One of Sheila Tobias's well known books is They're Not Dumb, They're Different: Stalking the Second Tier. “They” are otherwise successful students, graduate students in non-science disciplines who had not been successful in college-level science courses. They were asked to enroll in such courses and keep journals of their experiences, documenting what worked and what didn't -- mostly the latter. In a nutshell, entry-level science courses for the masses were being taught as a trial by fire by faculty who were among the few to survive such experiences when they themselves were students. The graduate students were able to identify the factors that interfered with their success in understanding science. Much of the book is about documented techniques that accommodate a wide variety of learning styles and lead to broad-based and substantial understanding, both for those who will and those who will not become scientists. Furthermore, these techniques open doors to science careers for traditionally underrepresented groups of students.
What I learned from Tobias is that almost all the students in our calculus courses are in a mathematical second tier, even the science and engineering majors. At Duke the first-tier mathematics students place into Calculus III or beyond, and on most campuses they are a tiny percentage of the calculus enrollments. The message about the overwhelming majority of our students is they're not like us -- and that doesn't mean they're dumb. If we use ourselves as models for how students learn mathematics, we always get it wrong.
From the outset of Project CALC, we knew from our own and others' experiences that there was hope for accommodating a broader variety of learning styles by using small group activities, laboratory experiences, and writing. But we had no idea how any of this might be related to gender differences. Furthermore, we were not aware that we had a gender-discrimination problem in our traditional course, so that was not a problem we set out to solve. When we first saw women succeeding in ways we had not seen before, we attributed this -- on average, not for every individual -- to the greater verbal content of our course and to ways to succeed by expressing ideas in writing. But we also observed women speaking up more in small groups than we had seen in whole-class discussions. Later in the course we were seeing more participation by women in the whole-class discussions as well. And all of our teaching experience suggested that -- on average -- those who spoke up in the classroom were most likely to succeed in the course.
Later we learned of research pointing to a potential danger for young women of placing them in groups in which they were a minority -- e.g., a single woman in a four-person group. I adopted a policy of not doing that until I could see enough evidence of the strength necessary to hold her own and not be suppressed by male peers. I often see this kind of growth in less than a year, sometimes in less than a semester.
Every time I mentioned these gender-related observations in a faculty workshop, a female participant would respond, “You know, you really should read Women's Ways of Knowing.” The third time this happened, I added this book (by M. F. Belenky et al.) to the Project CALC collection and read it carefully. I learned that the phenomenon of first speaking up in a small group and then in a larger one is called “finding her voice.” More importantly, I learned much more about stages of development and how they differ by gender. In particular, I gained a better understanding of the work of William Perry on learning stages -- all based on studies of male students at Harvard.
Learning about learning stages has helped us see that some of the things we attempted early on were inappropriate, and we changed them. It also helped us understand better why so much of the traditional course and its methods are inappropriate for the intended audience -- at least if we really want all those students to succeed. That course was an excellent filter precisely because it was so mismatched with such a large segment of its audience.
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Send comments to the author <das@math.duke.edu>Last modified: May 17, 1997