David M. Bressoud June, 2006
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C.1: Develop mathematical thinking and communication skills
Courses designed for mathematical sciences majors should ensure
that students
For me, the greatest revelation to come out of the Calculus Reform movement was the central importance of writing in the effective teaching of mathematics. When I began to give students challenging problems that would take several days to solve and then required them to explain the solution in detail, I discovered for the first time how very confused their thinking could be, even when they were able to find the correct answer. When they had to explain themselves in writing, I began to appreciate where they were having difficulty, which definitions and concepts were not clear, and how they were thinking about a problem. To an extent that was totally impossible with short answer assignments and exams, I began to understand what I needed to emphasize and clarify. And, as I critiqued early drafts and forced students to rework their writing, I witnessed real learning take place, learning that would be reflected in subsequent assignments.
We who teach and who write professionally know that nothing clarifies our own understanding of an idea or concept so thoroughly as having to explain it, either in writing or orally, to another person. This is the gift that we give to our students when we force them to convey mathematical knowledge through written and oral communication. I have found that these are the experiences that the students remember when the course is over, the lessons that stick with them.
I design each course around roughly three major projects, projects for which I expect clear explanations of how the problem was solved, how it is justified, what it means. All project reports involve at least one preliminary draft on which I comment. There is no getting around the fact that this takes time and effort on my part, but there is now a lot of help available on how to provide feedback that is most helpful as well as how to use my time most efficiently. I especially recommend Steve Maurer’s A Short Guide to Writing Mathematics [4] and Annalisa Crandall’s A Guide to Writing in Mathematics Classes and her Checklist for Writing and Grading Essays [2]. The MAA has several Notes volumes with great advice on the use of writing [3, 5, 6]. What I find to be the most useful general reference on writing across the curriculum with suggestions for different types of writing assignments, a discussion of their relative strengths and weaknesses, and a great chapter on how to read, comment on, and grade student writing is John C. Bean’s Engaging Ideas [1].
Few of us have been trained to use writing as a tool for teaching mathematics. Fear of the cost in time and effort keeps many of us from attempting it. But there are many levels at which writing can be used to effectively support our teaching. We owe it to our students to draw on the expertise that has been developed and is now readily available.
[1] John C. Bean, Engaging Ideas: The Professor’s
Guide to Integrating Writing, Critical Thinking, and Active Learning in the
Classroom, Jossey-Bass, San Francisco, 1996.
[2] Annalisa Crandall, A Guide to Writing in Mathematics Classes and Checklist for Writing and Grading Essays, http://server1.fandm.edu/departments/Mathematics/writing_in_math/writing_index.html
[3] Bonnie Gold, Sandra Z. Keith, William A. Marion, eds., Assessment Practices in Undergraduate Mathematics, MAA Notes #49, Mathematical Association of America, Washington, DC, 1999.
[4] Stephen Maurer, A Short Guide to Writing Mathematics, contact information at http://www.swarthmore.edu/NatSci/smaurer1/WriteGuide/
[5] John Meier and Thomas Rishel, Writing in the Teaching and Learning of Mathematics, MAA Notes #48, Mathematical Association of America, Washington, DC, 1998.
[6] Andrew Sterrett, ed., Using Writing to Teach Mathematics, MAA Notes #16, Mathematical Association of America, Washington, DC, 1990.
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We would appreciate more examples that document experiences with the use of
technology as well as examples of interdisciplinary cooperation.
David Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College in St. Paul, Minnesota, he was one of the writers for the Curriculum Guide, and he currently serves as Chair of the CUPM. He wrote this column with help from his colleagues in CUPM, but it does not reflect an official position of the committee. You can reach him at bressoud@macalester.edu. |