This course is designed to provide middle school teachers with a solid foundation in the algebra and geometry on the Cartesian coordinate system in both two and three dimensions. Graduates of this course will be able to design and implement class demonstrations and hands-on exercises for their students. They will be able to lead their students in explorations and in thought processes for relating algebra and geometry. The class will emphasize active learning, oral and written communication. Students will construct lesson plans, lead discussions and demonstrations, and create course materials with an algebra/geometry focus, laying the foundation for their students for future work with functions and the Cartesian Plane.

Topics will cover a broad range of concepts that all have the common thread of a geometric and algebraic relationship centered on the Cartesian coordinate system. The material will have an emphasis on applications and relationships. Topics may include: the measurements of geometric objects, an introduction to right triangle and functional trigonometry, relations between geometry and algebra, functions and their graphs in the plane, functional transformations, matrices, elementary fractal geometry and concepts leading to the foundations of Calculus.

NCTM standards will be used to guide both the content and pedagogy of the course. Students will use an array of tools from physical objects to computer applications. Some software systems the students will utilize include Geometer's Sketchpad, Maple, java applets on NCTM's Illuminations page, and WinGeom, as well as several fractal construction and linear algebra packages. All topics will be viewed geometrically, algebraically and numerically as well as be related to other fields of study both in and out of the sciences.