MTE 598 – Fall 2005

Extended Analysis of Functions


Dr. Patrick Thompson



Dr. Marilyn Carlson


Or PSA 637 



or PSA 644

Office Hours:

By appointment



Class Time:

Monday, 4:15-7:15pm




Gilbert High School



About this Course

The course is about mathematics--teaching it, doing it, and thinking it. We will use computers extensively in it, but only because, sometimes, if used properly, computer programs can be useful in all three.

We will be engaged in two qualitatively different kinds of activity over the semester. In the first kind of activity, content activities, you will be students of mathematics. In the second kind of activity, pedagogical activities, you will be teachers of mathematics. The programs you use as students will be the programs you use as teachers. The purpose for this structure is that to teach for understanding you must first have an image of what you want your students to understand. That image will be what guides you when selecting/designing course materials, preparing your instruction, and engaging your students during instruction.

The content activities are intended to enrich your images of algebra, geometry, and calculus. The pedagogical activities are intended for you to learn to express those images in ways that are conducive for students to build powerful mathematical understandings.

Conversations and Explanations

One of the most important abilities you must develop to be a good mathematics teacher is the ability to conduct conceptual conversations, with yourself and with your students. A conceptual conversation is one that has a diminished emphasis on technique and procedure, and an increased emphasis on images, ideas, reasons, goals, and relationships. The one thing I hope you develop through this course, and which I will value and reward, is the orientation to look for big ideas--to realize that mathematics is not about getting answers to questions, but rather it is about developing insight into relationships and structures, and that solutions to a sophisticated or complex problems emerge from understanding them deeply instead of memorizing a procedure. Click here for an example.


An undergraduate degree in mathematics or secondary mathematics education.

Technology Requirements

You will be given a laptop (to be returned if you do not continue the program) and the program Graphing Calculator for use in this class.

Grades are determined as follows:  

Due Date


Attendance and Class participation



Written assignments



Final Project