Writing to Calculate: Ideas for Incorporating Writing into Math Coursework

Estes (1989), in his discussion of the importance of writing in math, refers to writing as a “thinking clarifier,” in that the act of writing out a concept requires understanding that concept. This understanding may even occur in the sometimes painful process of getting a few complete sentences typed out. Unfortunately, though, “a major concern with writing projects in mathematics (and other courses as well) is that they often feel tacked on and artificial” write Parker and Mattison (2010: 47).  “The paper is something they had to do in order to receive ‘writing credit’ for a course. It’s a game and everyone is playing along” (38). Most of us—students, math faculty, and non-math faculty, can relate to this opinion, or recognize it.

Parker and Mattison astutely describe this discrepancy in attitudes toward writing, from one discipline to another, as being—in the case of math—the difference between “writing about math,” which often comes in the form of an assigned paper on a mathematician, and “writing math,” which is actually writing on math content concepts, to facilitate their absorption. Luckily, there are a number of ways to incorporate writing into the math curriculum, that are not only painless, but productive and purposeful as well. For example, they suggest a “textbook writing assignment,” which requires students to write out the mathematical equations they learn in textbook style, and also to explain why the equations are the way they are. By having students write out textbook chapters that will be distributed to the rest of the class, by way of making study materials for everyone, in this example, students are given a clear audience, beyond the professor, and an opportunity to uncover any difficulties they may be having with the material.

Alternatively, there are ways for math professors to incorporate less formal (more lower-stakes) math writing assignments, or instead to incorporate more writing into exams, and therefore into exam study guides. As Estes points out, including short-answer questions on exams need not merely be traditional math “word problems,” which are limited to a short section of the algebra curriculum. In other words, asking students to write out concepts taught, a step beyond only writing out the equations numerically, is beneficial for exams and for exercises to practice for the exams. Estes’ example prompt is as follows: “If two variables have a correlation coefficient of -0.98, explain the meanings of the negative sign and the absolute value of 0.98” (12).

While the non-mathematician reader may need to leave the details of this example aside, it is a helpful illustration of how such word problems may apply to other non-Humanities fields. For example, in my social science field, linguistics, I assign language datasets to my students, and when students volunteer a correct solution in class, I am usually obligated to ask, “and how do you know?” While our students often get the correct answer by calculating it, at other times they arrive at the answer by guessing, or—perhaps more common—by erroneously using incorrect reasoning that accidentally led them to the correct answer. We all know that this will not help them with similar questions in the future. So, this act of explaining out loud how the answer was determined is something we can all apply to our own classes. A parallel example to Estes’ (above) in my own linguistic coursework could be:

Question 1: “For the two morphemes below, identify which morpheme is inflectional and which is derivational.”

Question 2: “For the next two morphemes, explain why morpheme A is inflectional, and why morpheme B is derivational.”

My exams and assignments usually do include a “what is your evidence” question, but asking students to write this evidence out, in prose, is taking the process of writing to learn one step further.

For additional convincing and thought-provoking evidence that it is beneficial to integrate prose into math, Estes also describes an elementary math class lesson plan on fractions, in which the teacher starts with a sentence like “half of ten is five,” then replaces the numbers with digits, “half of 10 is 5,” then the remaining words with symbols, “½ x 10 = 5,” showing that the equal sign functions like the verb “to be,” and so on.

Another idea is to come up with reasons for mathematical concepts that students may not know. For example, Strogatz (2014: 287) describes the light bulbs that go off when he explains that the term “rational number” is so named for fractions like ¾ because that number is a ratio of whole numbers. He also finds it helpful to explain that “squaring” a number is so named because the results can fit in a square, like the number nine, illustrated below:

Without being able to predict exactly what would work for math professors here at City Tech, I imagine that, when I was a student in an introductory math class, I would have greatly appreciated answering an exam question such as, “Write out the meaning of and reason behind the term ‘to square a number.’ Feel free to provide examples and drawings to make your answer clear.”

What kinds of “word problems” do you use in your various disciplines?



Estes, Paul L. (June 1989). Writing across the mathematics curriculum. Writing across the Curriculum. 10–16.

Parker, Adam, and Mattison, Michael. (November 2010). The WAC Journal, 21. 37–51.

Strogatz, Steven. (March 2014). Writing about math for the perplexed and the Traumatized. Notices of the AMS, 61, 3. 286–291.

Updates + WAC Beyond City Tech

What’s new at City Tech WAC?

On Tuesday, February 18, 2014, Jacob Cohen and I presented a faculty workshop on thesis statements. If you missed it, you can view our slides here, and our handout here.

Tomorrow, Tuesday, March 11, 2014 Fellow Heather Zuber and I will be giving our next faculty workshop, “Avoiding Plagiarism and Using Library Sources,” in collaboration with Instructional Design Librarian Bronwen Densmore, and Instruction/Reference Librarian Anne Leonard. Please attend! Our other upcoming events include our workshop on working with English learners in April, and a workshop on incorporating technology, creatively, into your classes, in May. Please check out our flier with all of these workshops and information for how to RSVP, here.

In other news, you can now follow us on twitter, here.

WAC Elsewhere

It is always useful and inspiring to hear about how other institutions are promoting and continuing the WAC movement. Exploring the work of like-minded WAC philosophy-followers is validating, and fun, especially when expressed via media, and not just written articles. For example, here is a short and informative “cheat-sheet” video on WAC practices by Purdue Owl.

A great resource on WAC philosophy, and on incorporating WAC principles into your classroom, can be found at the WAC Clearing House. The Clearing House folks eloquently cover all of the topics in our work and workshops this year, plus more. One aspect they highlight well is one that is particularly relevant for faculty in our CUNY system: an assurance that adding more writing to coursework across the curriculum will not increase grading or prep time much, if at all. For example, see this link on peer review and supplemental writing assignments, and this one on how to handle responding to draft grading, with links on time-saving tips such as using shorthand for grading, and not correcting grammar too much.

For any faculty who don’t have a chance to go through these links, and even for those who do, our workshops are a useful shortcut, and they even come with lunch. We can also be contacted, as always, for an appointment for an individual consultation.

Writing to Learn

As the fall semester of 2013 draws to a close, it is useful to reflect on what we have accomplished over the course of the semester. We the Writing Across the Curriculum fellows have led three main faculty workshops since September: Effective Assignment Design, Peer Review, and Effective Grading. Despite the three varied topics of these workshops, they share a common thread, which is the WAC philosophy of “writing to learn,” and in addition, their content overlaps nicely.

In order to highlight WAC principles, I wish to focus on one particular aspect of the effective grading strategies that Jake Cohen and I discussed in our workshop on Tuesday, December 12 (the last of the semester). We went over some techniques to improve student writing and work, most of which also incidentally result in reduced grading time, which is always welcome, especially at this end-of-semester crunch grading time. To view our workshop slides, please click here, and check out the handout. (You can also visit this page to download documents from all of our workshops.) We discussed minimal marking, supportive responding when writing comments on student papers, rubrics, and planning assignments ahead of time to make grading more efficient. This last category is closely related to the two previous workshops from this semester: assignment design, clearly, and also peer review, in that having students assess each others’ work can save time, and greatly improve student writing.

This assignment design category is also the “one particular aspect” that I choose to elaborate on for this post. Among the several techniques we suggested for planning ahead to make assignments more “gradable,” one sticks out as being particularly WAC-esque: the uncollected writing assignment. The value of this notion, which is generally under-utilized by faculty in all departments, is two-fold: It is easy to see how uncollected assignments decrease the overall amount of time we spend grading work, of course, but why assign them at all? The answer lies in the foundation of WAC philosophy, which is that people learn by doing—and more specifically, by writing. So, what kind of uncollected writing do we recommend you assign, how do you enforce such assignments without collecting them, and, finally, how do students “learn by writing”?

One of the best illustrations of this concept is provided eloquently by Toby Fulwiler in “Why We Teach Writing in the First Place”: “Writing the thought on paper objectifie[s] the thought in the world… [which] even happens when I write out a grocery list—when I write down ‘eggs’ I quickly see that I also need ‘bacon.’ And so on” (127). This concept works well for professors across the curricula: Think about assigning a five-minute, in-class free-write asking students to describe course content covered in the past month/week/hour, by way of ensuring that they can articulate it well for whatever type of exam they have coming up, and by way of allowing them to discover holes in their understanding of what you have covered so far. If you are concerned that they won’t oblige the assignment without the potential for reward, then you can choose, for example, to select three at random to read aloud in class, or to be posted on your Blackboard/OpenLab page that same evening.

We hope that those who incorporate this technique will ultimately find that the grading process of the final papers you assign will be ameliorated, in that the students have now had a chance to “practice” or “train” for the final writing process, something akin to athletes who could never run a marathon without similar training, without you having been required to grade an intermediary draft. Ideally, as students come across “holes” in their own comprehension of your course content, they may come to you with more questions, or make better use of your office hours. I know that they will arrive at a deeper understanding of your course material in the same way that I have done regarding WAC philosophy, in the process of writing out this blog post.

Happy Holidays!