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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