Higher Order Thinking Skills in
Science & Mathematics
(HOTsSM
HOTsSM))
BAHAGIAN PEMBANGUNAN KURIKULUM
KEMENTERIAN PELAJARAN MALAYSIA
akhir sesi ini anda akan dapat:
Memahami apa itu HOTs dalam Matematik.
Matematik
Menerapkan HOTs dalam kalangan murid.
Menyampaikan taklimat berkaitan HOTs kepada
guru-guru
guru
guru lain.
lain
Sesi Taklimat ini mengandungi DUA
komponen:
1) Penerangan & Perbincangan
2) Perbengkelan
Apa itu HOTs dalam Matematik?
LOWER ORDER THINKING (LOTs)
Resnick (1987) Lower-order thinking (LOT) is often characterized by the
recall of information or the application of concepts or knowledge to
familiar situations and contexts
contexts.
Schmalz (1973) LOT tasks requires a student “… to recall a fact,
perform a simple operation
operation, or solve a familiar type of problem.
problem
It does not require the student to work outside the familiar”
Senk, Beckman, & Thompson (1997) LOT is involved when
students are solving tasks where the solution requires applying a
well-known algorithm, often with no justification, explanation, or proof
required, and where only a single correct answer is possible
Thompson 2008 generally characterized LOT as solving tasks while
working in familiar situations and contexts; or, applying algorithms
already familiar to the student.
HIGHER ORDER THINKING SKILLS (HOTs)
snick (1987) characterized higher-order thinking (HOT) as
n-algorithmic.”
in and Lane (1996) describe HOT as “the use of complex,
n-algorithmic thinking to solve a task in which there is not a
di t bl well-rehearsed
dictable,
ll h
d approach
h or pathway
th
explicitly
li itl suggested
t d
the task, task instruction, or a worked out example.”
nk, et al (1997) characterized HOT as solving tasks where no
nk
orithm has been taught, where justification or explanation are
uired, and where more than one solution may be possible.
ompson (2008) generally characterized HOT involves solving
ks where an algorithm has not been taught or using known
orithms while working
g in unfamiliar contexts or situations.
HIGHER ORDER THINKING SKILLS (HOTs)
Higher order thinking
ills are normallyy those
skills in the top four
levels of the revised
Bloom’s
l
’ taxonomy:
applying, analysing,
aluating and creating.
aluating,
creating
HIGHER ORDER THINKING SKILLS (HOTs)
“Higher-order” questions promote learning
because these types of questions require
students to apply, analyze, synthesize, and
evaluate information instead of simply recalling
facts.
HIGHER ORDER THINKING SKILLS (HOTs)
Termasuk
pemikiran kritikal,
pemikiran kreatif,
p
pemikiran logikal,
pemikiran reflektif dan
meta-kognitif
meta
kognitif.
HOTs dicetuskan melalui
masalah bukan rutin,
rutin
masalah yang tidak jelas
atau dilema.
Mengapa perlu HOTs dalam
Matematik??
Matematik
Menghasilkan modal insan yang cerdas,
kreatif dan inovatif bagi memenuhi
cabaran abad ke-21 agar negara mampu
bersaing di persada dunia.
dunia
If we want students to develop the
capacity to think, reason, and
problem solve then we need to
start with high-level
high level, cognitively
complex tasks.
Stein & Lane 1996
ds in International Mathematics and Science Studies
TIMSS 2007 Average Achievement in the
Mathematics Content and Cognitive Domains
aysia performed below TIMSS average in both Mathematics
• Berubah ke arah lebih daripada kefahaman asas
dan rote memorization.
memorization
• Meningkatkan tahap kefahaman
• Meningkatkan kemampuan menjustifikasikan
penyelesaian dan dapatan.
• Konsep matematik dapat dipelajari dengan
l bih berkesan
lebih
b k
melalui
l l i HOTs.
HOT
• Meningkatkan keupayaan murid dalam
menyiasat dan meneroka idea matematik
memerlukan HOTs.
HOTs DALAM KURIKULUM MATEMATIK
• Pernyataan Standard Kurikulum ditulis
menggunakan kata kerja mengikut Taksonomi
Bloom.
Bloom
Kata Kerja
Metaperwakilan
• Bagi HP yang menggunakan kata kerja seperti
menyatakan dan menerangkan turut
menuntut guru menyediakan
di k aktiviti
k i i i yang
menekankan HOTs
Bagaimana meningkatkan HOTs?
erlu kepada transformasi dalam PdP:
uru perlu berubah cara:
berfikir
Mengajar - kurangkan chalk and talk, perbanyakkan
hands on
Menyoal (ms 4 & 5)
Memotivasi
Mentaksir
Tingkatkan kualiti tugasan yang diberi kepada murid
PELAKSANAAN HOTs MENUNTUT
Sikap Positif
ngaging
Pelbagai
Pendekatan
Non-algorithmic
Pemikiran
Reflektif
untukan Masa
Membuat &
menguji
konjektur
Pelbagai
Perkaitan
Kritikal &
Analitikal
Komunikasi
Penaakulan &
Pembuktian
Pelbagai Strategi
Penerokaan &
P
Penyiasatan
i t
Kefahaman
Mendalam
Kreatif &
Inovatif
PELAKSANAAN HOTs MENUNTUT
uru perlu merancang
oalan, tugasan dan
tiviti yyang
g menuntut
urid berfikir, berlatih
berfikir secara
rterusan dan menilai
mikiran mereka dan
mikiran individu lain.
lain
Worthwhile and Rich t k
task
Different levels of response
by Robert Sternberg
(A
(American
i
C
Cognitive
ii P
Psychologist)
h l i )
Teacher should answer children's
questions in a wayy that p
q
promotes
HOTs.
Level 1: Reject the question
Example:
p
"Why do I have to eat my vegetables?"
"Don't ask me any more questions.“
"Because I said so."
Level 2: Restate or almost restate
th question
the
ti as a response
Example:
p
"Why do I have to eat my vegetables?"
"Because you have to eat your vegetables."
"Why is that man acting so crazy?"
"Because
Because he's
he s insane.
insane "
Why is it so cold?
cold?"
"Why
"Because it's 15° outside."
Level 3: Admit ignorance or
present information
Example:
"I don't know, but that's a good
question."
or,
Give a factual answer to the question.
Level 4: Voice encouragement to
seek response through authority
Example:
l
“Let's look that up on the internet.”
“Let's look that up in the
encyclopedia ”
encyclopedia.
“Who
Who do we know that might know the
answer to that?”
Level 5: Encourage brainstorming,
or consideration of alternative
explanations
Example:
l
"Why are all the people in Holland so
tall?
tall?“
"Let's
Let s brainstorm some possible
answers."
"Maybe
y it's g
genetics,, or maybe
y it's diet,,
or maybe everybody in Holland wears
elevator shoes, or…" etc.
Level 6: Encourage consideration
of alternative explanations and a
means of evaluating them
Example:
"Now how are we going to evaluate the
possible answer of g
p
genetics? Where
would we find that information?
Information on diet? The number of
elevator shoes sold in Holland?”
Level 7: Encourage consideration of
alternative explanations plus a means
of evaluating them, and follow-through
on evaluations
Example:
"Okay, let's go find the information for a
few days — we'll search through the
encyclopedia and the Internet, make
telephone calls, conduct interviews, and
other
th things.
thi
Th
Then we will
ill gett b
back
k
together next week and evaluate our
findings "
findings.
Bring
B
i a closure
l
to
t
Sternberg,
g, so what?
• Teacher should answer
children's questions in a way that
promotes HOT, so which level
shall the teachers pitched on?
NINGKATKAN PEMIKIRAN MATEMATIK MURID
S 310-311)
310 311)
Soalan Bukan Rutin yang
memerlukan tahap kognitif yang
tinggi dapat membentuk HOTs
dalam kalangan murid.
RUTIN
“Problems can be solved using methods familiar to students by replicating eviously learned methods n a step‐by‐step
fashion.”
n a step
by step fashion.
Routine problem solving stresses the use
of sets of known or f t fk
prescribed procedures (algorithms) to solve problems”
BUKAN RUTIN
q
“Problems that require mathematical
analysis and reasoning;
many non routine problems
many non‐routine problems can be solved in more than one way, and may have more than one solution.”
RUTIN
BUKAN RUTIN
• Perlunya keseimbangan antara soalan rutin
dengan bukan rutin.
• Penekanan kepada soalan bukan rutin penting
bagi:
 Membentuk modal insan yang berfikrah.
 Merealisasikan hasrat negara untuk
mencapai satu pertiga teratas dalam TIMSS dan PISA.
Contoh Soalan TIMSS & PISA
CONTOH SOALAN TIMSS
Place either + or - into each box so
th t this
that
thi expression
i h
has th
the llargestt
possible total?
5
6
3
9
CONTOH SOALAN TIMSS
Which circle has approximately the same fraction
of its area shaded as the rectangle above?
A
D
B
C
E
CONTOH SOALAN TIMSS
What is the perimeter of a rectangle
whose area is 100 square meters?
Answer:
CONTOH SOALAN LAIN
Antara nombor-nombor
nombor nombor berikut, nombor yang
mana berbeza? Mengapa?
23, 20, 15, 25
CONTOH SOALAN TIMSS
Brad wanted to find three consecutive whole
numbers that add up to 81. He wrote the
equation
equa
o (n −1)+
) n + (n +1)) = 81.
8 What
a does
the n stand for?
A) The least of the three whole numbers
B) The middle whole number
C) The greatest of the three whole numbers.
D)) The difference between the least and the
greatest of the three whole numbers.
TIMSS Population 2 Item Pool (Released Items).
Copyright © 1994 by IEA, The Hague
CONTOH SOALAN TIMSS
A car salesman placed this advertisement
in the newspaper: “Old and new cars for sale,
different prices, average price RM 50,000.”
From the advertisement,
advertisement which of the following
must be true?
A) Most of the cars would cost between 68
RM40,000 and RM60,000.
B) Half of the cars would cost less than
35
RM50 000 and half would cost more than
RM50,000,
RM50,000.
C) At least one of the cars would cost RM50,000.
D) Some of the cars would cost less than
RM 50,000. 28
Daripada 153 orang pelajar hanya 18%
22
CONTOH SOALAN TIMSS
John and Cathy were told to divide a number by
100. By mistake John multiplied the number by
100 and
d obtained
bt i d an answer off 450
450.
Cathy correctly divided the number by 100. What
was her answer?
A. 0.0045
B. 0.045
C 0.45
C.
0 45
D. 4.5
TIMSS 2003 8th-Grade Mathematics Concepts
and Mathematics Items
CONTOH SOALAN PISA
1) (a) Which of the figures has the largest area?
Show your reasoning.
(b) Describe a method for estimating the area of figure C.
2) Nick wants to pave the rectangular patio of his new
house. The patio has length 5.25
2 metres and width 3
3.00
00
metres. He needs 81 bricks per square metre.
Calculate how many bricks Nick needs for the whole
patio.
patio
CONTOH SOALAN LAIN
Mary claims that you can find the area
of any 30
30-60-90
60 90 triangle given the
length of only one side. Is Mary correct
or not? Justify your answer.
CONTOH SOALAN LAIN
Panjang sisi sebuah segiempat sama B adalah
empat kali ganda segiempat sama A. Berapa
kalilah lebih besar luas B berbanding luas A?
Segiempat sama A
Segiempat sama B
CONTOH AKTIVITI
ken Pottery
herd” is part of a piece of pottery that one might dig up at an
aeological site where pottery‐making people once lived.
aeologists usually want to figure out how big the original piece of
ery was, as that can tell them something about who might have
e the piece and when it was made.
g the sherd shown on the right, devise a hod for determining the diameter of the nal plate.
a: Can you come up with another method?
a: Can you come up with another method?
ONTOH AKTIVITI
Nombor Perdana
Bagaimana cikgu mengajar
Nombor Perdana?
Nombor Perdana
ONTOH AKTIVITI
FAKTOR
BIL.
FAKTO
R
KUMP
NO.
14
15
16
17
18
19
20
21
22
23
24
25
FAKTOR
BIL.
FAKTO
R
KUMP
Nombor Perdana
ONTOH AKTIVITI
FAKTOR
BIL.
FAKTO
R
KUMP
NO.
FAKTOR
BIL.
FAKTO
R
1
1
A
14
1,2,7,14
4
1,2
2
B
15
1,3,5,15
4
1,3
2
B
16
1,2,4,8,16
5
1,2,4
3
17
1,17
2
1,5
2
18
1,2,3,6,9,18
6
1236
1,2,3,6
4
19
1 19
1,19
2
1,7
2
20
1, 2, 4,5,10,20
6
1,2,4,8
4
21
1,3,7,21
4
1,3,9
3
22
1,2,11,22
4
1,2,5,10
4
23
1,23
2
1 11
1,11
2
24
7
1,2,3,4,6,12
6
1,2,3,6,8,12,
1
2 3 6 8 12
24
B
B
B
KUMP
B
B
B
ONTOH AKTIVITI
How many one‐by‐one tiles are required to surround a 5x5 p
pool?
Develop a generalization that predicts the number of tiles required to surround a square pool of any size
required to surround a square pool of any size.
Explain how your generalization relates to the size of the pool and the number of border tiles.
ONTOH AKTIVITI
M k k Masalah
Menukarkan
M l h Rutin
R t kepada
k d
Masalah Bukan Rutin
OTS
HOTS
MASALAH RUTIN KEPADA BUKAN RUTIN
TUGASAN 1
Maria membeli sekotak susu dengan
g harga
g
RM1.55 dan sebungkus biskut dengan harga
RM1.70. Berapakah jumlah wang yang dibayar
oleh Maria?
TUGASAN 2
Maria membeli sekotak susu dengan harga
RM1.55 dan sebungkus biskut dengan harga
RM1 70 Dia
RM1.70.
Di memberikan
b ik RM4.00
RM4 00 kepada
k
d
jurujual. Berapakah bilangan syiling yang
diterima oleh Maria sekiranya jurujual itu
memberikannya
b ik
b b
beberapa
syiling
ili 5 sen, 10 sen
MASALAH RUTIN KEPADA BUKAN RUTIN
TUGASAN 2
HOTS
TUGASAN 1
Cari perimeter segi empat
tepat yang mempunyai
panjang
p
j g 8 meter dan lebar 17
meter.
Cari panjang sebuah segi
empat tepat yang
mempunyai luas 48 meter
persegi dan lebar 6 meter.
Mamat ingin membina pagar bagi
reban ayam yang berbentuk segi
empat. Dia mempunyai 20 meter
wayar pagar.
1. Apakah saiz segiempat yang
boleh beliau hasilkan?
2. Bentuk manakah yang terbaik?
LOTS
MASALAH RUTIN KEPADA BUKAN RUTIN
SOALAN RUTIN:
Satu sisiempat mempunyai sudut-sudut 100, 60,
and 130. Apakah nilai sudut yang keempat?
• Boleh Dikembangkan Kepada:
 Bolehkah sisiempat mengandungi empat sudut
cakah? Bagaimana anda tahu?
 Bolehkah segitiga mengandungi lebih daripada
satu
t sudut
d t cakah?
k h? Terangkan.
T
k
 Bolehkah sisiempat mengandungi dua sudut
y boleh, lukiskan rajah.
j
cakah? Sekiranya
Sekiranya tidak, terangkan.
 Bolehkah sisiempat mengandungi tiga sudut
cakah? Sekiranya boleh,
boleh lukiskan rajah.
rajah
Sekiranya tidak, terangkan.
MASALAH RUTIN KEPADA BUKAN RUTIN
Bundarkan 726 kepada ratus
yang terdekat?
HOTS
LOTS
Apakah
A
k h nombor
b yang boleh
b l h
dibundarkan kepada 700?
MASALAH RUTIN VS. BUKAN RUTIN
SOALAN RUTIN
Tidak memerlukan
murid untuk
menggunakan
kemahiran berfikir
pada aras tinggi.
Operasi yang perlu
digunakan adalah
elas.
SOALAN BUKAN RUTIN
•
Memerlukan tahap pemikiran pada aras tinggi.
•
Meningkatkan kemahiran menaakul.
•
Jawapan dan prosedur yang perlu digunakan
tidak serta merta jelas.
•
Menggalakkan
gg
lebih daripada
p
satu cara
penyelesaian dan strategi.
•
Terdapat lebih daripada satu jawapan.
• Lebih mencabar.
mencabar
• Berupaya membentuk murid yang kreatif dan
inovatif
• Penyelesaian memerlukan lebih daripada
membuat keputusan dan memilih operasi
matematik.
g sesuai untuk
• Memerlukan masa yyang
diselesaikan.
Skema Pemarkahan
TIMSS & PISA
SKEMA PEMARKAHAN TIMSS
SKEMA PEMARKAHAN PISA
SKEMA PEMARKAHAN PISA
Tidak semua tugasan
g
sama,, tugasan
g
yyang
g berbeza
menggalakkan tahap dan jenis pemikiran yang
berbeza.
Tahap pemikiran di
mana murid
id
melibatkan diri
akan menentukan
tahap pembelajaran
mereka.
ERBINCANGAN DALAM
UMPULAN KECIL:
engembangkan Soalan Rutin(LOTs)
epada Bukan Rutin(HOTs)
1. Bentukkan kumpulan 2 orang.
2. Tukarkan soalan rutin yang diberi
kepada soalan bukan rutin.
Kembangkan soalan berikut agar menjadi
soalan bukan rutin.
rutin
1) 825  5 =
2) Cari perimeter bagi rajah dibawah.
8 cm
3 cm
3) Cari min, median dan mod bagi data
berikut:
15, 16, 18, 37, 39
4) Cari isi padu kotak yang mempunyai
dimensi
4 cm x 2 cm x 8 cm.
cm
CONTOH JAWAPAN
1) Marcella had 825 cupcakes and sold all but 5. If she sold
them in packages, what might be the size and number of
the packages? How do you know?
2) Is it possible for two rectangles to have an area of 24 sq
cm but
b th
have diff
differentt perimeters?
i t ?E
Explain
l i h
how you k
know.
3) Find five data values so that the mean is 25 and the
median is 18. Explain your answers.
4)) Can two different boxes have the same area for the base
but different volumes? Can two different boxes have
different dimensions for the base but the same volume?
Explain.
Tindakan Susulan Guru
•
•
•
•
•
Adakan taklimat dalaman di sekolah masingg
masing kepada semua guru Sains dan Matematik.
Gunakan kandungan dan tempoh masa taklimat
seperti
ti yang diterima.
dit i
Semua guru Sains dan Matematik menggunakan
soalan HOTs
soala
O s dala
dalam pdp.
Guru Sains dan Matematik Tingkatan 1 mula
menyediakan murid untuk Gerak Gempur HOTsSM
pada
d Jun
J dan
d Okt 2013 & 2014 untuk
t k persediaan
di
murid ke TIMSS 2014 dan PISA 2015.
Soalan dan skema Gerak Gempur akan disediakan
secara berpusat dan pelaporan perlu disediakan.
TERIMA KASIH