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This article gives many helpful hints to the instructor who wants to assign writing projects, both on what to think about when making the assignment, and what to do with the projects once they're turned in.
Background and Purpose
This article will attempt to illuminate the issues of how, when and why to assign writing in mathematics classes, but it will focus primarily on the first of these three questions: how to make and grade an expository assignment.
I have been writing and using writing projects for just over four years at Franklin & Marshall College, a highly selective liberal arts college in bucolic Lancaster, Pennsylvania. The majority of our students hail from surrounding counties in Pennsylvania, Delaware, and New Jersey, but we also draw some 15% of our students from overseas. We have no college mathematics requirement, but there is a writing requirement. Those of our students who choose to take mathematics usually begin with differential or integral calculus; class size is generally limited to 25 students. Our students tend to be more career-oriented than is usual at liberal arts colleges (an implication of which is that post-class wrangling about the distinction between a B and B+ is common).
I have worked with instructors who come from a variety of geographic regions and from a variety of types of institutions: liberal arts colleges, community colleges, branch campuses of state universities. I have found that their experiences with having students write mathematical essays are remarkably similar to my own. Therefore, although I will use my own projects as specific examples, what I would like to discuss in this paper are general guidelines that have helped me and my colleagues. I will present some of the key ingredients to first assigning and then grading a writing experience which are both beneficial to the students and non-overwhelming to the instructor.
Method
The first question to address when creating an assignment is: why assign writing in the first place? What is the goal of the assignment, and how does it fit into the larger course? Other articles in this volume will address this question in greater detail, so I will risk oversimplifying the treatment of this question here. Let me then posit several possible reasons for assigning writing: (1) to improve students' mathematical exposition; (2) to introduce new mathematics; (3) to strengthen understanding of previously encountered mathematics; or (4) to provide feedback from the student to the instructor. Closely related to this question of "why do it?" is the question of audience: to whom is the student writing? Students are most used to writing to an omniscient being: the instructor. Other possibilities include a potential boss, the public, a fellow student, or the student him/herself.
Deciding for yourself the answers to these two questions, and then explaining these to the students, is a very important part of creating an assignment. It focuses the student on your intentions, it reduces the student's level of confusion and angst, and it results in better papers.
Knowing the answers to the above questions, you can design your assignments to match your goals. For example, I want my Calculus students to explain mathematics to those who know less mathematics than they do, and I want their writing experience to reinforce concepts being taught in the course. The projects I assign take the form of three letters from fictional characters who know little mathematics but who need mathematical help. My students are expected to translate the problems from English prose into mathematics, to solve the problems, and to explain the solutions in prose which the fictional characters could understand. I require that these solutions be written up on a word processor. (An example of one such problem can be found in [2]).
Once you have decided the over-arching purpose behind your assignment, you should try to pin down the specifics. The "details" that matter little to you now matter a great deal to the students—and will haunt you later. Do you want the papers to be word processed or handwritten? What is a reasonable length for the final product (one paragraph/one page/several pages)? What is the quality of writing that you expect: how much do the mechanics of English writing matter? How much mathematical detail do you expect: should the students show every step of their work, or instead provide an overview of the process they followed? Will students be allowed or required to work in groups? How much time will they be given to complete the paper? What will the policy on late assignments be? What percentage of class grade will this assignment be?
Especially for shorter papers, students find it very helpful if you can provide an example of the type of writing you expect. I have made it a habit to ask permission to copy one or two students' papers each semester for this purpose, and I keep my collection of "Excellent Student Papers" on reserve in the library for the use of future students.
Findings
After you assign and collect the papers, you face the issue of providing feedback and grades. There is a considerable literature which documents that instructors provide poor feedback to our students on writing. What students see when they get their papers back is a plethora of very specific comments about spelling and grammar, and only a few (confusing) comments on organization and structure. As a result, students do not in general rewrite papers by thinking about the process of writing. Instead, when rewriting is permitted they go from comment to comment on their draft, and change those things (and only those things) that their instructor pointed out. For this reason, I avoid assignments that require rewriting whenever I can: the instructor does a lot of work as an editor, and the student learns a minimal amount from the process.
One of my favorite assessment tools is the rubric, "a direction or rule of conduct." My own rubrics take the form of a checklist with specific yes or no questions, which I list here:
In this paper,
Certainly I am not advocating that this is the only form a cover sheet could take. Other rubrics might be more general in nature: for example, having one section for comments on mathematical accuracy and another for comments on exposition, and then a grade for each section. At the other extreme, there are rubrics which go into greater detail about what each subdivision of the rubric entails, with a sliding scale of grades on each. There is a growing literature on the use of rubrics—see Houston, et al [3], or Emenaker's paper in this volume, p. 116.
Use of Findings
Students get a copy of my checklist even before they get their first assignment; they are required to attach this sheet to the front page of their completed papers. I make almost all of my comments directly on the checklist, with a "yes" or "no" next to each question. The total number of "yes's" is their grade on the paper.
The main reason I like the rubric as much as I do is that it serves as both a teaching and an assessment tool. Students really appreciate having the guidance that a checklist provides, especially on their first paper. Moreover, the fact that the checklist remains consistent from one paper to the next (I assign three) helps the student to focus on the overall process of writing, rather than on each specific mistake the instructor circled on the last paper.
I said that my foremost reason for using the checklists is pedagogical idealism, but running a close second is practicality. Using this checklist has saved me a considerable amount of time grading. For one thing, it makes providing feedback easier: I can write "X?" next to question (6) above instead of the longer "What does X stand for?" Moreover, the checklist makes it less likely that the student will neglect to describe "X." Using the checklist gives the appearance of objectivity in grading; I have had very little quibbling over scores that I give—this is unusual at my college. I describe this checklist in greater detail in [2]; and I refer the interested reader there.
Success Factors
If an instructor does decide to have students rewrite their work, one way to provide valuable commentary but still leave responsibility for revision in the students' hands is to ask students to turn in a cassette tape along with their draft. A simple tape player with a microphone allows for much more detailed comments of a significant kind: "In this paragraph, I don't understand whether you're saying this or that … you jumped between three topics here without any transitions … oh, and by the way, you really need to spell-check your work before you turn it in again." I've found that students much prefer this kind of feedback. It means less writing for me; and it results in significantly changed (and better) final drafts.
If you assign a long-term project, it is extremely helpful to mandate mini-deadlines which correspond to relevant subtasks. These help to reduce student anxiety and to avoid procrastination. For example, when I assign a semester-long research paper, I have a deadline every week or two, in which students are expected to turn in:
One last piece of advice: As you prepare your assignments, make sure that you have resources available on campus to help the anxious or weak student. One of these resources will necessarily be you, but others might include math tutors, a writing center, and books or articles on writing mathematics (such as [1] or [4]).
References
[1] Crannell, A., A Guide to Writing in Mathematics Classes, 1993. Available upon request from the author, or from http://www.fandm.edu/Departments/Mathematics/Writing.html
[2] Crannell, A., "How to grade 300 math essays and survive to tell the tale," PRIMUS 4 (3), 1994.
[3] Houston, S.K., Haines, C. R., Kitchen, A. , et. al., Developing Rating Scales for Undergraduate Mathematics Projects, University of Ulster, 1994.
[4] Maurer, S., "Advice for Undergraduates on
Special Aspects of Writing Mathematics,"
PRIMUS, 1 (1), 1990.
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