hots matematik

7/28/2019 Hots Matematik

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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.



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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.



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Termasuk

pemikiran kritikal,

pemikiran kreatif,

pemikiran logikal,pemikiran reflektif dan

meta-kognitif.


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.pdf


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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.pdf


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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)
http://localhost/var/www/apps/conversion/tmp/scratch_6/TCM2007-02-308a.pdfhttp://localhost/var/www/apps/conversion/tmp/scratch_6/TCM2007-02-308a.pdf


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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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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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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



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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


HOTS

LOTS



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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.




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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

hots matematik

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