TPC Functions Course I

Fall 2005



We have spent almost three months studying functions and graphs with a focus on covariation of quantities. Functions as covariation of quantities is often not emphasized in high school mathematics texts. In this project, you will interview a student, design instruction, enact that instruction, and reflect on your planning and on your session with the student. The project will be in lieu of a final exam. Therefore, we expect you to do your project indvidually, although you will have opportunities to discuss general issues within your PLC.

Your Task


Design a lesson unit (i.e., a coherent set of at least 2 lessons) that will enable a high school student to reason covariationally about functions and graphs. The idea is to take the student from wherever he or she is with respect to covariational reasoning to a much higher level.

Note: Part of your project will be to define "to a much higher level".

Phases of the Mini-Project

Goal Setting

  1. Define what you mean by "sophisticated covariational reasoning" for students at the level of the one you will teach. Give both general characteristics of this kind of reasoning and examples that would convey what you mean. Make it only as long as it needs to be.


  1. Create interview questions and tasks that you will use to determine a student's ability to reason covariationally prior to your working with him or her on this project.
  2. Conduct the interview with your student on his or her covariational reasoning.
  3. Write a 2-4 page report of your interview that communicates what you find about your student's covariational reasoning.
  4. Prepare a logic of your instructional plan.
  5. Send logic to Pat and Marilyn for their comments.
  6. Revise according to comments and create lessons.
  • Lesson and Report

    1. Teach your lessons.
    2. Write a 5-10 page report on (a) what your student learned; (b) what you learned in this mini-project.