Is Aunt Frieda FUNCTIONally Literate?

Janet M. McShane

Northern Arizona University

Many mathematics departments have a semester long course for majors where the students are introduced to the techniques of writing proofs. At Northern Arizona University our course is MAT 320W – Foundations of Mathematics. The content of this course covers symbolic logic, set theory, functions and number systems and focuses on the techniques of proof and mathematical writing. In addition, it satisfies the junior-level writing requirement for mathematics majors. (As part of the Liberal Studies requirements at NAU, all students must take a junior-level course that focuses on improving their writing abilities.) Thus this course is not only trying to cover content and get the students to become proficient at writing proofs but also is attempting to improve their general writing skills. This is a tall order for a three-hour course.

Throughout the semester the students are constantly doing homework assignments the bulk of which involve writing proofs. Oftentimes, students present their proofs to the class. The assignments are then handed in, critiqued and if need be are resubmitted. The resubmission process enables me to give the students feedback on what they have done and gives them the chance to improve the content and exposition of their work.

What this presentation will discuss is a few of the “writing assignments” I have tried in this course. Specifically, I will focus on the assignments that bridge the many goals of this course.

During the first week of the course I have the students do a Mathematical Autobiography. This gets them immediately in the writing mode, gives them a chance to talk about their mathematical background and future goals, and gives me some valuable information regarding both their mathematical background and their writing abilities.

Once we have finished discussing the various methods of proof, usually about 5 weeks into the semester, I have the students write a paper on a particular method. I tell them to pick a method of proof and write a paper that explains that method making sure they give necessary examples. They are to write this paper with the idea that the person reading it is non-mathematically inclined. I encourage them to have their classmates read their papers as well as having some non-math major read their paper, such as their roommate majoring in history, to be sure that the method is understandable to a lay person.

Toward the end of the semester the students write another paper on the concept of function. Here I instruct them that on Memorial Day (3 weeks after they finish the course) they will be attending a family reunion. While there they talk with Frieda, their spunky 55-year-old aunt who has recently decided to return to school to get her college degree. Aunt Frieda is of course very interested in what courses they have taken in college and when they mention Foundations of Mathematics she wants to know what they learned in that class. The mention of functions has Aunt Frieda puzzled and the student must then explain to Aunt Frieda the concept of function. I tell the students to start from first principles being sure to use examples that would be accessible to Aunt Frieda.

In both of these papers, I require the students to submit a first draft (after someone else has already read it) and then a final submission. I critique the first draft trying to point out any mathematical errors as well as grammatical and syntax errors. In my presentation, I will discuss these writing assignments and give the audience some samples of students writing.