EDU 6379. Numerical Reasoning: Numbers and Operations
This course covers topics including number systems and their properties: integers, rational numbers, irrational numbers, and complex numbers; real number line; numerical base systems; significant historical developments; decimal representation; axiomatic systems and introductory group theory; set theory; cardinality; recurrence relations; prime numbers; the fundamental theorem of arithmetic; greatest common divisors; least common multiple; division algorithm; Euclidean algorithm; introductory number theory; modular arithmetic; and problem solving. In addition to advanced mathematical content that informs elementary, middle, and secondary teaching, practical models for effectively teaching numerical reasoning, number systems, and operations for EC-12 mathematics will be discussed, as will components for developing effective mentoring relationships.
EDU 6380. Algebraic Reasoning and Patterns
This course discusses functional relationships and their properties: patterns; variable expressions; definitions and properties of functions; graphs; one-to-one; invertibility; compositions; various linear, quadratic, polynomial, rational, trigonometric, exponential and logarithmic models; the fundamental theory of algebra; algebraic applications of functions in everyday life; modeling; significant historical developments; rates of change; calculus; introductory analysis; and problem solving. In addition to advanced mathematical content that informs elementary, middle, and secondary teaching, practical models for effectively teaching students about patterns, variables and functional relationships for EC-12 mathematics will be discussed, as will components for developing effective mentoring relationships.
EDU 6381. Geometry and Measurement
This course delves into Euclidean geometry and proof: axiomatic systems; definitions, theorems, postulates, proofs; similarity; proportional reasoning; constructions; measurement; spatial reasoning; plane isometries, translations, rotations, reflections; dilations; trigonometric functions; inductive/deductive reasoning; mathematical induction; symbolic logic, proofs and invalid arguments; significant historical developments; introductory topology; coordinate geometry; vectors; matrices; introduction to non-Euclidean geometries, Elliptic and Hyperbolic; and problem solving. In addition to advanced mathematical content that informs elementary, middle, and secondary teaching, practical models and available technological tools for effectively teaching students about geometry, measurement and proof for EC-12 mathematics will be discussed, as will components for developing effective mentoring relationships.
EDU 6382. Everyday Mathematics: Probability and Statistics
This course focuses on methods of representing and analyzing data: measures of central tendency and measures of dispersion; introductory combinatorics; discrete and continuous random variables; expected value; statistical foundations; inference; random samples; properties of binomial, geometric and normal distributions; law of large numbers; central limit theorem; significant historical developments; stochastic matrices; regression; and problem solving. In addition to advanced mathematical content that informs elementary, middle, and secondary teaching, practical models and available technological tools for effectively teaching probability and statistics and overcoming common student misconceptions in EC-12 mathematics will be discussed, as will components for developing effective mentoring relationships.