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Topic: Excellent Videotape and Workbook Modules
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Jerry P. Becker

Posts: 16,576
Registered: 12/3/04
Excellent Videotape and Workbook Modules
Posted: Mar 13, 1999 9:41 PM
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[Note: If you are an elementary teacher and receive this, please share it
with middle and high school mathematics teachers in your school district.
If you are a middle or high school teacher, share this information with
other teachers. These are excellent materials for use in mathematics
courses, and in teacher preparation courses. Go to the website indicated
below - see Distribution Network at the site for information about getting
the materials.]


Project description

Project MATHEMATICS! produces videotape-and-workbook modules that explore
basic topics in high school mathematics in ways that cannot be done at the
chalkboard or in a textbook. The tapes use live action, music, special
effects, and imaginative computer animation. They are distributed on a
nonprofit basis.

The goal of the project is to attract young people to mathematics through
high-quality instructional modules that show mathematics to be
understandable, exciting, and eminently worthwhile. Each module consists of
a videotape together with a workbook, and explores a basic topic in
mathematics that can be easily integrated into any existing high school or
community college curriculum. The modules are crafted to encourage
interaction between students and teachers.

More than 9 million students have seen one or more of the videotapes. They
have been received enthusiastically by teachers and students nationwide and
have captured first-place honors at eleven major film and video festivals.

Project modules were produced by Tom M. Apostol, James F. Blinn, and Joe
Corrigan at the California Institute of Technology in Pasadena, CA.

The following modules are currently available:

The Theorem of Pythagoras Several engaging animated proofs of the
Pythagorean theorem are presented, with applications to real-life problems
and to Pythagorean triples. The theorem is extended to 3-space, but does
not hold for spherical triangles.

The Story of Pi Although pi is the ratio of circumference to diameter of a
circle, it appears in many formulas that have nothing to do with circles.
Animated sequences dissect a circular disk of radius r and transform it to
a rectangle of base pi*r and altitude r. Animation shows how Archimedes
estimated pi using perimeters of approximating polygons.

Similarity Scaling multiplies lengths by the same factor and produces a
similar figure. It preserves angles and ratios of lengths of corresponding
line segments. Animation shows what happens to perimeters, areas, and
volumes under scaling, with various applications from real life.

Polynomials Animations show how the Cartesian equation changes if the graph
of a polynomial is translated or subjected to a vertical change of scale.
Zeros, local extrema, and points of inflection are discussed. Real-life
examples include parabolic trajectories and the use of cubic splines in
designing sailboats and computer-generated teapots.

Sines and Cosines, Part 1 (Periodic functions) Sines and cosines occur as
rectangular coordinates of a point moving on a unit circle, as graphs
related to vibrating motion, and as ratios of sides of right triangles.
They are related by reflection or translation of their graphs. Animations
demonstrate the Gibbs phenomenon of Fourier series.

Sines and Cosines, Part 2 (Trigonometry) This program focuses on
trigonometry, with special emphasis on the law of cosines and the law of
sines, together with applications to The Great Survey of India by
triangulation. The history of surveying instruments is outlined, from
Hero's dioptra to modern orbiting satellites.

Sines and Cosines, Part 3 (Addition formulas) Animation relates the sine
and cosine of an angle with chord lengths of a circle, as explained in
Ptolemy's Almagest. This leads to elegant derivations of addition formulas,
with applications to simple harmonic motion.

The Tunnel of Samos: This video describes a remarkable engineering work of
ancient times -- excavating a one-kilometer tunnel straight through the
heart of a mountain, using separate crews that dug from the two ends and
met in the middle. How did they determine the direction for excavation? The
program gives Hero's explanation (ca. 60 A.D.), using similar triangles, as
well as alternate methods proposed in modern times.

Teachers Workshop This 28-minute tape, accompanied by a 90-page transcript,
contains excerpts from a two-day workshop held in 1991 for teachers who
have sucessfully used project materials in their classrooms.

Project MATHEMATICS! Contest In 1994 Project MATHEMATICS! conducted a
contest open to all teachers who had used project materials in their
classrooms. Entries were judged on the basis of innovative and effective
use of the materials. This videotape, accompanied by a 30-page booklet,
shows the classroon implementation of the entires of the first-place

The following module is currently in production:

Sines and Cosines, Part 4 (Area and slope)

An interactive version of Project MATHEMATICS! modules is also planned

Distribution network

The modules, produced under a National Science Foundation grant, are issued
on a nonprofit basis. Project materials are distributed at little or no
cost through an extensive distribution network consisting of

35 State Departments of Education
The Caltech Bookstore
The National Council of Teachers of Mathematics
The Mathematical Association of America
The NASA Educator Resource Center Network
Science Screen Report
Commercial Availability
Foreign Distribution

Modules may also be copied freely in the USA for educational purposes under
the conditions described on the cassette label. The label reads:

"You may reproduce, distribute, perform and display copies of this
copyrighted work in the U. S. A. for non-commercial purposes, provided that
each copy shall consist of only the entire contents hereof, including this
label verbatim, and provided further that no compensation or remuneration,
direct or indirect, may be received therefrom."

Joe Corrigan/Project MATHEMATICS!/

Go to the Project MATHEMATICS! website and get the details:


Jerry P. Becker
Dept. of Curriculum & Instruction
Southern Illinois University
Carbondale, IL 62901-4610 USA
Fax: (618)453-4244
Phone: (618)453-4241 (office)

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