Both authors were graduate students in the mathematics department at the University of Michigan. They began as graduate student instructors, and were trained in the professional development component of the Michigan Calculus Project. They both taught Precalculus, Calculus I, and Calculus II. Near the ends of their graduate careers, both authors then became instructor trainers. This appendix gives an overview of the Michigan Calculus/Precalculus program, which frames the experiences and backgrounds of the authors.

Course Goals

The following are the goals of the introductory courses as stated in the “Michigan Introductory Program Instructor's Guide” [104].

Establish constructive student attitudes about math:

1. interest in math

2. value of math, and its link to the real world

3. the likelihood of success and satisfaction

4. the effective ways to learn math

Strengthen students' general academic skills:

1. critical thinking

2. writing

3. giving clear verbal explanations

4. working collaboratively

5. assuming responsibility

6. understanding and using technology

Improve students' quantitative reasoning skills:

1. translating a word problem into a math statement, and back again

2. forming reasonable descriptions and judgments based on quantitative information

Develop a wide base of mathematical knowledge:

1. understanding of concepts

2. basic skills

3. mathematical sense (quantitative, geometric, symbolic)

4. the thinking process (problem-solving, predicting, generalizing)