22M:006 Logic of Arithmetic                 3 s.h.

Mathematical and conceptual foundations of the natural numbers used in elementary school arithmetic teaching. Includes multiple algorithmic approaches to arithmetic and their mathematical and contextual relationships, extensions to integers, rational and irrational numbers, multiple representations.

GE: quantitative or formal reasoning- recommended by the GECC
 

Prerequisite: 22M:001 Basic Algebra or satisfactory score on math placement exam or equivalent or consent of instructor.

Discussion: This is a new course at about the level of 22M:004. Assuming the course is approved for GE credit, Education plans to require it of all elementary education majors except those specializing in mathematics who will take 22M:012. This class will be offered in a large lecture/discussion format 2-2.

22M:012 Theory of Arithmetic                 3 s.h.

Sets, cardinalities, reasoning in proofs, counterexamples, arithmetic with integers, rationals, irrationals, number theory, functions and algebraic expressions. Open only to elementary teaching certificate candidates and certified elementary teachers; or others with consent of department chair.

GE: quantitative or formal reasoning- recommended by the GECC

Prerequisite: 22M:009 Elementary Functions or satisfactory score on math placement exam or equivalent or consent of instructor.

Discussion: This course will be at a slightly higher level than our present 22M:004 which it will replace. It is intended for elementary education majors specializing in mathematics. It will be taught in the same format as 22M:004 (a single class meeting three times a week).