LESSON 6: Problem Solving and Reasoning

Problem solving

It is the ability to make choices, interpret, formulate, model and investigate problem situations, and communicate solutions effectively.

Reasoning

The sophisticated capacity for logical thought and actions, such as analyzing, proving, evaluating, explaining, inferring, justifying, and generalizing.

Deductive reasoning

The process of reaching a conclusion by applying general assumptions, procedures, or principles

Premises

These are the general ideas used in reasoning.

Deductive arguments

These are meant to prove a conclusion.

False

The conclusion of Inductive reasoning is right if it can be proven by recognized rules, laws, theories, and other widely accepted truths. True or False?

Syllogism

The most basic form of deductive reasoning in practice is the ______.

Syllogism

This is where two premises that share some idea support a conclusion.

Deductive reasoning

The theorem below shows what type of reasoning?

If: A=B and C=A, then B=C

Inductive reasoning

This reasoning is a process of reaching a general conclusion by examining specific examples.

Conjecture

This is the conclusion which may or may not be correct.

Inductive reasoning

It uses specific observations before reaching into a conclusion.

True

Inductive reasoning is usually used when making predictions, creating generalizations, and analyzing cause and effect. True or False?

Inductive arguments

These are meant to predict a conclusion and try to show that the conclusion is probable based on the given premises.

Counterexample

If you can find one case for which a statement is not true, it is called _______.

Intuition

It is the ability to understand something instinctively, without the need for conscious reasoning.

Mathematical proof

It is an argument, which convinces other people that something is true.

Proof

It is an inferential argument for a mathematical statement.

Certainty

It is a total continuity and validity of inquiries to the highest degree of precision. It is a conclusion that is beyond doubt.

George Polya

He is one of the foremost recent mathematicians to make a study of problem solving

Hungary

Where was Polya born?

United States

Where did Polya moved in 1940?

Stanford University

Which university Polya moved in 1942 and taught until his retirement?

10 books

How many books did Polya published during his stay at Stanford University?

How to Solve It (1945)

What is one of the best known book of Polya?

Understand the Problem

What is the 1st step in Problem-Solving strategy of Polya?

Devise a Plan

What is the 2nd step in Problem-Solving strategy of Polya?

Carry Out the Plan

What is the 3rd step in Problem-Solving strategy of Polya?

Review the Solution

What is the 4th step in Problem-Solving strategy of Polya?

Guess and Check, Act it Out, Draw, List / Tabulate

What are the 4 Problem-Solving strategies?

Sequence

This is an ordered list of numbers.

Comma

What is used to separate numbers in a sequence?

Terms of the sequence

These are the numbers in a sequence separated by commas.

1st term of a sequence

a₁ represents what?

nth term of a sequence

aₙ represents what?

aₙ = 3n - 1

What is the nth term formula for the sequence below?

ex: 2, 5, 8, 11 . . .

23

What is the eighth term of the sequence?

ex: 2, 5, 8, 11 . . .

107

What term of the sequence is 320?

ex: 2, 5, 8, 11 . . .

Recreational Mathematics

This is mathematics carried out for recreation or entertainment rather than as a strictly research and application-based professional activity.

Math puzzles and Riddles

These are fun and interesting, and they help improve problem solving skills and thinking capacity.

Inductive reasoning

Determine the type of reasoning:

During the past 10 years, a tree has produced plums every other year. • • •Last year, the tree did not produce plums.

•So, this year the tree will produce plums.

Deductive reasoning

Determine the type of reasoning:

All students need an internet connection these days.

•Juan is a student.

•Therefore, Juan needs an internet connection.