Writing in the Discipline
1. Why or in what ways is writing important to your discipline/field/profession?
In any career involving mathematics – including business, research, teaching, and other pursuits – written communication regarding process and results is important. People in careers in mathematics need to be able to explain results (including explanations for non-technical audiences), need to be able to detail the steps of a solution process, and need to be able to write precise mathematical proofs.
2. Which courses are designated as satisfying the WID requirement by your department? Why these courses?
The Math Department offers two mathematics majors: the B.A. in Liberal Arts Mathematics and the B.A. in Secondary Education, Mathematics. The department has identified two required courses in each of these majors to be designated as satisfying the WID requirement.
Liberal Arts Mathematics: MATH 300: Bridge to Advanced Mathematics & MATH 461: Seminar in Mathematics
Secondary Education, Mathematics: MATH 300: Bridge to Advanced Mathematics & MATH 458: History of Mathematics
Our rationale for designating the courses described above as satisfying the WID requirement is as follows:
- Bridge to Advanced Mathematics is dedicated to the teaching of how to write formal mathematical proofs. It also contains process-oriented and explanatory writing, although to a lesser degree.
- History of Mathematics involves a large amount of process-oriented and explanatory writing, and, like all other upper-level mathematics courses, involves formal proofs.
- Seminar in Mathematics involves a large amount of process-oriented and explanatory writing, and, like all other upper-level mathematics courses, involves formal proofs.
3. What forms or genres of writing will students learn and practice in your department’s WID courses? Why these genres?
Writing in the discipline of mathematics is likely to fall into one of three categories. The first is explanatory, in which the writer communicates the essentials of a mathematical concept. The second is process-oriented, in which the writer details the reasoning throughout an analysis of a particular problem (this category can be thought of as an expanded version of the familiar instruction to “show your work”). The final category is formal mathematical proofs, detailed logical arguments that could be said to be the mathematician’s version of persuasive essays. (Source: (Russek, 1998; Flesher, 2003)
All three of the categories can inform a reader, and all three can serve to demonstrate the writer’s understanding of the topic at hand. Moreover, all can also serve as “writing-to-learn” activities as the writer must analyze and perfect his or her own understanding in order to create and revise a product.
4. What kinds of teaching practices will students encounter in your department’s WID courses?
In Bridge to Advanced Mathematics, a scaffolded approach to teaching proofs is used. The proofs begin at a simple level, with templates and guidelines available. All instructors strive to give detailed criteria for how to construct a proof: what must be said, what pattern to follow, what wording to use and to avoid, and so on. Repetition and revision are universally employed. All instructors use frequent assignments and provide feedback, and some instructors choose to use group work, peer discussion, and low-stakes class presentations. As the semester progresses, the proofs that are being studied and written get more complex, and different techniques and topics are introduced.
In History of Mathematics and Seminar in Mathematics, styles and assignments vary from instructor to instructor. However, all use daily assignments with an attempt to provide rapid feedback, and low-stakes student presentations and discussions are a staple. When projects are assigned, they are clearly defined and structured using a series of deadlines and discussions with the instructor. A survey of reading and some brief summaries is typically used to start the process, followed by a choice of topic, a collection of sources, an outline, a rough draft, and so on, with feedback from the instructor at every step.
5. When they’ve satisfied your department’s WID requirement, what should students know and be able to do with writing?
A student who has successfully completed either Mathematics major should be able to
- Read, construct, and write formal mathematics proofs. This includes understanding the most common techniques of proof and the logic that underlies them.
- Write clear process-oriented work that details the reasoning and steps in solving a mathematics problem. This includes the ability to justify each step in a solution.
- Write clear explanatory work to describe mathematical concepts. This includes the ability to describe mathematical concepts to an audience new to the topic at hand.