DPVC (CV/Teaching)

Another important tool in my classroom is what I call the "two-part quiz." Particularly in my lower-level courses, I will give a 15-minute quiz in class on Friday and then have the students take the same quiz home (with one or two additional problems) to redo over the weekend at their own pace and with their notes if they need them. This serves several purposes: first, it gets them into the habit of rethinking problems, particularly ones where they had trouble; the idea of going back to a hard problem again and again until they get it right is something they don't seem to have on their own. Second, it gives them the incentive to learn the material they should have known for the quiz but didn't. Third, it helps them to realize that making mistakes is part of the process, and that they can view them as opportunities to learn, not as failures. Fourth, it gives them a greater sense of control over their grades since they have the chance to improve on their in-class performance. Finally, it gives me the ability to ask harder or less-computational questions (which are the kind I really want to ask) on the take-home portions, and require more writing than is possible in an in-class exam. These two-part quizzes seem to be successful in achieving these goals, and students frequently comment favorably on them in the evaluations at the end of the course.

To help them analyze their quizzes and midterm exams, I write up several pages of comments for each quiz or exam that explain the most common errors, why they are considered errors, and what should have been done instead. In the past, I had used class time to make these comments, but since I give a quiz or exam every week, this tended to take considerable time, and I ended up rushing the material at the end of the course. It also was unnecessary for the students who did well, and could be intimidating to those who didn't. Handing out written comments seems to address both these shortcomings while still getting the information across. While some students certainly will not take time to internalize these, they are a valuable source of information for those who do. A number of students have told me that these are useful not only because it helps them understand the material better, but also because it tells them that other students have made the same mistakes, so they don't feel quite so singled out. As a final aid, I make copies of the best solutions and put them in a notebook outside my office. Any student can browse through these to see what I am looking for in their write-ups. This notebook also shows them that students can do what I am asking, and, I hope, gives them encouragement to do better themselves.

In my courses, I require a considerable amount of writing, perhaps more than is expected by most of the other department members. I am quite frank with the students about this and why I do it. Most students think that mathematics is about numbers and formulas and that their homework should be a series of equations with an answer circled at the bottom with as few words a possible. They are surprised, then, when I ask them to write in complete sentences and to explain what they are doing. One of the differences between high-school and college-level work is that in high school, it is enough to know how to do something, but in college, you need to be able to articulate that knowledge. So when my students perform a computation, they need to tell me why they are doing it, and justify each step in writing. When they evaluate a derivative, for example, they must cite the rules used to obtain it (e.g., the power rule). Frequently my homework assignments include a problem where they must talk about something rather than compute it. Since clear writing reflects clear thinking, if a student understands a problem, it should not be a hardship to write a brief explanation of what she is doing; on the other hand, if she does not really understand, then it will become apparent to her when she tries to write about it and so can work harder at understanding. Thus the writing is as much for them as it is for me; as any teacher knows, having to put our knowledge into words is the best way to really understand it, so I work hard to have my students do this. While they may resist it at first, by the end of the term most recognize the value of this approach, and many have commented that they thought it helped them to learn the material better.

Davide P. Cervone's web pages Created: 08 Sep 2001 Last modified: 07 Jan 2002 06:56:27 Comments to: dpvc@union.edu

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