Project PRIME

Concrete Ideas

Note: Project PRIME has developed into the larger "Discovering the Art of Mathematics" project. The resources of Project PRIME remain as they were circa 2009. We encourage you to visit "Discovering the Art of Mathematics" for the continuation of the work begun by this project.

As we move forward, this page will be one of the most important locations for concrete ideas and resources for classroom use. We expect to have everything from short pedagogical ideas through extensive curriculum resources.

We will update things regularly beginning as soon as Spring, 2009 classes let out. For now, here is a small sample of the curricular work that we have done so far.

Discovering the Art of Mathematics

We propose a ten-volume series of inquiry-based learning guides and supplemental teacher resources for college-level Mathematics for Liberal Arts (MLA) students. Our goal is to provide compelling, high quality curriculum materials where:
  1. The pedagogy is radically student-centered, providing a striking alternative to traditional texts which are generally structured around a lecture dominant mode of teaching. By pragmatically employing insights from many different inquiry-based and active learning traditions, our approach supports a continuum of individual teaching styles without compromising the student focus.
  2. The content is engaging, intellectually challenging, and nurtures in-depth explorations of mathematical topics which demonstrate the continuing role of mathematics as a cornerstone of the liberal arts tradition. This liberal arts focus includes: the role of mathematics as an intellectual pursuit, its continuing impact in shaping history, culture, logic, philosophy, and knowledge, its status as humanistic and aesthetic discipline, and its extensive contemporary growth. Two volumes in this series are in their final revision and draft sections of others will be forthcoming. Extensive information about this project is available from the project site:

Palindromes in Mathematics and Music

by Christine von Renesse appearing soon in PRIMUS.

Google Sketchup

"Google SketchUp: A Powerful Tool for Teaching, Learning and Applying Geometry" by Julian F. Fleron.

Abstract: We introduce the reader to the free, sophisticated, and widely used Computer Aided Design (CAD) software Google SketchUp. We provide rich, interactive examples which illustrate the utility of this Google SketchUp in transforming the teaching of geometry and measurement. We also provide student activities and resources we hope will enable many other middle school teachers to begin to integrate Google SketchUp in to their curricula.

Mathematics and Salsa Dancing

by Christine von Renesse and Volker Ecke in the "Journal of Mathematics and the Arts".

Our paper investigates Salsa dance positions and dance moves from a mathematical point of view. We will define a mathematical "space of salsa dancing" which can help a dancer to become more flexible in his or her choices. The process shows how a mathematician can face the challenges of creating a model for a very large and seemingly chaotic set of movements. Moreover we are presenting a topic that can be used in a class like "Mathematics for Liberal Arts Students," in which the art of mathematics in dance is the focus of inquiry. In reading this paper, you may find it helpful and more enjoyable to work with a partner, so that you can actually and physically try out the various dance positions and dance moves.

Hex, Games, and Critical Thinking

A talk delivered by Volker Ecke on January 14, 2010 at the Joint MAA/AMS Meetings in San Fransisco, CA on work by Volker Ecke, Christine von Renesse, Julian Fleron, and Philip Hotchkiss.

The investigation of games can provide worthwhile material for an inquiry-based Mathematics for Liberal Arts course. For many students, exploring strategies and thinking critically about good moves is naturally motivated by their desire to play well and win (yet, we also make sure the competitive aspect does not turn o others). In addition, the absence of common triggers for math anxiety (such as formulas) allows students to give mathematical investigations a fresh second look.
We have successfully used so-called connection games (such as Hex, ConHex, Stymie) in our "Explorations of Math- ematics" courses.
In class, we use small group and whole class discussions to consider, clarify and re ne the various ideas students develop. Questions such as: Is that always the case? Will your suggestion always work, no matter what your opponent does? can lead the class into proof territory.
Beyond these investigations into strategy, the class also explores mathematical connections to large numbers, com- plexity, geometric tessellations, and computational tractability.
In this talk, we will share some of our materials, pedagogical considerations, and our experiences in the class- room.

Slide Show

© The material which makes up this Internet site is copyright 2009 by Julian Fleron, Phil Hotchkiss, Volker Ecke, Christine von Renesse.