Pattern Exploration:

Integrating Math and Science

for the Middle School

Summary  People  |  Materials  |  Related Literature   |   Software   |   Math Science Partnership Institute


Significance.  Fractal geometry is a new language for the complex forms and patterns found in nature.  It represents a change in the way that scientists "do science".  It provides new tools to describe, model, analyze, and measure the natural world, and wonderful new connections within the world of mathematics.  Fractal geometry is exciting, visual, relevant to many disciplines, and lends itself naturally to technology supported activities.  Both students and teachers with relatively little mathematical background  can approach a large number of current research problems in this area and appreciate the integration across traditional disciplines.

Experience.  The experiences and discoveries of our previous NSF supported work (Teacher Enhancement through Chaos and Fractals 1995 - 1998, Florida Atlantic University and Broward County School District) provided the cornerstones of this proposal.  Approximately 180 upper level middle and high school math and science teachers were trained.  A supplement to this grant extended the training to 35 teachers from grades 4 through 6 in the summer of 1998.  The content of this program was far broader than indicated by the title.  Selected topics from chaos theory and fractal geometry provided the connective tissue to interrelate and support many curriculum content areas in algebra, number theory, geometry, and current science problems.  Two elements that evolved during the previous work (a small cadre of dedicated, enthusiastic, and well-trained lead teachers; and immediate teaching experience at a camp as part of the summer institutes) play a critical role in the current program.

Goals.  The foremost goals of the program are to promote teachers as self-directed learners, and to promote the discovery method of learning for both students and teachers.

Based on the success, experience, and discoveries of our 1995-98 NSF project, our current program expands the geographic reach of the program to the eight urban and rural counties of south Florida: Broward, Collier, Miami-Dade, Hendry, Lee, Martin, Monroe, and Palm Beach.  These counties total 180,279 students in grade levels 6-8 and cover 139 middle schools with 2724 teachers.  This program focuses on the middle school, where the potential impact and the need for integrating science and math are the greatest.

The current program has two phases.  Phase one, which covers the first program year trains an initial regional cadre of 54 lead teachers in curriculum development and teaching in the subject area.  Phase two, which covers years two and tree of the program, trains 120 additional middle school science and math teachers each year.  Our target is to train a pair of science and math teachers from each middle school.  The lead teachers trained in phase one will help to train, coach, and mentor the teachers form phase two in teams of six.

The core activities of the program includes spring writing and development seminars, 3-week summer institutes, with instruction through lectures and hands-on workshops and a teaching camp with children, follow-up sessions, and small group mentoring thougtout the following school year.


Telephone Numbers
Electronic Mail Address
Heinz-Otto Peitgen
Florida Atlantic University
561 297-2482
Richard F. Voss
Florida Atlantic University
561 297-3358
Nancy Barba
Broward County School District
954 767-8547
Judith A. Jordan
Broward County School District
954 765-6853
Connie Boutwell
Palm Beach School District
561 434-8250
Geneva Woodwrd
Miami-Dade School District
305 995-1908
Franklin J. Vodolo
Broward County School District
954 765-6061


CABRI for the Classroom
During the spring semester 2004 at Florida Atlantic University MST program, we experimented with the dynamic geometry software package Cabri, and found many interesting classroom applications. We were not only interested in examples of its application to Euclidean Geometry, but also to Calculus, Art and Science. The levels of difficulty of the exercises we developed apply to middle school, high school, and college. Many of the examples we were working on can already be found on the Web. In this page, we provide examples of problems that can be visually represented and explored using Cabri Geometry and not easily found on the Internet.

Pattern Exploration
Integrating Mathematics and Science for the Middle Grades

The materials in the following CATEs (Curriculum and Textbook Enhancements) were developed through the National Science Foundation Grant Pattern Exploration: Integrating Mathematics and Science for the Middle Grades,
a collaboration between Florida Atlantic University, Boca Raton, Florida, and The School Board of Broward County, Florida. 
All links refer to pdf files.

Message Board

Please see our Message Board which will allow you to use any browser to view and post messages to the Pattern Exploration message board. Use this public forum for communication with fellow participants, lead teachers, and FAU personnel. Please post questions, answers, comments, experiences, and suggestions.

Related Literature  


Software Developed by 

KLM Programming: 
Heather L. Kanser, Martin Logan, and Joe McPherson.

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