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T
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u
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in
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m
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1
3
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b
y
m
o
s
t
lear
n
er
s
in
t
h
eir
d
a
y
to
d
a
y
liv
es
th
r
o
u
g
h
p
lay
a
n
d
d
aily
in
ter
ac
tio
n
s
wh
ich
in
clu
d
e
s
k
ills
s
u
ch
as
b
asic
co
u
n
t
in
g
,
co
m
p
a
r
is
o
n
s
an
d
th
e
ab
ilit
y
to
d
if
f
er
en
tiate
,
r
ec
o
g
n
izin
g
s
h
ap
es
an
d
p
o
s
itio
n
s
,
an
d
p
r
o
b
lem
s
o
lv
in
g
[
1
4
]
,
[
1
5
]
.
Fu
tu
r
e
m
ath
a
b
ilit
y
is
clo
s
ely
lin
k
ed
to
th
e
d
ev
el
o
p
m
en
t
o
f
th
ese
ea
r
ly
m
ath
a
b
ilit
ies
an
d
th
er
e
is
ev
id
en
ce
o
f
th
is
in
s
ev
er
al
l
o
n
g
itu
d
i
n
a
l
s
tu
d
ies
[
1
6
]
-
[
1
8
]
.
T
h
e
ab
ilit
y
o
f
a
s
tu
d
e
n
t
to
g
r
asp
m
ath
e
m
atica
l
co
n
ce
p
ts
in
t
h
e
f
u
tu
r
e
is
v
e
r
y
m
u
ch
d
ep
en
d
en
t
o
n
h
o
w
s
tr
o
n
g
th
eir
f
o
u
n
d
atio
n
is
,
b
ased
o
n
wh
at
t
h
ey
wo
u
ld
h
av
e
lear
n
t
d
u
r
in
g
th
eir
ea
r
ly
y
ea
r
s
o
f
s
ch
o
o
lin
g
.
I
n
a
s
tu
d
y
b
y
Har
r
is
an
d
Peter
s
en
[
1
4
]
,
a
co
r
r
elatio
n
was
f
o
u
n
d
,
s
u
ch
th
at
s
tu
d
en
ts
wh
o
u
n
d
e
r
p
er
f
o
r
m
e
d
in
later
g
r
a
d
es
h
ap
p
en
e
d
to
p
o
s
s
ess
p
o
o
r
m
ath
em
atica
l
s
k
ills
in
th
eir
ea
r
ly
s
ch
o
o
lin
g
d
a
y
s
.
W
ith
o
u
t
th
ese
b
asic
s
,
s
tu
d
e
n
ts
wer
e
b
o
u
n
d
to
s
tr
u
g
g
le
later
o
n
,
with
m
o
r
e
co
m
p
lex
m
ath
em
atic
al
co
n
ce
p
ts
.
Hen
ce
,
it
is
c
lear
th
at
cu
ltiv
atin
g
m
ath
em
atica
l
an
d
n
u
m
er
ac
y
s
k
ills
ar
e
in
ess
en
ce
,
s
tep
p
in
g
s
to
n
es
to
war
d
s
f
u
tu
r
is
tic
ex
ce
llen
ce
i
n
th
is
d
o
m
ain
,
an
d
f
o
llo
win
g
s
o
,
th
e
o
p
tim
u
m
s
o
lu
tio
n
wo
u
ld
ce
r
tain
l
y
b
e
to
en
s
u
r
e
s
u
ch
m
ath
s
lear
n
in
g
a
n
d
in
t
e
r
v
en
tio
n
tak
es
p
lace
at
a
n
e
ar
ly
en
tr
y
lev
el
in
s
ch
o
o
ls
.
2
.
2
.
Dev
elo
pm
ent
o
f
nu
m
er
a
cy
s
k
ills
v
ia
inte
rv
ent
io
n
T
h
e
b
u
ild
in
g
b
lo
ck
s
as
th
e
s
co
p
e
o
f
th
e
s
tu
d
y
r
elate
s
to
th
e
m
ea
n
in
g
o
f
n
u
m
b
e
r
s
,
th
e
r
ep
r
esen
tatio
n
o
f
n
u
m
b
er
s
,
th
e
co
n
n
ec
tio
n
b
e
twee
n
th
em
an
d
ca
lcu
latio
n
s
t
h
at
ar
e
ess
en
tial
in
th
e
d
ev
elo
p
m
en
t
o
f
n
u
m
er
ac
y
s
k
ills
.
T
h
ese
s
k
ills
,
s
o
m
etim
es
in
ter
ch
an
g
ea
b
ly
ca
lled
n
u
m
b
er
s
en
s
e,
ca
n
b
e
d
escr
ib
ed
a
s
a
lear
n
e
r
’
s
o
v
er
all
k
n
o
wled
g
e
o
f
n
u
m
b
er
s
an
d
o
p
er
atio
n
s
co
m
b
in
ed
with
th
e
ca
p
ab
ilit
y
o
f
u
s
in
g
th
is
u
n
d
e
r
s
tan
d
in
g
in
ad
a
p
tab
le
way
s
in
th
e
d
e
v
elo
p
m
e
n
t
o
f
tech
n
iq
u
es
in
th
e
s
o
lu
tio
n
o
f
co
m
p
le
x
p
r
o
b
lem
s
an
d
f
o
r
m
in
g
m
ath
em
atica
l
ju
d
g
em
en
ts
[
1
9
]
,
[
2
0
]
.
W
ith
th
e
p
ass
ag
e
o
f
tim
e,
s
tu
d
ies
h
av
e
d
ep
icted
v
ar
io
u
s
in
ter
v
en
tio
n
p
r
o
g
r
am
s
in
en
h
an
cin
g
n
u
m
er
ac
y
s
k
ills
.
I
n
a
s
tu
d
y
b
y
Pap
ad
ak
is
,
et
a
l.
[
2
1
]
,
th
e
i
m
p
ac
t
o
f
two
v
ar
y
in
g
d
i
g
ital
tech
n
o
lo
g
ies
in
th
e
u
n
d
er
s
tan
d
i
n
g
o
f
n
u
m
b
er
s
a
m
o
n
g
s
t
s
tu
d
en
ts
wer
e
ass
ess
ed
in
th
e
ea
r
ly
ch
ild
h
o
o
d
s
tag
e
its
elf
.
T
h
r
ee
h
u
n
d
r
ed
an
d
s
ix
ty
-
f
iv
e
ch
ild
r
e
n
ag
ed
ap
p
r
o
x
im
ately
f
iv
e
y
ea
r
s
o
l
d
p
ar
ticip
ated
in
th
is
ex
p
er
im
en
tal
d
esig
n
s
tu
d
y
,
wh
er
e
th
er
e
was
ac
tiv
e
p
ar
ti
cip
atio
n
am
o
n
g
s
t
th
e
lear
n
er
s
.
T
h
e
f
in
d
in
g
s
d
ep
icted
th
at
b
o
th
th
e
tech
n
o
lo
g
ical
d
ev
ices
o
u
tp
er
f
o
r
m
e
d
th
e
tr
ad
itio
n
al
g
r
o
u
p
in
th
e
co
m
p
r
eh
e
n
s
io
n
o
f
n
u
m
b
er
k
n
o
wled
g
e.
I
n
an
o
th
er
s
tu
d
y
b
y
Kath
leen
,
et
a
l.
[
2
2
]
i
n
v
esti
g
a
tin
g
th
e
ef
f
ec
ts
o
f
tap
ed
p
r
o
b
l
em
(
T
P)
in
ter
v
e
n
tio
n
r
elatin
g
to
th
e
ac
q
u
i
r
in
g
o
f
ad
d
itio
n
-
f
ac
t
s
k
ills
at
th
e
o
u
ts
et
in
a
f
ir
s
t
-
g
r
ad
e
g
en
e
r
al
ed
u
ca
tio
n
class
r
o
o
m
was
lo
o
k
ed
i
n
to
.
I
t
was
g
ath
er
ed
th
at
s
tu
d
en
ts
wh
o
ar
e
a
ctiv
ely
en
g
a
g
ed
i
n
r
e
p
ea
ted
p
r
ac
tice
with
q
u
ick
r
ec
all
an
d
r
esp
o
n
s
e
o
f
ad
d
itio
n
al
f
ac
ts
co
u
ld
d
r
aw
o
n
t
h
eir
r
ea
s
o
n
in
g
ab
ilit
ies
in
th
e
lea
r
n
in
g
o
f
co
n
ce
p
ts
an
d
o
th
er
s
k
ills
.
Yet,
i
n
an
o
t
h
er
s
tu
d
y
b
y
Heir
d
s
f
ield
[
2
3
]
,
t
h
e
f
in
d
in
g
s
r
ev
ea
led
th
at
th
e
teac
h
in
g
o
f
ea
r
ly
m
ath
em
atica
l
co
n
ce
p
ts
an
d
tech
n
iq
u
es
was
n
o
t
o
n
ly
cr
u
cial
in
th
e
d
e
v
elo
p
m
en
t
o
f
m
en
tal
co
m
p
u
tatio
n
s
tr
ateg
ies,
b
u
t
was
in
s
tr
u
m
en
tal
in
th
e
d
ev
elo
p
m
e
n
t
o
f
h
ig
h
e
r
o
r
d
er
t
h
in
k
in
g
s
k
ills
,
an
aly
s
is
an
d
a
d
ee
p
er
u
n
d
er
s
tan
d
i
n
g
o
f
n
u
m
b
er
s
an
d
o
p
er
atio
n
s
.
Acc
o
r
d
in
g
Au
b
r
e
y
an
d
Go
d
f
r
ey
[
1
6
,
p
.
1
]
,
am
o
n
g
1
1
8
s
tu
d
en
ts
in
5
th
g
r
ad
e
(
1
1
-
12
-
y
e
ar
-
o
l
d
s
)
,
th
e
r
elatio
n
s
h
ip
b
etwe
en
m
e
n
tal
c
o
m
p
u
tatio
n
an
d
m
ath
em
atica
l
r
ea
s
o
n
in
g
was e
x
p
l
o
r
ed
.
T
h
eir
f
in
d
in
g
s
s
h
o
w:
(
Th
ere
)
is
a
s
ig
n
ifica
n
t
p
o
s
itive
co
r
r
ela
tio
n
b
etw
ee
n
men
ta
l
co
mp
u
ta
tio
n
a
n
d
ma
th
ema
ti
ca
l
r
ea
s
o
n
in
g
.
I
t
is
n
o
tew
o
r
th
y
th
a
t
r
a
th
er
th
a
n
ex
p
o
s
in
g
s
tu
d
e
n
ts
to
fa
milia
r
cla
s
s
ica
l
p
r
o
b
lems,
s
tu
d
en
ts
n
ee
d
to
b
e
en
a
b
led
t
o
d
ea
l
w
ith
ex
ce
p
tio
n
a
l/n
o
n
-
r
o
u
tin
e
p
r
o
b
lems,
a
n
d
esp
ec
ia
lly
yo
u
n
g
c
h
ild
r
en
s
h
o
u
l
d
b
e
e
n
c
o
u
r
a
g
ed
t
o
d
o
men
ta
l
co
mp
u
tin
g
in
o
r
d
er
fo
r
d
ev
elo
p
in
g
b
o
th
s
kills
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
C
a
r
d
g
a
me
a
s
a
p
e
d
a
g
o
g
ica
l t
o
o
l fo
r
n
u
mera
cy
s
kills
d
ev
elo
p
men
t
(
P
a
r
mjit S
in
g
h
)
695
I
t
is
th
er
eb
y
s
u
g
g
ested
th
at
in
s
tr
u
ctio
n
in
ter
v
en
tio
n
in
m
en
tal
co
m
p
u
tatio
n
an
d
esti
m
atio
n
ca
n
s
u
p
p
o
r
t
th
e
d
ev
elo
p
m
e
n
t
o
f
r
ea
s
o
n
in
g
in
ch
ild
r
e
n
.
T
h
e
r
es
u
lts
o
f
th
e
s
tu
d
ies
[
1
6
]
,
[
21
]
-
[
2
3
]
,
s
h
o
we
d
th
at
in
ter
v
en
tio
n
p
r
o
g
r
am
s
an
d
p
r
ac
ticin
g
m
en
tal
s
tr
ateg
ies
h
ad
a
n
o
tab
le
ef
f
ec
t
o
n
s
tu
d
e
n
ts
’
p
ar
ad
ig
m
s
to
war
d
s
th
eir
m
en
tal
m
eth
o
d
o
lo
g
ies an
d
n
u
m
b
er
s
en
s
e
ab
ilit
ies.
All t
h
ese
ac
tiv
ities
as
s
u
g
g
ested
b
y
th
e
r
esear
ch
er
s
ar
e
b
ased
o
n
a
ctiv
e
p
ar
ticip
a
tio
n
o
f
lear
n
e
r
s
[
2
4
]
.
Hig
h
lig
h
ted
t
h
at
ch
ild
r
en
lear
n
b
est
wh
en
t
h
ey
ar
e
en
g
a
g
ed
in
m
ea
n
in
g
f
u
l
an
d
lo
g
ical
ac
tiv
it
ies,
as
th
er
e
is
a
d
ee
p
er
lear
n
i
n
g
ex
p
er
ien
ce
t
h
ey
ca
n
r
elate
to
,
wh
er
e
t
h
ey
ca
n
in
ter
ac
t
s
o
cially
an
d
ar
e
g
iv
e
n
clar
ity
as
to
a
s
p
ec
if
ic
g
o
a
l
.
T
h
is
is
wh
er
e
th
e
co
n
ce
p
t
o
f
lear
n
in
g
with
p
lay
co
m
es in
to
ac
tio
n
.
2
.
3
.
G
a
m
e
ba
s
ed
lea
rning
Pro
m
o
tin
g
n
u
m
er
ical
f
l
u
en
c
y
in
m
en
tal
c
o
m
p
u
tatio
n
v
i
a
ac
tiv
e
p
ar
ticip
atio
n
is
o
f
p
ar
am
o
u
n
t
s
ig
n
if
ican
ce
f
o
r
e
n
h
an
cin
g
m
ath
em
atica
l
lear
n
in
g
am
o
n
g
s
t
s
tu
d
en
ts
.
Le
ar
n
in
g
th
r
o
u
g
h
ex
p
e
r
ien
ce
an
d
in
ter
ac
tio
n
lay
s
th
e
f
o
u
n
d
atio
n
o
f
th
e
lear
n
in
g
th
r
o
u
g
h
g
a
m
es
th
eo
r
y
.
E
x
p
e
r
ien
tial
lear
n
in
g
th
r
o
u
g
h
g
a
m
es
p
r
o
v
id
es
an
av
e
n
u
e
f
o
r
s
tu
d
en
ts
to
p
lay
ar
o
u
n
d
in
a
s
af
e
en
v
ir
o
n
m
e
n
t
an
d
g
ain
k
n
o
wled
g
e
b
y
p
r
ac
ticin
g
a
n
d
in
ter
ac
tin
g
s
o
cially
with
th
eir
p
lay
m
ates
an
d
th
e
en
v
ir
o
n
m
e
n
t.
Hav
in
g
u
n
d
e
r
s
to
o
d
th
is
,
ed
u
ca
to
r
s
en
d
o
r
s
e
th
e
im
p
o
r
tan
ce
o
f
ac
tiv
e
s
tu
d
en
t
in
v
o
lv
em
e
n
t
in
m
ath
em
atica
l
lear
n
in
g
r
ath
e
r
th
an
ju
s
t
f
o
llo
win
g
th
e
teac
h
er
’
s
d
ir
ec
tio
n
[
2
5
]
,
[
26]
.
C
o
n
s
tr
u
ct
iv
is
ts
s
u
p
p
o
r
t
th
is
n
o
tio
n
wh
e
r
e
th
e
p
ar
ad
i
g
m
f
o
r
lear
n
in
g
i
s
o
n
e
th
at
in
v
o
lv
es
ac
tiv
e
co
n
s
tr
u
ctio
n
[
2
6
]
,
w
h
e
r
e
k
n
o
wled
g
e
is
co
n
s
tr
u
cted
b
ased
o
n
p
r
io
r
ac
tiv
e
lear
n
in
g
.
Kn
o
wled
g
e
ca
n
n
ev
er
j
u
s
t
s
tay
in
a
h
o
m
eo
s
tasi
s
.
R
ea
lizin
g
th
is
,
it
is
b
e
s
t
f
o
r
c
h
ild
r
en
to
b
e
t
h
e
au
t
h
o
r
s
o
f
th
eir
o
wn
k
n
o
wled
g
e.
T
o
d
o
s
o
,
elem
en
ts
s
u
ch
as
s
h
ar
in
g
,
d
is
cu
s
s
in
g
,
r
ef
lectin
g
an
d
n
eg
o
tiatin
g
ar
e
o
f
u
tm
o
s
t
im
p
o
r
tan
ce
.
T
h
u
s
,
n
ew
ed
u
ca
tio
n
al
m
eth
o
d
s
n
ee
d
to
b
e
ex
p
lo
ited
f
o
r
th
ese
p
ed
ag
o
g
ical
ad
v
an
tag
es.
T
h
is
is
wh
er
e
th
e
co
n
ce
p
t o
f
lear
n
in
g
with
p
lay
c
o
m
es in
to
ac
tio
n
.
T
h
er
e
h
av
e
b
ee
n
n
u
m
er
o
u
s
s
ch
o
o
ls
o
f
th
o
u
g
h
t
th
at
v
iew
ed
u
ca
tio
n
as
an
o
r
g
an
ic
p
r
o
ce
s
s
th
at
ca
n
n
o
t
b
e
f
o
r
ce
d
th
r
o
u
g
h
d
r
illi
n
g
.
O
n
e
o
f
s
u
ch
v
iews
co
m
e
f
r
o
m
th
e
f
ield
o
f
Neu
r
o
lin
g
u
is
tics
t
h
at
em
p
h
asized
th
e
f
ac
t
th
at
ch
ild
r
e
n
n
ee
d
to
b
e
all
o
wed
to
p
lay
as
it
is
n
o
t
a
p
r
o
ce
s
s
o
p
p
o
s
ite
to
ed
u
ca
tio
n
,
b
u
t
a
y
o
u
n
g
er
lear
n
in
g
p
r
o
ce
s
s
[
2
7
]
.
T
h
is
c
o
n
test
s
th
e
co
m
m
o
n
n
o
tio
n
t
h
at
p
lay
in
g
is
d
etr
im
en
tal
to
ed
u
ca
tio
n
al
g
r
o
wth
.
T
h
is
h
as
p
r
o
p
elled
ed
u
ca
tio
n
a
l
r
esear
ch
es
to
ex
p
lo
r
e
an
d
as
s
im
ilate
g
am
es
in
t
o
t
h
e
lear
n
i
n
g
p
r
o
ce
s
s
.
T
h
er
e
is
a
co
m
m
o
n
v
iew
th
at
g
am
es a
r
e
d
ev
elo
p
e
d
m
ain
ly
f
o
r
p
r
o
m
o
tin
g
th
e
lear
n
er
s
’
e
f
f
ec
tiv
e
u
s
a
g
e
o
r
ap
p
licatio
n
in
ed
u
ca
tio
n
th
r
o
u
g
h
d
if
f
er
en
t
l
ev
els
o
f
e
n
g
ag
e
m
en
t
[
2
8
]
.
G
iv
en
th
at
th
e
m
e
r
e
m
e
n
tio
n
o
f
th
e
wo
r
d
‘
g
am
e’
p
o
s
its
th
e
n
o
tio
n
o
f
f
u
n
,
wh
at
b
etter
way
ca
n
th
er
e
b
e
to
i
n
v
o
k
e
lear
n
in
g
am
o
n
g
s
t
ch
ild
r
en
?
A
p
leth
o
r
a
o
f
ed
u
ca
to
r
s
an
d
r
esear
c
h
er
s
h
av
e
b
eg
u
n
to
ac
k
n
o
wled
g
e
th
e
im
p
o
r
tan
ce
o
f
Gam
e
-
B
ased
L
ea
r
n
in
g
.
I
n
ess
en
ce
,
g
am
e
-
b
ased
lear
n
in
g
u
s
es
ce
r
tain
g
am
i
n
g
p
r
in
cip
les
i
n
a
r
ea
l
-
life
co
n
te
x
t
o
f
lear
n
in
g
to
in
cr
ea
s
e
its
ap
p
ea
l
to
s
tu
d
en
ts
[
2
9
]
.
So
m
e
o
f
th
e
ad
v
an
tag
es
o
f
g
a
m
e
-
b
ased
lear
n
in
g
in
clu
d
es
its
ab
ilit
y
to
in
clu
d
e
b
o
th
in
d
iv
id
u
alis
tic
an
d
s
o
cial
ef
f
icac
y
to
th
e
p
lay
er
s
;
co
n
tain
i
n
g
m
u
ltip
le
elem
en
ts
a
n
d
s
tr
u
ctu
r
es
th
at
ca
n
b
e
em
b
ed
d
e
d
in
lear
n
in
g
;
m
o
tiv
atin
g
s
tu
d
en
ts
th
r
o
u
g
h
th
e
s
en
s
e
o
f
b
elo
n
g
in
g
to
th
e
lea
r
n
in
g
p
r
o
ce
s
s
;
an
d
r
ed
u
cin
g
m
en
tal
s
tr
ain
s
d
u
r
i
n
g
th
e
lea
r
n
in
g
p
r
o
ce
s
s
[
3
0
]
,
[
31]
.
T
h
e
c
o
n
ten
tio
n
is
th
at
b
y
u
s
in
g
g
am
es
as
a
m
ed
iu
m
,
th
e
p
ed
a
g
o
g
ical
is
s
u
es
r
aised
ea
r
lier
co
u
ld
b
e
r
eso
lv
ed
in
a
f
u
n
an
d
in
ter
esti
n
g
m
an
n
er
.
T
h
e
r
e
is
a
v
al
id
h
y
p
o
th
esis
th
at
in
s
tr
u
ctio
n
al
g
am
es
in
cr
ea
s
e
s
tu
d
en
ts
’
lear
n
in
g
p
e
r
f
o
r
m
an
ce
s
in
ce
th
e
lev
el
o
f
m
o
tiv
atio
n
is
co
n
s
id
er
e
d
o
n
e
o
f
th
e
p
er
f
o
r
m
a
n
ce
f
ac
to
r
s
[
2
9
]
,
[
30
]
,
[
3
2
]
.
W
h
ile
v
id
eo
g
am
es
m
a
y
b
e
a
d
d
ictiv
e
an
d
d
is
r
u
p
ti
v
e
[
3
3
]
,
[
34]
,
th
er
e
is
a
n
o
b
le
id
ea
o
f
u
s
in
g
ca
r
d
g
am
es
as
a
m
eth
o
d
o
f
lear
n
in
g
.
Stu
d
ies
s
h
o
wed
th
at
in
s
tr
u
c
tio
n
al
g
am
es
s
u
ch
as
ca
r
d
g
a
m
es
s
u
p
p
lem
en
t
th
e
lear
n
in
g
p
r
o
ce
s
s
,
an
d
s
tu
d
en
ts
wh
o
en
g
ag
e
in
s
u
ch
g
am
es
attain
b
etter
m
ath
g
r
ad
es
an
d
d
ev
elo
p
a
m
o
r
e
p
o
s
itiv
e
attitu
d
e
t
o
war
d
s
m
at
h
em
atic
s
[
3
5
]
,
[
3
6
]
.
Fu
r
th
er
m
o
r
e,
ca
r
d
g
am
es
k
ill
two
b
ir
d
s
with
o
n
e
s
to
n
e:
as
o
n
o
n
e
h
a
n
d
,
it
s
tr
en
g
th
en
s
f
a
m
ily
an
d
f
r
ien
d
s
h
ip
b
o
n
d
s
s
in
ce
ev
er
y
o
n
e
co
m
es
to
g
eth
er
to
p
lay
th
e
g
am
e;
an
d
in
th
e
p
r
o
ce
s
s
,
c
h
ild
r
en
r
ea
p
th
e
b
en
e
f
its
o
f
ac
q
u
ir
i
n
g
m
ath
em
atica
l
k
n
o
wled
g
e
a
m
id
s
t
th
e
f
u
n
[
3
7
]
.
C
ar
d
g
am
es h
av
e
s
ev
er
al
r
esu
ltin
g
b
en
ef
its
,
f
r
o
m
s
o
cio
lo
g
ical
to
d
ev
elo
p
m
en
tal
asp
ec
ts
[
3
7
]
b
ec
au
s
e
ch
ild
r
en
b
u
ild
m
en
tal
co
m
p
u
tatio
n
s
k
ills
d
u
r
in
g
p
lay
tim
e
in
a
d
d
itio
n
to
im
b
ib
in
g
k
ey
v
alu
es
s
u
c
h
as
s
p
o
r
ts
m
an
s
h
ip
an
d
h
o
n
esty
[
3
8
]
.
As
Sh
af
f
e,
et
a
l.
[
3
9
]
elu
cid
ated
,
th
ese
g
am
es
m
e
r
g
e
t
h
e
d
i
f
f
e
r
e
n
t
m
e
t
h
o
d
s
o
f
k
n
o
w
i
n
g
,
d
o
i
n
g
,
b
e
i
n
g
a
n
d
ca
r
in
g
.
T
h
er
e
is
a
s
ca
r
city
o
f
r
esear
ch
f
in
d
in
g
s
p
e
r
tain
in
g
t
o
th
e
im
p
ac
t
o
f
ed
u
ca
tio
n
al
ca
r
d
g
am
e
s
to
b
o
o
s
t
s
tu
d
en
ts
’
m
ath
lear
n
in
g
,
esp
ec
ially
in
th
e
co
n
tex
t
o
f
n
u
m
er
a
cy
s
k
ills
d
ev
elo
p
m
en
t.
I
n
th
is
s
tu
d
y
,
th
e
r
esear
ch
team
f
ir
s
tly
o
u
tlin
ed
t
h
e
p
h
ases
in
v
o
lv
ed
in
th
e
d
ev
elo
p
m
en
t
o
f
th
e
Ma
th
Z
ap
ca
r
d
g
am
e
as
a
lear
n
i
n
g
to
o
l f
o
r
en
h
an
cin
g
n
u
m
er
ac
y
s
k
ills
v
ia
m
en
tal
co
m
p
u
tatio
n
in
th
e
ar
ea
s
o
f
wh
o
le
n
u
m
b
e
r
s
,
f
r
ac
tio
n
s
,
d
ec
im
als
an
d
p
er
ce
n
tag
es
f
o
r
lo
wer
s
ec
o
n
d
ar
y
s
ch
o
o
l
s
tu
d
en
ts
(
ag
es
1
2
-
1
3
)
.
Seco
n
d
ly
,
it
ex
am
i
n
ed
th
e
im
p
ac
t
o
f
th
e
ca
r
d
g
am
e
as
a
p
ed
ag
o
g
ical
to
o
l
f
o
r
n
u
m
er
ac
y
s
k
ills
d
ev
elo
p
m
e
n
t.
T
h
ir
d
ly
,
it
ev
alu
ated
s
tu
d
en
t
s
’
attitu
d
e
to
war
d
s
th
e
Ma
th
Z
ap
ca
r
d
g
am
e
as a
p
ed
ag
o
g
ical
to
o
l f
o
r
n
u
m
er
ac
y
d
ev
elo
p
m
en
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
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t
J
E
v
al
&
R
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d
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c
,
Vo
l
.
10
,
No
.
2
,
J
u
n
e
2
0
2
1
:
6
9
3
-
7
0
5
696
3.
RE
S
E
ARCH
M
E
T
H
O
D
T
h
is
s
ec
tio
n
d
etails
th
e
m
et
h
o
d
o
lo
g
y
em
p
lo
y
ed
f
o
r
th
e
s
tu
d
y
in
te
r
m
s
o
f
th
e
d
esig
n
,
s
am
p
les
in
v
o
lv
ed
,
in
s
tr
u
m
en
tatio
n
an
d
an
aly
s
is
p
r
o
ce
d
u
r
es.
3
.
1
.
Resea
rc
h desi
g
n
T
h
is
two
p
h
ase
s
tu
d
y
e
m
p
lo
y
ed
two
d
if
f
er
e
n
t
r
esear
ch
d
esi
g
n
s
n
am
ely
R
esear
ch
an
d
De
v
elo
p
m
en
t
m
o
d
el
(
R
an
d
D
m
o
d
el)
an
d
an
ex
p
er
im
e
n
tal
d
esig
n
.
I
n
t
h
e
f
ir
s
t
p
h
ase,
t
h
e
r
esear
ch
er
s
u
tili
ze
d
th
e
r
esear
ch
an
d
d
e
v
elo
p
m
e
n
t
m
o
d
el
o
f
Ga
ll
,
et
a
l.
[
4
0
]
f
o
r
th
e
d
e
v
elo
p
m
en
t
o
f
th
e
Ma
th
Z
ap
ca
r
d
g
am
e
.
T
h
is
m
o
d
el
was
u
s
ed
with
a
s
y
s
tem
atic
p
r
o
ce
s
s
in
p
lace
,
wh
ich
in
v
o
lv
ed
f
iel
d
test
in
g
an
d
ev
alu
atio
n
u
n
til
th
e
p
r
o
d
u
ct
m
e
t
its
s
p
ec
if
ic
p
r
ed
eter
m
in
ed
cr
iter
i
a.
T
h
is
Ma
th
Z
ap
C
ar
d
Gam
e
was
d
ev
elo
p
ed
,
v
alid
ated
an
d
ev
alu
ated
b
ased
o
n
th
e
f
iv
e
-
p
h
ase
d
ev
elo
p
m
en
t p
r
o
ce
s
s
(
Fig
u
r
e
1
)
.
Fig
u
r
e
1
.
Dev
el
o
p
m
en
t
f
r
am
e
wo
r
k
Ph
ase
1
-
3
m
ar
k
ed
th
e
d
ev
el
o
p
m
en
t
s
tag
e
o
f
th
e
Ma
th
Z
ap
ca
r
d
g
am
e,
wh
ile
p
h
ase
4
-
5
co
n
ce
r
n
ed
th
e
ass
es
s
m
en
t o
f
th
e
ef
f
ec
tiv
e
n
ess
an
d
ev
alu
atio
n
o
f
t
h
e
ca
r
d
g
a
m
e
d
ev
elo
p
ed
.
T
h
e
d
escr
ip
tio
n
o
f
th
e
p
h
ases
is
:
Ph
ase
1
.
T
h
e
id
en
tific
atio
n
o
f
th
e
lea
r
n
in
g
co
m
p
eten
cies
co
n
ten
t
wh
ich
in
clu
d
e
Fra
ctio
n
s
,
Per
ce
n
tag
es,
Dec
im
a
ls
,
W
h
o
le
Nu
m
b
er
s
&
R
o
m
an
Nu
m
er
als.
Ph
ase
2
.
Desig
n
,
d
ev
elo
p
m
en
t
an
d
p
r
e
-
im
p
lem
en
tatio
n
o
f
th
e
Ma
th
Z
ap
ca
r
d
g
am
e
was
in
clu
d
e
d
in
th
i
s
p
h
ase.
I
t
also
in
clu
d
e
d
s
elec
tio
n
o
f
co
n
ten
t
f
o
r
ea
c
h
to
p
ic,
co
n
ten
t
lev
el,
ca
r
d
d
esig
n
,
co
lo
u
r
co
n
tr
ast &
s
ize,
an
d
r
u
l
es o
f
th
e
g
am
e.
Ph
ase
3
.
T
h
r
ee
s
ch
o
o
l
m
ath
s
teac
h
er
s
a
n
d
two
g
am
in
g
e
x
p
er
ts
wer
e
s
elec
ted
to
co
n
d
u
ct
an
e
v
alu
ati
o
n
o
f
th
e
ca
r
d
g
am
e
b
ased
o
n
th
e
lear
n
i
n
g
co
m
p
eten
cies id
en
tifie
d
.
Ph
ase
4
.
T
h
e
r
esear
ch
team
u
tili
ze
d
th
e
p
r
etest
–
p
o
s
ttes
t
o
n
e
g
r
o
u
p
ex
p
er
im
en
tal
d
esig
n
a
m
o
n
g
s
t
1
6
s
tu
d
en
ts
f
r
o
m
g
r
ad
e
6
to
test
th
e
ef
f
ec
ti
v
en
ess
o
f
th
e
ca
r
d
g
am
e
.
Ph
ase
5
.
Fiv
e
m
ain
cr
iter
ias
wer
e
u
s
e
d
f
o
r
th
e
ev
alu
atio
n
o
f
th
e
c
ar
d
g
am
e:
1
)
Go
als
an
d
o
b
je
ctiv
es;
2
)
Desig
n
; 3
)
C
o
m
p
o
n
en
ts
an
d
o
r
g
an
izatio
n
; 4
)
Play
ab
ilit
y
an
d
p
lay
f
u
ln
ess
; a
n
d
5
)
Usef
u
ln
ess
.
3
.
2
.
Descript
io
n o
f
ca
rd
g
a
m
e
a
nd
it
s
rules
T
h
e
in
v
en
tio
n
,
ca
lled
,
“M
ath
Z
ap
”
is
a
ca
r
d
g
am
e
th
at
e
n
h
a
n
ce
s
th
e
d
ev
elo
p
m
en
t
o
f
n
u
m
er
ac
y
s
k
ills
in
en
h
an
ci
n
g
m
e
n
tal
co
m
p
u
tatio
n
.
Nu
m
b
er
o
f
Play
er
s
:
2
to
6
p
lay
er
s
C
o
n
ten
t
:
1
)
N
u
m
er
al’
s
r
ec
o
g
n
itio
n
;
2
)
Fu
n
d
am
e
n
tals
o
f
f
o
u
r
m
e
n
tal
o
p
er
at
o
r
s
k
ills
;
3
)
Op
er
ato
r
s
an
d
r
elatio
n
s
h
i
p
b
etwe
en
f
r
a
ctio
n
s
,
d
ec
im
als
an
d
p
er
ce
n
t
ag
es
;
4
)
R
o
m
an
n
u
m
e
r
als
;
5
)
W
h
o
le
n
u
m
b
er
s
;
an
d
6
)
R
elatio
n
s
h
ip
b
etwe
en
N
u
m
er
als an
d
R
o
m
an
Nu
m
er
als.
Sk
ills
d
ev
elo
p
ed
:
T
h
e
ab
ilit
y
to
m
atch
,
h
ig
h
er
aler
tn
ess
,
lo
n
g
er
atten
tio
n
,
in
cr
ea
s
ed
m
en
tal
an
d
v
is
u
al
s
p
ee
d
,
an
d
t
h
e
ab
ilit
y
to
p
r
o
v
id
e
v
er
b
al
r
esp
o
n
s
es.
Aim
o
f
th
e
g
a
m
e
:
T
h
e
m
ain
aim
o
f
th
is
g
am
e
i
s
to
g
et
all
th
e
ca
r
d
s
in
th
e
p
ac
k
,
an
d
if
it d
o
esn
’
t h
ap
p
en
,
th
e
g
am
e
g
o
es o
n
.
Star
t o
f
p
lay
:
All
p
lay
er
s
s
h
o
u
ld
h
av
e
with
th
em
an
e
q
u
al
n
u
m
b
er
o
f
ca
r
d
s
,
an
d
th
e
d
ea
lin
g
p
lay
er
h
as
to
en
s
u
r
e
th
is
.
T
h
e
ca
r
d
s
ar
e
to
b
e
p
lace
d
f
ac
in
g
d
o
wn
an
d
n
o
o
n
e
is
allo
wed
to
h
av
e
a
lo
o
k
at
th
eir
d
ec
k
s
.
T
o
g
et
th
e
b
all
r
o
llin
g
,
th
e
p
lay
er
s
ea
ted
o
n
th
e
r
ig
h
t
-
s
id
e
o
f
th
e
d
ea
ler
b
eg
in
s
th
e
g
am
e
b
y
p
r
o
m
p
tly
p
u
ttin
g
a
ca
r
d
in
th
e
m
id
d
le
o
f
th
e
tab
le,
f
ac
in
g
u
p
.
T
h
e
d
r
aw
:
T
h
e
cy
cle
o
f
co
n
tin
u
ally
p
la
cin
g
ca
r
d
s
af
ter
ca
r
d
s
o
n
th
e
t
o
p
to
f
o
r
m
a
p
ile
in
th
e
m
id
d
l
e
co
n
tin
u
es
u
n
til
a
m
atch
o
r
p
a
ir
is
f
o
u
n
d
,
f
o
r
in
s
tan
ce
:
5
an
d
5
;
2
+2
an
d
4
;
½
+½
an
d
1
(
Fig
u
r
e
2
)
.
Me
ld
in
g
:
T
h
e
f
ir
s
t p
lay
er
t
o
p
lace
h
is
h
an
d
s
-
o
n
to
p
o
f
th
e
p
ile
a
n
d
s
h
o
u
t “
Z
ap
”
g
ets th
em
all.
Fo
r
f
eit
: T
h
e
m
ain
aim
o
f
th
is
g
am
e
is
to
g
et
all
th
e
ca
r
d
s
in
th
e
p
ac
k
,
an
d
if
it d
o
esn
’
t h
ap
p
en
,
th
e
g
am
e
g
o
es
o
n
.
W
h
en
th
e
p
lay
er
s
h
o
u
ts
“Z
a
p
”
at
t
h
e
wr
o
n
g
tim
e,
h
is
/h
er
t
u
r
n
g
ets
f
o
r
f
eited
an
d
a
p
e
n
alty
is
in
cu
r
r
e
d
.
Gam
e
en
d
s
:
T
h
e
f
ir
s
t p
lay
er
t
o
g
et
all
th
e
ca
r
d
s
is
d
ec
la
r
ed
th
e
win
n
er
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
C
a
r
d
g
a
me
a
s
a
p
e
d
a
g
o
g
ica
l t
o
o
l fo
r
n
u
mera
cy
s
kills
d
ev
elo
p
men
t
(
P
a
r
mjit S
in
g
h
)
697
A
d
esig
n
-
b
ased
r
esear
ch
co
n
s
id
er
atio
n
as
s
u
g
g
ested
b
y
B
ar
ab
an
d
Sq
u
ir
e
[
4
1
]
was
also
u
tili
s
ed
f
o
r
th
is
r
esear
ch
.
T
h
is
im
p
r
o
v
es
th
e
f
o
cu
s
o
f
th
e
ex
p
er
im
en
tal
d
esig
n
p
r
o
ce
s
s
in
its
to
tality
as
Sch
o
en
f
eld
[
4
2
]
elu
cid
ated
th
at
‘
th
e
p
r
o
d
u
cts
o
f
well
co
n
d
u
cted
d
esig
n
ex
p
er
im
en
ts
ar
e
im
p
r
o
v
ed
in
ter
v
en
t
io
n
s
an
d
im
p
r
o
v
ed
u
n
d
er
s
tan
d
i
n
g
s
o
f
th
e
p
r
o
ce
s
s
es
th
at
r
esu
lt
in
th
eir
p
r
o
d
u
cti
v
en
ess
’
.
T
h
e
d
etailed
co
n
s
id
er
atio
n
s
o
f
th
is
s
tu
d
y
ar
e
d
ep
icted
in
T
ab
le
1
.
Fig
u
r
e
2.
Sam
p
le
p
ictu
r
es o
f
Ma
th
Z
ap
T
ab
le
1
.
Desig
n
-
b
ased
co
n
s
id
e
r
atio
n
s
in
Ma
th
Z
ap
r
esear
ch
D
e
si
g
n
-
b
a
se
d
c
o
n
s
i
d
e
r
a
t
i
o
n
s
D
e
t
a
i
l
s
Lo
c
a
t
i
o
n
o
f
r
e
s
e
a
r
c
h
C
o
n
d
u
c
t
e
d
i
n
a
c
l
a
ssr
o
o
m
e
n
v
i
r
o
n
m
e
n
t
w
h
e
r
e
t
h
e
a
c
t
u
a
l
t
e
a
c
h
i
n
g
a
n
d
l
e
a
r
n
i
n
g
p
r
o
c
e
ss
t
o
o
k
p
l
a
c
e
i
n
t
w
o
d
i
f
f
e
r
e
n
t
sc
h
o
o
l
s
C
o
m
p
l
e
x
i
t
y
o
f
v
a
r
i
a
b
l
e
s
V
a
r
i
a
b
l
e
s i
n
c
l
u
d
e
d
M
a
t
h
C
o
n
t
e
n
t
C
o
mp
u
t
a
t
i
o
n
(
F
r
a
c
t
i
o
n
s,
P
e
r
c
e
n
t
a
g
e
s,
D
e
c
i
ma
l
s,
W
h
o
l
e
N
u
mb
e
r
s &
R
o
ma
n
N
u
mera
l
s)
,
A
t
t
i
t
u
d
e
t
o
w
a
r
d
s
M
a
t
h
Za
p
(
l
e
a
r
n
i
n
g
,
e
n
j
o
y
men
t
a
n
d
i
n
t
e
r
a
c
t
i
o
n
)
F
o
c
u
s
o
f
r
e
s
e
a
r
c
h
Th
e
e
f
f
e
c
t
o
f
p
l
a
y
i
n
g
t
h
e
c
a
r
d
g
a
m
e
s
o
n
t
h
e
i
r
M
a
t
h
C
o
n
t
e
n
t
a
n
d
A
t
t
i
t
u
d
e
t
o
w
a
r
d
s
i
t
.
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n
f
o
l
d
i
n
g
o
f
p
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c
e
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r
e
s
P
u
p
i
l
s
w
e
r
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g
i
v
e
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p
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t
e
st
a
n
d
t
h
e
n
e
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p
l
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d
t
h
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u
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o
f
t
h
e
c
a
r
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a
m
e
p
r
o
c
e
d
u
r
e
s.
U
p
o
n
p
l
a
y
i
n
g
t
h
e
g
a
m
e
s
1
2
t
o
1
5
t
i
m
e
s,
p
u
p
i
l
s w
e
r
e
g
i
v
e
n
a
p
o
s
t
-
t
e
st
.
A
mo
u
n
t
o
f
so
c
i
a
l
i
n
t
e
r
a
c
t
i
o
n
Lo
t
s
o
f
i
n
t
e
r
a
c
t
i
o
n
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m
o
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s
t
p
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p
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l
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h
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l
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i
n
g
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a
c
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o
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e
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r
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o
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e
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o
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l
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t
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w
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h
e
c
a
r
d
s
.
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h
a
r
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h
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n
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Tw
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e
c
t
i
n
v
o
l
v
e
d
n
a
m
e
l
y
a
s
s
e
ssi
n
g
p
u
p
i
l
’
s
me
n
t
a
l
c
o
m
p
u
t
a
t
i
o
n
t
e
s
t
sc
o
r
e
s
b
e
t
w
e
e
n
P
r
e
a
n
d
P
o
st
a
n
d
p
u
p
i
l
s’
a
t
t
i
t
u
d
e
t
o
w
a
r
d
s
p
l
a
y
i
n
g
t
h
e
c
a
r
d
g
a
me
(
p
o
st
t
e
s
t
)
R
o
l
e
o
f
p
a
r
t
i
c
i
p
a
n
t
s
P
u
p
i
l
s
w
e
r
e
g
i
v
e
n
t
h
e
r
o
l
e
a
s
l
e
a
r
n
e
r
s
a
s t
h
e
y
p
l
a
y
ed
t
h
e
g
a
me
w
h
i
l
e
t
h
e
t
e
a
c
h
e
r
s
f
a
c
i
l
i
t
a
t
e
d
.
W
h
e
n
t
h
e
r
e
w
e
r
e
d
i
s
p
u
t
e
s
,
t
h
e
t
e
a
c
h
e
r
s
b
e
c
a
me
t
h
e
me
d
i
a
t
o
r
s
.
I
n
th
e
s
ec
o
n
d
p
h
ase,
a
o
n
e
-
g
r
o
u
p
p
r
etest
-
p
o
s
ttes
t
q
u
asi
ex
p
er
im
en
tal
d
esig
n
(
Fig
u
r
e
3
)
was
em
p
lo
y
ed
in
w
h
ich
th
e
Me
n
ta
l
C
o
m
p
u
tatio
n
T
est
was
ad
m
i
n
is
ter
ed
b
ef
o
r
e
a
n
d
a
f
ter
th
e
tr
ea
tm
en
t
to
e
x
am
in
e
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
ca
r
d
g
am
es
in
en
h
an
cin
g
s
tu
d
e
n
ts
’
n
u
m
er
ac
y
s
k
ills
.
T
h
e
r
esear
ch
e
r
s
ac
k
n
o
wled
g
e
o
f
th
e
lim
itatio
n
o
f
th
is
d
esig
n
o
f
n
o
co
n
tr
o
l
g
r
o
u
p
th
at
ar
e
p
r
o
n
e
to
t
h
r
ea
ts
o
f
in
ter
n
al
v
alid
it
y
.
T
h
is
d
esig
n
was
ch
o
s
en
b
ec
au
s
e
o
f
s
o
m
e
eth
ical
is
s
u
e
s
r
elate
d
to
s
am
p
le
s
el
ec
tio
n
.
T
h
e
s
elec
ted
ad
m
in
is
tr
ato
r
o
f
th
e
s
ch
o
o
l
in
s
is
ted
th
at
all
g
r
o
u
p
s
b
e
all
o
wed
to
p
lay
th
e
ca
r
d
g
a
m
e
an
d
in
s
is
ted
t
h
at
n
o
s
tu
d
en
t
b
e
d
ep
r
iv
e
d
o
f
th
is
ac
tiv
ity
.
T
h
u
s
,
th
is
in
h
ib
ited
th
e
s
elec
tio
n
o
f
a
co
n
tr
o
l
g
r
o
u
p
.
Du
e
to
th
e
cir
c
u
m
s
tan
c
es,
th
e
r
esear
ch
er
s
ac
k
n
o
wled
g
e
d
co
n
f
o
u
n
d
in
g
f
a
cto
r
p
o
s
s
ib
ilit
ies wh
ich
m
ig
h
t
in
h
ib
it th
e
ab
ilit
y
f
o
r
ca
u
s
al
in
f
er
en
ce
.
Fig
u
r
e
3
.
T
h
e
o
n
e
-
g
r
o
u
p
q
u
asi
ex
p
er
im
en
tal
d
esig
n
3
.
3
.
Sa
m
ples
o
f
s
t
ud
y
T
h
ir
ty
-
f
o
u
r
Seco
n
d
a
r
y
O
n
e
s
tu
d
en
ts
,
b
etwe
en
ag
es
1
2
to
1
3
,
as
an
in
tact
class
was
r
an
d
o
m
l
y
s
elec
ted
u
s
in
g
a
b
lo
ck
s
am
p
lin
g
f
r
o
m
f
iv
e
class
es
f
r
o
m
a
p
u
b
lic
s
ch
o
o
l
in
a
d
is
tr
ict
in
S
elan
g
o
r
,
M
alay
s
ia.
T
h
ese
s
tu
d
en
ts
h
av
e
f
o
r
m
ally
lear
n
t
th
e
to
p
ics
(
Fra
ctio
n
s
,
Per
ce
n
tag
es,
Dec
im
als
&
W
h
o
le
Nu
m
b
er
s
)
b
ased
o
n
th
eir
s
ch
o
o
l
cu
r
r
ic
u
lu
m
s
in
ce
g
r
ad
e
5
.
Fo
r
th
e
q
u
alita
tiv
e
d
ata,
a
s
am
p
le
o
f
f
iv
e
t
ea
ch
er
s
wh
o
wer
e
in
v
o
lv
ed
in
f
ac
ilit
atin
g
t
h
e
s
tu
d
en
ts
p
l
ay
in
g
o
f
th
e
Ma
th
Z
ap
ca
r
d
g
am
e
wer
e
in
ter
v
iew
ed
in
s
ee
k
in
g
th
eir
v
iews r
eg
ar
d
in
g
th
e
g
am
e
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
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t
J
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v
al
&
R
es
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d
u
c
,
Vo
l
.
10
,
No
.
2
,
J
u
n
e
2
0
2
1
:
6
9
3
-
7
0
5
698
3
.
4
.
I
ns
t
rum
ent
a
t
io
n
T
wo
in
s
tr
u
m
en
ts
wer
e
u
s
ed
in
ass
es
s
in
g
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
ca
r
d
g
a
m
e
in
d
e
v
elo
p
in
g
n
u
m
er
ac
y
s
k
ills
an
d
a
p
o
s
itiv
e
atti
tu
d
e
to
war
d
s
p
lay
in
g
th
e
ca
r
d
g
am
e
.
T
h
e
f
ir
s
t
in
s
tr
u
m
en
t,
Me
n
tal
C
o
m
p
u
tatio
n
T
est,
f
o
cu
s
ed
o
n
r
ein
f
o
r
cin
g
b
asic
m
ath
s
k
ills
in
ter
m
s
o
f
id
en
tify
in
g
n
u
m
b
er
s
,
co
m
p
ar
in
g
n
u
m
er
ical
v
alu
es
wh
ich
r
eq
u
ir
e
ac
cu
r
ate
o
b
s
er
v
atio
n
,
an
d
q
u
ick
r
ea
ctio
n
s
.
T
h
is
test
was
ad
ap
ted
f
r
o
m
Mc
I
n
to
s
h
,
et
a
l.
[
4
3
]
wh
e
r
e
it
co
m
p
r
is
ed
4
0
item
s
o
f
f
o
u
r
s
tr
an
d
s
in
th
e
f
r
am
ewo
r
k
:
Dec
im
als,
Fra
ctio
n
s
,
Per
ce
n
tag
es
an
d
R
o
m
an
Nu
m
er
als.
E
ac
h
item
was
s
co
r
ed
b
ased
o
n
a
co
r
r
ec
t
an
d
in
co
r
r
ec
t
r
esp
o
n
s
e,
ca
p
itu
latin
g
a
m
ax
im
u
m
s
co
r
e
o
f
4
0
.
T
h
e
s
ec
o
n
d
in
s
tr
u
m
en
t,
a
d
ap
ted
f
r
o
m
Gu
tier
r
ez
[
3
5
]
was
u
tili
ze
d
to
ev
alu
ate
t
h
e
s
tu
d
en
ts
’
v
iew
o
f
th
e
d
ev
elo
p
e
d
Ma
th
Z
ap
as
a
lea
r
n
in
g
to
o
l.
T
h
is
q
u
esti
o
n
n
air
e
wh
ich
c
o
m
p
r
is
ed
2
5
item
s
u
tili
ze
d
a
f
iv
e
-
p
o
in
t
r
atin
g
s
ca
le
b
ased
o
n
f
iv
e
cr
iter
ia,
n
am
ely
:
1
)
Go
als
an
d
o
b
jectiv
es;
2
)
Desig
n
;
3
)
C
o
m
p
o
n
e
n
ts
an
d
o
r
g
an
izatio
n
;
4
)
Play
ab
ilit
y
an
d
p
lay
f
u
ln
ess
;
an
d
5
)
Usef
u
ln
ess
.
Ho
wev
er
,
f
o
r
th
is
p
ap
er
,
d
u
e
to
s
p
ac
e
co
n
s
tr
ain
t,
o
n
ly
t
h
r
ee
c
r
iter
ia
ar
e
d
is
cu
s
s
ed
,
n
am
ely
g
o
als
an
d
o
b
jectiv
es
,
p
lay
ab
ilit
y
a
n
d
p
lay
f
u
ln
ess
,
a
n
d
u
s
ef
u
ln
ess
ar
e
d
is
p
lay
ed
.
3
.
5
.
P
ro
ce
du
re
Prio
r
to
th
e
e
x
p
er
im
e
n
t,
a
2
0
-
m
in
u
te
p
r
e
-
test
was
p
er
f
o
r
m
e
d
to
ev
alu
ate
t
h
e
n
u
m
er
ac
y
p
r
o
f
icien
cy
am
o
n
g
s
t
s
tu
d
en
ts
v
ia
th
e
Me
n
tal
C
o
m
p
u
tatio
n
T
est.
Fo
llo
win
g
th
e
p
r
e
-
test
,
th
e
3
4
s
am
p
les
wer
e
r
an
d
o
m
ly
d
iv
id
ed
i
n
to
g
r
o
u
p
s
o
f
4
o
r
5
wh
er
e
th
ey
p
lay
ed
th
e
g
am
e
f
o
r
ap
p
r
o
x
im
atel
y
1
2
-
1
5
tim
es
ea
ch
in
th
e
d
u
r
atio
n
o
f
4
wee
k
s
.
So
m
e
s
tu
d
en
ts
p
l
ay
ed
it
m
o
r
e
o
f
ten
th
an
o
th
er
s
d
u
e
to
atten
d
an
ce
c
o
n
s
tr
ain
ts
.
Af
ter
th
e
4
wee
k
s
,
a
p
o
s
t
-
test
(
co
m
p
r
is
in
g
o
f
q
u
e
s
tio
n
s
th
at
wer
e
s
im
ilar
to
th
e
p
r
e
-
test
)
as
well
as
an
attitu
d
e
q
u
esti
o
n
n
air
e
wer
e
ad
m
in
is
ter
ed
with
a
tim
e
d
u
r
a
tio
n
o
f
3
0
m
in
u
tes
s
et
f
o
r
its
co
m
p
letio
n
.
As
th
e
m
e
n
tal
co
m
p
u
tatio
n
test
was
aim
ed
at
t
h
e
ass
ess
m
en
t
o
f
s
tu
d
en
ts
’
m
e
n
tal
p
r
o
wess
,
3
0
s
ec
o
n
d
s
wer
e
g
iv
e
n
f
o
r
ea
ch
item
an
d
th
ey
wer
e
g
iv
en
o
n
l
y
an
an
s
wer
s
h
ee
t
to
wr
ite
th
eir
an
s
wer
s
o
n
.
A
Po
wer
Po
in
t
Pre
s
en
tatio
n
was
u
s
ed
to
s
h
o
w
th
e
p
ar
ticu
lar
q
u
esti
o
n
o
n
s
cr
ee
n
an
d
th
e
f
o
llo
win
g
q
u
esti
o
n
was
p
o
s
ed
af
ter
a
lap
s
e
o
f
3
0
s
ec
o
n
d
s
,
th
er
eb
y
g
iv
in
g
n
o
r
o
o
m
f
o
r
th
e
s
tu
d
en
t
s
to
u
s
e
wr
itten
co
m
p
u
tatio
n
t
o
s
o
lv
e
th
e
p
r
o
b
l
em
s
.
3
.
6
.
Va
lid
it
y
a
nd
re
lia
bil
it
y
I
n
estab
lis
h
in
g
th
e
co
n
ten
t
v
al
id
ity
o
f
th
e
m
en
tal
co
m
p
u
tatio
n
test
,
th
e
s
u
g
g
esti
o
n
s
o
f
3
ex
p
er
ien
ce
d
s
ch
o
o
l te
ac
h
er
s
wer
e
tak
en
.
T
h
e
s
u
b
ject
co
n
ten
t,
p
e
r
ce
n
tag
e
o
f
item
s
in
ea
ch
ar
ea
,
an
d
th
e
co
g
n
itiv
e
p
r
o
ce
s
s
es
in
v
o
lv
ed
wer
e
in
co
r
p
o
r
ated
in
to
a
tab
le
o
f
s
p
ec
if
icatio
n
.
R
ec
o
m
m
en
d
atio
n
s
th
at
h
ad
b
ee
n
m
ad
e
f
o
r
an
im
p
r
o
v
em
e
n
t
o
f
th
e
in
s
tr
u
m
e
n
t
wer
e
co
n
s
id
er
ed
.
On
th
e
o
th
er
h
an
d
,
t
o
estab
lis
h
th
e
r
eliab
ilit
y
co
ef
f
icien
t
an
aly
s
is
,
a
test
-
r
etest
r
eliab
ili
ty
m
eth
o
d
o
lo
g
y
was
u
ti
lized
o
n
a
g
r
o
u
p
o
f
1
6
(
in
tact
class
)
s
ec
o
n
d
ar
y
o
n
e
s
tu
d
en
t (
ag
es 1
3
)
f
r
o
m
a
d
i
f
f
er
en
t sch
o
o
l.
As
s
h
o
wn
in
T
ab
le
2
,
th
e
s
co
r
es
f
o
r
b
o
t
h
test
s
(
M=
1
2
.
3
2
,
SD=5
.
2
6
)
an
d
r
e
-
test
s
(
M=
1
2
.
5
8
,
SD=5
.
1
7
)
wer
e
h
ig
h
ly
s
im
ilar
o
n
b
o
th
test
in
g
o
cc
asio
n
s
.
I
t
r
esu
lted
in
a
h
ig
h
Pear
s
o
n
Pro
d
u
ct
Mo
m
en
t
C
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r
r
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o
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9
1
7
(
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ab
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3
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g
th
e
m
en
tal
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m
p
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test
as
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l
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e
n
tal
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p
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o
f
n
u
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k
ills
.
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ab
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2
.
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al
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f
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n
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15
Similar
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4.
RE
SU
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T
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as
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4
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On
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Sam
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Fra
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Dec
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W
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T
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
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2
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3
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4
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ased
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3
.
9
5
,
SD
=
.
6
6
)
o
b
t
ain
ed
a
m
ea
n
s
co
r
e
o
f
m
o
r
e
t
h
an
4
.
0
d
ep
ictin
g
a
v
er
y
s
atis
f
ac
to
r
y
p
e
r
ce
iv
ed
v
iew
f
o
r
ea
ch
item
.
I
n
f
ac
t,
it
em
6
“
T
h
e
ca
r
d
g
a
m
e
h
el
p
s
with
m
y
r
ec
all
o
f
co
n
ce
p
ts
/ter
m
s
”
o
b
tain
ed
a
h
ig
h
m
ea
n
s
co
r
e
o
f
4
.
5
9
w
ith
a
s
tan
d
ar
d
d
ev
iatio
n
o
f
0
.
6
1
in
d
icatin
g
an
o
u
ts
tan
d
in
g
v
iew
b
y
s
tu
d
en
ts
o
n
th
eir
r
e
v
is
io
n
o
f
th
e
c
o
n
c
ep
ts
in
v
o
lv
ed
n
am
ely
d
ec
im
a
ls
,
p
er
ce
n
tag
es
an
d
f
r
ac
tio
n
s
.
T
h
e
o
v
e
r
all
m
e
an
s
co
r
e
o
f
4
.
2
2
(
SD
=
.
6
2
)
f
o
r
th
e
cr
iter
ia
o
f
g
o
als
an
d
o
b
jectiv
es
o
f
th
e
Ma
th
Z
ap
C
ar
d
Gam
e
d
ep
icts
a
v
er
y
s
atis
f
ac
to
r
y
ev
alu
atio
n
v
iew
b
y
th
e
s
tu
d
en
ts
.
T
h
e
f
o
u
r
th
cr
iter
ia
(
as
th
e
s
ec
o
n
d
a
n
d
th
ir
d
wer
e
n
o
t
d
i
s
cu
s
s
ed
)
r
elate
s
to
th
e
p
lay
a
b
ilit
y
an
d
p
lay
f
u
ln
ess
o
f
th
e
Ma
th
Z
ap
C
ar
d
Gam
e
th
at
co
m
p
r
is
ed
f
o
u
r
item
s
(
T
ab
le
7
)
.
All
th
e
item
s
in
th
is
cr
iter
io
n
d
ep
icted
a
m
ea
n
s
co
r
e
o
f
m
o
r
e
th
an
4
.
2
0
wh
ich
ca
n
b
e
i
n
ter
p
r
eted
as
v
er
y
s
atis
f
ac
to
r
y
b
y
th
e
s
tu
d
en
ts
.
T
h
e
h
ig
h
est
m
ea
n
s
co
r
e
was
o
b
tain
ed
f
o
r
item
1
7
“
T
h
e
g
am
e
p
r
o
v
id
es
o
p
p
o
r
tu
n
ity
f
o
r
h
ea
lth
y
co
m
p
etitio
n
an
d
co
o
p
er
atio
n
”
an
d
item
2
0
“
P
lay
in
g
th
e
g
am
e
was
f
u
n
”
with
s
co
r
es
o
f
4
.
5
0
(
SD
=
.
6
6
)
an
d
4
.
3
9
(
SD
=
.
9
2
)
r
esp
ec
tiv
ely
.
T
h
e
o
v
er
all
m
e
an
s
co
r
e
o
f
4
.
3
4
(
SD
=
.
6
5
)
d
ep
icts
a
v
er
y
s
atis
f
ac
to
r
y
ev
a
lu
atio
n
b
y
s
tu
d
en
ts
to
war
d
s
th
e
p
lay
a
b
il
ity
an
d
p
lay
f
u
ln
ess
o
f
th
e
Ma
t
h
Z
ap
ca
r
d
g
am
e
.
T
ab
le
8
s
h
o
ws
t
h
e
f
in
al
cr
iter
i
a
th
at
co
m
p
r
is
in
g
f
iv
e
item
s
r
elate
to
th
e
ev
alu
atio
n
o
f
s
tu
d
en
ts
o
n
t
h
e
u
s
ef
u
ln
ess
o
f
th
e
Ma
th
Z
ap
ca
r
d
g
am
e.
All
th
e
item
s
in
th
ese
cr
iter
ia
o
b
tain
ed
h
ig
h
m
e
an
s
s
co
r
es
o
f
4
.
3
2
(
item
2
3
)
a
n
d
a
b
o
v
e
.
T
h
e
h
ig
h
est
m
ea
n
s
co
r
es
ar
e
o
b
tain
ed
f
o
r
item
2
1
(
m
ea
n
=
4
.
7
6
,
SD=.
4
3
)
,
item
2
5
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es
E
d
u
c
,
Vo
l
.
10
,
No
.
2
,
J
u
n
e
2
0
2
1
:
6
9
3
-
7
0
5
700
(
m
ea
n
=
4
.
5
6
,
SD
=
.
5
5
)
an
d
item
2
2
(
m
ea
n
=
4
.
5
0
,
SD
=
.
6
6
)
i
n
d
icatin
g
an
o
u
ts
tan
d
in
g
ev
al
u
atio
n
b
y
s
tu
d
en
ts
.
T
h
e
o
v
er
all
m
ea
n
s
co
r
e
o
f
4
.
5
2
(
SD
=
.
7
5
)
ca
n
b
e
i
n
ter
p
r
et
ed
as
o
u
ts
tan
d
in
g
b
y
s
tu
d
en
ts
o
n
th
eir
ev
al
u
atio
n
to
war
d
s
th
e
u
s
ef
u
ln
ess
o
f
t
h
e
Ma
th
Z
ap
ca
r
d
g
am
e.
T
ab
le
6
.
Go
als an
d
o
b
jectiv
es
ev
alu
atio
n
o
f
th
e
Ma
th
Z
a
p
ca
r
d
g
am
e
(
N=
3
4
)
G
o
a
l
s
a
n
d
o
b
j
e
c
t
i
v
e
s
F
r
e
q
u
e
n
c
y
M
e
a
n
SD
I
n
t
e
r
p
r
e
t
a
t
i
o
n
5
4
3
2
1
1
Th
e
p
u
r
p
o
s
e
a
n
d
r
a
t
i
o
n
a
l
e
f
o
r
t
h
e
g
a
m
e
a
r
e
f
u
l
l
y
e
x
p
l
a
i
n
e
d
.
9
18
6
1
0
4
.
0
3
.
7
6
V
e
r
y
s
a
t
i
sf
a
c
t
o
r
y
2
Th
e
g
o
a
l
s
a
n
d
o
b
j
e
c
t
i
v
e
s
o
f
t
h
e
g
a
m
e
a
r
e
c
l
e
a
r
l
y
d
e
f
i
n
e
d
.
10
20
4
0
0
4
.
1
8
.
6
3
V
e
r
y
s
a
t
i
sf
a
c
t
o
r
y
3
Th
e
g
a
me
w
a
s
t
h
o
u
g
h
t
p
r
o
v
o
k
i
n
g
.
3
25
4
2
0
3
.
9
5
.
6
6
V
e
r
y
s
a
t
i
sf
a
c
t
o
r
y
4
Th
e
g
a
me
e
n
c
o
u
r
a
g
e
d
st
u
d
e
n
t
i
n
t
e
r
a
c
t
i
o
n
.
20
8
6
0
0
4
.
4
1
.
7
8
V
e
r
y
s
a
t
i
sf
a
c
t
o
r
y
5
Th
e
g
a
me
p
r
o
m
o
t
e
d
d
i
sc
u
ssi
o
n
o
f
k
e
y
t
o
p
i
c
s.
13
17
4
0
0
4
.
2
6
.
6
7
V
e
r
y
s
a
t
i
sf
a
c
t
o
r
y
6
Th
e
c
a
r
d
g
a
me
h
e
l
p
s
w
i
t
h
my
r
e
c
a
l
l
o
f
c
o
n
c
e
p
t
s/
t
e
r
ms
.
22
10
2
0
0
4
.
5
9
.
6
1
O
u
t
s
t
a
n
d
i
n
g
A
v
e
r
a
g
e
mea
n
4
.
2
2
.
6
2
V
e
r
y
s
a
t
i
sf
a
c
t
o
r
y
T
ab
le
7
.
Play
ab
ilit
y
a
n
d
p
la
y
f
u
ln
ess
ev
alu
atio
n
o
f
th
e
Ma
th
Z
ap
ca
r
d
g
am
e
(
N=
3
4
)
P
l
a
y
a
b
i
l
i
t
y
a
n
d
p
l
a
y
f
u
l
n
e
ss
F
r
e
q
u
e
n
c
y
M
e
a
n
SD
I
n
t
e
r
p
r
e
t
a
t
i
o
n
5
4
3
2
1
17
Th
e
g
a
m
e
p
r
o
v
i
d
e
s
o
p
p
o
r
t
u
n
i
t
y
f
o
r
h
e
a
l
t
h
y
c
o
m
p
e
t
i
t
i
o
n
a
n
d
c
o
o
p
e
r
a
t
i
o
n
.
20
12
2
0
0
4
.
5
0
.
6
6
O
u
t
s
t
a
n
d
i
n
g
18
Th
e
r
u
l
e
s
o
f
t
h
e
g
a
me
p
r
o
v
i
d
e
p
l
a
y
e
r
s
w
i
t
h
e
q
u
a
l
c
o
n
d
i
t
i
o
n
s
f
o
r
a
f
a
i
r
p
l
a
y
.
13
16
4
1
0
4
.
2
4
.
7
0
V
e
r
y
s
a
t
i
sf
a
c
t
o
r
y
19
Th
e
r
u
l
e
s
o
f
t
h
e
g
a
m
e
p
r
o
v
i
d
e
a
s
e
t
o
f
o
p
t
i
o
n
s
f
o
r
f
l
e
x
i
b
i
l
i
t
y
i
n
ma
k
i
n
g
d
e
c
i
s
i
o
n
s w
h
e
n
p
l
a
y
i
n
g
t
h
e
g
a
m
e
.
10
22
1
2
0
4
.
2
3
.
5
5
V
e
r
y
s
a
t
i
sf
a
c
t
o
r
y
20
P
l
a
y
i
n
g
t
h
e
g
a
me
w
a
s f
u
n
.
21
7
5
1
0
4
.
3
9
.
9
2
V
e
r
y
s
a
t
i
sf
a
c
t
o
r
y
A
v
e
r
a
g
e
mea
n
4
.
3
4
.
6
5
V
e
r
y
s
a
t
i
sf
a
c
t
o
r
y
T
ab
le
8
.
Us
ef
u
ln
ess
ev
alu
atio
n
o
f
th
e
Ma
th
Z
ap
ca
r
d
g
am
e
(
N=
3
4
)
P
l
a
y
a
b
i
l
i
t
y
a
n
d
p
l
a
y
f
u
l
n
e
ss
F
r
e
q
u
e
n
c
y
M
e
a
n
SD
I
n
t
e
r
p
r
e
t
a
t
i
o
n
5
4
3
2
1
21
Th
e
g
a
me
w
a
s
e
f
f
e
c
t
i
v
e
i
n
r
e
v
i
e
w
i
n
g
t
h
e
mat
e
r
i
a
l
.
26
8
0
0
0
4
.
7
6
.
4
3
O
u
t
s
t
a
n
d
i
n
g
22
Th
e
g
a
me
e
n
c
o
u
r
a
g
e
d
t
h
e
p
l
a
y
e
r
s
t
o
d
i
g
d
e
e
p
e
r
i
n
t
o
t
h
e
su
b
j
e
c
t
m
a
t
t
e
r
.
18
14
1
1
0
4
.
5
0
.
5
6
O
u
t
s
t
a
n
d
i
n
g
23
P
l
a
y
i
n
g
t
h
e
g
a
me
i
s
a
p
r
o
d
u
c
t
i
v
e
u
se
o
f
t
i
me
.
14
17
3
0
0
4
.
3
2
.
6
4
V
e
r
y
s
a
t
i
sf
a
c
t
o
r
y
24
P
l
a
y
i
n
g
t
h
e
g
a
m
e
h
e
l
p
e
d
m
e
e
s
t
a
b
l
i
s
h
b
e
t
t
e
r
r
e
l
a
t
i
o
n
s
h
i
p
s
w
i
t
h
t
h
e
m
e
m
b
e
r
s
o
f
t
h
e
g
r
o
u
p
.
19
12
2
1
0
4
.
4
7
.
6
6
V
e
r
y
s
a
t
i
sf
a
c
t
o
r
y
25
I
w
o
u
l
d
r
e
c
o
mm
e
n
d
t
h
e
g
a
me
t
o
m
y
p
e
e
r
s.
23
8
3
0
0
4
.
5
6
.
5
5
O
u
t
s
t
a
n
d
i
n
g
A
v
e
r
a
g
e
mea
n
4
.
5
2
.
7
5
O
u
t
s
t
a
n
d
i
n
g
T
ab
le
9
s
h
o
ws
th
e
o
v
er
all
d
escr
ip
tiv
e
ev
alu
atio
n
o
f
th
e
Ma
th
Z
ap
ca
r
d
g
a
m
e
b
ased
o
n
th
e
f
iv
e
cr
iter
ia.
T
h
e
h
i
g
h
est
m
ea
n
s
co
r
e
was
o
b
tain
ed
f
o
r
t
h
e
cr
iter
i
a
o
f
“u
s
ef
u
ln
ess
”
(
m
ea
n
=
4
.
5
2
,
SD
=
.
7
5
)
f
o
llo
wed
b
y
“Play
ab
ilit
y
an
d
Play
f
u
ln
e
s
s
”
an
d
“Car
d
Desig
n
”
(
m
ea
n
=
4
.
2
3
,
SD
=
.
7
5
)
.
On
th
e
o
th
er
h
an
d
,
t
h
e
lo
west
m
ea
n
s
co
r
e
was
r
ec
o
r
d
ed
f
o
r
th
e
cr
iter
ia
o
f
“Co
m
p
o
n
en
ts
an
d
Or
g
a
n
izatio
n
”
with
a
m
ea
n
s
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
R
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N:
2252
-
8
8
2
2
C
a
r
d
g
a
me
a
s
a
p
e
d
a
g
o
g
ica
l t
o
o
l fo
r
n
u
mera
cy
s
kills
d
ev
elo
p
men
t
(
P
a
r
mjit S
in
g
h
)
701
4
.
2
.
1
.
I
nte
rv
iews
wit
h t
ea
cher
s
T
h
is
s
ec
tio
n
d
etails
th
e
f
o
cu
s
g
r
o
u
p
in
ter
v
iew
with
th
e
f
iv
e
teac
h
er
s
in
v
o
l
v
ed
i
n
th
e
s
tu
d
y
.
A
s
am
p
le
o
f
5
teac
h
er
s
wh
o
wer
e
in
v
o
lv
ed
in
th
e
f
ac
ilit
atio
n
o
f
th
e
Ma
th
Z
ap
ca
r
d
g
am
e
we
r
e
in
t
er
v
iewe
d
in
s
ee
k
in
g
th
eir
v
iews
r
eg
ar
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g
th
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m
e.
T
h
ey
wer
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in
itially
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r
ief
ed
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th
e
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als,
r
u
les
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p
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o
ce
d
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r
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o
f
th
e
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am
e.
T
h
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f
iv
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teac
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s
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o
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th
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ce
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elv
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b
etwe
en
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tim
es)
an
d
wer
e
also
in
v
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lv
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d
in
p
lay
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g
with
th
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s
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d
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ts
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h
ese
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h
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s
wer
e
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ter
v
iewe
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u
s
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a
f
o
c
u
s
g
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p
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te
r
v
iew
m
eth
o
d
to
s
h
ar
e
th
eir
f
in
d
in
g
s
(
R
: Res
ea
r
ch
er
;
T
: T
ea
ch
er
s
)
.
Stu
d
en
ts
in
th
is
s
tu
d
y
th
o
r
o
u
g
h
ly
en
j
o
y
ed
t
h
e
ca
r
d
g
am
e
s
im
p
ly
b
ec
au
s
e
it
was
ca
p
tiv
atin
g
an
d
en
g
ag
in
g
.
I
n
th
e
m
id
s
t
o
f
co
m
p
etin
g
,
th
e
r
e
was
a
s
en
s
e
o
f
jo
y
,
as
th
ey
g
r
ap
p
led
with
n
u
m
er
o
u
s
c
h
allen
g
es
,
in
clu
d
in
g
tr
y
in
g
t
o
o
u
twit e
ac
h
o
th
er
,
an
d
f
in
ally
ce
leb
r
atin
g
th
eir
v
icto
r
y
u
p
o
n
win
n
in
g
.
T1
:
I
ca
n
s
ee
s
tu
d
en
ts
h
a
vin
g
g
r
ea
t
fu
n
p
la
yin
g
th
e
g
a
me
…
b
y
th
e
w
a
y
I
en
jo
ye
d
it
to
o
….
s
ee
in
g
th
em
z
a
p
p
in
g
,
s
tu
mp
in
g
th
e
ta
b
le,
s
ta
n
d
in
g
o
n
th
eir
feet,
a
n
d
o
n
ma
n
y
o
cc
a
s
io
n
s
ex
p
r
ess
in
g
th
eir
jo
y
b
y
s
h
o
u
tin
g
“Ho
o
r
a
y!
” o
r
“I
w
o
n
!
”
T2
:
Th
e
s
tu
d
en
ts
,
esp
ec
ia
lly
th
e
b
o
ys,
w
h
en
th
ey
w
in
q
u
ite
o
ften
b
r
a
g
g
ed
t
o
th
eir
fr
ien
d
s
a
n
d
a
ls
o
to
me…
a
s
I
w
a
s
s
ea
ted
in
a
d
is
ta
n
ce
,
s
a
yin
g
,
“T
ea
ch
er,
I
w
o
n
.
”
T
h
e
m
o
s
t
ap
p
ar
e
n
t
f
o
r
m
o
f
th
e
'
jo
y
o
f
lear
n
i
n
g
'
is
in
tr
in
s
ic
m
o
tiv
atio
n
w
h
ich
lea
d
s
to
w
a
n
tin
g
mo
r
e
o
f
it.
W
h
en
s
tu
d
en
ts
ar
e
in
v
o
l
v
ed
an
d
en
g
a
g
ed
in
p
lay
in
g
,
t
h
ey
ar
e
m
o
r
e
m
o
tiv
ated
to
lea
r
n
.
Nu
r
tu
r
in
g
j
o
y
in
th
is
m
an
n
er
is
im
m
en
s
ely
r
ewa
r
d
in
g
an
d
lead
s
to
a
v
er
y
p
leasan
t
en
v
ir
o
n
m
e
n
t,
g
iv
en
t
h
at
n
atu
r
ally
,
wh
en
s
tu
d
en
ts
lo
v
e
wh
at
th
ey
d
o
,
th
ey
p
ar
ticip
ate
m
o
r
e
in
it.
T1
:
I
a
ls
o
n
o
ticed
th
a
t
n
o
t
o
n
ly
d
id
th
ey
fin
d
in
teres
t
i
n
th
e
g
a
me
b
u
t
a
ls
o
w
a
n
ted
to
ex
p
erien
ce
w
in
n
in
g
a
s
th
ey
r
ep
ea
ted
ly
p
a
r
ticip
a
ted
in
th
e
g
a
me.
T3
:
…
a
n
d
th
e
b
est p
a
r
t,
I
d
o
n
’
t
h
a
ve
to
fo
r
ce
th
em…
.
t
h
ey
ju
s
t wa
n
t to
co
n
tin
u
e
to
p
l
a
y
th
is
g
a
me.
T4
:
…
ev
en
th
e
l
o
s
ers
w
i
s
h
ed
to
co
n
tin
u
e
w
ith
th
e
g
a
me.
Ch
ild
r
en
lear
n
b
est
th
r
o
u
g
h
ac
tio
n
r
ath
er
th
an
in
s
tr
u
ctio
n
,
w
h
ich
th
en
lead
s
to
fir
s
t
-
hand
ex
p
erien
ce
.
T
h
e
co
n
s
tr
u
ctiv
is
t
p
h
ilo
s
o
p
h
y
b
eh
in
d
p
e
d
ag
o
g
ical
ap
p
r
o
ac
h
es
in
m
ath
em
atica
l
lear
n
in
g
p
lace
s
an
em
p
h
asis
o
n
m
ea
n
in
g
an
d
v
iew
th
e
lea
r
n
er
’
s
r
o
le
as
o
n
e
to
c
o
n
s
tr
u
c
t
k
n
o
wled
g
e.
W
h
en
ch
ild
r
en
en
jo
y
lea
r
n
in
g
,
th
e
th
ir
s
t
an
d
m
o
tiv
atio
n
f
o
r
f
u
r
th
er
k
n
o
wled
g
e
co
m
es
n
atu
r
ally
with
o
u
t
f
o
r
ce
,
an
d
ac
q
u
is
itio
n
o
f
it
in
th
is
m
an
n
er
is
ex
tr
em
el
y
im
p
o
r
tan
t f
o
r
k
ic
k
s
tar
tin
g
ea
r
ly
d
ev
elo
p
m
en
t o
f
n
u
m
e
r
ac
y
s
k
ills
.
T1
:
Th
is
ca
r
d
g
a
me
p
r
esen
t
o
p
p
o
r
tu
n
ities
fo
r
p
r
a
ctice
,
o
fte
n
w
ith
o
u
t
th
e
n
ee
d
fo
r
u
s
to
p
r
o
vid
e
a
n
y
q
u
esti
o
n
s
.
T3
:
Wh
en
I
s
ee
th
em
p
la
yin
g
,
…
I
ca
n
s
ee
th
a
t
t
h
ey
a
r
e
q
u
ite
fa
s
t
in
z
a
p
p
in
g
o
n
th
e
p
ile
o
f
ca
r
d
s
.
F
o
r
ex
a
mp
le,
in
th
e
r
ela
tio
n
s
h
ip
b
etw
ee
n
five
p
ercen
t
(
5
%)
a
n
d
p
o
in
t
z
ero
five
(
0
.
0
5
)
o
r
o
n
e
-
ten
th
(
1
/1
0
)
a
n
d
p
o
in
t
o
n
e
(
0
.
1
)
o
r
p
o
in
t
tw
o
five
(
0
.
2
5
)
a
n
d
a
q
u
a
r
ter
(
1
/4
)
…
a
n
d
mo
s
t
o
f
th
e
t
ime
th
ey
w
ere
co
r
r
ec
t!
T2
:
Th
is
g
a
me
d
efin
itely
imp
r
o
ve
s
th
eir
ma
tch
in
g
co
n
ce
p
ts
o
f
F
r
a
ctio
n
s
,
d
ec
ima
ls
a
n
d
p
ercen
ta
g
e
s
.
F
u
r
th
ermo
r
e,
th
is
g
a
me
a
ls
o
in
clu
d
es
th
e
u
s
e
o
f
r
o
ma
n
n
u
mera
ls
.
Desp
ite
it
n
o
t
b
ein
g
p
a
r
t
o
f
th
e
cla
s
s
r
o
o
m
s
ylla
b
u
s
,
h
a
vin
g
s
o
me
kn
o
w
led
g
e
o
n
th
is
is
imp
o
r
ta
n
t,
a
n
d
Ma
th
Za
p
d
o
es th
a
t.
T4
:
I
w
ill
s
a
y
mo
s
t
o
f
th
e
p
la
ye
r
s
w
ith
g
r
ea
t
en
th
u
s
ia
s
m
w
i
ll
ju
mp
fo
r
jo
y
w
h
en
th
ey
“Z
a
p
p
ed
”
…
th
e
visu
a
l sp
ee
d
o
f so
me
s
tu
d
en
ts
w
a
s
a
w
eso
me,
a
t time
s
fa
s
ter t
h
a
n
me.
.
.
T
h
e
co
n
ce
p
t o
f
p
ed
ag
o
g
y
in
it
s
en
tire
ty
h
as e
x
p
er
ien
ce
d
m
ass
iv
e
d
ev
elo
p
m
en
t a
s
o
f
late,
as f
ar
as th
e
class
r
o
o
m
teac
h
in
g
p
r
ac
tices
ar
e
co
n
ce
r
n
ed
.
C
h
ild
r
en
lea
r
n
b
est
th
r
o
u
g
h
ac
tio
n
r
ath
e
r
th
an
in
s
tr
u
ctio
n
,
an
d
th
is
lead
s
to
f
ir
s
th
an
d
ex
p
er
ie
n
ce
.
W
h
ile
th
is
f
o
r
m
o
f
lear
n
in
g
th
r
o
u
g
h
a
ca
r
d
g
am
e
is
n
o
t
to
b
e
v
iewe
d
as
a
s
o
le
lear
n
in
g
m
ec
h
an
is
m
,
u
n
d
er
m
in
in
g
th
e
p
ed
ag
o
g
y
cu
r
r
en
tly
in
e
f
f
ec
t,
it
c
o
u
ld
ce
r
tai
n
ly
wo
r
k
as
a
g
o
o
d
s
u
p
p
lem
en
tal
to
o
l
to
th
e
tea
ch
in
g
p
r
o
ce
s
s
,
en
h
an
cin
g
th
e
en
g
ag
em
en
t
p
r
o
ce
s
s
b
etwe
en
ed
u
ca
to
r
s
an
d
lear
n
er
s
.
I
n
ess
en
ce
,
th
e
v
ital
asp
ec
ts
in
clu
d
e
p
r
e
m
is
es
s
u
ch
as
lo
g
ic,
ten
ac
ity
an
d
cr
ea
tiv
i
ty
,
b
r
o
u
g
h
t
ab
o
u
t
in
th
e
f
o
r
m
o
f
a
m
en
tally
s
tim
u
la
tin
g
g
am
e.
R
:
Do
es th
is
ca
r
d
g
a
me
en
h
a
n
c
e
p
ed
a
g
o
g
ica
l
p
r
a
ctice
s
o
f stu
d
en
ts
’
men
ta
l c
o
mp
u
ta
tio
n
flu
en
cy
in
F
r
a
ctio
n
s
,
d
ec
ima
ls
,
p
ercen
ta
g
es a
n
d
R
o
ma
n
n
u
mera
ls
,
a
n
d
Wh
y?
T5
:
Th
eir me
n
ta
l c
o
mp
u
ta
tio
n
h
a
s
d
efin
itely
imp
r
o
ve
d
,
g
a
th
erin
g
fr
o
m
th
eir
a
ctio
n
o
f za
p
p
in
g
a
w
a
y
a
t th
e
p
ile
o
f c
a
r
d
s
.
T3
:
A
s
I
s
a
id
ea
r
lier
,
th
is
ca
r
d
g
a
me
p
r
o
vid
es a
p
la
tfo
r
m
fo
r
s
tu
d
en
ts
to
p
r
a
ctice
,
a
n
d
th
e
m
o
r
e
th
ey
p
r
a
ctice
,
th
e
b
etter th
ey
g
et
a
t
th
e
co
n
ce
p
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es
E
d
u
c
,
Vo
l
.
10
,
No
.
2
,
J
u
n
e
2
0
2
1
:
6
9
3
-
7
0
5
702
T4
:
I
b
eliev
e
th
a
t in
co
mp
a
r
is
o
n
t
o
th
e
fo
r
ma
l c
la
s
s
r
o
o
m
lea
r
n
in
g
o
f fra
ctio
n
s
,
d
ec
ima
ls
a
n
d
p
ercen
ta
g
es
co
mp
u
ta
tio
n
,
th
e
lea
r
n
in
g
p
r
o
c
ess
is
a
cc
elera
ted
th
r
o
u
g
h
Ma
th
Za
p
d
u
e
to
ma
s
s
ive
en
g
a
g
eme
n
t a
n
d
in
tera
ctio
n
a
mo
n
g
s
t stu
d
en
ts
.
All
f
iv
e
teac
h
er
s
h
eld
th
e
s
am
e
v
iew,
n
am
ely
th
at
t
h
is
g
am
e
in
cr
ea
s
es
m
en
tal
co
m
p
u
tatio
n
in
ter
m
s
o
f
th
e
ab
ilit
y
o
f
s
tu
d
en
ts
to
m
atch
th
e
c
o
n
ce
p
ts
o
f
f
r
ac
tio
n
s
,
d
ec
im
als,
p
er
ce
n
tag
es
an
d
m
o
s
t
im
p
o
r
tan
tly
h
ig
h
aler
tn
ess
an
d
v
is
u
al
s
p
ee
d
.
T
h
ey
f
u
r
th
e
r
c
o
n
clu
d
e
d
t
h
at
th
e
s
tu
d
en
ts
wer
e
ce
r
tain
ly
h
a
v
in
g
a
b
all
o
f
a
tim
e.
Ho
wev
er
,
o
n
e
te
ac
h
er
c
o
m
m
e
n
ted
th
at
th
e
g
r
o
u
p
in
g
o
f
p
lay
er
s
b
ased
o
n
th
ei
r
lev
el
o
f
ab
il
ity
was im
p
o
r
tan
t.
T3
:
Th
ese
p
la
ye
r
s
w
e
r
e
s
tr
u
g
g
li
n
g
to
co
m
p
ete
w
ith
th
e
b
etter
s
tu
d
en
ts
a
n
d
a
t
times
I
n
o
ticed
th
a
t
th
ey
d
i
d
n
o
t h
a
ve
th
e
o
p
p
o
r
tu
n
ity
to
z
a
p
…
w
h
ich
ca
n
b
e
d
emo
r
a
liz
in
g
.
T3
:
S
tu
d
en
ts
w
ith
lo
w
er
men
ta
l
co
mp
u
ta
tio
n
ca
p
a
b
ilit
ies
w
ere
s
tr
u
g
g
lin
g
to
p
la
y
w
ith
th
ei
r
h
ig
h
er
a
b
ilit
y
co
u
n
terp
a
r
ts
.
I
b
eliev
e
it sh
o
u
l
d
b
e
p
l
a
ye
d
b
a
s
ed
o
n
s
imila
r
l
ev
els o
f a
b
ilit
y.
T
h
is
g
am
e
th
at
in
v
o
lv
es
s
p
ee
d
d
o
es
im
p
ac
t
lear
n
er
s
wh
o
ar
e
o
f
d
if
f
er
e
n
t
lev
els
o
n
th
e
p
la
y
in
g
f
ield
.
W
h
en
p
lay
er
s
co
m
p
ete
with
p
lay
er
s
o
f
h
ig
h
er
s
k
ill
lev
els,
th
ey
ten
d
to
d
ep
ict
lo
wer
lev
el
s
o
f
en
jo
y
m
en
t
an
d
en
g
ag
em
e
n
t
af
ter
g
am
e
-
p
lay
in
g
.
I
n
o
th
e
r
wo
r
d
s
,
wh
en
p
lay
e
r
s
co
m
p
ete
with
o
th
er
s
o
f
eq
u
al
s
k
ill
lev
els,
th
ey
t
en
d
to
ex
p
en
d
m
o
r
e
ef
f
o
r
t
an
d
b
e
m
o
r
e
en
g
ag
ed
in
in
ter
a
ctio
n
ac
tiv
ity
th
an
wh
en
th
ey
co
m
p
ete
ag
ain
s
t
a
p
lay
er
o
f
u
n
e
q
u
al
s
k
ill lev
els.
T
h
e
d
ata
f
r
o
m
t
h
e
in
ter
v
iew
a
m
o
n
g
t
h
e
f
iv
e
teac
h
er
s
s
u
g
g
e
s
t
th
at
p
lay
in
g
th
e
Ma
th
Z
a
p
ca
r
d
g
am
e
was
b
en
ef
icial
in
r
ein
f
o
r
cin
g
th
eir
p
r
i
o
r
lear
n
in
g
in
f
r
ac
tio
n
s
,
d
ec
im
als
an
d
p
e
r
ce
n
tag
es.
T
h
ese
f
in
d
in
g
s
ec
h
o
th
e
f
in
d
in
g
s
o
b
tain
e
d
b
y
Od
e
n
weller
,
et
a
l.
[
4
4
]
th
at
also
p
o
in
ted
to
n
u
m
er
o
u
s
a
d
v
an
ta
g
es
o
f
u
s
in
g
ca
r
d
g
am
es
f
o
r
an
ed
u
ca
tio
n
al
p
u
r
p
o
s
e
b
y
m
o
tiv
atin
g
s
tu
d
e
n
ts
to
n
atu
r
al
ly
d
is
cu
s
s
th
e
to
p
ics
i
n
v
o
lv
ed
in
t
h
e
g
am
e;
b
o
o
s
tin
g
t
h
e
p
r
o
ce
s
s
o
f
r
ec
al
lin
g
co
n
ce
p
ts
;
an
d
g
en
er
ally
p
r
o
m
o
tin
g
lear
n
in
g
in
a
h
ea
l
th
ier
en
v
i
r
o
n
m
e
n
t.
Similar
ly
,
B
ey
lef
eld
an
d
Str
u
wig
[
4
5
]
also
f
o
u
n
d
th
at
th
e
u
s
ag
e
o
f
ca
r
d
g
am
es
as
an
in
f
o
r
m
al
lear
n
in
g
m
eth
o
d
o
l
o
g
y
ca
n
s
ca
f
f
o
l
d
th
e
p
r
o
ce
s
s
o
f
r
ec
allin
g
f
ac
t
u
al
k
n
o
wled
g
e.
T
h
e
q
u
alitativ
e
f
in
d
in
g
s
also
s
u
g
g
est
th
at
th
is
ca
r
d
g
am
e
h
as
th
e
p
o
ten
tial
to
b
e
an
e
f
f
icien
t
s
u
p
p
o
r
tin
g
ed
u
ca
tio
n
m
ater
ial
in
r
ein
f
o
r
cin
g
ac
q
u
ir
e
d
s
k
ills
an
d
k
n
o
wled
g
e.
5.
DIS
CU
SS
I
O
N
Fin
d
in
g
s
f
r
o
m
t
h
e
o
n
e
Gr
o
u
p
p
r
etest
–
p
o
s
ttes
t
ex
p
e
r
im
en
tal
d
esig
n
d
ep
icts
a
m
ea
n
g
ai
n
o
f
2
0
.
4
1
in
b
etwe
en
th
e
in
cu
b
atio
n
p
er
i
o
d
.
T
h
u
s
,
o
n
e
ca
n
co
n
clu
d
e
th
at
th
e
Ma
th
Z
ap
C
ar
d
Gam
e
is
an
ef
f
ec
tiv
e
ed
u
ca
tio
n
al
g
am
e
in
en
h
an
cin
g
r
ap
id
m
en
tal
co
m
p
u
t
atio
n
in
lear
n
in
g
f
r
ac
tio
n
s
,
d
ec
im
als,
p
er
ce
n
tag
es,
wh
o
le
n
u
m
b
er
s
an
d
r
o
m
an
n
u
m
er
als.
I
n
o
th
er
wo
r
d
s
,
p
lay
in
g
th
is
ca
r
d
g
am
e
en
h
a
n
ce
s
q
u
ick
th
in
k
in
g
an
d
g
i
v
es
r
is
e
to
th
e
ab
ilit
y
to
r
ap
id
ly
p
er
f
o
r
m
m
en
tal
co
m
p
u
tatio
n
s
(
e.
g
.
,
b
etwe
en
f
r
ac
tio
n
s
,
d
ec
im
als
an
d
p
er
ce
n
tag
es).
Alo
n
g
s
id
e
th
at,
it
b
r
in
g
s
ab
o
u
t
h
ig
h
er
lev
els
o
f
ale
r
tn
ess
,
in
cr
ea
s
ed
m
en
tal
an
d
v
is
u
al
s
p
ee
d
,
an
d
th
e
a
b
ilit
y
to
p
r
o
v
id
e
v
er
b
al
r
esp
o
n
s
es.
An
ar
r
ay
o
f
r
esear
ch
d
o
n
e
ea
r
lier
[
3
5
]
,
[
4
6
]
y
ield
ed
s
im
ilar
f
in
d
i
n
g
s
o
n
th
e
u
s
ag
e
o
f
ca
r
d
g
am
es in
e
n
h
an
ci
n
g
co
n
c
ep
tu
al
lear
n
in
g
am
o
n
g
s
t stu
d
en
ts
.
B
ased
o
n
th
e
f
in
d
in
g
s
,
it
is
ev
i
d
en
t
th
at
s
tu
d
e
n
ts
th
o
r
o
u
g
h
ly
en
jo
y
ed
th
e
Ma
th
Z
ap
ca
r
d
g
a
m
e,
an
d
in
th
e
s
p
ir
it
o
f
s
u
ch
f
u
n
,
th
ey
ac
q
u
ir
ed
b
etter
n
u
m
er
ac
y
s
k
ill
s
.
As
h
ig
h
lig
h
ted
ea
r
lier
,
wh
er
e
t
h
er
e
is
jo
y
,
f
u
n
an
d
en
g
ag
em
e
n
t,
th
e
b
etter
th
e
o
u
t
co
m
e
o
f
th
e
lear
n
i
n
g
p
r
o
ce
s
s
.
I
n
f
ac
t,
r
esear
ch
er
s
[8
]
,
[
21]
h
av
e
g
o
n
e
as
f
ar
as
s
ay
in
g
th
at
en
g
ag
em
en
t
as
s
u
c
h
is
a
p
r
e
-
r
e
q
u
is
ite
f
o
r
m
ea
n
in
g
f
u
l
lear
n
i
n
g
to
tak
e
p
lace
,
w
h
ich
ca
lls
f
o
r
a
s
h
if
t
in
b
eh
a
v
io
u
r
al
p
atter
n
s
o
f
s
tu
d
en
ts
,
f
r
o
m
b
ein
g
‘
p
ass
iv
e
v
ess
els’
to
‘
ac
tiv
e
p
ar
ticip
an
t
s
’
.
Su
ch
m
o
d
es
o
f
lear
n
in
g
,
in
its
to
tality
g
iv
es
r
i
s
e
to
a
d
ee
p
er
lear
n
in
g
ex
p
er
ie
n
ce
th
at
s
tu
d
en
ts
ca
n
r
elate
to
.
T
h
r
o
u
g
h
it,
s
o
cial
in
ter
ac
tio
n
is
b
o
r
n
as
well,
an
d
th
ey
a
r
e
g
iv
e
n
clar
ity
as
to
a
s
p
ec
if
ic
g
o
al.
T
h
e
th
e
o
r
y
b
e
h
in
d
th
e
s
u
cc
ess
o
f
s
tu
d
en
ts
in
m
en
tal
c
o
m
p
u
tatio
n
m
ig
h
t
b
e
d
u
e
t
o
th
e
d
ev
elo
p
m
en
t
o
f
a
h
a
b
itu
al
m
in
d
,
a
n
d
m
o
r
e
o
f
ten
th
a
n
n
o
t,
th
is
h
ap
p
en
s
s
u
b
co
n
s
cio
u
s
ly
,
with
o
u
t
th
em
ev
en
r
ea
lizin
g
o
r
k
n
o
win
g
it.
T
h
e
d
ev
el
o
p
m
en
t
o
f
th
is
h
ab
itu
al
m
in
d
d
ep
icts
th
e
n
o
tio
n
wh
e
r
e
lear
n
er
s
a
r
e
u
n
awa
r
e
o
f
h
o
w
t
h
ey
o
b
tain
ed
th
e
an
s
wer
.
Fo
r
ex
am
p
le,
i
n
a
s
tu
d
y
by
Par
m
jit
[
4
7
]
,
an
in
ter
esti
n
g
th
o
u
g
h
t
p
r
o
ce
s
s
b
y
a
s
tu
d
en
t
was o
b
s
er
v
ed
(
R
=
R
esear
ch
er
,
S
=
Stu
d
en
t)
:
R
:
Wh
a
t is 1
5
x
1
5
?
S
:
225
R
:
Ho
w
d
id
yo
u
g
et
it so
fa
s
t?
(
As th
e
s
tu
d
en
t r
esp
o
n
d
e
d
in
s
e
co
n
d
s
)
S
:
I
ju
s
t k
n
o
w
it.
R
:
Go
o
d
R
:
Wh
a
t is 1
6
x
1
5
?
S
:
240
(
with
in
s
ec
o
n
d
s
)
R
:
Ho
w
d
id
yo
u
k
n
o
w
th
a
t?
S
:
I
t’
s
tw
o
h
u
n
d
r
ed
tw
en
ty
-
five
p
lu
s
fift
ee
n
(
2
2
5
+
1
5
)
a
n
d
y
o
u
g
et
tw
o
h
u
n
d
r
ed
a
n
d
fo
r
ty
(
2
4
0
)
.
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