Intern
ati
o
n
a
l
Jo
urn
a
l
o
f
E
v
al
ua
ti
o
n
and
Rese
arch in
Education (I
JE
RE)
V
o
l.5
,
No
.2
,
Jun
e
2
016
, pp
. 93
~100
I
S
SN
: 225
2-8
8
2
2
93
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJERE
Card Games and Algebra Tic Ta
cmatics on Achievement of
Junior Secondary II Student
s in Algeb
r
ai
c Expressi
ons
Okpu
be Nn
ae
meka
Mich
ael
,
Anu
g
wo M.
N.
Department o
f
S
c
ien
c
e Educatio
n, Ebon
y
i
S
t
ate
Univers
i
t
y
,
Abakaliki,
Nigeria
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
Mar 03, 2016
Rev
i
sed
Ap
r
13
, 20
16
Accepted
May 16, 2016
This stud
y
inves
tigat
ed the Card
Ga
mes and Alge
bra tic-
T
acmatics on
Junior
Secondar
y
II
Students’ Achievement
in Algebraic Express
i
ons. Three
research
questio
ns and three nu
ll h
y
poth
e
ses guided th
e stud
y
.
The stu
d
y
adopted
the pre-
test, post-test co
ntro
l group
design. A to
tal of
two hundred
and forty
(240) J
unior Second
ar
y School
II
students were used
as
sample for
this stud
y
.
Th
e experimental gro
up wa
s taught us
ing games while the
contro
l
group was taught using the conventi
onal (lectur
e) method. Algebraic
Achievem
ent T
e
st (AAT) was used to colle
ct da
ta for this stud
y.
AAT was
valid
ated b
y
thr
ee exp
e
rts
in m
a
them
at
ics
edu
c
ation
and m
eas
urem
ent and
evalu
a
tion r
e
s
p
e
c
tiv
el
y. T
h
e re
li
abili
t
y
index of
AAT was 0.79. Mean and
standard d
e
viation were used
to an
s
w
er th
e
res
ear
ch ques
t
ions
while
ANCOV
A was
used to test the
hy
pothese
s at 0.05 level of significan
ce. The
findings of the stud
y
showed
among ot
hers that there was a significan
t
differen
c
e betw
een stud
ents taught al
g
e
braic
expressions with games and
those taught without games, ther
e was
also a sig
n
ificant diff
eren
ce between
the achievement of males and
female
s taught
algebr
aic expr
essions with
games and
those taugh
t withou
t
g
a
mes in f
a
vour o
f
the males.
Keyword:
Academ
ic achievem
e
nt
Al
ge
brai
c e
x
pr
essi
ons
ANC
OV
A
Card
g
a
m
e
s
Tic-tacm
a
tics
Copyright ©
201
6 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Okpube
Nnae
meka Michael,
Depa
rtem
ent of Scie
nce E
d
uc
ation,
Ebo
n
y
i State
Un
iv
ersity,
Ab
ak
alik
i, Nigeria.
Em
a
il: ch
u
k
wue
m
ek
a
m
ich
aels@yaho
o.co
m
1.
INTRODUCTION
In an
y
hu
m
a
n
activ
ity, th
ere
ex
ists
an
el
em
ent
o
f
m
a
t
h
em
at
i
c
s whi
c
h c
o
ul
d
be
i
n
f
o
rm
of
Al
geb
r
a
,
C
a
l
c
ul
us, Ge
o
m
et
ry
, Tri
g
o
n
o
m
e
t
r
y
or St
at
i
s
t
i
c
s and t
h
ey
use si
gns, s
y
m
bol
s and/
or
pro
o
f
s t
o
de
scri
be
rel
a
t
i
ons
hi
p
(
s)
.
Hence
,
M
a
t
h
e
m
at
i
c
s as a scho
ol
s
u
b
j
ect
i
s
t
a
ug
ht
p
r
i
m
aril
y
for t
h
e
de
ve
l
opm
ent
of t
h
i
nki
ng
sk
ills, reflectio
n
s
on
on
esel
f, en
v
i
ron
m
en
t, so
cial
issu
es
and
o
r
g
a
n
i
zin
g
on
e’s
experien
ce for po
ssib
l
e
solution(s) t
o
problem
s
[1
]. Otunu-Ogbisi (2009) de
fine
d
m
a
the
m
a
tics teaching a
nd le
arni
ng a
s
the
act of
i
m
p
a
rtin
g
and
acq
u
i
ring
o
f
skills,
k
nowledg
e,
ap
titud
e
,
ab
ilities an
d
attitu
de cap
ab
le of m
a
k
i
ng
th
e ind
i
vid
u
a
l
fu
nct
i
o
nal
an
d
pr
od
uct
i
v
e
fo
r al
l
rou
n
d
ac
hi
evem
ent
of
a nat
i
o
n
’
s
dev
e
l
opm
ent
a
l
go
al
s [2]
.
O
d
um
osu
,
Ol
u
w
ay
em
i
and
Ol
at
u
nde
(2
0
1
2
)
de
scri
bed m
a
t
h
em
ati
c
s as an ess
e
nt
i
a
l
i
ngre
d
i
e
nt
i
n
m
a
nufa
c
t
u
ri
n
g
in
du
stries, econ
o
m
ic activ
it
ie
s, b
r
i
d
e of scien
ces, ch
ief
bri
d
e’s m
a
id of s
o
cial sciences, ladies in waiting
for
engi
neeri
n
g
,
c
o
sm
et
ol
ogy
o
f
art
s
an
d
una
v
o
i
d
a
b
l
e
ser
v
a
n
t
of m
a
nagem
e
nt
sci
e
nces
[3
]
.
It
i
s
not
s
u
r
p
ri
si
n
g
that because
of this,
m
a
the
m
a
tics is reco
mmende
d as a
core subject in both prim
ar
y and secondary sc
hool in
Ni
ge
ri
a an
d m
a
ny
co
u
n
t
r
i
e
s
of t
h
e w
o
rl
d.
As
An
u
g
w
o
(2
01
1
)
st
at
ed, t
h
i
s
i
s
t
o
ena
b
l
e
st
ude
nt
s ac
qui
r
e
an
d
b
r
o
a
d
e
n
t
h
eir
kn
owledg
e, sk
ill
s, and
ou
tlo
ok
in
m
a
th
e
m
a
tics
b
ecau
s
e
o
f
its
ap
p
licab
ility to m
a
n
y
areas o
f
life
[4]. It the
r
efore
m
eans that
mathem
atics can be applied
in
every facets
of life even
in t
h
e s
m
all-scale business
en
terp
rises wh
i
c
h
is th
e life wire o
f
e
v
ery econom
i
c sector. The applicati
on o
f
m
a
t
h
em
at
ics t
o
pr
obl
em
area
s
depe
n
d
s
on t
h
e
un
de
rst
a
n
d
i
n
g
of t
h
e co
nce
p
t
s
an
d t
h
e
pri
n
c
i
pl
es of m
a
t
h
em
at
i
c
s by
t
h
e pr
o
b
l
e
m
sol
v
er. Thi
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
252
-88
22
I
J
ERE
Vo
l.
5
,
N
o
.
2
,
Jun
e
201
6 :
9
3
– 100
94
would e
n
able the students experie
n
ce,
di
sc
o
v
er
, di
scu
ss an
d cha
nge t
h
e
misconception
of m
a
the
m
atic
s as an
abstract a
n
d di
fficult to learn
subject,
especi
al
l
y
as i
t
conce
r
ns
al
ge
bra
rel
a
t
e
d t
o
pi
cs.
Alge
bra
,
as an aspect of m
a
them
atics
m
ean
s fi
ndi
ng t
h
e u
n
k
n
o
w
n
o
r
p
u
t
t
i
ng real
l
i
f
e pr
obl
em
s i
n
t
o
eq
u
a
tion
s
and
th
en
so
l
v
ing
the
m
[5
].
It cou
l
d
also
be
seen
as a bran
ch of
math
e
m
atics th
at sub
s
titu
tes letters
for num
b
ers [6]. Algebra ca
n include
real num
bers, c
o
m
p
l
e
x num
bers, m
a
t
r
i
x
vect
ors
,
et
c [
7
]
.
It
i
s
t
h
e
gene
ral
i
zed
ari
t
hm
et
i
c
[8]
w
h
i
c
h
eve
r
y
ec
on
om
i
c
sect
or
nee
d
a
s
t
h
e
m
e
di
um
t
h
rou
g
h
w
h
i
c
h m
a
them
ati
c
s
p
r
ob
lem
s
e
ith
er wo
rd
s
o
r
m
ech
an
ical are seman
tically
an
d
syste
m
at
ically
tran
slated
,
written
an
d
m
a
n
i
pu
lated
to
g
i
v
e
th
e
d
e
sired log
i
c (an
s
wer) th
at is b
e
en
in
terpreted fo
r th
e
g
i
v
e
n
sit
u
atio
n [9
].
Ed
ucat
o
r
s a
n
d
M
a
t
h
em
at
i
c
i
a
ns co
nsi
d
er al
geb
r
a t
o
be o
n
e
of t
h
e m
o
st
im
port
a
nt
ar
ea
s of sc
h
ool
math
e
m
atics [
1
0
]
,[11
]. In
math
em
at
ics, an
alg
e
b
r
ai
c ex
pression
is an
ex
pressi
o
n
b
u
ilt u
p
fro
m
co
n
s
tan
t
s,
v
a
riab
les, and a fin
ite n
u
m
b
e
r o
f
alg
e
b
r
aic o
p
e
ration
s
(ad
d
ition
,
sub
t
ractio
n
m
u
lt
ip
licatio
n
s
, d
i
v
i
sion
and
exp
o
n
ent
i
a
t
i
o
n
s
)
by
an e
x
p
one
nt
t
h
at
i
s
a rat
i
o
nal
n
u
m
ber [1
1]
. S
o
m
e
of t
h
e e
x
am
pl
es of al
geb
r
ai
c
expressi
on are:
2
3
x
-
2xy
+c a
n
d
2
2
1
1
x
x
.
Al
ge
bra
f
o
rm
s an i
m
port
a
nt
aspect
of t
h
e
m
a
t
h
em
at
i
c
s cur
r
i
c
ul
um
. It
i
s
di
s
h
eart
e
ni
n
g
t
o
say
t
h
at
stu
d
e
n
t
s’ ach
iev
e
m
e
n
t
s in
m
a
th
em
a
tics at b
o
th
in
tern
al and ex
tern
al ex
amin
atio
n
s
h
a
v
e
rep
o
r
t
ed
ly
b
een poor
especially in
algebraic proc
esses [1
0
]
,[1
2
]
. Ku
ru
m
e
h
and
En
iayeju
(20
08) attribu
t
ed
th
is
ug
ly tren
d of
stude
nts’ poor academ
ic
achievem
e
nt
in
m
a
them
atics to a very wea
k
m
a
th
e
m
atics
founda
tion whic
h begins
i
n
th
e prim
ary le
v
e
l and
is carried
ov
er to
t
h
e ju
n
i
o
r
se
cond
ar
y, and
is cu
lmin
ated
in
sen
i
or
seco
nd
ary [
1
3
]
.
Am
os (2001)
posite
d that the sim
p
le cause of m
a
ss fa
ilure in,
m
a
the
m
atics academic perform
a
nce of
m
o
s
t
stu
d
e
n
t
s in
m
a
n
y
cou
n
t
ries inclu
d
i
ng
Nig
e
ria is th
e in
ab
ility o
f
m
a
th
e
m
a
tics ed
u
cator’s to
do
wh
at they are
suppose
d to do in term
s of
m
e
thod of
teaching [14].
Resea
r
ch
e
v
ide
n
ce
a
g
reed
that
ina
d
e
q
uate
m
e
thod
of instruction is
a
problem
m
ilitating a
g
ainst
th
e un
d
e
rstandin
g
o
f
m
a
th
e
m
atical co
n
cep
ts. Od
ili (20
0
6
)
an
d
Galad
i
m
a
(200
2) po
sited th
at p
oor qu
al
ity o
f
instructional techni
que em
ployed by
the teachers is one of the
m
a
jor
ca
uses of poor a
c
hievem
ent am
ong
seconda
ry school stude
n
ts in
m
a
the
m
atics [15],[16]. The
use of irreleva
nt teaching m
e
thods and abse
nce of
mathe
m
atics
resource m
a
terials are so
m
e
o
f
the problem
areas in the t
eaching and learni
ng
of m
a
thematics
th
at
m
i
litate
ag
ain
s
t stud
ents tak
i
n
g
career cho
i
ce in
furth
e
ring
stud
ies requ
iri
n
g th
e k
n
o
w
ledg
e of
mathe
m
atics. Agwagah
(2004)
stated
categorically that traditional m
a
th
e
m
atics
teaching is still the
norm
in
our nation’s
sc
hools
a
n
d has continue
d
t
o
dom
i
nate
th
e mathem
at
ics classroom
[17]
. In traditional teaching,
stude
nts acqui
re m
a
the
m
atic
al skills by i
m
i
t
ating
demonst
r
ation
by
the t
eacher and the te
xtbook.
Furt
herm
ore, in tra
d
itional
mathe
m
a
tics instruction, the
t
eacher on
da
ily basis sh
ows the st
ude
nts
severa
l
ex
am
p
l
es o
f
ho
w to
so
lv
e a
certain
typ
e
o
f
p
r
ob
lem
a
nd
have
t
h
em
pra
c
t
i
ce t
h
i
s
m
e
t
hod
i
n
t
h
e cl
ass
an
d i
n
h
o
m
ework. This ro
te m
e
m
o
rizatio
n
is no
t
o
n
l
y in
effec
tive but also se
riously st
unts st
ude
nts’ interes
t
and
growt
h
i
n
m
a
t
h
em
at
ical reasoni
ng a
n
d problem
solving
skills [18]. This teacher-di
r
e
c
ted inst
ruction,
rote
me
m
o
rizatio
n
,
d
r
ill an
d
v
e
rb
al recitatio
n
an
d
wo
rk
sh
eet co
m
p
letio
n
ap
pro
ach
es m
o
st o
f
th
e tim
e
fail to
devel
op
students’ ge
neric skills and i
n
terest.
Am
os sugg
este
d that m
a
the
m
atics teaching
shoul
d
be st
ruc
t
ure
d
su
ch
th
at kn
owledg
e is bu
ilt o
n
a fou
n
d
a
tio
n
alread
y po
ssessed
,
en
cou
r
ag
e stud
en
ts to
learn
b
y
d
o
i
n
g
,
ens
u
ri
n
g
t
h
at
l
earni
n
g
g
r
o
w
s o
u
t
of
us
eful
ex
pe
ri
enc
e
s and e
xpe
ri
m
e
nt
at
i
ons, b
y
effect
i
v
e u
s
e of
math
e
m
atica
l
man
i
p
u
l
ation
t
h
at stim
u
l
ates
co
gn
itiv
e, af
fectiv
e and
p
s
ych
o
m
o
t
o
r
do
m
a
in
s’
d
e
v
e
lop
m
en
t. Th
is
can be
ac
hieve
d
with
t
h
e use of
appr
opriate
mathe
m
atica
l
gam
e
s to teach
differe
n
t m
a
the
m
atical concepts a
t
th
e seco
nd
ary
scho
o
l
lev
e
l.
Mathem
a
tical
gam
e
s also called educational
gam
e
s ha
ve be
en de
fine
d as a
n
enjoyable s
o
cial activity
with
g
o
a
ls, rules, and
regu
l
a
tio
n
a
l obj
ectiv
es
[19
]
. Ma
t
h
em
atical games are
one
of the strate
gies
of the
National Mat
h
e
m
atical Centre (NMC
) for i
m
proving t
h
e
t
eaching a
n
d learni
ng of m
a
the
m
atics in schools
.
M
a
t
h
em
at
i
cal
gam
e
appr
oac
h
i
n
v
o
l
v
es t
w
o
or
m
o
re st
u
d
e
n
t
s
w
o
rki
ng t
o
get
h
e
r
t
o
fi
n
d
a sol
u
t
i
on t
o
a
gi
ve
n
math
e
m
atics
p
r
ob
lem
.
In
a
math
em
at
ical g
a
me, th
e win
n
e
r, the loser and
the spectat
or(s
) are all expect
ed to
learn
th
e m
a
th
e
m
atics co
n
cept b
e
in
g
p
r
acticed
in
th
e
gam
e
. Educat
ors a
n
d
researc
h
ers
ha
ve rec
o
m
m
ended t
h
e
use of
m
a
thematical ga
m
e
s
in teach
ing and learning of
m
a
the
m
a
tics
b
ecause it is
found to sustain and
d
e
v
e
l
o
p stud
ents’ in
terest and
ach
iev
e
m
e
n
t
in m
a
th
e
m
atics.
Acco
r
d
i
n
g t
o
An
u
g
w
o
(
2
01
1)
, m
a
t
h
em
at
ics gam
e
s
encoura
g
e student
s
to
d
i
scu
s
s math
e
m
atica
l
strategies with
the others i
n
cludi
ng t
h
eir
pee
r
s, teachers a
n
d pa
re
nts [4].
As
they a
r
e joking a
r
ound, int
e
rest is
capt
u
red
an
d
un
us
ual
s
o
l
u
t
i
ons
(s
ol
ut
i
o
ns
t
h
at
we
re
not
easy
t
o
com
e
by
w
h
e
n
t
h
e
c
o
n
v
e
n
t
i
onal
t
e
achi
n
g
m
e
t
hod i
s
bei
n
g u
s
ed
) t
o
pr
o
b
l
e
m
s
are achi
e
ved
.
M
a
t
h
em
at
i
cal
gam
e
s can t
a
ke t
h
e f
o
r
m
s of puzzl
es,
m
a
gi
c
t
r
i
c
ks,
fal
l
aci
es para
d
oxe
s,
o
r
any
t
y
pe
of
m
a
t
h
em
at
i
c
s
whi
c
h p
r
ovi
de
s am
usem
ent
or c
u
ri
osi
t
y
[1
0]
. They
bri
ng
joy
t
o
t
h
e l
ear
ner,
br
eakd
o
w
n
resi
s
t
ance t
o
l
ear
n
i
ng
by
red
u
ci
ng t
e
nsi
o
n, cl
eari
n
g b
o
re
d
o
m
, and
p
r
ov
id
ing
an
en
v
i
ron
m
en
t wh
ere t
h
e st
ud
en
t
can d
e
v
e
lo
p sk
ills an
d
acq
u
i
re m
o
re
k
nowledg
e. Th
ey also
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ERE
I
S
SN
:
225
2-8
8
2
2
Card Games
and Alge
br
a Tic
Tac
m
atics on
Achieveme
n
t
of
Junior
Sec
o
ndary
II St
ude
nts ....
(N.
M. Ok
pube)
95
st
im
ul
at
e
m
a
them
ati
cal
t
h
i
nki
n
g
an
d ge
n
e
rat
e
exci
t
e
m
e
nt
and s
p
i
r
i
t
of i
n
di
vi
dual
i
s
m
,
co-o
pe
rat
i
o
n an
d
co
m
p
etitio
n
[11
]
. Th
is
work fo
und
wh
et
h
e
r th
ey enh
a
n
ce m
a
th
em
at
ics ach
iev
e
m
e
n
t
.
The
iss
u
e of mathe
m
atics
a
c
hievem
ent
and gende
r
ha
s attracted
th
e
atten
tio
n of so
m
e
research
ers.
The pe
rform
a
nce of bot
h male and female students
vary from
place to place, but the
m
o
st re
markabl
e
d
i
fferen
ces m
a
y o
ccur
du
e t
o
sp
atial and
m
ech
an
ical tests an
d su
ch ab
ility mig
h
t
b
e
attri
b
u
t
ed
t
o
th
e cultu
ral
influe
nces
of t
h
e students
bac
k
ground
[20]-[22].
A substant
ial am
ount of re
search i
n
learning and teachi
ng
of
al
geb
r
a i
s
foc
u
sed o
n
t
h
e ef
f
ect
i
v
eness
of
m
a
ni
pul
at
i
v
e [
7
]
,
[
23]
an
d co
m
put
er appl
i
cat
i
ons [
6
]
on st
ude
nt
s
ab
ility to
g
e
n
e
ralize p
a
tterns and
so
l
v
e algeb
r
aic
relatio
ns. Althou
gh
t
h
ese stud
ies h
a
v
e
p
r
o
d
u
c
ed
ex
citin
g
resu
lts, th
e m
a
j
o
rity o
f
th
em
fav
o
r th
e use of co
m
p
u
t
er
ap
p
lication
s
in d
e
v
e
lop
i
ng
st
u
d
e
n
t
s’ ab
ilities and
interest in s
o
l
v
ing alge
braic proble
m
s
than teache
r
- de
velope
d
gam
e
s. Th
e latter ca
n be
use
d
in situations
whe
r
e these c
o
m
puter applications (for e
x
a
m
ple
in rura
l areas) m
a
y not be available
or scarce
. He
nc
e this
study sa
w t
h
e
need to
find t
h
e actua
l effect
o
f
m
a
th
e
m
a
tic
al g
a
m
e
s to
students
’ ac
hieve
m
ent in alge
bra.
1.
1.
Specific Pur
p
oses
of the Study
i.
Effect
of m
a
the
m
atical ga
m
e
s on
the m
ean
achievem
e
nt scores
of
juni
o
r
seco
nda
ry
sc
h
ool
II st
u
d
ent
s
i
n
algebraic expre
ssions
,
i
i
.
Effect
o
f
t
h
e
m
a
t
h
em
at
i
c
al
gam
e
s on t
h
e
m
ean achi
e
ve
m
e
nt
sco
r
es
of
m
a
l
e
and fem
a
l
e
st
ude
nt
s i
n
ju
ni
o
r
seco
nda
ry
sc
ho
ol
I
I
st
ude
nt
s a
l
geb
r
ai
c ex
p
r
es
si
ons
, a
n
d
iii.
Interacti
on
e
f
fect
of
m
e
thod and ge
nde
r on the
m
ean
achievem
e
nt scores
of
juni
or sec
ondary sc
hool two
st
ude
nt
s i
n
al
g
e
brai
c e
x
pressi
ons
.
1.
2.
Rese
arch Que
s
tions
i.
What is the effect of m
a
the
m
atical ga
m
e
s on the m
ean achi
e
vem
e
nt
scores of
ju
ni
o
r
sec
o
n
d
a
r
y
st
ude
nt
s i
n
algebraic expre
ssions
?
i
i
.
What
i
s
t
h
e
ef
f
ect
of m
a
t
h
em
at
i
cal
gam
e
s on t
h
e m
ean ach
i
e
vem
e
nt
score
s
of m
a
l
e
and
f
e
m
a
l
e
st
udent
s
i
n
algebraic expre
ssions
?
iii.
What is t
h
e interaction effe
ct of m
e
thod
and ge
nder
on the m
ean achievem
e
nt scores of stude
n
ts in
algebraic expre
ssions
?
1.
3.
Null Hypothes
es
Ho
1
:
Th
ere
was no
statistical
ly
sig
n
i
fican
t d
i
fferen
ce
in
t
h
e m
e
an ac
hievem
ent scores
of students ta
ught
al
geb
r
ai
c ex
p
r
e
ssi
ons
wi
t
h
m
a
t
h
em
at
i
cal
gam
e
s an
d t
hose
t
a
ug
ht
wi
t
h
o
u
t
g
a
m
e
s.
Ho
2
:
There
was no
statistically s
i
gnificant di
ffe
re
nce in
t
h
e m
e
an achi
e
vem
e
nt
scores o
f
m
a
le and fem
a
l
e
st
ude
nt
s t
a
u
g
h
t
al
geb
r
ai
c e
x
p
r
essi
ons
wi
t
h
m
a
t
h
em
ati
cal
gam
e
s and
t
h
ose
t
a
ug
ht
wi
t
h
o
u
t
gam
e
s.
Ho
3
:
There was n
o
st
at
i
s
t
i
call
y
si
g
n
i
f
i
cant
i
n
t
e
rac
t
i
on
ef
fect
bet
w
een
m
e
t
hod and ge
nde
r of t
h
e
st
u
d
ent
s
i
n
their m
ean achievem
e
nt score
s
in al
gebraic e
x
pressi
ons
.
2.
R
E
SEARC
H M
ETHOD
The desi
gn a
d
opt
e
d
fo
r t
h
i
s
st
udy
was q
u
a
s
i
-
ex
peri
m
e
nt
al
desi
gn w
h
i
c
h
used a pre
-
t
e
s
t
, post
-
t
e
st
,
no
n
-ra
nd
om
i
z
ed co
nt
r
o
l
gr
o
u
p
. T
h
e p
o
p
u
l
a
t
i
on wa
s m
a
de
up
of
16
8
9
Ju
ni
o
r
Seco
n
d
ar
y
Two (J
S2
) S
t
ude
nt
s
in
21
pu
b
lic seco
nd
ar
y schools in
O
n
ich
a
Lo
cal Gov
e
rn
men
t
Ar
ea
of
Ebo
n
y
i State, N
i
g
e
r
i
a. A to
tal
o
f
two
hu
n
d
re
d a
nd
f
o
rt
y
(2
40
) JS
2 s
t
ude
nt
s we
re
u
s
ed as sam
p
l
e
fo
r t
h
e st
udy
.
Sim
p
l
e
ran
d
o
m
sam
p
l
i
ng t
echni
qu
e
of
bal
l
o
t
i
n
g wa
s use
d
t
o
sel
ect
(4
) sch
o
o
l
s
o
u
t
of t
h
e
21 sc
h
ool
s a
nd al
s
o
t
w
o sc
h
ool
s eac
h f
r
om
t
h
e 4 scho
ol
s
fo
r t
h
e e
x
peri
m
e
nt
al
and c
o
nt
r
o
l
gr
o
u
p
s
.
Tw
o i
n
t
act
cl
asses we
re si
m
p
l
e
random
ly
sel
ect
ed fr
o
m
t
h
e 4
scho
o
l
s fo
r
each
gr
oup
. Ex
p
e
ri
m
e
n
t
al g
r
o
u
p
(
t
aug
h
t
w
ith
g
a
mes)
w
e
r
e
136 stu
d
e
n
t
s and
co
n
t
r
o
l gro
u
p
(
t
au
gh
t
wi
t
h
co
nve
nt
i
onal
l
ect
ure
m
e
t
hod we
re
10
4. The i
n
st
rum
e
nt
for
dat
a
col
l
ect
i
on was an
Al
geb
r
ai
c
Achi
e
v
em
ent
Test
(
AAT
) devel
ope
d by
t
h
e researc
h
ers whi
c
h
c
o
nt
ai
ns q
u
est
i
o
ns fr
om
Al
g
e
brai
c
Ex
pressi
on
s, S
i
m
p
l
e
Li
near Al
ge
brai
c Eq
u
a
t
i
ons an
d Al
geb
r
ai
c Ex
pa
n
s
i
ons (
J
SS
1
1
t
opi
cs
). C
a
r
d
g
a
m
e
s
suitable for the teaching
of t
h
ese topics
we
re used a
n
d al
gebra tic-ticm
a
tics was used i
n
teachi
ng
algebraic
expa
nsi
ons
. A
A
T was
a 5
0
m
u
lt
i
p
l
e
choi
c
e
o
b
ject
i
v
e
q
u
e
stio
n
s
with
op
tio
ns A-D.
On
e
o
p
tion
is t
h
e k
e
y th
e
rest are distrac
t
ers. It is 2m
ar
ks pe
r question. The inst
rum
e
nt was use
d
as pre
-
test and aft
e
r the treatm
e
n
t
was
adm
i
ni
st
ered, t
h
e sam
e
i
n
st
ru
m
e
nt
was c
h
a
n
ged
i
n
t
e
rm
s of
col
o
r a
n
d
posi
t
i
on
of
i
t
e
m
s
and
us
ed
as
po
st
-t
est
.
The i
n
st
r
u
ct
i
o
nal
pr
oce
d
u
r
e (car
d gam
e
s and al
ge
b
r
a t
i
c
-t
i
c
m
a
ti
cs and l
e
sso
n pl
an
) al
so de
vel
o
pe
d
by
the resea
r
c
h
ers
were
validated
by
three
(3
) M
a
them
atics specialists and t
w
o
(2) e
x
perts in Meas
urem
ent
an
d
Ev
al
u
a
tio
n. Th
e i
n
stru
m
e
n
t
and
th
e t
o
o
l
s were trial tested
in
2
sch
o
o
l
s ou
tsid
e th
e area o
f
t
h
e stud
y
.
The
reliab
ility o
f
AAT was estab
l
ish
e
d
u
s
ing
Ku
d
e
r-Rich
a
rd
so
n
20
Fo
rm
u
l
a an
d
h
a
d
a reli
ab
ility in
d
e
x
of 0.79
.
Descri
p
tiv
e statistics o
f
Mean
and
Stand
a
rd
Dev
i
ation
were
use
d
to answer the
res
earch
que
stions while
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
252
-88
22
I
J
ERE
Vo
l.
5
,
N
o
.
2
,
Jun
e
201
6 :
9
3
– 100
96
Anal
y
s
i
s
of C
ova
ri
ance
(
A
N
C
OV
A)
was
u
s
ed t
o
t
e
st
t
h
e
hy
p
o
t
h
es
es at
al
pha
l
e
vel
of
0.
0
5
usi
n
g
pr
e-t
e
st
score
s
as c
o
variates.
In
orde
r to c
o
ntrol teache
r
quality
variable, teachers i
n
bot
h
groups
we
re trained by
the researc
h
ers.
The re
gular cl
assroom
teachers taught the
two
groups
(e
xpe
rim
e
ntal and control
groups). The e
x
perim
e
ntal
g
r
ou
p
was taugh
t with lesson
p
l
an
on
g
a
m
e
s
wh
ile th
e con
t
ro
l group
was al
so
taugh
t th
e
sa
m
e
u
n
its (al
g
eb
raic
fract
i
o
ns, si
m
p
l
e
l
i
n
ear al
geb
r
ai
c equat
i
ons
and al
geb
r
ai
c expa
nsi
ons
) f
r
o
m
JS2
m
a
t
h
em
at
i
c
s syl
l
a
bus fo
r a
peri
od of si
x
weeks i
n
volvi
n
g
four
contacts
of
40 m
i
nutes each
week.
3.
RESULT AND DIS
C
USSI
ON
As i
ndi
cat
e
d
i
n
Tabl
e 1, t
h
e expe
ri
m
e
nt
al
grou
p ha
d an a
d
j
u
st
ed m
ean score o
f
7
2
.
5
1 an
d a st
anda
rd
devi
at
i
o
n of 1
0
.
5
2
.
T
h
e
c
ont
rol
gr
o
up ha
d an
a
d
j
u
st
ed
m
ean of 5
4
.
08
a
n
d
a
st
an
dar
d
devi
at
i
o
n of 7.
04
.
T
h
e
score
s
s
h
ow t
h
at the expe
rimental group
ac
hieve
d
better t
h
an the c
o
ntrol group.
Tabl
e 1.
M
e
a
n
and
St
an
da
rd
Devi
at
i
o
n
of
A
c
hi
evem
ent
Sc
ores
o
f
E
x
peri
m
e
nt
al
and
C
o
nt
r
o
l
G
r
o
u
p
s i
n
Al
ge
brai
c E
x
pr
essi
ons
Gr
oup M
ean
SD
N
E
xper
i
m
e
ntal 72.
51
10.
52
136
Contr
o
l
54.
08
7.
04
104
In Ta
bl
e 2, t
h
e
m
a
l
e
st
udent
s had a
n
ad
just
e
d
m
ean score of 79
.4
4 an
d a st
anda
rd de
vi
at
i
on sc
ore
o
f
8.
14
whi
l
e
t
h
ei
r fem
a
l
e
count
erpa
rt
s had a
n
adj
u
st
e
d
m
ean score
of 6
4
.
9
5
and a st
anda
r
d
de
vi
at
i
on sc
ore o
f
7.
06
. T
h
e
sco
r
es i
n
di
cat
e t
h
at
t
h
e m
a
l
e
st
ud
ent
s
per
f
o
r
m
e
d bet
t
e
r
t
h
a
n
t
h
e
i
r fem
a
l
e
cou
n
t
erpart
s
w
h
e
n
t
a
ug
ht
with
m
a
th
e
m
at
ical g
a
m
e
s.
Tabl
e
2. M
e
a
n
s an
d St
a
n
dar
d
Devi
at
i
o
n
of
P
o
st
Test
Ac
hi
evem
ent
Scores
of
M
a
l
e
an
d Fe
m
a
l
e
St
ude
nt
s
i
n
Al
ge
brai
c E
x
pr
essi
ons
Gr
oup M
ean
SD
N
M
a
le 79.
44
8.
14
71
Fem
a
le 64.
95
7.
06
65
I
n
Tab
l
e
3
,
the m
ean
sco
r
es f
o
r
t
h
e ex
p
e
ri
m
e
n
t
al g
r
oup sho
w
ed
t
h
at
th
e m
a
le stu
d
e
n
t
s had
an
adj
u
st
e
d
m
ean sco
r
e o
f
7
9
.
4
4 a
nd a
st
an
d
a
rd
de
vi
at
i
on
score
o
f
8.
14
whi
l
e
t
h
e
fem
a
l
e
st
ude
nt
s
h
a
d a
n
adj
u
st
e
d
m
ean
score
of 6
4
.
9
5 an
d a st
and
a
rd
devi
at
i
o
n sc
ore
of
7.
06
. Thi
s
sh
owe
d
t
h
at
gam
e
s favo
r
e
d t
h
e
m
a
l
e
st
udent
s
m
o
re t
h
an t
h
ei
r fem
a
l
e
count
erpa
rt
s. F
o
r t
h
e cont
r
o
l
g
r
o
u
p
, t
h
e m
a
l
e
st
udent
s
had a
n
a
d
j
u
st
e
d
m
ean sco
r
e
o
f
55
.8
2
an
d a
st
anda
r
d
devi
at
i
o
n
sc
ore
o
f
6.
9
2
whi
l
e
t
h
e
fe
m
a
l
e
st
udent
s
had
a
n
a
d
j
u
st
e
d
m
ean
score
o
f
5
2
.
0
4
and
a st
a
nda
rd
devi
at
i
o
n sc
o
r
e
o
f
6.
69
.
Tabl
e
3. M
e
a
n
and
St
an
da
rd
Devi
at
i
o
n Sc
o
r
e o
f
t
h
e
St
u
d
e
n
t
s
i
n
t
h
e
Ex
pe
ri
m
e
nt
al
and
C
o
nt
r
o
l
G
r
o
u
p
s B
a
sed
on
I
n
t
e
ract
i
o
n
bet
w
ee
n M
e
t
h
od
an
d
Ge
nde
r
Gr
oup Gender
M
ean
SD
N
E
xper
i
m
e
ntal M
a
le
79.
44
8.
14
71
Fem
a
le
64.
95
7.
06
65
Contr
o
l
M
a
le
55.
82
6.
92
56
Fem
a
le
52.
04
6.
69
48
T
h
e analysis
of c
o
varia
n
ce resu
lt presen
ted in
Tab
l
e 4
sho
w
s th
at
the
r
e
is significa
nt d
i
ffere
nce i
n
achievem
e
nt of students
bet
w
een t
h
e expe
rim
e
ntal gro
u
p
and t
h
e co
nt
r
o
l
g
r
o
u
p
(
p
‹
0.
05
).
He
nce, t
h
e n
u
l
l
h
ypo
th
esis
which
states th
at th
ere is
n
o
statistical
ly
significant differe
n
c
e
in the m
ean achievem
e
nt score
s
b
e
tween
th
e stu
d
e
n
t
s taug
h
t
with
g
a
m
e
s an
d
th
ose tau
g
h
t
with
ou
t g
a
m
e
s was rejected. Th
is i
m
p
lies th
at
gam
e
s (C
ard
Gam
e
s and Al
geb
r
a Ti
c-Ta
c
m
at
i
c
s) si
gni
fi
cant
l
y
enha
nce
d
st
u
d
ent
s
'
ach
i
e
vem
e
nt
i
n
algeb
r
ai
c
exp
r
essi
ons
. Thi
s
fu
rt
he
r i
ndi
cat
es t
h
at
t
h
e expe
ri
m
e
nt
al
grou
p achi
e
ved s
i
gni
fi
ca
nt
l
y
bet
t
e
r t
h
an t
h
e cont
rol
gr
o
u
p
.
Thi
s
t
h
us,
j
u
st
i
f
i
e
d t
h
e gr
o
u
p
’
s a
d
j
u
s
t
ed m
ean score
s
i
n
t
a
bl
e 3 i
n
whi
c
h t
h
e e
x
p
e
ri
m
e
nt
al
grou
p
score
d
hi
g
h
er t
h
an t
h
e cont
rol
gr
o
u
p
. T
h
us, t
h
e u
s
e of
gam
e
s si
gni
fi
cant
l
y
en
hance
s
st
u
d
e
n
t
s
’ achi
e
vem
e
nt
m
o
re
th
an
t
h
e
n
on-
use of
g
a
m
e
s.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ERE
I
S
SN
:
225
2-8
8
2
2
Card Games
and Alge
br
a Tic
Tac
m
atics on
Achieveme
n
t
of
Junior
Sec
o
ndary
II St
ude
nts ....
(N.
M. Ok
pube)
97
Tabl
e
4.
A
n
al
y
s
i
s
of
C
o
va
ri
an
ce (
ANC
OV
A)
R
e
sul
t
s
of t
h
e
Ex
peri
m
e
nt
al
and
C
o
nt
r
o
l
G
r
o
ups
wi
t
h
P
r
et
es
t
Scores as
Cova
riates
Sour
ce of Var
i
atio
n
Su
m
of Squar
e
s
Df
M
ean Squar
e
s
F
Sig.
Cor
r
ected M
odel
2832
6.
308
4
7081.
5
7
7
141.
46
8
.
000
I
n
ter
cept 1846
5.
428
1
1846
5.
428
368.
88
3
.
000
Pr
etest 804.
91
5
1
804.
91
5
16.
080
.
000
T
r
eat
m
e
nt gr
oup
1526
5.
399
1
1526
5.
399
304.
95
6*
.
000
Gender
4023.
3
2
8
1
4023.
3
2
8
80.
374
.
000
M
e
thod and Gender
1318.
8
7
8
1
1318.
8
7
8
26.
347
.
000
E
r
r
o
r 1176
3.
542
235
50.
058
T
o
tal 1039
324.
0
0
0
240
Cor
r
ected T
o
tal
4008
9.
850
239
*Significant at 0.
0
5
alpha level
The a
n
alysis in Ta
ble 5 s
hows that the
r
e
was a
si
gnific
a
nt differe
n
ce
in academ
ic achievem
e
nt of
m
a
l
e
and fem
a
l
e
st
ude
nt
s t
a
u
ght
al
ge
b
r
ai
c exp
r
essi
ons
wi
t
h
gam
e
s and t
h
ose t
a
u
g
h
t
wi
t
h
out
gam
e
s (p ‹
0.
05
)
.
Hen
c
e, the
n
u
l
l
h
ypo
th
esis which
states th
at t
h
ere was
no statistical
ly sig
n
i
fican
t
d
i
ffe
re
nce in ac
hievem
ent in
al
geb
r
ai
c exp
r
essi
ons
bet
w
ee
n m
a
l
e
and fe
m
a
l
e
st
udent
s t
a
ug
ht
wi
t
h
ga
m
e
s and t
hose
t
a
ug
ht
wi
t
h
o
u
t
gam
e
s
is rejected. T
h
is im
plies that
gam
e
s have signi
ficant
effect on t
h
e acade
m
ic achievem
e
nt of m
a
le and fem
a
le
i
n
al
ge
brai
c e
x
pressi
o
n
s. F
r
o
m
t
h
e resul
t
i
n
Tabl
e
5, t
h
e
g
a
m
e
s fav
o
re
d
si
gni
fi
ca
nt
l
y
t
h
e m
a
l
e
st
udent
s t
h
an
th
eir fem
a
le cou
n
t
erp
a
rts. Th
at is, th
e m
a
le stu
d
e
n
t
s ach
i
ev
ed
b
e
tter th
an
t
h
eir fem
a
le co
un
terp
arts.
Tabl
e
5.
A
n
al
y
s
i
s
of
C
o
va
ri
an
ce (
ANC
OV
A)
R
e
sul
t
s
of M
a
l
e
an
d Fem
a
l
e
St
ude
nt
s Ta
ug
ht
wi
t
h
Gam
e
s and
th
o
s
e
Taugh
t with
ou
t Gam
e
s
Sour
ce of Var
i
atio
n
Su
m
of Squar
e
s
Df
M
ean Squar
e
s
F
Sig.
Cor
r
ected M
odel
2832
6.
308
2
7081.
5
7
7
141.
46
8
.
000
I
n
ter
cept 1846
5.
428
1
1846
5.
428
368.
88
3
.
000
Pr
etest 804.
91
5
1
804.
91
5
16.
080
.
000
T
r
eat
m
e
nt gr
oup
1526
5.
399
1
1526
5.
399
304.
95
6
.
000
Gender
4023.
3
2
8
1
4023.
3
2
8
80.
374
*
.
000
M
e
thod and Gender
1318.
8
7
8
1
1318.
8
7
8
26.
347
.
000
E
r
r
o
r 1176
3.
542
131
50.
058
T
o
tal 1039
324.
0
0
0
136
Cor
r
ected T
o
tal
4008
9.
850
135
*Significant at 0.
0
5
alpha level
In Ta
bl
e 6, t
h
e anal
y
s
i
s
sho
w
ed a si
g
n
i
f
i
cant
i
n
t
e
ract
i
o
n
effect
bet
w
ee
n t
h
e
m
e
t
hod
use
d
and t
h
e
gen
d
e
r
of
t
h
e
st
u
d
ent
s
(
p
‹
0.
0
5
)
.
T
h
us,
t
h
e
nul
l
hy
p
o
th
esis
wh
ich
st
ates th
at th
ere was no
statisticall
y
significa
nt inte
raction e
ffect
between t
h
e m
e
thod a
n
d ge
nd
er of th
e
stud
ents in
th
e m
ean achievem
e
nt scores
in
alg
e
b
r
aic ex
pressi
o
n
s
was rej
ected
. This m
ean
s
th
at th
e
facilitati
n
g
effect of
g
a
m
e
s o
n
st
ud
en
ts’
achi
e
vem
e
nt
scores i
s
not
t
h
e sam
e
at
all
l
e
vel
s
o
f
ge
nder. The analysis in Table
6 s
h
ows that the int
e
racti
on
effect
bet
w
een
m
e
t
hod a
nd
ge
nde
r fa
v
o
re
d t
h
e
m
a
l
e
st
udent
s
m
o
re t
h
an t
h
e fem
a
l
e
st
udent
s. Th
at
i
s
, t
h
e
m
a
l
e
st
ude
nt
s ac
hi
ev
ed
bet
t
e
r t
h
a
n
t
h
ei
r
fem
a
l
e
count
e
r
pa
rt
s.
Tabl
e 6.
Analysis of Cova
riance (ANC
O
V
A
)
of
th
e In
ter
actio
n b
e
t
w
een M
e
th
od
an
d G
e
nd
er
Sour
ce of Var
i
atio
n
Su
m
of Squar
e
s
Df
M
ean Squar
e
s
F
Sig.
Cor
r
ected M
odel
2832
6.
308
4
7081.
5
7
7
141.
46
8
.
000
I
n
ter
cept 1846
5.
428
1
1846
5.
428
368.
88
3
.
000
Pr
etest 804.
91
5
1
804.
91
5
16.
080
.
000
T
r
eat
m
e
nt gr
oup
1526
5.
399
1
1526
5.
399
304.
95
6
.
000
Gender
4023.
3
2
8
1
4023.
3
2
8
80.
374
.
000
M
e
thod and Gender
1318.
8
7
8
1
1318.
8
7
8
26.
347
*
.
000
E
r
r
o
r 1176
3.
542
235
50.
058
T
o
tal 1039
324.
0
0
0
240
Cor
r
ected T
o
tal
4008
9.
850
239
*Significant at 0.
0
5
alpha level
3.
1.
Discussions
Fr
o
m
th
e f
i
n
d
i
n
g
s
o
f
th
e st
u
dy, it w
a
s f
o
und o
u
t
th
at th
er
e
ex
ist a sig
n
i
f
i
can
t
d
i
f
f
er
en
ce b
e
tw
een
th
e
academ
ic achievem
e
nt of
students
taught
wi
th gam
e
s an
d t
hos
e taught wit
h
out
gam
e
s. The
result s
h
owed that
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
252
-88
22
I
J
ERE
Vo
l.
5
,
N
o
.
2
,
Jun
e
201
6 :
9
3
– 100
98
t
h
e ex
peri
m
e
nt
al
gr
ou
p
ha
d a
hi
g
h
er
ad
j
u
st
ed m
ean t
h
an t
h
e c
ont
r
o
l
gr
o
u
p
.
T
h
u
s
, t
h
e
use
of m
a
t
h
em
at
i
cal
gam
e
s enha
nce
s
t
h
e l
ear
ni
n
g
o
f
al
ge
brai
c
ex
p
r
essi
o
n
s t
h
an
t
h
e
no
n
-
use
o
f
gam
e
s.
The s
u
ccess o
f
t
h
e expe
ri
m
e
nt
al
gro
up m
a
y
be at
t
r
i
but
e
d
t
o
t
h
e anc
h
ori
n
g ef
fects th
at math
e
m
atica
l
gam
e
s have
o
n
l
ear
ni
n
g
.
Th
e nat
u
re
of
m
a
t
h
em
ati
cal
gam
e
s pr
ovi
de t
h
e
pot
e
n
t
i
a
l
of
hel
p
i
n
g l
e
a
r
ne
rs t
o
co
n
c
ep
tu
alize
math
e
m
atics a
s
b
e
ing
tran
sp
aren
t and
th
e co
n
cep
ts as
b
e
ing
in
terrelated
.
Th
is aid
s
informatio
n
i
n
t
e
grat
i
o
n a
n
d
t
h
u
s
pr
ovi
des
ro
om
for
m
eani
n
g
f
ul
l
ear
ni
ng
.
Th
e abov
e f
i
nd
ing
s
ar
e co
n
s
isten
t
w
ith
th
e f
i
n
d
i
n
g
s
o
f
I
ji, A
b
ak
pa and Tak
o
r
(2
013
), Etu
kudo
(
201
2)
and
Ebele (
2
010
)
th
at
sh
ow
ed
si
gni
f
i
cant
di
ffe
renc
e i
n
achi
e
vem
e
nt
bet
w
ee
n t
h
e expe
ri
m
e
nt
al an
d
co
n
t
r
o
l
g
r
ou
ps
w
h
en
th
e ex
p
e
ri
m
e
n
t
al g
r
oup
w
a
s exp
o
s
ed
to m
a
th
e
m
atical
g
a
m
e
s [
2
4
]-[2
6].
The fi
ndi
ng i
s
ho
weve
r i
n
c
ont
rast
wi
t
h
t
h
at
of
Nwac
h
uk
w
u
(
2
0
0
2
) t
h
at
sh
owe
d
n
o
si
g
n
i
f
i
cant
di
ffe
re
nce bet
w
een t
h
e ex
p
e
ri
m
e
nt
al
and cont
r
o
l
g
r
o
u
p
s w
h
e
n
t
h
e
expe
ri
m
e
nt
al
gr
o
up
was ex
pos
ed t
o
adva
nce o
r
ga
n
i
zer
[
27]
. The
si
gni
fi
ca
nt
di
fference
is as a
result
of t
h
e
a
n
choring effec
t
s that m
a
the
m
atical
gam
e
s has on l
earni
ng a
n
d the efficacy of mathem
atical ga
mes in incorporating
ne
w in
form
ation. T
h
us,
if the
seconda
ry school m
a
the
m
a
t
ics teacher
s adopt appropriat
e
m
a
the
m
a
tica
l
ga
m
e
s in tea
c
hing of the s
u
bject,
stu
d
e
n
t
s
will un
d
e
rstand
t
h
e
math
e
m
atics c
o
n
c
ep
ts tau
g
h
t
to
th
em
. Th
is is b
ecau
s
e the d
i
fficu
lty and
low
p
opu
larity in
d
e
x
o
f
m
a
th
e
m
a
t
i
c
s is lin
k
e
d
with
th
e d
i
fficu
lty
in
u
n
d
e
rstand
in
g m
a
n
y
co
n
c
ep
ts in m
a
th
e
m
a
tics.
The fi
ndi
ng
of
t
h
i
s
st
udy
al
so
sho
w
e
d
a si
g
n
i
f
i
can
t differe
n
ce betwee
n the
m
ean achieve
ment scores
of m
a
l
e
and fe
m
a
l
e
st
udent
s i
n
al
ge
brai
c ex
pressi
o
n
s. T
h
e
fi
n
d
i
n
gs al
so
r
e
veal
ed t
h
at
t
h
e
m
a
l
e
st
udent
s had
a
higher a
d
justed m
ean than t
h
e fem
a
le students. T
h
is
im
p
l
i
e
s th
at th
e
g
a
mes favo
ured th
e m
a
le stu
d
e
nts th
an
th
e fem
a
le o
n
e
s.
The hi
ghe
r ac
hi
evem
ent
of m
a
l
e
st
udent
s i
n
t
h
i
s
st
udy
c
oul
d be
due t
o
t
h
e fact
t
h
at
m
a
t
h
em
at
i
c
s
gam
e
s have l
e
d t
o
great
e
r
u
n
d
erst
a
ndi
ng
, i
n
crease i
n
m
o
t
i
v
at
i
on an
d de
vel
opm
ent
of p
o
si
t
i
v
e at
t
i
t
ude t
o
war
d
s
t
h
e c
once
p
t
of
al
geb
r
ai
c e
x
p
r
essi
ons
. T
h
e
hi
ghe
r ac
hi
evem
en
t
o
f
t
h
e m
a
le
stud
en
ts cou
l
d also
b
e
attributed
to
th
e fact th
at as lit
tle ch
ild
ren
,
th
e
m
a
les
lo
ve p
l
ayin
g
g
a
mes a lo
t th
an
th
e fem
a
les. And
th
is lo
v
e
fo
r
g
a
m
e
s
has s
p
u
rre
d t
h
em
t
o
achi
e
ve
m
o
re t
h
an t
h
ei
r fem
a
l
e
count
erpa
rt
s i
n
t
h
i
s
st
udy
.
Al
so
, t
h
e hi
g
h
er ac
hi
e
v
em
ent
of t
h
e m
a
l
e
st
udent
s c
o
ul
d
be
at
t
r
i
but
ed t
o
t
h
e fact
t
h
at
they
are intere
sted
in prof
essi
ons suc
h
as
E
ngi
ne
eri
n
g
an
d Arch
itectu
r
e
wh
ich
h
a
s math
em
at
ics in
clin
atio
n
.
C
ont
ra
ry
t
o
t
h
ese resul
t
s
,
Iji
,
Aba
k
pa an
d
Tak
o
r (
2
01
3
)
obt
ai
ne
d
no si
gni
fi
cant
di
f
f
er
ence bet
w
ee
n
m
a
l
e
and
fem
a
l
e
st
ude
nt
s i
n
t
h
ei
r
st
u
d
y
[
2
4]
. T
h
ey
obse
r
ve
d t
h
at
b
o
t
h
m
a
le an
d
fem
a
l
e
stude
nt
s c
o
ul
d
d
o
wel
l
in
alg
e
braic lin
ear
g
r
aph
wh
en
exp
o
s
ed
t
o
similar
learn
i
ng
cond
itio
ns. A
l
so
, Etukud
o
(201
2) foun
d
no
significa
nt difference
betwee
n the academ
ic achievem
e
nt
of m
a
le and fe
m
a
le students
after treatm
e
n
t
[25].
Ebel
e
(2
0
1
0
)
al
so f
o
un
d t
h
a
t
no
si
g
n
i
f
i
c
a
n
t
di
ffe
re
nce e
x
i
s
t
s
bet
w
ee
n
m
a
l
e
and
fem
a
l
e
st
ude
nt
s ac
adem
i
c
achi
e
vem
e
nt
i
n
m
a
t
h
em
at
i
c
s [2
6]
.
Gal
a
di
m
a
and
O
k
eg
b
e
ni
n
(
2
0
1
2
) al
so a
dde
d c
r
e
d
ence t
o
n
o
si
g
n
i
f
i
cant
diffe
re
nce bet
w
een m
a
le and fem
a
le stude
nts academ
ic
achievem
e
nt in m
a
the
m
atics
whe
n
e
x
pose
d to the
sam
e
learn
i
n
g
co
nd
itio
ns [12
]
.
Th
e fi
n
d
i
n
g
s
rev
ealed
th
at the d
i
fferen
c
es in
in
tellectu
a
l ab
ility b
e
tween
male an
d
fem
a
le stu
d
e
n
t
s
can
p
r
ob
ab
ly b
e
attribu
t
ed to
d
i
ffe
rences
in s
o
cialization. T
h
us, a
n
y
go
od
teach
i
ng
strateg
y
like th
e
mathe
m
atica
l
gam
e
s will improve the
acade
m
ic achieve
ment of m
a
le
students
.
This is evide
n
t
by the gain in
th
e m
ean
sco
r
es of
b
o
t
h
sex
e
s, alth
oug
h th
e
g
a
in
was h
i
g
h
e
r in th
e m
a
le th
an
th
e fem
a
les.
On in
teraction effect, th
e fi
n
d
i
n
g
s
o
f
th
e
stu
d
y
re
v
e
aled a sign
ifican
t
in
teractio
n effect b
e
tween
m
e
t
hod a
nd
g
e
nde
r. T
h
e i
n
t
e
ract
i
on
was
ho
we
ver
hi
g
h
e
r
i
n
t
h
e m
a
l
e
s t
h
an i
n
t
h
e
f
e
m
a
l
e
s. Thi
s
was as
rev
ealed
b
y
th
e an
alysis in
Ta
b
l
e 3
th
at sh
owed
h
i
gh
er ad
ju
sted
m
ean
in
th
e
m
a
les
th
an
in
th
e fe
m
a
les. T
h
is is
h
o
w
e
v
e
r
in
con
t
r
a
st w
ith
th
e
f
i
nd
ing
s
of
Ebele (
2
010
), Etuk
udo
(2
012
)
and
Ij
i, Ab
ak
p
a
an
d
Tako
r
(
2013
)
th
at
showe
d
no significant i
n
terac
tion e
ffect
bet
w
een m
e
thod
(teaching m
e
thods
)
and ge
nde
r [24]-[26].
4.
RECO
M
M
E
N
D
A
TIO
N
S
B
a
sed on
t
h
e fi
ndi
ng
s of
t
h
i
s
s
t
udy
,
t
h
e fol
l
o
wi
n
g
recom
m
endat
i
o
ns
we
re m
a
de:
a.
Mathem
a
tics teachers at the
junior
sec
o
nda
r
y school level
should a
d
opt
appropriate
m
a
them
a
tical
ga
mes
in the teaching of m
a
the
m
at
ics c
oncepts. This is j
u
dge
d from
the f
acil
itating and ret
e
ntive abilities of
math
e
m
atica
l
g
a
m
e
s.
b.
Au
t
h
ors
o
f
m
a
th
em
a
tics tex
t
b
ook
s are en
co
urag
ed
t
o
emp
l
o
y
m
a
th
e
m
at
ical g
a
m
e
s in
writing
tex
t
boo
k
s
.
This
will
m
a
ke for ea
sy adopti
on
by the
m
a
t
h
em
at
ics teachers.
c.
M
a
t
h
em
at
i
c
s cur
r
i
c
ul
um
at
the j
uni
or sec
o
nda
ry
sh
oul
d be revi
e
w
e
d
wi
t
h
t
h
e aim
of i
n
c
o
r
p
orat
i
n
g
appropriate m
a
them
a
tical ga
mes
curric
u
lum
devel
opm
ent stage.
d.
The f
e
de
ral
a
nd
st
at
e go
ve
r
n
m
e
nt
s and
ot
her
pr
o
f
essi
o
n
a
l
bo
di
es l
i
k
e
t
h
e Ni
geri
a
n
Ed
ucat
i
onal
and
Research C
o
uncil (NER
DC
), Science T
eachers
As
s
o
ciation of
Nigeria
(STAN), Mathem
a
tic
al
Asso
ciatio
n
of Nig
e
ria and
th
e Nation
a
l cou
n
c
il fo
r
Teach
e
rs
o
f
Math
ematics (NCTM) sh
ou
ld
sensitize
othe
r stake
h
olders in the e
d
uc
ation sect
or
on the
efficacy
of mathe
m
atica
l
ga
m
e
s.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ERE
I
S
SN
:
225
2-8
8
2
2
Card Games
and Alge
br
a Tic
Tac
m
atics on
Achieveme
n
t
of
Junior
Sec
o
ndary
II St
ude
nts ....
(N.
M. Ok
pube)
99
5.
CO
NCL
USI
O
NS
B
a
sed o
n
t
h
e
fi
n
d
i
n
gs o
f
t
h
i
s
st
udy
, t
h
e f
o
l
l
o
wi
n
g
co
ncl
u
si
ons
were
d
r
a
w
n:
M
a
t
h
em
ati
cal
gam
e
s
(Card Gam
e
s
and Alge
bra
Tic-Tacm
atic
s)
a
r
e
e
ffectiv
e strate
gy for m
eaningful
learning t
o
occur i
n
m
a
t
h
em
at
i
c
s.
The
use
of
ga
m
e
s im
prove
d
bet
t
e
r t
h
e m
a
l
e
st
ude
nt
s’ ac
hi
evem
ent
i
n
al
geb
r
ai
c ex
pr
essi
ons
.
Th
us,
fo
r
bet
t
e
r achi
e
vem
e
nt
i
n
al
ge
brai
c
exp
r
essi
ons
, te
achers
of m
a
them
atics
sho
u
l
d be
enc
o
ura
g
ed
t
o
adopt appropri
ate
m
a
them
a
t
ical ga
m
e
s in c
o
njunction wi
t
h
othe
r appropriately selecte
d
teaching m
e
thods.
The
variety of
teaching m
e
th
ods will th
us help to inc
r
ease
the students’
un
de
rstanding
of t
h
e subj
ect.
In t
h
is
way
,
hi
ghe
r a
c
hi
evem
ent
coul
d
be ens
u
re
d an
d t
h
e
per
cei
ved a
b
st
rac
t
nat
u
re
of m
a
t
h
em
ati
c
s (algeb
rai
c
exp
r
essi
ons
) re
duce
d
.
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nder di
fferen
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y
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t
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e
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e t
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l
gebr
a a
t
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h
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e
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a
G. O.,
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c
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atics,
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atic
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ematics,
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os S.
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a
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i
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