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Toh Khar Peng KEW080022
Assignment 5
Critical Thinking Survey
1.)
i.) Thinking
thinking is mental activity which allows beings to model the world, and so to deal with the world effectively according to their own goals, plans, ends and desires. Thinking is manipulating information, as when we form concepts, engage in problem solving, reason and make decisions
ii.) Critical Thinking
Critical thinking is the purposeful and reflective judgement about what to believe or what to do in response to observations, experience, verbal or written expressions, or arguments. Critical thinking involves determining the meaning and significance of what is observed or expressed, or, concerning a given inference or argument, determining whether there is adequate justification to accept the conclusion as true.
iii.) Creative Thinking
Looking at problems or situations from a fresh perspective that suggests unorthodox solutions (which may look unsettling at first). Creative thinking can be stimulated both by a freewheeling (unstructured) process such as brainstorming, and by a step by step (structured) process such as lateral thinking.
iv.) Mathematical Thinking
mathematical thinking is a way to solve 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
Lateral thinking is a term coined by Edward de Bono, for the solution of problems through an indirect and creative approach. Lateral thinking is about reasoning that is not immediately obvious and about ideas that may not be obtainable by using only traditional stepbystep logic
2.) Have you ever being taught critical thinking in school or before entering the faculty of engineering?
No. But I have learnt from the book I found in bookstore and had been applying it without knowing it was critical thinking that I was applying.
3.) What do you understand by “analysis”?
Analysis is the process of breaking a complex topic or substance into smaller parts to gain a better understanding of it..
i.) What do you do when you analyze an argument?
When an argument is a fact or statement put forth as proof or evidence, we 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?
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?
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).
When the solution of 4x3 – x4 and equals a positive integer, this means that the value of x must be smaller than 4. This is due to 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. So 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?
An inductive reasoning 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.
From above, we can 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.
A deductive argument which is invalid or has one or more false premises or both is said to be not sound. 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?
I think the most common way of both of it is 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?
I think the similarities between two are there is more than one solution to a problem, and solving question part by part.
7.) Have you being taught how to think mathematically in school or in your engineering mathematics courses?
No, never. Although I have taking so many mathematics courses in schools but I never been taught to think mathematically, and I was given a lot of mathematics questions in those courses but never been 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, definitely. The mathematics is a very important field for engineers, as an undergraduate 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?
Be able to think critically, mathematically and inductively to solve and find more than one solution to a problem. And solve it part by part, it is solving in mathematics.
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?
Yup, it is a must. Both kinds of thinking skills are important for engineers. Critical thinking will allow engineers to be able to think out of the box and not just solving a particular problem in normal way. And mathematical thinking will let the 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 xaxis on the curve y = ln x? Explain your solution.
In 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 xaxis does not exist.
Assignment 5
Critical Thinking Survey
1.)
i.) Thinking
thinking is mental activity which allows beings to model the world, and so to deal with the world effectively according to their own goals, plans, ends and desires. Thinking is manipulating information, as when we form concepts, engage in problem solving, reason and make decisions
ii.) Critical Thinking
Critical thinking is the purposeful and reflective judgement about what to believe or what to do in response to observations, experience, verbal or written expressions, or arguments. Critical thinking involves determining the meaning and significance of what is observed or expressed, or, concerning a given inference or argument, determining whether there is adequate justification to accept the conclusion as true.
iii.) Creative Thinking
Looking at problems or situations from a fresh perspective that suggests unorthodox solutions (which may look unsettling at first). Creative thinking can be stimulated both by a freewheeling (unstructured) process such as brainstorming, and by a step by step (structured) process such as lateral thinking.
iv.) Mathematical Thinking
mathematical thinking is a way to solve 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
Lateral thinking is a term coined by Edward de Bono, for the solution of problems through an indirect and creative approach. Lateral thinking is about reasoning that is not immediately obvious and about ideas that may not be obtainable by using only traditional stepbystep logic
2.) Have you ever being taught critical thinking in school or before entering the faculty of engineering?
No. But I have learnt from the book I found in bookstore and had been applying it without knowing it was critical thinking that I was applying.
3.) What do you understand by “analysis”?
Analysis is the process of breaking a complex topic or substance into smaller parts to gain a better understanding of it..
i.) What do you do when you analyze an argument?
When an argument is a fact or statement put forth as proof or evidence, we 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?
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?
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).
When the solution of 4x3 – x4 and equals a positive integer, this means that the value of x must be smaller than 4. This is due to 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. So 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?
An inductive reasoning 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.
From above, we can 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.
A deductive argument which is invalid or has one or more false premises or both is said to be not sound. 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?
I think the most common way of both of it is 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?
I think the similarities between two are there is more than one solution to a problem, and solving question part by part.
7.) Have you being taught how to think mathematically in school or in your engineering mathematics courses?
No, never. Although I have taking so many mathematics courses in schools but I never been taught to think mathematically, and I was given a lot of mathematics questions in those courses but never been 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, definitely. The mathematics is a very important field for engineers, as an undergraduate 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?
Be able to think critically, mathematically and inductively to solve and find more than one solution to a problem. And solve it part by part, it is solving in mathematics.
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?
Yup, it is a must. Both kinds of thinking skills are important for engineers. Critical thinking will allow engineers to be able to think out of the box and not just solving a particular problem in normal way. And mathematical thinking will let the 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 xaxis on the curve y = ln x? Explain your solution.
In 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 xaxis does not exist.
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