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.4
,
No
.3
, Sep
t
em
b
e
r
20
15, pp
. 138
~145
I
S
SN
: 225
2-8
8
2
2
1
38
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
The P
r
ocess of T
h
inking amon
g J
unior High School Students in
Solving HOTS Question
Ba
kry
,
Md Nor Bin Ba
ka
r
Departem
ent
of
Educa
tion Ma
th
em
atics,
Univers
iti
Tekno
logi M
a
la
y
s
ia
, Malaysia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Aug 10, 2015
Rev
i
sed
Au
g
20
, 20
15
Accepted Aug 30, 2015
Higher order th
inking skills (
HOTS) is one
of the im
portan
t
aspect o
f
teaching
and learning mathem
atics. B
y
using H
O
TS, student will be able to
acquir
e
a deep
understand of mathematic
al con
cepts and can b
e
applied in
real
lif
e. Stud
en
ts abil
it
y to
dev
e
lop th
e c
a
pa
cit
y
of
the HOTS
is close
l
y
rela
ted wi
th thi
nking processes
while solving
m
a
them
atics pro
b
lem
s
. This
res
earch
focus
e
d, at
des
c
rib
i
ng
the
th
inking pr
ocess of students in solving
mathematical pr
oblem involvin
g
HOT
S problem. The method
used is
a
qualitativ
e method and case
stud
y
de
sign
, the data
collected through
m
a
them
atics
t
e
s
t
s
and intervi
e
ws
.
There
are 3 s
t
ud
ents
s
e
le
cted
as
parti
c
ipan
t
Data an
al
ys
is
te
c
hniques
are d
e
s
c
riptive qu
al
ita
tiv
e, an
al
ys
is
a
ccor
d
ing to the
model
proposed
b
y
Miles and Huberman
, namely
data redu
ction
,
data
presentation
and
conclusion
. Th
e result of
the s
t
u
d
y
s
howed th
at
t
h
e think
i
ng
skills of student with high m
a
th abili
t
y
, m
e
dium
m
a
th abilit
y,
an
d low m
a
th
ability
in solvin
g Hots problem
are d
i
ffer
e
nt. Th
e studen
t
who h
a
s high math
abili
t
y
is ab
le
to
crea
te m
e
aning,
make opinion
and can
conclud
e
, while the
student who has medium
ma
th abili
t
y
is able
to crea
te m
e
a
n
ing, m
a
ke
opinion but
cann
o
t conc
lude
, and
the stud
ent who
has low m
a
th a
b
ilit
y
is no
t
able to
create meaning
and
canno
t con
c
lude.
Keyword:
HOT
S Que
s
tio
n
Math
em
a
tics
Pro
cess of
T
h
i
nki
ng
Copyright ©
201
5 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
:
Bak
r
y,
Depa
rtem
ent of E
ducation M
a
them
atics,
Un
i
v
ersity Tech
no
log
y
o
f
Malaysia,
Sk
udai
,
J
o
h
o
r
B
a
hr
u.
Em
a
il: b
a
k
r
y.af@g
m
a
i
l
.co
m
1.
INTRODUCTION
Math
em
a
tics a
b
ility o
f
j
u
n
i
or h
i
g
h
scho
o
l
st
u
d
e
n
t
s is still a
t
a lo
w lev
e
l. Accord
ing
to
th
e rep
o
rt o
f
national e
x
am
, the a
v
era
g
e
math score
wa
s 5.78 (scale
10
.0
), wh
ile th
e report of
n
a
tio
n
a
l ex
am
fo
r
j
u
n
i
or
h
i
gh
scho
o
l
stu
d
e
n
t
s in
Makassar is 4
.
68
.
Th
is score in
dicates th
at
th
e math
e
m
atica
l
ab
ility o
f
stu
d
en
ts in
Mak
a
ssar is still at
a
lo
w lev
e
l [1
]. Stu
d
e
n
t
s’ lo
w
m
a
th
ab
ili
ty in
th
e assess
men
t
o
f
th
e n
a
tio
n
a
l ex
am
in
at
ion
sh
owed
th
at some p
r
ob
lem
s
e
x
ist in
th
e pro
c
ess o
f
t
eac
hing and learning
mathe
m
a
tics
in
th
e classroo
m
.
Th
e
teachers
need to dive
rsify activitie
s in the classroom
through the us
e of
various
teaching m
e
thods t
o
en
courag
e and
d
e
v
e
l
o
p th
ink
i
n
g
sk
ills in stud
en
ts [2
]. Th
ink
i
ng
sk
ills is an
im
p
o
r
tan
t
asp
ect fo
r stud
ents th
at
can
h
e
lp
th
e
b
r
ain
activ
ity o
f
stu
d
e
n
t
s in
un
derstand
ing
and re
m
e
m
b
erin
g
th
e lesso
n.
W
ith
th
is sk
ill, stu
d
e
n
t
s
are ab
le to
u
s
e
k
nowledg
e in
so
lv
ing
ev
ery
d
ay p
r
o
b
l
em
s [3
]. Th
ey
n
o
t
o
n
l
y n
eed
th
i
n
k
i
ng
sk
ills th
at inv
o
l
v
e
p
r
ob
lem so
lv
in
g
b
u
t
also
inv
o
l
v
e
find
ing
th
e p
r
ob
lem a
n
d
ex
p
l
o
r
ation o
f
n
e
w op
portun
ities as well as
gene
rat
i
n
g new
i
d
eas.
Th
ink
i
ng
is an activ
ity in
wh
ich
th
e m
i
n
d
is u
s
ed
to
m
a
k
e
d
ecisi
o
n
s
u
s
ing
inform
at
io
n
to
find
m
eani
ng,
t
o
m
a
ke
ju
d
g
m
e
nt
s, sol
v
e
p
r
o
b
l
e
m
s
or m
a
ke deci
si
ons
o
n
a
pr
o
b
l
e
m
based o
n
t
h
e i
n
f
o
rm
ati
on an
d
expe
rience
exi
s
ting i
n
e
v
ery
d
ay life.
T
h
i
n
ki
ng
i
s
a
dy
nam
i
c p
r
oces
s t
h
at
can
be
desc
ri
b
e
d
by
t
h
e
p
r
oc
ess.
It
is essentially a proces
s
of thi
nki
ng whe
r
e there a
r
e th
ree st
eps, nam
e
ly the creatio
n of
m
eani
ng,
f
o
rm
i
ng
a
n
opi
ni
o
n
a
n
d
co
ncl
u
si
on
[
4
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ERE
I
S
SN
:
225
2-8
8
2
2
The Proce
ss of
Thi
n
ki
n
g
am
o
n
g
Ju
ni
o
r
Hi
g
h
Sc
ho
ol
St
u
d
en
t
s
i
n
Sol
vi
n
g
H
O
T
S
Quest
i
on
(
B
akry)
13
9
Stu
d
e
n
t
s’ t
h
ink
i
ng
ab
ility in
j
u
n
i
or h
i
g
h
sch
o
o
l
can
b
e
d
e
v
e
l
o
p
e
d
throu
g
h
learn
i
ng
activ
ities an
d
teaching m
a
the
m
atics. This is supporte
d
by
the purpos
e
of learning m
a
them
atics
that
had been decla
r
ed by
th
e Ind
o
n
e
sian Natio
n
a
l Educatio
n
Min
i
stry th
at th
e p
u
r
po
ses of learn
i
ng
m
a
th
e
m
atics
are (1
) to
th
i
n
k
and
reason
to
co
n
c
lu
d
e
,
(2) d
e
v
e
l
o
p
creativ
e activ
ities th
at in
v
o
l
v
e
im
ag
in
at
io
n
,
in
t
u
itio
n, an
d
the d
i
scovery,
o
r
i
g
in
ally, curio
s
ity, con
j
ect
ure and
sup
p
o
s
itio
n
and
d
a
re to
try, (3) d
e
v
e
lop
p
r
o
b
l
em-so
l
v
i
ng
sk
ills, (4)
d
e
v
e
l
o
p th
e
ab
i
lity to
co
nv
ey i
n
fo
rm
atio
n
an
d to
state th
e argu
m
e
n
t
[5
].
The im
ple
m
entation of teaching an
d learning m
a
the
m
atic
s has not been able to devel
op stude
n
ts'
thinki
ng skills; the proce
ss
of teaching and l
earni
ng m
a
th
ematics in Indonesia is s
till focuse
d on the
teacher,
n
o
t
f
o
cu
sed
on stu
d
e
n
t
, so
lear
n
i
n
g
i
n
schoo
ls in
vo
lv
es m
o
re
m
e
m
o
r
i
zin
g
o
r
f
actu
a
l know
ledg
e [6
]. I
t
i
s
v
e
r
y
m
u
ch di
ffere
nt
from
t
h
e nat
i
onal
ed
ucat
i
o
n
goal
s
o
f
de
ve
l
opi
n
g
t
h
e abi
l
i
t
y
of st
udent
s
t
o
t
h
i
nk cri
t
i
cal
l
y
,
th
in
k
l
o
g
i
cally, syste
m
atica
lly, b
e
ob
j
ect
iv
e, hon
es
t
a
nd
di
sci
p
l
i
n
e
d
. The
r
ef
o
r
e, t
h
i
s
pa
pe
r f
o
c
u
ses
on
descri
bi
n
g
t
h
e
t
h
i
nki
ng
p
r
oce
ss o
f
st
ude
nt
s i
n
s
o
l
v
i
n
g
m
a
t
h
em
at
i
cal
probl
em
s i
n
v
o
l
v
i
n
g
HOT
S
pr
o
b
l
e
m
.
2.
R
E
SEARC
H M
ETHOD
This
study us
ed qualitative m
e
thods
.The
re
are
thr
ee m
a
in
objectives
for t
h
e im
plem
entation
of
q
u
a
litativ
e an
alysis, wh
ich
are 1
)
in
cl
u
d
e
d
a v
a
riety
o
f
d
a
ta co
llectio
n
and m
o
re to
fo
rm
a con
c
ise an
d easy to
un
de
rst
a
n
d
,
2)
est
a
bl
i
s
h a cl
ear l
i
nk
bet
w
e
e
n t
h
e o
b
j
ectives of the study and
a sum
m
a
ry
of t
h
e fi
ndi
n
g
s
obt
ai
ne
d
fr
om
t
h
e raw
dat
a
s
e
t
and t
o
e
n
s
u
r
e
t
h
at
t
h
e rel
a
t
i
ons
hi
p i
s
ca
pa
bl
e of
su
p
p
o
r
t
i
ng t
h
e o
b
j
ect
i
v
es of
th
e stud
y an
d 3)
b
u
ild a m
o
d
e
l or th
eo
ry
related
to the
re
view
process i
n
st
udies
undertaken
[7].
Th
ere are three d
i
fferen
t
levels o
f
stud
en
t ab
ility in
m
a
th
em
a
tics fo
llo
wi
n
g
th
is st
ud
y,
n
a
m
e
l
y
stu
d
e
n
t
s
with
h
i
gh
m
a
th
ab
ility (ANS), stud
en
ts with
m
o
d
e
rate m
a
th
abilit
y (ALY) and
st
u
d
e
n
t
s l
o
w m
a
th
ab
ility (NRS).
Th
e criteria are b
a
sed
on
th
e stu
d
y
partic
ipan
ts, in
cl
u
d
i
n
g
(1) Th
e resu
lt o
f
m
a
th
e
m
atic
s fin
a
l
exam
, (2) st
ud
ent
has
bee
n
l
earne
d m
a
terial
Pythagoras a
n
d (3)
The st
uden
t is ab
le to
co
mm
u
n
i
cate v
e
rb
ally
.
Data co
llectio
n in
stru
m
e
n
t
u
s
ed
in
th
e stud
y o
f
m
a
th
e
m
at
ics p
r
o
b
l
em
b
a
sed o
n
HOT Sk
ill is in
terv
iew sessio
n
with stude
n
ts.
Data analysis m
e
thod th
at
will be carried
out in this resear
ch is desc
riptive qualitative analysis
according t
o
t
h
e m
odel
propose
d
by
Miles
and Hube
rm
a
n
, nam
e
ly
data
re
duction,
data pre
s
entation a
n
d
concl
u
si
o
n
[8]
.
3.
R
E
SU
LTS AN
D ANA
LY
SIS
Th
is st
u
d
y
was cond
u
c
ted
to t
h
ree stud
en
ts
who
h
a
v
e
d
i
fferen
t m
a
th
em
a
t
i
c
s ab
ilities. Each
st
u
d
e
n
t
is
g
i
v
e
n
a qu
estion
of m
a
th
e
m
ati
c
s b
a
sed
o
n
HOTS sk
ill, an
d th
en
th
eir answers
were an
alyzed
referri
n
g
to
th
e
i
ndi
cat
o
r
s bel
o
w:
Tabl
e 1. In
di
ca
t
o
r of
T
h
i
n
ki
n
g
Pr
ocess
Think
i
ng Process
Cr
eation of
m
eaning(
C1)
form
ing an opinion (
C
2)
Conclution(
C3)
T
h
e student is
able to e
xplai
n the
inform
ation in question as deter
m
ining
elem
ents /
co
m
ponents that ar
e known in
the questio
n an
d the com
ponent in
question.
(
C
1.
1)
T
h
e student is able to wr
ite down
m
a
the
m
a
tics concepts related t
o
pr
oblem
s
.
(
C
2.
1)
T
h
e student can conclude
towards the solution
of
pr
oblem
s
.
(
C
3.
1)
T
h
e student is less able to explain the
inform
ation in question as deter
m
ining
elem
ents /
co
m
ponents that ar
e known in
the questio
n an
d the com
ponent in
question.
(
C
1.
2)
The student is less able to write
down
m
a
the
m
a
tics concepts related t
o
pr
oblem
s
.
(
C
2.
2)
Less co
m
p
let
e
in the
conclusion to
solve the
pr
oblem
.
(
C
3.
2)
T
h
e student cannot
explain the inform
ation
in question as deter
m
ining ele
m
e
n
ts /
co
m
ponents that are known in t
h
e qu
estion
and the co
m
ponent in question.
(
C
1.
3)
T
h
e student cann
o
t to wr
ite dow
n
m
a
the
m
a
tics concepts related t
o
pr
oblem
s
.
(
C
2.
3)
Inco
m
p
le
te i
n
the
conclusions
of the
resolution
of pr
oblem
s.
(
C
.
3
.3)
In t
h
i
s
st
udy
, a
l
l
st
udent
s w
e
r
e
gi
ve
n a m
a
t
h
quest
i
o
n at
n
o
n
-
r
o
u
t
i
n
e l
e
vel
of a
ppl
i
cat
i
o
n
,
t
h
e H
O
T
Skill com
pone
nt that is expec
t
ed to be
done
by the stude
nts
is the ability to
use the c
onc
ept of Pytha
goras in a
new
si
t
u
at
i
o
n
.
The
que
st
i
on t
h
at
was
gi
ven
t
o
st
u
d
ent
s
i
s
“S
ya
m will cro
ss the river w
h
ich
ha
s
a
width
o
f
12
m, a
fter
a
rrivin
g
a
c
ro
ss th
e
river,S
ya
m
d
r
ifts a
s
fa
r a
s
5m. Determi
n
e the d
i
sta
n
ce
o
f
th
e cu
rren
t a
c
ro
ss th
e
river."
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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252
-88
22
I
J
ERE
Vo
l. 4
,
N
o
. 3
,
Sep
t
emb
e
r
201
5
:
1
38
–
14
5
14
0
3.1. Mathematics
Test
3.
1.
1 S
ubje
c
t
AN
S
Subject ANS i
s
a student ha
s highe
r m
a
th
e
m
atics ab
ility accordi
n
g to the fi
nal exam in the last
sem
e
s
t
er. Th
e resu
lt of m
a
th
ematics test b
y
su
bj
ect
ANS:
Fi
gu
re 1.
A
N
S Ans
w
e
r
S
h
eet
Fi
gu
re
1 ab
o
v
e
sh
ows t
h
at
Su
bject
ANS can find
all th
e inform
at
io
n
in
t
h
e q
u
e
stio
n, and th
en
write
th
e in
fo
rm
atio
n
in
m
a
th
e
m
at
i
c
form
u
l
a, lik
e th
e stu
d
e
n
t
is ab
le to
write th
e in
form
atio
n
in
to
th
e
righ
t trian
g
l
e
(C
1.
1
)
. T
h
e
n
,
f
o
r
t
h
e
ne
xt
st
e
p
, t
h
e st
ude
nt
m
a
kes t
h
e
o
p
inio
n
,
ANS d
e
termin
es th
at th
e
p
r
ob
lem
is rela
ted
to
Pyth
ago
r
as fo
rm
u
l
a u
n
til sh
e wro
t
e
Pyth
ago
r
as con
c
ep
t an
d correlate
with
qu
estion
s
. (C2
.
1
)
, and
last
ly, th
e
st
ude
nt
c
oncl
u
ded
t
h
at
t
h
e
di
st
ance i
n
w
h
i
c
h
Sy
am
crosses
t
h
e
ri
ver
i
s
13
m
e
t
e
rs (C
3.
1
)
3.
1.
2 S
ubje
c
t
AL
Y
Subj
ect ALY is where a student ha
s m
odera
te
m
a
the
m
atics
ability accordi
ng to last se
m
e
ster’s final
exam
last se
m
e
ster.
Here
are t
h
e
results
of mathem
atics test by s
u
bject
AL
Y:
Fi
gu
re
2.
AL
Y
A
n
swe
r
Sheet
Fig
u
r
e
2
above sho
w
ed
th
at
su
bj
ect
A
L
Y
can
n
o
t
wr
ite all th
e in
for
m
at
i
o
n
i
n
th
e
qu
estio
n
(
C
1
.
2
)
.
Next
,i
n t
h
e
st
ep
of m
a
ki
ng t
h
e
opi
ni
o
n
, s
u
bject
AL
Y
det
e
rm
i
n
es t
h
at
t
h
e
pr
obl
em
i
s
rel
a
t
e
d t
o
Py
t
h
ago
r
as
C1
.1
C2
.1
C3
.1
C1
.2
C2
.2
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ERE
I
S
SN
:
225
2-8
8
2
2
The Proce
ss of
Thi
n
ki
n
g
am
o
n
g
Ju
ni
o
r
Hi
g
h
Sc
ho
ol
St
u
d
en
t
s
i
n
Sol
vi
n
g
H
O
T
S
Quest
i
on
(
B
akry)
14
1
form
ula but
he
cannot
write Pythag
oras
formula,
(C2.2)
unt
il he obtains
less accurate a
n
s
w
er is 13
2
, and th
en
cann
o
t
be ful
l
concl
ude
d (C
3
.
2 )
3.
1.
3 S
ubje
c
t
NR
S
Subject
NRS is whe
r
e a student has low m
a
them
a
tics
ability accordi
ng t
o
last se
m
e
ster’s final exam
last se
m
e
ster.
Th
e
resu
lt o
f
math
em
at
ics test
b
y
su
bj
ect
NR
S is:
Fi
gu
re 3.
NR
S
Ans
w
e
r
S
h
eet
Fig
u
re 3
abo
v
e
sh
owed
th
at su
bj
ect NR
S can
no
t write all t
h
e in
form
at
io
n in
qu
estio
n
(C
1
.
2
)
. Th
en,
in
th
e
step
of mak
i
n
g
th
e op
in
ion
,
subj
ect NRS
canno
t
determ
in
e th
e id
eas/co
n
c
ep
ts
related
to th
e proble
m
in
q
u
e
stio
n and
so
, sh
e is un
ab
le to
so
lv
e th
e
prob
lem
.
(C2
.
3
)
. Lastly, ALY
was
n
o
t
ab
le t
o
con
c
lud
e
(C3
.
3
)
3.
2. I
n
ter
v
i
e
w
An
al
ysi
s
Int
e
r
v
i
e
w
s
we
re con
d
u
ct
ed i
n
a sy
st
em
ati
c
proce
d
ure t
o
descri
be t
h
e
pr
ocess o
f
t
h
i
nki
ng
whi
l
e
sol
v
i
ng m
a
t
h
pro
b
l
e
m
s
. In t
h
i
s
st
udy
,
resear
chers
ha
ve ap
p
l
i
e
d t
h
e su
gge
s
t
ed pr
oce
d
ure
by
B
o
y
ce an
d
Neal
e
to
d
e
sign
th
e in
terv
iew
g
u
id
elin
es. Pro
c
ess o
f
in
terv
i
e
w is d
i
v
i
d
e
d in
to
th
ree main
sectio
n
s
:
1
)
the
in
trodu
ctio
n,
wh
ich
is in
tend
ed
t
o
d
e
term
i
n
e th
e id
en
tity
o
f
st
u
d
e
n
t
s,
2) th
e
q
u
e
stion p
a
rt, i
n
th
is sectio
n
researc
h
er
s t
y
pi
cal
l
y
ask a
b
o
u
t
st
ude
nt
resp
o
n
ses
w
h
i
l
e
sol
v
i
n
g
ch
al
l
e
ngi
n
g
m
a
th
que
st
i
ons
, i
n
par
t
,
researc
h
er
s al
s
o
di
sc
o
v
er t
h
e
pr
ocess
of t
h
i
nki
n
g
,
3
)
C
o
ncl
u
si
on
, i
s
t
h
e fi
nal
pa
rt
o
f
t
h
e i
n
t
e
r
v
i
e
w
t
o
be
con
d
u
ct
ed.
R
e
s
earche
r
s al
s
o
r
a
i
s
e ot
he
r
que
s
t
i
ons
de
pen
d
i
n
g
on
t
h
e a
n
s
w
e
r
s
gi
ve
n
by
t
h
e
st
u
d
ent
s
[
9
]
.
3.
2.
1 S
ubje
c
t
AN
S
Accord
ing
to
th
e resu
lt written
test b
y
ANS, it sh
ows that sh
e was ab
l
e
to
an
swer the q
u
e
stion
s
com
p
letely. She has
been m
a
king the
m
eani
ng
o
f
i
n
fo
rm
ation a
v
ai
l
a
bl
e
o
n
th
e qu
estio
n.
Sub
j
ect
ANS i
s
able
to
write th
e Py
th
ago
r
as con
c
ep
t, and
th
en
she u
s
ed
t
h
e Pythagoras conce
p
t to sol
v
e th
e
p
r
ob
lem
.
Th
e resu
lts
o
f
in
terv
iews with
resear
c
h
ers and s
u
bject
ANS:
R
:
If t
h
is,
Pyth
agorean.
Wh
at is t
h
e
q
u
e
stio
n ask
i
ng
for
?
S :
H
ypo
tenu
se
R
:
H
o
w
d
i
d kno
w wh
at th
e
h
ypoten
u
s
e is?
S
:
Because, t
h
is i
s
widt
h…
12
m
R :
W
i
d
t
h
fo
r
?
S
:
B
a
sed
on
wi
dt
h
fo
r t
h
e
ri
ver
In
tran
scri
p
tion
abo
v
e
, th
e ANS reco
gn
izes th
at th
is
q
u
e
stio
n
is a Pyth
ago
r
as, and
th
en
sh
e tried
to
dra
w
a
ri
g
h
t
t
r
i
a
ngl
e,
wi
t
h
t
h
e
wi
dt
h
of t
h
e ri
ver
1
2
m
e
t
e
rs hi
g
h
a
n
d
hy
pot
enu
s
e i
s
t
h
e
di
st
ance
o
f th
e cu
rr
en
t
acros
s t
h
e
ri
ve
r by
Sy
am
.
ANS i
s
w
r
i
t
i
ng t
h
e Py
t
h
a
g
orea
n f
o
rm
ul
as
and m
a
king opini
o
n ass
o
ciated
with t
h
e
q
u
e
stio
n. Th
e
fo
llo
wi
n
g
is th
e in
terv
iew transcrip
t
s:
R
:
H
e
r
e
(
a
,b
, and
c)
…
ho
w do
y
o
u kno
w
?
S
:
a i
s
based, b i
s
hi
gh
, an
d c i
s
hy
pot
e
n
u
s
e i
n
t
h
e
q
u
e
stio
n is h
y
po
tenu
se so
c
2
= a
2
+ b
2
R :
Emm
S
:
So…
he
re a
d
justed a…
b…c
…
The t
r
ansc
ripti
o
n indicates t
h
at the
ANS
stude
nt
can
deter
m
in
e h
i
s
op
in
ion on
t
h
e pr
ob
lem
in
que
st
i
on
wi
t
h
t
h
e Py
t
h
a
g
o
r
e
a
n t
h
e
o
ry
.
Ne
xt
, m
a
t
h
em
atical
ope
rat
i
o
ns
were
pe
rf
orm
e
d s
o
as t
o
o
b
t
a
i
n
a
C3
.2
C3
.3
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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252
-88
22
I
J
ERE
Vo
l. 4
,
N
o
. 3
,
Sep
t
emb
e
r
201
5
:
1
38
–
14
5
14
2
concl
u
sion that
Sya
m
swim
s a
s
far as 13 m
to cross the
river. Th
is can
be seen
in
th
e fo
l
l
o
w
ing
transcri
p
tio
n
bel
o
w:
R
:
M
m
m
…
, so
the n
e
x
t
step
?
S :
c
2
= a
2
+ b
2
c
2
= 12
2
+5
2
c
2
= 14
4 +
2
5
c
2
= 1
69
c = 13
R
:
Wh
at is th
e con
c
lu
si
o
n
?
S
:
Hy
p
o
t
e
n
u
se i
s
13 m
,
or
Sy
am
crosse
d t
h
e
ri
ver
as fa
r as
1
3
m
3.
2.
2 S
ubje
c
t
AL
Y
On
this question, ALY
also succes
sfully a
n
swe
r
e
d
this question
e
v
en though the
r
e a
r
e still som
e
m
i
st
akes. She has bee
n
m
a
king t
h
e m
eani
ng of i
n
f
o
rm
at
i
on avai
l
a
bl
e o
n
t
h
e que
st
i
on
b
u
t
she can
n
o
t
i
d
ent
i
f
y
th
e fo
rm
u
l
a n
a
me to
so
l
v
e th
e prob
lem
.
Refer to th
e i
n
terv
iew tran
scrip
t
s
belo
w:
R
:
Can
you
exp
l
ain
,
wh
at is th
e in
fo
rm
atio
n
you
will
tak
e
fro
m
th
is
q
u
e
stio
n
?
S
:
Pyth
ago
r
ean
,
gen
e
rally if t
h
e
q
u
e
stio
n lik
e t
h
at…
In
th
e tran
scrip
tio
n
abo
v
e
, ALY canno
t p
r
ov
id
e so
m
e
arg
u
m
en
t fo
r d
e
term
in
in
g
th
e characteristics
of t
h
e
Py
t
h
ag
o
r
ean
que
st
i
ons
, she
begi
ns w
r
i
t
i
ng d
o
w
n t
o
i
d
ent
i
f
y
w
h
at
she k
n
o
ws
. T
h
e f
o
l
l
o
wi
ng i
s
t
h
e
in
terv
iew tran
scrip
t:
R
:
Can
you
d
r
aw ag
ain
?
S
:
So
…, th
is is a t
r
iang
le … t
h
e
Pyth
ago
r
ean
R
:
Wh
ere is t
h
e trian
g
l
e
fro
m
?
S :
From
here
…
R
:
A
r
e you
su
r
e
?
S
:
1
2
is
b
a
sed,…5
is t
h
e
d
i
stan
ce in
riv
e
r
Fro
m
th
e tran
scrip
tion
ab
ov
e, it seem
s less c
o
nv
in
ci
ng that
ALY can dete
rmine the elem
e
n
ts that a
r
e
in
qu
estion
,
so
sh
e less und
ersto
o
d
in co
llectin
g th
e i
n
fo
rm
ation in question, s
u
c
h
as
, s
h
e
said
5m
is distance.
3.
2.
3 S
ubje
c
t
NR
S
NRS is th
e stud
en
t
wh
o
h
a
s lo
w m
a
th
ab
ilit
y, h
e
was
no
t ab
le to
an
swer t
h
is qu
estion
b
e
cau
se
h
e
was
n
o
t
ab
le to und
erstan
d all the in
fo
rm
atio
n
in
qu
estio
n
,
an
d h
e
do
es not h
a
v
e
pr
ior
kn
ow
ledg
e abou
t th
e
rel
a
t
i
ons
hi
p
be
t
w
een t
h
e c
o
n
cept
s
o
f
Pyth
ag
oras
with
th
e p
r
ob
lem
in
quest
i
o
n,
fol
l
o
w
i
ng t
h
e t
r
a
n
scr
i
pt
i
o
n
stude
nts with researche
r
s.
R
:
Do
y
o
u
un
de
rs
t
a
nd t
h
e
que
st
i
o
n
?
S :
No….
R
:
A
h
… w
h
y do
n’
tyo
u
kno
w
?
S :
….(feel
confus
ed)
In t
h
e t
r
a
n
scri
pt
i
on a
b
o
v
e, S
t
ude
nt
NR
S s
a
i
d
t
h
at
he
di
d
not
un
de
rst
a
n
d
t
h
e q
u
est
i
o
n,
so
he i
s
n
o
t
ab
le to
m
a
k
e
mean
in
g
.
Th
en
, th
e subj
ect
NRS said
g
i
v
e
n
th
at it can
no
t form
a n
o
tio
n. Th
e sub
s
eq
u
e
n
t
discussi
ons he
lped resea
r
c
h
e
r
s trying to determ
ine
t
h
e opi
ni
o
n
of
Ad
ar NR
S
/
m
a
them
atical idea
s and
co
n
c
ep
ts th
at can
b
e
u
s
ed
in
so
lv
i
n
g
th
is questio
n
,
fo
llowin
g
th
e resu
lts o
f
in
terv
iews with
research
ers NR
S
subject:
R
:
Th
e
n
e
x
t
qu
est
i
o
n
,
how to fi
nd
th
is
?
S
:
What..
?
Re
peat please…
!
R
:
Ho
w t
o
fi
n
d
(
h
y
pot
en
use
)
?
S
:
I do
n’t
k
n
o
w
R
:
Here is th
e h
y
p
o
t
en
use, th
is is a trian
g
l
e, th
is m
ean
s th
at
is
Pythagorea
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ERE
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S
SN
:
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2-8
8
2
2
The Proce
ss of
Thi
n
ki
n
g
am
o
n
g
Ju
ni
o
r
Hi
g
h
Sc
ho
ol
St
u
d
en
t
s
i
n
Sol
vi
n
g
H
O
T
S
Quest
i
on
(
B
akry)
14
3
S :
Ow
w…
.
here
c
2
= a.b
Th
e in
terv
iew
tran
scrip
tion
ab
ov
e showed
t
h
at th
e sub
j
ect
NRS can
no
t set o
p
i
n
i
on
s rel
a
ted
to
th
is
que
st
i
o
n
,
s
o
t
h
at
he ca
nn
ot
de
t
e
rm
i
n
e t
h
e a
n
s
w
ers
an
d m
a
ke co
ncl
u
si
ons
.
4.
DIS
C
USSI
ON
Th
e obj
ectiv
e
o
f
th
e
research in
th
is p
a
p
e
r is to
d
e
scrib
e
the p
r
o
cess
o
f
th
i
n
k
i
n
g
wh
ile solv
in
g
HOTS
que
st
i
ons
. T
h
i
nki
ng
i
s
a
dy
n
a
m
i
c proces
s t
h
at
can
be
des
c
ri
be
d
by
t
h
e
pr
ocess a
n
d t
h
e im
pl
em
ent
a
t
i
on
. T
h
e
process
of thi
n
king is a
proc
ess that c
onsis
ts of t
h
e
receipt of inte
rnal
and exte
rnal i
n
form
ation as
well as
m
a
nagem
e
nt
, st
ora
g
e an
d re
cal
l
of i
n
f
o
rm
at
i
on fr
om
m
e
m
o
ry
. The pr
o
cess of t
h
i
nki
ng i
s
t
h
e p
r
o
c
ess of
col
l
ect
i
ng i
n
f
o
r
m
at
i
on, st
o
r
i
n
g
,
creat
i
n
g
opi
ni
on
, c
o
n
d
u
ct
i
n
g
o
p
erat
i
o
ns a
n
d
m
a
ki
ng i
n
fe
re
nces
or
co
ncl
u
si
ons
[1
0]
.
The steps of the process of thinki
ng a
r
e:(1) the
creat
i
o
n o
f
m
eani
ng,
nam
e
ly
by
anal
y
z
i
ng t
h
e
characte
r
istics of a
num
b
er of sim
ilar object
s, and
diffe
re
n
tiate th
o
s
e feat
ures (2
)
set of th
e op
in
i
o
n
,
th
at p
u
t
s
t
h
e rel
a
t
i
o
ns
hi
p
bet
w
ee
n t
w
o
or
m
o
re u
nde
rs
t
a
ndi
n
g
a
n
d
(3
)
m
a
ki
ng co
ncl
u
si
o
n
or
i
n
fere
nce t
h
at
i
s
a
re
sul
t
o
f
t
h
e act
o
f
u
nde
rst
a
n
d
i
n
g t
o
f
o
rm
a new
o
p
i
n
i
o
n
ba
sed
o
n
t
h
e exi
s
t
i
n
g
opi
n
i
ons
[
11]
.
4
.
1
.
The student with High
ma
th
a
b
ility
Th
e stud
en
t wh
o
h
a
s h
i
gh
abilit
y in
m
a
th
ematics
is th
e st
u
d
e
n
t
wh
o
g
e
ts a sco
r
e aro
und
90
–
100
in
m
a
t
h
em
at
i
c
s final
exam
. AN
S i
s
a st
udent
wh
o get
s
a sc
o
r
e of 95
. Accord
ing
to
d
a
ta analysis an
d
th
e resu
lt o
f
in
terv
iews, t
h
e
p
r
o
cess of th
i
n
k
i
ng
wh
ile so
l
v
ing
m
a
th
qu
es
t
i
ons
HO
TS i
s
descri
bed
i
n
t
h
e fl
o
w
c
h
art
bel
o
w:
Fig
u
re
4
.
Hi
g
h
ab
ility o
f
st
u
d
e
n
t
’s t
h
ink
i
ng
pro
cess
Fig
u
re
4
abov
e sh
owed
th
at t
h
e stud
en
t wh
o h
a
s
h
i
gh
m
a
th
ab
ility is ab
le
to
create m
ean
in
g
lik
e t
h
e
stu
d
e
n
t
is ab
le to
co
llect in
form
at
io
n
in qu
estio
n
,
t
h
e
n
e
x
t
step
in m
a
k
i
n
g
o
f
op
in
ion
t
h
e stud
en
t is ab
le to
d
e
term
in
e th
e m
a
th
e
m
atics
co
n
c
ep
t an
d usin
g
t
h
ese con
cep
t t
o
so
lv
e qu
estio
ns. Lastly th
e stu
d
e
n
t
can
det
e
rm
i
n
e t
h
e f
i
nal
ans
w
er
an
d m
a
ki
ng c
o
nc
l
u
si
o
n
.
4
.
2
.
The student with
medium math
a
b
ility
ALY is t
h
e student
who
has the m
e
diu
m
m
a
th ability
according to the sc
ore of
m
a
the
m
a
t
ics in final
exam
. She get
s
a m
a
thscore
of
85.
Acco
rd
in
g
t
o
th
e
d
a
ta
an
alysis and
the resu
lt
o
f
i
n
terv
iews in
t
h
is
stu
d
y
,
th
e pro
cess
o
f
th
ink
i
ng
wh
ile
so
lv
i
n
g m
a
th
q
u
e
stion
s
base
d-
HOT
S i
s
desc
r
i
bed i
n
t
h
e
fl
o
w
cha
r
t
bel
o
w:
5.
6.
7.
8.
9.
10
.
11
.
12
.
13
.
14
.
Fig
u
re
5
.
Med
i
u
m
ab
ility o
f
stu
d
e
n
t
th
i
n
k
i
ng
p
r
o
cess
Cr
eatio
n
of
m
e
an
ing
Mak
i
ng
o
f
op
in
ion
C
oncl
u
si
o
n
s
The student is able to
collect inf
o
r
m
ation
in question.
The student is able to
wr
ite down the
pr
oblem
in question
The student is able to
determ
ine the
m
a
the
m
a
tics conce
p
ts
used.
The student is able to
using these concepts
to solve questions
T
h
e student can
determ
ine the
final
answer, and
m
a
king
conclusion
Cr
eation of
m
eaning
M
a
king of opini
on
Conclusio
n
s
The student is less
able
to collect inform
ati
on in
the question.
T
h
e student wr
ites
down
the pr
oblem
in question
but do not co
m
p
lete it
The student is less
able to
determ
ine the
m
a
the
m
a
tics conce
p
ts
used.
T
h
e student is able to use
these concepts to solve
questions.
T
h
e student can
determ
ine the
final
answer
,
and concluded
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I
S
SN
:
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252
-88
22
I
J
ERE
Vo
l. 4
,
N
o
. 3
,
Sep
t
emb
e
r
201
5
:
1
38
–
14
5
14
4
Fig
u
re
5
showed
that th
e
stud
en
t
wh
o
h
a
s
med
i
u
m
m
a
th
ab
ility is th
e stu
d
e
n
t
is less ab
le to co
llect
in
fo
rm
atio
n
in qu
estion
,
t
h
e n
e
x
t
step
i
n
m
a
k
i
n
g
of
op
in
ion
t
h
e st
ud
en
t is less ab
le to
d
e
term
i
n
e th
e
m
a
t
h
em
at
i
c
s conce
p
t
use
d
a
n
d t
h
e
st
u
d
e
n
t
c
a
n
det
e
rm
i
n
e t
h
e
fi
nal
a
n
swe
r
an
d m
a
ki
ng
co
ncl
u
si
on
.
4
.
3
.
The student with lo
w ma
th ability
NRS is t
h
e st
ud
en
t
wh
o h
a
s l
o
w m
a
th
ab
ilit
y, wh
ere sh
e go
t a sco
r
e of less th
an
7
5
po
ints in
th
e fi
n
a
l
ex
am
in
atio
n
.
Accord
ing
to
th
e d
a
ta an
alysis an
d
th
e resu
lt
o
f
in
terv
iews i
n
th
is stu
d
y
, the p
r
o
cess of thin
k
i
ng
whi
l
e
s
o
l
v
i
n
g
m
a
t
h
que
st
i
ons
base
d-
H
O
TS
i
s
desc
ri
be
d i
n
t
h
e
fl
o
w
cha
r
t
b
e
l
o
w:
15
.
Fig
u
re
6. Lo
w ab
ility o
f
st
uden
t
’s t
h
ink
i
ng
p
r
o
cess
Fig
u
re
6
above sho
w
ed
th
at
th
e stud
en
t
w
h
o
h
a
s low
m
a
t
h
ab
ility is n
o
t
ab
le to
create
o
f
m
ean
in
g,
th
e stud
en
t is
no
t ab
le to
co
llect in
form
atio
n
in
qu
estion
.
The n
e
x
t
step
in
mak
i
n
g
o
f
op
inio
n
the stud
en
t
is n
o
t
ab
le to
d
e
termin
e th
e
m
a
t
h
em
at
ics co
n
c
ep
t an
d
the stu
d
e
n
t
is n
o
t
ab
le to
u
s
e th
ese co
n
c
ep
ts to so
lv
e
que
st
i
ons
. Last
l
y
t
h
e st
u
d
ent
c
a
nn
ot
det
e
rm
i
n
e t
h
e
fi
nal
a
n
s
w
er
an
d ca
n
not
co
ncl
u
de.
5.
CO
NCL
USI
O
N
Th
e th
i
n
k
i
n
g
sk
ills o
f
st
u
d
e
n
t
with
h
i
g
h
m
a
t
h
ab
ility,
m
e
d
i
u
m
math
ab
ilit
y, an
d
l
o
w m
a
t
h
ab
ility in
so
lv
i
n
g Ho
ts
prob
lem
are d
i
fferen
t. Th
e
stud
en
t
wh
o h
a
s
h
i
gh
m
a
th
ab
ility is ab
le to
create m
ean
in
g
,
m
a
k
e
opi
ni
o
n
an
d ca
n co
ncl
u
de,
w
h
i
l
e
t
h
e st
ud
en
t
wh
o has m
e
di
um
m
a
t
h
abi
l
i
t
y
i
s
abl
e
t
o
creat
e
m
eani
ng,
m
a
ke
o
p
i
n
i
on
bu
t can
n
o
t
con
c
lud
e
, and
t
h
e st
u
d
e
n
t
who
h
a
s low m
a
th
ab
ility
is no
t ab
le to create m
ean
ing
and
can
no
t co
n
c
l
ude.
REFERE
NC
ES
[1]
Balitb
ang,
”Lap
oran Hasil Ujian
Nasional Tahun
2013 Siswa Sek
o
lah Meneng
ah Pertam
a di Indo
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,
Jakar
t
a:
Kemdikbud, 201
3.
[2]
Ram
i
rez.
B.
, R
a
chel
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a
tri
c
ia
, G
a
naden
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M
i
ldred
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e
activities
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Order Think
i
ng
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Journal:
Education
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6
(1), pp
. 22-23
,
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[3]
De Bono, Edwar
d
, ”Teaching
Th
inking”, Pe
nguin
Book Ltd: 27
Wrights Lane: Lon
don, 1976
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[4]
Sur
y
abr
a
ta, S., “
P
sikologi Pendid
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kan”, Ja
k
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ja Graf
indo
Persada, 1993
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Depdiknas, “Permendiknas No. 22 Tahun
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ngah Atas”, Dep
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[6]
Ros
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awati,
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”Enam
T
a
hap
a
n
Aktivit
as
a
l
am
P
e
m
b
elaj
aran
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a
tem
a
tik
a Unt
uk M
e
nda
yagun
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rpikir
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[7]
Thomas, A. Th
orne, G.
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l
l
,
R.
, De
sa
nt
i,
P., L
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uson. C, “Mindwork and H
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w
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[8]
Miles,
Matthew
B.,
Huberman
, Michael
A, ”Qu
a
litativ
e Data A
n
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v
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[9]
Bo
y
c
e, C., Neale, “Conducting in-d
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Marpaung, Y., “Pende
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pembelajaran
matematika dan s
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Sur
y
abrata, S., “Psikologi
Pendidikan
”
, Jak
a
rta: PT. Raja
Grafindo Persad
a,
1993.
Cr
eation of
m
eaning
M
a
king of opini
on
Conclusio
n
s
T
h
e student is not able
to collect inf
o
r
m
ati
on
in question
T
h
e student wr
ite
down the pr
oblem
in
question b
u
t do no
t
co
m
p
lete the pr
oblem
in question
T
h
e student is not able to
determ
ine the
m
a
the
m
a
tics conce
p
ts
used
T
h
e student is not able to
use these concepts to
solve questions
T
h
e studentcannot
determ
ine the
final
answer
,
and cannot
conclude
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ERE
I
S
SN
:
225
2-8
8
2
2
The Proce
ss of
Thi
n
ki
n
g
am
o
n
g
Ju
ni
o
r
Hi
g
h
Sc
ho
ol
St
u
d
en
t
s
i
n
Sol
vi
n
g
H
O
T
S
Quest
i
on
(
B
akry)
14
5
BIOGRAP
HI
ES OF
AUTH
ORS
Bakr
y
was born
in Makassar o
n
October
,
14, 1
982. Bach
elor o
f
Mathematics
Education from
Makassar State
University
,
a master of edu
cation planning fro
m Hasa
nuddin University
,
and
now activ
e as a
student in Dep
a
r
t
ment of Math
e
m
atics Educ
atio
n, Facu
lty
Education Univ
ersiti
T
e
c
hnol
o
gy
Ma
lay
s
ia
.
Md.Nor Bin Bakar, is a Professor mad
y
a in Depa
rtment of Mathematics
Edu
cat
ion, F
acul
t
y
of
Education Univ
ersiti
Technolog
y
Malay
s
i
a
. B
a
ch
elor
in Math
em
atics Edu
cat
io
n from
Malay
a
Univers
i
t
y
, M
a
l
a
y
s
i
a
,
.
M
a
s
t
er o
f
M
a
them
ati
c
s
Educa
tion F
r
om
Univers
i
t
y
Of
Keele
,
Unit
ed
Kingdom and Ph.D in
Mathematics Education
Fr
o
m
Uinversity
of
Warwick, United Kingdom.
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