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1. What do you understand by:
I. Thinking
Thinking is a mental process by which people can analyze and synthesize the surrounding and situation and then make a decision or generate an idea.
II. Critical thinking
Critical thinking is the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action
III. Creative thinking
Creative thinking is a mental process involving the discovery of new ideas or concepts, or new associations of the existing ideas or concepts, fueled by the process of either conscious or unconscious insight.
IV. Mathematical thinking
Mathematical thinking is a mental process by which people generalize and analyze problems mathematically.
V. Lateral thinking
Lateral thinking is a mental process involving 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 thought critical thinking in school or before entering the faculty of engineering?
No.
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.
What do you do when you analyze
I. Argument
An argument is a set of one or more declarative sentences (or "propositions") known as the premises along with another declarative sentence (or "proposition") known as the conclusion. When analyzing an argument, I will look at its propositions and conclusion.
II. Reasoning
Reasoning is the cognitive process of looking for reasons, beliefs, conclusions, actions or feelings. Since reasoning varies depending on people, I will carefully look at the problem and analyse it.
III. Claims
Claim is a demand for something as due, an assertion of a right or an alleged right. Since claims vary depending on people and situation, I will carefully analyze them.
Solve the equation 4x^3 – x^4 = 30. If there is no solution give reason(s).
Let y = 4x^3 – x^4 – 30
y’ = 12x^2 – 4x^3
When y’ = 0, x = 3.
When x = 3, y = 3
As x approaches infinity, y approaches negative infinity.
As x approaches negative infinity, y approaches negative infinity.
By sketching a graph, we notice that y does not intersect with the xaxis. Hence, the equation has no solution.
4. What do you understand by
I. Inductive reasoning in mathematics. Why is it useful to reason inductively in mathematics?
Inductive reasoning in mathematics is a moving from a set of specific facts to a general conclusion in mathematics. It is useful to reason inductively in mathematics because mathematics itself is a logical problem and by using inductive reasoning, mathematics can be solved.
II. Inductive argument. Give example.
An inductive argument is the 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 probably from the premises and inferences. Here is an example:
1. Socrates was Greek. (premise)
2. Most Greeks eat fish. (premise)
3. Socrates ate fish. (conclusion)
III. Deductive argument. Give example.
Arguments can be separated into two categories: deductive and inductive. A deductive argument is one in which it is impossible for the premises to be true but the conclusion false. Thus, the conclusion follows necessarily from the premises and inferences. In this way, it is supposed to be a definitive proof of the truth of the claim (conclusion). Here is a classic example:
1. All men are mortal. (premise)
2. Socrates was a man. (premise)
3. Socrates was mortal. (conclusion)
5. What do you notice in common about inductive reasoning in mathematics and inductive argument in real life situation?
The common thing is that if the premises are correct, the conclusion or outcome must be correct.
6. Where do you find the similarities in application of mathematical thinking in mathematics and in real life situation?
Both of them require analysis and sometimes logical thinking.
7. Have you being taught how to think mathematically in school or in your engineering mathematics course?
Yes.
8. Do you think a more depth knowledge of mathematical thinking will help you in your engineering mathematics course? In what way do you think?
Yes. Despite we need creative thinking to become an engineer, mathematical thinking can really give a lot of helps when facing mathematical problems.
9. What do you understand by problem solving in mathematics?
Problem solving in mathematics is a stepbystep approach of solving mathematics by using the theorem and analysis.
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?
A combination of critical thinking and mathematical thinking should be learned by all engineering students. It is because after learning critical thinking, students are able to analyze, synthesize and generalize things in their career, whereas mathematical thinking can help them to solve mathematics.
I. Thinking
Thinking is a mental process by which people can analyze and synthesize the surrounding and situation and then make a decision or generate an idea.
II. Critical thinking
Critical thinking is the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action
III. Creative thinking
Creative thinking is a mental process involving the discovery of new ideas or concepts, or new associations of the existing ideas or concepts, fueled by the process of either conscious or unconscious insight.
IV. Mathematical thinking
Mathematical thinking is a mental process by which people generalize and analyze problems mathematically.
V. Lateral thinking
Lateral thinking is a mental process involving 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 thought critical thinking in school or before entering the faculty of engineering?
No.
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.
What do you do when you analyze
I. Argument
An argument is a set of one or more declarative sentences (or "propositions") known as the premises along with another declarative sentence (or "proposition") known as the conclusion. When analyzing an argument, I will look at its propositions and conclusion.
II. Reasoning
Reasoning is the cognitive process of looking for reasons, beliefs, conclusions, actions or feelings. Since reasoning varies depending on people, I will carefully look at the problem and analyse it.
III. Claims
Claim is a demand for something as due, an assertion of a right or an alleged right. Since claims vary depending on people and situation, I will carefully analyze them.
Solve the equation 4x^3 – x^4 = 30. If there is no solution give reason(s).
Let y = 4x^3 – x^4 – 30
y’ = 12x^2 – 4x^3
When y’ = 0, x = 3.
When x = 3, y = 3
As x approaches infinity, y approaches negative infinity.
As x approaches negative infinity, y approaches negative infinity.
By sketching a graph, we notice that y does not intersect with the xaxis. Hence, the equation has no solution.
4. What do you understand by
I. Inductive reasoning in mathematics. Why is it useful to reason inductively in mathematics?
Inductive reasoning in mathematics is a moving from a set of specific facts to a general conclusion in mathematics. It is useful to reason inductively in mathematics because mathematics itself is a logical problem and by using inductive reasoning, mathematics can be solved.
II. Inductive argument. Give example.
An inductive argument is the 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 probably from the premises and inferences. Here is an example:
1. Socrates was Greek. (premise)
2. Most Greeks eat fish. (premise)
3. Socrates ate fish. (conclusion)
III. Deductive argument. Give example.
Arguments can be separated into two categories: deductive and inductive. A deductive argument is one in which it is impossible for the premises to be true but the conclusion false. Thus, the conclusion follows necessarily from the premises and inferences. In this way, it is supposed to be a definitive proof of the truth of the claim (conclusion). Here is a classic example:
1. All men are mortal. (premise)
2. Socrates was a man. (premise)
3. Socrates was mortal. (conclusion)
5. What do you notice in common about inductive reasoning in mathematics and inductive argument in real life situation?
The common thing is that if the premises are correct, the conclusion or outcome must be correct.
6. Where do you find the similarities in application of mathematical thinking in mathematics and in real life situation?
Both of them require analysis and sometimes logical thinking.
7. Have you being taught how to think mathematically in school or in your engineering mathematics course?
Yes.
8. Do you think a more depth knowledge of mathematical thinking will help you in your engineering mathematics course? In what way do you think?
Yes. Despite we need creative thinking to become an engineer, mathematical thinking can really give a lot of helps when facing mathematical problems.
9. What do you understand by problem solving in mathematics?
Problem solving in mathematics is a stepbystep approach of solving mathematics by using the theorem and analysis.
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?
A combination of critical thinking and mathematical thinking should be learned by all engineering students. It is because after learning critical thinking, students are able to analyze, synthesize and generalize things in their career, whereas mathematical thinking can help them to solve mathematics.
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