Writing well requires mastery of writing principles at a variety of different scales, from the sentence and paragraph scale (e.g., ordering information within sentences so content flows logically) to the section and paper scale (e.g., larger-scale structure). To simplify teaching, you can begin the term with shorter assignments to address the smaller-scale issues so you can more easily focus on the larger-scale issues when you assign longer assignments later in the term. At all scales, students best learn to communicate as mathematicians if the assignments are as authentic as possible: if the genre and rhetorical context are as similar as possible to those encountered by mathematicians.
Examples of short assignments
- Require that at least one question on each problem set be typed up and written in the style of an expository paper (rather than the usually terse and sometimes scattered style of a homework solution).
- Assign short exposition tasks such as summarizing the proof of a theorem done in class or filling in the gaps in an explanation given briefly in class.
- To help students learn LaTeX or how to use equation editors, have an assignment requiring at least basic math formatting due early in the semester so students aren’t required to learn it as they’re researching and writing their term papers. Begin with simple math formatting exercises, building to more complex: e.g., see the assignments for M.I.T.’s Real Analysis recitations 1 (text with math), 2 (table and figure) and 13 (slides containing a figure with LaTeXed labels).
- Begin with communicating simple arguments, building to more complex (e.g., having students explain the heapsort algorithm and then revise the explanation based on feedback provides a rich opportunity for teaching about writing clear definitions, giving conceptual explanations as well as rigorous details, and presenting information in an order that is helpful to readers.) See the sequence of assignments from M.I.T.’s Principles of Applied Mathematics.
- Have students revise part of a concise textbook such as Rudin’s, Principles of Mathematical Analysis in the style of a more-thorough lecture note.
- Before an exam, have students formulate and submit to you a list of 2+ questions they have about the material. Students have a hard time formulating precise questions, yet this is an important communication and learning skill. Some students may feel they understand the course material, so permit questions that go beyond the scope of the course. You can use the questions to focus a review session. More detail about this assignment is given in this lesson plan from M.I.T.’s communication-intensive offering of Real Analysis.
The following books, articles, and websites contain short writing assignments.
- Stephen Maurer’s Undergraduate Guide to Writing Mathematics has an extensive appendix of writing exercises designed to target various aspects of writing mathematics.
- Writing Projects for Mathematics Courses: Crushed Clowns, Cars, and Coffee to Go, by A Crannell et al. [link goes to MAA review] This 119 page book from the MAA contains “writing projects suitable for use in a wide range of undergraduate mathematics courses, from a survey of mathematics to differential equations.” Each prompt is written in the form of an (often amusing) letter from someone who needs help with a “real-world” problem that requires math expertise. Students must solve the problem and write a letter of response. On his website, Tommy Ratliff (one of the co-authors) gives a brief account of using such projects in his calculus course.
- Annalisa Crannell’s Writing in Mathematics website has writing assignment for Calculus I, II, and III as well as links to colleagues’ websites that have further writing assignments.
- Quantitative Writing from Pedagogy in Action, the SERC Portal for Educators, has many examples of short and long writing assignments based on “ill-structured problems,” which are “open-ended, ambiguous, data-rich problems requiring the thinker to understand principles and concepts rather than simply applying formulae. Assignments ask students to produce a claim with supporting reasons and evidence rather than ‘the answer.'”
- The Nuts and Bolts of Proofs by Antonella Cupillari includes exercises for an introductory proof-writing course. Proof topics include calculus and linear algebra.
- Platt, M. L.. (1993). Short essay topics for calculus. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies 03.1, 42-46.
Additional information about journal-writing assignments and other writing-to-learn assignments can be found on the page about using writing to help students learn math.
For each assignment, indicate your expectations about audience and length, so students know how much explanation to include. An appropriate audience is often other students in the class who are unfamiliar with the specific topic of the assignment, or other math majors not in the class.
Term papers enable students to pursue areas of their own interest and so can be among the most rewarding assignments for students. To help students succeed, give students guidance for choosing a sufficiently focused topic, for finding helpful sources, and for using sources appropriately. See this assignment for proposing a term paper topic, from M.I.T.’s Principles of Applied Mathematics–it includes guidance for how to choose a good paper topic.
One of the (interesting) challenges of assigning a term paper is generating a list of possible paper topics. Ideally, each topic should have well-defined scope and have at least two or three available resources accessible to students in the course. You may want to emphasize to the students that they are not expected to do original mathematics research. However, the paper must be their own — they cannot paraphrase and closely follow a published survey paper.
One of your institution’s librarians may be happy to collaborate with you to show students how to find useful sources.
To provide students with an authentic rhetorical context for their term papers, consider showing them samples of expository papers and suggesting that they write for a journal that publishes expository papers (e.g., The American Mathematical Monthly, Math Horizons, Mathematics Magazine, andThe College Mathematics Journal.
Don’t assign a term paper unless a variety of topics exist at an appropriate level. For example, a term paper may not be appropriate for an introductory class in analysis.
Be aware that plagiarism may be an issue particularly in large classes on subjects for which a wealth of material is available online. In such classes, you may find it to be helpful to tightly specify the paper topics or to supply a specific slant to the papers (e.g., apply such-and-such method to an application of your choice). Vary the assignments from year to year. These precautions may be less important in small classes.
In some classes (e.g., applied mathematics classes), it may be necessary to carefully guide students to choose topics that contain sufficient mathematical content. For that reason, using caution when approving unfamiliar topics.
Designing assignments that enable students to write well
A poorly focused assignment will leave students confused about what is expected of them and is likely to result in poor writing. Students are likely to write their best if the assignment is interesting and if students are told (or are able to confidently identify for themselves) the following:
- educational objectives of the assignment
- audience knowledge and interest, and author’s relationship to the audience
- purpose of the text to be written (e.g., to convince, to entertain mathematically, to teach, to spark interest)
- content to be addressed
- details of the genre (proof? research paper? funding proposal?)
- how the writing will be graded
- an effective writing process (you can provide support by assigning intermediate due dates or revision)
The following resources explain these points and give further guidance for designing effective assignments:
- Bahls, P., Student Writing in the Quantitative Disciplines: A Guide for College Faculty, Jossy-Bass 2012, pp. 36-46, contains sections on structuring writing assignments (includes sample prompts), sequencing assignments throughout a course, and sequencing writing from course to course.
General resources (not specific to mathematics)
- The WAC Clearinghouse
- The webpage Integrating Writing and Speaking Into Your Subject, provided by MIT’s Writing Across the Curriculum, has several subpages about writing assignments.
- Creating Writing Assignments, MIT’s Writing Center
- Assignment Design from George Mason University’s Writing Across the Curriculum is a short video with supporting materials.