MTE 598 – Fall 2006

Extended Analysis of Functions I


Dr. Marilyn Carlson



Office Hours:

By appointment



Class Time:

Daily, 1-4; Thursday, 4:15-7:15pm




CRESMET classroom



About this Course

 This course will focus on the processes of understanding and learning the concept of function as a representation of covarying quantities. Our aim is to assist you in acquiring foundational reasoning abilities so that you are better equipped to provide coherent and conceptually focused instruction for your students’ continued mathematics, science and engineering course taking. We will explore various function models, including linear, polynomial and trigonometric. Written assignments will include problems and activities designed to engage you in “ways of reasoning” that should enhance your mathematical thinking and confidence in approaching novel mathematics tasks. 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.

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.

Classroom Rules of Engagement

I will expect each of you to exhibit expert reasoning behaviors when approaching a problem and discussing with your colleagues. General “rules of engagement” that I would like for us all to practice and enforce:  1) Speak meaningfully—what you say should carry meaning; 2) Exhibit mathematical integrity--base your conjectures on a logical foundation; don’t pretend to understand when you don’t ; 3) Strive to make sense—persist in making sense of problems and your colleagues’ thinking. 4) Respect the learning process of your colleagues—allow them the opportunity to think, reflect and construct. When assisting your colleagues, pose questions that will help them construct meaning.


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