SIFAT MATEMATIK

THE NATURE OF MATHEMATICS

SIFAT MATEMATIK

• Penyelesaian masalah

• Logik / mantik

• Perkiraan (Calculation)

• Sistem nombor

• Sukatan

• Algebra

STANDARD MATEMATIK NCTM

• NCTM’s thinking mathematics standards

– Problem solving (Penyelesaian masalah)

– Communication (Komunikasi)

– Reasoning (Penaakulan)

– Making connections (Membuat perkaitan)

THE HEART OF MATHEMATICS.

• Through problem solving, children learn that there are many different ways to solve a problem and that more than one answer is possible. It involves the ability to explore, think through an issue, and reason logically to solve routine as well as non-routine problems. In addition to helping with mathematical thinking, this activity builds language and social skills such as working together.

Penyelesaian Masalah

• Apa itu masalah?

– 2+2=?

– 12x34=?

• Apakah yang andafaham tentangmasalah?

• Bagaimana andamenakrifkan sesuatumasalah matematik?

Proses Penyelesaian Masalah

• Apabila berhadapandengan situasibermasalah, anda perlu

– berfikir untuk mencaripenyelesaian

– menggunakan satumodel penyelesaianmasalah yang berkesan

• Apakah model penyelesaian masalahyang anda ketahui ataupernah gunakan?

Model Polya

• Apakah langkah-langkahdalam Model Polya?

Rumusan

• Penyelesaian masalah

– merupakan suatu proses

– perlu berfikir(memahami situasi, organise data)

– kegunaan model bolehmembantu

– perlu menguasaipelbagai strategi

• Apakah strategi-strategipenyelesaian masalahyang anda tahu?

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 was doubled and that of the other man was halved, how long would they have taken to finish the wall?

A Simple Solution

Day 1

Day 5

1st workman 2nd workman

After Day 1

After Day 2

After Day 3

After Day 4

Refleksi

• Adakah anda

– Memahami masalahyang diberikan?

– Merancang satu pelantindakan / strategi yang baik?

– Melaksanakan pelantindakan yang disediakan?

– Menyemak jawapananda?

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

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.

LOGIK

• Penaakulan induktif

• Penaakulan deduktif

• Pemikiran mantik(Operators and laws of logic)

• Bukti matematik

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

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 with certainty, a conclusion is then made eg “Figure ABC is a triangle”

NOMBOR & PERKIRAAN (NUMBERS & CALCULATION)

• Sistem nombor

– Mesir / Babylon

– Hindu-Arab

• Alat perkiraan

• Nombor

– Nombor asli

– Nombor perdana

– Nombor integer

– Nombor nisbah

– Nombor tak nisbah

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 uses and relationships. Number sense is about understanding the different uses for numbers (describe quantities and relationships, informational tools).

MATHEMATICAL CALCULATION

• Number sense is the ability to count accurately and competently, to see relationships between numbers, and to be able to take a specific number apart and put it back together again.

• It is about counting, adding, and subtracting. Counting and becoming familiar with numbers will help children understand all other aspects of math.

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.

ALGEBRA

• Polinomial

• Pemfaktoran

• Persamaan

• Ketaksamaan

• Nisbah, perkadaran

SUKATAN & UKURAN

• Perimeter

• Luas

• Luas permukaan

• Isipadu