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1. What do understand by
(i) Thinking

Answer:
Thinking is to analyze, examine and sort out information and form in the mind idea or opinions, to perform any mental operation, to reason, to bring to mind or recollect, to determine, resolve and to work things out. Thinking also is the out of reasoning from factual knowledge and evidence. Thinking is to use the mind for processing imagination and information, to arrive at logical conclusions, from premises know and assumed to be true for making imaginative decision.

(ii) Critical Thinking

Answer:
Critical thinking is characterized by a watchful, exact and repeat evaluation and judgment, to conduct a serious search, to read and contemplate before making a decision, ofr forming an opinion. Critical thinking is to consider carefully, at length and evaluate all the angles, before reaching the crucial and decisive point of decision making. Critical thinking is to lineup all the essential critical elements of the subject matter in question, and cautiously analyzes them one by one, over and over again, before deliberating and rendering a decision.

(iii) Creative Thinking

Answer:
Creative is the ability to image or invert something new. Creative thinking is the thinking to accept change and newness, a willingness to play with the ideas and possibilities, a flexibility of outlook, while looking for ways to improve it. Creative thinking is described as making and communicating connection to think of many possibilities, think and experience in various ways and use different point of view; think of new and unusual possibilities, and guide generating and selecting alternatives. Critical thinking is described as analyzing and developing possibilities to compare and contrast many ideas; improve, refine ideas and provide a sound foundation for effective action.

(iv) Mathematical Thinking

Answer:
Mathematical thinking involves sorting objects by different traits, using words to describe things and what they are use for; Identifying and copying simple patterns; using words to talk about position( over, in, top, etc); counting object and using words to communicate an understanding of number of relationships( more, less, etc).

(v) Lateral Thinking

Answer:
Lateral thinking is about reasoning that is not immediately obvious and about ideas that may not be obtainable by using only traditional step by step logic. Lateral thinking, is the ability to think creatively, or “outside the box”. Lateral thinking involves discarding the obvious, leaving behind traditional modes of though, and throwing away preconceptions.

2. Have you ever being thought critical thinking in school or before entering the faculty of engineering?

Answer: no

3. What do you understand by ‘analysis’

Answer: Analysis is the process of breaking a complex topic or substance into smaller parts to gain a better understanding of it.

What do you do when you analyze
(i) Argument

Answer: First I will identifying the argument, take argument to be list of statement, one of which is conclusion and others are premises of the argument. Check the validity and soundness; the conclusion should be follow premises. Find out the patterns of valid argument because valid argument may have a false conclusion and identifying hidden assumptions.

(ii) Reasoning

Answer: Ignore the content of the argument and focuses on the form or structure of the argument.

(iii) Claims

Answer: First step is to identify the claim. Second step is to examine the claims to see if the writer uses any qualifiers. Final step is to examine the claims for exception, determine what the writer consider to be the situations in which the claim doesn’t apply.





Could you analyze this problem?
Solve the equation 4x3 – x4 = 30. If there is no solution give reasons.

Let y = 4 x3 – x4
y’ = 12 x2 – 4 x3
y’=0
12 x2 – 4 x3 = 0
x2 (12 – 4x) = 0
x= 0, 3
y’’ = 24x – 12x2
when x=3 y’’=-36 (max point)
ymax = 4(3)3 - 34
= 108 -81
= 27
Since the max y is 27 so the equation is no solution.

4. What do you understand by
(i) Inductive reasoning in mathematics. Why is it useful to reason inductively in mathematics

Answer: Inductive reasoning is a type of reasoning that involves moving from a set of specific facts to a general conclusion. The premises of an inductive logical argument indicate some degree of support for me conclusion but do not entail it. Inductive reasoning in mathematical is very useful for making a conclusion for what type of the answer will be through the pattern of the question, example
3 + 5 = 8
So conclusion is any addition of two odd number will come out a even number.

(ii) Inductive argument. Give example.

Answer: One in which is impossible for the premises to be true but the conclusion false. Thus the conclusion follows necessarily from the premises and inferences.
Example : all men are mortal ( premise)
Socrates was a man (premises)
Socrates was mortal (conclusion)
If one of the premises is false, then the conclusion will also be false.





(iii) Deductive argument. Give example.

Answer: One in which the premises are supposed to support the conclusion in such a way that if the premises are true, it is improbable that the conclusion would be false. Thus the conclusion follows the probably from the premises and inferences.
Example: Socrates was Greek (premise)
Most Greeks ate fish premise)
Socrates ate fish conclusion)
Even both premise true, the conclusion may be false.

5. What do you notice in common about inductive reasoning in mathematics and inductive argument in real life situation?

Answer: In real life most of the thing is related to inductive reasoning and also inductive argument. Before any decision is making we will analysis the problem first and assume different situation might happen, so that a suitable conclusion can come out.


6. Where do you find the similarities in application of mathematical thinking in mathematics and in real life situation?

Answer: Such as finding the same pattern of the problem.
Example: by making a cake different size of cake need different quantity of ingredient, so that we can use scale to find out how much quantity is needed when different size of cake is making.

7. Have you being taught how to think mathematical in school or in you engineering mathematics course?

Answer: Yes. Such as finding the patterns of the problem.

8. Do you think a more in dept knowledge of mathematical thinking will help you in your engineering mathematics courses? In what way do you think?

Answer: Yes. Because most of the engineering mathematics problem are similar, we need to assume for same value to solve the problem or finding the type of answer by finding the pattern of the problem.





9. What do you understand by problem solving in mathematics?

Answer: Problem solving in mathematics where we need to understand the question, find all the clues and determine what the question is asking to find. Once understand the question and clues, use previous similar problems to look for strategies and tools to answer the question. After that, try it and see what answer come up with, go back to the problem and see whether it is really answered the question.

10. Do you think critical thinking skill should be learned by all engineering students or a combination of critical thinking and mathematical thinking and why?

Answer: Yes. Because we need it for problem solvin