For All Practical Purposes (9-College)
Twenty-six half-hour programs on 15 cassettes;
Available from Annenberg/CPB Multimedia Collection (address in
Appendix A); $39.95 per cassette (or $85 per module of three
cassettes)
These video tapes accompany the text FAPP discussed in Section 2; there is an introductory tape, plus five half-hour programs for each of the five sections of FAPP.
Geometry: New Tools for Technologies
(5-12)
Graph Applications; Codes
Five units, 10-15 minutes each (1 hr. total);
COMAP, 1992; $70 (user's guide, $10).
The following description is from a teacher's recommendation:
This well-done ...video, complete with user's guide, illustrates the geometry of the 20th century: motion planning, error-correcting codes, Euler circuits, vertex coloring, and tomography. (Ethel Breuche LP `91 [3])
The five unit titles are as follows:
This videotape was conceived and directed by Joseph Malkevitch who says (private communication) that he ``still finds parts of the tape very robust in attracting interest. For example, the piece on CAT scans shows people that math is behind tomography as well as computing and engineering and physics.'' (See also Malkevitch's article [26] on the value of addressing real-world problems in teaching mathematics.)
Several teachers have also mentioned that the tape appeals to a broad audience. For example, the segment entitled ``Snowbound'' begins with a charming cut of young children trying to draw a house without lifting a pencil, before getting into more practical applications. Another cut in this segment uses interesting graphics to let you ``ride along'' a graph. The segment ``Connect the Dots'', shows an application of graph coloring to creating zoo habitats. Both of these segments have been very successful as a follow-up to problems on Eulerian paths and graph coloring with all teachers in the Leadership Program in Discrete Mathematics. One of us (Franzblau) likes to use the segment on error-correcting codes as part of teaching a unit on codes, using the first half to motivate the concept of error correction.
Powers of Ten (6-12)
Iteration; Exponential Growth and Decay
10-15 minutes; W.H. Freeman; $40.
Teachers are very enthusiastic about this short video. It has been
used at a number of grade levels, as well as in teacher-training programs,
especially for number sense, positive and negative exponents, and
scientific notation. Most find the graphics very powerful, and show it
two or more times with discussion in between. It could be a good
resource when discussing the exponentially growing time needed to run
many exhaustive search algorithms.
Here are some comments made by teachers who have used it:
There are other good videos available that are less well known. We list below a few that have been especially recommended.
Mathematical Eye Series (9-12)
Graphs; Probability; Logic
20 min. each (approx.); Journal Films; $270 each.
This series was recommended enthusiastically by high-school teacher Diane DePriest LP `93 (who borrowed the films from a district library). She provided the following description.
This outstanding series includes 18 titles, including the following on discrete math topics:
Futures Series (9-12)
Narrated by Jaime Escalante; PBS; $450 for the entire 12-part series.
This series was also recommended by Diane DePriest LP `93 (private communication):
Each part deals with a different aspect of math and how it is used by real people in the real world. There are many famous guests (such as Cindy Crawford, Arnold Schwarzenegger, Jackie Joyner Kersee, and Sally Ride). The titles with some discrete math content are Statistics and Sports performance, and Water Engineering and Optics. The series is excellent!
Fractals: The Colors of Infinity
(8-up)
52 min.; Films for the Humanities, 1994; $149
This film is recommended by high-school teacher Edward Polakowski LP `92 (email posting):
In addition to beautiful images of the Mandelbrot set (the best I've seen), it includes interviews with Benoit Mandelbrot, who talks about his discovery, the rise of fractal geometry as a means of looking at the world, and the ``practical'' uses of fractals. It is narrated by Arthur C. Clarke in an understandable fashion and even includes an interview with Stephen Hawking: ``Is the world infinitely small?''
Professor Devaney Explains the Fractal Geometry of the
Mandelbrot Set (10-College)
Key Curriculum Press, $25.
This is another good video for teaching fractals. Although recommended for higher grades, one teacher (Erica Voolich LP `94, email posting) found that her 7th-grade students responded enthusiastically. The only background concepts needed are that of a function and multiplication of complex numbers. (An article by Devaney on chaos is included in this volume [10] and in [19].)
NOVA Series (6-up)
NOVA/WGBH; some of the videos in the
series can be purchased or rented; otherwise, check local televion
listings or your library (teacher's guides and transcripts are also
available).
This television series, shown regularly on PBS, has occasional programs in areas relevant to discrete mathematics. For example, ``The Man Who Loved Numbers'' (1988) is about the self-taught Indian mathematician Srinivasa Ramanujan, who developed many remarkable facts in number theory. More recently, a program on codes used in WWII, ``The Codebreakers'' (1994), was shown.