What is Writing in Mathematics?

Objective: Students will be able to recognize mathematical writing as writing, even though it may look different from the writing they have done in other courses. In addition, they will be able to recognize commonalities between mathematical writing and more general writing, such as the use of complete sentences and the use of nouns and verbs, even if the nouns and verbs are sometimes represented by symbols. Moreover, students will recognize the varied genres of mathematical writing, including pen-and-paper calculations, proofs, exposition, and coding, and recognize various audiences that mathematics can be written for, including the general public, students, and experts in the field. Finally, and perhaps most importantly, students will recognize that mathematical writing can serve not only to communicate ideas, but also to clarify the thinking of the writer. 

Key Terms: Genre, audience.

Timing: These lessons could be particularly appropriate in lower-division courses, or any course where students are learning or broadening their idea of what comprises mathematical writing. 

Lesson

Part I: Writing and Exposition in Lower Division Courses

1. Consider these slides, Writing and Exposition in MA 124, created by Li-Mei Lim. You may wish to modify them to better match the content of your course.
2. Present these slides to your students within the first, or second, week of the semester. 
3. Consider taking presentation and exposition into account in assessments, for example by allocating points on quizzes and exams for them. You can see the corresponding MA 124 syllabus to see how it was done in the above course. 
4. When presenting examples at the board, consider being explicit about which things you write are complete sentences, and which aren’t, and about which variables play the role of nouns, verbs, etc. 
5. Explicitly state that the type of writing done in, say, a calculus exam, is one specific genre of mathematical writing, where the audience is the teaching fellow and/or instructor of the course who will be grading the exam. 

Part II: Mathematics as a Process of Creative Discovery

1. Consider these slides, Why are we here? Developing a mindset for success in math, created by Jared Weinstein. You may wish to modify them to better match the content of your course.
2. Present these slides to your students, perhaps at the beginning of the semester to frame how you think about mathematics, or you may present it later, so you can relate it to how students have been thinking about mathematics in the early part of your course.  
3. Emphasize that mathematics is largely about process, and not primarily about getting the right answer, even though it may sometimes seem that way.