Syllabus
Course Title: Mathematics for Teaching – Algebraic Reasoning
Course Number: MTHE 6760
Course Credit Hours: 3 credit hours
Prerequisites: Elementary teaching experience
Catalog Description:
Provides practicing teachers a deeper understanding of algebraic expressions, equations, functions, real numbers, and instructional strategies to facilitate the instruction of this content for elementary students.
Course Objectives:
During this course teachers will:
· Demonstrate in-depth knowledge of problem-solving and reasoning using algebraic notation and functions.
· Use a variety of tools, technology, and mathematical representations to explore and model algebra and functions concepts.
· Make connections among mathematical topics, concepts, and real-world situations.
· Communicate algebraic ideas orally, visually, and in writing, as well as facilitate effective discourse related to these topics in a positive mathematics learning environment.
Suggested Texts:
Parker, T. H. & Baldridge, S. J. (2004). Elementary mathematics for teachers. USA: Sefton-Ash Publishing. Chapters 1-5.
Ministry of Education, Singapore (1981). Primary Mathematics 1A-6A,Marshall Cavendish Education, 2003.
References:
Course Coverage:
1. Algebraic Symbols: introduce use of variables, write expressions to represent mathematical relationships, simplify expressions (add, subtract, multiply, divide, use associative, commutative, and distributive properties), factor, rational exponents, laws of exponents, recognize the difference between expressions and equations.
2. Real Number System: represent the nested nature of real numbers, introduce rational and irrational numbers, fractional exponents, real number line, emphasize different representation of numbers and their relationships.
3. Equations and Inequalities: solve linear equations and inequalities with fluency, solve and graph applications of linear equations and inequalities. Solve and graph systems of linear equations and inequalities. Solve and graph quadratic equations.
4. Patterns: extend and generalize patterns using explicitly defined and recursively defined formulas, arithmetic sequences (general term, missing terms, sum), geometric sequence (general term, missing terms, finite and infinite sum).
5. Functions: define relations and functions, use multiple representations for relations and functions, find the sum, difference, multiplication and division of functions, graph functions and analyze zeros, intercepts, rates of change, local and global behavior and perhaps asymptotes, linear functions and their graphs ( slope, point-slope formula, parallel and perpendicular lines), quadratic functions and their graphs ( vertex, x-intercepts), applications and rate of change word problems.