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Darrah Chavey: Cultural Approaches to Mathematics

Goal: Students in Math 103, Cultural Approaches to Mathematics, must do a large term project for the course, which counts for 25% of their course grade. The goal of this project is to help them work their way through developmental steps in producing the final project. It consists of regular milestones which they must meet.

Background: Math 103 studies mathematical ideas from (usually) non-technological cultures, both historical and current. The primary ideas we look at are: (1) Patterns, symmetry, and repetition in art and various crafts; (2) One-line drawing traditions of various cultures, such as the kolam; (3) Number systems, both in language and symbolic or written form; (4) Mathematically based games, both strategic and probabilistic; (5) Views of space, geometry, or the world around us that differ from the Western norm; (6) Calendar systems.

The term project is a 25 page term paper, or the equivalent in work for projects that are not just a written paper. For example, students often construct examples of artifacts that imitate the artifacts of the culture being studied, and this construction effort can replace as much as 10 pages worth of writing. A few students have constructed multi-media projects; some have done creative writing projects about a culture we studies and the setting in which the mathematical ideas arose; a few have constructed games that imitate the mathematical games of various cultures; etc.

Schedule for Math 103 Paper Development

Week 1: In the first two class periods, I survey the 6 areas described above, so that students will have some sense of what we will be doing, what might be of interest to them, and what they should be looking for as they begin their research.

Week 2 Assignment: Read through the list of suggested term project ideas on Moodle. As discussed, you can choose a topic not on this list, but you should make sure you have cleared it with me first. Note that the Moodle list includes a couple of “forbidden” term project topics. These are ideas that students have often thought of as term project topics, but where experience shows that they turn out to be poor choices.

Decide on descriptions of two possible term projects: the one you expect to be your term project, and one other option that you could use as a backup. For the primary choice, include all of these elements: A possible paper title; your name; the description of the project; and any background you have that is relevant to the project.

Week 4 Assignment: Do an initial resource search for sources you can use for your project. Use the format shown below, and make sure that you have done a preliminary analysis for all of the resource categories shown below, or else justify why you feel that a particular resource category is irrelevant to your project. This should build on the previous submission.

Sample Submission:
Title: The Symmetries and Significance of Tibetan Buddhist Mandalas
Author: Stew Dent
Description: My intent is to look at the geometric symmetries of various Tibetan Buddhist Mandalas, see which symmetries are common, and see if it’s possible to identify any reasons behind the use of those frequent symmetries.

Wikipedia Search:

Google Search:

Google Image Search:

BelCat Search:

WorldCat Search:

ARTstor Search:

Article Journal Search:

Week 6 Assignment: From the list of sources found for week 4, evaluate what you think will be the most important sources. (It’s only now that you need to actually read many of them.) For each of these sources, determine which major part of your paper (Culture, Artifact, Examples & Analysis) this source will be particularly useful with. (Of course some sources may be useful in multiple parts.) Write a short synopsis of what each of your references is expected to contribute to the paper. (In some cases, writing a paragraph or other small section of your paper, or extracting quotes you expect to use, might be the most effective way to handle this task.)

Verify that you have enough sources that apply to each major part of your paper that you expect you will be able to write that part of the paper.