How can I review a bag of assorted jellybeans? On one hand, they're all essentially the same -- a sugary crust enclosing an ellipsoidal blob of gel. On the other hand, they're different in the details of color, size, and most importantly, taste. So the statement "I like jellybeans" is only a broad generalization; some flavors, sizes and colors I like a lot, some are okay, and there might even be a few kinds I dislike. My review can only give you my overall feeling, and I can provide a few specific examples for illustrative purposes (personally, I love the sky-blue mints, but I can't stand red-hot cinnamons). Assessment Practices in Undergraduate Mathematics is a tasty collection of seventy-odd different jellybeans... oops, I mean, articles. Some are tastier than others, but as a whole, the collection is a worthwhile treat.
Assessment techniques offered in this book range from several-minute classroom exercises and examples of alternative assignments and cooperative exercises, to examples of how departments may evaluate their course placement, major, service to other departments, and teaching. This nearly overwhelming variety of information is organized into something sensible through the use of two clever editorial fiats described below.
- The articles are brief and uniformly formatted. A five-line summary precedes no more than five pages covering background and purpose, method, findings, use of findings, and success factors. Enough information is given about the context of the assessment that you can decide how well you could transfer the techniques to your specific academic situation. Generalizable results are not the point of these articles, but useful, transferable skills and methods are. This makes the book ideal for browsing. When you have no specific assessments needs in mind, you can page randomly and very quickly decide if the article describes something personally meaningful to you, how it was done, and what the results were. If you are particularly intrigued by particular article, points of contact for the authors are included in an index.
- The book has two extremely useful tables of contents. The breadth of coverage of the book is somewhat daunting, but makes it a very useful reference when you have a specific assessment need. Perhaps you're on the committee that writes the report for regional accreditation, and you need to know about assessing the major. Or your department has recently embarked on a reform initiative, and you're wondering what worked. Or you're simply looking for an alternative to a formal end-of-term teacher evaluation form as a way to examine the quality of your teaching. All of these assessment techniques are in the book, but best of all, you can find them. The table of contents covers 17 topics, broken into 4 parts: assessing the major, the individual classroom, the department, and teaching. If these 17 topic labels don't cover what you're looking for, check the list of articles arranged by topic a few pages further on. Multi-topic articles are cross-listed, and therefore easier to find. Also, new topics are included, ones that cross-cut the 4 parts of the table of contents (e.g., "Exams," "Portfolios," "Cooperative Learning").
I could conclude this book review by providing an analysis of several of the articles, but I feel that wouldn't really do justice to the variety of topics and usefulness of presentation in Assessment Practices in Undergraduate Mathematics. Instead, I'll recount four examples of how I used it last semester (Fall 1999).
- Part II, Assessment of the Individual Classroom included a topic category called Projects and Writing to Learn Mathematics, which helped me because I just switched institutions, and my new department uses projects and writing much more extensively than my old one.
- Another article in Part II dealt with using e-mail to provide feedback for students' problem solving in a way that balanced individualized attention with the efficiency of semiautomation. I found this article quite dense with ideas, perhaps even too telegraphic, but the author noted it was an excerpt from a longer work. I haven't yet contacted him, but I might if I find my thoughts wandering back to his methods and results.
- Student understanding is one of my research interests, so I read the article by Kathy Heid that discussed using interviews to understand student understanding. The assessment she suggests has strong shades of educational research; the boundary between assessment and research is fuzzy, and practicing the kind of thoughtful, explorative assessment she suggests would be excellent training for doing mathematics education research.
- I ran across a "gem" on page 270 while browsing through Part IV, Assessing Teaching. It shows a way to get feedback from your students about how well they understand the material. Instead of asking "Does anyone still not get this?" during a lecture, say "Raise your hand if you understand this part." It's a gem because it is so simple and easy, but it's something I would have never thought of myself.
Gideon L. Weinstein (firstname.lastname@example.org) is an assistant professor of mathematics at the US Military Academy in West Point, NY. He shares his joy of calculus with future Army officers by morning and tries to write mathematics education articles by afternoon. His academic interests include mathematical sophistication, motivation, technology, and assessment.