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The National Curve Bank Project: A MATH Archive
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by Shirley B. Gray
Dept. of Mathematics
California State University
Los Angeles, California
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| | The National Curve Bank Project is celebrating its second anniversary by expanding into primetime viewing for a wide national and international audience. Having built a repository of almost 50 "deposits" into a mathematics archive, we now offer a free and hopefully engaging resource for students of mathematics.
The Voice of Experience Now Suggests...
Based on hundreds, if not thousands of email responses to the National Curve Bank (NCB) over the past two years, we offer crucial observations on the current science, technology, engineering, and mathematics community, better know as "STEMs" among federal agencies. We find there are two types of audiences. One type includes computer savvy users who want sophisticated downloads, e.g., Java applets. This group enjoys the hunt and pursuit of any and all new happenings in computer science, software, and equipment. But even for this highly sophisticated audience, mathematical notation for non-image based communication remains difficult. There is a second, far larger audience in STEMs whose members do not want to update familiar browsers, use special downloads, or change to newer versions of software. This group is quite content to continue with their older, but more familiar, computer environment. This audience is enormous.
Now superimpose upon both of these groups our mathematics students who have grown up with the computer. Undergraduate students and AP Calculus enthusiasts belong to both of the above groups. But their tastes are slightly different. Students have repeatedly given positive feedback for "Q & A" components, animation, color, and audio. Several have contacted us asking for more information about special projects. In response, publications now include extensive use of color. Journals and the newest editions of calculus textbooks are beautiful. We find that all of these groups still dislike reading on a computer screen, however. All but a few individuals will print hard copies of longer material if it must be read closely. Thus longer, journal type articles on the Web have a more limited audience.
In view of this significant challenge, we at the NCB and the 33 members of our National Advisory Board are consistently monitoring and responding to the needs of the entire STEMs audience.
 National Advisory Board
In addition to monitoring the STEMS community, Board Members have given talks on the NCB at several regional and international conferences. Those attending the annual Joint AMS -- MAA Mathematics Meeting select the Renie Award for the best deposit of the year. The Renie is announced on March 31, the anniversary of René Descartes' birthday. Other Board Members may not attend this meeting but provide feedback from their work in Silicon Valley or at NASA's Jet Propulsion Laboratory. The strength of comments from this varied source of expertise is indispensable. Many of these Board Members have also been Readers of the AP exams.
How We Work
The NCB seeks to enhance, not replace, classroom instruction using Java scripting, Maplesoft, MATHEMATICA, Flash, MATLAB, Geometer's Sketchpad, Excel, graphing calculators, ImageReady and others. The NCB strives to provide features -- for example, animation and interaction -- that a printed page cannot offer. We focus on supporting a new generation of Web users that is likely to log on outside the classroom, hoping to find examples of a topic probably first encountered on a chalkboard or in a textbook.
In particular, the past year has brought interactive Java applets on Goodstein's Theorem, streaming video on converging geometric series, and interesting photo deposits from Stephen Hawking, Gordon Moore, and Alan Turing's family. Yes, Gordon and Betty Moore of Moore's Law fame have been kind enough to deposit a photo taken at the dedication of the new Centre for Mathematical Sciences at Cambridge University.
We offer Goodstein's Theorem as an example of an NCB deposit. Reuben Goodstein (1912-1985), a student of John E. Littlewood's at Cambridge, made an interesting discovery.
Working in precomputer age mathematics, Goodstein found the sequence always converging to zero. Most people incorrectly guess the sequence goes to infinity.
Interestingly, this sequence is unique in that it may produce very large numbers before the size of the base forces the sequence to converge to zero. The calculation for larger numbers reaches a point where the computer may be unable to continue. Many personal computers will simply cease the calculation.
A large and varied collection of animated plane curves created in MATHEMATICA and Maplesoft continue to be assembled. Deposits have arrived from physicians, unemployed ".com" staffers, engineers, scholars, mathematics faculty, and most importantly, mathematics and computer science students.
Most recently, the NCB project has initiated a new section that we have informally labeled our "series series." Using streaming video recorded by Robert Meyer, a veteran teacher, students have the opportunity to view a demonstration on an important topic in calculus -- why a geometric series converges to a limit (see the link below in "See also" to the Geometric Series Web page). Meyer's video models this concept succinctly for all mathematics instructors.
We plan to tape a demonstration of the harmonic series as well. We hope to find good illustrations of the many important tests for convergence. But please note, we avoid "text only" material. If a topic is better on the printed page, we choose to put our time elsewhere. After all, we have a plethora of printed explanations in good Calculus textbooks.
We also plan to continue to collect images that are especially related to mathematics and mathematicians. With global travel and conferences, many of our students will have the opportunity to visit historic sites. Recognizing that other cultures have held mathematics in high esteem should motivate or enrich the lives of our STEMs community.
Closing Invitation
We wish to underscore a major achievement of the National Curve Bank Project: A MATH Archive. The strong lines of communication based on mutual respect among faculty at research-based institutions, universities, community colleges, and high schools have impressed close observers. What is more, those of us working on the NCB have watched our students develop the skills and interests of highly trained adults. It is far more fun to do science, mathematics, and engineering than it is to merely listen or take tests.
Please take the time to find deposits that complement your classroom instruction. Encourage your students to use these "deposits." Then, should you, or your student, create a terrific animation or interactive project, please consider sharing your work with our audience. Each "deposit" should feature the strengths of Web-based publishing, i.e., animation, interaction, audio, inexpensive color, and speed of communication.
Shirley B. Gray has been a member of the Department of Mathematics at California State University, Los Angeles, for 15 years. Earlier in her career, she taught AP Calculus in New York and California high schools. She asserts that AP Calculus has been the single best mathematics program developed in the United States and possibly the world. She also believes that the opportunity for teachers to showcase their talents in motivating students via the AP Program cannot be overstated.
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