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“If It’s a Math Class, Do We Really Have to Write?”
Meeting the NCTM Process Standard, Mathematics as Communication

Margaret Wirth
Department of Mathematics, Science and Instructional Technology Education

When asked to write reflections, summaries or essays in a mathematics class a student will often say, “I always have trouble writing English papers, but I don’t worry about it because in mathematics we are not really expected to write.” Unfortunately, once one student states his abhorrence for writing, others chime in, and soon a chorus of students shares their distain for writing and its irrelevance to succeeding in a mathematical world.  The inability to write coherently using proper English is widely viewed as acceptable among most American mathematics students.  The first national mathematics curriculum guidelines addressed this problem in 1989 when the National Council of Teachers of Mathematics (NCTM) incorporated writing and verbal communication in mathematics into its ten national standards.  In the Mathematics as Communication Standard, the NCTM clearly stated that mathematics instruction should include relevance to real-life applications and incorporate written and verbal communication of mathematical ideas in every mathematics classroom.

Creating an atmosphere where writing is accepted as a daily form of mathematical communication was a major challenge many earlier math teachers chose not to pursue.  But today’s modern mathematics teachers have accepted the NCTM challenge and expect students to explain their problem solving techniques and summarize their findings both verbally and in written form on a regular basis. Communication skills are now as valued in mathematics classes as they are in liberal arts classes, but since most mathematics teachers are not also English teachers, the difficulty in creating writing assignments that will produce acceptable written results in a variety of mathematical contexts is a serious challenge.

For example, as a secondary mathematics teacher in a local high school I asked my students to write a typed minimum three-page paper about their personal mathematical histories. The paper was to include their evolution mathematically from grade school until the present, their best and worst mathematical moments, and the influential mathematical people in their lives.  My sole writing requirement was for them to employ acceptable grammar and Standard English. My directions were not extremely detailed, and there was no proofreading or pre-submission requirement. My high school students were not “declared math majors,” so the moaning and groaning about writing a paper in a math class was minimal. My purpose in the writing exercise was twofold: I wanted to learn more about my students as individuals, and I wanted them to think about the important role mathematics had played in their lives. Without any writing guidance from me, my high school students wrote the most amazing histories, full of detail and heartfelt descriptions of their mathematical experiences. Each typed paper exceeded the minimum page request and included complete sentences, good grammar, and correct spelling. In general they were well-written and engaging. I learned a tremendous amount about each student from these papers, and they loved sharing their very personal mathematics experiences with me. Overwhelmingly the students praised this writing assignment consistently as one of their favorites in my math class. After each student graduated, I mailed their papers to their parents who were as delighted as I was with their children’s products. These student mathematical histories became instant keepsakes for many of these families.

Now we fast forward to my college classes. I am teaching pre-service mathematics secondary education students in my methods class during their senior year. The methods class is during the Senior 1 experience when students are assigned to their high school clinical teacher and visit the school one full day a week. During the following semester, they will be in the field, student teaching every day at their assigned high school. For this group of pre-professionals I altered my mathematical history paper assignment and requested that students write a brief mathematical autobiography (see Appendix A). I asked them to include a short math history, describe themselves, explain why they want to teach, and state their career goals in a typed paper about three pages in length that could be shared with their clinical teachers. The purpose of the paper was still two-fold: I wanted to learn about each of my interns, and I wanted to have a product to send to their clinical teachers prior to their field service to acquaint their clinical teachers with them.

From the moment the assignment was made the complaining began.
    Why do we have to write this?
    Exactly how long should it be? Really 3 full pages?
    Double spaced or not? 
    Exactly what do we need to include?  How will it be graded?

Following lengthy classroom discussions concerning written and verbal mathematical communication, the students begrudgingly accepted the rationale for this assignment. The autobiographies were submitted two weeks later, and the results were simply disheartening. The vast majority of the papers were poorly written, lacked direction, and almost trivialized the assignment. It was evident that these senior mathematics students were in need of serious literary and grammatical help. I was astounded at the difference between my high school students’ writing skills and my college students’ writing skills.

It was at that point that I realized that I was going to have to change the way I asked my college students to write. I was dealing with a very different audience. I recognized that for so many to have failed in completing the assignment satisfactorily simply demonstrated that I had not prepared them adequately to accomplish the written task successfully. It was obvious the students needed more detail and better instruction from me for the writing assignment to produce the desired results.

I gradually began changing my writing assignments by redesigning the overall directions as more detailed requirements. By allowing little creativity and emphasizing only the facts, the written submissions improved, but the papers still lacked the writing qualities (polish and clarity) that I expected. Eventually I found a remarkable technical writing assignment in a set of teacher resource materials that seemed perfect for my needs. Created by a fellow mathematician, Dan Yates, it was created to teach students to follow directions in his statistics classes. I adapted the Yates writing model to meet the needs of my pre-service teacher’s autobiographical writing assignment. Using this very explicit one page autobiographical document the writing results have been excellent. His students follow the specific directions carefully and answer the prompts precisely. Since using this very explicit format, the autobiographical submissions have been excellent (see Appendix B). The grammatical errors are now few and far between, and the English is now correct. I am still getting the “I cannot write, but I can do math” comments from a few students when I make the assignment, but the paper no longer seems daunting to them. The content is descriptive and yet concise. The students are now proud of their papers, and I can easily share their stories with their clinical teachers via email. Once I discovered this use of short descriptors for each step in a writing assignment produces better results, I patterned my other writing assignments using the same detailed technique.

Of course, my nagging concern has been that I have oversimplified each writing assignment to the point that now I have trivialized the writing level of my students. My biggest question to the WAC Academy participants was how to improve my writing assignments so that my students would continue to write better on demand yet somehow allow a more open and creative venue for them to describe their thoughts. The suggestions that resulted were very useful and could easily be implemented in my methods classes. One suggestion included modeling situations, like a classroom management problem, in class. Then, instead of simply discussing the situation, I could ask students to write their responses to the situation. Critically discussing the solutions and the written responses in class will strengthen both behavioral and writing skills. Another idea included giving students writing prompts on a daily basis. For instance, when describing a mistake that occurs when teaching students, the instructor can ask the students to script what they would say to correct the modeled mistake. A third suggestion employed the fish bowl technique. This technique creates a situation in which some students model a behavior while the remainder of the class strictly observes and writes about what they observe. Again the students have opportunities for both written and verbal dialogue during class time to discuss and develop their problem solving and communication skills.

All of these WAC suggestions might create consistent writing experiences in the class that will allow the mathematics students to build their writing skills with constructive input from the instructor and their peers. As stated in the NCTM Communication Standards, “As students develop clearer more coherent communication, they will become better mathematical thinkers.” With improved writing practice experiences, these pre-service teachers should be better prepared to convey written mathematical thinking processes and problem solving techniques with each other and their future students. Eventually maybe writing in mathematics classes will become the norm for effective teaching, and the echoes of “I do math, I don’t need to write” will no longer be heard in the halls of mathematics classes.

References

National Council of Teachers of Mathematics. (2000.) Principles and Standards for School Mathematics, Reston, Virginia, 348-352.

Yates, Dan. (2008.) Platinum Resource Binder, Special Problem 0, The Practice of Statistics, W. H. Freeman and Company, New York, 11.


View the Appendices to Dr. Wirth's article here.