Why a course portfolio for a mathematics course?

The idea of course portfolios sprang out of Ernest Boyer's (citation) work: Scholarship Reconsidered. Boyer argued that scholarly teaching needed to be rewarded and peer-reviewed. One question, however, was how to conduct peer-review. Perhaps more important was the simple question of how one makes scholarly teaching public. Teaching portfolios certainly provide documentation for people to review, but the wealth of material makes it hard for any one person to actually review it, and in many respects, the teaching portfolio becomes an artifact for promotion, where we often overwhelm readers with the quantity of information. Our hope is that the course portfolio will be something different.

The course portfolio movement gained momentum with the Carnegie Foundation's publication of the 1998 book: The Course Portfolio. Currently, the American Historical Society is hosting a set of course portfolios at Insert website. Other on-line portfolios that can be found are Randy Bass's English course portfolio (insert link) and Bruce Cooperstein's mathematics problem solving course portfolio (insert link), T. Mills Kelly's American history course portfolio (insert link), and Catherine Schifter's teacher education course portfolio (insert link).

The purpose of a course portfolio.

Pat Hutchings (Hutchings, 1998) makes the argument that a course portfolio can serve multiple purposes and have various frameworks. Five main purposes that a course portfolio might fulfill would be: (1) A vision of the possible, (2) an aid to memory, (3) an occasion to investigate student learning, (4) an escape route from the isolation of the classroom, and (5) a way of bringing recognition and reward to teaching excellence (Hutchings 1998). Let me discuss each of these briefly.

A vision of the possible: Any time we teach a course, we begin with a vision of what a course will do. Rarely is this initial vision brought about exactly as we picture it. Thus, while we have a vision, in some sense, the vision is not truly possible. A course portfolio yielding a vision of the possible shows what the course actually does, and provides a vision to others teaching similar courses of what they might be able to accomplish. The course portfolio can also become a place to center an argument for change around, by allowing for others to see what is done. The important part of this vision, however, is the notion of capturing student work. Some years ago I was a member of a committee, whose job it was to decide whether certain courses satisfied general education requirements in science. An unusual course came in front of us, that may well have satisfied the requirements, but the assessments were not of the form that could easily be judged and the course descriptors were too vague for the committee to decide in favor of its inclusion for general science credit. What was missing from the argument was student work and more complete data for the committee to judge the course on.

An aid to memory: Some faculty manage to keep copious course notes for there classes. These notes will include great details about what they do each day and how they will present material. After a class is over, however, they will frequently have ideas about what they might have done better that are never written down. The idea in the course portfolio is to preserve this reflection for future years, so that when teaching the course in a year or two, the professor is not left thinking, "what was it that went wrong with this lesson?" or "I had a great insight last year, but I don't remember it."

An occasion to investigate student learning: A course portfolio can also function as a way to investigate our students' learning. Keeping a careful record of the artifacts that students produce throughout a term provides a wealth of information on how their learning has proceeded. It allows us to see what students are learning in our classroom (often a frightening prospect). Moreover, it allows others to see this learning happening and can provide a database of information for scholarly research.

An escape route from the isolation of the classroom: Teaching a course is usually an individual experience. The isolation of the classroom can be extreme. Many of us use our colleagues as sounding boards for ideas, but the actual day-to-day experience is solitary. The course portfolio is an opportunity to make public these classroom experiences.

A way of bringing recognition of teaching excellence: The course portfolio provides data that our scholarly peers can look at and analyze. Teaching is often hard to reward precisely because so much of it happens without scholarly witnesses. The portfolio provides an artifact of our teaching that can make clear how we come at a class, and what we do to create the class. Thus judging teaching can become less dependent on student evaluations and personal taste. Rather, we can put our work on public display.


The purpose of my portfolio.

I see my portfolio as a combination of the first three purposes above.

A vision of the possible: I designed the mathematics capstone course I teach, and I feel that I have captured a possible vision of what such a capstone course for secondary education majors can do. I hope that others will look at my portfolio and find it helpful in designing their own capstone courses for their students.

An aid to memory: This portfolio documents the fourth time I taught the capstone class. Each time the course has been quite different, although the students are not so different from term to term. What I have found is that when I prepare the course each term, I only remember some of what went on, not all. I hope that as I teach the course again in the fall term of 2001 that I will be able to use this portfolio to help me remember key issues.

An occasion to investigate student learning: In the spring of 2000 I was named a Carnegie Fellow of the Academy for the Scholarship of Teaching. As part of this fellowship, I wanted to investigate how certain portions of the capstone class affected student learning. Parts of this course portfolio contain the details of my investigation. Indeed some of the results of the investigation will be presented within.