Examines different conceptions of algebra as the study of (1) generalized arithmetic, (2) reasoning with symbols, (3) reasoning with patterns and functions, (4) structure in the number system, and (5) modeling. Distinguishes arithmetic from algebraic reasoning, and develops an appreciation for the pervasiveness of the function concept in the K-8 school mathematics curriculum. Features algebraic thinking and representation using algebra tiles and other concrete models, realistic problems, dynamic geometry software, graphing calculators, and a variety of virtual tools and Web sites. Topics include, but are not limited to: patterns, relations, functions and covariational thinking; multiple conceptions of quantity, variables, constants, and unknowns; inductive, deductive, and analogical reasoning; rate of change and proportional thinking; algebra learning trajectories; and comparisons of additive vs. multiplicative, absolute vs. relational, and arithmetic vs. algebraic thinking.
Enrollment requirements: Prerequisite(s): admission to the Professional Program