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 nontechnical audiences), need to be able to detail the steps of a solution process and need to be able to write precise mathematical proofs.
Which courses are designated as satisfying the Writing in the Discipline (WID) requirement by your department? Why these courses?
The Department of Mathematical Sciences offers two undergraduate degrees in mathematics: the B.A. in liberal arts mathematics and the B.A. in secondary education, with a concentration in 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, with a Concentration in Mathematics
- MATH 300: Bridge to Advanced Mathematics
- MATH 458: History of Mathematics
MATH 300 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. MATH 458 involves a large amount of process-oriented and explanatory writing, and, like all other upper-level mathematics courses, involves formal proofs. MATH 461 involves a large amount of process-oriented and explanatory writing, and, like all other upper-level mathematics courses, involves formal proofs.
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 their own understanding in order to create and revise a product.
What kinds of teaching practices will students encounter in your department’s WID courses?
In MATH 300, 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 MATH 458, 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.
