#### Description

Reasoning and proof as addressed in the middle school curriculum. Topic include proportional reasoning, logic and proof, types of numbers, field axioms, Euclidean and non-Euclidean geometry.

#### Prerequisite

MATH212 and MATH213. Restriction: Must be in one of the following programs (Elementary Education; Special Education; Middle School Education).

#### Topics

**Mathematical reasoning: proof versus nonproof**

Nonproof and logical fallacies: Truth tables and implication, Backward or circular reasoning, Invalid proofs from pictures, Insufficient proof schemes

Incomplete or vague reasoning

**Mathematical reasoning and methods of proof**

Logical and historical development of Euclidean and non-Euclidian geometry: Axiomatic reasoning and proof, Axiomatic systems in geometry, Proof of Pythagorean theorem, law of sines, law of cosines

Forms of proof: Direct proof, Proof by contradiction, Proofs using contrapositive, Proof by mathematical induction

**Axiomatic foundations for number systems, and theory and application of rational numbers**

Logical and historical development of number systems

The role of zero

Exploration of rational number system

**Proof and argumentation underlying the foundation of middle school mathematics**

Analysis and application of problem solving involving variation and invariance: Multiplicative compensation, Additive compensation

Analysis and application of problem solving involving linear relationships

Analysis and application of problem solving involving proportional reasoning