Welcome, dear reader -- or welcome back if you have visited JOMA before.
Our BIG NEWS for May, announced in a separate piece on the front page, is that JOMA will have a new Editor as of January 1, 2006. While I had nothing to do with the selection process, I am personally delighted that Kyle Siegrist has been chosen to succeed me. Almost from the beginning of MathDL (of which JOMA is a part), Kyle has been involved on the editorial board of Digital Classroom Resources. He has also been a regular participant in an informal alliance of developers of online mathematics education materials that for three years was known as "the Conference Group". The formal title was longer than that, but it's obsolete now, as this group has been funded by the National Science Foundation (through MAA) to create a portal site called the Math Gateway. MathDL will be a key player in the Gateway project, which in turn will be the key mathematics presence in the National Sciences Digital Library (NSDL). With Kyle leading JOMA, I expect the journal to thrive and become ever more popular within the MathDL/Math Gateway/NSDL hierarchy.
Informally, I'm declaring May to be Linear Algebra Month at JOMA. We have two new feature articles this month, both on tools for visualizing various aspects of linear algebra.
David Meel and Tom Hern have built their tools in JavaSketchpad, going well beyond the intended uses of that product. Most of their work is 2-dimensional, but they have also explored the (limited) capabilities to present 3-dimensional interactions in an inherently 2D tool. With a collection of several tools, they enable students to explore the geometry of linear transformations, eigenvalues and eigenvectors, and the singular value decomposition. They also include samples of student assignments and student work on those assignments. The article provides separate reading "tracks" for those interested in just the tools and related assignments, those also interested in the pedagogy of using these tools, and those additionally interested in research aspects of student learning with these tools.
Focusing more on a "micro" level of the standard linear algebra course, Przemyslaw Bogacki describes a clever way to get students to understand the geometry of elementary row operations in three dimensions in terms of doors swinging on hinges. The activity challenges students to detect from "continuous" animations the operations that are necessary to bring each of three planes into parallelism with the three axes -- and then to relate the corresponding motions to the mathematical language in their textbooks. He reports briefly on early student work with this activity as a "proof of concept".
Over the past two years or so, we have had several articles and modules that explored uses of spreadsheets for teaching mathematics. It appears that the "hot" topic right now for interactivity is JavaSketchpad, which first appeared in this journal in a Developers' Area article by Mike Mays in Volume 3. In addition to the Meel-Hern article already available, we expect to soon have two more articles based on uses of JavaSketchpad.
One of these will concentrate on the ways in which technology can alter our (and our students') perceptions of how hard a given problem is and where it belongs in the curriculum. The authors illustrate their points with a single, nontrivial optimization problem that can be posed and solved at four different levels (at least) ranging from first-year algebra to calculus, depending in part on available technology. This piece is especially thought-provoking for pre-service mathematics teachers and their college instructors, but its messages are important for all of us.
The other JSP-based article-to-be reports on a Dynamic Geometry course developed for a Masters degree program for in-service mathematics teachers. The course actually used the "parent" product, Geometer's Sketchpad, and JSP is being used here for Web-based delivery of the same types of challenges and interactions that were provided for the students. Here we have an application that may be closer to what the developers of GSP/JSP (and similar products) had in mind -- enabling students to play with the concepts of Euclidean geometry, come up with conjectures about relationships, and perhaps even discover proofs of those conjectures. But the target audience here is not the students we usually think of as theorem-provers, let alone theorem-discoverers (i.e., proto-mathematicians). Nevertheless, this course led to a rich mathematical experience, widely shared by the members of the class.
We have new mathlets on the way as well. Last September we published two calculus mathlets by Barbara Kaskosz, who is implementing very innovative ideas in Flash. (She has three others in DCR.) Soon we will have two more of her mathlets, on numerical sequences and series and on sequences and series of functions.
There are many other significant contributions in the pipeline -- ones we can't discuss publicly yet. The ones mentioned here are, in some cases, undergoing final revisions, but they have been accepted and will appear as we can get them ready. Come back often to see what's new -- and consider submitting an article, module, mathlet, review, or Developers' Area article on your own work. We welcome new submissions at any time.