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Higher Order Thinking Skills inScience & Mathematics(HOTsSM)
BAHAGIAN PEMBANGUNAN KURIKULUM
KEMENTERIAN PELAJARAN MALAYSIA
2012
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Di akhir sesi ini anda akan dapat:
Memahami apa itu HOTs dalam Matematik.
Menerapkan HOTs dalam kalangan murid.
Menyampaikan taklimat berkaitan HOTs kepada
guru-guru lain.
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Sesi Taklimat ini mengandungi DUAkomponen:
1) Penerangan & Perbincangan
2) Perbengkelan
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Apa itu HOTs dalam Matematik?
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Resnick (1987) Lower-order thinking (LOT) is often characterized by the
recall of information or the application of concepts or knowledge tofamiliar situations and contexts.
Schmalz (1973) LOT tasks requires a student to recall a fact,
perform a simple operation, or solve a familiar type of 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.
LOWER ORDER THINKING (LOTs)
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HIGHER ORDER THINKING SKILLS (HOTs)
Resnick (1987) characterized higher-order thinking (HOT) asnon-algorithmic.
Stein and Lane (1996) describe HOT as the use of complex,
non-algorithmic thinking to solve a task in which there is not a
predictable, well-rehearsed approach or pathway explicitly suggested
by the task, task instruction, or a worked out example.
Senk, et al (1997) characterized HOT as solving tasks where no
algorithm has been taught, where justification or explanation are
required, and where more than one solution may be possible.
Thompson (2008) generally characterized HOT involves solving
tasks where an algorithm has not been taught or using known
algorithms while working in unfamiliar contexts or situations.
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Higher order thinkingskills are normally thoseskills in the top fourlevels of the revisedBlooms taxonomy:applying, analysing,
evaluating, and creating.
HIGHER ORDER THINKING SKILLS (HOTs)
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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)
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Termasuk
pemikiran kritikal,
pemikiran kreatif,
pemikiran logikal,pemikiran reflektif dan
meta-kognitif.
HIGHER ORDER THINKING SKILLS (HOTs)
HOTs dicetuskan melalui
masalah bukan rutin,
masalah yang tidak jelas
atau dilema.
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Mengapa perlu HOTs dalamMatematik?
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Menghasilkan modal insan yang cerdas,kreatif dan inovatif bagi memenuhi
cabaran abad ke-21 agar negara mampu
bersaing di persada dunia.
If we want students to develop the
capacity to think, reason, and
problem solve then we need to
start with high-level, cognitivelycomplex tasks.
Stein & Lane 1996
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Trends in International Mathematics and Science Studies
TIMSS 2007 Average Achievement in the
Mathematics Content and Cognitive Domains
Malaysia performed below TIMSS average in both Mathematics
Content and Cognitive Domains
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Berubah ke arah lebih daripada kefahaman asasdan rote memorization.
Meningkatkan tahap kefahaman
Meningkatkan kemampuan menjustifikasikan
penyelesaian dan dapatan. Konsep matematik dapat dipelajari dengan
lebih berkesan melalui HOTs.
Meningkatkan keupayaan murid dalam
menyiasat dan meneroka idea matematikmemerlukan HOTs.
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HOTs DALAM KURIKULUM MATEMATIK
Pernyataan Standard Kurikulum ditulis
menggunakan kata kerja mengikut Taksonomi
Bloom.
Bagi HP yang menggunakan kata kerja seperti
menyatakan dan menerangkan turut
menuntut guru menyediakan aktiviti yang
menekankan HOTs
Kata Kerja
Metaperwakilan
http://localhost/var/www/apps/conversion/tmp/scratch_6/Draf%20metaperwakilan.pdfhttp://localhost/var/www/apps/conversion/tmp/scratch_6/Draf%20metaperwakilan.pdfhttp://localhost/var/www/apps/conversion/tmp/scratch_6/Draf%20metaperwakilan.pdf7/28/2019 Hots Matematik
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Bagaimana meningkatkan HOTs?
Perlu kepada transformasi dalam PdP:
Guru perlu berubah cara:
berfikir
Mengajar - kurangkan chalk and talk, perbanyakkanhands on
Menyoal (ms 4 & 5)
Memotivasi
Mentaksir Tingkatkan kualiti tugasan yang diberi kepada murid
http://localhost/var/www/apps/conversion/tmp/scratch_6/CBS_AskingEffectiveQuestions.pdfhttp://localhost/var/www/apps/conversion/tmp/scratch_6/CBS_AskingEffectiveQuestions.pdf7/28/2019 Hots Matematik
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Bahagian Pembangunan Kurikulum
Kementerian Pelajaran Malaysia
Engaging Non-algorithmic
PemikiranReflektif
Pelbagai
Pendekatan
Kritikal &
Analitikal
Sikap Positif PelbagaiPerkaitan
Kefahaman
Mendalam
Komunikasi
Pelbagai Strategi
Kreatif &
Inovatif
Penaakulan &
Pembuktian
Penerokaan &
PenyiasatanMembuat &
menguji
konjektur
Peruntukan Masa
PELAKSANAAN HOTs MENUNTUT
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Guru perlu merancang
soalan, tugasan dan
aktiviti yang menuntut
murid berfikir, berlatihberfikir secara
berterusan dan menilai
pemikiran mereka dan
pemikiran individu lain.
Worthwhile
and Rich
task
PELAKSANAAN HOTs MENUNTUT
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Different levels of response
by Robert Sternberg
(American Cognitive Psychologist)
Teacher should answer children's
questions in a way that promotesHOTs.
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Level 1: Reject the question
Example:
"Why do I have to eat my vegetables?"
"Don't ask me any more questions."Because I said so."
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Level 2: Restate or almost restate
the question as a response
Example:"Why do I have to eat my vegetables?"
"Because you have to eat your vegetables."
"Why is that man acting so crazy?"
"Because he's insane."
"Why is it so cold?""Because it's 15 outside."
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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.
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Level 4: Voice encouragement to
seek response through authority
Example:
Let's look that up on the internet.
Let's look that up in the
encyclopedia.
Who do we know that might know theanswer to that?
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Level 5: Encourage brainstorming,
or consideration of alternative
explanations
Example:
"Why are all the people in Holland so
tall?
"Let's brainstorm some possible
answers."
"Maybe it's genetics, or maybe it's diet,or maybe everybody in Holland wears
elevator shoes, or" etc.
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Level 6: Encourage consideration
of alternative explanations and a
means of evaluating them
Example:
"Now how are we going to evaluate thepossible answer of genetics? Where
would we find that information?
Information on diet? The number of
elevator shoes sold in Holland?
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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 afew days we'll search through the
encyclopedia and the Internet, make
telephone calls, conduct interviews, and
other things. Then we will get backtogether next week and evaluate our
findings."
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Bring a closure to
Sternberg, so what?
Teacher should answer
children's questions in a way thatpromotes HOT, so which level
shall the teachers pitched on?
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MENINGKATKAN PEMIKIRAN MATEMATIK MURID(MS 310-311)
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Soalan Bukan Rutin yangmemerlukan tahap kognitif yangtinggi dapat membentuk HOTsdalam kalangan murid.
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Problems can be solved
using methods familiar to
students by replicatingpreviously learned methods
in a step-by-step fashion.
Routine problem solving
stresses the use
of sets of known orprescribed procedures
(algorithms) to solve
problems
Problems that require
mathematicalanalysis and reasoning;
many non-routine problems
can be solved in more than
one way, and may have more
than one solution.
RUTIN BUKAN RUTIN
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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.
RUTIN BUKAN RUTIN
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Contoh Soalan TIMSS & PISA
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Place either + or - into each box sothat this expression has the largest
possible total?
5 6 3 9
CONTOH SOALAN TIMSS
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Which circle has approximately the same fraction
of its area shaded as the rectangle above?
A B C
D E
CONTOH SOALAN TIMSS
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What is the perimeter of a rectangle
whose area is 100 square meters?
Answer:
CONTOH SOALAN TIMSS
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TIMSS Population 2 Item Pool (Released Items).
Copyright 1994 by IEA, The Hague
Brad wanted to find three consecutive whole
numbers that add up to 81. He wrote the
equation (n1)+ n + (n +1) = 81. What does
the n stand for?
A) The least of the three whole numbersB) The middle whole number
C) The greatest of the three whole numbers.
D) The difference between the least and thegreatest of the three whole numbers.
CONTOH SOALAN TIMSS
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37
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, which of the following
must be true?
A) Most of the cars would cost between
RM40,000 and RM60,000.B) Half of the cars would cost less than
RM50,000, and half would cost more than
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.
68
35
22
28
Daripada 153 orang pelajar hanya 18%
yang menjawab dengan betul.
CONTOH SOALAN TIMSS
CONTOH SOA AN TIMSS
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38
John and Cathy were told to divide a number by
100. By mistake John multiplied the number by100 and obtained an answer of 450.
Cathy correctly divided the number by 100. What
was her answer?
A. 0.0045B. 0.045
C. 0.45
D. 4.5
TIMSS 2003 8th-Grade Mathematics Concepts
and Mathematics Items
CONTOH SOALAN TIMSS
CONTOH SOALAN PISA
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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 newhouse. The patio has length 5.25 metres and width 3.00metres. He needs 81 bricks per square metre.
Calculate how many bricks Nick needs for the wholepatio.
CONTOH SOALAN PISA
CONTOH SOALAN LAIN
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Mary claims that you can find the areaof any 30-60-90 triangle given the
length of only one side. Is Mary correct
or not? Justify your answer.
CONTOH SOALAN LAIN
CONTOH SOALAN LAIN
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Panjang sisi sebuah segiempat sama B adalah
empat kali ganda segiempat sama A. Berapakalilah lebih besar luas B berbanding luas A?
Segiempat sama A
Segiempat sama B
CONTOH SOALAN LAIN
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CONTOH AKTIVITI
Broken Pottery
A sherd is part of a piece of pottery that one might dig up at an
archaeological site where pottery-making people once lived.
Archaeologists usually want to figure out how big the original piece of
pottery was, as that can tell them something about who might havemade the piece and when it was made.
Using the sherd shown on the right, devise a
method for determining the diameter of the
original plate.
Extra: Can you come up with another method?
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Nombor PerdanaCONTOH AKTIVITIBagaimana cikgu mengajar
Nombor Perdana?
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Nombor PerdanaNO. FAKTOR
BIL.
FAKTO
R
KUMP
1
2
3
45
6
7
8
9
10
11
12
13
NO. FAKTOR
BIL.
FAKTO
R
KUMP
14
15
16
1718
19
20
21
22
23
24
25
CONTOH AKTIVITI
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Nombor PerdanaNO. FAKTOR
BIL.
FAKTO
R
KUMP
1 1 1 A
2 1,2 2 B
3 1,3 2 B
4 1,2,4 35 1,5 2 B
6 1,2,3,6 4
7 1,7 2 B
8 1,2,4,8 4
9 1,3,9 3
10 1,2,5,10 4
11 1,11 2 B
12 1,2,3,4,6,12 6
13 1,13 2 B
NO. FAKTOR
BIL.
FAKTO
R
KUMP
14 1,2,7,14 4
15 1,3,5,15 4
16 1,2,4,8,16 5
17 1,17 2 B18 1,2,3,6,9,18 6
19 1,19 2 B
20 1, 2, 4,5,10,20 6
21 1,3,7,21 4
22 1,2,11,22 4
23 1,23 2 B
24 1,2,3,6,8,12,
24
7
25 1,5,25 3
CONTOH AKTIVITI
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1) How many one-by-one tiles are required to surround a 5x5
pool?
2) Develop a generalization that predicts the number of tiles
required to surround a square pool of any size.
3) Explain how your generalization relates to the size of the
pool and the number of border tiles.
CONTOH AKTIVITI
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CONTOH AKTIVITI
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Menukarkan Masalah Rutin kepadaMasalah Bukan Rutin
MASALAH RUTIN KEPADA BUKAN RUTIN
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MASALAH RUTIN KEPADA BUKAN RUTIN
Maria membeli sekotak susu dengan harga
RM1.55 dan sebungkus biskut dengan harga
RM1.70. Berapakah jumlah wang yang dibayar
oleh Maria?
Maria membeli sekotak susu dengan hargaRM1.55 dan sebungkus biskut dengan harga
RM1.70. Dia memberikan RM4.00 kepadajurujual. Berapakah bilangan syiling yangditerima oleh Maria sekiranya jurujual itumemberikannya beberapa syiling 5 sen, 10 sendan 20 sen? Terangkan jawapan anda?
TUGASAN 1
TUGASAN 2
LOTS
HOTS
MASALAH RUTIN KEPADA BUKAN RUTIN
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1. Cari perimeter segi empattepat yang mempunyai
panjang 8 meter dan lebar 17
meter.
2. Cari panjang sebuah segi
empat tepat yang
mempunyai luas 48 meter
persegi dan lebar 6 meter.
Mamat ingin membina pagar bagireban ayam yang berbentuk segi
empat. Dia mempunyai 20 meter
wayar pagar.
1. Apakah saiz segiempat yang
boleh beliau hasilkan?
2. Bentuk manakah yang terbaik?
TUGASAN 1
TUGASAN 2
MASALAH RUTIN KEPADA BUKAN RUTIN
HOTS
LOTS
MASALAH RUTIN KEPADA BUKAN RUTIN
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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 sudut cakah? Terangkan.
Bolehkah sisiempat mengandungi dua sudutcakah? Sekiranya boleh, lukiskan rajah.Sekiranya tidak, terangkan.
Bolehkah sisiempat mengandungi tiga sudutcakah? Sekiranya boleh, lukiskan rajah.Sekiranya tidak, terangkan.
MASALAH RUTIN KEPADA BUKAN RUTIN
MASALAH RUTIN KEPADA BUKAN RUTIN
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Bundarkan 726 kepada ratus
yang terdekat?
Apakah nombor yang boleh
dibundarkan kepada 700?
HOTS
LOTS
MASALAH RUTIN VS BUKAN RUTIN
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SOALAN RUTIN SOALAN BUKAN RUTIN
Tidak memerlukan
murid untukmenggunakan
kemahiran berfikir
pada aras tinggi.
Operasi yang perlu
digunakan adalahjelas.
Memerlukan tahap pemikiran pada aras tinggi.
Meningkatkan kemahiran menaakul.
Jawapan dan prosedur yang perlu digunakan
tidak serta merta jelas.
Menggalakkan lebih daripada satu cara
penyelesaian dan strategi.
Terdapat lebih daripada satu jawapan.
Lebih mencabar.
Berupaya membentuk murid yang kreatif daninovatif
Penyelesaian memerlukan lebih daripadamembuat keputusan dan memilih operasimatematik.
Memerlukan masa yang sesuai untukdiselesaikan.
Menggalakkan perbincangan dalam kumpulandalan mendapatkan penyelesaian.
MASALAH RUTIN VS. BUKAN RUTIN
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Skema PemarkahanTIMSS & PISA
SKEMA PEMARKAHAN TIMSS
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SKEMA PEMARKAHAN PISA
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SKEMA PEMARKAHAN PISA
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Tidak semua tugasan sama, tugasan yang berbeza
menggalakkan tahap dan jenis pemikiran yang
berbeza.
Tahap pemikiran di
mana murid
melibatkan diriakan menentukan
tahap pembelajaran
mereka.
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PERBINCANGAN DALAM
KUMPULAN KECIL:Mengembangkan Soalan Rutin(LOTs)Kepada Bukan Rutin(HOTs)
1. Bentukkan kumpulan 2 orang.
2. Tukarkan soalan rutin yang diberikepada soalan bukan rutin.
K b k l b ik t j di
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1) 825 5 =
2) Cari perimeter bagi rajah dibawah.
3) Cari min, median dan mod bagi databerikut:
15, 16, 18, 37, 39
4) Cari isi padu kotak yang mempunyaidimensi 4 cm x 2 cm x 8 cm.
8 cm
3 cm
Kembangkan soalan berikut agar menjadi
soalan bukan rutin.
CO O
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1) Marcella had 825 cupcakes and sold all but 5. If she sold
them in packages, what might be the size and number ofthe packages? How do you know?
2) Is it possible for two rectangles to have an area of 24 sq
cm but have different perimeters? Explain how you 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.
CONTOH JAWAPAN
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Tindakan Susulan Guru Adakan taklimat dalaman di sekolah masing-
masing kepada semua guru Sains dan Matematik.
Gunakan kandungan dan tempoh masa taklimat
seperti yang diterima.
Semua guru Sains dan Matematik menggunakansoalan HOTs dalam pdp.
Guru Sains dan Matematik Tingkatan 1 mula
menyediakan murid untuk Gerak Gempur HOTsSM
pada Jun dan Okt 2013 & 2014 untuk persediaanmurid ke TIMSS 2014 dan PISA 2015.
Soalan dan skema Gerak Gempur akan disediakan
secara berpusat dan pelaporan perlu disediakan.
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TERIMA KASIH