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