
s
t
he
t
ea
c
h
e
r
t
o
“
s
tay
in
t
ouc
h
e
v
e
n
w
ith
t
h
e
most
q
u
i
et
a
n
d
rese
rved
s
t
ude
nt”
[2
4]
.
Tea
c
her
s
i
n
m
a
the
m
atics
pl
ay
a
s
i
gni
fi
c
a
n
t
r
ol
e
i
n
c
rea
ting
a
pl
ea
sa
nt
and
he
lp
fu
l
a
t
m
o
sp
here
f
or
t
he
i
r
s
tu
de
nts.
T
his
l
e
a
d
s
t
o
t
he
i
m
pro
v
em
e
n
t
of
t
he
l
a
t
ter’
s
fe
eli
n
gs
o
r
bel
i
e
f
s
tow
a
rd
t
he
su
b
j
ect,
bu
i
l
di
n
g
u
p
t
o
a
p
o
s
i
t
ive
a
tti
tu
de t
ow
a
r
d
m
athem
a
tics
[12].
A
m
i
xe
d-m
e
t
h
od
ap
proa
c
h
w
a
s
u
se
d
for
th
i
s
s
t
u
dy
i
n
p
ar
tic
ula
r
,
t
h
e
c
o
nv
erg
e
n
t
p
ara
l
l
e
l
d
e
si
gn
.
A
mixe
d-me
t
hod
s
tu
d
y
i
nte
g
ra
te
s
bo
th
qua
n
t
i
t
a
t
iv
e
a
nd
q
u
a
l
i
t
a
t
i
v
e
r
e
s
e
a
r
c
h
m
e
t
h
o
d
s
[
4
0
]
.
T
h
e
c
o
m
b
i
n
e
d
rese
arc
h
e
lem
e
nt
s
ar
e
use
d
t
o
in
t
e
grate
fi
ndi
n
g
s
w
i
thi
n
a
s
i
n
g
l
e
sy
stem
at
ic
r
e
v
i
e
w
[4
1].
C
r
eswell
a
n
d
Tasha
k
k
o
ri
[
4
2
]
ex
pla
i
ns
t
ha
t
the
s
t
ud
y,
w
it
h
i
t
s
t
w
o
w
e
l
l
-
d
eve
l
ope
d
d
i
st
i
n
c
t
s
tra
n
ds,
ea
ch
c
om
ple
t
e
w
i
t
h
i
t
s
ow
n
que
sti
o
n
s
,
da
ta,
a
n
al
ys
i
s
a
nd
i
nfere
n
ces
m
ust
as
w
e
l
l
i
n
teg
ra
t
e
,
con
n
ec
t,
o
r
relate
t
hes
e
s
tran
ds.
H
e
yva
ert
et
a
l
.
[
4
1
]
st
r
e
ssed
t
h
a
t
t
h
i
s
me
t
h
o
d
h
a
s
a
p
r
o
mis
i
n
g
u
t
i
lity
f
or
r
e
s
ear
ch
a
nd
prac
t
i
ce
a
s
it
c
o
m
b
i
n
es
t
h
e
st
r
e
n
g
t
h
s o
f
both
q
u
a
lita
t
i
ve
a
nd q
u
a
n
ti
ta
ti
ve
te
c
hn
ique
s.
F
o
r
p
u
r
p
ose
s
o
f
va
l
i
da
t
i
o
n
,
con
v
e
r
ge
n
t
p
a
r
alle
l
de
s
i
gn
w
ill
b
e
a
ppl
ied.
A
c
c
ordi
n
g
t
o
Cre
s
w
e
l
l
a
nd
P
l
ano
C
l
ark
[
4
3],
thi
s
d
es
i
gn
i
s
m
ade
to
u
n
d
e
rst
a
n
d
o
r
de
v
e
l
o
p
a
mor
e
c
onc
rete
u
n
d
e
r
st
and
i
ng
of
a
r
es
ea
rch
pro
b
lem
t
h
ro
u
gh
a
n
a
l
ysis
o
f
di
ffe
re
nt
b
u
t
c
om
p
l
e
m
e
n
t
a
ry
d
a
t
a
.
T
w
o
i
n
d
e
pe
nde
nt
s
t
r
an
ds
o
f
q
u
a
l
i
t
a
t
i
v
e
an
d
qua
n
t
i
t
a
tive
da
ta
w
ill
be
c
ol
le
cted
a
nd
a
n
al
yze
d
a
t
a
sin
g
l
e
ph
a
s
e
p
r
i
o
r
i
t
i
zi
n
g
t
he
m
eth
ods
e
qua
ll
y.
F
or
t
he
overa
ll
i
n
t
e
rpre
t
a
t
i
on,
t
he
r
e
s
u
l
ts
w
i
l
l
be
m
ixe
d
t
o
lo
ok
f
or
c
o
n
v
e
r
ge
nc
e,
d
iv
er
genc
e
,
c
on
trad
ic
ti
o
n
s,
o
r
rela
tio
ns
hips
o
f the
tw
o sourc
e
s of
d
ata.
F
igur
e 1
illus
t
rate
s
t
h
e
proc
ess i
n
vo
l
v
e
d
i
n t
h
is m
etho
d.
F
i
gur
e 1.
Co
n
v
e
rge
n
t
para
lle
l
des
i
g
n
Evaluation Warning : The document was created with Spire.PDF for Python.
IJERE
I
S
S
N
:
2252-
88
22
T
h
e
Role
of
Jo
urn
a
l
Wri
tin
g i
n
Se
n
i
or
H
i
g
h
Sch
o
o
l S
t
ude
n
t
s’ Atti
tude
t
o
ward
M
a
the
m
a
t
i
c
s(
Ive
e
K. G
u
ce)
13
5
To
m
easure
the
a
t
t
i
t
u
de
o
f
the
st
u
d
en
ts
t
owar
d
m
a
t
h
em
atics,
t
he
S
c
a
le
on
A
t
t
i
tu
d
e
T
o
w
ard
Ma
them
at
ics
(SATM)
b
y
Gu
ce
&
T
ale
n
s
[1
2]
w
as
u
sed.
S
A
T
M
is
a
3
2
-
i
t
e
m
scale
w
i
t
h
f
o
u
r
subsc
a
l
es
:
l
i
kin
g
and
d
i
sli
k
i
n
g
ma
them
at
i
c
s,
t
ende
nc
y
t
o
e
n
g
age
in
o
r
av
o
i
d
ma
the
ma
tic
s
a
c
ti
v
i
t
i
es,
be
l
i
e
f
t
ha
t
one
i
s
go
o
d
o
r
bad
i
n
m
athem
a
tic
s,
a
n
d
b
e
lie
f
tha
t
m
athe
ma
tic
s
is
u
se
fu
l
or
u
s
e
l
ess.
T
he
i
ns
trum
ent
w
a
s
a
d
min
i
s
t
e
r
ed
b
efore
and
after
the
im
plem
entation o
f
j
o
ur
nal writ
ing activity.
F
o
r
th
e
qua
nti
t
a
ti
ve
d
ata
a
n
a
l
ys
is,
the
a
t
t
i
t
u
d
e
o
f
the
s
t
ude
nt
s
to
wa
rd
t
h
e
m
at
h
e
mati
cs
w
as
d
esc
r
ib
e
d
us
i
n
g
the
m
ean
o
f
a
ll
t
h
e
respo
n
ses
f
o
r
e
ach
o
f
th
e
fo
ur
s
ubs
ca
l
e
s
in
t
he
p
r
e
test
a
nd
post
t
est.
T
o
deter
m
in
e
w
h
et
her
e
t
he
re
is a si
g
n
i
fic
a
n
t
di
ffe
renc
e i
n
t
he
a
t
t
i
t
u
d
e of t
he st
ude
n
t
s t
o
w
a
rd the
s
u
b
j
e
c
t
be
f
o
r
e an
d
a
f
ter
t
h
e
implem
e
n
t
i
ng
jo
urna
l
w
r
iti
n
g
,
a
depe
nde
n
t
s
am
pl
e
t-te
st
w
as
d
o
n
e
.
A
l
l
s
t
a
tis
tica
l
t
e
s
ts
w
ere
do
ne
u
s
i
n
g
SPS
S
so
f
t
ware.
To
p
robe
o
n
t
h
e
s
t
u
d
e
n
t
s
’
in
sigh
ts
on
jour
nal
w
r
it
in
g,
a
f
oc
us
gro
up
d
i
scuss
i
o
n
w
as
c
on
d
u
cte
d
.
It
w
a
s
partic
ipa
t
ed
i
n
b
y
t
e
n
s
t
ude
n
t
s
w
ho
w
e
re
r
andom
ly
s
elec
t
e
d.
A
n
e
xperie
n
c
e
d
qua
lita
t
i
v
e
rese
arc
h
er
fa
ci
lita
te
d
th
e
s
e
ssi
on us
i
n
g th
e
fol
l
ow
i
ng ke
y que
st
i
ons:
1.
Do
y
ou
l
ik
e o
r
n
o
t
l
i
k
e ma
th
ema
t
i
c
s
?
2.
A
r
e
you the
t
y
pe w
ho
w
ill
en
gage
i
n m
a
the
m
atics a
c
t
i
v
i
t
i
e
s
or
t
he
t
y
p
e
w
ho
w
ill a
v
o
i
d
the
m
?
3.
H
o
w
w
o
u
l
d
y
ou
descr
i
be
y
ourse
lf
a
s
a
s
t
u
d
e
n
t
i
n
a
m
athem
a
t
i
cs
c
l
a
ss
?
H
o
w
do
yo
u
man
a
g
e
i
n
the s
u
b
j
ec
t
?
4.
D
o
yo
u
t
h
i
nk
m
a
the
m
a
tics
i
s
u
sefu
l or
usele
ss
?
5.
Wha
t
a
re
your
t
ho
ug
h
t
s a
n
d
fe
elin
gs
a
b
o
u
t
j
our
nal w
r
itin
g a
s
a
m
a
them
ati
c
s c
l
a
s
s
ac
t
i
v
i
t
y
?
6.
D
o
y
ou
f
ind
i
t
h
e
lpf
u
l?
I
f
y
e
s
, i
n
w
h
a
t
w
a
y
?
The
first
four
que
st
i
ons
t
ac
k
l
e
the
st
u
d
en
ts’
att
i
t
ude
t
ow
ard
m
a
t
he
m
a
ti
c
s
w
hi
le
l
a
s
t
tw
o
a
ttem
p
t
to
e
xp
l
o
r
e
the
i
r
per
c
e
p
ti
o
n
o
n
jo
urna
l
w
r
i
t
in
g
as
a
m
athem
a
ti
cs
c
la
ss
a
cti
vit
y
.
Wi
th
t
he
p
er
miss
i
o
n
of
t
he
s
tu
de
nt
s,
t
h
e
di
sc
ussi
o
n
w
as a
ud
i
o
-r
ecor
d
e
d
for the
a
c
c
ur
a
t
e
tra
n
sc
ri
p
t
i
o
n a
n
d
co
di
ng
of d
a
t
a
.
F
o
r
the
qua
l
ita
ti
v
e
d
a
t
a
a
n
a
l
y
s
is,
a
transcr
i
p
t
i
o
n
gri
d
w
as
d
e
v
e
l
ope
d
for
eac
h
of
t
he
s
ix
que
s
t
i
o
ns.
The
re
spo
n
se
s
w
e
re
c
a
r
efully
a
nd
o
b
j
e
c
t
i
v
e
l
y
c
ode
d.
K
e
y
t
er
ms
f
rom
the
prel
imina
r
y
co
des
w
e
r
e
s
tu
di
ed
a
n
d
the
n
g
r
o
u
p
e
d
acc
ord
i
n
g
t
o
sim
i
l
a
ri
ty
t
o
ob
ta
i
n
t
he
e
m
e
r
g
i
ng
the
m
e
s.
F
urt
h
e
r
,
freque
nc
ie
s
of
r
epl
y
w
ere
no
te
d
to es
t
ab
l
i
sh re
l
e
v
an
t i
d
ea
s t
h
a
t
we
r
e raised
d
uri
ng t
h
e i
n
ter
v
i
ew.
Tr
i
a
n
g
u
l
a
tio
n w
a
s used
t
o va
li
da
te
t
he
a
na
l
y
sis for the
q
u
al
ita
ti
ve
d
at
a.
D
i
f
f
e
re
nt
s
tu
di
es,
eit
h
er t
ho
se
t
h
a
t
c
o
n
f
o
r
m
o
r
c
o
n
t
r
a
d
i
c
t
w
e
r
e
g
a
t
h
e
r
e
d
a
n
d
r
e
l
a
t
e
d
t
o
t
h
e
r
e
s
ul
ts
o
f
thi
s
s
t
u
d
y
t
o
e
s
t
a
b
l
i
s
h
s
o
u
n
dne
ss
o
f
t
h
e
fi
n
d
in
gs
c
o
n
v
e
y
ed.
A
l
s
o
,
the
re
sul
t
s
of
t
he
q
ua
n
tita
t
i
v
e
da
t
a
a
nal
y
sis
w
e
r
e
lin
ke
d
u
p
w
i
t
h
t
he
qua
l
ita
t
i
ve
d
ata
to furt
h
e
r
stre
ngt
he
n
and
sup
p
o
rt
t
he
fi
n
d
i
n
g
s.
Th
rou
gho
ut
t
he
s
tu
dy
,
e
t
hi
cal
c
o
n
s
id
e
r
ati
ons
w
ere
f
o
l
l
o
w
e
d
an
d
o
b
se
rv
ed.
Wit
h
t
he
r
e
s
pon
de
nt
s
bei
n
g
o
f
m
inor
a
ges,
l
e
tter
s
o
f
co
nse
n
t
w
e
re
s
en
t
to
t
he
p
a
r
ent
s
inf
o
rmin
g
them
o
f
the
n
a
ture
a
nd
p
u
rp
ose
o
f
the
stu
d
y
.
Thes
e
w
e
re
a
lso
d
i
s
c
usse
d
w
ith
t
h
e
s
t
u
de
nts
a
nd
the
i
r
c
onse
n
t
t
o
p
a
r
t
i
c
i
pa
te
w
as
a
lso
s
o
u
g
h
t
bef
o
r
e
the
c
o
nd
uc
t
o
f
a
ny
da
ta
g
a
t
he
rin
g
.
A
n
o
n
y
m
i
t
y
o
f
t
he
r
e
s
pon
de
nt
s
w
a
s
a
ssur
ed.
A
n
y
ki
n
d
o
f
de
ce
p
tio
n
o
r
exa
gge
rat
i
on a
bou
t
t
h
e
a
i
m
s
o
f
the st
u
dy a
s
w
ell a
s
re
s
u
l
ts in
t
h
e
da
ta
g
a
t
h
e
rin
g
w
as c
ertai
n
l
y
a
vo
ide
d
.
3.
RESULT
S
A
N
D
DISCU
SSIO
N
3
.
1
.
S
tudents’ A
tt
i
t
ud
e
to
w
a
rd
M
a
t
hema
tics
SATM
[
1
2
]
m
e
a
su
re
s
t
h
e
a
t
tit
ud
e
in
f
ou
r
asp
e
c
t
s
n
a
me
l
y
l
i
k
in
g
o
r
d
i
s
lik
i
n
g
m
a
t
h
em
atic
s,
t
e
n
de
ncy
t
o
e
ng
a
g
e
in
o
r
a
v
o
i
d
ma
th
ema
t
i
cal
a
c
t
i
v
itie
s,
a
b
el
i
e
f
th
at
o
n
e
is
g
o
o
d
or
b
a
d
i
n
ma
th
em
ati
c
s,
a
n
d
a
b
el
ie
f
tha
t
m
a
t
he
ma
ti
cs
i
s
use
f
ul
o
r
use
l
e
s
s.
T
he
s
u
cce
edi
n
g
fo
ur
t
abl
e
s
s
how
t
he
r
e
s
ults
f
or
t
he
p
rete
st
a
n
d
p
o
s
tte
st
o
f
t
h
e
resp
onden
t
s.
I
n
t
e
r
ms
o
f
l
i
kin
g
o
r
disl
i
k
i
ng
m
a
them
at
ics
,
m
ajorit
y
of
t
he
s
t
u
d
en
ts
d
u
r
i
n
g
t
h
e
pre
t
e
s
t
w
e
r
e
a
t
a
range
o
f
sli
g
htly
d
is
l
i
k
i
ng
(
n=
15)
t
o
s
l
i
g
htl
y
l
i
k
ing
(
n
=
1
4
)
t
h
e
subj
e
c
t
a
s
sho
w
n
in
T
ab
l
e
1
.
Alth
ough
m
o
r
e
stude
n
t
s
sh
ow
ed
t
o
ha
ve
a
lik
i
ng
in
t
he
s
ub
je
ct
(
n
=
2
4
)
com
p
are
d
t
o
t
hose
w
h
o
d
o
n
o
t
(
n=20),
sti
l
l
n
o
st
u
d
e
nt
resul
t
ed
t
o
ha
ve
v
ery
m
u
c
h
l
i
k
i
n
g
in
i
t
.
F
or
t
he
p
ostte
st,
th
er
e
w
a
s
a
slig
h
t
i
nc
rea
s
e
in
t
h
e
n
umbe
r
o
f
s
tude
nts
w
ho
l
i
ke
t
h
e
s
ub
j
e
c
t
(
n
=
3).
C
o
nseq
ue
n
t
l
y
,
m
a
jorit
y
o
f
the
s
t
ude
nts
s
how
e
d
t
o
ha
v
e
a
s
li
g
h
t
li
k
i
ng
in
ma
them
at
i
c
s u
n
l
i
ke
in t
h
e
pre
t
e
s
t
where
m
o
re
s
t
u
de
n
t
s
som
e
w
h
at
di
sl
ik
ed
i
t
.
Ta
b
l
e
1.
Lik
ing
or D
i
s
li
k
i
n
g
M
a
t
hem
a
t
i
c
s
Attitude
Pre
t
e
s
t
Postte
st
Fre
q
u
e
n
c
y
%
Fre
que
n
c
y
%
V
e
r
y
m
u
c
h
disl
iki
ng
m
a
th
2
4
.
5
5
1
2.
2
7
Disliki
n
g
m
a
th
3
6
.82
1
2.2
7
So
m
e
w
h
a
t
d
is
liking m
a
th
1
5
34.
09
1
5
34.
09
So
m
e
w
h
a
t
l
i
k
ing m
a
t
h
1
4
31.
82
1
6
36.
36
L
i
king m
a
th
1
0
22.
73
9
20.
45
V
e
r
y
m
u
c
h
li
king m
a
th
0
0
.
0
0
2
4.
5
5
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2252-
8822
IJERE
V
ol
.
7,
N
o.
2,
June
2
0
1
8
:
13
2
– 14
1
13
6
F
o
r
th
e
st
u
d
en
t
s
’
ten
d
enc
y
t
o
enga
ge
i
n
or
a
vo
i
d
m
athem
a
t
i
ca
l
a
c
t
i
v
i
tie
s,
t
he
r
esu
lts
a
re
s
umm
a
r
i
z
e
d
in
T
a
b
l
e
2
.
For
bo
th
t
he
p
re
te
st
a
nd
p
o
s
t
te
st,
th
e
m
a
jor
i
t
y
h
a
v
e
a
(l
ow
)
t
e
n
d
e
n
cy
t
o
e
n
gage
i
n
the
su
bjec
t
rathe
r
t
ha
n
a
v
oid
i
t
.
F
u
r
t
he
r,
it
is
w
orth-
n
o
t
i
ng
t
h
at
t
h
e
re
w
a
s
a
shift
fr
om
m
ostl
y
ha
vi
n
g
t
he
t
e
n
d
e
nc
y
t
o
avo
i
d
ma
the
m
a
t
i
c
a
l
a
c
t
iv
i
t
ie
s
to
p
red
o
m
i
na
nt
ly
h
a
v
in
g
t
h
e
ten
d
e
ncy
t
o
e
nga
ge
i
n
t
h
em
(
fr
om
n
=
2
5
t
o
n
=20)
.
Ev
ide
n
tly,
ther
e
w
a
s
an
i
nc
rea
s
e
in
n
um
ber
,
from
19
(43
%
)
to
2
4
(
55
%),
of
t
ho
se
s
tude
n
t
s
w
ho
s
h
ow
ed
t
o
have
a
t
en
de
nc
y
to en
g
a
g
e i
n
m
athe
ma
tica
l
a
c
tiv
it
i
e
s d
u
ri
n
g
the
p
o
s
ttes
t
.
Tab
l
e
2.
T
ende
nc
y t
o
En
g
a
g
e
in or
A
v
o
i
d M
a
them
a
tica
l
A
cti
v
i
t
ies
Attitude
Pre
t
e
s
t
Pos
tte
st
Fre
que
n
c
y
%
Fre
q
u
e
n
c
y
%
Hi
g
h
t
e
n
d
e
n
c
y
to avoi
d
m
a
th
e
m
at
i
c
a
l
ac
tivit
i
e
s
2
4.
5
5
1
2
.
2
7
M
ode
r
a
t
e
t
e
n
d
e
n
c
y
to a
void m
a
thema
t
i
c
al a
c
t
i
v
iti
e
s
8
18.
18
4
9.
09
Low t
e
nde
n
c
y t
o
a
void ma
th
em
ati
c
al
ac
tivitie
s
15
34.09
15
34.09
Low
t
e
nde
n
c
y
t
o
e
nga
g
e
i
n m
a
them
a
t
ic
a
l
ac
t
iviti
e
s
1
6
36.
36
18
4
0.
91
Mo
d
e
r
a
t
e
t
en
d
e
n
c
y t
o
e
n
g
ag
e
i
n
m
a
t
h
e
mat
i
cal
act
iv
i
t
i
es
3
6
.8
2
6
13.
64
Hi
g
h
t
e
n
d
e
n
c
y to enga
ge in m
a
the
m
at
i
c
a
l
ac
tivitie
s
0
0.0
0
0
0
.0
0
Ta
b
l
e
3
s
how
s
the
resu
lt
s
o
f
t
he
s
tu
de
n
t
s’
b
e
lie
f
as
t
o
w
h
et
her
t
he
y
ar
e
g
o
od
or
b
a
d
i
n
m
a
them
a
tics.
Ma
jori
ty
o
f
t
h
e
st
u
d
en
ts
f
or
b
ot
h
pr
ete
s
t
(
n
=1
8)
a
n
d
p
os
ttes
t
(
n
=
1
5
)
sl
i
ght
ly
b
e
l
ie
ve
t
ha
t
the
y
a
re
n
o
t
perform
ing
w
e
ll
in
t
he
s
ub
j
e
c
t
.
A
l
t
hou
gh
t
h
e
r
e
is
a
n
inc
r
ea
s
e
i
n
t
h
e
n
u
mbe
r
o
f
stu
d
e
n
ts
w
ho
be
l
i
e
v
e
t
h
a
t
t
he
y
are
good
in
m
a
t
he
ma
tic
s
d
u
ri
ng
t
h
e
p
o
s
t
t
e
st
,
resul
t
s
re
vea
l
e
d
t
ha
t
the
num
ber
of
s
t
ude
n
t
s
w
ho
see
them
sel
v
es
as poor
in m
a
t
h
em
ati
c
s are
still
pred
om
ina
n
t
t
h
an t
h
o
se w
h
o
fe
e
l ot
her
w
ise
. A
s a
m
a
tter of fac
t
,
ther
e
w
ere
34
(77%)
and
2
7
(61
%)
stu
den
t
s
un
der
this
case
for
prete
s
t
an
d
pos
t
t
e
st
, re
s
p
e
ct
iv
el
y
.
Tab
l
e
3.
B
e
lie
f that
O
ne
i
s
G
o
od or
B
a
d
i
n
M
a
them
a
tics
Attitude
P
r
et
es
t
P
o
s
t
tes
t
F
r
e
que
n
c
y
%
Fre
que
n
c
y
%
H
i
ghly
b
e
lie
v
e
s
th
a
t
one
’
s
se
l
f
is
b
a
d
i
n m
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th
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m
at
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c
s
5
11.
36
6
13.
64
M
ode
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te
l
y
b
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l
i
e
v
e
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th
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c
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11
2
5
.
0
0
6
13.
64
Sli
ghtly
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v
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l
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a
d
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n ma
th
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m
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18
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1
1
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34.
09
Sli
ghtly
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l
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t
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6
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29.
55
M
ode
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tic
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4
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3
20.
55
H
i
ghly
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lie
v
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th
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t
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s
se
l
f
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good
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a
t
h
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m
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ti
c
s
0
0
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0
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1
6
.
8
2
A
m
ong
the
f
o
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r
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s
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a
t
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t
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de
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m
at
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cs,
t
h
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b
e
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i
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th
at
ma
them
at
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c
s
i
s
u
sef
u
l
or
u
se
le
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s
t
o
od
o
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t
to
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a
v
e
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be
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e
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ul
t
s
i
n
t
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rms
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in
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Fo
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t
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seless.
I
n
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ma
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athe
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or
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p
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te
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n
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f
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r
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b
l
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4
show
s
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f
t
ha
t m
a
them
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sel
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s
.
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4.
Bel
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t
h
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t
M
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cs is Use
f
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or
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Pre
t
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lightly
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lightly
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ul
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pre
t
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t
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pos
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ur
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ubs
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score resul
t
s
Evaluation Warning : The document was created with Spire.PDF for Python.
IJERE
I
S
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N
:
2252-
88
22
T
h
e
Role
of
Jo
urn
a
l
Wri
tin
g i
n
Se
n
i
or
H
i
g
h
Sch
o
o
l S
t
ude
n
t
s’ Atti
tude
t
o
ward
M
a
the
m
a
t
i
c
s(
Ive
e
K. G
u
ce)
13
7
Ta
bl
e 5
.
P
re
t
e
st
-Po
s
tt
e
s
t
M
e
a
n
Sco
re
R
esu
l
ts
S
u
b
s
cal
e
T
e
s
t
N
M
ean
St
d
.
De
vi
a
tion
t
p-va
lue
L
i
king
or
d
i
s
liki
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m
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Te
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re
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para
graphs
o
f
th
is
s
ec
ti
on
p
r
esent
t
h
e
re
sp
ons
e
s
g
i
ve
n
b
y
t
he
s
t
ude
n
t
s
in
t
he
f
oc
u
s
gro
up
dis
c
uss
i
on
c
o
n
c
e
r
ni
n
g
the
i
r
a
t
t
i
t
ude
t
ow
a
r
ds
m
at
hem
a
ti
cs
a
s
w
ell
a
s
t
he
d
isc
u
ss
ion
l
i
nk
i
ng
th
e
qua
n
t
i
t
a
tive
an
d
qua
l
i
ta
t
i
v
e
d
a
ta
i
n
the
st
u
d
y
.
D
a
ta
s
how
e
d
t
hat
a
l
l
te
n
re
spo
n
d
en
ts
e
x
p
r
e
sse
d
l
i
k
i
n
g
in
t
he
s
u
bjec
t
b
u
t
n
o
t
t
o
the
s
a
me
e
xte
n
t.
W
h
il
e
t
h
ree
direc
t
ly
a
c
k
no
wl
ed
g
e
d
th
e
i
r
li
ki
ng
i
n
t
h
e
su
bj
ec
t
,
the
r
e
are
s
e
ve
n
w
h
o
me
nti
o
ned
tha
t
t
h
e
y
ar
e
midd
l
i
n
g
i
n
ter
m
s
of
a
c
t
ua
l
l
y
enj
o
y
i
n
g
t
he
s
ub
jec
t
.
The
y
d
o
n
o
t
t
ot
al
ly
l
ik
e
it
y
et
t
h
e
y
d
o
no
t
di
sl
i
k
e
i
t
.
T
hi
s
agre
es
w
i
t
h
t
h
e
resul
t
i
n
the
SA
TM
w
here
som
e
w
h
at l
i
k
i
ng m
a
th
got
t
h
e
m
o
s
t
n
u
mbe
r
o
f
fre
qu
en
cy
.
W
h
en
aske
d
if
h
e
l
i
ke
s
m
a
t
h
e
m
a
t
ic
s
or
n
o
t
,
S
t
ud
e
n
t
7
sai
d
t
ha
t
“it is ok
a
y
”
f
o
r
h
i
m
.
H
e
f
u
r
t
h
e
r
a
d
d
s
t
h
a
t
t
h
e
r
e
ce
rtai
nly
are
ti
me
s
when
h
e
l
i
ke
s
t
h
e
su
b
j
ec
t
b
u
t
n
o
t
t
o
a
p
o
i
n
t
w
h
e
n
it
i
s
a
l
l
t
ha
t
he
e
njo
y
s.
A
nal
y
z
i
n
g
t
he
respo
n
ses
o
f
t
he
s
t
u
den
t
s,
t
h
r
e
e
poi
n
t
s
e
m
e
r
ged
a
s
r
ea
so
ns
w
h
y
t
h
ey
e
njo
y
m
athem
a
t
i
cs
:
its
r
e
l
eva
n
ce
o
r
w
o
rth,
i
ts
b
e
i
n
g
c
ha
l
l
en
g
i
n
g
,
and
t
hose
ce
rt
a
i
n
top
i
cs
t
ha
t
t
h
e
y
l
i
ke
.
The
f
i
r
s
t
is
t
h
e
m
os
t
answ
e
r
ed
r
e
s
pons
e.
F
r
om
p
ast
st
ud
ies,
s
t
u
den
t
s
fe
el
a
t
ea
se
i
n
s
o
l
v
i
n
g
rea
l
-l
i
f
e
m
at
h
e
mati
ca
l
p
r
ob
l
e
ms
b
e
cau
se
f
o
r
t
h
e
m
t
h
ey
can
be
s
ol
ved
a
t
d
if
f
e
rent
l
e
v
els
an
d
in
d
if
fere
nt
w
ays
[
4
4]-[45].
Whe
n
s
t
u
den
t
s
bec
o
me
a
w
a
re
o
f
t
h
e
c
onne
c
t
i
o
n
s
and
rele
va
nce
of m
athe
ma
tic
s
i
n
t
he
ir li
v
es,
t
h
ey te
nd
to see
i
ts
i
mp
orta
nc
e
[46].
Whe
n
it
c
o
m
e
s
to
e
nga
g
i
ng
t
hem
s
e
l
ve
s
i
n
m
at
hem
a
t
i
ca
l
ac
tiv
i
t
i
e
s
,
si
x
s
t
udents
e
x
p
r
e
ssed
w
illi
n
gne
ss
to
e
nga
ge
i
n
suc
h
a
ct
iv
itie
s
w
h
i
l
e
t
h
e
re
ma
i
n
in
g
c
o
n
v
e
y
e
d
a
p
p
r
e
he
nsi
o
ns
i
n
do
i
n
g
so.
T
h
e
f
o
rm
e
r
like
s
e
ng
a
g
i
n
g
in
m
athe
ma
ti
ca
l
a
c
t
i
v
i
t
i
es
f
or
d
iffer
e
n
t
r
easo
n
s
.
F
o
r
one
,
S
t
ude
n
t
3
s
h
a
r
e
d
t
h
a
t
d
o
i
n
g
t
hos
e
a
c
t
i
vit
i
es
a
l
l
ows
h
i
m
t
o
e
x
p
l
o
re
t
h
e
s
u
b
j
ect
w
h
o
w
as
s
eco
nd
ed
b
y
S
t
u
d
e
nt
8
w
ho
nar
r
ated
t
ha
t
in
s
ol
v
i
n
g
ma
them
at
i
c
al
p
r
oble
m
s
“
h
e
g
e
t
s
to disc
ov
er
ho
w
i
t
(m
ath)
can
b
e
app
li
e
d
to
real
-li
f
e”
.
A
lso,
s
tude
n
t
s
bel
i
e
v
e t
h
at
b
y
enga
gi
n
g
i
n ma
th
e
m
a
t
i
c
a
l
a
ct
iv
itie
s, the
ir skil
ls
i
n
t
h
e su
b
j
e
c
t
w
i
l
l
b
e
de
ve
lo
p
e
d, as articu
l
at
e
d
by
S
t
u
d
e
n
t
2. Th
i
s re
sp
onse
w
a
s com
p
lem
e
nte
d
by
tha
t
of S
t
ude
nt
6’ w
h
o said
:
“
I
f
e
el
v
e
ry ha
p
p
y whe
n
e
ver I
get results fr
om solving math problems.
”
The
i
n
cr
ease
i
n
t
he
s
tu
de
n
t
s
’
e
njo
y
me
n
t
i
n
m
a
them
at
ics
and
the
i
r
wi
ll
ing
n
e
ss
to
e
ng
a
g
e
in
t
he
sub
j
e
c
t
a
lig
ns
w
it
h th
e
s
t
u
dy m
a
de b
y
S
a
nc
h
a
l
a
n
d
S
h
ar
ma
[
4
7
]
.
The
i
r fin
d
in
gs su
gge
st
tha
t e
nga
g
e
me
n
t
lev
e
l
als
o
incr
ease
s
w
it
h
a
n
incre
as
ed numbe
r of s
tude
nts e
n
j
o
ying
m
a
them
at
ic
s
less
o
n
s
w
h
i
l
e
stud
y
i
n
g
t
he s
ubje
c
t
.
The
y
f
urt
h
er
s
ta
ted
t
h
a
t
s
e
e
i
n
g
t
h
e
rele
va
nc
e
of
m
at
he
ma
tics
l
e
ssons,
s
t
u
d
en
ts’
a
t
t
i
t
u
d
e
s
t
ow
ard
the
s
u
b
j
ec
t
als
o
im
p
rove
d.
A
s
r
e
g
ards
h
o
w
t
he
s
tu
de
n
t
s
ra
te
t
he
mse
l
v
e
s
a
t
h
ow
t
he
y
fare
i
n
t
h
e
s
u
b
j
e
c
t
,
h
a
l
f
o
f
t
h
e
m
r
e
g
a
r
d
them
se
lves
a
s
ave
r
age
stu
d
e
n
ts
i
n
ma
the
m
a
tic
s.
T
h
i
s
is
i
n
con
t
r
ast
w
i
t
h
t
he
q
u
a
nti
t
a
t
i
v
e
data
w
hi
c
h
r
e
v
e
a
le
d
tha
t
b
y
a
n
d
la
rge,
s
tude
n
t
s
fe
lt
tha
t
t
he
y
a
r
e
no
t
g
o
od
i
n
m
ath
.
F
o
r
bo
t
h
p
r
e
tes
t
a
n
d
pos
tte
st,
the
b
i
gge
st
com
p
o
n
e
n
t
is
f
or
t
he
sl
i
g
h
t
l
y
be
lieve
s th
at
on
e
’
s sel
f
i
s
ba
d
i
n
m
a
the
m
atics
,
w
h
ic
h
ga
ve
4
1
%
a
n
d
34%,
respe
c
t
i
ve
l
y
.
S
t
u
d
e
n
t
2
re
co
u
n
te
d
t
h
a
t
t
here
a
re
t
o
p
i
c
s
w
h
ic
h
s
he
c
o
u
l
d
u
n
d
e
r
st
a
nd
a
n
d
t
h
er
e
are
ot
her
s
w
hic
h
she
c
o
ul
d
n
o
t.
S
tude
n
t
9
m
ad
e
a
fo
llow
-
up
s
ta
t
e
me
nt
o
n
t
h
i
s
by
sa
yi
ng
“
T
here
are
tes
t
s w
h
ic
h
I w
a
s
a
b
le
t
o
p
a
s
s
a
nd th
e
r
e
a
r
e
al
so
so
me whi
c
h I fai
l
e
d.”
When
a
ske
d
a
bo
u
t
h
ow
t
hey
m
a
na
ge
i
n
t
h
e
s
u
bj
e
c
t,
m
os
t
o
f
the
s
e
st
ude
n
t
s
c
o
n
v
eye
d
t
ha
t
t
h
ey
p
e
r
seve
r
e
i
n
the
su
b
j
ect
by
n
ot
e
asi
l
y
givi
ng
u
p
wh
en
t
ry
ing
so
lv
i
n
g
ma
them
at
i
c
al p
r
o
b
l
e
m
s.
They
seek
t
he
he
l
p
o
f
ot
h
er
s as
w
ell.
F
o
r
the
l
a
st
s
ubs
ca
le
—t
he
b
el
ie
f
tha
t
m
a
t
hem
a
t
i
c
s
i
s
u
s
e
f
u
l
o
r
use
l
e
s
s,
s
tude
n
t
s
w
e
re
one
i
n
rega
rdi
ng tha
t
ma
t
he
ma
tic
s is
u
sef
u
l.
T
h
i
s
i
s
c
ons
i
s
ten
t
w
it
h t
he
r
e
s
ults in
t
h
e
pr
e
t
est
a
n
d
pos
ttest w
h
i
c
h
s
how
tha
t
m
ajor
ity
o
f
the
s
e
s
t
ude
n
t
s
be
l
i
eve
i
n
t
h
e
u
se
ful
n
ess
o
f
m
a
t
h
e
m
a
tic
s.
I
n
the
i
n
te
rvi
e
w
,
not
onl
y
d
i
d
t
h
ey
artic
ula
t
e
t
h
e
rele
va
nce
of
m
athem
a
t
i
cs
i
n
t
e
rm
s
of
i
ts
p
ra
ct
i
c
a
l
a
p
p
lic
a
t
i
o
ns
;
the
y
a
ls
o
c
l
aim
e
d
tha
t
ma
them
at
i
c
s
hone
s
th
e
m
t
o
be
b
e
tter
st
u
d
e
nt
s.
S
uc
h
is
e
vi
de
nt
i
n
the
fol
l
ow
i
n
g
tra
n
scri
bed
re
sp
onse
s
:
“
M
a
t
he
m
a
t
i
cs
trai
ns us
t
o
be m
o
re
pers
e
v
e
r
ing
in
fin
di
ng
so
l
u
t
i
on
to
a
n
y g
i
v
e
n
prob
lem
”
(S
tude
nt
3
)
,
“Do
i
ng
nu
mb
ers i
s
not
th
e
on
l
y
esse
n
c
e
o
f
ma
t
h
emat
i
c
s bu
t
al
so
th
at
of
b
e
ing
l
o
g
i
cal
th
in
k
e
r
”
(S
t
ude
nt
7
),
“
I
t
teac
hes
us v
a
lue
s
l
i
ke
det
e
rm
in
a
t
i
o
n a
n
d
in
de
pe
n
d
e
n
c
e
”
S
tude
n
t
1
a
nd
“
M
athe
m
a
t
i
c
s
is use
f
u
l
be
cau
s
e
I
am
tr
a
i
ne
d
to
b
e
c
r
i
t
ic
al
t
h
in
ker”
(S
t
ude
n
t
9).
The
las
t w
a
s affirm
ed b
y
S
t
ude
n
t
1
0
b
y
say
in
g
:
“
I
n
re
al
it
y
,
y
ou
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2252-
8822
IJERE
V
ol
.
7,
N
o.
2,
June
2
0
1
8
:
13
2
– 14
1
13
8
m
a
y n
o
t
ac
t
ually
a
p
p
ly
t
h
e e
x
a
ct
t
h
in
gs t
h
at
w
e
re
l
e
arne
d in
t
h
e c
l
as
sroom
.
Y
e
t
i
n
th
e
fut
u
re,
we
w
ill
be
trai
ne
d to
be c
r
i
t
ic
al t
h
i
n
ke
rs.
”
Th
e
re
sult
s
usin
g
th
e
qu
an
tita
t
i
v
e
an
d
qu
a
l
i
t
a
t
i
v
e
d
a
t
a
i
nd
i
c
a
t
e
s
t
hat
t
h
e
stude
n
t
s’
a
tti
tu
de
t
ow
ar
d
ma
them
at
i
c
s
is
g
ener
al
ly
p
o
s
iti
ve
f
or
t
he
s
ub
sc
ales
:
lik
i
ng
o
r
disli
k
i
n
g
m
a
them
a
t
i
c
s,
t
en
d
e
ncy
t
o
e
nga
ge
i
n
or
a
v
oid
ma
t
h
e
m
a
t
i
c
al
act
iv
i
t
i
e
s,
a
n
d
b
e
li
ef
t
hat
mat
h
emati
c
s
i
s
u
se
fu
l
or
u
s
e
le
ss.
Conc
ern
i
n
g
b
e
l
ief
tha
t
one’s
self
i
s
goo
d
or ba
d
i
n m
a
them
atic
s,
the
r
esul
t
is sligh
t
ly ne
g
a
ti
v
e
.
3.2.
Stu
d
e
n
t
s’ In
s
igh
t
s
on
Jou
r
n
al Writin
g
I
n
t
he
r
es
po
ns
es
o
f
t
h
e
st
u
d
e
nt
s
rega
rd
in
g
the
i
r
tho
u
g
h
t
s
and
f
ee
li
ng
s
a
b
out
j
ou
rn
al
w
ri
t
i
ng
a
s
a
mat
h
e
m
a
t
i
c
s
c
l
ass
ac
ti
vi
ty
,
it
i
s
ve
ry
e
v
i
de
nt
t
ha
t
t
h
e
y
g
r
a
sp
the
a
c
t
ivi
t
y’s
bene
f
i
ts
t
o
b
o
t
h
the
teac
her
a
n
d
t
h
e
stude
n
t
s.
S
tud
e
nt
1
w
as
f
irst
t
o
m
e
n
t
ion
t
h
at
h
e
fin
d
s
j
o
ur
nal
w
r
it
ing
a
s
a
good
i
d
ea
b
e
c
a
u
se
t
he
a
c
t
i
v
ity
“e
nab
l
e
s
t
h
e t
e
ache
r to
k
n
o
w
w
h
a
t
t
o
p
i
cs
t
h
e
stude
n
t
s f
i
nd e
a
sy or
d
i
ffic
u
l
t
”
.
H
e
a
dds
:
“I
f
sh
e
(teacher)
re
ad
s
th
at
m
any
are hav
ing
di
ff
i
c
ulty
at a
ce
r
t
ai
n
to
p
i
c
,
she
m
i
g
h
t
d
i
sc
uss i
t
a
g
a
i
n for
us
ne
xt
m
e
et
i
ng so we
c
a
n
un
ders
tan
d
it”
.
A
not
her
in
ter
e
st
i
n
g
p
o
i
n
t
w
a
s
r
aised
by
S
t
ude
n
t
2
s
a
y
in
g
th
a
t
“
W
he
n st
ude
n
t
s
g
i
ve
f
e
e
d
b
a
ck
,
the
te
ac
her
is
able
t
o
t
h
ink
wha
t
ne
e
d
s t
o
be
a
ddre
ssed
an
d co
ns
ide
r
inte
re
st
i
ng
ide
a
s th
at s
h
e
ca
n
use in
class.”
T
h
i
s
wa
s
a
g
ree
d
u
pon
b
y
St
ud
en
t
7
who
sh
a
r
ed
:
“
I
t
is a
w
a
y
for
the
t
e
ac
her
t
o
k
now
wh
at
nee
d
s
fu
rt
her im
pr
ov
em
ent or rev
i
ew.”
O
n
t
h
e
ot
her
h
a
n
d
,
S
t
ude
n
t
7
a
nd
S
tude
n
t
1
0
ex
pre
s
se
d
on
di
ffe
rent
occ
a
s
i
ons tha
t
jo
urna
l
w
r
i
tin
g
cre
a
tes
tim
e
for
t
h
em
t
o
ref
l
e
c
t
o
n
wha
t
h
as
b
een
l
ea
rn
ed
a
n
d
wh
at
y
et
n
ee
d
s
t
o
be
l
e
a
rne
d
.
T
h
e
s
t
u
d
e
n
t
s
’
t
a
k
e
o
n
t
h
e
u
s
e
f
u
l
n
e
s
s
o
f
t
h
e
a
c
t
i
v
i
t
y
t
a
c
k
l
e
s
t
w
o
th
i
ngs
t
ha
t
jo
urn
a
l
pr
ov
ide
s
:
com
m
unic
a
t
io
n
a
n
d
refl
ect
i
o
n.
I
ndee
d
,
jo
ur
nal
w
r
iti
ng
s
e
r
ved
as
a
n
i
n
d
i
r
ect
c
om
mun
i
c
a
tio
n
be
tw
ee
n
the
m
and
the
tea
c
her
.
S
tuden
t
3
t
o
l
d
tha
t
she
li
k
es t
he ac
t
i
v
it
y
bec
ause
t
hr
ou
gh
it
“give
s
the st
u
d
en
ts a c
h
a
n
ce
to le
t
the
t
e
ac
her k
n
o
w
t
h
e
i
r c
o
nce
r
ns”
.
L
ikew
ise
,
S
t
ude
nt
9
r
ec
ou
n
t
e
d
t
ha
t
“
J
ourn
a
l
wri
t
i
n
g is a go
o
d
ide
a
fo
r
t
h
e
stude
n
t
s who
f
e
el
s
h
y to te
ll
t
h
e
te
ac
her
w
h
a
t
t
h
ey do
no
t
u
nde
rst
an
d.
”
t
o
w
h
i
c
h
S
t
ude
n
t
6
a
g
r
ee
d
on.
Ac
co
rd
ing
to
h
i
m
m
a
n
y
fe
el
s
h
y
to
act
ua
l
l
y
t
e
l
l
th
e
tea
c
h
er
w
h
e
n
the
y
do
no
t
gr
asp
c
e
rta
i
n
t
o
p
i
cs
dur
in
g cla
s
s.
O
f
t
he
t
e
n
r
es
po
n
d
en
ts,
S
t
u
d
e
nt
1
0
ha
d
t
h
e
m
o
st
p
rofo
un
d
t
h
ing
t
o
s
a
y
a
b
o
u
t
t
h
e
a
c
t
i
v
i
t
y
i
n
t
h
a
t
i
t
e
n
ca
psul
a
t
es the
p
o
i
nt
s sh
a
r
e
d
b
y
t
h
e re
st
. H
e
sai
d
:
“
I
t is goo
d
t
o
h
a
ve
jour
n
a
l w
r
i
t
i
ng be
c
a
use i
t
is be
ne
fic
i
a
l
p
r
i
m
ar
i
l
y
f
o
r M
i
ss
(
the tea
c
he
r)
and
t
h
e
n
f
o
r
u
s
.
T
h
rou
g
h
t
h
e
act
i
v
i
ty,
she can
assess if
t
h
e
r
e
are st
i
ll
s
o
m
e
th
i
n
gs
t
h
a
t
we
do
n’t u
n
de
rst
a
n
d
. And
f
o
r
us, it
gives us
ti
m
e
t
o
re
flec
t
on wh
a
t
we
ha
v
e
le
arne
d,
wh
at
par
t
o
f
t
h
e less
on we
fi
n
d
di
f
f
i
c
u
l
t, an
d
w
h
a
t
are
a
s
we nee
d
t
o
im
prov
e on
.
”
All
i
n
a
ll,
t
hr
ee
them
es
e
m
e
rge
d
c
o
n
cer
ni
ng
the
st
u
d
en
t
s
’
i
n
s
i
g
h
t
s
ab
ou
t
jo
urna
l
w
r
it
i
ng.
F
irst,
jo
urna
l
w
r
i
tin
g
w
a
s
perc
ei
ve
d
b
y
t
he
s
t
u
de
nt
s
as
a
u
se
fu
l
com
m
u
n
i
ca
ti
o
n
b
e
t
w
e
e
n
t
he
m
and
the
tea
c
her.
Wri
t
i
n
g
ac
t
u
a
l
l
y
o
ffer
s
a
n
a
l
t
e
r
nat
i
ve
t
o
the
us
ual
c
l
a
ssr
o
o
m
c
omm
unica
t
i
o
n
w
h
i
c
h
i
s
most
l
y
o
ral
i
n
n
a
t
u
r
e
[4
8].
A
c
cordin
g
to
L
ie
bar
s
[
27]
,
t
h
e
a
c
t
ivi
t
y
p
r
o
v
i
de
s
a
m
eans
of
c
om
munica
ti
on
bet
w
ee
n
t
h
e
teac
her
an
d
st
u
d
e
nt
s,
a
n
d
affo
rd
s
t
h
e
oppo
rt
u
n
it
y
fo
r
the
st
ud
en
t
s
t
o
c
o
mmu
n
i
cat
e
ma
t
h
e
m
at
i
c
a
l
i
d
eas
w
i
t
h
th
e
i
r
t
eac
h
e
r.
F
u
r
t
he
r,
j
our
n
a
l
w
r
i
t
i
ng
g
i
v
e
s
t
h
e
stu
d
e
n
ts
t
h
e
c
ha
nce
t
o
r
e
a
l
i
ze
w
h
e
n
t
o
as
k
for
h
e
lp
w
hi
c
h
e
ve
ntua
lly
con
t
ri
b
u
tes
to t
he
t
eac
h
i
n
g
-le
a
r
ni
ng e
n
viron
m
ent
[4
9].
S
i
nce
for
t
h
e
st
ude
n
t
s,
a
n
o
p
e
n
l
i
n
e
of
c
om
m
uni
c
a
t
i
o
n
w
a
s
cre
a
t
e
d
t
hro
u
g
h
j
ou
rn
al
w
ri
t
i
ng
,
th
e
y
re
co
gn
i
zed
a
s
wel
l
th
a
t
th
e
a
c
t
i
vi
t
y
e
n
a
bl
es
th
e
i
r
t
ea
ch
er
t
o
a
ssess t
h
eir lea
r
ning.
It hel
p
s
t
h
e te
ac
he
r stra
te
giz
e
in
h
e
r
i
nstr
u
c
t
i
on.
I
n
t
h
e
st
u
dy
m
a
de
b
y
A
d
d
i
s
on
[2
4],
one
o
f
t
he
r
ew
a
r
ds
o
f
s
t
u
d
e
n
t
s
’
journa
l
w
r
i
t
i
ng
i
s
incre
a
se
d
aw
a
r
e
n
e
ss
of
s
tu
de
nt
c
om
pre
h
e
n
s
i
o
n
o
f
c
once
p
t
s
,
fe
eli
ngs,
and
att
itu
de
t
ow
ar
d
ma
t
h
e
m
a
tic
s.
W
ha
t
the
s
t
u
d
e
n
t
s
s
h
a
re
a
bo
ut
t
he
i
r
l
e
a
rn
in
g
e
xper
i
e
n
ce
s
a
l
l
o
w
s
t
h
e
teac
her
t
o
m
oni
t
o
r
t
h
e
stude
nts’
u
nder
s
t
a
n
d
i
n
g
of
t
he
t
op
i
c
[50
]
and
affec
t
h
o
w
tea
cher
s
app
r
oa
ch
t
he
sub
je
ct
m
a
tter
aga
i
n
[51].
Rec
o
g
n
iz
in
g
t
h
at
t
he
a
c
t
iv
ity
n
o
t
o
nly
be
ne
fi
ts
t
h
e
t
ea
c
h
er
but
a
l
s
o
the
st
ude
n
t
s
ar
e
t
h
e
th
ird
t
h
em
e
d
e
du
c
e
d
f
r
o
m
th
e
r
e
s
pon
s
e
s. Thi
s co
nfo
r
ms
t
o
th
e f
i
ndi
ng
s mad
e
b
y
V
an
D
er
Mo
l
en
[
15]
a
nd
O
dafe
[
4
9
]. The
form
er
e
m
phasized
t
ha
t
i
n
c
o
r
pora
t
i
n
g
refl
e
c
t
i
v
e
jo
urna
l
i
n
g
is
b
e
n
efic
i
a
l
for
bo
t
h
i
nstruc
t
o
r
an
d
the
s
t
u
d
en
ts.
A
c
c
o
rdi
n
g
to
h
im
,
the
be
ne
fits
o
f
com
m
un
ica
t
i
o
n
a
n
d
im
pro
v
in
g
s
t
u
d
e
nt
l
e
a
r
ni
ng
e
xpe
ri
en
c
e
ou
t
w
eig
h
t
h
e
pro
b
lem
of
r
e
f
lec
t
i
v
e
jour
na
l
i
ng
a
s
tim
e
c
o
n
s
um
i
ng.
W
h
ile
,
for
Od
af
e
[49
]
,
h
e
f
ou
nd
t
hat
wh
en
t
e
ach
er
a
n
d
stude
n
t
s
bec
o
m
e
p
a
r
tners
in
m
athem
a
t
i
cs
t
e
ach
i
ng
a
n
d
l
e
arni
n
g
p
ro
ce
ss,
r
e
flec
t
i
o
n
p
roce
ss
r
e
s
ults
i
n
impro
v
e
d
st
u
d
e
nt lea
r
n
i
ng
en
vir
onm
en
t.
Li
nk
i
n
g
jo
urna
l
w
r
i
t
i
n
g
w
i
th
s
t
ude
n
t
s’
a
t
t
i
t
u
d
e
tow
a
rd
m
a
t
he
ma
t
ics
dr
aws
in
a
n
in
di
re
c
t
a
ss
o
c
i
a
ti
on
betw
ee
n
t
h
e
t
w
o.
I
n
t
h
is
s
tu
dy,
j
o
u
rna
l
s
w
e
re
u
se
d
by
t
h
e
t
e
a
c
h
e
r
t
o
i
d
ent
i
fy
t
he
p
r
o
ble
m
s
t
h
a
t
t
h
e
s
t
u
de
nts
ma
y
have
a
n
d
the
n
t
o
e
v
e
n
t
u
al
ly
i
m
p
r
ove
t
h
e
ir
a
t
tit
u
d
e
t
o
w
a
rd
m
athem
a
tic
s.
T
he
s
tat
e
m
e
nts
give
n
by
t
h
e
stude
n
t
s
a
b
o
u
t
j
our
nal
w
r
i
t
i
n
g
a
n
d
th
e
i
n
fo
rm
atio
n
a
bou
t
the
i
r
a
t
t
i
t
u
de
t
ow
ard
ma
t
h
em
ati
c
s
for
bo
t
h
p
rete
st
and
p
o
s
t
te
st
c
oi
nc
ide
i
n
t
he
i
dea
t
h
a
t
j
o
u
rn
al
w
rit
i
ng
is
a
n
ai
d
for
a
te
a
c
he
r
t
o
i
m
p
ro
ve
s
tu
de
nt
s’
a
t
t
i
t
u
d
e
tow
a
rd ma
t
he
ma
ti
c
s
. In
p
a
r
ti
cular,
t
he m
eas
ure
or stu
de
nts’
lik
ing ma
t
h
e
m
ati
c
s
a
n
d
te
n
d
enc
y
t
o
e
n
ga
g
e
in
t
h
e
sub
j
e
c
t
c
ha
nge
d
p
o
sit
i
v
el
y
du
rin
g
t
he
p
eri
o
d
w
h
en
j
o
u
rna
l
w
rit
i
ng
w
as
i
mp
l
e
me
nt
ed
.
Th
is
i
s
supp
o
r
t
e
d
b
y
a
Evaluation Warning : The document was created with Spire.PDF for Python.
IJERE
I
S
S
N
:
2252-
88
22
T
h
e
Role
of
Jo
urn
a
l
Wri
tin
g i
n
Se
n
i
or
H
i
g
h
Sch
o
o
l S
t
ude
n
t
s’ Atti
tude
t
o
ward
M
a
the
m
a
t
i
c
s(
Ive
e
K. G
u
ce)
13
9
numbe
r
o
f
s
t
u
d
i
es.
F
i
r
s
tl
y,
A
ddi
son
[24]
f
o
u
nd
th
at
“
j
o
ur
na
ls
o
ffer
a
g
li
m
p
se
i
n
t
o
w
h
a
t
t
he
s
t
u
den
t
s
li
k
e
d
an
d
di
sl
i
k
ed
a
bo
u
t
m
a
t
he
ma
ti
c
s
c
lasses”
(
p.
3
4).
In
c
onnec
t
io
n
w
i
th
s
tude
nt
e
nga
ge
me
n
t
,
K
l
ein,
P
fl
e
d
ere
r
&
Trucke
nmi
ller
[5
2],
ob
t
a
ine
d
a
s
i
m
i
l
a
r
r
esu
l
t
to
t
h
i
s
st
ud
y’s.
H
i
s
f
i
n
d
i
n
gs
s
h
o
w
e
d
tha
t
j
ourn
a
ls
r
efl
e
c
t
e
d
grea
ter
e
n
j
o
y
m
e
n
t
of
t
he
c
lass
w
h
i
c
h
u
l
t
i
ma
te
ly
i
ncr
e
a
s
e
d
t
he
m
o
tiv
ati
o
nal
le
ve
l
o
f
e
very
one
i
n
v
o
l
ve
d.
Tea
c
her
s
c
an
f
in
d
w
a
y
s
t
o
e
n
c
o
urage
st
ud
ent
e
n
ga
ge
me
nt
i
n
m
a
t
h
e
ma
t
i
c
s
[4
6
]
w
hi
ch
c
an
b
e
a
c
hi
ev
ed
by
i
m
p
l
e
m
en
tin
g
me
an
i
ngf
ul
a
cti
v
it
i
e
s
fo
r
th
e
m
[
53
].
T
h
e
t
e
ach
er’s
m
eth
ods
ha
v
e
a
m
a
j
o
r i
n
fl
uence
o
n
st
u
den
t
s’
att
itu
de
t
ow
ard
ma
t
h
e
m
a
t
i
c
s [13],
[54].
4.
CONCL
U
S
ION
I
n
m
a
t
h
cla
ssroom
w
here
t
he
p
rim
a
ry
f
oc
us
i
s
c
o
mp
u
t
at
i
o
n
a
n
d
n
o
t
th
e
mo
t
i
v
a
ti
ng
f
act
o
r
s
th
a
t
w
il
l
ma
ximize
l
e
a
rni
n
g,
s
t
u
de
nts
are
ofte
n
le
ft
b
e
i
n
g
d
isi
n
tere
ste
d
i
n
m
a
t
he
ma
ti
c
s
.
Teac
hers
h
ave
t
h
e
prim
a
r
y
role
of
c
rea
t
i
n
g
o
p
por
tu
n
i
t
i
es
t
o
c
o
n
n
ec
t
w
i
t
h
t
h
e
s
t
ude
n
t
s
t
o
e
st
a
b
lis
h
m
a
t
t
ers
t
h
at
w
ork
a
g
ain
s
t
p
o
s
iti
ve
a
tti
tu
de
tow
a
rd
t
he
s
ub
ject.
Th
i
s
s
tu
d
y
e
x
p
lor
e
d
ho
w
journ
a
l
w
r
it
ing
tak
e
s
p
art
i
n
c
ha
ng
i
ng
s
t
u
d
en
ts’
a
tti
t
ude
t
ow
ar
d
ma
them
at
i
c
s.
A
s
hy
po
t
h
es
iz
ed,
the
im
p
l
e
m
e
n
t
a
t
i
o
n
o
f
the
sai
d
a
c
ti
vi
ty
i
m
p
rove
d
t
h
e
a
t
tit
ude
o
f
the
s
t
ude
n
t
s
tow
a
rd
t
he
m
a
t
hem
a
t
i
c
s
m
ai
nly
i
n
t
w
o
a
re
as—li
k
i
n
g
t
h
e
sub
j
ec
t
a
n
d
w
i
l
lin
gn
e
ss
to
e
ng
ag
e
in
m
a
t
h
e
ma
t
i
c
al
a
c
t
i
vit
i
es.
Th
e
stu
d
e
nt
s
pe
rce
i
v
e
j
ou
rn
al
w
ri
ti
ng
a
s
a
h
e
lp
ful
to
o
l
f
or
t
he
m
to
e
n
j
oy
m
a
th
em
atics
a
n
d
e
n
gag
e
i
n
i
t
.
T
h
e
a
c
t
i
v
i
t
y
,
t
h
u
s
,
m
a
y
b
e
r
e
g
a
r
d
e
d
a
s
a
m
e
a
n
s
t
o
i
m
p
r
o
v
e
one
’s
a
t
t
i
t
u
de
i
n
m
a
t
h
e
m
atics.
T
h
e
b
e
n
e
f
its
o
f
w
ri
t
i
ng
i
n
a
mat
h
emat
i
c
s
c
l
a
ss
can
not
b
e
d
i
smisse
d
for
t
h
e
w
riti
ngs
s
ha
ll
bi
n
d
c
l
o
s
e
r
t
h
e
teac
her
and
t
h
e
stude
n
t
s
i
n
a
t
t
a
i
ni
ng
a
n
e
ffe
c
tive
le
arn
i
n
g
e
nv
iro
n
me
n
t
.
Wha
t
t
he
s
tud
e
nts
share
w
ill
d
irec
t
t
h
e
tea
c
her
in
impro
v
i
n
g the
att
itu
de
o
f
t
h
e
st
ude
n
t
s
tow
a
r
d
t
he
s
ub
jec
t
.
REFE
RENCES
[1]
Carpen
ter,
T
.,
C
o
r
bi
tt,
M.
,
Ke
p
n
er,
H.
,
Lin
dqui
st
,
M.
,
&
Re
y
s
,
R
.
(
19
80
)
.
S
tud
e
nt
s'
a
ffe
c
tiv
e
re
spo
n
se
s
to
mathe
m
atics: Re
s
ults and i
mplicat
ion
s
f
ro
m na
ti
o
n
al
assessment.
Ar
it
h
m
e
t
ic
T
e
a
c
he
r
,
27
(4),
34-3
7
.
[2]
P
a
ul
os,
J
.
(19
88).
Innum
e
racy
. N
ew Yor
k:
H
ill
a
n
d
W
a
n
g
.
[3]
Sh
ut
t,
J
.
(2
00
3
)
.
T
h
e u
s
e
of
wr
itin
g
as
f
o
u
n
d
a
ti
o
n
for
clas
sr
oo
m envi
ron
m
en
t
pr
o
m
o
t
i
n
g
en
ga
gemen
t
in
t
h
e
mi
dd
le
level
m
a
t
h
ema
t
ics cla
ssr
oo
m: A
les
s
o
n
fr
om th
e fiel
d
(Mast
e
r’
s
the
s
is
).
R
et
r
i
eved
f
ro
m
ProQuest
D
issertations
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nd
Th
eses
d
atab
ase.
(
UM
I
n
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4
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6404
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[4]
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How
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l
uenc
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n
th
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h
clas
sroom
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T
hes
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Retr
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f
r
om
ProQ
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d achievemen
t of
st
ude
n
t
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ll
eg
e
mathe
m
a
t
ics course
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t
at
i
o
n).
Retr
ieved
f
r
o
m
P
roQuest
Diss
erta
ti
ons
a
nd
T
hese
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da
ta
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c
h
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ve
m
e
nt in
a
n
d
a
tti
tu
d
e
s
to
w
a
rd
m
a
t
he
ma
t
i
c
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.
S
c
ho
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s
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n
achiev
e
m
e
nt
a
n
d
a
ttit
ude
i
n
mat
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e
m
atics
(Doctoral
Di
s
s
ertat
i
on,
Un
iversity
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f
No
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t
h
Te
x
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Diss
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h
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tudes
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evement
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Un
pu
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s
h
e
d
d
o
c
t
oral
d
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s
sert
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U
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M
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f
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a
l wri
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i
n
g
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e
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a
c
hi
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inte
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an
d stu
d
e
nts’ at
ti
tu
de
s towa
rd
ma
the
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atic
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i
s
sert
at
ion).
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r
o
Q
uest
D
iss
e
rtatio
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n
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ip
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r
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b
etw
een
m
athematic
s
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acad
em
ic
m
o
tivati
o
n
an
d
intel
l
igen
ce
q
u
o
tien
t
w
ith
m
a
them
atics
a
c
h
ie
ve
m
e
nt.
P
r
o
c
ed
ia Soci
a
l
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Beh
a
vio
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nces,
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3
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-1
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ti
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a
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.
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c
atio
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t
t
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ath
e
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ievem
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2252-
8822
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P
roceedi
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g
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f
the
3
0
th
a
nn
ual
c
o
n
f
erence
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f
t
h
e
m
athe
m
a
tics
edu
catio
n
res
earch
g
r
ou
p o
f
Au
s
tra
l
a
s
ia
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98
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0
7
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s
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M
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e
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atti
tu
de
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t
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ward
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lear
ni
ng
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ath
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m
a
ti
cs:
Im
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o
f
teach
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i
n
a
s
p
o
rtin
g
con
t
ex
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T
e
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her
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An
a
lternat
iv
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rm
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f
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r acad
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s.
L
e
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ni
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Disabilit
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e
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n
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atics,
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at
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d
st
u
d
e
nt
s’
i
nteres
ts:
An
A
lb
ani
a
n
st
ud
y
(Do
c
to
ral
di
sser
tat
i
on,
Univers
ity
o
f
Agde
r,
K
ristians
and,
N
orway).
R
e
t
r
i
ev
ed
f
ro
m
ht
tp:/
/ww
w
.
n
b.
n
o
/
i
dtj
e
nest
e/U
R
N:N
B
N:
no
-b
ib
sy
s_
brage_
37
09
4
Evaluation Warning : The document was created with Spire.PDF for Python.
IJERE
I
S
S
N
:
2252-
88
22
T
h
e
Role
of
Jo
urn
a
l
Wri
tin
g i
n
Se
n
i
or
H
i
g
h
Sch
o
o
l S
t
ude
n
t
s’ Atti
tude
t
o
ward
M
a
the
m
a
t
i
c
s(
Ive
e
K. G
u
ce)
14
1
[54]
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s
ah
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yere,
M.
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01
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t
u
d
en
t
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i
t
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d
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ards
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ath
e
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an
d
p
e
rf
o
r
m
a
n
ce:
D
o
e
s
the teacher attitude
m
atter?
J
ourn
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o
f
E
d
ucation
a
n
d
Pract
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(3),
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3
2–
13
9
.
B
I
OG
RAP
HY
O
F
A
U
T
H
O
R
Dr.
Iv
ee
K.
G
u
ce
i
s
a
m
at
hemati
cs
t
eacher
a
n
d
a
r
es
e
a
rch
e
r.
S
he
i
s
a
n
a
ss
oci
a
te
prof
es
so
r
o
f
t
h
e
M
ath
e
m
a
ti
cs
D
epart
m
en
t
o
f
t
h
e
C
olleg
e
o
f
Ed
uca
t
i
on,
A
rts
an
d
S
c
i
e
nces
o
f
th
e
De
L
a
S
a
ll
e
Li
pa.
S
h
e
fi
nis
h
ed
h
er
B
S
M
a
th
emat
i
cs
M
a
j
or
i
n
Actu
arial
S
c
i
e
nce
at
t
h
e
U
ni
v
e
rs
it
y
o
f
S
to.
Tomas
.
S
he
o
b
t
a
i
ned
h
e
r
M
a
s
t
e
r
i
n
Mat
h
em
atics
deg
r
ee
f
r
o
m
t
he
D
e
La
S
a
l
le
U
n
i
v
e
rsi
t
y
,
a
n
d
earned
th
e
de
gree
P
h
il
os
op
hy
in
E
d
u
cat
ion
M
a
jo
r in
Mathema
tics
from the
Universi
t
y
of
B
atan
gas.
Dr.
Gu
ce
is
c
u
r
ren
t
l
y
t
h
e
P
rogram
C
hai
r
i
n
Mat
h
em
ati
c
s
.
B
es
ides
t
eachi
n
g
,
s
h
e
i
s
activ
ely
eng
a
ged
in
r
esearch.
She
h
a
s
p
u
b
l
i
s
h
e
d
a
n
u
m
b
er
o
f
pap
ers
at
i
n
t
ernati
on
al
jo
urn
a
ls
a
nd
p
re
se
nte
d
h
e
r
w
o
r
ks
a
t
se
ve
ra
l
c
o
n
f
e
r
e
n
c
e
s
b
oth
lo
call
y
a
n
d
int
e
rnatio
nall
y.
M
os
t
of
h
er
w
o
r
ks
a
re
f
o
c
used
o
n
m
a
t
h
em
ati
c
s
e
d
u
c
a
tion
.
He
r
pa
ssion
fo
r
t
eachin
g
m
a
t
h
em
at
ics
is
h
er
m
o
t
i
v
ation
in
s
hari
ng
h
er
k
no
wl
edge
t
o
ot
her
educat
ors
th
rou
g
h
the
st
ud
i
e
s
she
cond
uct
s
Evaluation Warning : The document was created with Spire.PDF for Python.