Math Reasoning And Problem Solving

Question 0

What are some methods students can use to solve problems in a variety of ways?

Answer 0

Words, numbers, symbols, charts, graphs, diagrams, and concrete models can help students understand a problem better.

Question 1

How should students begin solving complex problems?

Answer 1

Identify and prioritize information. Then have students break down problem into smaller and simpler parts.

Question 2

Logical fallacies:

Circular arguments

Answer 2

Drawing a conclusion based on a premise that is itself dependent on the conclusion

Question 3

Logical fallacies:

Assuming the truth of the converse

Answer 3

The fact that A implies B doesn’t necessarily mean that B implies A.

All dogs are mammals therefore all mammals are dogs

Question 4

Logical fallacies:
Faulty Generalizations
Aka Inductive Reasoning

Answer 4

aka inductive fallacy. Assuming a rule based on specific instance

Bridge is hard so all card games are difficult

Question 5

Logical fallacies:

Faulty analogy

Answer 5

Mistaking since two things are alike in one way, they are alike in other ways, too

People who need coffee in the morning are as bad as alcoholics

Question 6

What are two types if logical proofs?

Answer 6

Direct (proving the point based on axioms)

Indirect ( proof by contradiction) reductio ad absurdum

Question 7

Syllogism

Answer 7

Deductive reasoning strategy composed of a major premise, minor premise and a conclusion

Mike knew all 4th graders shower after gym(major), and that as a 4th grader(minor), he had to shower, too.(conclusion)