Publication Type: Conference Paper/Unpublished Manuscript
Review Method: Peer Reviewed
Abstract: A graph $\$G\$$ is a $\{\backslash bf\; prime-distance\; graph\}$ if the vertices can be labeled with distinct integers in such a way that the differences between the labels on adjacent vertices are all prime. A graph is $\{\backslash bf\; 2-odd\}$ if the differences are either exactly 2 or odd. We present a characterization of 2-odd graphs and a family of 2-odd circulant graphs. We also offer a conjecture relating prime distance graphs and 2-odd graphs.

Publication Type: Conference Paper/Unpublished Manuscript
Abstract: There have been recent advances in DNA self-assembly of nanoscale mathematical constructs, in particular graphs such as a cube, truncated octahedra, and more recently a rigid octahedron. One construction method uses k-armed branched junction molecules, called tiles, whose arms are double strands of DNA with one strand extending beyond the other, forming a ‘sticky end’ at the end of the arm that can bond to any other sticky end with complementary Watson-Crick bases. A vertex of degree k is formed from a k-armed branched molecule, and joined sticky ends form the edges of the target graph.

A good undergraduate research project was determining the minimum number of tiles and edge types necessary to create a given graph under three different laboratory scenarios: 1. Where the incidental creation of complexes of smaller size than the target graph is acceptable; 2. Where the incidental creation of complexes the same size as the target graph is acceptable, but not smaller complexes; 3. Where no complexes the same size or smaller than the target graph are acceptable. In each of these cases, we found bounds for the minimum and maximum number of tile and edge types that must be designed and gave specific minimum values for common graph classes (complete, bipartite, trees, regular, etc.). For these classes of graphs, we provided either explicit descriptions of the set of tiles achieving the minimum number of tile and edge types, or efficient algorithms for generating the desired set.

Publication Type: Conference Paper/Unpublished Manuscript
Abstract: This paper investigates the ways in which Advanced Placement Calculus AB students use the graphing calculator when problem solving independently. When students were solving problems on their own they used the graphing calculator in four of the five tool modes suggested by Doerr & Zangor (2002). The students were prompted to use the calculator for five purposes: to skip a step, to get oriented in the problem, to save time, as a new approach, or to check a conjecture. Preliminary findings suggest that students are most often prompted to use the graphing calculator as a visualizing tool when they need a new approach for a problem.

Publication Type: Short Oral Report
Abstract: This study investigates teachers’ perceptions of the role of graphing calculators in the mathematics instruction of students from different SES schools. Findings showed that the nature of graphing calculator use was strongly influenced by the various contexts and that the low-SES school’s respondents appeared not to involve their students in lessons that capitalized on the powerful characteristics of graphing calculators.

Publication Type: Poster
Abstract: We present an activity design that uses networked graphing calculators to help students explore mathematical concepts in a collaborative setting. In the design, each student in a small group controls an individual point on a graph such that together they can jointly manipulate curves defined by their collective points to perform a variety of tasks and investigations.