The catalog description of the precalculus course we teach at Georgia State lists the content areas: trigonometric functions, identities, inverses, and equations; vectors; polar coordinates; conic sections. The current textbook is Barnett, Ziegler, and Byleen (2001).
The content standards (CS) developed by our department and used as guidelines for teaching the course are organized into eight groups:
Each CS contains detailed requirements regarding the acquisition of knowledge and skills that students are expected to meet upon the completion of the course. These standards move beyond simple computations to understanding and relating concepts. When possible, problems are based on the use of multiple representations. For example, consider the problem of conversion between rectangular and polar coordinates for a point P. Instead of using only algebraic formulas, an item may encourage or even require students to also use a diagram with rectangular and polar coordinate systems overlaid, as shown in Figure 1. After plotting the point in one system, the coordinates can be read from the other.
The concepts and problems of a precalculus course can be very different from those of the prerequisite algebra courses. In preceding courses, students may have seen computation and algebraic manipulations emphasized. By contrast, this course should be highly visual. Our materials emphasize the geometry of triangles and circles. Properties of functions such as increasing, slope, asymptotes, foci, vertex, directrix, periodicity, and amplitude are illustrated through their graphs. In addition, many concepts are understood, explored, and manipulated using diagrams. This includes diagrams for winding functions, transformations of graphs, transformations of coordinate systems, vector addition, and vector resolution.
In the next section we describe the course design and organization of the WebCT-based Precalculus as taught by four faculty in our department. We refer to these classes as the "experimental sections."