Estes (1989), in his discussion of the importance of writing in math, refers to writing as a âthinking clarifier,â 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, âa major concern with writing projects in mathematics (and other courses as well) is that they often feel tacked on and artificialâ write Parker and Mattison (2010: 47). Â âThe paper is something they had to do in order to receive âwriting creditâ for a course. Itâs a game and everyone is playing alongâ (38). Most of usâstudents, math faculty, and non-math faculty, can relate to this opinion, or recognize it.

Parker and MattisonÂ astutely describe this discrepancy in attitudes toward writing, from one discipline to another, as beingâin the case of mathâthe difference between âwriting about math,â which often comes in the form of an assigned paper on a mathematician, and âwriting math,â 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 âtextbook writing assignment,â 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 âword problems,â 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. Estesâ example prompt is as follows: âIf two variables have a correlation coefficient of -0.98, explain the meanings of the negative sign and the absolute value of 0.98â (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, âand how do you know?â While our students often get the correct answer by calculating it, at other times they arrive at the answer by guessing, orâperhaps more commonâby 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 Estesâ (above) in my own linguistic coursework could be:

Question 1: âFor the two morphemes below, identify which morpheme is inflectional and which is derivational.â

Question 2: âFor the next two morphemes, explain *why* morpheme A is inflectional, and why morpheme B is derivational.â

My exams and assignments usually do include a âwhat is your evidenceâ 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 âhalf of ten is five,â then replaces the numbers with digits, âhalf of 10 is 5,â then the remaining words with symbols, âÂœ x 10 = 5,â showing that the equal sign functions like the verb âto be,â 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 ârational numberâ is so named for fractions like ÂŸ because that number is a **ratio** of whole numbers. He also finds it helpful to explain that âsquaringâ 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, âWrite out the meaning of and reason behind the term âto square a number.â Feel free to provide examples and drawings to make your answer clear.â

What kinds of âword problemsâ do you use in your various disciplines?

References

Estes, Paul L. (June 1989). Writing across the mathematics curriculum. *Writing across the Curriculum. *10â16.

Parker, Adam, and Mattison, Michael. (November 2010). *The WAC Journal, 21.* 37â51.

Strogatz, Steven. (March 2014). Writing about math for the perplexed and the Traumatized. *Notices of the AMS, 61,* 3. 286â291.

Incorporating writing into #math #coursework in our latest blog post #WACWID #quantitativereasoning http://t.co/TMDycHDzcP