Conventions in Mathematical Writing
Objective: Students will be able to recognize and utilize a variety of conventions used in mathematical writing.
Key Terms: Convention, audience, discipline, stylistic choice.
Timing: These lessons could be particularly appropriate in any course where students are learning to think of mathematical work as writing.
Conceptual Framework
Students can often feel difficulty in knowing where to start with their mathematical writing, particularly because they may be used to mathematics courses that feel largely algorithmic, where most problems have a sort of recipe they can follow to produce a correct result. When that framework is removed, students can be unsure of what to do or where to start, and they can feel confused at the freedom they have in choosing how to write about their ideas. Providing them with some basic mathematical conventions can feel grounding, in that it gives them something fairly concrete to focus on. On the other hand, some students can also feel overwhelmed at having to be mindful of such conventions while also learning new context and new forms of writing, such as proof writing.
When discussing conventions, it can be helpful to frame them not as rules that must be strictly adhered to, but rather as guidelines that can help make their writing more clear for their intended audience. Moreover, it can be helpful to also discuss the concept of stylistic choice, and that there can be two successful proofs of the same result that read very differently. However, often such stylistically different proofs still adhere to a similar set of basic conventions. Furthermore, there can be times when it is desirable to explicitly violate a known convention (for example a notational convention), but if one is going to do so, it can be helpful to potentially flag that choice for the reader, and to explain why that choice is made.
Lesson
Part I: Basic Mathematical Conventions
- Consider the essay “Some guidelines for good mathematical writing” by Francis Su.
- Have students read this essay and a piece of mathematical writing of your choice that is tailored to your course, either during class or as homework. This could be, for example, a portion of your textbook, a sample of anonymized student writing, a purpose-written sample that you create, or something more advanced, depending on the course.
- Put the students into small groups.
- Have the students evaluate the writing based on the suggestions in the essay, and answer the following questions in their groups.
Questions for the Francis Su reading
- Did the writing follow all of the conventions suggested in the essay?
- In places where it did not, did this impact the clarity of the writing? If so, how?
- Do you have any ideas why the author did not follow the conventions in those places?
Variations and Follow-Ups
Create a purpose-written sample that intentionally does not follow the conventions described in the essay. Ask students to rewrite it so that it follows the conventions to a greater extent that it originally did. Also ask the students to identify places where they feel the conventions are not needed, and explain why.
Further Reading
“
Practical suggestions for mathematical writing” by Bell et al, Notices of the AMS, 68(6), 2021. This essay is a bit more advanced and could be more useful in upper-level courses. For example it could just be offered as a resource, or, if a final paper/project is being assigned, it could be used to frame that writing assignment, or any peer feedback they may undertake related to that assignment.