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The Nature of Mathematics

Ouida B. Kinzey
Birmingham-Southern College, Birmingham, Alabama

Subject: Mathematics
Grade: Higher Education

"I have tried everything but the fan and feathers to generate interest in and relieve anxiety about mathematics. One of my most successful approaches has been with photography."

Purpose and Description of Project

Ouida Kinzey's goal in this project and throughout her career of how mathematical concepts are an integral aspect of everything around them-from the world of nature to the architectural design of historic homes-she helps young people "realize that mathematics is an exciting, viable part of their everyday lives." Rather than focusing on mathematics as an abstraction-or indeed on math as math-Kinzey helps students become familiar and comfortable with math concepts by helping them to see how these concepts relate to their own fields of study, whether music, art, English, or history.

The final product of the project is a 30-minute, 35 mm slide/tape photographic essay about "The Nature of Mathematics," which was developed by Kinzey and the 16 students taking her interim course between semesters. Each of the 16 students did individual projects using photographs to highlight the mathematical aspects of papers on their chosen topic, and material for the overall project was then drawn from this work.

One student, for example, did a study of attitudes toward high school math by juniors and seniors in the area, while another, who started out studying card games to understand probabilities, became so interested in genetics that he made charts on all his family members to compare characteristics. Once the individual projects were completed, teacher and students started putting together the slides to be used in the slide show and writing the script.

The resulting slide/tape show, comprising 140 slides synchronized to a taped narration, is, according to Kinzey, really a study in awareness. "It is designed with a humanistic and mathematical approach to aid the student in seeing the world as a combination of historical sites, spatial environment, and the interaction of humans and animals," she explains. And, she adds, while it was developed primarily for pre-college and college algebra students, she has found that the program is really suitable for fourth-grade through adult viewers.

The slide show focuses on five basic mathematical concepts: (1) the distance around a point, demonstrated through such vehicles as the antics of animals and insects, ripple patterns in a lake, flowers, and the configurations of both deep and surface mining sites; (2) the relationship of lines, shown in the branching of trees, flowers, and plants, human arteries, mountains, roads, covered bridges, old homes, old mills, and churches; (3) the meander; (4) the spiral, found in roads, streams, and plants; and (5) packing and cracking, as exemplified by dried mud, giraffes, turtles, and oil.

The students' investigations of the math concepts demonstrated in familiar surroundings-which they had "seen" before but never really "noticed"-produced a wide range of positive outcomes, according to Kinzey. Among these were motivation, an increase in sensitivity, development of a more positive self-image, an appreciation of cultural heritage and an integration of the old and the new, and a better understanding of the field of mathematics. In the process, the students overcame the tension and apprehension they had felt about confronting math.

Activities

The project opened with previous slide shows developed by Kinzey, who is a veteran photographer and has put together several acclaimed productions, including "Patterns-A Mathematician's View" and "How Do You See Your World?" This beginning stimulated free-brainstorming sessions and agreement on course goals. Subsequently, Kinzey took the students to her home for a get-acquainted session and to view her collections of non-math items-from rocks to Indian artifacts to Alabama memorabilia. From this exploration came a number of the topics for students' individual projects, including several old homes and a Civil War furnace. Students also took part in discussions about prominent individuals in the field of mathematics, which also led to discoveries. For example, it transpired that one student had as a child met Werner Von Braun. This student then made several trips to Kinzey's house to rummage through her collection of material on the space program and chose "Rockets and Winged Flight" as his topic.

The class also worked its way through a vast bibliography ranging from the writings of science and science fiction writer Isaac Asimov to Uses of Infinity by Leo Zippin.

One of the most successful activities, according to the teacher, was a discussion of the "language of mathematics," which Kinzey says gave the students an appreciation of the need for precise language. An understanding of mathematical terms-such as real, imaginary, rational, and irrational-was a springboard to understanding of the underlying concepts.

Kinzey and her students also did extensive field work as part of their "awareness training," and this was where most of their photographs were taken. Among these sites were: four covered bridges, Mountain Top State Park, the oldest house in the state, an old barn with a display of primitive tools, a waterfall, and a farm.

Once the field work was completed, each student made an oral presentation (based on his or her written report and photographs) on his or her chosen topic, and the work on the slide/tape show began.

Materials, Resources, and Expenses

In addition to other faculty members and members of the community, three individuals were instrumental in ensuring that the slide show was "mathematically correct, historically accurate, and professionally acceptable," according to Kinzey. These were the math and physical science editor of the W. H. Freeman and Co. (which produces "Scientific American," among other publications); the director of the Alabama Historical Commission; and an audiovisual specialist from Westbrook Electronics.

Students provided their own cameras and film. Also required were cassette tapes, slide carousels, and professional film processing and slide duplication.

Outcomes and Adaptability

Kinzey found that this project did indeed "encourage student participation and interest in identifying and recording the wonders of their surroundings, and the application of those observations to the field of mathematics." The reaction of students to the course and the slide show has been energetic and lasting, she says, remarking that "the course is over, the grades are in, but they forgot to stop!" Two students have started their own tour of the 14 remaining covered bridges in the state, for example, and the musician in the class now has the college physics department involved in photographing the patterns created on the ceiling when sunlight bounces off his drum.

In short, declares the teacher (who is close to a more than 40-year career), "They're making it hard for me to retire. This project will encourage the students to carry on my journey through the 'World of Mathematics.' I can think of no greater legacy." The project has also spurred extensive community interest-and invitations to present the slide/tape show-coverage in the local paper, and a one-person show of the professor's still photography at the college library.

Since an interdisciplinary approach is the essence of this project with students being urged to relate math concepts to virtually any other field, Kinzey believes that "the possibilities for adaptation are limitless." The slide show itself, she has found during her community showings, draws positive responses from all ages.

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