higher order thinking skills in science & mathematics ... · pdf filehigher order thinking...

Higher Order Thinking Skills in Higher Order Thinking Skills in Higher Order Thinking Skills in Higher Order Thinking Skills in Science Science & Mathematics& MathematicsScience Science & Mathematics& Mathematics

((HOTsSMHOTsSM))((HOTsSMHOTsSM))

BAHAGIAN PEMBANGUNAN KURIKULUMKEMENTERIAN PELAJARAN MALAYSIAKEMENTERIAN PELAJARAN MALAYSIA

2012

akhir sesi ini anda akan dapat:akhir sesi ini anda akan dapat:

Memahami apa itu HOTs dalam MatematikMemahami apa itu HOTs dalam Matematik.

Menerapkan HOTs dalam kalangan murid.

Menyampaikan taklimat berkaitan HOTs kepada

guru-guru lainguru guru lain.

Sesi Taklimat ini mengandungi DUA kkomponen:

1) Penerangan & Perbincangan

2) Perbengkelan

Apa itu HOTs dalam Matematik?Apa itu HOTs dalam Matematik?

LOWER ORDER THINKING (LOTs)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 contextsfamiliar situations and contexts.

Schmalz (1973) LOT tasks requires a student “… to recall a fact, perform a simple operation or solve a familiar type of problemperform 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.

HIGHER ORDER THINKING SKILLS (HOTs)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 ll h d h th li itl t ddictable, well-rehearsed approach or pathway explicitly suggested the task, task instruction, or a worked out example.”

nk et al (1997) characterized HOT as solving tasks where nonk, et al (1997) characterized HOT as solving tasks where no 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 in unfamiliar contexts or situations.g


Higher order thinking ills are normally those yskills in the top fourlevels of the revised

l ’Bloom’s taxonomy: applying, analysing, aluating and creatingaluating, and creating.


“Higher-order” questions promote learning because these types of questions require

students to apply, analyze, synthesize, and evaluate information instead of simply recalling

facts.facts.


TermasukTermasukpemikiran kritikal, pemikiran kreatif, ppemikiran logikal,

pemikiran reflektif danmeta-kognitif

HOTs dicetuskan melaluimasalah bukan rutin meta kognitif. masalah bukan rutin,

masalah yang tidak jelasatau dilema.

MengapaMengapa perluperlu HOTs HOTs dalamdalamMengapaMengapa perluperlu HOTs HOTs dalamdalamMatematikMatematik??MatematikMatematik??

Menghasilkan modal insan yang cerdas, kreatif dan inovatif bagi memenuhi

cabaran abad ke-21 agar negara mampu bersaing di persada duniabersaing 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 cognitivelystart with 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 ntent and Cognitive Domains

• Berubah ke arah lebih daripada kefahaman asasdan rote memorization dan rote memorization.

• Meningkatkan tahap kefahaman• Meningkatkan kemampuan menjustifikasikanMeningkatkan kemampuan menjustifikasikan

penyelesaian dan dapatan.• Konsep matematik dapat dipelajari dengan

l bih b k l l i HOTlebih berkesan melalui HOTs.• Meningkatkan keupayaan murid dalam

menyiasat dan meneroka idea matematikmenyiasat dan meneroka idea matematikmemerlukan HOTs.

HOTs DALAM KURIKULUM MATEMATIKHOTs DALAM KURIKULUM MATEMATIKHOTs DALAM KURIKULUM MATEMATIKHOTs DALAM KURIKULUM MATEMATIK

• Pernyataan Standard Kurikulum ditulismenggunakan kata kerja mengikut TaksonomiBloom Bloom. Kata Kerja

Metaperwakilan

• Bagi HP yang menggunakan kata kerja sepertimenyatakan dan menerangkan turut

di k k i i i menuntut guru menyediakan aktiviti yang menekankan HOTs

Bagaimana meningkatkan HOTs?Bagaimana meningkatkan HOTs?Bagaimana meningkatkan HOTs?Bagaimana meningkatkan HOTs?

erlu kepada transformasi dalam PdP:

uru perlu berubah cara:berfikirMengajar - kurangkan chalk and talk, perbanyakkanhands onMenyoal (ms 4 & 5)Menyoal (ms 4 & 5)MemotivasiMentaksirMentaksirTingkatkan kualiti tugasan yang diberi kepada murid

PELAKSANAAN HOTs MENUNTUTPELAKSANAAN HOTs MENUNTUT

PelbagaiPendekatanSikap Positif

PelbagaiPerkaitan

ngaging Non-algorithmicKritikal & Analitikal

Perkaitan

PemikiranReflektif

Komunikasi

Pelbagai StrategiPenaakulan & Pembuktian Pelbagai StrategiPembuktian

Penerokaan & P i t

untukan Masa

Kefahaman

Kreatif & Inovatif

PenyiasatanMembuat & menguji

konjekturBahagian Pembangunan Kurikulum

Mendalamkonjektur

PELAKSANAAN HOTs MENUNTUTPELAKSANAAN HOTs MENUNTUT

uru perlu merancang Worthwhile uru perlu merancangoalan, tugasan dantiviti yang menuntut

and Rich t k

y gurid berfikir, berlatih

berfikir secaratask

rterusan dan menilaimikiran mereka dan

mikiran individu lainmikiran individu lain.

Different levels of responseDifferent levels of response

by Robert Sternberg(A i C i i P h l i )(American Cognitive Psychologist)

Teacher should answer children's questions in a way that promotes q y p

HOTs.

Level 1: Reject the questionLevel 1: Reject the questionExample: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 tithe question 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 he's insane "Because he s insane.

"Why is it so cold?"Why is it so cold?"Because it's 15° outside."

Level 3: Admit ignorance or present informationpresent information

Example: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 authorityseek response through authority

lExample:“Let's look that up on the internet.”

“Let's look that up in the encyclopedia ”encyclopedia.

“Who do we know that might know the Who do we know that might know the answer to that?”

Level 5: Encourage brainstorming, or consideration of alternativeor consideration of alternative explanations

lExample:"Why are all the people in Holland so tall?“tall?

"Let's brainstorm some possible Let s brainstorm some possible answers.""Maybe it's genetics, or maybe it's diet, y g , y ,or maybe everybody in Holland wears elevator shoes, or…" etc.

Level 6: Encourage consideration of alternative explanations and aof alternative explanations and a means of evaluating them

Example:

"Now how are we going to evaluate the possible answer of genetics? Where p gwould we find that information? Information on diet? The number of elevator shoes sold in Holland?”

Level 7: Encourage consideration of alternative explanations plus a meansalternative explanations plus a means of evaluating them, and follow-through on evaluations

Example: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 th thi Th ill t b k other things. Then we will get back

together next week and evaluate our findings "findings.

B i l tBring a closure to Sternberg, so what?g,

• Teacher should answerTeacher should answer children's questions in a way that promotes HOT, so which levelpromotes HOT, so which level shall the teachers pitched on?

NINGKATKAN PEMIKIRAN MATEMATIK MURID S 310 311)S 310-311)

Soalan Bukan Rutin yang memerlukan tahap kognitif yang

tinggi dapat membentuk HOTs tinggi dapat membentuk HOTs dalam kalangan murid.

RUTIN BUKAN RUTIN

“Problems can be solved using methods familiar to “Problems that require students by replicating eviously learned methods n a step‐by‐step fashion.”

qmathematical

analysis and reasoning;many non routine problemsn a step by step fashion.

Routine problem solving stresses the usef t f k

many non‐routine problems can be solved in more than one way, and may have more

of sets of known or prescribed procedures (algorithms) to solve

than one solution.”

problems”

RUTIN BUKAN RUTIN

• Perlunya keseimbangan antara soalan rutinPerlunya keseimbangan antara soalan rutindengan bukan rutin.

• Penekanan kepada soalan bukan rutin penting• Penekanan kepada soalan bukan rutin pentingbagi: Membentuk modal insan yang berfikrah. Merealisasikan hasrat negara untuk

mencapai satu pertiga teratas dalam TIMSS dan PISA.

ContohContoh SoalanSoalan TIMSS & PISATIMSS & PISA

CONTOH SOALAN TIMSSCONTOH SOALAN TIMSS

Place either + or - into each box so th t thi i h th l tthat this expression has the largest possible total?

5 6 3 9


Which circle has approximately the same fractionWhich circle has approximately the same fraction of its area shaded as the rectangle above?

A B CA B C

D E


What is the perimeter of a rectangle whose area is 100 square meters?

Answer:Answer:

CONTOH SOALAN LAINCONTOH SOALAN LAIN

Antara nombor-nombor berikut, nombor yang Antara nombor nombor berikut, nombor yang mana berbeza? Mengapa?

23, 20, 15, 25

CONTOH SOALAN TIMSSCONTOH SOALAN TIMSSBrad wanted to find three consecutive whole numbers that add up to 81. He wrote the equation (n −1)+ n + (n +1) = 81. What does equa o (n ) n (n ) 8 a doesthe 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

A car salesman placed this advertisementCONTOH SOALAN TIMSSCONTOH SOALAN TIMSS

A car salesman placed this advertisementin the newspaper: “Old and new cars for sale,different prices, average price RM 50,000.”From the advertisement which of the followingFrom the advertisement, which of the followingmust be true?

A) Most of the cars would cost between 68A) 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

68

35RM50,000, and half would cost more thanRM50,000.

C) At least one of the cars would cost RM50,000. 22D) Some of the cars would cost less than

RM 50,000. 28

Daripada 153 orang pelajar hanya 18% j b d b t l


John and Cathy were told to divide a number by 100. By mistake John multiplied the number by 100 d bt i d f 450100 and obtained an answer of 450.Cathy correctly divided the number by 100. What was her answer?A. 0.0045B. 0.045C 0 45C. 0.45D. 4.5

TIMSS 2003 8th-Grade Mathematics Concepts and Mathematics Items

CONTOH SOALAN PISACONTOH 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 2 3 00house. The patio has length 5.25 metres and width 3.00

metres. He needs 81 bricks per square metre.Calculate how many bricks Nick needs for the whole patiopatio.


Mary claims that you can find the area of any 30 60 90 triangle given theof any 30-60-90 triangle given the

length of only one side. Is Mary correct or not? Justify your answer.or not? Justify your answer.


Panjang sisi sebuah segiempat sama B adalahempat kali ganda segiempat sama A. Berapakalilah 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 anaeological site where pottery‐making people once lived.

aeologists usually want to figure out how big the original piece ofaeologists usually want to figure out how big the original piece ofery was, as that can tell them something about who might havee 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?

Nombor PerdanaONTOH AKTIVITI

Bagaimana cikgu mengajarNombor Perdana?


FAKTORBIL.

FAKTOR

KUMP NO. FAKTORBIL.

FAKTOR

KUMP

141516161718191920212223242425


FAKTORBIL.

FAKTOR

KUMP NO. FAKTORBIL.

FAKTOR

KUMP

1 1 A1,2 2 B1,3 2 B

14 1,2,7,14 415 1,3,5,15 416 1,2,4,8,16 51,3 2 B

1,2,4 31,5 2 B

1 2 3 6 4

16 1,2,4,8,16 517 1,17 2 B18 1,2,3,6,9,18 619 1 19 2 B1,2,3,6 4

1,7 2 B1,2,4,8 4

19 1,19 2 B20 1, 2, 4,5,10,20 621 1,3,7,21 4

1,3,9 31,2,5,10 4

1 11 2 B

22 1,2,11,22 423 1,23 2 B24 1 2 3 6 8 12 71,11 2 B

1,2,3,4,6,12 624 1,2,3,6,8,12,

247

ONTOH AKTIVITI

How many one‐by‐one tiles are required to surround a 5x5 pool?p

Develop a generalization that predicts the number of tiles required to surround a square pool of any sizerequired 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 kM k k M l hM l h R tR t k dk dMenukarkanMenukarkan MasalahMasalah RutinRutin kepadakepadaMasalahMasalah BukanBukan RutinRutinMasalahMasalah BukanBukan RutinRutin

MASALAH RUTIN KEPADA BUKAN RUTINMASALAH RUTIN KEPADA BUKAN RUTIN

Maria membeli sekotak susu dengan harga

TUGASAN 1g g

RM1.55 dan sebungkus biskut dengan hargaRM1.70. Berapakah jumlah wang yang dibayaroleh Maria?

OTS

oleh Maria?

TUGASAN 2Maria membeli sekotak susu dengan hargaRM1.55 dan sebungkus biskut dengan hargaRM1 70 Di b ik RM4 00 k d

TUGASAN 2

HOTS RM1.70. Dia memberikan RM4.00 kepadajurujual. Berapakah bilangan syiling yang diterima oleh Maria sekiranya jurujual itu

b ik b b ili 5 10

HOTS

memberikannya beberapa syiling 5 sen, 10 sendan 20 sen? Terangkan jawapan anda?

TUGASAN 2


Mamat ingin membina pagar bagireban ayam yang berbentuk segi

TUGASAN 2HOTS

reban ayam yang berbentuk segiempat. Dia mempunyai 20 meter wayar pagar. 1. Apakah saiz segiempat yang

TUGASAN 1

Cari perimeter segi empattepat yang mempunyaipanjang 8 meter dan lebar 17

boleh beliau hasilkan?2. Bentuk manakah yang terbaik?

p j gmeter.Cari panjang sebuah segiempat tepat yang

LOTSmempunyai luas 48 meter persegi dan lebar 6 meter.

LOTS

SOALAN 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 Bolehkah sisiempat mengandungi empat sudut

cakah? Bagaimana anda tahu? Bolehkah segitiga mengandungi lebih daripada

t d t k h? T ksatu sudut cakah? Terangkan. Bolehkah sisiempat mengandungi dua sudut

cakah? Sekiranya boleh, lukiskan rajah. y jSekiranya tidak, terangkan.

Bolehkah sisiempat mengandungi tiga sudutcakah? Sekiranya boleh lukiskan rajahcakah? Sekiranya boleh, lukiskan rajah. Sekiranya tidak, terangkan.


Bundarkan 726 kepada ratusyang terdekat?

LOTS

yang terdekat?

A k h b b l hHOTS Apakah nombor yang bolehdibundarkan kepada 700?

HOTS

SOALAN RUTIN SOALAN BUKAN RUTIN

MASALAH RUTIN VS. BUKAN RUTINMASALAH RUTIN VS. BUKAN RUTINSOALAN RUTIN SOALAN BUKAN RUTINTidak memerlukanmurid untukmenggunakan

• Memerlukan tahap pemikiran pada aras tinggi.• Meningkatkan kemahiran menaakul.

menggunakankemahiran berfikirpada aras tinggi.Operasi yang perlu

• Jawapan dan prosedur yang perlu digunakantidak serta merta jelas.

• Menggalakkan lebih daripada satu caraOperasi yang perludigunakan adalahelas.

gg ppenyelesaian dan strategi.

• Terdapat lebih daripada satu jawapan.• Lebih mencabarLebih mencabar.• Berupaya membentuk murid yang kreatif dan

inovatif• Penyelesaian memerlukan lebih daripada• Penyelesaian memerlukan lebih daripada

membuat keputusan dan memilih operasimatematik.

• Memerlukan masa yang sesuai untuky gdiselesaikan.M gg l kk bi g d l k l

SkemaSkema PemarkahanPemarkahanSkemaSkema PemarkahanPemarkahanTIMSS & PISATIMSS & PISATIMSS & PISATIMSS & PISA

SKEMASKEMA PEMARKAHAN TIMSSPEMARKAHAN TIMSS

SKEMASKEMA PEMARKAHAN PISAPEMARKAHAN PISA

Tidak semua tugasan sama, tugasan yang berbezag , g y gmenggalakkan tahap dan jenis pemikiran yang berbeza.

Tahap pemikiran diidmana murid

melibatkan diriakan menentukan

tahap pembelajaranmereka.

ERBINCANGAN DALAMERBINCANGAN DALAMERBINCANGAN DALAM ERBINCANGAN DALAM UMPULAN KECIL: UMPULAN KECIL: engembangkan Soalan Rutin(LOTs) engembangkan Soalan Rutin(LOTs) epada Bukan Rutin(HOTs)

1. Bentukkan kumpulan 2 orang.

2. Tukarkan soalan rutin yang diberikepada soalan bukan rutin.

Kembangkan soalan berikut agar menjadisoalan bukan rutin

1) 825 5 =

soalan bukan rutin.

1) 825 5 =2) Cari perimeter bagi rajah dibawah.

8 cm8 cm

3 cm

3) Cari min, median dan mod bagi data berikut:15, 16, 18, 37, 39

4) Cari isi padu kotak yang mempunyaidimensi 4 cm x 2 cm x 8 cmdimensi 4 cm x 2 cm x 8 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?the packages? How do you know?

2) Is it possible for two rectangles to have an area of 24 sq b t h diff t i t ? E l i h k 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.

Tindakan Susulan GuruTindakan Susulan Guru

• Adakan taklimat dalaman di sekolah masing-gmasing kepada semua guru Sains dan Matematik.

• Gunakan kandungan dan tempoh masa taklimatti dit iseperti yang diterima.

• Semua guru Sains dan Matematik menggunakansoalan HOTs dalam pdp.soala O s dala pdp.

• Guru Sains dan Matematik Tingkatan 1 mulamenyediakan murid untuk Gerak Gempur HOTsSM

d J d Okt 2013 & 2014 t k dipada Jun dan Okt 2013 & 2014 untuk persediaanmurid ke TIMSS 2014 dan PISA 2015.

• Soalan dan skema Gerak Gempur akan disediakanSoalan dan skema Gerak Gempur akan disediakansecara berpusat dan pelaporan perlu disediakan.

TERIMA KASIHTERIMA KASIH

higher order thinking skills in science & mathematics ... · pdf filehigher order thinking...

Documents