Thinking Like a Mathematician

Mathematical reasoning is the logical process of making sense of problems and arguments. Proofs show why something is always true, not just that it works in one case.

Logical Steps

Good reasoning follows clear steps: make a claim, support it with evidence, and draw a conclusion.

Types of Proof

• Direct Proof: Show it works step by step.
• Indirect Proof (Contradiction): Assume the opposite and find a problem.
• Counterexample: Show one case where it fails to disprove a statement.

Teaching Application

Encouraging students to explain their thinking helps them understand math deeply and communicate clearly.