Mathematical Reasoning (Deductive VS Inductive)

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Mathematical Reasoning (Deductive VS Inductive)

Specific Learning Outcomes:

At the end of the lesson, you are expected to:

1. Distinguish inductive or deductive reasoning through identification of the statements.

2. Use reasoning skills to draw logical conclusion through induction and deduction process.

3. Apply inductive and deductive reasoning to solve problems.

Processing:

1. Which of the following best matches between the shapes in the image?

Correct Answer: D

[The arrow changes direction and the shape on the right has 1 more side than the counterpart on the left.]

2. How did you come up with that answer? This will lead to the discussion of mathematical reasoning. As observed, you get the correct answer by observing the properties/characteristics of the images, and arrived at a general rule.

3. Then we will have a discussion on "what is Mathematical reasoning and the two types of reasoning".

WHAT IS MATHEMATICAL REASONING?

It refers to the ability of a person to analyze problem situations and construct logical arguments to create both conceptual foundations and connections to be able to process the available information and solve the problem. In our daily lives, we make decisions based on our reasoning but this is a process that varies depending on the situation obtained on the ground.

There are two types of reasoning:

1. inductive reasoning

2. deductive reasoning

WHAT IS INDUCTIVE AND DEDUCTIVE REASONING?

Inductive Reasoning is the process of making general conclusions based on specific examples.

Examples:

1. Every object that I release from my hand falls to the ground. Therefore, the next object I release from my hand will fall to the ground.

2. Every crow I have ever seen is black. Therefore all crows are black.

3. Based on available data, the Earth has revolve around the sun following an elliptical path for millions of years. Therefore, the Earth will continue to revolve around the sun in the same manner next year.

Deductive Reasoning is the process of making general conclusions based on general examples.

Examples:

All men are mortal. I am a man. Therefore, I am mortal.

(General principle: If p implies q and p holds, then q must follow.)

Given two supplementary angles with one of them measuring 120 degrees, the measure of the other angle 60 degrees.

(General principle: supplementary angles add up to 180 degrees)

3. If 6x = 12, then x = 2.

(General principle: if a, b, and c are real numbers and a = b, then ac = bc.)

HOW DO YOU SOLVE PROBLEMS THROUGH REASONING?

Inductive Reasoning is a reasoning that is based on patterns you observe. If you observe a pattern in a sequence, you can use inductive reasoning to decide the next successive terms of the sequence. A conclusion you reach using inductive reasoning is called a conjecture.

Deductive reasoning usually follows steps. First, there is a premise, then a second premise, and finally an inference. A common form of deductive reasoning is the syllogism, in which two statements — a major premise and a minor premise — reach a logical conclusion.

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