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V
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ISSN
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Effectiveness of e
xperienti
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ning-base
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a
terial
in M
athematics
Mu
tmainah
1
, R
u
ka
yah
2
,
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nt
a
s
i
h
I
nd
ri
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y
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3
1
M
a
st
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rog
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a
m
of Elem
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ntary
Schoo
l T
eacher Traini
n
g
and
Ed
u
cat
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elas
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aret U
n
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versity
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don
esi
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e
bela
s Ma
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Un
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Art
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fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
Re
ce
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d
O
c
t
9
,
2018
R
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v
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d
Oct
29
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0
18
A
c
c
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pte
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J
a
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2019
Th
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a
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rial
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n
Mat
h
em
a
t
ics
on
t
he
M
ath
e
m
a
t
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cog
n
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t
i
v
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abil
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of
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h
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if
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tud
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elem
en
tary
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ch
o
ol.
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research
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sed
q
u
asi
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pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
Scien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
Mu
t
m
ai
na
h,
D
e
pa
rtme
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a
ry S
cho
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ache
r
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rain
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g an
d
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ucat
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on,
Se
belas Ma
ret
U
n
i
v
e
r
sity,
Ind
one
sia,
Jl
.
I
r
. S
u
tar
m
i
N
o
. 36A
,
Je
bre
s
, S
ur
akar
t
a
,
Jaw
a
T
enga
h, I
ndone
si
a (5
71
26).
Em
ail:
mutm
ai
nah
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m
a
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st
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t
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u
ns.ac
.
id
1.
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N
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the
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he
m
a
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j
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tan
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h
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m
a
t
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l
t
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or
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nterna
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t
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s
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ss
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s
how
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tha
t
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nke
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m
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[
1].
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her
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ISA
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a
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2252-
8822
Int.
J
.
Ev
al. & R
es. Educ.
Vol.
8, No. 1, March
2
019
:
57
- 6
3
58
Base
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d
e
n
t
s
o
ny
fo
c
u
se
d
o
n
t
he
c
onve
nti
o
n
a
l
tea
c
h
in
g
m
a
teria
l
w
h
ic
h
caus
e
d
t
h
e
l
o
w
co
g
n
it
i
v
e
ab
i
lit
y.
T
he
l
ow
c
og
n
i
t
i
ve
a
bil
i
t
y
o
f
t
h
e
stude
n
t
i
s
i
n
d
i
ca
t
e
d
b
y
t
he
l
ow
r
e
s
ult
of
M
at
hem
a
t
i
c
s
t
est
c
o
m
p
are
d
t
ha
n
o
t
he
r
subje
c
t
s.
T
hi
s
pro
b
le
m
is
s
up
por
t
e
d
b
y
t
he
r
esea
rch
con
d
u
cte
d
by
Zu
lfiah
w
h
i
c
h
sta
t
e
s
t
ha
t
t
h
e
una
va
ila
b
i
l
i
t
y
o
f
a
d
e
qua
t
e
t
e
a
c
hi
n
g
m
a
t
e
r
ia
l
cause
s
low
tes
t
r
e
s
ult
of
t
he
st
ude
n
t
[3].
Th
e
t
e
a
c
h
i
n
g
ma
t
e
ri
al
h
as
t
he
g
re
a
t
est
ro
l
e
a
s
t
h
e
medi
u
m
t
o
at
t
a
in
M
a
t
h
e
ma
t
i
c
s
l
ea
rni
n
g
ob
je
ct
ive
.
The
i
m
plem
en
tat
i
o
n
o
f
M
a
t
h
e
m
a
tics
le
arni
ng
proc
ess
re
q
u
i
r
es
t
he
e
ffec
t
i
ve
t
ea
c
h
i
n
g
m
a
teria
l
.
The
te
ac
h
i
n
g
ma
terial
c
a
n
a
ssist
t
he
s
t
ude
nt
s
i
n
l
ear
nin
g
som
e
th
i
n
g
[4
]
.
T
he
e
ffe
ct
iv
e
tea
c
h
i
ng
m
a
ter
i
a
l
w
i
l
l
he
l
p
t
he
stude
n
t
s’
e
x
p
e
r
ienc
e
in
l
e
a
r
ni
n
g
a
c
tiv
it
ies
;
t
her
e
for
e
,
th
e
Ma
t
hem
a
tics
lear
ni
ng
is
m
ore
m
e
a
n
i
n
g
f
ul
a
n
d
resul
t
s
i
n
i
m
p
r
ove
d
s
t
ude
nt
c
og
n
i
t
i
ve
a
b
ili
t
y
.
In
M
a
t
he
ma
ti
c
s
l
ea
rn
ing
p
r
oce
ss,
t
he
l
e
a
r
ni
ng
w
h
ic
h
d
i
rec
t
l
y
rela
t
e
s
the
m
a
t
e
r
i
a
l
t
o
t
h
e
r
eal
d
ai
l
y
e
x
p
erie
n
c
es
i
s
re
quire
d.
O
n
e
o
f
t
h
e
t
e
ach
i
n
g
ma
t
e
ri
als
t
h
at
can
b
e
us
ed
i
s
the e
x
perien
t
i
a
l
le
a
rn
i
ng-
base
d tea
c
h
ing m
a
t
e
rial in
Mat
h
e
m
atic
s. Ex
p
eri
e
nt
ia
l le
ar
ni
n
g
is de
ve
lo
pe
d b
a
se
d o
n
K
o
l
b
’s the
ory
em
phas
i
zi
n
g
th
e
centra
l
role
o
f
the
ex
p
e
r
ie
nc
e
in
lea
rn
in
g pr
oc
ess.
Ex
pe
rien
t
i
a
l
l
e
a
rni
ng
the
o
r
y
d
efi
n
es
l
e
a
rn
i
n
g
as
t
he
p
roce
ss
wh
e
r
eby
kn
ow
le
dg
e
is
c
re
ated
t
hr
ou
g
h
the
tra
n
sf
orma
tio
n
of
e
xpe
r
i
e
n
ce
.
K
now
le
dge
r
e
s
u
l
ts
f
ro
m
the
co
m
b
i
n
ati
o
n
of
g
r
a
sp
i
ng
a
nd
tra
n
sf
o
r
ming
expe
r
i
ence
[
5].
Ex
per
i
e
n
tia
l
l
e
a
r
ni
ng
r
e
f
lec
t
s
t
h
e
le
arn
i
n
g
w
hi
c
h
i
s
a
ttai
n
ed
t
hr
oug
h
t
h
e
perso
n
a
l
e
xpe
rie
n
c
e
and
i
n
v
o
l
ve
me
nt
[
6]
.
Exper
i
e
n
tia
l
lea
r
ni
n
g
c
an
s
ti
m
u
la
te
t
h
e
s
t
u
d
e
n
t
-
cen
te
r
e
d
lea
r
n
i
ng
proc
ess
t
o
m
ake
the
m
bu
ild
t
he
ex
p
e
r
ienc
e t
h
a
t
t
he
y
get
dur
in
g
t
h
e
l
e
a
r
ni
ng proc
e
s
s.
Ex
pe
rien
t
i
a
l
l
e
a
rni
ng
st
im
ula
t
e
s
t
he
s
tu
de
nts
in
t
he
ir
a
c
tiv
i
t
i
e
s
t
o
t
h
in
k,
e
x
p
lor
e
,
a
s
k,
m
a
k
e
dec
i
s
i
on,
and
a
p
p
l
y
w
h
a
t
t
he
y
ha
ve
l
e
a
rne
d
.
Expe
r
i
en
t
i
a
l
l
e
a
rn
in
g-ba
se
d
t
eac
hing
m
a
terial
u
ses
student-cent
e
red
appr
oa
ch
t
hat
is
s
ta
rte
d
by
th
e
un
der
l
y
i
n
g
p
rinc
ip
le
t
ha
t
p
e
op
l
e
l
e
arn
be
st
f
r
o
m
t
h
e
e
xpe
rie
n
c
e
.
It
i
s
in
l
in
e
wi
t
h
t
h
e
r
es
ea
rch
ca
rri
e
d
ou
t
b
y
Ll
ewel
l
y
n
&
Frame
wh
i
c
h
st
a
t
e
t
h
a
t
e
xp
erien
tia
l
l
e
arn
i
ng
i
s
d
es
i
gne
d
to
g
i
v
e
the c
o
mpr
e
hen
s
i
v
e
l
e
arni
n
g
e
xper
i
enc
e
[
7].
Ex
pe
rien
t
i
a
l
l
e
a
rni
ng-ba
se
d
t
e
a
c
hi
n
g
m
a
t
e
r
ial
i
n
M
a
t
he
ma
t
i
c
s
c
o
nsis
ts
o
f
f
our
s
t
a
ges
:
C
o
n
cr
ete
Ex
perie
n
c
e
(
CE),
R
efle
ct
ion
O
b
se
rva
tion
(RO),
A
b
s
t
ract
C
onceptu
al
iz
at
io
n
(AC
)
,
a
n
d
Ac
t
i
v
e
Ex
perim
e
n
t
at
i
on
(
A
E)
[
8].
Thos
e
fo
ur
p
ri
nc
ip
les
a
i
m
to
m
a
k
e
the
s
tu
de
nt
s
ha
ve
t
he
e
x
p
e
rienc
e
t
o
e
xpe
rience
,
obs
erve
,
th
ink,
a
nd
a
c
t
duri
n
g
M
a
the
m
a
t
i
c
s
l
e
arn
i
n
g
p
r
o
c
e
ss.
B
a
sed
on
t
h
e
a
b
o
v
e-m
e
nt
io
ne
d
st
atem
en
ts,
the
ob
jec
t
i
v
e
t
h
a
t
w
il
l
be
a
t
t
a
i
ne
d
in
t
h
i
s
rese
arc
h
i
s
to
f
i
nd
o
u
t
t
he
e
ffe
c
t
i
v
ene
ss
o
f
e
xper
i
en
t
i
a
l
l
ea
rni
n
g
-
based
teac
h
i
ng
m
a
ter
i
a
l
i
n
Ma
them
atic
s
o
n
t
he
i
m
p
rove
me
nt
o
f
Ma
the
m
a
t
i
c
s
c
o
gn
iti
v
e
a
bi
li
ty
o
f
th
e
fi
fth-g
r
ad
e
stude
n
t
s
i
n
e
l
e
m
e
ntar
y sch
o
o
l
.
2.
RESEARCH
M
ETH
O
D
Thi
s
r
ese
a
r
c
h
u
si
ng
q
u
a
si
-exp
eri
m
e
n
t
a
l
met
hod
s
,
t
h
e
e
xpe
ri
me
n
t
a
l
de
s
i
gn
i
n
t
hi
s
re
se
ar
ch
i
s
t
h
e
mat
c
h
i
ng
onl
y
p
r
e
t
e
s
t
-
po
stt
e
st
c
o
n
t
r
ol
g
ro
up
d
esi
g
n
[9
].
B
e
c
a
u
s
e
t
h
is
r
e
s
ea
r
c
h
t
o
f
in
d
out
t
he
e
ffec
t
i
ve
ne
ss
of
expe
r
i
en
t
i
a
l
l
e
a
rni
ng-ba
se
d
te
ac
h
i
n
g
m
ater
ia
l
in
M
a
t
he
ma
t
i
c
s
o
n
t
h
e
i
m
p
r
o
v
e
m
e
n
t
o
f
M
a
t
h
e
m
a
t
i
c
s
c
o
g
n
i
t
i
v
e
abi
l
i
t
y
o
f
t
h
e
fift
h-gra
d
e
s
t
u
d
e
nt
s,
t
he
n
n
e
e
d
a
b
ala
n
c
e
d
c
ond
i
ti
on
be
tw
ee
n
the
ex
pe
rime
nt
a
l
a
nd
t
h
e
c
o
n
t
r
o
l
gro
up
be
fore
t
he su
b
j
e
c
t
t
re
a
t
me
nt. A
f
ter to
k
n
o
w
t
w
o
gr
ou
ps st
atu
s
i
s
homo
g
e
n
e
ou
s,
t
he
e
x
p
e
ri
ment
g
ro
up
i
s
gi
ve
n
t
h
e
trea
tm
ent
us
i
ng
e
x
perie
n
tia
l
lea
r
n
i
n
g
-base
d
t
ea
c
h
i
n
g
ma
terial,
w
h
ile
t
he
c
o
n
tr
ol
g
ro
up
is
g
iv
en
t
h
e
trea
t
m
en
t
w
i
t
h
ou
t e
xpe
rie
n
t
i
a
l
lea
rn
in
g-base
d
t
e
ac
h
i
ng
ma
te
rial
.
Thi
s
r
ese
a
r
c
h
w
a
s
c
ond
u
c
te
d
in
t
wo
e
l
e
me
n
t
a
r
y
sc
hool
s
in
G
unu
ng
pat
i
,
S
e
m
a
ra
ng,
I
ndo
ne
s
i
a
.
S
a
mplin
g
te
ch
ni
que
s
i
n
t
h
i
s
re
se
arc
h
w
as
s
im
ple
rand
om
s
am
pl
i
n
g
.
Th
e
su
bj
e
c
t
in
t
hi
s
re
se
arc
h
w
as
5
4
f
i
fth
-
g
r
a
d
e
el
e
m
e
n
t
a
ry
s
c
h
ool
s
tu
d
e
n
t
s
i
n
G
unu
ngp
a
t
i
201
7/
2
018
sc
h
o
o
l
y
e
a
r.
T
he
d
a
t
a
so
ur
ce
in
t
h
i
s
r
e
sea
r
ch
w
as
the sc
ores of te
sts o
b
ta
i
n
ed
b
y
the st
ude
n
t
s,
e
it
her
t
h
e
e
xpe
ri
me
ntal gr
o
u
p
o
r
the
con
t
rol
grou
p.
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Int.
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88
22
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r
ejec
t
e
d),
if
t
o
b
ta
ined
<
t
tabl
e
r
ej
ec
t
e
d
(H
0
a
c
cepte
d)
.
Form
ula
in
de
pen
d
e
n
t t-
te
st
is
:
1
1
3.
RESULT
S
A
N
D
DISCU
SSIO
N
The
da
t
a
o
f
th
is
r
e
s
ear
ch
w
as
o
bta
i
ne
d
b
y
d
istri
b
ut
ing
th
e
que
s
t
i
on
s
of
p
re
t
e
st
a
nd
p
o
s
t
t
est
to
t
he
expe
r
i
me
n
t
a
l
a
nd
c
on
t
r
ol
g
r
o
up.
T
he
r
esu
l
t
of
p
r
e
tes
t
a
n
d
post
t
es
t
i
s
a
na
l
y
z
e
d
to
f
i
nd
o
u
t
th
e
e
f
fec
t
ive
n
ess
o
f
expe
r
i
en
t
i
a
l
l
e
a
r
ni
ng-ba
se
d
t
e
achi
n
g
ma
teri
al
i
n
Mat
h
em
a
t
i
c
s
o
n
t
he
s
t
u
den
t
c
og
n
i
t
i
ve
a
bi
lit
y
of
t
h
e
f
i
f
t
h
-
g
r
a
d
e
el
e
m
e
n
ta
ry
s
c
hool
i
n
Gu
nu
ngp
a
t
i
Su
b
-
d
i
st
ri
ct
.
The
stud
e
n
t
c
o
g
n
it
i
v
e
a
b
il
ity
i
s
o
n
e
of
t
he
i
n
d
ica
t
ors
w
h
en
t
he
l
ea
rnin
g
proc
e
ss
runs
w
e
l
l
.
T
he
c
og
n
i
t
i
ve
a
b
i
l
i
ty
i
n
I
nd
o
n
esi
a
c
an
b
e
s
t
a
t
e
d
a
s
succe
ssf
u
l
i
f
t
h
e
stude
nt
p
asses
the
Minim
u
m
P
a
ssi
n
g
G
ra
d
e
(
KKM)
that
h
as
b
een
d
e
te
rmine
d
[
10].
K
K
M
i
n
Ma
the
m
atics
sub
j
e
c
t
f
or
t
he
f
i
f
t
h
-gr
a
de
s
t
ude
n
t
i
n
G
u
nu
n
gpa
t
i
S
u
b
-di
s
t
r
i
c
t
is
6
0.
T
he d
ata
for
t
h
e pret
est
a
nd pos
ttes
t
r
e
s
ult
of
t
he
st
ude
n
t
cog
n
i
t
i
ve
a
bil
i
t
y
is
s
how
n i
n
Ta
b
l
e
1.
Ta
b
l
e
1
sh
ow
s
tha
t
t
here
i
s
si
gnif
i
c
a
n
t
d
i
ffe
renc
e
b
e
tw
een
t
he
pr
etes
t
and
p
o
stte
st
s
cor
e
o
f
t
h
e
expe
r
i
me
n
t
a
l
a
nd
c
on
tro
l
g
ro
up.
T
he
p
re
te
st
a
ve
rage
s
c
o
r
e
of
t
h
e
ex
pe
rim
e
nt
a
l
g
ro
u
p
i
s
44.2
9
an
d
t
h
e pos
tte
st
sc
o
r
e
i
s
i
mp
rov
e
d
t
o
7
5
.
71
.
M
e
an
whi
l
e
,
t
h
e
p
r
e
t
est
a
v
era
g
e
sco
r
e
o
f
t
h
e
c
on
t
r
ol
g
rou
p
i
s
42
.9
5
an
d
t
h
e
pos
ttes
t
s
c
o
re i
s
im
p
r
ove
d
t
o
63.7
2
.
In
p
ostt
est,
t
he
s
c
o
re o
f
t
h
e
e
xperim
e
nta
l
g
r
o
up is
h
i
gher t
h
an
t
he
p
os
tt
e
s
t
of
t
he
c
o
n
tr
ol
g
ro
up.
M
o
s
t
o
f
t
he
s
t
ude
n
t
s
i
n
e
xper
i
m
e
nta
l
g
ro
u
p
has
pas
s
ed
K
K
M
,
w
h
ile
s
e
v
era
l
s
t
u
d
e
nt
s
in
the c
o
n
t
r
o
l
gro
up ha
ve n
ot pa
s
se
d K
K
M
.
I
n
a
dd
iti
o
n
t
o
t
h
e
prete
s
t
a
nd
po
s
t
tes
t
s
c
o
re
o
f
the
e
x
per
i
m
e
nt
a
l
a
nd
c
o
n
t
r
o
l
g
r
o
up,
t
h
i
s
rese
arc
h
a
l
s
o
p
r
ov
id
e
s
t
h
e
cal
cul
a
ti
on
d
at
a
o
f
t
h
e
hyp
ot
hesi
s
t
e
st
o
f
p
r
e
t
est
a
n
d
post
t
e
s
t
grou
p
in
e
x
p
e
rim
e
nta
l
a
n
d
c
ontr
o
l
g
r
ou
p
.
T
h
e
h
y
pot
h
e
si
s
t
e
st
i
n
t
h
i
s
r
e
s
e
a
rc
h
was
co
nduc
t
e
d
to
f
i
n
d
out
t
he
e
ffec
t
i
v
e
ness
o
f
t
he
u
se
o
f
expe
r
i
en
t
i
a
l
l
e
a
rni
ng-ba
se
d
te
ac
hin
g
m
ater
ia
l
i
n
M
a
t
he
ma
t
i
c
s
w
h
e
t
her
or
n
o
t
t
he
re
i
s
t
h
e
d
i
ffe
r
enc
e
b
e
t
w
e
en
expe
r
i
me
n
t
a
l
g
rou
p
t
ha
t
used
e
xperie
n
tia
l
le
arni
ng-ba
se
d
tea
c
h
i
n
g
ma
t
e
r
i
al
i
n
M
a
t
h
emat
i
c
s
a
n
d
t
h
e
co
nt
rol
g
r
ou
p
th
at
d
i
d
n
ot
e
xp
eri
e
nti
a
l
l
e
a
r
ni
ng
-b
a
s
e
d
t
e
achi
n
g
ma
t
e
ri
a
l
in
m
athe
ma
t
i
c
s
.
Be
for
e
c
arryin
g
ou
t
t
h
e
hy
p
o
the
s
is
t
e
s
t
,
bala
n
ce
t
e
s
t
w
as
done e
arli
er
to the
ex
per
i
m
e
n
tal
gr
ou
p and
t
h
e c
o
nt
r
o
l
gro
up.
Ba
lanc
e
tes
t
w
as
a
i
m
ed
a
t
f
i
ndi
n
g
o
u
t
w
he
th
er
o
r
no
t
t
h
e
e
xper
i
m
e
nta
l
g
rou
p
a
nd
t
h
e
c
o
n
t
r
o
l
gro
u
p
are
in
t
he
b
a
l
a
n
ced
s
i
t
ua
t
i
on.
T
he
d
a
t
a
th
at
w
e
r
e
use
d
i
n
ba
la
n
c
e
t
e
s
t
i
s
t
h
e
d
a
t
a
o
f
p
r
e
t
e
s
t
s
c
o
r
e
o
f
t
h
e
expe
r
i
me
n
t
a
l
a
nd
c
o
n
t
r
o
l
gr
oup.
B
e
f
ore
cal
cula
t
i
n
g
t
h
e
b
alanc
e
te
st,
th
e
pre
r
equ
i
s
ite
t
e
s
t
w
a
s
d
o
n
e
to
t
he
expe
r
i
me
n
t
a
l
a
nd
c
o
n
t
ro
l
gr
o
up.
T
he
p
re
requi
si
t
e
t
e
s
t
c
ons
i
s
ts
o
f
n
orm
a
li
ty
t
es
t
a
n
d
h
o
m
o
g
e
n
e
i
ty
t
es
t
.
T
he
resul
t
of pre
r
eq
ui
site
t
es
t of
t
he
pre
test scor
e
in
ex
perim
e
n
t
a
l a
nd c
o
n
t
ro
l
g
r
ou
p is sh
o
w
n
i
n Ta
b
l
e 2.
Ta
bl
e
1
. Th
e
p
ret
e
st
a
nd
p
os
tte
s
t
re
su
lt
o
f
th
e st
ud
ent
c
o
g
n
iti
ve
ab
i
l
ity
No
E
xpe
ri
m
e
nt
C
ontrol
P
r
e
t
e
s
t
Postt
e
st
P
r
e
t
e
s
t
P
ostte
st
Me
a
n
1240
2120
1117
1657
A
v
e
r
a
g
e
44.
29
75.
71
42.
95
63.
72
M
i
n
30
6
0
23
4
7
Ma
x
57
8
7
57
8
0
Me
di
a
n
4
5
78
4
5
65
Tabl
e 2
.
Pre
req
u
is
it
e
t
e
st
re
s
u
lt
T
h
e
t
e
sts
d
one
T
e
s
t
t
y
pe
S
ig.
Te
st
d
e
c
i
si
on
p
r
e
r
e
quisite
t
e
s
t
a.
Nor
m
a
lity te
s
t
Kol
m
ogrov
-
Sm
irnov
Pre
t
e
s
t
0.
819
H
0
ac
cep
t
e
d
Postt
e
st
0.
644
H
0
ac
cep
t
e
d
b.
Ho
m
oge
nit
y
t
e
s
t
Le
ve
n
e
’s
t
e
s
t
0.
431
H
0
ac
cep
t
e
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2252-
8822
Int.
J
.
Ev
al. & R
es. Educ.
Vol.
8, No. 1, March
2
019
:
57
- 6
3
60
Ta
b
l
e
2
sh
ow
s
t
h
a
t
t
he
d
istr
ib
ut
i
o
n
of
t
he
p
r
e
t
e
st
s
core
d
a
t
a
i
n
t
h
e
ex
pe
ri
me
nt
a
l
a
n
d
c
o
n
tr
ol
g
r
o
u
p
i
s
norm
a
l
a
n
d
h
o
m
oge
no
us.
It
i
s
sh
ow
n
in
t
he
r
e
s
u
l
t
o
f
n
orm
a
lit
y
t
es
t
a
n
d
h
o
moge
ne
i
t
y
te
s
t
.
The
norm
a
l
i
t
y
t
e
s
t
wa
s
ca
l
c
ul
at
ed
u
si
ng
kol
mog
r
o
v
s
mi
rnov
.
In
p
ret
e
st
,
t
h
e
ex
p
e
ri
me
n
t
al
g
ro
up
g
ot
t
h
e
s
i
g
nif
i
c
a
n
c
e
l
e
ve
l
of
0.81
9
(S
ig
>
0
.
05),
so
H
0
i
s
a
cce
pte
d
w
hi
c
h
m
eans
t
h
a
t
t
he
d
i
s
t
ri
b
u
ti
on
o
f
t
h
e
p
r
ete
s
t
score
i
n
e
x
p
eri
m
ental
gro
up
i
s
n
orm
a
l.
M
e
a
nw
hi
l
e
,
t
h
e
pre
t
e
s
t
in
c
on
tro
l
g
r
o
up
g
o
t
th
e
si
gn
i
f
ica
n
ce
le
ve
l
of
0
.
6
4
4
(
S
i
g.
>
0
.
0
5),
so
Ho
i
s ac
ce
p
t
ed
wh
i
c
h
me
a
n
s t
h
e d
i
st
ri
bu
tion
o
f
t
h
e p
r
et
e
s
t
sc
o
r
e
in c
o
n
t
r
o
l
g
ro
up is n
orm
a
l.
Th
e
h
o
m
og
e
n
it
y
t
e
st
o
f
th
e
pret
est
in
e
x
p
erimen
t
a
l
a
n
d
con
t
ro
l
gro
u
p
w
a
s
a
na
lyze
d
usi
n
g
Leve
ne’s
Test.
The
s
i
gn
i
f
ic
a
n
ce
l
e
v
e
l
i
n
h
o
mo
ge
ne
i
t
y
t
e
st
i
s
0.
43
1
(
S
ig.
>
0
.
0
5
)
,
s
o
H
0
i
s
a
c
c
e
p
t
e
d
w
h
i
c
h
m
e
a
n
s
t
h
a
t
the
pre
t
e
s
t
sc
ore
s
o
f
t
h
e
e
xper
i
m
e
nta
l
a
nd
c
o
n
t
rol
gr
ou
p
are
ho
m
o
g
e
n
e
o
u
s
.
A
f
t
e
r
t
h
e
p
r
e
r
e
q
u
i
s
i
t
e
t
e
s
t
,
the
bala
nce
t
e
s
t
w
a
s
c
on
d
u
c
t
e
d
.
Bala
nc
e
t
e
s
t
u
sed
Inde
pe
nd
ent
T
-tes
t.
T
he
r
e
s
ult
o
f
t
h
e
b
alance
t
e
s
t
is
s
how
n
in Ta
b
le
3.
Ta
b
l
e
3.
Inde
p
e
nde
n
t
T
t
est re
su
lts
T
e
s
t
T
yp
e
Si
g
.
T
es
t
d
eci
s
i
o
n
Inde
pe
nde
nt
S
am
p
l
e
T
-
Te
st
0
.
600
H
0
ac
ce
pte
d
The
ba
l
a
nce
te
st
b
etw
e
e
n
t
he
e
xpe
r
i
m
e
nta
l
a
nd
c
o
ntr
o
l
grou
p
use
d
i
n
de
pen
d
e
n
t
sam
p
le
t
-tes
t.
T
he
sign
ifica
n
ce
le
v
el
i
s
0.6
00(S
i
g.
> 0.
0
5) w
hic
h
m
eans
t
h
a
t
H
0 s
t
at
i
ng t
h
a
t
t
her
e
i
s
n
o
d
i
ffe
renc
e i
n
pre
tes
t
sc
o
r
e
betw
ee
n
e
xpe
r
i
me
nta
l
a
n
d
c
o
n
tr
ol
g
ro
u
p
i
s
a
c
c
e
pt
ed.
It
i
n
d
ica
t
e
s
tha
t
b
o
t
h
gro
u
p
s
have
t
he
b
a
l
a
n
ce
d
i
n
i
tia
l
c
o
gni
ti
v
e
a
bi
lit
y
.
Base
d
o
n
t
he
b
a
l
anc
e
t
es
t,
b
o
t
h
gr
o
u
ps
h
av
e
t
h
e
ba
la
nced
c
o
gni
t
iv
e
ab
ili
ty
.
Aft
e
rward
,
t
h
e
hy
p
o
the
s
is
t
es
t
w
a
s
c
o
nd
uc
ted
t
o
f
i
n
d
o
u
t
the
effec
t
i
v
ene
s
s
o
f
t
h
e
pr
od
uc
t
s
b
e
i
ng
de
ve
l
ope
d.
T
h
e
effec
t
i
v
e
n
e
s
s
t
e
st
i
s
base
d
o
n
t
he
i
m
p
ro
ve
m
e
nt
o
f
the
M
a
t
h
e
m
a
t
i
c
s
c
ogn
it
i
v
e
ab
i
l
i
t
y
o
f
t
he
s
t
u
d
e
nt
s
i
n
expe
r
i
me
n
t
a
l
a
nd
c
on
tro
l
c
las
s
a
fte
r
b
e
i
ng
g
i
ven
t
h
e
d
i
f
f
er
ent
tre
a
t
m
e
nt.
It
can
b
e
see
n
from
t
h
e
di
ffere
n
c
e
o
f
the
prete
s
t
a
n
d
po
st
tes
t
o
f
t
h
e
t
w
o
gr
oups
(
N
ga
in).
If
th
e
dat
a
of
N
g
ai
n
fro
m
th
e
ex
p
e
ri
me
n
t
al
a
nd
t
h
e
con
t
ro
l
gro
u
p
a
re
d
i
s
tri
bute
d
a
s
norma
l
a
n
d
homo
g
e
n
ous
,
the
h
y
p
o
t
hes
i
s
tes
t
w
il
l
be
u
se
d
w
h
i
c
h
i
s
t
h
e
in
de
pen
d
e
n
t
T-
tes
t
. The
re
s
ul
t
of pre
requ
isi
t
e
test of t
h
e
ex
p
e
rim
e
nta
l
a
nd
c
o
n
t
r
o
l
gro
up i
s
show
n i
n
T
ab
le 4.
Ta
b
l
e
4
show
s
t
h
e
sc
ore
da
ta
o
f
N
gai
n
o
f
t
h
e
e
xpe
r
i
me
nta
l
a
nd
c
ont
rol
g
r
o
u
p
w
hi
c
h
a
re
d
i
s
t
r
i
buted
norm
a
l
a
nd
h
o
moge
nou
s.
I
t
is
i
n
d
ica
t
e
d
b
y
t
h
e
r
e
su
lt
of
n
orm
a
li
t
y
t
est
a
n
d
homo
g
ene
ity
t
e
s
t
a
s
t
he
p
r
e
r
e
q
ui
si
t
e
t
e
s
t
.
T
h
e
n
o
r
mal
ity
t
e
s
t
in
t
his
eff
e
cti
v
en
ess
t
e
s
t
i
s
a
na
l
y
z
e
d
usin
g
k
o
lm
ogr
ov-
smirn
o
w
.
The
expe
r
i
me
n
t
a
l
g
rou
p
o
bta
i
ne
d
t
h
e
s
i
gn
ifi
c
a
n
c
e
leve
l
of
0
.
5
0
4
(
S
i
g.
>
0
.
05)
,
so
H
0
sta
t
i
n
g
tha
t
N
g
a
i
n
o
f
t
he
expe
r
i
me
n
t
a
l
g
rou
p
is di
str
i
b
u
t
e
d
n
orm
a
ll
y. The N
ga
i
n
o
f
t
he
c
o
n
t
r
ol
g
roup
o
bt
ai
ne
d
t
h
e
sig
n
i
f
i
can
c
e
l
ev
el
o
f
0.08
4
(
S
ig.
>
0.
05),
so
H
0
stat
ing
tha
t
t
he
v
a
l
ue
o
f
N
ga
in
o
f
t
h
e
c
o
n
t
ro
l
gr
ou
p
is
a
ls
o
d
i
s
t
rib
u
te
d
norm
a
l
l
y is ac
c
e
pte
d
.
The
h
o
m
o
g
e
ni
t
y
t
e
s
t
o
f
t
he
e
xper
i
m
e
nta
l
a
n
d
c
on
tro
l
g
r
o
up
i
n
t
h
i
s
e
ff
ecti
v
en
e
ss
t
e
st
w
as
a
n
a
ly
z
e
d
us
i
n
g
Le
vene’
s
t
est.
T
he
s
ig
ni
fica
nce
leve
l
o
f
t
he
h
omo
g
en
e
i
t
y
t
e
s
t
w
a
s
0
.
2
0
5
(
S
i
g
.
>
0
.
0
5
)
,
s
o
H
0
s
t
a
t
i
n
g
i
s
ac
cept
e
d
w
h
ic
h
st
a
t
e
s
t
ha
t
N
ga
in
o
f
t
h
e
exper
i
m
e
n
t
a
l
a
n
d
c
o
n
tr
ol
g
ro
up
i
s
homo
g
e
nou
s.
A
f
t
e
r
t
h
e
prer
equ
i
s
i
te
t
e
s
t,
t
he
e
ffec
ti
vene
ss
t
es
t
w
a
s
c
o
n
d
u
ct
ed
u
s
i
n
g
i
nd
e
p
end
e
nt
s
a
m
pl
e
t
-
t
e
st
.
Th
e
re
sult
o
f
T
in
de
pen
d
e
n
t
te
st
i
s
show
n
i
n
Tab
le
5.
Ta
b
l
e 4.
Resu
lt
of
N
-gain pr
ere
q
u
i
s
i
te te
s
t.
T
h
e
te
sts
done
T
e
s
t
ty
pe
S
ig.
Te
st
d
e
c
i
s
i
on
pre
r
e
quis
ite
t
e
s
t
a.
Nor
m
a
lity te
s
t
K
o
l
m
ogr
ov
-Sm
i
r
nov
P
r
et
es
t
0
.
5
0
4
H
0
ac
cep
t
e
d
P
o
stte
st
0
.
084
H
0
ac
cep
t
e
d
b.
H
o
m
o
g
e
ni
ty
t
e
s
t
Le
ve
n
e
’s
t
e
s
t
0
.
205
H
0
ac
cep
t
e
d
Ta
ble
5.
I
ndep
e
nde
n
t
T-Te
s
t
of
N
-gai
n
Te
st
T
y
p
e
t
co
u
n
t
Si
g.
T
e
s
t
Dec
i
sion
Inde
pe
nde
nt
S
a
m
p
l
e
T-Te
st
6
.
321
0
.
000
H
0
r
e
j
e
ct
ed
The
re
sul
t
o
f
i
nde
pe
nde
n
t
s
am
ple
t-tes
t
o
b
t
aine
d
t
h
e
si
g
n
i
f
ica
n
c
e
l
e
v
e
l
o
f
0.
000
(S
ig.
>
0.
05),
so
i
t
ca
n
be
c
onc
l
u
ded
t
h
a
t
H
0
is
r
e
j
e
c
te
d
w
h
i
c
h
s
t
ate
s
t
ha
t
t
h
er
e
is
no
d
i
f
f
er
ent
score
be
tw
e
e
n
the
ex
per
i
m
e
nta
l
and
c
o
n
t
ro
l
gr
oup
af
ter
be
in
g
gi
ven
th
e
d
i
f
f
er
ent
tre
a
t
me
nt
.
In
p
o
s
t
t
e
s
t
,
t
h
e
s
c
o
r
e
o
f
t
h
e
e
x
p
e
r
i
m
e
n
t
a
l
g
r
o
u
p
i
s
hi
ghe
r
tha
n
t
h
e
c
on
tro
l
g
r
o
u
p
.
There
f
ore,
it
can
b
e
c
o
n
c
l
ude
d
t
h
a
t
th
e
e
x
p
e
ri
e
n
ti
al
l
earn
i
n
g
-b
ase
d
t
ea
ch
i
ng
ma
terial
i
n
ma
them
atic
s is effec
tive
t
o
im
p
ro
ve
t
he
M
at
hem
a
tic
s
c
og
n
i
t
i
ve
a
bi
lit
y i
n
t
he
e
xpe
r
i
me
nt
a
l
g
r
o
u
p
.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int.
J
. Eva
l
. & Re
s
. Educ
.
IS
S
N
:
2252-
88
22
The
effec
t
iv
e
n
e
ss
of
t
h
e use of expe
r
i
e
n
tia
l
le
arn
i
n
g
-ba
s
ed
t
e
a
c
h
i
ng m
a
ter
i
al
in m
a
t
h
em
a
t
i
c
s
(M
ut
m
a
i
n
a
h
)
61
Base
d
o
n
t
he
r
e
s
u
l
t of t
he
r
es
ear
ch,
it
i
n
dica
te
s
t
h
a
t
t
he
e
x
p
e
rien
ti
a
l
l
ea
rni
ng-
based teac
h
i
n
g
m
ateria
l
in
M
at
hem
a
t
i
c
s
i
s
effec
t
i
v
e
t
o
i
m
p
r
o
ve
t
he
s
t
u
den
t
M
a
t
h
e
m
a
tics
cog
n
it
i
v
e
a
b
ili
t
y
.
The
ef
f
ecti
v
en
e
ss
of
t
h
e
expe
r
i
en
t
i
a
l
l
e
a
r
ning-
ba
sed
te
ac
hin
g
m
a
t
erial
in
M
at
he
m
a
tics
i
s
s
how
n
i
n
t
he
i
mpr
ovem
e
n
t
o
f
t
h
e
M
a
t
h
e
m
a
t
i
c
s
co
gni
tiv
e
a
bi
li
ty
i
n
t
h
e
ex
p
e
ri
men
t
a
l
g
roup
a
f
t
er
u
si
ng
t
he
t
e
ach
i
n
g
m
a
te
rial
p
r
o
d
u
c
t
.
The
e
f
f
e
c
t
iv
en
ess
of
t
h
e
e
x
p
eri
e
ntia
l
l
e
arnin
g
-
b
a
se
d
t
e
a
c
h
i
ng
mat
er
ia
l i
n
M
a
t
he
ma
ti
c
s
ca
n
be
s
e
e
n
i
n th
e sta
tist
i
cal
ca
l
c
u
l
a
tio
n u
s
i
ng i
nde
pe
nde
n
t
t-tes
t. Indepe
n
d
en
t t-tes
t
fro
m t
he p
r
e
te
st a
nd p
o
stte
st res
ul
t in t
he ex
p
er
i
m
ent
a
l
and
co
n
t
rol
gr
ou
p
has
the
sig
n
i
f
ica
n
ce
l
e
v
e
l
o
f
0.
0
0
0
w
hic
h
i
s
less
t
h
a
n
α
=
0
.0
5.
T
hus,
H
0
s
ta
tin
g
tha
t
t
he
re
is
d
iffe
rent c
o
g
n
it
ive
ab
i
lit
y b
e
tw
e
e
n t
h
e
ex
p
e
rime
nt
a
l
a
nd
con
tro
l
gro
up i
s
r
ejec
t
e
d.
The
d
i
f
f
er
ence
can
b
e
se
en
b
ase
d
on
t
h
e
m
e
a
n
o
f
p
o
s
t
t
e
st
s
cor
e
i
n
t
h
e
e
xper
i
m
e
n
t
a
l
a
nd
c
o
ntr
o
l
gro
up.
T
he
e
x
p
er
ime
n
ta
l
gro
u
p
tha
t
u
sed
e
xper
i
e
n
t
i
al
l
e
a
r
n
i
n
g-b
as
e
d
t
e
a
c
h
ing
ma
t
e
ri
al
i
n
M
a
t
h
emat
ics
h
a
s
the
m
e
a
n
t
hat
is
h
i
gher
tha
n
t
he
c
on
t
r
o
l
g
ro
up
t
ha
t
use
d
t
he
c
o
m
m
on
teac
h
i
n
g
m
a
t
e
r
ial
i
n
M
a
t
he
m
a
tic
s
lear
n
i
n
g
p
r
o
ce
ss.
T
he
m
ea
n
of
p
os
t
t
e
s
t
sc
or
e
in
e
xpe
rime
nta
l
g
r
oup
i
s
75
.7
1
,
w
hi
l
e
t
h
e
m
e
a
n
o
f
t
h
e
po
st
t
e
st
score
in
c
on
tro
l
g
r
o
u
p
i
s
63.
7
2
.
It
i
ndic
a
t
es
t
ha
t
t
h
e
c
o
g
n
i
t
i
v
e
ab
i
l
i
t
y
o
f
t
h
e
expe
r
i
me
nt
a
l
g
r
o
up
is
b
e
tte
r
tha
n
the c
o
n
t
r
o
l
gro
up.
The
teac
h
i
ng
m
a
te
rial
i
s
one
o
f
the
fac
t
ors
tha
t
h
a
s
t
he
g
r
e
a
t
role
i
n
de
te
r
m
ini
ng
the
s
u
cc
ess
of
t
he
teac
h
i
ng
a
n
d
l
e
a
rni
ng
proc
es
s
[1
1].
Mat
h
e
m
atics
lea
r
n
i
ng
usi
n
g
lea
r
n
i
ng-
based
tea
c
h
in
g
ma
teria
l
i
s
m
o
re
effec
t
i
v
e
as
i
t
inv
o
l
ve
s
t
h
e
st
u
d
en
ts
a
c
t
i
v
e
l
y
dur
in
g
t
h
e
lea
r
n
i
n
g
proce
ss.
T
he
e
x
p
erie
nc
e-ba
sed
lea
r
ning
ca
n
ma
ke
t
he
s
tu
de
nts
ac
tive
[1
2]
.
The
expe
r
i
enc
e
-
based
lea
r
ni
ng
ge
ne
rate
s
t
h
e
bene
fi
t
s
i
n
i
n
t
e
gra
tin
g
the
th
e
o
ry,
rese
arc
h
,
and
pr
act
ice
to
t
he
s
tude
nts’
s
k
i
l
l
s
in
t
he
r
ea
l
li
fe
.
Ex
per
i
e
n
tia
l
lear
nin
g
h
a
s
t
he
e
ffec
t
o
n
the
impro
v
e
m
e
n
t o
f
t
he
lea
rn
i
ng
succe
ss [13].
Ex
pe
rien
t
i
a
l
l
ea
rni
ng-ba
sed
tea
c
h
in
g
m
a
ter
i
a
l
i
n
M
a
the
m
a
tic
s
ha
s
four
p
ri
nc
ip
l
e
s:
C
o
n
cr
ete
Ex
perie
n
c
e
(
CE),
R
efle
ct
ion
O
b
se
rva
tion
(RO),
A
b
s
t
ract
C
onceptu
al
iz
at
io
n
(AC
)
,
a
n
d
Ac
t
i
v
e
Ex
perim
e
n
t
at
i
o
n
(
A
E).
F
i
rst
,
t
he
c
oncre
t
e
e
xper
i
e
n
ce
t
ha
t
i
s
p
r
ov
id
ed
a
s
t
h
e
t
e
a
c
h
i
ng
mat
e
ri
a
l
i
s
ai
me
d
a
t
ma
kin
g
t
he
s
t
u
den
t
s
fu
lly
i
n
v
o
l
v
e
t
h
em
se
l
v
e
s
i
n
t
h
e
ne
w
e
xper
i
e
nce
.
T
he
c
oncre
t
e
e
xpe
rie
n
ce
is
p
rov
i
ded
as
t
h
e
t
e
a
c
hi
ng
m
at
eri
a
l
by
d
i
s
pla
y
ing
t
h
e
pi
c
t
ure
i
l
l
u
st
rat
i
o
n
w
h
i
c
h
i
s
s
ui
ta
b
l
e
to t
he
m
a
t
e
r
i
a
l.
T
he pi
c
t
u
re
i
n
t
h
e
teac
h
i
ng
m
ate
r
i
a
l
c
a
n
c
lar
i
f
y
t
he
m
a
t
e
r
ial
co
nte
n
t,
i
ncre
ase
t
h
e
a
t
tra
c
ti
ve
ness,
a
n
d
r
e
duce
the
st
ude
n
t
s’
bore
dom
t
o
u
nde
rsta
nd
t
he
m
ateria
l
[1
4]
.
S
e
con
d
,
the
ref
l
e
c
ti
o
n
o
b
s
e
r
vat
i
on
is
a
im
ed
a
t
m
a
kin
g
t
h
e
s
tu
de
n
t
s
able
t
o
obser
v
e
a
nd
r
e
fle
c
t
o
r
thi
nk
a
b
o
u
t
t
he
e
x
p
e
r
ie
nce
from
var
i
o
u
s
p
o
i
n
ts
o
f
v
i
ew
.
It
i
s
u
nderla
i
n
by
th
e
val
u
e
o
f
e
x
p
e
r
ien
t
ia
l
lea
r
n
i
n
g
a
c
t
i
v
i
t
y
i
s
i
n
c
r
e
a
sed
by
as
ki
ng
the
s
t
u
d
e
n
t
s
t
o
re
flec
t
o
n
h
eir
new
ex
perie
n
c
e
and
e
x
p
l
ore
v
a
rio
u
s
im
pl
ica
t
i
o
n
[1
5].
I
n
t
hi
s
sta
g
e
,
t
he
s
tude
n
t
s
l
e
a
r
n
by
o
b
s
e
r
vi
ng
a
nd
l
i
s
t
e
ning
e
v
e
n
obs
ervi
n
g
m
o
r
e
ca
refull
y
befor
e
d
r
a
w
i
n
g
t
he
c
onc
lu
si
on
o
f
t
h
eir
o
w
n
t
hou
gh
t
[
1
6
]
.
Thi
r
d,
t
h
e
c
o
n
cept
u
ali
zat
io
n
st
ag
e
i
s
a
i
m
e
d
a
t
maki
ng
t
h
e
s
tud
e
nt
s
cre
a
t
e
the
co
nce
p
t
tha
t
i
nte
g
ra
tes
the
obser
va
ti
o
n
s
to
bec
o
me
t
he
c
om
prehe
n
si
o
n
o
f
t
h
e
m
a
teria
l
b
e
i
n
g
s
t
u
die
d
.
F
our
t
h
,
t
h
e
i
mp
l
e
me
nt
at
io
n
st
a
g
e
i
s
a
imed
a
t
ma
kin
g
t
he
s
t
u
den
t
s
a
p
p
l
y
t
h
e
m
a
teria
l
t
ha
t
has
b
e
e
n
t
a
u
ght
t
o
so
lve
t
h
e
pr
ob
l
e
ms
w
hic
h
a
re
r
elate
d
t
o
t
h
e
ma
terial.
Th
os
e
four
p
ri
nci
p
l
e
s
aim
to
m
ak
e
t
h
e
s
t
ud
e
n
t
s
h
ave
t
he
a
b
i
lit
y
t
o
e
xpe
ri
enc
e
,
o
bse
r
ve,
t
h
ink,
a
n
d
ac
t
dur
in
g Ma
t
h
em
ati
c
s le
arn
i
ng pr
oc
ess.
Ex
pe
rien
t
i
a
l
l
e
a
r
n
ing
em
pha
s
i
z
e
s
t
h
e
proce
ss
i
n
w
h
i
c
h
t
he
s
tu
de
n
t
s
a
r
e
l
e
arni
ng
by
d
o
i
ng
w
h
ic
h
i
s
base
d o
n
t
he as
s
ump
t
i
o
n tha
t
t
he s
t
u
de
n
t
w
i
ll
more
c
ompre
h
end
t
he
m
ater
i
a
l
i
f
t
he
y are
a
c
tive
l
y
i
nvo
l
v
e
i
n
the
ma
terial
c
om
p
a
re
d
t
h
a
n
t
he
y
o
n
ly
l
i
s
te
n
t
o
t
he
l
ec
t
u
r
e
o
r
rea
d
c
e
rta
i
n
m
a
teria
l
[
1
7
].
E
x
p
erien
t
ia
l
le
arni
ng-
base
d
te
ach
i
n
g
m
a
ter
i
al
e
nc
o
u
r
a
ges
the
s
t
ude
n
t
-
c
e
n
te
red
l
e
arni
n
g
proces
s.
T
herefore,
th
e
st
ud
ent
s
c
a
n
b
uil
d
the
i
r
ow
n
k
n
o
w
l
e
d
ge
f
rom
t
h
e
ex
pe
rie
n
ce
t
ha
t
t
h
ey
g
e
t
d
uri
ng
th
e
l
e
ar
n
i
n
g
p
roce
ss.
E
xper
i
en
t
i
al
l
ea
r
n
ing
conc
er
ns
m
or
e
on
pr
oces
s
rathe
r
t
ha
n
t
h
e
r
e
su
l
t
.
The
st
u
d
e
n
t
s
a
re
i
nv
o
l
ve
d
d
i
rec
tly
i
n
t
h
e
lea
r
ni
n
g
p
roc
e
ss.
I
t
is in
l
i
n
e w
i
t
h
the
s
ta
tem
e
nt
o
f
G
e
h
s
t
at
i
ng w
h
en
some
one
l
e
a
rn
s from
his
or her
ow
n e
x
p
e
rie
n
ce,
t
he lea
r
n
ing
bec
o
me
s
m
e
a
n
i
n
g
f
u
l
[
1
8
].
H
ow
t
he
s
tude
n
t
o
b
t
a
i
ns
a
nd
c
h
an
ge
t
he
ir
e
xpe
rie
n
c
e
i
s
ver
y
i
m
p
orta
nt
f
o
r
t
he
lear
n
i
n
g
p
roce
ss.
Base
d
o
n
t
he
r
esul
t
o
f
t
he
r
esea
rch
t
h
at
h
a
s
b
e
e
n
c
o
n
d
u
c
ted,
e
x
per
i
e
n
tial
lear
n
i
ng-
ba
sed
teac
h
i
ng
ma
terial
i
n
Ma
them
at
ics
be
in
g
de
ve
lo
pe
d
is
e
ffec
ti
ve
i
n
i
m
pr
ov
i
n
g
t
he
s
tu
de
nt
c
ogn
i
t
i
v
e
abi
l
ity
o
f
t
h
e
fi
ft
h-
grade
e
l
em
en
t
a
r
y
s
ch
oo
l
.
T
h
e
e
ffe
c
t
ive
n
ess
of
t
he
u
se
o
f
expe
r
i
en
t
i
a
l
l
e
a
rni
ng-ba
se
d
t
e
ac
hi
ng
m
ater
i
a
l
in
M
a
t
h
e
m
a
t
i
c
s
in
i
mp
rovi
ng
t
h
e
s
tud
e
nt
c
o
g
n
it
iv
e
ab
il
i
t
y
i
s
s
upp
o
r
t
e
d
by
t
h
e
r
e
l
e
v
a
nt
r
ese
a
rc
hes
.
T
he
rese
arc
h
es
car
ried
o
u
t
b
y
A
m
i
r
,
et
a
l
[1
9],
a
nd
Wo
o
[2
0]
p
rove
th
at
t
he
l
e
a
rni
n
g
w
h
ic
h
use
s
t
h
e
t
ea
ch
i
ng
ma
terial
c
a
n
i
m
p
rove
t
he
s
t
u
den
t
l
ear
ni
ng
r
e
su
lt.
T
he
r
e
s
e
a
rc
he
s
w
h
ich
a
l
so
c
on
duc
t
e
d
by
Tana
ka,
e
t
a
l.
[
2
1
],
Ma
tias
an
d
G
o
nza
l
e
z
[2
2]
,
A
r
th
ur
a
n
d
R
a
i
ne
[
2
3
],
a
n
d
J
u
d
ge
,
e
t
a
l
.
[24]
p
r
ove
t
ha
t
e
x
p
e
rie
n
t
i
a
l
l
ea
rn
i
ng
c
a
n
gi
ve
t
he go
o
d
o
p
p
o
rt
un
i
t
y for
the stu
d
e
n
t
s
a
nd the s
t
ude
n
t
w
ill
be i
n
ter
e
st
ed in the
le
ar
ni
ng proc
ess
s
i
nc
e
the
y
are
gi
ve
n
the
c
oncr
e
te
e
xam
p
l
e
s
i
n
t
he
d
a
ily
l
ife.
I
n
a
d
d
iti
on,
t
he
r
e
s
ear
ch
c
ond
uc
t
e
d
b
y
S
h
o
li
hah
[2
5
]
a
l
s
o
pro
v
es
t
hat
the
pos
iti
ve
e
ffe
c
t
s
of
e
x
p
e
r
ie
nt
i
a
l
l
e
arn
i
ng
are
c
rea
t
ed
s
i
n
ce
i
t
ca
n
a
t
tra
c
t
a
n
d
cha
lle
n
g
e
so
me
one
to
l
ear
n
i
ng
s
o
i
t
a
lso
cre
a
te
s
the
m
o
t
i
v
at
ion
t
h
a
t
f
ur
ther
w
ill
a
ffe
c
t
t
he
l
e
a
rni
ng
proc
es
s.
T
he
s
t
ude
n
t
s
us
i
n
g
expe
r
i
en
t
i
a
l
l
e
a
rni
ng-ba
se
d
t
e
a
c
hi
ng
ma
terial
i
n
Ma
t
h
e
m
atics
in
t
he
i
r
s
cho
o
ls
t
e
n
d
to
h
ave
the
hi
g
h
er
cog
n
i
t
i
ve
a
b
i
lity
t
han
t
h
e
s
t
ude
nts
tha
t
do
no
t
use
e
xpe
r
i
en
t
i
a
l
lea
r
ning-
ba
sed
te
a
c
hi
n
g
m
ateri
a
l
in
Ma
them
at
ics i
n
the
ir
s
cho
o
l
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2252-
8822
Int.
J
.
Ev
al. & R
es. Educ.
Vol.
8, No. 1, March
2
019
:
57
- 6
3
62
4.
CONCL
U
S
ION
Base
d
o
n
t
he
r
e
s
ult
o
f
a
na
ly
sis
an
d
disc
us
si
on,
i
t
ca
n
be
c
onc
l
ude
d
t
h
at
t
he
u
se
o
f
exper
i
e
n
tial
l
e
a
r
ni
ng
-b
ased
t
e
a
c
hi
ng
m
a
t
eri
a
l
i
n
M
a
t
h
e
mat
i
c
s
i
s
p
r
ov
en
e
ff
e
c
t
i
ve
i
n
im
pro
v
i
n
g
the
Ma
th
e
m
a
t
i
c
s
c
o
g
n
it
ive
a
b
ili
ty
o
f
t
h
e
fi
fth
-
g
r
ad
e
stude
n
t
s
i
n
t
h
e
volu
m
e
of
c
ub
e
an
d
b
eam
.
It
i
s
pro
v
en
b
y
t
h
e
resul
t
o
f
t-tes
t
i
n
the
expe
r
i
me
n
t
a
l
a
nd
c
o
ntr
o
l
gro
up
w
h
ic
h
ob
ta
i
n
s
t
h
e
s
i
gn
i
f
i
c
a
n
c
e
l
e
v
e
l
o
f
0.
00
0
w
h
ic
h
is
l
e
s
s
t
h
an
α
=
0
.05.
S
o,
H
0
s
ta
ti
n
g
t
ha
t
t
h
e
r
e is di
ffe
re
nt c
o
g
n
iti
ve ab
i
l
ity be
t
w
een t
h
e ex
per
i
m
e
n
t
al an
d
c
o
n
t
r
o
l
gro
up is rejec
te
d. The
mea
n
o
f
po
stte
st
s
c
o
re
i
n
t
h
e
e
x
p
e
ri
me
nt
al
g
ro
up
i
s
hi
ghe
r
t
h
a
n
t
h
e
c
o
n
t
r
o
l
g
r
o
u
p
.
T
h
e
r
e
f
o
r
e
,
t
h
e
u
s
e
o
f
expe
r
i
en
t
i
a
l
l
e
a
r
ni
n
g
-
b
a
s
ed
t
eac
hin
g
m
ateri
a
l
i
n
M
a
t
hem
a
tic
s
is
e
ffe
c
tive
i
n
i
m
p
ro
v
i
ng
the
Ma
the
m
atics
cog
n
i
t
i
ve
ab
i
l
i
t
y
of t
he
f
i
f
th-g
ra
de stu
den
t
s.
B
a
se
d
on
t
h
e
r
es
ea
rch
t
h
a
t
h
as
b
een
c
on
du
ct
e
d
,
i
t
i
s
s
u
g
g
e
st
ed
t
o
(
1)
t
he
t
eac
her
tha
t
s
ho
ul
d
implem
e
n
t
t
h
e
e
xperie
n
tia
l
le
arni
ng-ba
se
d
tea
c
h
i
ng
m
a
t
e
r
i
a
l
i
n
M
a
t
h
emat
i
c
s
th
at
h
as
b
een
p
revi
ou
sly
deve
l
ope
d,
(
2)
t
he
s
t
u
den
t
t
ha
t
is
e
xpec
t
e
d
t
o
b
e
a
b
l
e
ac
t
i
v
e
ly
i
n
c
o
mpre
h
e
nd
i
n
g
t
h
e
m
a
t
e
rial
a
nd
t
o
im
pro
v
e
the
c
o
g
n
i
t
i
v
e
abi
l
ity
u
si
n
g
e
xpe
r
i
en
t
i
al
l
e
a
r
n
ing-
ba
sed
t
e
a
c
hi
n
g
ma
terial
i
n
Mat
h
e
m
atics,
(
3)
t
he
o
t
h
er
rese
arc
h
ers
tha
t
c
a
n
u
se
t
h
i
s
r
e
se
arc
h
a
s
t
h
e
refe
renc
e
f
o
r
t
h
e
s
i
m
il
a
r
r
e
s
ea
rch
re
l
a
t
e
d
to
t
h
e
d
ev
el
op
me
n
t
o
f
expe
r
i
en
t
i
a
l
l
ea
r
n
ing-
ba
sed te
a
c
hi
n
g
m
ater
ial in
M
at
hem
a
t
i
c
s
.
REFE
RENCES
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CD-P
IS
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.
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s
s
e
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s
i
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c
ien
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ng and
M
a
them
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t
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o
r P
I
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ateri
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ls
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or
m
at
he
m
atics
f
o
r
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h
igh
s
c
ho
ol
S
tu
dent
s
based
o
n
Au
su
bel'
s
th
eory
o
f L
earn
i
n
g
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tha
g
o
ras:
M
a
th
e
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atic
s
Ed
uc
a
t
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n J
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a
r
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i
n
g
De
vic
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pe
S
tad
w
i
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S
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e
th
od
on
M
a
teri
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r
di
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u
r
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l O
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i
m
u
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a
ti
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i
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g
A
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EL
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)
M
o
del
to
T
e
ach
Susta
i
nability
t
o
Inte
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na
l
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a
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t
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een
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heo
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n
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rld
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evel
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d L
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a
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ducatio
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e
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et
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a
nt
itativ
e,
q
ualit
a
t
i
v
e
A
p
p
r
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d
R&D),"
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a
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i
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u
m
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e
t
unt
asan
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riteri
on
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sed
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ear
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ur
nal
of
res
e
arch
an
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u
ation
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n
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ucat
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Co
m
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eten
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i
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g
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ateri
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ls
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ent
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emi
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E
ng
a
g
in
g
Ex
pe
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i
e
n
tia
l
S
e
r
v
i
c
e
Le
a
r
ning
T
h
r
ou
gh
A
C
o-Cu
rric
u
l
ar
C
l
ub:
T
he
C
has
e
C
h
a
rl
ie
Races,"
Int
e
rna
t
i
o
n
a
l
Co
unci
l
for Hea
l
t
h
,
P
h
ysi
c
al
E
d
u
c
a
t
ion,
Recr
eati
on
, Sp
ort,
an
d Da
nce Jou
r
n
a
l o
f
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e
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o
n
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Yo
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utor
I
s
Yo
ur
F
rie
n
d
:
Using
Exp
e
riential
L
earn
i
n
g
To Enhance S
eco
nd
Y
ear
Transit
i
on,
"
Jo
ur
nal o
f
A
ppli
e
d
R
e
sear
ch i
n
Higher
Ed
uca
t
io
n
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ol.
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r
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e Creati
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u
ide M
a
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o
v
a
ti
ve L
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a
: Diva Press
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i
l
b
erm
a
n,
M
.,
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dbo
ok
E
x
p
erien
t
i
a
l
L
earn
i
ng:
L
earn
i
ng
s
t
r
ate
g
i
es
from
th
e
real
w
orld.
T
r
ans
l
ate
b
y
K
ho
z
i
m,
M.,"
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nd
un
g: Nu
sam
e
di
a
,
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Wi
cakso
no
,
et
a
l.,
"Th
e
e
ff
ecti
v
e
n
ess
o
f
a
M
od
el
o
f
E
x
p
e
rientia
l
Le
a
r
ning
t
o
i
m
pr
o
v
e
Exp
l
o
r
a
t
io
n
a
n
d
c
o
mm
it
me
nt
Careers
i
n
h
i
gh
sch
ool
s
tu
de
nt
s,
"
Jour
na
l
of
edu
c
at
ion
:
theo
ry, r
e
sea
r
ch
, a
nd
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op
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e
nt
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83-7
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7
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Bali
ch,
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e
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al
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Y
ear
T
w
o
:
The
Im
p
act
O
f
Add
i
ction
s
E
d
u
ca
ti
o
n
and
Experi
ential
Ac
ti
v
ities
On
A
tti
t
u
des
O
f
Stud
e
n
ts,
"
Jo
ur
n
a
l
of A
ppli
e
d R
e
sea
r
ch
in
Hi
gher
Ed
uca
t
i
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n
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01
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Geh
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E
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ani
zatio
nal
S
p
iritual
L
eadersh
ip
O
f
W
o
rld
s
“
M
a
de
”
an
d
“
F
oun
d”:
A
n
E
xp
erien
tial
L
earni
ng
M
odel
F
o
r “F
eel
”,"
L
e
a
d
er
sh
ip
&
Or
ganiz
a
t
i
o
n
D
evelo
p
men
t
Jo
ur
nal
,
v
o
l
.
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01
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Ami
r
,
M.
M
uris
,
&
Arsyad,
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"
D
evelo
p
m
e
n
t
o
f
Dev
i
ce
p
hys
ics-ba
sed
Learni
ng
e
xperi
ences
o
n
Learn
e
rs
N
i
n
t
h
-
Cla
s
s
Sc
ie
n
c
e
hi
g
h
sc
h
o
o
l
9
Pinr
a
n
g,"
Jou
r
n
a
l o
f
sci
e
nce
a
nd phys
i
cs
edu
c
ation
,
vo
l.1
1
(3
)
,
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. 2
02
-
2
1
3
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01
5.
[20]
Woo,
T
.
K
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,
"
Devel
opi
ng
Q
ua
lity
L
earning
M
ateri
a
l
s
f
or
E
ff
ect
i
v
e
T
eachi
ng
and
Learn
i
n
g
i
n
an
O
DL
E
nvironm
ent:
M
a
ki
ng
T
h
e
Ju
m
p
F
rom
P
r
int
M
odu
les
To
O
n
l
i
n
e
M
o
d
u
l
e
s,
"
Asian Associ
a
t
i
o
n of
Op
en Uni
versities Journal
,
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l.
6
(1),
p
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1-58
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01
1.
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Tanaka,
K.
et a
l
.
.
"Learn
i
n
g
H
o
w
t
o
Learn
Th
ro
ug
h
E
xperi
ential
L
earni
ng
P
r
o
m
otin
g
M
e
t
a
c
o
gn
it
iv
e
S
k
i
l
ls
t
o
Im
prov
e
Kn
owled
g
e
Co
-c
r
eat
io
n
A
b
ilit
y
,
"
Jo
ur
na
l Intern
atio
na
l
Proced
ia Com
put
er S
c
ien
ce,
v
o
l.
9
(10),
pp
.
1
46-1
5
6
,
2
0
1
6.
[22]
M
a
t
i
a
s
,
A
.
&
G
o
n
z
a
l
e
z
,
A
.
A
.
,
"
W
h
a
t
D
o
G
e
o
l
o
g
y
A
n
d
I
t
H
a
v
e
I
n
C
o
mm
on’?
T
he
C
as
e
Of
A
n
Int
e
rnati
o
nal
Col
l
abo
r
ati
o
n
Th
rou
g
h
Ex
peri
enti
a
l
L
earni
ng
,"
J
o
urna
l o
f
Inn
o
v
a
tio
n
in
H
i
gh
e
r
Ed
uc
atio
n Te
a
c
hi
ng
a
n
d
Le
arn
i
n
g
,
vo
l.
9
,
p
p
.
1
0
7
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2
0
1
7
.
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Int.
J
. Eva
l
. & Re
s
. Educ
.
IS
S
N
:
2252-
88
22
The
effec
t
iv
e
n
e
ss
of
t
h
e use of expe
r
i
e
n
tia
l
le
arn
i
n
g
-ba
s
ed
t
e
a
c
h
i
ng m
a
ter
i
al
in m
a
t
h
em
a
t
i
c
s
(M
ut
m
a
i
n
a
h
)
63
[23]
Art
hur,
A.D
.
&
R
ain
e
,
J.W
.,
"Exp
erien
t
i
a
l
Learni
ng
a
n
d
T
each
in
g
A
t
A
D
i
stan
ce:
H
o
w
D
isti
nctiv
e
A
n
Ex
perien
ce
?
,
"
Jo
u
r
na
l
of Develo
p
i
n
g
Pu
blic
M
anager
s
f
o
r
Cha
ngin
g
W
o
rl
d
,
vol.
5
(
1),
pp
.
1
41-1
5
9
,
2
017
.
[24]
Jud
g
e,
L
.W.
et
a
l
.
,
"
En
ga
g
i
ng
E
xp
e
r
ie
nt
ia
l
Se
r
v
ic
e
Le
a
r
ning
T
h
r
ou
gh
A
C
o
-
Curric
u
l
a
r
Clu
b
:
Th
e
Chas
e
Charl
i
e
Races,"
Int
e
rna
t
i
o
n
a
l
Co
unci
l
for Hea
l
t
h
,
P
h
ysi
c
al
E
d
u
c
a
t
ion,
Recr
eati
on
, Sp
ort,
an
d Da
nce Jou
r
n
a
l o
f
Res
e
arch
,
vo
l.
6
(2),
p
p
.
3
0-38
,
2
01
1.
[25]
S
h
o
l
i
h
ah,
M
.
e
t
al
.,
"Influ
ence
M
o
d
e
l
Of
E
x
p
eri
e
n
t
i
a
l
Learn
i
n
g
Towa
rd
s
Th
in
ki
ng
A
bili
ty
H
ig
h
Sc
ho
o
l
S
tu
de
n
t
s,
"
Jou
r
n
a
l
o
f
edu
c
ati
o
n
:
th
eor
y
, resear
ch, a
n
d
devel
op
ment
,
v
ol.
1
(11),
pp
.
20
96
-21
0
0
,
2
0
1
6
.
Evaluation Warning : The document was created with Spire.PDF for Python.