Exploring Mathematical Concepts Through Writing in a Liberal Arts Mathematics Course

Julianne M. Labbiento

Lehigh-Carbon Community College

Writing papers, as an alternative to traditional exams, has proven an invaluable tool in my liberal arts mathematics classes. In addition to learning mathematics in the course, writing also reinforces the art of written communication as a means of comprehensively yet concisely conveying a thought to another person.

Using writing as a means of assessing a student's knowledge of a particular mathematical concept allows for a more in-depth probe into that student's mastery of the topic. It allows the student to provide greater detail in illustrating what they do and do not know about a mathematical topic. Having a student choose his or her own example to illustrate in the analysis also allows the student to discuss something that he or she finds interesting, which keeps him or her focused on the task at hand. By applying the required mathematical concepts in the analysis of the example students see the connection between something they enjoy and the mathematics course. Mathematics throughout the curriculum can also be fostered utilizing writing as an assessment method by enabling these papers to encompass a broad array of subject areas.

I will discuss three large research papers that are required for my course. The first paper explores Mathematics in Another Culture. Students are encouraged to choose a culture other than their own, although this is not required, and explore the history, customs, and religious practices. Mathematically, the student is then required to find a piece of textile or pottery, etc., and analyze the pattern(s) in its design. The second paper addresses Mathematics in Architecture. Students choose a piece of architecture, describe it, and discuss its history and purpose, give a brief biographical sketch of the architect(s) if possible, then analyze the piece mathematically. Topics eligible for inclusion in the analysis may be: rosette, border and wallpaper patterns, golden ratio, similarity, proximity, figure/ground, tessellations, assimilation, etc. The third paper allows the student to consider Mathematics in Visual Art, including paintings, sculpture, drawing, cartooning, graphic design, etc. Since this is the last paper of the course, and students have a wide variety of mathematical concepts to choose from when analyzing the work.

I have found that students appreciate the substitution of papers for exams, in that they too feel that they are given the chance to explain themselves more clearly and concisely. I also find that the retention of the mathematical knowledge gained in the course is increased, since so much time is spent on the various tasks involved in writing a good paper.