Executive Summary

How to use this portfolio

This portfolio is to serve many different purposes, and every purpose might lead one to experience the portfolio differently. In many ways, I have attempted to style the portfolio after an artist's portfolio, in that the main portion of it consists of ten “snapshots” of my teaching in this course. That is ten artifacts from the course from which I hope that the interested reader/viewer can get a feel for how I teach. Snapshots are meant to be viewed for any length of time between 5 minutes to hours. Moreover, I have attempted to link relevant pieces together, so that you might never return to the main page of the portfolio and still be able to see everything. Experiencing the portfolio on the one hand just to get an idea of my teaching will not be most people's desire. Consequently, below I have listed a variety of “problems” or questions to be addressed in this portfolio. By chasing these links, you will be led to a page with frames that gives an outline for a path that you might want to follow through the portfolio.

I have been asked to teach this course, what should I know?

The course the portfolio describes is a capstone course in mathematics primarily aimed at future high school mathematics teachers. In the fall of 1997, I was given the job to design this course by the Department of Mathematics and Statistics undergraduate committee at Bowling Green State University. The fourth time I taught the course was at Michigan State University while I was on sabbatical. That year I received a fellowship from the Carnegie Academy for the Scholarship of Teaching and Learning. As part of my work on that fellowship, I learned about course portfolios. I decided to write a course portfolio for this course as a way to pass the course along to other faculty members that will teach it in the future. Thus, the central purpose of this portfolio is to be a course record, suitable for other faculty members in the department to use as the main resource when they teach the course.

A centerpiece to this course is the semester long student research projects. How do you do them, and how do they affect student learning?

One piece of the research I have been doing as part of my Carnegie fellowship is on examining these student research projects and trying to see whether they make the students think more mathematically. This thread leads you through the links associated with the research projects. One of the main findings here is that the projects change the course far more than I had expected, and in particular, the projects changed how the content of the class was covered.

How did this course affect students? What changes do we see in them after they have taken the course? Did your students learn from this course? Did they reach the desired outcomes?

This thread leads to the investigation of student understanding by analyzing a single student as a case study. In addition, one of the surprising developments in this course, was that classroom conversations appear to have become more mathematical. In particular, it appears that one of the reasons that mathematical conversations happen so rarely in mathematics courses has to do with students feeling that deeper mathematical questions may direct us away from the main content of the course.

I want to see examples of student work. What sort of work did they turn in?

This link will lead you through the links where (graded) student work is presented.

I want to understand your teaching.

In this link we look at the vignettes that describe my teaching.

You may either click on one of the above five links or return to the main portfolio page.