__Enduring Understandings__

1. The student will begin to see the underlying structure of the Cartesian system of mathematics, in particular as it relates to the interplay between graphical and algebraic representations. Primarily, this will be achieved through an understanding o the similarities among and differences between the various members of the families of functions.

2. The student will begin to understand that lower level math made things seem more simple than they really are and that advanced level mathematics is not made up of discrete chunks of knowledge and skills, but rather relies greatly upon the synthesis and through-threads of the material that came before as a jumping off point for further explorations.

3. The student will begin to understand the nature and purpose of the equations for a function and its derivative in their algebraic and graphical representation and in the interplay between to two.

4. The student will develop a confidence and tenacity when approaching lengthy and intricate math problems. By breaking down a problem into its component parts, analyzing and resolving each part, and then reassembling the whole, the student will develop a sense that no problem is beyond his or her grasp.

5. The student will begin to understand that the calculator is a tool to supplement and clarify mathematical thinking, not to replace it, and that answers from the calculator need to be anticipated and interpreted. The student will begin to understand the differences between Euclidean and Cartesian approaches to Trigonometry.

6. The student will hopefully go beyond the utilitarian mode of learning (“When are we going to use this?” or “Is this going to be on the test?”) and begin to learn new things for the sake of learning them. Ultimately, the student might begin to appreciate the power and the intrinsic beauty people find in the material.