mte - nature of mathematics

7/27/2019 MTE - Nature of Mathematics

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Mathematics Education


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Nature of Mathematics

Nature of problem

solving Nature of logic

Nature of

calculation Nature of numbers

Nature of measurement
http://g/nature%20in%20math.flv


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Nature of Problem solving

In Mathematics, problem solving generally involvesbeing presented with a written out problem in whichthe learner has to interpret the problem, devise amethod to solve it, follow mathematical procedures toachieve the result and then analyze the result to see ifit is an acceptable solution to the problem presented.

Problem solving is an important component ofmathematics education which is an easy way toconsistently arrive at effective and satisfying solutions.

Polyas Model which is developed by George Polya. It

plays a important role for problem solving.


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4 steps:

1. Understand the problemYou must read the problem carefully.

Identify which quantity the problem is

asking you to solve for.2.Devise a plan

Polya mentions that there are many

reasonable ways to solve problems. The skillat choosing an suitable strategy is best

learned by solving many problems.


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A partial list of strategies:

Look for a pattern

Draw a picture

Guess and checkSolve a simpler problem

Use a model

Use a formula

Use algebra


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3. Carry out the plan

Carrying out your plan of thesolution, check each step

4. Look back.

Examine the solution obtained. Does the

answer you found seem reasonable?


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Example of problem solving :

The subscription fee of a club for men and womenare in the ratio 4:3. There is a group of 2 men and 5

women who paid RM 4600 as the total subscriptionfee. How much is the subscription fee for a man?

Step 1: Understanding the problem.

The ratio is 4:3 for man and women. The totalsubscription fee is RM 4600 for 2 men and 5 women.We have to find out the subscription fee for a man.

Step 2: Devise a plan.Since the ratio for men and women is 4:3 and RM4600 is the total subscription fee for 2 men and 5women, we can use algebra to solve this problemaccording to this equation.


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Strategy 1 : Using Algebra

Lets say that x = man and y = woman,

x : y = 4 : 3

x / y = 4 / 3

4y = 3x

y = 3/4 x

The total subscription fee for 2 men and 5 women is RM 4600, thus:

2x + 5y = 4600

2x + 5 (3/4 x) = 4600

2x + 15/4 x = 4600

x (2 + 15/4) = 4600

x (23/4) = 4600x = 4600 4/23

x = 800

Answer: The subscription fee for a man is RM 800.


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Step 4: Looking back.

1 man = RM 800

2 men = RM 800 x 2= RM 600

= RM 1600

1 woman = RM 200 x 35 women = RM 600 x 5

= RM 3000

The total subscription fee

= RM 1600 + RM 3000

= RM 4600


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Nature of Logic

Logic - the study of the principles of correctreasoning.

The word logic originally derived from theGreek word logos.

Aristotle- the first philosopher organized thelaws of reasoning.


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Divided into two main categories:

Inductive reasoning

Deductive reasoning

Inductive reasoning (inductive logic) is a type

of reasoning that involves moving from a set of

specific facts to a general conclusion.

1+3=4 (even number)

5+11=16 (even number)

Therefore, an odd number added to another

odd number will result in an even number.

Induction


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Deductive reasoning (deductive logic)

is reasoning which constructs or evaluates

deductive arguments.

A deductive argument is valid if and only ifthe

truth of the conclusion actually does follow

necessarily.

All men are mortal

John is a man

John is mortal

Deduction


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Nature of Calculation

A calculation is a deliberate process for

transforming one or more inputs into one or

more results, with variable change.

Arithmetical calculation is an oldest and most

elementary branch of mathematics used by

almost everyone.

It involves the study of quantity, especially as

the result of combining numbers.


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In common usage, it refers to the simpler

properties when using the traditional

operations of addition, subtraction,multiplication and division with smaller values

of numbers.

Addition (mathematical process ofcombining quantities)

Subtraction (inverse of addition)

Multiplication (repeated addition)

Division ( inverse of multiplication)


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Other calculations which are involving of use

of algebra formulas:

Laws of exponents

Quadratic formulaBinomial theorem


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Nature of Numbers

Natural numbers (counting numbers)

In our daily life, we often use the numbers

1,2,3,4 for counting the number of things

or objects.

For example, we mention 3 apples, 5 meters

of cloths, 10 liters of oil , sunflower with 34

petals and so on.

Sunflower with 34

petals
http://g/nature%20n%20numbers.flv


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Prime numbers( 2, 3, 5, 7, )

Integrals is the number include zero and

negative number

Rational numbers is the sets of number

that in the form of m/n Irrational number is the numbers which

are not rational numbers. Irrational

number are often found in the solutionof algebra equations. (etc: X^2 = 2)


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Nature of Measurements

To measure an object is assign a number to its

size. The number representing its lineardimension, as measured from end to end, is

called its measure or length.

To measure length, we use meter (m),centimeter (cm), kilometer (km) and others.

Perimeter

Area Volume

Capacity


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Discrete Quantity

Half a chair is not also a chair; half a tree is

not also a tree; and half an atom is surely not

also an atom. A chair, a tree, and an atom

are examples of a discrete unit.

A discrete unit is indivisible, in the sense

that if it is divided, then what results will notbe that unit, that thing, any more -- half a

person is not also a person


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To determine how much there is of a discrete

quantity, one simply has to count the number

of items in a collection. For example ,one

person, two, three, four, and so on.

In addition, a collection of discrete units will

have only certain parts. For example ten

people can be divided only in half, fifths, and

tenths. You cannot take a third of them.
http://www.themathpage.com/areal/ratio-natural-numbers.htmhttp://www.themathpage.com/areal/ratio-natural-numbers.htm


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Continuous Quantity

A continuous quantity is nothing to count andIt is not a numberof anything.

To determine how much there is of a

continuous quantity, however, one mustmeasure it.

That distance is not made up of discrete units.

There is nothing to count. It is not a numberof

anything.

That means that as we go from A to B, the

line "continues" without a break.

A B
http://g/Discrete%20Quantity%20and%20Continuos.pptxhttp://g/Discrete%20Quantity%20and%20Continuos.pptxhttp://g/Discrete%20Quantity%20and%20Continuos.pptxhttp://g/Discrete%20Quantity%20and%20Continuos.pptxhttp://g/Discrete%20Quantity%20and%20Continuos.pptx


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The End!

Thank You!

mte - nature of mathematics

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