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SIFAT MATEMATIK

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SIFAT MATEMATIK THE NA TURE OF MA THEMATICS
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SIFAT MATEMATIK

THE NATURE OF MATHEMATICS

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SIFAT MATEMATIK

• Penyelesaian masalah

• Logik / mantik

• Perkiraan (Calculation)

• Sistem nombor

• Sukatan

• Algebra

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STANDARD MATEMATIK NCTM

• NCTM’s thinking mathematics standards

 – Problem solving (Penyelesaian masalah)

 – Communication (Komunikasi)

 – Reasoning (Penaakulan)

 – Making connections (Membuat perkaitan)

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THE HEART OF MATHEMATICS.

• Through problem solving, children learn thatthere are many different ways to solve aproblem and that more than one answer is

possible. It involves the ability to explore,think through an issue, and reason logically tosolve routine as well as non-routine problems.In addition to helping with mathematical

thinking, this activity builds language andsocial skills such as working together.

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Penyelesaian Masalah

• Apa itu masalah?

 – 2+2=?

 – 12x34=?

• Apakah yang andafaham tentang

masalah?

• Bagaimana anda

menakrifkan sesuatu

masalah matematik?

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Proses Penyelesaian Masalah

• Apabila berhadapan

dengan situasi

bermasalah, anda perlu

 –berfikir untuk mencaripenyelesaian

 – menggunakan satu

model penyelesaian

masalah yang berkesan

• Apakah model

penyelesaian masalah

yang anda ketahui atau

pernah gunakan?

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Model Polya

• Apakah langkah-langkah

dalam Model Polya?

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Rumusan

• Penyelesaian masalah

 – merupakan suatu proses

 – perlu berfikir

(memahami situasi,organise data)

 – kegunaan model boleh

membantu

 –

perlu menguasaipelbagai strategi

• Apakah strategi-strategi

penyelesaian masalah

yang anda tahu?

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Men at Work

Two men, working at the

same rate, took 5 days to

lay the bricks of a wall. If 

the rate of one man wasdoubled and that of the

other man was halved,

how long would they have

taken to finish the wall?

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A Simple Solution

Day 1

Day 5

1st workman 2nd workman

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After Day 1

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After Day 2

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After Day 3

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After Day 4

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Refleksi

• Adakah anda

 – Memahami masalah

yang diberikan?

 –

Merancang satu pelantindakan / strategi yang

baik?

 – Melaksanakan pelan

tindakan yang

disediakan?

 – Menyemak jawapan

anda?

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PROBLEM SOLVING

Polya’s Model (How to solve it)

1. Understand the problem

2. Devising a plan

3. Carrying out the plan

4. Looking back

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MATHEMATICAL LOGIC

• Reasoning is used to think through a question

and come up with a useful answer. It is a

major part of problem solving.

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LOGIK

• Penaakulan induktif 

• Penaakulan deduktif 

• Pemikiran mantik

(Operators and laws of logic)

• Bukti matematik

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REASONING

• Inductive reasoning

 – First observing patterns then predicting the

answers to more complicated problems

 – Reasoning from particular facts or cases to a

general conjecture

 – A generalisation made based on observed

occurrences – Also called the scientific method

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REASONING

• Deductive reasoning

 – Reaching a conclusion based on a given set of 

assumptions or premises

 – A general axiom is given to the learner eg

“Triangles are closed, three-sided figures”

 – The learner considers a given figure and if the

figure contains the features of a triangle withcertainty, a conclusion is then made eg “Figure

ABC is a triangle”

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NOMBOR & PERKIRAAN

(NUMBERS & CALCULATION)

• Sistem nombor

 – Mesir / Babylon

 – Hindu-Arab

• Alat perkiraan

• Nombor

 – Nombor asli

 – Nombor perdana

 –Nombor integer

 – Nombor nisbah

 – Nombor tak nisbah

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NUMBERS

• Number sense and numeration: Number

sense is much more than merely counting, it

involves the ability to think and work with

numbers easily and to understand their usesand relationships. Number sense is about

understanding the different uses for numbers

(describe quantities and relationships,informational tools).

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MATHEMATICAL CALCULATION

• Number sense is the ability to countaccurately and competently, to seerelationships between numbers, and to be

able to take a specific number apart and put itback together again.

• It is about counting, adding, and subtracting.Counting and becoming familiar with numberswill help children understand all other aspectsof math.

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MEASUREMENT

• Measurement is finding the length, height,

and weight of an object using appropriate

units. Time is measured using hours, seconds,

and minutes.

• Measurement is an important way for young

children to look for relationships in the real

world.

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ALGEBRA

• Polinomial

• Pemfaktoran

• Persamaan

• Ketaksamaan

• Nisbah, perkadaran

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SUKATAN & UKURAN

• Perimeter

• Luas

• Luas permukaan

• Isipadu


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