22M:012 Theory of Arithmetic
This is a math content course, not a methods course, for students in elementary education who plan on being math specialists. Topics covered include problem solving techniques such as pattern recognition, logical deduction, the structure of numbers and arithmetic algorithms, and function and algebra concepts pertinent to elementary school teaching, sets, cardinalities, reasoning in proofs including mathematical induction and indirect reasoning, counterexamples, arithmetic with integers, rationals, irrationals, number theory, functions and algebraic expressions. The goal is to enhance prospective and current elementary teachers' understandings of the mathematical ideas underlying solutions to a wide variety of problems. To be successful in this course the student should be familiar with the material in the Arithmetic and Algebra Modules. This course typically has a small lecture format (approximately 25 students) with three hours of lecture by a faculty member. The prerequisite is 22M:009, or a satisfactory score on the math placement exam, or equivalent. This course may be used to satisfy the College of Liberal Arts and Sciences quantitative or formal reasoning requirement.