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