# CHIA LI-YAN KEW080007

## CHIA LI-YAN KEW080007

1. i)

The process of using mind to consider something carefully.

ii)

An intellectual process which involves synthesizing, applying, analyzing, evaluating and conceptualizing information.

iii)

The ability to invent something new.

iv)

A cognitive approach to a problem that is both logical and mathematically sound. It allow us to solve problem and not

restrict us to saying that there is only one correct solution.

v)

Solving problem through an indirect and creative approach. It is about reasoning that is not immediately obvious and

about ideas that may not be obtainable by using only traditional step-by-step logic.

2. I have never been taught critical thinking until I take this subject.

3.

among various alternatives.

i)

Analyze premises in order to find out whether the argument is valid or invalid. If conclusion logically follows the

premises, the argument is valid.

ii)

Analyze base on logic, facts and evidence.

iii)

Use reasoning. Argument is valid if reasons justify claims.

4x^3 - x^4 = 30

x^4 - 4x^3 + 30 = 0

Because 4x^3 - x^4 equals a positive integer, x cannot be a negative integer since ‘negative integer power 3’ will get

negative answer. Substituting x=0 or x=4 will get 4x^3 - x^4 = 0. The above equation do not have solution because

the graph y_1 = x^4 , y_2 = - 4x^3 and y_3 = 30 do not intersect each other.

4. i) I

Process of reasoning that a general principle is true because the special cases that we’ve seen is true. For example

after seeing that all triangle angle’s sums are 180 degrees even for different shapes of triangle, a conclusion can be

made that triangles has angle sum of 180 degrees.

It is useful to reason inductively in mathematics because it plays a part in discovery of mathematical truth.

ii)

Most fish lay eggs.

Salmon are fish.

Therefore, salmon probably lay eggs.

It is possible for premises to be true and for conclusion to be false. Substitue Mako shark for salmon, and this would

be the case.

iii)

All fish lay eggs.

Whale is a fish.

Therefore, whales lay egg.

Both premises are factually incorrect, so the conclusion though valid, is nonsense.

5. A conclusion made base on what we’ve seen to be true.

6. There are lot of solution to a problem. We are no restricted to only one solution. All solution have their pro and cons.

7. I have never been taught how to think mathematically in school or engineering mathematics courses.

8. Yes because I will then be able to solve any kinds of mathematical problem with different solution available.

9. Analyzing the problem from different perspective. Apply deductive, inductive thinking and mathematical thinking.

10. i) Yes, all students should learn both mathematical thinking and critical thinking so that we’ll be able to solve any

problem at ease, think out of the box, be able to not just look at something the way it is, and able to apply our

knowledge in engineering field effectively.

ii) Mathematically, the tangent can be obtained to be at infinity by taking the differential of y to be 0. Therefore, the

tangent parallel to x-axis does not exist.

**Thinking**The process of using mind to consider something carefully.

ii)

**Critical Thinking**An intellectual process which involves synthesizing, applying, analyzing, evaluating and conceptualizing information.

iii)

**Creative Thinking**The ability to invent something new.

iv)

**Mathematical Thinking**A cognitive approach to a problem that is both logical and mathematically sound. It allow us to solve problem and not

restrict us to saying that there is only one correct solution.

v)

**Lateral Thinking**Solving problem through an indirect and creative approach. It is about reasoning that is not immediately obvious and

about ideas that may not be obtainable by using only traditional step-by-step logic.

2. I have never been taught critical thinking until I take this subject.

3.

**Analysis**– The examination and evaluation of the relevant information to select the best course of action fromamong various alternatives.

i)

**Argument**Analyze premises in order to find out whether the argument is valid or invalid. If conclusion logically follows the

premises, the argument is valid.

ii)

**Reasoning**Analyze base on logic, facts and evidence.

iii)

**Claims**Use reasoning. Argument is valid if reasons justify claims.

4x^3 - x^4 = 30

x^4 - 4x^3 + 30 = 0

Because 4x^3 - x^4 equals a positive integer, x cannot be a negative integer since ‘negative integer power 3’ will get

negative answer. Substituting x=0 or x=4 will get 4x^3 - x^4 = 0. The above equation do not have solution because

the graph y_1 = x^4 , y_2 = - 4x^3 and y_3 = 30 do not intersect each other.

4. i) I

**nductive reasoning in mathematics**Process of reasoning that a general principle is true because the special cases that we’ve seen is true. For example

after seeing that all triangle angle’s sums are 180 degrees even for different shapes of triangle, a conclusion can be

made that triangles has angle sum of 180 degrees.

It is useful to reason inductively in mathematics because it plays a part in discovery of mathematical truth.

ii)

**Inductive argument. Give example**.Most fish lay eggs.

Salmon are fish.

Therefore, salmon probably lay eggs.

It is possible for premises to be true and for conclusion to be false. Substitue Mako shark for salmon, and this would

be the case.

iii)

**Deductive argument. Give example.**All fish lay eggs.

Whale is a fish.

Therefore, whales lay egg.

Both premises are factually incorrect, so the conclusion though valid, is nonsense.

5. A conclusion made base on what we’ve seen to be true.

6. There are lot of solution to a problem. We are no restricted to only one solution. All solution have their pro and cons.

7. I have never been taught how to think mathematically in school or engineering mathematics courses.

8. Yes because I will then be able to solve any kinds of mathematical problem with different solution available.

9. Analyzing the problem from different perspective. Apply deductive, inductive thinking and mathematical thinking.

10. i) Yes, all students should learn both mathematical thinking and critical thinking so that we’ll be able to solve any

problem at ease, think out of the box, be able to not just look at something the way it is, and able to apply our

knowledge in engineering field effectively.

ii) Mathematically, the tangent can be obtained to be at infinity by taking the differential of y to be 0. Therefore, the

tangent parallel to x-axis does not exist.

**Chia Li - Yan KEW080007**- Posts : 30

Join date : 2010-01-11

Age : 29

Location : kuantan

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