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?

 

References

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.