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Using Writing to Teach Mathematics
Andrew Sterrett, editor
Publisher: Mathematical Association of America (1990)
Details: 190 pages, Paperback
Series: MAA Notes
Topics: Teaching Mathematics, Mathematics Education
This book is in the MAA's basic library list.
MAA Review[Reviewed by Marion Deutsche Cohen, on 11/14/2010]
I jumped at the chance to review this book. First, I’m a writer, in particular a “math poet”, meaning a poet some of whose writing is inspired or informed by mathematics. Second, recently I’ve been teaching math courses involving writing — History of Mathematics, where grades are mainly determined by weekly papers, and Mathematics in Literature, a course I developed, where students read writings inspired by math, then write creatively and sometimes personally about the readings, eventually writing “math poems” of their own.
The purpose of neither course is specifically “using writing to teach mathematics” (the title of this book). Nonetheless I felt it would be helpful to read this collection of thirty-one essays by teachers at various institutions who engage in this activity. What I found was a goldmine. Immediately after the Table of Contents, we’re treated to a Jeff MacNelly cartoon ending, “Good grief! I think life is an essay question!” Then comes the Introduction, basically about the rationale and potentials, consisting of three essays: “Mathematicians Write: Mathematics Students Should, Too” by Ann Stehney, “Writing for Educational Objectives in a Calculus Course” by Sandra Keith, and “Writing in Mathematics: A Plethora of Possibilities” by Timothy Sipka. A few “possibilities” are “math autobiographies,” “write a letter to the author of the text identifying the good and bad points…” and “write a letter to a student who plans to take discrete mathematics next term…”
Section II, Getting Started, is in part a “how-to” for teachers planning to do a little WAC (writing across the curriculum). There’s a lot of repetition in this section; a few wheels get reinvented. An important consideration is skepticism on the part of teachers. From the essay by Emelie Kenney: “Some may be unfamiliar with the principles of writing to learn, or… believe that writing has no place in the teaching of mathematics… time is limited enough as it is… Others argue that their job would be… more difficult because of the additional work involved. Many do not feel qualified ….”
In this essay appear some good suggestions, mostly for the university higher-ups rather than within the power of teachers. “…one can cover fewer topics….” (For that we need changes in departmental syllabi.) “We need not simply abandon material… we can give students the primary responsibility to cover some… abandon weekly or frequent quizzes in favor of, say, journals…” (We hope our departments won’t frown on these practices.)
In this essay, too, appear further “possibilities”. “Describe a problem or topic that you found particularly… fascinating…” “List all the mistakes you have made on homework problems… and exams. Do these errors have anything in common?” And in an essay by Ann Stehney, “write… a letter to a former teacher.”
Section III, On Grading seems to be (happily) not mainly about grading, but more about advice, suggestions, admonitions, etc., that can be given students about writing. Here’s one from Andre Lubecke: “Summary papers will not be accepted. I want to know what you thought about what you read; I already know what it says.”
About to read Section IV, What Do Students Say?, I wondered, “Are there any papers here by students?” Indeed there was… well, half a paper; the other half was by the instructor of the course, Coreen Mett. Perhaps the student chosen, Mary Margaret Hart McDonald, was specifically one who loved and was good at writing, but she didn’t hesitate to express negative feelings. “Okay, I’m still confused!” as well as “Oh Boy! We’re starting some good stuff now! …” She also describes some “Reservations” about the writing component: “My fears lie in not having covered as much material as… other students…”
Perhaps the most important article in this book is “Using Expressive Writing to Support Mathematics Instruction: Benefits for the Student, Teacher, and Classroom” by Barbara Rose. This article is kind to students; it’s not full of “shoulds,” “musts,” and other perhaps-scary words. It’s true to its title, “expressive writing”. Here are some benefits she notes: “Writing promoted understanding.” “…facilitated reasoning….” “…helped ‘tie together’ the content.” “…was a revealer of understanding.” “…promoted concentration.” “…helped retention.” “…served as a study tool.” “…stimulated the posing of questions.” She also mentions “transfer benefits”: some voluntarily began journals in other courses. The article gives a great overview of, perhaps, most of the book; in particular, it describes the benefits to the student/teacher relationship.
“Rewriting Our Stories of Mathematics” by Linda Brandau is possibly my favorite among the articles, probably because rewriting stories of math is a huge chunk of what I do. The article talks about childhood memories and unfinished emotional business, directly or indirectly related to the learning of math. “We all have a story to tell of our mathematical lives… [and] our own perception of what mathematics is …” Students harbor myths, such as “mathematics problems are always solved in less than 10 minutes” and “I recall teachers using these types of problems in elementary school — they were sort of ‘trick’ questions — …the teachers posed the problem and… took great delight in holding the answers while we poor students struggled…”
So much of this book sounds wonderful! But I’m cautious. As a teacher, I’ve usually liked to keep things simple — course topics to a minimum, ditto complications (or what students might perceive as complications) such as special projects, students grading one another’s papers — and writing. I tend to feel that students have enough complications in their lives — registering for courses, roommate problems, technology, part- and fulltime jobs. I don’t like “too many variables,” time-taker-uppers — nor energy-taker-uppers. I’m concerned that, when presented with WAC, students will react, “Oh no! Something else to do, maybe get graded on!” Negativity can go a long way. And I seldom talk “education-ese.” There are words and phrases I’m tired or suspicious of, sometimes for subtle reasons — “skills,” “assessment,” “students must,” “you are to include.” And when I hear “have students write,” I can’t help being aware that “have” means possess.
Still, this book is loaded with wonderful and successful ideas. I need to think about them, incorporate them into my own personality and credo. For example, many of the authors say, and show, that students in general learn better when they write about what they’re learning. But I know students who’ve solved problems correctly without writing, telling me “I don’t know how I did it.” Usually I feel they did it unconsciously; they do know how they did it but not on the speaking, or writing, level.
A mathprof friend tells the story of a student who had “real trouble” graduating because, although he was great at math and science, he was terrible at writing. “But how will he write in his career when he needs to?” this book would plausibly ask. Well, it seems he managed. In fact, over the decades many non-writers have managed (or others “managed” for them). Whatever writing needed to be done did get done. I recall longago postal mail from journals, sloppily typed on non-electric typewriters. The journals still flourished. Richard Millman writes, “the impetus for many of the writing programs comes from people in industry who complain that our students cannot write.” However, which came first, those complaints or WAC? Are they both the result of some phenomenon or trend? There is, these days, more emphasis on things being done “correctly.” Many employers automatically throw out application letters with typos or incorrectly constructed sentences, but does that make it right? History is full of accomplished individuals who wrote more than one incorrectly constructed sentence. Writing often makes people’s lives easier but how absolutely necessary is it?
This book’s first essay is “Mathematicians Write; Mathematics Students Should, Too.” I’d say that depends. I wrote math before I became a math student, before college. Many working mathematicians did likewise (and wouldn’t have needed WAC). Developments follow varied trajectories. In order to write, one needs something to write about. Math students might feel they have nothing to write about, perhaps until or unless they begin to have their own mathematical ideas. True, sometimes writing helps students develop ideas, but that’s an individual and subtle thing. In general, students need to be gauged rather than coerced. I also might conjecture that there are mathematicians who don’t write.
I’m also concerned about students writing about math they don’t understand; might such writing reinforce misconceptions? The authors in this book who advocate journal-keeping do emphasize “immediate feedback”; that can counteract the dangers of developing misconceptions. Sometimes, though, feedback the next class, rather than a moment later, isn’t immediate enough.
A recurring thought as I was reading this book was, “But I already do that — without WAC”. Barbara Rose writes, “everything… the students wrote was feedback to me, … could be used for diagnosis… evaluation, increased sensitivity to students and their needs, short-term adjustments in the course, and long-term changes in teaching. Where else could I get this kind of first-hand information…?” By talking with and listening to students, that’s how! Last spring a student up and asked me, “Could you write on the board more? I know you have these handouts but I learn by taking notes.” Next class I asked how many felt that way; about six raised their hands. So I immediately made both “short-term adjustments in the course” and “long-term changes in teaching”. Without “having students write”, I get the feedback that Professor Rose and other authors in this book describe. I’m not saying my way is better, only that requiring writing from students isn’t the only way.
Yes, some quieter students express in writing what they don’t in speaking. It’s for that reason that, on the first day of every course I teach, I ask students to write impromptu “info-sheets,” with anything about themselves they’d like me to know — interests, hobbies, pets, strengths/weaknesses as students, attitudes about and experience with math and math teachers, and any disabilities or stresses in their lives they’d like to share. (I precede this by sharing “info” about me with the class.) And it’s for that same reason (consideration of the quieter students) that, in one course this term, I made journal writing optional. I invited students to keep a journal. What has emerged is, some students have written on their test papers, informally and sometimes humorously, about the trials and tribs in doing the test problems. With one such student I then connected on a non-writing level; after some classes I ask, “How’re you doing? Did you understand what we did today?” The answer is usually positive. (Update: he did much better on the second than on the first test.)
Several of this book’s authors made extensive comments to the effect that while students were often initially put off by, for example, the journal-writing requirement, they eventually came around and made the heartening statements appearing on the back cover of the book: “… once I got used to writing them, I couldn’t stop.” “The more I wrote in my journal, the easier it was to communicate in class.” I’m not sure I have the patience or confidence to wait for students to “come around.” And I don’t like to require patience and confidence in students, either. Just as I prefer children to have happy rather than over-disciplined childhoods, I like students to feel comfortable throughout a course, not only towards the end.
However, these concerns might be more than balanced by how writing has helped my own learning and teaching. In college and grad school I often felt that I hadn’t learned a topic unless I wrote it in my own words. And fifteen years ago I was working on a particularly difficult problem, simultaneously writing poems about the process. The poems weren’t all about the specific math involved; some were about math itself, its mystery, my passion for it, how it connected with my non-mathematical life. Perhaps the writing helped me solve the problem; perhaps it didn’t. But I couldn’t imagine not doing that writing.
I write limericks for every course I teach; this writing helps me get a better review, and overview, of the course. Along more personal lines, I’ve had two pieces of major life-stuff — loss of a newborn daughter and spousal chronic illness. While embroiled in both I wrote, poems and diary. That helped me sort things out, helped me learn, walked me through the grieving process, the way writing walked many of this book’s students through the math-doing process. For me and for some others, writing facilitates learning. But does that work for everyone? There are many ways to learn. While students should be offered the idea of writing, it should not be expected that all will take to it. Because we can’t know until we try, I do like the idea of offering the opportunity.
A student once told me, “I feel that you relate to me as a writer.” I hadn’t even known she was a writer! Perhaps my simply being a writer did the trick. I do tell my classes about my writing, in particular about being a “math poet”, and I ask for a show of hands, those who also are writers; often a student who didn’t put up a hand mentions writing on the info-sheet. Perhaps all that is WAC enough! Perhaps students don’t necessarily have to actually do writing in a course, in order for their math learning to benefit. Perhaps simply knowing about the possibility of writing is enough, or enough for the time being.
As a writer of poetry and creative non-fiction, I never expected to have the pleasure of teaching writing in math courses. Now that I do, I’ve been thrilled to supplement the WAC workshops I’ve taken part in with the material in this book. But again, I proceed with caution, and perspective. Caution and perspective are in this book, but no entire articles against “using writing to teach mathematics”; we don’t get an unbiased sample.
WAC is becoming fashionable, perhaps rightly so. But I’d be mindful against going overboard. I’d also be supportive of teachers who might feel, somehow, guilty for not doing as much WAC as they see their colleagues doing.
I’ll conclude with a comment about perspective: suppose it was decided that every course had to have, not necessarily a writing component, but an X component, where X might not equal writing? Suppose, for example, X = math? Think how upsetting “MATH across the curriculum” could be to some students, and some professors too!
Marion Deutsche Cohen teaches at Arcadia University in Glenside PA. Her course, “Truth and Beauty: Mathematics in Literature”, has been popular with students. Crossing the Equal Sign, her poetry book about the experience of mathematics, is from Plain View Press. Her new book, Chronic Progressive also has “math poems” in it. She would like to thank her colleague and friend, Freda Robbins, for helpful discussion and support.
BLL — The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.