How do we know what other people think? In the academic world, we read what they write, we listen to them speak, and we ask questions. Verbal interactions are often informative, but they are not necessarily a “clean” look at the thoughts of others because our own thoughts are part of the process. Usually we don't care. However, if we really want to know whether another mathematician has proved a theorem, say, we want to see the proof in written form with all the details -- and no intervention by others, including ourselves. Given that you have read this far, you may actually care about my thoughts on learning, and you are getting as good a look at those thoughts as I can provide.
Why should it be any different with students? If we are to take seriously our goal of having them understand concepts, we need a window on their minds. They have to tell us what and how they are thinking. We can listen to them talk, and we can ask them questions. That's a start, but our own thoughts are inevitably part of that process. The cleanest window we have is student writing.
Faced with a demand that we see their thoughts, students will find -- consciously or unconsciously -- many ways to darken or obscure the window. Some of those tactics have actually been taught to them, e.g., not showing up in their expositions in the first person. Some tactics are intuited, such as using passive voice or expressing their actions in nouns rather than verbs -- so they don't have to reveal themselves as the agents of any action. Other tactics include using apparent nouns as pronouns without clear antecedents -- e.g., “the function” when there are two or three that might be the antecedent -- or using non-specific verbs, such as “manipulate,” which can refer to any mathematical technique they have ever learned.
Even in evasive mode, students often reveal more in their writing than they think. For example, a favorite expression is “We received the following answer: ”. First, this reveals a belief that the only important thing is the answer, not how they found it -- but they have to satisfy the assignment by putting in some words. Second, their choice of verb reveals that they believe mathematics is not something they do but something that gets done to them.
We have to make it clear to students -- early and often -- that we will not tolerate evasion, obfuscation, or misdirection in their writing. They must actually reveal their thoughts, and they must do so as clearly and directly as possible. However, in order for them to trust us enough to do this, we must respond in supportive -- not punitive -- ways. We must convince them it is in their interest to reveal their ignorance and misinformation -- along with their valid knowledge -- so that we can help them replace ignorance and misinformation with valid knowledge.
This is hard for both faculty and students because both have long seen each other as adversaries in the process of assessment -- it's us against them on both sides. If the only things we ever mark on papers are mistakes, where will they get the idea that we are on their side? If we really believe that only a few can succeed at the highest level -- that most students are not very good (implicitly, can't become very good) -- how will students come to believe in their potential to succeed?
Most schools have people whose job it is to teach writing -- and a requirement that students learn from those folks. Writing programs that take seriously the concept of writing to learn can be very helpful to faculty who need to learn techniques for positive responses that will induce students to write clearly about their thought processes. Of course, this means we have to initiate a contact across what looks like a very high wall. But once that contact is made, the folks on the other side of the wall are usually delighted to hear from us. Often it turns out they never believed someone on the science side of the campus would actually care about them. If they're any good at all, they can make the task of reading and responding to student writing much less burdensome -- often even fun. It's time-consuming work at first, but with practice -- like anything else -- it becomes quite doable.
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Send comments to the author <das@math.duke.edu>Last modified: May 15, 1997