We are presenting at the 2011 Joint Meetings of the AMS/MAA in New Orleans. If you are interested in learning more about our project, please join us:
1. Thursday January 6, 2011, 2:15 p.m.-6:10 p.m.
MAA Session on The Mathematics of Games and Puzzles, I
Grand Chenier Room, 5th Floor, Sheraton 3:15 p.m.
Discovering the Art of Mathematics: Straight-Cut Origami.
Christine von Renesse*, Volker Ecke, Julian Fleron,
Philip K. Hotchkiss, Westfield State University
Abstract: Together with our students in "Explorations of Mathematics," a course for Liberal Arts majors, we have been exploring the mathematics of games and puzzles for a number of years now. Among the most successful topics with students are the Rubik's Cube, Hex strategy games, Sudoku puzzles, and paper-folding puzzles. The audience will have an opportunity to explore the mathematics of a few sample activities inspired by Eric Demaine's work on straight-cut origami from our inquiry-based learning guide "Discovering the Art of Mathematics: Games and Puzzles," so come ready to play! We find a number of strengths with this material: triggers for mathematics anxiety are avoided; success with the Rubik's Cube changes students' self-image; natural curiosity and competitiveness fuel the inquiry into game strategies (e.g. Hex); sophisticated, multi-step logical arguments arise organically (e.g. Sudoku); working with physical objects provides concrete models that support thinking, reasoning, and communicating mathematics; symbols and notation arise as convenient means to clearly communicate mathematical thinking; "pressing the math" occurs through a focus on students reflecting on and explaining their reasoning.
See attached: JMM 2011 Origami Handout
2. Friday January 7, 2011, 2:00 p.m.-4:00 p.m.
MAA Poster Session on Projects Supported by the NSF Division of Undergraduate Education
Napoleon A1-A3, 3rd Floor, Sheraton 2:00 - 4:00 pm
Discovering the Art of Mathematics.
Julian F. Fleron*, Philip K. Hotchkiss,
Volker Ecke, Christine von Renesse,
Westfield State University
3. Sunday January 9, 2011, 1:00 p.m.-6:00 p.m.
MAA Session on Humanistic Mathematics, II
Mardi Gras GH, 3rd Floor, Marriott 2:00 p.m.
Student Inquiry into the Limits of Knowledge - Removing Barriers in Mathematics for Liberal Arts.
Philip K Hotchkiss*, Julian F Fleron,
Volker Ecke, Christine von Renessee,
Westfield State University
Abstract: Liberal arts students often face a huge barrier in mathematics because they think it does not touch their world in significant ways. In this talk we share inquiry-based materials and approaches we have developed to help move beyond these barriers by focusing on the themes "What do we know?" and "Are there limits to knowledge?" Spurred by Catherine's admonishment "It doesn't prove anything!" to Hal in David Auburn's `Proof', students consider questions of existence, and the limits of knowledge, by interacting with: debates about perception (including Plato's Allegory of the Cave and Descartes cogito); types of reasoning and burdens of proof; mathematical logic and proof, including non-existence proofs; relativity, uncertainty, and incompleteness - their scientific and cultural roles; chaos and sensitive dependence on initial conditions (via Ray Bradbury's "Sound of Thunder" whose 1952 butterfly predates the "founding work" by Lorenz); etc. We will discuss how one can integrate these deep mathematical topics into inquiry based approaches, why these topics are important for mathematics for liberal arts students, and how we hope students will benefit from these experiences.