Ooi Tiang Chien KEW080018

Critical Thinking Survey

1.)
i.) Thinking
To think is to judge something we see and not just making blind conclusions about it.

ii.) Critical Thinking
To be able to intellectually evaluate, synthesize, analyze, conceptualize and apply data or information.

iii.) Creative Thinking
To be able to think in such a way which generates more ideas - ideas which are usable or better than the ones previously available.

iv.) Mathematical Thinking
An approach to a problem which is mathematically and logically sound. In short, it gives us the knowledge of the varieties of solutions to a problem and not just one concrete solution.

v.) Lateral Thinking
To be able to find solution for problems in an indirect and creative approach.

2.) Have you ever being taught critical thinking in school or before entering the faculty of engineering?
No. But I believe I learnt it myself and had been applying it without knowing it was critical thinking that I was
applying.

3.) What do you understand by “analysis”?
To study something by breaking them into constituent parts and study it part by part.

i.) What do you do when you analyze an argument?
Since an argument is a fact or statement put forth as proof or evidence, analyzing an argument means determining whether the statement can be used as the fact or not.

ii.) What do you do when you analyze reasoning?
Since reasoning is the use of reason, especially to form conclusions, inferences, or judgments, analyzing reasoning means determining whether the reason is suitable for that particular conclusion, inference or judgment or if there are any other better reasoning available.

iii.) What do you do when you analyze claims?
Since to claim is to state to be true, especially when open to question, analyzing a claim means to determine the claim whether it is logical to be a fact.

Analyze and solve the equation 4x3 – x4 = 30. If there is no solution give reason(s).
Since it is 4x3 – x4 and equals a positive integer, this means that the value of x must be smaller than 4. This is because if the value of x is greater than 4, 4x3 – x4 will become negative. If the value of x is negative, if can be seen that the term “4x3” will always be negative while the term “x4” will always become positive, resulting a negative value of 4x3 – x4. If x is 0 or 4, 4x3 – x4 = 0. Therefore it can be concluded that the values of x are in the range 4>x>0. There is no solution for this question.

4.) What do you understand by

i.) inductive reasoning in mathematics. Why is it useful to reason inductively in mathematics?
To reason inductively is to reason from specific facts to a general conclusion. In mathematics, to be able to generalize a problem helps us towards solving it at times. For example, take 3+5 = 8. Eight is an even number and both three and five are odd numbers. We can generalize this fact into “an addition of two odd numbers result in an even number”. This statement can help us solve a more complicated problem in mathematics.

ii.) inductive argument. Give example.
As stated above, to argue inductively is to argue from specific facts to general conclusion. An example of inductive argument is: X percent of the sample of plants have chlorophyll. Therefore X percent of the whole world’s plants have chlorophyll.

iii.) deductive argument. Give example.
Deductive argument is the opposite of Inductive argument, which is to argue from general conclusion to specific facts. For example, all who are caned learnt their lesson. X is caned. Therefore he learnt his lesson.

5.) What do you notice in common about inductive reasoning in mathematics and inductive argument in real life situation?
Both are used to help solve problems in mathematics and real life situations.

6.) Where do you find similarities in application of mathematical thinking in mathematics and in real life situation?
Both lead us to one thing: there is more than one solution to a problem.

7.) Have you being taught how to think mathematically in school or in your engineering mathematics courses?No. Not directly. I was given a lot of mathematics questions but was not taught on the ways to think mathematically or what is mathematical thinking.

8.) Do you think a more in depth knowledge of mathematical thinking will help you in your engineering mathematics courses? In what way do you think?
Yes it will. Since mathematics is an important field for engineers, as an engineer I will learn more mathematical theorems in the near future and with a deeper knowledge of mathematical thinking, I will be able to solve more problems with greater varieties of solutions. A greater variety of solutions brings about better understanding of that particular problem.

9.) What do you understand by problem solving in mathematics?
To be able to think critically, mathematically and inductively to solve and find more than one solution to a problem.

10.)
a.) Do you think critical thinking skills should be learned by all engineering students or a combination of critical thinking and mathematical thinking and why?
Both critical thinking and mathematical thinking skills are important for engineers. Critical thinking allows engineers to be able to think out of the box and not just solving a particular problem just like that. Mathematical thinking allow engineers to be able to obtain more than one solution to a problem and hence improve their knowledge for that particular problem.

b.) Can you find a tangent parallel to x-axis on the curve y = ln x? Explain your solution.
Mathematically, the tangent can be obtained to be at infinity by taking the differential of y to be 0. In reality, the term infinity does not exist. The term refers to a quantity without bound or end. Therefore, the tangent parallel to x-axis does not exist.