Mathematical Modeling

The goal of the mathematical modeling curriculum is for students to pose their own questions about the world and to use mathematics to answer those questions. The curriculum's culminating modeling experience is a project that has student groups create an original model and analysis for a question that they generate. One group of students decided to design a movie theater with unimpeded viewing angles. They discovered that the constantly sloped floor of most theaters was not optimal and that certain curved floors were better. Other groups explored pricing schemes for a record store, how to evenly illuminate a room, how to seat friends and enemies at the United Nations, and how to model heart tissue and study the disruptions that lead to heart attacks. These problems, like all real ones, did not come with instructions attached saying "use the quadratic formula now" or "check out the problem on page 27 that is just like this one." Students learn to identify which of their many skills will help them solve a problem and learn how to teach themselves new mathematics when necessary.

Class activities involve discussion, investigations in groups, computer explorations, presentations by students, and peer evaluations of each other's writings. Major assignments linked to these activities include a poster, essays, several problem sets, papers, experiments, and projects.

This curriculum is well-developed and has been used as a yearlong course in lieu of an Algebra II or Precalculus experience. It can also be adapted as a modeling strand for grades seven through twelve. The written description of the curriculum is a work in progress. Some chapters are complete and others are in an embryonic form. Updated versions will be posted over time. Please sign up to receive notice of these additions.

Downloads

Each of the following chapters is available as a PDF document. The handouts and bibliography associated with each chapter are at the end of their respective documents. In order to view these documents, you will need a PDF reader (see below for additional information).

Chapter One: The Pedagogy of Modeling (143 kb, first installment)

Chapter Two: The Modeling Cycle (170 kb, final version)

Software for the Modeling Cycle activity:

Chapter Three: Numbers in Context (1 Mb, final version)

Chapter Four: Functions in Context (first installment coming this winter)

Chapter Five: Statistics, Probability, and Simulation

Chapter Six: The Modeling Projects (first installment coming this winter)

 

PDF (Portable Document Format) Files

To see these documents, you must have Adobe Acrobat Reader installed on your computer. PDF documents display and print mathematics more crisply than HTML documents, and they include pagination. Installing and using Adobe Acrobat Reader is relatively easy. Adobe Acrobat Reader is free. In fact, many new computers come with Adobe Acrobat Reader already installed. You can read more about Adobe Acrobat Reader and download it, if necessary, at the following Adobe web sites.
Macintosh users: http://www.adobe.com/support/downloads/acrmac.htm
Windows users: http://www.adobe.com/support/downloads/acrwin.htm

 

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