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.
8
, N
o. 1, Mar
c
h
201
9,
pp.
103~
1
0
9
ISSN
: 2252-
88
22,
D
O
I
:
10.11
59
1
/ijer
e
.
v8i
1.
155
14
103
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
ERE
Designing lesson pla
n of integer numb
er op
eration based on
fun
and eas
y
mat
h (FEM) approach
D
a
rin
Fou
r
y
z
a,
S
iti M
agh
fi
rot
u
n
A
m
in
, R
oose
l
yn
a E
k
aw
at
i
Prim
ary
E
d
u
c
a
t
io
n
S
t
ud
y
P
r
o
g
ra
m
,
U
n
i
vers
itas
Ne
g
eri
S
u
rabay
a
,
I
nd
on
esia
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
Sep
1
0
,
2
018
Re
vise
d D
e
c 20,
201
8
Ac
ce
p
t
ed
J
an
26
,
2
0
19
Th
is
p
aper
d
eal
t
with
t
he
d
es
i
g
n
o
f
l
earni
ng
t
ools
,
t
hat
was
t
h
e
d
e
v
e
lo
pm
ent
of
l
earni
ng
i
mpl
e
men
t
atio
n
p
l
an
o
r
R
e
nc
an
a
P
e
lak
s
an
aan
P
em
b
e
laj
aran
(RP
P
)
bas
e
d
o
n
F
un and
Eas
y
M
at
h
(F
EM
)
app
r
oach
i
n
th
e
f
o
rm
o
f
a nu
mb
er
li
ne
m
od
el.
F
E
M
w
a
s
an
a
p
p
roach
i
n
o
r
der
to
t
each
m
ath
e
m
a
ti
cs
e
ff
ective
l
y
to
s
tu
dents
in
a
f
u
n
a
nd
easy
w
a
y
acco
rdi
ng
to
t
he
p
att
e
rns
and
r
ules
,
m
a
king
it
easi
e
r
fo
r
st
udents
to
u
n
d
erst
a
n
d
m
a
th
e
m
atical
c
onc
ep
ts
a
nd
dr
iving
t
h
em
to
act
iv
ely
partici
p
ate
in
l
earni
ng
acti
v
i
t
y.
F
u
r
th
erm
o
re,
t
h
e
nu
m
b
er
l
in
e
m
o
d
e
l
bas
e
d
o
n
t
h
e
r
ules
a
im
e
d
t
o
p
r
o
v
i
d
e
t
h
e
re
al
i
d
ea
of
m
ath
em
a
tical
con
cept
and
av
o
i
d
th
e
m
a
th
em
ati
cal
m
an
ipulat
io
n.
T
he
d
es
ig
n
o
f
RPP
dev
e
lo
pm
ent
w
a
s
i
n
t
e
nd
ed
t
o
create
a
new
RPP
w
h
i
c
h
w
a
s
di
v
i
ded
into
t
hree
acti
v
iti
e
s
,
n
am
ely
int
r
od
uction
,
c
ore,
a
nd
c
l
o
s
i
n
g
.
Th
e
m
e
t
h
o
d
o
f
l
e
s
so
n
pla
n
dev
e
lo
pm
ent
used
a
P
lo
m
p
’s
d
ev
e
l
op
m
e
nt
m
odel
wh
ich
w
a
s
co
ns
iste
d
o
f
th
ree
phas
e
s,
n
a
m
e
l
y
p
r
e
lim
i
n
ary
res
earch,
p
r
ototy
p
e,
a
n
d
e
valu
a
t
io
n.
T
he
resu
lts
o
f
t
h
is
d
evelo
p
m
e
n
t
w
ere
ex
p
ected
t
o
h
e
lp
s
tu
dents
in
u
nd
erst
andi
ng
th
e
m
a
th
ematical
c
on
cepts
,
n
a
m
e
l
y
i
nt
eger
cal
c
u
latio
n
o
p
erati
o
n
s
es
peci
ally
addition
and
subt
racti
on,
i
ncr
easi
n
g
student
activeness
in
l
ear
nin
g
p
ro
cess
,
a
n
d a
v
oiding
t
h
e
e
xiste
n
c
e
o
f
m
a
t
he
ma
tic
a
l
ma
n
i
p
u
la
tio
n.
K
eyw
ord
s
:
F
un
and e
a
s
y
m
ath
(F
EM)
Inte
ge
r num
ber
opera
tio
n
Lesson plan
(
RPP)
Num
b
er
l
ine
m
o
d
e
l
P
l
om
p’s de
v
e
l
o
pm
en
t
mode
l
Co
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:
D
a
r
i
n
F
ouryz
a,
P
r
i
m
a
r
y Educa
t
i
o
n
S
t
ud
y P
r
ogram
,
Master
P
rogr
am
Uni
v
ersi
tas Ne
geri
S
ura
b
aya,
K
e
ti
nta
n
g S
u
raba
ya,
60
2
31, I
nd
one
s
i
a
Em
ail:
dari
nfo
u
ryz
a
1
6
0
7
0
8
551
1
8
@m
hs.u
n
e
sa
.ac
.
id
1.
I
N
TR
OD
U
C
TI
O
N
O
n
e
of
t
he
o
bjec
t
i
v
e
s
g
i
ve
n
t
o
m
at
he
ma
t
i
c
s
i
n
elem
en
ta
ry
s
c
h
o
o
l
i
s
tha
t
s
t
u
de
nts
ar
e
able
t
o
un
dersta
n
d
ma
t
he
ma
t
i
c
a
l
c
o
n
cept
s
a
nd in
ter
r
e
lat
i
ons
hi
p
be
t
w
een
t
h
e
c
o
nc
ept
s
, as w
ell
a
s
a
pp
ly t
he
c
o
n
c
e
pt in
a
f
l
e
x
ible
,
e
f
fi
cien
t,
a
nd
a
p
p
r
opr
i
a
te
w
a
y
t
o
so
l
v
e
dai
l
y
pr
ob
l
e
m
s,
b
oth
c
once
p
ts
t
hat
h
a
ve
b
ee
n
lear
ne
d
a
n
d
conc
e
p
ts
t
hat
w
i
l
l
b
e
st
ud
ie
d
[1].
T
he
c
on
ce
pt
u
n
d
ersta
n
di
ng
w
i
ll
b
e
use
d
b
y
s
t
u
d
e
n
t
s
a
s
a
prepa
r
at
io
n
t
o
t
a
k
e
the
ne
x
t
l
e
v
e
l
o
f
s
t
u
d
y
a
n
d
t
o
so
l
v
e
da
il
y
pro
b
lem
s
[
2].
Be
s
i
de
s
t
h
at,
it
w
i
ll
a
l
s
o
b
e
a
ba
sis
f
o
r
de
ve
lo
pin
g
adva
nc
e
d
a
b
i
lit
ies,
s
uc
h
as
t
he
a
b
i
l
ity to
a
p
ply
ma
them
at
i
c
a
l
c
o
n
ce
pt
s,
u
se
o
f
ma
the
m
a
tic
al
r
easo
n
i
n
g,
c
rit
i
cal
t
h
i
n
kin
g
,
a
nd
p
rob
l
e
m
s
olv
i
ng
[
3
]
.
Th
u
s
,
t
h
e
st
ud
en
t
’
s
und
e
r
st
a
nd
ing
a
b
ou
t
ma
t
h
em
atic
al
c
o
n
ce
pt
i
s
one
o
f
the a
b
il
it
y q
u
al
ifica
t
i
o
ns t
hat
m
u
st be
ac
hie
v
ed in
ma
t
h
e
m
a
t
ic
s
s
ubje
c
t
s [1
].
The
c
o
nce
p
t
o
f
m
athem
a
t
i
cs
i
s
bas
i
ca
ll
y
o
n
e
o
f
t
h
e
d
i
r
ect
o
b
j
e
c
t
s
i
n
a
d
dit
i
o
n
t
o
thr
e
e
othe
r
di
r
ect
o
b
j
e
c
t
s
,
n
a
m
e
l
y
f
a
c
t
s
,
o
p
e
r
a
t
i
o
n
s
,
a
n
d
p
r
o
p
e
r
t
i
e
s
.
T
h
e
m
a
t
h
e
m
a
t
i
c
s
con
cep
t
i
s
a
n
ab
st
rac
t
i
d
e
a
t
h
at
a
l
l
o
w
s
so
meon
e
t
o
c
l
a
ss
if
y
an
obj
ect
o
r
ev
ent
a
n
d
ex
pl
ai
n
wh
e
t
h
e
r
th
e
ob
j
e
c
t
o
r
e
v
en
t
is
a
n
e
x
am
ple
or
n
o
t
[
4]
.
F
u
r
t
he
rm
o
r
e,
t
he
c
o
n
c
e
p
t
i
s
g
ene
r
a
l
l
y
c
om
pos
ed
b
y
the
pr
ev
io
us
con
cep
t
s
a
nd
f
ac
ts.
In
o
rd
e
r
t
o
sh
o
w
a
part
icu
l
ar
c
onc
ept, i
t
is
v
er
y i
m
porta
nt to
pr
ovi
de
l
imita
t
i
ons
or defi
ni
tio
n
s
. Thi
s
g
ives
a
n
i
d
ea
t
hat, ge
n
e
r
al
ly,
a
conc
e
p
t
can
b
e
use
d
c
o
n
t
i
n
uous
l
y
t
o
e
xpl
a
i
n
ot
her
co
nc
ept
s
i
n
m
athe
m
a
tics,
s
o
tha
t
s
tu
de
nts
c
a
n
k
n
o
w
,
un
dersta
n
d
,
a
n
d
cal
l
ob
j
e
c
t
t
he
y
kn
o
w
t
hrou
g
h
t
he
c
onc
ept
[5].
Co
nseq
u
e
nt
ly
,
th
e
mi
scon
c
e
p
ti
ons
t
h
a
t
stude
n
t
s
rec
e
iv
e
can
b
e fatal
to
l
e
a
rn
f
ur
ther
conc
e
p
ts.
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
:
103
-
1
09
10
4
I
n
t
he
r
ela
t
io
n
of
e
le
me
nta
r
y
stude
n
t
’
s
u
nde
rst
a
n
d
in
g
c
onc
ept,
t
h
e
mo
st
i
mp
o
r
t
a
n
t
t
hi
ng
to
b
e
noted
is
h
ow
s
t
u
de
nts
de
ve
lo
p
a
c
o
ncep
t
i
n
t
he
ir
c
og
n
i
t
i
ve
s
truc
t
u
r
e
.
W
it
h
out
t
h
i
s
p
r
in
c
i
pl
e,
i
t
c
a
nn
ot
b
e
ex
p
e
c
t
ed
tha
t
st
u
den
t
s
u
nders
tan
d
t
he
sub
jec
t
m
a
t
te
r give
n
b
y
teac
her.
O
n
e
of
m
at
he
m
a
tica
l
c
o
n
cep
ts
i
s
i
n
te
ge
r
n
u
m
b
er
opera
t
i
on,
e
spe
c
ia
l
l
y
add
i
tio
n
an
d
s
u
b
t
rac
t
i
on.
I
n
gene
ra
l,
t
he
d
e
f
i
n
i
t
i
on
o
f
s
u
c
h
c
onc
e
p
t
is
k
n
o
w
n
b
y
s
t
u
d
en
ts
f
r
om
t
h
e
e
nv
iro
n
m
e
n
t
d
i
r
ec
tl
y,
f
or
e
xa
mpl
e
thr
o
u
g
h
t
he
a
c
t
i
v
it
i
e
s
of
b
u
y
i
n
g
a
nd
se
ll
ing,
p
ro
fit
,
a
n
d
los
s
,
e
tc.
Th
ere
f
ore,
b
efore
stu
d
y
i
ng
a
t
s
cho
o
l
,
stude
n
t
s
ha
ve
a
l
r
ead
y
u
nders
to
o
d
t
he
a
d
d
i
t
i
o
n
a
nd
s
u
btrac
t
i
o
n
o
pe
rat
i
o
n
o
f
in
te
ger
num
ber
in
t
he
p
hy
sica
l
ob
jec
t
s.
H
ow
eve
r
,
in
f
a
c
t
,
stude
n
t
s
sti
l
l
fin
d
t
he
d
i
f
fic
u
l
t
y
t
o
und
e
r
st
a
n
d
th
e
mat
h
emat
i
cal
c
o
n
cept
.
T
h
e
g
e
n
e
ral
dif
f
i
c
ul
ty
i
s
t
h
e
re
c
o
gn
iti
on
a
n
d
underst
a
nd
i
n
g
o
f
s
y
m
b
ols
(
+
,
-,
–
)
,
t
he
d
iffere
n
t
ia
t
i
on
o
f
c
a
l
c
u
l
ati
on
opera
tio
n
func
ti
o
n
(
add
i
tio
n
and
s
u
b
t
r
a
c
t
i
o
n)
w
i
t
h
i
n
t
e
ge
r
m
a
rk
,
a
nd
t
h
e
re
place
me
n
t
o
f
nega
tiv
e
n
u
m
bers
r
o
l
e
[
6
]
.
Fo
r
ex
a
m
p
l
e,
7
-
(
-
3
)
=
4
.
I
n
o
r
d
er
t
o
un
de
rst
a
nd
ing
t
h
e
conc
ep
t
of
i
nte
g
er
ope
rat
i
ons
p
r
e
ci
sel
y
a
nd
me
a
n
i
n
gfu
lly,
t
e
ac
he
r’s
abi
l
i
t
y
t
o
pla
n
l
e
a
rn
in
g
in
d
e
t
ail
is
h
i
g
h
l
y
r
e
qu
ired
w
hi
c
h
i
s
rea
l
iz
e
d
i
n
t
h
e
de
sig
n
o
f
lea
r
ni
ng
t
o
o
l
s,
n
a
m
el
y
the
de
v
e
l
o
pme
n
t
of
R
P
P
t
hro
u
g
h
t
he
u
se
o
f
F
E
M
a
pproac
h
a
ssi
st
e
d
b
y
t
h
e
n
u
m
b
e
r
l
i
n
e
m
o
d
e
l
.
I
t
i
s
i
n
l
i
n
e
w
ith
M
ul
yasa
t
ha
t
a
n
e
ffe
c
t
i
ve
a
ppr
oac
h
n
e
e
ds
t
o
be
c
ho
sen
t
o
c
re
at
e
a
c
o
n
d
u
c
i
v
e
and
en
joy
a
bl
e
l
e
a
r
n
i
ng
env
i
ro
nm
en
t,
s
o
tha
t
st
u
den
t
s ca
n ea
sily
f
i
gur
e
o
u
t
abs
t
rac
t
m
a
them
at
i
c
al c
once
p
t [7].
I
n
t
r
o
d
uc
ing
t
h
e
co
nc
e
p
t
o
f
i
nte
g
e
r
oper
a
ti
o
n
c
a
n
b
e
c
o
n
d
uc
te
d
t
hrou
g
h
t
hree
s
ta
ges,
n
am
el
y
:
1
)
in
t
r
o
duc
ti
on
o
f
c
once
p
t
i
n
c
oncre
t
e
s
ta
ge,
2)
i
n
t
rod
u
c
t
io
n
of
c
on
cep
t
in
s
e
m
i
-
c
o
n
c
re
te
(
semi
-ab
s
t
r
ac
t
)
,
3
)
rec
o
g
n
it
io
n
of
c
onc
e
p
t
i
n
a
bs
tra
c
t
[8]
.
T
h
i
s
is
i
n
l
i
ne
w
ith
A
u
su
be
l’s
o
p
i
n
ion
w
h
ic
h
arg
u
e
t
ha
t
t
h
e
f
o
r
m
a
tio
n
o
f
c
on
c
e
p
t
can
o
cc
u
r
t
o
s
o
me
o
n
e
t
h
r
ough
d
e
m
o
n
s
t
r
a
t
i
o
n
.
F
o
r
e
x
a
m
ple
,
c
hil
d
re
n
w
ho
ge
n
e
ra
l
l
y
k
now
in
form
ation
ab
ou
t som
e
t
h
ing
from
a
dult,
suc
h
as kn
o
w
i
ng c
h
airs,
cat,
penc
il
,
a
n
d
o
t
h
e
rs.
The
r
ef
ore,
t
he
d
esc
r
i
p
ti
on
s
pr
esen
ted
b
y
t
h
i
s
pa
per
ar
e
h
i
gh
ly
re
qu
i
r
e
d
b
y
t
e
a
c
h
e
rs
a
nd
o
t
h
er
r
e
a
d
e
rs
sinc
e
F
E
M
ap
proa
c
h
i
tsel
f
i
s
s
til
l
not
w
i
d
ely
dis
c
usse
d.
S
o,
i
n
t
his
stud
y,
F
EM
w
il
l
be
a
pp
lie
d
t
o
t
he
o
p
e
ra
t
i
o
n
s
o
f
a
d
din
g
a
nd
s
ub
t
r
a
c
t
i
on
o
f
i
n
t
e
g
e
r
nu
mb
e
r
f
o
r
p
ri
m
ary
st
ude
n
t
s,
e
spec
i
a
l
l
y
for
fourt
h
g
ra
de
stude
n
t
s
w
i
t
h
d
eve
l
opm
en
t
r
e
sea
r
ch
t
ype
a
ssis
te
d
by
n
u
m
be
r
l
i
ne
.
I
n
a
dd
iti
o
n
,
a
g
o
od
un
derst
a
n
d
i
ng
a
bou
t
F
E
M
ap
proa
c
h
a
n
d
i
ts
i
m
p
l
e
me
nt
a
t
io
n
in
t
he
d
eve
l
opm
e
n
t
o
f
l
ear
n
in
g
ma
terials
i
s
t
h
e
b
a
s
i
c
f
o
r
c
rea
tin
g
a
new
l
e
sson
p
l
a
n
w
hic
h
i
s
i
n
n
ova
ti
ve
and
cre
a
ti
ve ba
s
e
d
o
n
FEM.
2.
FUN AND
EAS
Y
MATH (FE
M
)
APPRO
ACH
F
E
M
appro
a
c
h
i
s
a
wa
y
to
t
e
a
c
h
ma
them
at
ic
al
c
o
n
ce
p
t
s
ea
sily
a
nd
p
lea
s
a
n
tl
y
base
d
o
n
p
at
terns
a
n
d
rules
[9]
.
T
his
appr
oac
h
c
o
n
s
i
sts
of
f
o
u
r
p
r
in
c
i
ple
s
,
nam
e
ly
s
i
m
p
le,
use
f
u
l
,
re
lat
i
on,
a
nd
f
un.
F
o
u
r
pri
n
c
i
ple
s
of
F
EM a
p
p
roa
c
h
w
ill
be de
s
c
r
ibe
d
b
el
ow
.
2.1.
Simp
le
S
i
mple
i
s
tec
hni
q
u
e
for
tea
c
h
in
g
m
a
t
h
em
at
i
c
s
su
bjec
t
as
e
a
s
y
as
pos
si
b
l
e
base
d
o
n
p
a
tte
r
n
s
an
d
ru
les
w
h
ic
h
are
e
a
sily
u
nder
s
to
o
d
by
st
u
d
en
ts
[
9]
.
These
p
a
t
t
erns
a
nd
r
ul
e
s
a
re
m
a
d
e,
s
o
t
h
at
m
at
h
e
ma
ti
ca
l
co
n
c
e
p
t
del
i
v
ere
d
b
y
te
a
c
her
i
s
n
o
t
d
i
ffi
c
u
l
t
t
o
be
u
n
d
erst
oo
d
by
s
t
ude
n
t
s.
F
ur
t
h
e
r
m
o
re,
the
num
ber
l
i
n
e
m
o
del
base
d
on t
h
e
F
E
M a
p
proac
h
is gi
ve
n
in
o
rder
t
o m
a
ke
m
a
t
hem
a
t
i
c
a
l c
onc
e
p
t e
a
si
er
t
o be
l
ear
ne
d.
2.2.
Usefu
l
Usef
ul
p
rin
c
i
p
l
e
r
el
at
e
s
t
o
how
s
t
u
d
e
nt
s
know
t
h
e
i
mpo
r
t
a
n
t
g
o
a
ls
o
f
le
a
r
ni
ng
m
a
t
h
em
atic
s,
s
o
tha
t
the le
arn
i
ng be
c
o
me
s m
e
a
n
in
gfu
l
[9]. Lea
rnin
g w
i
t
h
m
eani
n
g
f
ul
ne
ss ca
n
hel
p
s
tu
de
n
t
s t
o
e
asil
y rem
e
mber
the
ma
them
at
i
c
al
c
once
p
ts
t
ha
t
ha
ve
b
e
e
n
l
ea
rned
a
n
d
w
i
l
l
b
e
l
e
arne
d.
I
n
l
i
n
e
w
i
t
h
t
h
i
s,
J
am
ar
i
s
e
xp
la
in
ed
t
ha
t
“m
athem
a
t
i
cs
h
as
i
m
p
orta
nt
w
orth
f
or
our
d
a
i
l
y
l
i
f
e,
b
ec
a
u
se
a
l
mo
st
a
ll
r
e
g
io
n
of
l
i
f
e
req
u
i
r
e
s
t
h
e
a
p
p
l
i
cati
on
of
m
a
t
he
ma
tic
al abi
l
i
t
y
,
so w
i
t
h
o
u
t
t
he
b
es
t
un
dersta
n
d
i
n
g of t
ha
t,
our life
w
i
l
l
b
e d
i
ff
i
c
u
l
t
[1
0].
2.3.
Rel
a
tio
n
The
pri
n
c
i
p
l
e
of
r
e
l
a
t
io
n
me
ans
t
h
at
t
he
m
a
t
he
ma
t
i
c
a
l
l
e
a
r
ni
ng
ac
ti
vi
tie
s
mus
t
b
e
re
l
a
te
d
t
o
t
h
e
expe
r
i
ence
o
r
da
il
y
l
i
fe
o
f
stude
n
t
s
[9].
T
his
is
c
o
n
duc
te
d
sin
ce
i
t
ma
k
e
s
e
a
sy
f
o
r
s
tu
d
e
nt
i
n
und
erst
a
ndi
ng
o
f
ma
them
at
i
c
al
c
once
p
t
a
n
d
a
p
p
l
yin
g
t
h
e
c
o
n
ce
p
t
i
n
t
h
eir
dai
l
y
l
i
fe
w
e
ll.
M
ore
ove
r,
b
y
intr
od
uc
i
n
g
le
ar
ning
ma
them
at
i
c
s
c
onc
e
p
t
t
h
rou
g
h
t
he
ir
d
a
ily
l
i
f
e
or
d
ai
l
y
l
i
f
e
pr
o
b
l
e
ms
m
a
k
e
l
e
arnin
g
m
at
h
e
ma
ti
cs
m
o
r
e
in
t
e
rest
i
ng
a
n
d
me
ani
n
g
f
ul
f
o
r
s
t
u
de
nts
w
h
e
r
e
the
pro
b
l
em
s
w
e
r
e
i
n
t
h
e
st
ud
en
t
’
s
kn
o
w
le
d
g
e
a
nd
e
xp
eri
e
n
ce
[
1
1
]
.
Ex
pl
ai
n
e
d
t
h
a
t
s
t
u
d
e
n
t
s
u
s
u
a
l
l
y
don’t
enj
o
y
l
e
a
r
n
i
ng
a
ct
i
v
ities
w
e
ll
a
nd
ca
n
p
r
o
p
erly
n
ot
a
p
p
l
y
m
a
t
h
e
m
a
t
i
c
s
i
n
d
a
i
l
y
l
i
f
e
w
h
e
n
t
h
e
y
s
i
t
p
a
s
s
i
v
e
l
y
a
n
d
l
e
a
r
n
m
a
t
h
e
ma
ti
c
s
c
o
n
cept
t
h
at
a
re
n
ot
r
el
ev
an
t
t
o
t
h
e
i
r
d
a
ily
lif
e
[1
2
]
.
Th
ere
f
o
r
e
,
l
e
a
rn
ing
mat
h
emat
i
c
s
wit
h
r
el
a
t
ed
t
o
s
t
u
d
e
n
t
’
s
da
il
y
l
i
fe
o
r
t
h
e
i
r
dai
l
y
l
i
f
e
pr
ob
lem
is
n
ee
ded f
o
r thi
s
princ
i
p
l
e
.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
Eval & R
es E
d
u
c
.
IS
S
N
:
2252-
88
22
D
e
sign
in
g L
e
sson P
l
a
n
o
f
I
n
t
e
ger N
u
m
b
er
O
p
er
at
ion
b
a
se
d
on Fu
n
an
d Easy
Ma
th
…
(D
ar
in Fo
uryz
a)
10
5
2.4.
Fun
Th
e
fun
p
r
in
cip
l
e
mea
n
s
th
a
t
m
at
h
e
ma
ti
cal
l
ea
rni
n
g
acti
v
i
t
i
e
s
m
us
t
be
d
e
s
i
gne
d
m
o
re
f
un,
s
o
tha
t
stude
n
t
s
are
e
n
th
us
iast
ic
a
nd
h
a
v
e
a
h
i
gh
i
n
ter
e
s
t
i
n
lea
r
ni
n
g
m
a
them
at
ics.
H
e
r
ma
nsy
a
h
sta
t
e
d
t
hat
t
h
e
fun
lear
n
i
n
g
w
as
i
n
d
ic
a
t
e
d
by no
t
on
l
y
t
he
s
tude
n
t
’
s
f
e
e
l
i
n
g
o
f
p
le
as
ure
dur
i
n
g ma
them
at
i
c
al le
a
rni
ng
b
u
t
a
l
s
o
t
he
in
ner
mo
ti
va
ti
o
n
t
o
ha
ve
f
ur
th
e
r
l
e
a
rn
in
g
e
n
d
u
ranc
e
[13].
Th
is
end
u
r
anc
e
c
an
b
e
real
iz
e
d
i
f
stud
e
n
t
s
k
n
o
w
some
thi
n
g,
t
he
n the
y
a
lw
ay
s
w
a
nt t
o fin
d
o
u
t
m
or
e a
bou
t
th
i
s
.
F
u
rtherm
ore
,
G
riffit
hs
s
t
a
t
e
d
tha
t
“
chi
l
dr
en
w
ill
bec
o
me
s
ucce
s
sfu
l
m
a
t
he
ma
ti
c
i
ans
if
m
athem
a
t
i
cs
is
d
el
i
v
ere
d
i
n
a
fu
n
a
nd
use
f
u
l
w
ay
“
[
1
4
]
.
T
hi
s
ca
n
ce
rt
ain
l
y
b
e
d
o
n
e
by
tea
c
h
in
g
m
a
them
a
tica
l
c
o
n
ce
p
t
s
us
i
n
g
c
e
rta
i
n
me
tho
d
s
c
o
rrec
tly
a
nd
de
li
ve
r
i
n
g
t
he
c
onc
e
p
t
in
a
p
le
asan
t
en
v
i
ronm
en
t.
R
esea
rch
by
u
s
ing
the
con
t
e
x
t o
f
lea
r
n
in
g
ma
them
at
i
c
h w
i
th fu
n
t
o
un
dersta
n
d
m
a
t
he
ma
t
ic
s
conc
e
p
t ha
d
bee
n
d
o
n
e a
s
w
e
l
l
[1
5].
Le
arni
ng
m
a
t
h
em
atic
s
with
f
u
n
i
s
c
o
nsi
d
er
ed
a
s
a
m
e
c
h
an
ism
t
h
a
t
can
e
nc
o
u
rage
s
tu
de
nt’s
conc
e
n
trat
io
n
to
m
ore
easi
l
y
un
dersta
n
d
l
e
a
rni
ng
m
a
te
ria
l
s,
i
nc
r
ease
m
o
ti
vat
i
on
i
n
l
e
a
r
ni
ng,
a
n
d
p
r
o
v
i
de
con
v
e
n
ie
nc
e
i
n
r
ece
i
v
in
g
of
v
ario
us
l
e
a
rni
n
g
need
s
[16].
T
hus,
t
h
e
fu
n
pr
i
n
c
i
ple
i
n
t
he
F
EM
a
ppr
oac
h
c
an
b
e
prese
n
t
e
d b
y
p
l
a
yi
n
g
ga
m
e
s
,
g
i
v
i
ng r
e
w
a
r
d
s,
gi
v
in
g m
o
ti
vat
i
on,
and i
n
vi
ti
n
g
s
t
ude
n
t
s to s
i
ng.
3.
LESS
O
N PLAN
Less
on
p
l
a
n
,
cal
l
e
d
as
R
en
c
a
n
a
P
e
l
ak
san
aan
P
emb
e
l
a
j
a
ra
n
(R
PP),
is
a
g
u
i
de
o
f
l
e
arn
i
ng
act
i
v
it
ies
implem
e
n
ta
t
i
o
n
f
or
eac
h
m
e
e
tin
g
[1
7].
Th
e
lea
r
n
i
n
g
a
c
t
i
v
i
t
i
es
a
re
d
ivid
e
d
i
nt
o
th
ree
st
a
g
e
s
.
Name
l
y
1
)
in
t
r
od
uc
ti
on,
2
)
core, a
nd 3)
c
lo
si
ng.
The
pre
lim
ina
r
y
ac
tiv
it
y
a
i
m
s
t
o
b
u
il
d
s
t
u
d
e
n
t’s
re
ad
i
n
ess
i
n
c
a
rryi
ng
ou
t
c
l
assro
o
m
lear
nin
g
ac
t
i
v
i
ti
e
s
.
T
h
e
s
e
ac
ti
vi
t
i
e
s
i
n
c
l
ude
p
ra
yer,
g
i
v
in
g
m
o
tiv
a
tio
n,
a
p
p
er
ce
pt
i
on,
a
n
d
i
n
f
orm
i
n
g
t
he
l
e
a
r
n
ing
o
b
j
e
ct
iv
e
s
th
a
t
wi
ll
b
e co
ndu
c
t
ed
out
.
The
c
o
re
act
iv
itie
s
are
gi
ve
n
by
o
b
ser
v
i
ng
t
h
e
pri
n
ci
p
l
es
o
f
F
E
M
ap
pr
o
ach.
This
a
c
tiv
it
y
i
n
c
l
u
d
e
s
del
i
v
eri
ng su
b
j
ect
m
a
t
te
r,
f
orm
i
ng s
t
u
dy
gro
ups,
gro
up d
i
sc
uss
i
o
n
s,
and
pr
esen
ta
ti
on.
Th
e
clo
s
ing
a
c
t
i
vi
t
y
i
s
t
h
e
f
i
n
a
l
ac
tiv
i
ty
o
f
a
se
ri
es
o
f
l
e
a
r
n
in
g
a
c
tiv
i
tie
s
in
t
he
c
l
a
ssro
o
m
.
Th
e
s
e
ac
t
i
v
i
ti
e
s
i
ncl
u
de
m
a
k
in
g
su
mm
a
r
i
e
s
or
c
onc
lus
i
o
n
s
fr
o
m
l
ea
rni
n
g
ac
tiv
it
i
e
s
t
h
at
h
a
v
e
bee
n
c
arrie
d
o
u
t
,
eva
l
ua
tin
g,
r
efle
ct
ing,
d
el
i
v
e
r
in
g
fol
l
o
w
-
up
a
ctiv
i
ties,
a
n
d
p
r
ay
ing
.
R
PP
m
u
s
t
b
e
c
re
a
t
ed
b
a
s
ed
o
n
the
ob
jec
t
i
v
es
t
ha
t
a
r
e
state
d
i
n
the
c
u
r
r
icu
l
um,
w
h
i
c
h
i
s
t
o
e
s
t
a
b
lis
h
in
de
p
e
nde
nc
e
a
nd
in
c
r
ea
se
t
he
s
t
u
den
t
’s
lear
n
i
n
g
m
ot
iv
ati
on,
a
s
well as be
st
u
d
e
n
t
ce
nt
e
r
e
d
[
1
8
].
4.
METHOD
The
m
e
t
h
o
d
u
s
e
d
i
n
t
h
i
s
re
se
ar
ch
i
s
the
me
tho
d
o
f
de
ve
l
opm
ent
r
esearch
refer
to
t
he
d
eve
l
o
p
m
e
nt
the
o
ry
p
ro
p
o
se
d
by
P
lomp
a
s
de
pic
t
e
d
o
n
F
i
g
u
re
1
.
Tha
t
d
e
v
e
l
opm
en
t
wa
s
ren
e
wed
an
d
h
a
s
th
re
e
s
t
ag
es,
nam
e
ly
p
rel
i
m
i
na
ry
r
ese
a
rc
h,
p
ro
to
typ
i
ng
p
h
a
se,
and
e
v
al
u
a
ti
o
n
phase
[
1
9
].
T
hree
s
t
a
ge
s
in
t
he
d
e
v
e
l
opm
ent
rese
arc
h
w
ill b
e
d
escr
i
b
e
d
be
l
ow
.
4.1.
Ph
ase
I: P
relimin
ar
y re
sear
c
h
st
age
The
pr
el
i
m
inar
y
re
sear
ch
i
s
requ
ire
d
t
o
o
b
ta
in
t
he
i
nsi
g
ht
a
b
o
u
t
the
pr
o
b
l
e
ms
i
n
e
d
uc
a
t
io
n,
i
.
e
.
a
b
ou
t
the
ga
p
betw
e
e
n
t
h
e
curr
ent
si
tua
t
i
o
n
in
f
ie
ld
a
nd
the
d
e
sir
e
d
one
.
[1
9]
E
xpla
i
ne
d
tha
t
t
he
act
i
v
i
tie
s
in
t
h
i
s
pha
se
c
om
pri
s
e
d
o
f
a
s
t
u
dy
of
n
ee
ds
a
n
d
c
on
t
e
xt
a
na
l
y
s
i
s,
a
r
ev
iew
o
f
l
i
t
era
t
ure
,
a
nd
a
de
ve
lo
pm
ent
o
f
c
o
n
cept
u
al
o
r
th
e
o
re
t
i
cal
fra
me
wo
r
k
f
or
t
he
r
esea
rch.
T
he
refo
r
e
,
the
deve
lopm
en
t
of
l
e
s
s
on
pla
n
i
n
this
pha
se
on
ly
f
oc
use
s
o
n c
u
rricu
lum
ana
l
ys
is a
ct
ivi
t
i
e
s,
s
tude
n
t
a
na
l
y
s
i
s,
m
ater
ial ana
l
ysis,
and
t
a
sk
a
na
lys
i
s.
4.2.
Pha
s
e II: Pro
t
o
ty
pe
The
pro
t
ot
ype
pha
se
i
s
a
foll
ow
-
u
p
ac
ti
v
ity
o
f
t
h
e
pre
limi
n
ar
y
re
se
arc
h
w
hic
h
i
s
to
f
in
d
a
so
lu
t
i
o
n
from
t
he
p
re
li
m
i
n
a
ry
r
e
s
ear
ch
a
n
d
t
he
n
t
o
r
ea
li
z
e
t
he
l
ess
on
pl
a
n
i
nt
o
a
pr
oto
t
ype
d
ra
ft
p
rod
u
ct.
The
acti
v
ity
of th
i
s p
h
a
s
e
c
onsis
te
d of (
1
)
the rea
l
i
z
a
t
i
on of l
e
s
so
n p
l
a
n
i
nt
o a
pro
t
o
t
ype
dr
a
ft p
r
o
d
u
ct by a
d
j
u
sti
n
g t
h
e four
pri
n
ci
p
l
es
o
f
FEM
a
pproac
h
on
t
h
e
su
b
j
ec
t
m
a
tt
e
r
t
h
a
t
i
s
d
eterm
in
e
d
by
i
n
t
e
g
e
r
ca
l
c
ula
t
ion
op
e
r
ati
o
ns,
a
n
d
(2)
th
e
a
rra
ngem
e
nt of
rese
arc
h
in
s
t
r
ume
n
t
in
t
he f
orm
of
v
alid
a
tio
n
she
e
t
of les
s
o
n
p
lan.
4.3.
Phase III: Evaluat
i
on
The
e
v
a
l
ua
t
i
on
p
hase
a
i
m
s
t
o
a
sce
r
tai
n
w
he
t
h
er
t
he
d
e
v
el
o
p
ed
l
e
sson
p
l
a
n
h
as
r
eac
he
d
the
c
r
i
t
eria
o
f
a
g
o
o
d
qua
l
i
ty
l
ess
o
n
p
l
a
n
o
r
no
t
.
T
h
e
p
r
e
vi
o
u
sly
prepa
r
ed
d
raf
t
(d
r
a
f
t
p
rot
o
ty
p
e
)
wil
l
b
e
v
ali
d
at
ed
b
y
th
e
val
i
d
at
ors
a
nd
re
v
i
se
d
u
n
t
il
t
h
e
v
a
l
i
d
p
rot
o
ty
p
e
i
s
c
r
ea
te
d.
S
o
,
the
ac
tiv
it
ie
s
tha
t
h
a
v
e
t
o
b
e
co
n
d
u
c
te
d
in
t
his
pha
se
i
nc
l
u
d
e
v
a
l
i
d
at
i
o
n,
t
e
s
t
leg
i
bil
i
t
y,
a
nd fiel
d
t
r
i
a
ls.
The
deter
m
i
n
a
t
i
o
n
o
f
t
he
q
u
a
li
ty
o
f
the
de
vel
o
pme
n
t
o
f
t
he
l
e
s
s
o
n
p
l
a
n
ba
sica
lly
r
e
q
u
i
res
t
h
re
e
c
r
i
t
e
ri
a as
p
ropo
sed
b
y
Ni
ev
een
, n
a
me
l
y
v
al
id
it
y
,
p
rac
t
i
c
al
ly
,
and e
ffe
c
t
iv
eness [
20].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
2
5
2
-
88
22
In
t
.
J
.
E
v
a
l
.
&
R
e
s
.
E
d
u
c
.
V
o
l.
8
,
N
o
.
1
,
M
ar
c
h
2
0
1
9
:
1
0
3
-
1
0
9
10
6
V
a
li
di
ty
r
ef
er
s
t
o
t
he
t
r
u
th,
sig
n
if
i
c
a
n
ce
,
an
d
usef
ulne
ss
of
t
h
e
s
p
eci
fi
c
c
o
n
c
lu
si
on
s
th
e
re
sea
r
ch
e
r
s
m
a
de
b
ase
d
o
n
the
da
t
a
a
lr
e
a
dy
c
o
llec
t
e
d
t
o
me
asur
e
the
le
sso
n
p
l
a
n
t
ha
t
de
ve
l
ope
d
val
i
d
or
n
ot
[
21]
.
Th
us,
the
less
on
p
l
a
n
i
n
t
h
is
s
tu
dy
i
s
v
a
l
id
i
f
i
t
h
a
s
a
s
tr
ong
t
he
o
r
e
t
i
c
a
l
r
a
tio
n
a
le
(
c
o
nt
en
t
v
a
li
d
ity
)
and
a
l
l
dev
i
ce
co
mp
on
en
ts
a
re
c
on
si
st
e
n
t
l
y
co
nn
e
c
t
e
d
wit
h
o
t
h
ers
i
n
h
armo
n
y
(
c
on
st
ruc
t
v
al
id
ity
)
[2
2]
.
Th
e
framew
o
r
k
o
f
t
h
in
ki
n
g
a
bout
t
h
e
d
ev
el
op
men
t
of
l
e
a
r
n
i
ng
m
at
eri
a
l
s
i
s sho
w
n
i
n
F
i
gur
e
1.
F
i
gur
e
1.
F
low
c
ha
r
t
o
f
de
ve
l
o
pm
ent
p
l
a
n
ni
n
g
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
Eval & R
es E
d
u
c
.
IS
S
N
:
2252-
88
22
D
e
sign
in
g L
e
sson P
l
a
n
o
f
I
n
t
e
ger N
u
m
b
er
O
p
er
at
ion
b
a
se
d
on Fu
n
an
d Easy
Ma
th
…
(D
ar
in Fo
uryz
a)
10
7
P
r
ac
ti
c
a
l
ity
s
e
e
n
fr
om
t
he
c
o
n
sider
a
t
i
o
n
o
f
e
xper
t
s
a
nd
p
r
acti
t
ione
rs
r
e
l
a
t
ed
m
ater
i
a
ls
(
less
on
p
la
n)
use
d
w
he
t
h
er c
om
plic
a
t
e t
o
s
tude
n
t
s a
n
d tea
c
her
s
or n
o
t
[2
0
].
T
he
pra
ct
ic
ali
t
y
of this
resea
rch i
s
base
d
on
two
th
ing
s
,
tha
t
i
s,
i
f
bo
th
e
x
p
er
t
s
a
n
d
p
ra
ct
iti
oner
s
r
e
v
ea
l
t
h
at
the
les
s
o
n
pla
n
c
a
n
t
he
or
et
ical
l
y
b
e
u
s
ed
b
y
teac
hers
a
nd
st
ude
n
t
s
an
d
it
s
i
m
plem
e
n
ta
t
i
o
n
i
s
i
n
g
o
od
cr
iter
i
a
.
I
t
is
i
n
t
e
nde
d
tha
t
t
eac
hers
a
n
d
s
tu
de
nt
s
ar
e
able
t
o
ca
rry
o
u
t
w
el
l pla
n
ne
d
ac
t
i
v
i
t
i
e
s
[
2
2
]
.
Th
e
ef
fe
ct
iv
enes
s
of
l
e
s
s
o
n
pl
a
n
i
s
d
e
t
e
rmi
n
e
d
b
a
s
e
d
o
n
t
h
e
stu
de
n
t
's
r
es
po
nse
le
vel
i
n
t
h
e
l
ear
n
i
ng
ac
t
i
v
i
ti
e
s
a
n
d
h
ig
h
s
t
ude
nt
e
nt
hus
iasm
t
o
fol
l
ow
t
he
l
ea
rn
in
g
a
c
t
i
v
it
ies
c
o
n
tin
uo
us
l
y
[
2
0
].
L
e
s
so
n
pl
an
i
s
sa
id
to
b
e
ef
fec
t
i
v
e
,
i
f
t
h
e
stu
d
en
t
'
s
r
e
sp
o
n
se
t
o
t
h
e
lea
r
n
i
ng
ac
ti
v
i
t
y
i
s
p
o
s
i
tive
a
nd
the
ac
h
i
eve
m
e
n
t
of
s
tude
nt
lear
n
i
n
g
c
om
p
l
e
t
e
n
e
ss in c
la
ssic
a
l,
i
f ≥
80%
s
tu
de
nt
s c
o
mple
te
t
h
ei
r st
udy
.
5.
RESULT
S
A
N
D
DISCU
SSIO
N
T
h
e
l
e
s
s
o
n
p
l
a
n
i
s
d
e
v
e
l
o
p
e
d
b
a
s
e
d
o
n
f
o
u
r
p
r
i
n
c
i
p
l
e
s
o
f
F
E
M
a
p
proac
h
,
w
h
ich
are
s
i
m
p
le,
use
f
ul
,
rela
tio
n,
a
n
d
fun,
w
i
t
h
t
he
a
i
m
o
f
he
l
p
i
n
g
s
t
u
d
e
n
t
s
i
n
un
d
e
r
s
t
a
n
d
in
g
inte
g
e
r
n
u
mbe
r
o
p
e
rati
ons
i
n
a
n
e
asy,
usefu
l
,
m
e
a
n
ingf
u
l
,
and
fu
n
w
a
y
,
a
nd
e
nga
ged
s
t
ude
n
t
s
a
c
tive
l
y
i
n
c
la
ss
room
l
ear
n
i
n
g
a
ctiv
i
ties.
I
n
a
d
d
iti
o
n
,
i
t
als
o
u
se
d
nu
mb
e
r
l
in
e
mo
d
e
l
in
t
e
ach
in
g
th
e
ex
a
c
t
c
o
n
c
ept
o
f
i
n
t
e
g
e
r
n
umbe
r
o
p
er
at
i
o
ns,
in
p
a
r
tic
ula
r
add
i
tio
n
an
d
s
u
b
t
r
act
i
on
of
i
nte
g
e
r
s.
T
his
is
i
n
t
en
de
d
t
o
a
v
o
i
d
t
h
e
e
x
i
s
t
e
n
c
e
o
f
m
a
t
h
e
m
a
t
i
c
a
l
m
a
n
i
p
u
l
a
t
i
o
n
,
i
n
w
h
ic
h
stu
d
e
n
t
s
a
re
not
o
nl
y
g
i
ve
n
kn
ow
le
d
g
e
d
ire
c
tly
o
r
m
e
m
o
riz
e
it
,
b
u
t
t
h
ey
a
re
a
bl
e
to
kno
w
t
h
e
mean
i
n
g
of
eac
h lea
r
ni
ng
proce
ss.
F
o
r
exam
ple,
i
f
t
h
e
st
ude
n
t
i
s
asked
t
o
c
a
l
cu
late
t
he
s
um
o
f
ad
di
ti
on
-
2
+
(-3
)
=
-
5
,
i
t
i
s
n
o
t
o
bt
ained
from
me
m
oriz
i
ng t
h
e
r
u
l
e
, i
f
(
-) +
(-)
=
(
+),
but deri
v
e
d
fro
m
a
m
e
a
n
i
n
gf
ul pr
o
ce
ss thr
ou
gh t
h
e use
o
f
n
um
ber
line
m
o
del ba
s
e
d
o
n
pat
terns
:
(
1)
a
lw
ays
s
t
a
r
t
from
0,
(
2
) arro
w
fa
ces righ
t
, (3) po
s
i
t
i
ve
n
um
ber re
ad forw
a
r
d
,
(4)
ne
g
a
tive
nu
m
b
er
r
ead
b
a
c
k,
(
5)
a
ddi
tio
n
opera
t
i
o
n
r
ea
d
as
c
on
t
i
n
u
e
,
a
n
d
(
6)
s
u
b
trac
t
i
on
o
p
er
atio
n
re
ad
a
s
tur
n
righ
t
or
left
a
nd c
o
n
t
i
n
ue.
The
de
ve
lo
pm
ent of t
his less
on pla
n
is
foc
u
sed
o
n
s
t
u
de
nts
at
t
he four
th gr
a
de of prima
r
y sc
h
o
o
l
a
n
d
its
d
e
v
e
l
o
p
m
e
nt
i
s
d
i
v
i
de
d
in
t
o
t
hr
ee
a
c
tivi
t
i
es,
nam
e
l
y
i
ntro
d
uc
ti
on,
c
ore,
a
nd
c
o
v
e
r.
E
ach
o
f
t
h
em
i
s
descr
i
be
d i
n
T
a
b
l
e
1.
Tab
l
e
1. D
escri
p
t
i
on o
f
l
e
sso
n
pla
n
de
v
el
o
p
m
e
n
t
No.
P
r
i
n
cip
l
es
FE
M
St
ag
e
s
Si
m
p
le
(1
)
Us
ef
u
l
(2
)
Re
la
ti
on
(3
)
Fun
(4
)
1
P
r
e
l
i
m
ina
r
y
Ac
tivi
t
y
a
.
Pra
y
ing
b
.
Gi
v
i
ng
M
o
tiva
t
i
on
√
c
.
Appe
r
c
e
p
ti
on
√
d.
Expl
a
i
ning
the
purpose
of
lea
r
ni
ng
√
2
E
sse
n
c
e
A
c
tivity
a
.
Expl
a
i
ning
subje
c
t
m
a
tte
r
√
√
b.
Form
ing
s
m
a
l
l
gr
oup
study
√
c
.
Di
sc
ussion
√
d
.
Pre
s
e
n
t
a
t
i
on
√
3
C
l
osing
Ac
tivit
y
a
.
Ma
k
e
a
c
on
c
l
usion
b
.
Eva
l
u
a
t
i
on
√
c
.
R
e
f
l
ect
io
n
d
.
Motiva
t
ion
√
e
.
Pra
y
ing
Ea
ch
o
f
the
p
r
e
l
i
m
i
n
ary,
e
ss
e
n
ce,
a
n
d
c
los
i
n
g
a
c
t
iv
itie
s
con
t
a
i
n
s
t
he
a
cti
v
itie
s
o
f
t
ea
c
h
ers’
a
n
d
stude
n
t
s’
i
n
th
e
l
e
sson
as
d
es
cr
ib
e
d
i
n
Tab
l
e
2.
S
tude
nt
s
w
o
r
k
s
he
et
f
or
p
r
a
c
tise
t
h
ro
ug
h
t
h
e
gam
e
“
fa
st
f
i
g
ht”
is
s
h
o
w
n
i
n Ta
bl
e
3.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
2
5
2
-
88
22
In
t
.
J
.
E
v
a
l
.
&
R
e
s
.
E
d
u
c
.
V
o
l.
8
,
N
o
.
1
,
M
ar
c
h
2
0
1
9
:
1
0
3
-
1
0
9
10
8
Tab
l
e
2. D
escri
p
t
i
on o
f
act
iv
i
tie
s
for
ea
ch sta
ge
No.
Sta
g
e
s
T
e
a
c
h
e
r
s’ Ac
tivity
S
tude
nts’ Ac
tivit
y
1
P
r
el
i
m
i
n
ar
y
Act
i
vity
P
r
a
y
ing
tog
e
t
h
e
r
P
r
i
n
c
i
ple
of
F
EM
(
4)
-
Fu
n
G
i
ving
m
o
ti
v
a
tion w
ith a
c
t
ion a
nd
sing
“
te
puk
s
e
m
angat
”
(pa
t
s
pir
i
t)
.
On
e
ti
me
“
t
e
p
u
k
s
e
m
angat”
,
“prok”
Two
ti
mes
“t
e
p
u
k
se
mangat
”,
“
pro
k
-
p
r
o
k”
Th
r
e
e
ti
mes
“
t
e
puk se
m
a
n
gat
”
,
“
pr
ok
-
p
r
o
k-
pr
o
k
”
F
o
r
t
h
e
la
s
t
t
im
e
“
te
pu
k
s
e
m
anga
t
”,
“
se
-
m
a
-
nga
t
-
ye
s!
’’
Stude
nt
i
m
i
t
a
ting a
c
t
i
o
n
a
nd
sing
“
te
puk
s
e
mangat
”
Pr
in
ci
p
l
e o
f
F
E
M (3)
-
R
e
l
a
tio
n
G
i
ving
a
p
e
r
c
e
p
tion
w
ith a
s
k
i
ng
som
e
que
stions a
bout
t
he
pre
r
e
qui
site
ca
p
a
b
i
l
i
tie
s of
i
nte
g
e
r
num
b
e
r
op
e
r
a
tion
subje
c
t
,
s
t
a
rt
e
d
by te
ll
ing a
story
in c
on
t
e
xtua
l
situ
a
tion,
be
low
:
“L
ook,
I
h
a
v
e
5.
000
r
upia
h
s
from
Siska
.
T
h
e
n
S
i
sk
a
gi
ve
a
g
ain 3.000 rupiahs. How m
u
c
h
m
o
n
e
y I
h
a
v
e
now?
”
Li
st
e
n
i
n
g
w
e
l
l
a
nd a
n
swe
r
que
stions
f
r
o
m
t
ea
c
h
er
:
“
Y
ou
ha
ve
8.
000
rupia
h
s
now
.
T
h
a
t
is
obta
i
ne
d
f
r
o
m
5
.
000
r
upi
a
h
s
+
3.
000
r
upia
h
s
=
8.
000
rupia
h
s
P
r
i
n
c
i
ple
of
F
EM
(
2)
-
Use
f
u
l
E
xpla
i
n
th
e
lea
r
ning
pur
pose
“toda
y
we
w
ill
l
e
a
r
n a
bout
int
e
g
e
r
nu
m
b
e
r
ope
r
a
tions,
w
hi
c
h
a
r
e
i
m
porta
nt
t
o
l
e
a
r
n
fo
r our
d
a
i
ly
life,
e
xam
p
l
e
s:
i
n
th
e
e
v
e
n
t
of
b
uy
i
ng a
nd
se
lling,
borr
o
w
i
ng,
d
e
t
e
r
m
i
ning
te
m
p
e
r
a
t
ure
,
d
riving,
et
c
.
”
Li
st
e
n
i
n
g
w
e
l
l
a
nd a
s
k a
bout
som
e
thi
n
g
t
h
a
t
a
r
e
not
c
lea
r
2
E
sse
n
c
e
A
c
tivit
y
E
xpla
i
n
of
i
nte
g
e
r
num
b
e
r
ope
r
a
tion
subje
c
t
w
i
t
h
n
um
be
r
li
ne
m
ode
l.
(
1)
-
First,
t
ea
c
h
e
r
w
r
i
ting
a
qu
e
s
tion
a
t
t
h
e
b
l
a
c
kbo
a
r
d.
T
his
que
st
ion
is a
bout
c
onte
x
t
u
a
l
s
it
u
a
tion
:
(
3)
Di
an
a
m
o
v
e
s
b
ack
4
s
t
e
p
s
.
Th
en
, s
h
e
m
o
v
es
b
ack
3
ste
p
s.
How
m
a
n
y
ste
p
s
did
D
i
a
n
a
m
o
ve
b
ac
kw
a
r
ds
?
a
. Sh
o
w
with
n
u
m
b
e
r
lin
e
s!
b
. Wr
i
t
e
in
t
o
math
s
en
ten
c
e
s
!
An
sw
e
r
:
a.
b.
-
4
+
(
-3)
=
-7
Li
st
e
n
i
n
g
w
e
l
l
a
nd a
s
k a
bout
som
e
thi
n
g
t
h
a
t
a
r
e
not
c
lea
r
-
St
ude
nts
ste
p
f
o
r
w
a
rd
t
o a
n
swe
r
que
st
ions
on
the
b
o
a
r
d
-
St
ude
nts
de
m
onstra
t
e
to
t
h
e
ir
fr
i
e
nds
how
t
o
a
n
sw
e
r
q
u
e
st
ions
using
num
be
r
li
n
e
s
Pr
in
ci
p
l
e o
f
FEM
(
1
)
, (
3
)
–
S
im
p
l
e
,
R
e
l
a
tion,
F
or
m
i
ng
s
m
a
ll group
study
,
c
onsi
s
t
o
f
4
s
tude
nts
a
nd
gi
ve
the
m
t
h
e
oppo
rtuni
t
y
t
o
us
e
nu
m
b
e
r
line
ca
r
r
y
out
t
h
e
t
ea
c
h
e
r
'
s
i
nstruc
ti
on
s
b
y
f
o
rm
ing
s
m
a
ll
group
study
,
c
onsist
o
f
4
stude
nts a
nd
try
yourse
lf
u
si
ng
num
b
e
r
lin
e
Pr
in
ci
p
l
e o
f
F
E
M (4)
-
F
u
n
Disc
ussion:
R
e
qu
e
s
t
stude
nts
to
p
r
a
c
tice
so
m
e
que
stion
in
s
tude
nt’s
w
o
rkshe
e
t
i
n
gr
oup
w
ith
p
la
y
i
ng
gam
e
“
fa
st
f
i
ght"
w
i
t
h
othe
r grou
ps
b
y
using
a
nu
m
b
e
r
l
in
e
m
o
d
e
l
.
(St
u
d
e
nts
w
o
r
k
she
e
t
is
s
hown
i
n
Ta
b
l
e
3
.
Dis
c
ussing
in
g
rou
p
s
ac
tiv
e
l
y
Pr
in
ci
p
l
e o
f
F
E
M (4)
–
Fun
P
r
e
s
e
n
ta
tion:
R
e
qu
e
s
t
gr
oup
re
pr
e
s
e
n
t
a
t
i
v
e
s
t
o
pr
e
se
nt
t
h
e
r
e
s
ults
of
the
dis
c
ussion
a
nd a
l
s
o
g
ivi
ng
re
w
a
r
d
s
t
o
s
tude
nts a
nd
gr
o
ups
w
ho
a
r
e
a
c
t
iv
e
in
l
ea
r
n
ing,
a
sking
qu
e
s
ti
ons
o
r
a
n
sw
e
r
i
ng
que
stions
a
n
d
doi
ng
s
tude
nts
w
o
rkshe
e
t
quic
k
ly a
nd
c
o
r
r
ect
l
y
.
Doing
pre
s
e
n
t
a
tions
a
s i
n
struc
t
e
d
by
the
t
e
ac
h
e
r
3
C
l
osing
A
c
tivit
y
m
a
k
e
a
c
onc
lusion
toge
th
e
r
f
r
o
m
th
e
m
a
t
h
em
a
t
i
c
s
s
u
b
j
e
c
t
t
h
at
h
a
v
e
b
e
en
l
e
a
r
n
ed
G
ive
stud
e
n
ts
e
v
a
l
u
a
tion
she
e
t
(
items)
by
a
ski
n
g
ea
c
h
st
ud
e
n
t
to
m
a
k
e
1
que
stion
a
bout
t
he
m
ate
r
ial
tha
t
h
a
s
be
e
n
l
e
a
r
n
e
d,
t
hen
e
x
c
h
a
n
g
e
t
he
que
st
ion
w
i
t
h
a
nothe
r
st
ud
e
n
t
to
a
nsw
e
r
.
S
tude
nts
w
ho
a
r
e
c
o
rr
e
c
t
i
n
a
n
swe
r
ing
will
be
rewa
rde
d
.
Stude
nts
do
the
item
s
r
e
f
le
c
t
i
n
g
tog
e
t
h
e
r
w
ith
a
sk
que
sti
o
n
a
bout:
how
t
ea
c
h
e
r
s
t
e
a
c
h,
m
ethods
u
se
d,
a
nd
st
ude
nts
re
sponse
a
bout
t
his
l
e
a
r
ning
proc
e
ss
P
r
i
n
c
i
ple
of
F
E
M
(
4
)
–
Fu
n
G
i
ving
m
o
ti
v
a
tion w
ith a
c
t
ion a
nd
sing
“
te
puk
s
e
m
angat
”
a
nd
r
e
m
i
nd
stude
nt
s
to
l
e
a
r
n
th
e
n
e
xt m
a
t
h
e
m
a
ti
c
s
s
ubj
e
c
t
Stude
nt
i
m
i
t
a
ting a
c
t
i
o
n
a
nd
sing
“
te
puk
s
e
mangat
”
P
r
a
y
i
ng
tog
e
t
h
e
r
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
Eval & R
es E
d
u
c
.
IS
S
N
:
2252-
88
22
D
e
sign
in
g L
e
sson P
l
a
n
o
f
I
n
t
e
ger N
u
m
b
er
O
p
er
at
ion
b
a
se
d
on Fu
n
an
d Easy
Ma
th
…
(D
ar
in Fo
uryz
a)
10
9
Tab
l
e
3
.
S
tu
de
nt w
orks
hee
t
Proble
m
:
In
t
he
e
v
e
ning,
M
rs.
R
i
ni
d
rive
s
he
r
m
o
tor
c
yc
l
e
t
o
pic
k
s
up
R
e
n
dy
w
ho
is
i
nvol
ved
in
s
tudy
group
with
h
is
friends
a
t
Pe
ru
m
a
h
a
n
S
e
m
e
r
u
I
nd
a
h
B
lok
G
no.
3
.
H
o
w
e
v
e
r,
M
rs.
R
i
ni
a
rr
ive
s
i
n
th
e
w
r
ong
a
ddr
e
ss
tha
t
i
s
a
t
h
o
m
e
n
o
.
5.
W
h
a
t
should
she
d
o
i
n
o
r
de
r
to
a
r
r
ive
a
t
h
o
m
e
no.
3
?
a.
Wh
a
t
ca
n
b
e
know
n
a
nd a
s
k
e
d a
bout
t
h
e
a
bov
e
pr
oble
m
?
Answ
e
r
:
b.
How
do
y
ou
solve
the
pr
obl
em
a
bove?
Answ
e
r
:
c.
Prove
t
he
s
olution
to
t
he
p
r
obl
em
a
bo
ve
b
y
writi
ng a
num
b
e
r
lin
e
m
o
d
e
l
d
e
m
onstra
t
ion
Ba
se
d
on
th
e
rule
s
!
Answ
e
r
:
6.
CONCL
U
S
ION
Base
d
on
t
he
r
esu
l
t
an
d
d
i
sc
uss
i
o
n
,
i
t
c
a
n
b
e
c
onc
l
u
ded
tha
t
t
h
e
de
ve
lo
pm
ent
r
e
sear
ch
w
i
t
h
F
E
M
appr
oa
ch
a
ssis
t
ed
n
umbe
r
l
i
n
e
mo
de
l
ca
n
he
lp
s
tu
de
nts
unde
rs
tan
d
th
e
rig
h
t
c
onc
e
p
t
of
i
nte
g
er
n
um
ber
opera
tio
n
simp
ly,
use
f
ul
,
me
ani
n
gfu
lly,
and
fu
n.
I
n
ot
her
h
a
nd,
i
t
’
s
e
x
p
e
c
t
ed
t
o
b
e
a
good
w
ay
f
o
r
t
e
ach
e
r
i
n
cre
a
ti
ng
of
a
c
on
d
u
ci
ve
l
e
a
rn
in
g
e
n
v
i
ro
nme
n
t
t
o
i
n
v
o
l
ve
s
t
u
d
e
n
t
’s
a
c
t
i
v
ely
in
l
ea
rn
ing
mat
h
emati
c
s.
I
t
c
a
n
b
e
seen
f
rom
t
h
e
var
i
ous
a
c
t
i
v
i
t
y
o
f
pr
el
i
m
inar
y,
e
ssenc
e,
a
nd
c
lo
s
i
ng.
T
he
re
for
e
,
a
set
of
a
cti
v
itie
s
de
scri
be
i
n
role
o
f
teac
her
and
s
t
u
d
e
n
ts
h
ave
b
e
e
n
p
ro
p
o
se
d
for
a
bet
t
e
r
im
pl
e
m
e
n
ta
t
i
o
n
o
f
less
o
n
p
lan
to
l
e
a
rn
o
p
e
ra
tion
of
i
n
t
ege
r
num
ber
in
c
lassro
o
m
s
ett
i
ng.
I
n
thi
s
d
e
v
e
l
opme
n
ta
l
r
ese
a
rc
h,
t
her
e
w
e
r
e
con
t
ext
u
a
l
s
i
t
ua
t
i
o
n
,
i.e
.
cou
n
t
i
ng
m
one
y
etc.
I
n
a
d
d
i
t
i
on,
t
his
rese
arc
h
u
se
d
the
m
o
del
t
hat
w
e
r
e
r
ela
t
e
d
t
o
the
g
i
ven
c
o
nte
x
ts,
n
a
m
e
ly
numbe
r
l
i
n
e
m
ode
l.
S
o,
by
u
nder
s
t
a
n
d
i
n
g
t
he
F
EM
a
p
p
ro
ac
h
an
d
i
t
s
i
m
p
l
ement
a
t
i
o
n
in
t
h
e
d
ev
el
opme
n
t
of
less
on
p
la
n,
a
n
ew
l
e
sso
n
p
l
a
n
w
h
i
c
h
i
s
i
n
n
ova
t
i
ve
a
nd
c
r
ea
t
i
ve
c
a
n
b
e
b
u
i
l
t
.
U
ltim
ate
l
y,
I
hope
m
y
r
e
sea
r
ch
w
ill
con
t
ri
b
u
t
e
t
o t
h
a
t
de
v
el
o
p
m
e
n
t
.
REFE
RENCES
[1]
P
e
rm
endi
kn
as,
"
C
o
n
ten
t
S
t
a
nd
ards
f
or P
rim
a
ry
a
n
d
S
econ
d
ary
Ed
uc
at
ion
Unit
,"
Dep
d
i
k
nas
,
20
06
.
[2]
Fathan
i. A
. H.
,
"
Mat
h
emat
i
c
s Nature an
d
Log
i
c
,"
Ar-R
uz
z
M
e
di
a
,
200
9.
[3]
Dep
d
ik
nas
,
"
M
o
d
e
l
o
f
D
ev
elopm
ent
o
f
S
y
l
l
a
bu
s
f
o
r
S
ubjects
an
d
P
lan
s
f
o
r
t
he
I
m
p
l
e
m
e
nt
atio
n
o
f
I
ntegrat
e
d
S
c
ien
c
e
Learni
ng
,
"
2
0
06.
[4]
Darw
is
M
.,
"
T
eachi
ng
Con
cep
ts
i
n
M
a
the
m
atics
(Es
p
eci
ally
i
n
Mid
dle
an
d
H
i
gh
er
E
du
c
a
tio
n),
"
M
a
ka
lah
Kom
p
reh
e
ns
if
Ma
gi
ster
P
P
S
IKIP M
a
la
ng
,
1
992
.
[5]
S
u
da
r
m
in
ta
.
J.
,
"
B
a
s
i
c Epistemo
logy,"
Kanisius
,
20
02
.
[6]
Ruh
y
ana,
"
An
aly
s
i
s
o
f
Stu
d
en
t
di
fficu
lti
e
s
i
n
M
athem
a
tical
P
ro
b
le
m
S
o
l
v
in
g
,
"
Ju
rn
al
Co
mp
utech
&
Bisnis
,
v
o
l.
1
(2
), p
p.
10
6
-
1
1
8
, 20
1
6
.
[7]
M
u
l
y
asa, "Beco
m
i
ng P
r
ofes
s
i
onal T
eacher,"
Remaja R
o
sdakary
a
, 2
01
5.
[8]
Mu
hse
t
o.
G.,
"
Ele
me
n
t
a
r
y Ma
the
m
a
t
ic
s
Le
a
r
ning
,
"
Un
iv
e
r
s
itas
Te
rb
uk
a
,
2
01
4.
[9]
F
a
hru
r
, "The
A
m
azin
g
of
Ad
van
ced M
ath
e
m
a
tics,"
T
i
m
M
a
temat
i
ka Dah
s
ya
t Indo
nes
i
a
, 2
01
2.
[10]
Jamaris.
M
., "New
Or
ientation
i
n
E
d
u
cation
a
l P
s
y
c
h
o
log
y
,
"
Gh
al
ia
,
2
01
3.
[11]
Ars
a
yth
a
m
by.
V
.
an
d
Zu
bai
nur.
C.
M
.
,
"
H
ow
a
R
eal
ist
i
c
M
a
them
ati
cs
E
d
u
cation
a
l
A
ppro
ach
A
ff
ect
S
tud
e
nt
s’
Act
i
viti
es
i
n
P
r
im
ary S
c
h
o
o
l
s
?
,"
Soci
a
l an
d Behavio
ra
l S
c
ience
,
v
o
l.
1
59,
pp.
3
09
-31
3
,
2
01
4.
[12]
P
a
rimsav
ad.
S.,
"
C
re
ati
n
g
a
J
oyful
L
earni
ng
E
n
v
i
r
on
m
e
n
t
a
t
Prim
ary
L
e
vel
S
P
I
JE
,
"
An In
t
e
rnational Journal of
Educat
ion
, v
ol
. 4
(1
),
p
p.
1
0-1
4
,
2
0
1
4
.
[13]
S
a
if
u
ddi
n
,
"
M
a
n
a
gem
e
nt
o
f
Theo
reti
ca
l
an
d P
r
actical L
earni
ng",
D
eepu
b
l
i
s
h
,
20
14
.
[14]
Oz
do
ga
n.
E
.,
"
P
la
y,
M
a
t
h
e
ma
tic
s
,
a
n
d
Ma
th
e
m
a
t
ic
a
l
P
la
y
in
E
a
r
ly
C
hi
ld
ho
od
E
d
u
c
a
t
io
n"
,
Pr
oc
ed
ia
–So
cia
l
an
d
Be
ha
v
i
oral
Sc
ie
nc
e
s
,
v
ol.
1
5(1),
pp
.
3
11
8-31
20
, 2
014
.
[15]
S
i
l
i
g
a
r,
E
.
I.
P
.,
S
om
akim,
and
Hap
i
zah
,
"Learn
i
ng
t
he
P
ermutat
io
n
Concep
t
th
roug
h
Rol
e
-Playing
"
,
J
o
urna
l o
f
Ed
uca
t
io
n a
nd Lear
ni
ng
(
E
d
u
L
e
a
r
n)
,
vol.
1
2
(3
),
pp.
4
22
-43
1
,
2
018.
[16]
Lu
cardie.
D
.,
"
The
Im
p
act
o
f
F
u
n
and
Enj
oym
ent
on
Adult
’
s
L
earn
i
ngP
ro
cedi
a
",
S
o
ci
al
an
d
B
e
havi
o
r
a
l
Sc
i
e
nce
,
vo
l.
142
,
p
p
.
43
9
-
44
6,
2
0
14.
[17]
S
a
nj
aya. W
., "Ed
ucat
io
n P
r
o
c
es
s
Oriented
Learn
i
ng
Strat
egi
e
s",
Kenca
n
a
Pr
ena
da
M
e
d
i
a Gro
up
,
200
6.
[18]
Kem
d
i
k
b
ud, "Boo
k
o
f Na
t
u
ral S
c
ience T
eachers
"
,
201
3.
[19]
P
l
om
p.
T
.
,
"
E
d
u
cat
io
nal
Des
i
gn Research
"
,
Neth
e
r
la
nd
s Instit
ute
fo
r Cu
rricul
u
m
Devel
opm
ent
(
S
L
O
)
,
20
13
.
[20]
Ni
eveen.
N.,
"Prot
o
typ
i
ng
t
o
Re
search
P
roduct
Q
uality,
Design
A
pp
roach
a
nd
T
o
o
l
in
E
du
c
a
t
i
o
n
a
nd
Train
i
n
g
",
Klu
w
er A
c
adem
i
c
P
u
b
l
i
s
her
,
1
999.
[21]
W
a
l
l
en
.
N
. E
.
an
d
Fra
e
nk
el
.
J.
R.
,
"
H
o
w
to Design
and
E
v
a
lua
t
e
Res
earch i
n E
d
u
catio
n",
M
c
Gr
aw-H
i
l
l
,
2
009.
[22]
Ho
bri
,
"
Devel
o
p
m
ent
Re
s
earch M
et
ho
dol
og
y",
Pe
n
e
Sa
ls
a
b
i
la
,
20
10.
Evaluation Warning : The document was created with Spire.PDF for Python.