Creating and Using Effective Writing Prompts in the Calculus Sequence

M. E. (Murphy) Waggoner, Simpson College

I have always wanted to use a significant number of short writing assignments in the calculus sequence. In order to do this there were several issues to be resolved: there needed to be a ready supply of writing prompts to choose from, the students needed to clearly understand the objectives and requirements of the assignments, and the grading of the writing needed to be effective and efficient. I have made significant progress toward the resolution of these problems and, during the 2003-2004 school year, I assigned writing assignments to students in Calculus I, II and III on a regular basis. The response to the writing assignments from the students was strong and positive.

In calculus this year, I required the students to respond to writing prompts once or twice a week. For each response, I gave them 4 to 5 writing prompts from which to choose and the responses to these prompts were hand-written and ranged from 3/4 to 2 pages in length. The prompts directly addressed the concepts of the course and gave the students sufficient opportunity to integrate numerical and graphical representations of mathematics into the writing.

The first obstacle to resolve was the availability of writing prompts. In order to have a comprehensive list of questions, during sabbatical leave in the spring of 2003 I gathered and wrote 800 writing prompts that span the entire calculus sequence. These prompts are available on-line and the list continues to grow. I would like to help others begin to develop writing prompts that fit well with their own teaching styles by explaining how I develop new questions.

The second issue was to help the students understand the expectations and to set the tone of the assignments from the very beginning of the semester. I gave the students a carefully written set of expectations, but did not expect them understand that document without help. I spent time during the first two weeks of class trying to help them understand the expectations by providing them with examples of good and poor writing and explaining the strengths and weaknesses of each. During that time and as a group exercise, I also had the students write responses to selected writing prompts on the board. I graded the responses for the entire class so they could clearly see how I would grade.

Finally, I needed to be able to read 30 writing responses in a short time and still give the students effective feedback. I knew that I needed to develop a rubric that adequately reflected the expectations of the assignments and required mathematical rigor in the writing. In cooperation with a writing instructor, I created a rubric that has satisfied my needs.

Twenty-nine percent of the students in Calculus I said on the end-of-year evaluations that the writing assignments were the most valuable feature of the course. One student wrote, “Writing assignments help a lot, better sometimes than doing homework problems.” Another student wrote, “They’re very helpful because they make sure you understand the concepts and because they give you practice translating math formulas/ideas into words.” In some cases there seemed to be a love/hate relationship with the writing as with this student who said, “Writing assignments really stunk sometimes but were very helpful in forcing me to really understand what we were working on.”

My own impressions are that the students in this year’s calculus sequence were able to communicate about mathematics more effectively than previous calculus students did. I saw improvements in how well the students understood the lectures and how articulate the students were when asking questions and making comments in class. My calculus students have encouraged me to continue using the writing prompts in the future and I will.