Topic 3.1 REASONING INDUCTIVE AND DEDUCTIVE

a cognitive process that involves the use of logical and critical thinking to make sense of information, draw conclusions, and solve problems.

Reasoning

Reasoning is the ability to what?

analyze and evaluate evidence, arguments, and situations in a logical and systematic manner.

Reasoning plays a crucial role in what?

decision-making, problem-solving, and the formation of beliefs and opinions.

What are the two types of reasoning?

Deductive and Inductive reasoning

A top-down approach that involves drawing conclusions based on general principles, theories, or rules.

Deductive reasoning

Deductive reasoning starts with?

A general statement or premise and applies it to a specific situation to reach a specific conclusion.

A bottom-up approach that involves drawing conclusions based on specific examples, observations, or evidence.

Inductive reasoning

Inductive reasoning uses what?

A specific instances to form a general principle or hypothesis.

What are the skills involved in reasoning?

Analytical Thinking

Critical Thinking

Logical Reasoning

Problem-Solving

Decision-Making

The ability to break down complex problems or situations into smaller components, analyze their relationships, and understand their underlying patterns or structures.

Analytical Thinking

Requires questioning assumptions, identifying biases, and considering alternative perspectives.

Critical Thinking

Involves following a set of principles, rules, or logical steps to arrive at a valid and consistent conclusion.

Logical Reasoning

Involves a systematic approach, creativity, and the ability to generate and evaluate multiple solutions.

Problem-Solving

Combines critical thinking, problem-solving, and considering the potential consequences of different choices.

Decision-Making

A critical skill that enables students to analyze a given hypothesis without any reference to a particular context or meaning.

Mathematical Reasoning

What is Mathematical Reasoning in layman’s words?

when a scientific inquiry or statement is examined, the reasoning is not based on an individual's opinion. Derivations and proofs require a factual and scientific basis.

——- ——- ——- and ——- ——- are important

skills that are required to solve math reasoning questions.

Mathematical critical thinking and logical reasoning

This type of reasoning is not used in geometry, for instance, one may observe a few right triangles and conclude all triangles to be right triangles. Therefore, other mathematical tools are used to prove geometrical results.

Inductive Reasoning

This generalization is based on observation and therefore it may be false. ——- ——- is a logical guess which can be backed up by using valid reasons.

Inductive Reasoning

A Hypothesis is required or a statement that has to be true under specified conditions for deductive reasoning to be valid.

Deductive Reasoning

——- ——- is true in all cases. Therefore,——- reading is used for geometrical and mathematical proofs.

Deductive Reasoning