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Editor's Notes, November, 2003
Welcome, dear readers. As we near the end of our third year of publication -- and of Volume 3 -- I will provide a short guide to the contents of this volume. In contrast to my previous practice of linking to individual articles, I provide one link to the Table of Contents page [link now obsolete, 12/04], which will enable you to browse the whole volume. I will describe the newer contributions first, and then repeat some of the paragraphs from my notes earlier in the year.
We start with our most exciting acquisition of the year: Communications in Visual Mathematics, Vol. 1, No. 1. If you have been with us from the start, you may recall my reference in our very first issue to CVM as our "Godparent". The single issue of CVM appeared in 1998 as the prototype for MAA's first online journal -- not only a peer reviewed scientific journal, but also one that took full advantage of the interactive possiblities of the Web. With the demise of the Geometry Center, there was a risk that at least some of the content of CVM would eventually be lost. Now, through the efforts of CVM's original editors, Davide Cervone and Tom Banchoff, we have archived CVM as "Volume 0" of JOMA. You can link to it from our Archive page. Of course, you can also find the entire contents of Volumes 1 and 2 on that page.
Our most recent article is Searching for Patterns in Pascal's Triangle -- with a Twist, by Kathleen Shannon and Michael Bardzell. This work explores mathematical topics at several levels -- ranging from elementary number theory to quotient groups to cellular automata -- by means of color visualizations and animations. The authors start with color representations of Pascal's triangle mod n and eventually replace the elements of Zn with elements of other finite groups, in particular, the dihedral groups. Coset and quotient concepts are explored through color identifications. You can explore the ideas yourself with the aid of applets written by Andy Nagel as part of an undergraduate research project.
Next in the Table of Contents (in reverse chronological order) you will find Classroom-Ready Data Sets in Environmental Mathematics, by Greg Langkamp and Joe Hull. This article describes the content and classroom uses of an extensive collection of environmentally-oriented data sets, part of the Quantitative Environmental Learning Project (QELP). The data are real, and the sets are substantial enough to pose interesting and challenging problems. But they are also organized for easy download, plotting, and analysis, using standard statistical tools or WebStat, a publically accessible Java-based tool.
A third new article is Evolution of a Computer Application by John Wavrik. This article describes the process of a mathematician producing a computer software system for mathematical research or instruction, with the case in point being a system for finding and working with all groups of orders < 32. The article itself is interactive in the sense that you can download and experiment with the tools that are being being developed.
JOMA editor Draga Vidakovic and her colleagues Jean Bevis and Margo Alexander have contributed Precalculus with WebCT Support: Using Bloom’s Taxonomy in Developing Assessment Items, which describes the development of a database for online formative assessment to be used as independent or supplemental material for a precalculus course. They developed their questions in WebCT, a system for easy online course management, and they used Bloom’s Taxonomy as a theoretical framework for designing items to assess increasingly more complex thinking skills.
Coming soon: An article by Vadim Ponomarenko on DRILL, an acronym for Depository of Repetitive Internet-based probLems and Lessons. This is an online system for calculus and precalculus drill-and-practice that features adaptive testing, on-the-fly question generation, instant assessment, context-sensitive help, question balancing, and two-dimensional test design.
The Method of Characteristics with Applications to Conservation Laws, by Scott Sarra, is intended for undergraduates in a partial differential equations class, as well as for anyone who needs a brief graphical introduction to the solutions of nonlinear hyperbolic conservation laws or to the method of characteristics for first order hyperbolic partial differential equations. The article includes an applet that shows simultaneously the time evolution of the initial condition and the advance of the data along the characteristics in the x-t plane.
We have two more elementary articles (quite different from each other) that focus on the use of Excel as a tool for constructing interactive materials: A Graphical Method for Designing Attribute Acceptance Sampling Plans by Steve Ng and An Interactive Use of the Lanchester Combat Model by Bart Stewart. Ng's article focuses on use of the Spin Button and Stewart's on use of the Scroll Bar, both to give the end user control over interactivity. In the first case, the primary example involves using a binomial distribution to approximate hypergeometric distributions, and in the second the user controls parameter inputs to a system of ODE's that models battlefield competition. Both papers show readers how to construct their own spreadsheet materials using the respective Excel tools.
In our Developers' Area you will find Michael Mays' article, Quick Interactive Web Pages with Java Sketchpad. The current version of Geometer's Sketchpad, a popular dynamic geometry software package, includes the ability to export a Sketchpad construction to a Java applet that can be imbedded in a Web page, retaining the interactive features of the original construction. Once published on the Web, users do not need their own copy of Sketchpad to experience the dynamic geometry. Mays shows us how to use this tool to build interactive materials.
Our Modules section for Volume 3 has two entries. The more recent is a precalculus module, The Consumer Price Index and Inflation, by Elizabeth Appelbaum. Like the articles by Ng and Stewart, Appelbaum's work uses Excel (or any similar spreadsheet program) as a computational and graphics tool. Unlike those articles, this module uses "real world" data acquired from the Internet as the basis for several explorations. It also offers opportunities to review or develop functional relationships, graphing skills, logarithmic and exponential calculations, and regression concepts.
The module Estimating the Area of Virginia, by Julie Clark, Caren Diefenderfer, Steve Hammer, and Trish Hammer, is built on the Lite Applet concept introduced in Volume 2 by Frank Wattenberg, Bart Stewart, and Suzanne Alejandre. The module uses area of a state (the authors' own) as a prototypical problem for introducing standard approximations to the definite integral.
If you would like to join the growing group of JOMA authors, please visit our submission page [link now obsolete, 12/04] and let us know about your proposed contribution. The types of materials we solicit are listed on the About JOMA page. Let us know if you are interested in refereeing -- we can always use more help. Also, take advantage of our voluntary registration [link now obsolete, 12/04] that will enable us to notify you whenever something of interest (according to your profile) is posted. Whether you choose to be notified or not, you can drop in any time and see what's new.
This journal could not function without the volunteer work of dedicated referees. Each of our articles has been scrutinized prior to publication by at least one and usually several referees. It is our pleasure to acknowledge their dedicated work and express our sincere appreciation to all of those individuals who served as referees for the articles in Volumes 1 and 2 of JOMA.
There are many new articles, modules, and mathlets at various stages in our reviewing and editing pipeline. Thus, we expect to have a steady flow of new and interesting content for the next volume of JOMA. If you're working on or considering work in any of our areas of interest, we welcome your submission. Whether you are interested in writing for JOMA or not, we always welcome your contributions to our Discussions area[link now obsolete -- each article has its own discussion thread, 12/04]. Good reading and good interacting!