Publication Type: Conference Paper/Unpublished Manuscript
Abstract: Nine students in my May Term class designed and sewed baby quilts based on the symmetry concepts they had leaned. After the quilts were completed, they were donated to Caring Connections, an organization which distributes quilts to all newborn babies in Warren County, Iowa.

After studying rigid motions, the students developed their own classification schemes for finite figures, border patterns and wallpaper patterns. They also studied various schemes for creating tessellations. Simultaneously, the students learned about the mathematics of piecing quilts: geometry, the four color theorem, sequences and series, measurement and estimation. The students designed their own quilt tops, some based on traditional designs and others from original designs. They then cut and pieced the tops. Volunteers from the Simpson College community tied the quilts and applied bindings.

I will talk about the project in general, the designs of the quilts, and some mathematics covered in the course.

Publication Type: Student Paper
Abstract: A d-cube is defined as the set of all points whose coordinates lie between 0 and 1 in all d dimensions. The d-cubes have a high degree of geometric symmetry. The size of the symmetry group of a d-cube is $\$2^d*d!\$$. Clique replacements is a method of forming new polytopes from existing polytopes. We will be investigating the size and nature of the symmetry groups of near-cubes, which are the polytopes that are only a few clique replacements away from the d-cube.

Publication Type: Conference Paper/Unpublished Manuscript
Abstract: Gould (2003) posits that the (a)symmetry of a relationship between opponents influences whether violence is used to resolve the dispute. More specifically, Gould theorizes that opponents embedded in symmetrical, or equal, social relationships are more likely to resort to violence over symbolic issues. Conversely, opponents of asymmetrical social rank will avoid the use of violence to settle symbolic disputes, although they may use violence in substantive disputes. In this paper, we apply Gould’s model to data from a sample of incarcerated women in Toronto, Canada. We examine their disputes with both males and females, and extend Gould’s model in two ways. First, we examine non-lethal violence, which allows us to explore ongoing social contests for status or rank. Second, we distinguish between disputes involving violence and avoided violence. Avoiding violence in disputes that involve asymmetrical opponents is a central, yet untested aspect of Gould’s argument.

Publication Type: Conference Paper/Unpublished Manuscript
Abstract: Most universities require every student to take a course in mathematics to graduate. There is substantial debate in the mathematics community about how to best serve these students – is it more important to train students in basic mathematical skills, to show them how mathematics relates to other disciplines or to everyday life, or to give them an appreciation of mathematics as its own discipline and way of thinking?

This project studied a non-traditional course on the Mathematics of Symmetry, taught at Loyola Marymount University in Spring 2006, that emphasized mathematical thinking and connections with the visual arts. We collected both qualitative and quantitative data in the form of anonymous surveys on students’ attitudes towards mathematics as well as samples of students’ work in the class. We try to answer several questions: How did students’ attitudes towards mathematics change? How did their conception of what mathematics is, and its role in a liberal arts curriculum change? Did they demonstrate an ability to think mathematically?

The results will be compared to data collected for a fairly standard quantitative reasoning course taught to the same audience at LMU. We will discuss implications for developing and teaching general education mathematics courses.

Publication Type: Conference Paper/Unpublished Manuscript
Abstract: In this paper we describe one observed members’ method for doing learning and instruction in a collaborative peer group setting where an actor extends the ongoing activity of a situated expert in ways that call on that expert to assess the extending activity as a demonstration of achieved expertise.