Transformations

This course will focus on transformations, taken broadly to include functions, algebraic operations and geometrical changes such as rotations and expansions, and will build on the various representations introduced in Course 1. For example, a quadratic equation can be solved by factoring, completing the square, or using the quadratic formula. The relationship among these three algebraic approaches becomes clear when graphing the corresponding parabola and noticing how the solutions are related to intersection of the graph with the x-axis. Particular attention will be paid to transformations among physical quantities (such as distance and time, pressure and volume, and temperature). Research about middle-school children’s approaches to transformations (e.g. “building-up” strategies) will be examined in light of the distinction between input-output and differential approaches to functions that are congenial to closed-form and recursive descriptions, respectively.