When the Mathematical Association of America was founded in 1915, its first journal, the American Mathematical Monthly, was already publishing Volume 22. In Volume 1, now more than a century ago, editors B. F. Finkel and J. M. Colaw wrote this:
"... Most of our existing Journals deal almost exclusively with subjects beyond the reach of the average student or teacher of Mathematics or at least with subjects with which they are not familiar, and little, if any space, is devoted to the solution of problems. ... THE AMERICAN MATHEMATICAL MONTHLY will also endeavor to reach the average mathematician by devoting regular departments to the important branches of Mathematical Sciences.
"It is recognized that those improvements in the Science are most fruitful, which lead to improvements in the elementary treatises [i.e., textbooks], and yet it must be admitted that little has been accomplished by previous mathematical journals in this line, as the crudities and solecisms handed down from one text-book to another bear witness.
"While realizing that the solution of problems is one of the lowest forms of Mathematical research, and that, in general, it has no scientific value, yet its educational value cannot be overestimated. ..."
Reading this at the start of the 21st century, one is tempted to mutter Plus ça change ... . But in fact a lot has changed in over 100 years of MAA journal publication. Specifically:
- The Monthly and its younger siblings, Mathematics Magazine and the College Mathematics Journal, have published thousands of articles and problems addressing the needs identified by Finkel and Colaw.
- While we still see "crudities and solecisms" (not to mention outdated exercises and examples) "handed down from one textbook to another," our current textbooks have in fact benefitted from a century of scholarship devoted to undergraduate mathematics.
- The "important branches of Mathematical Sciences" have grown substantially in both number and scope.
- The value of problem-solving (in the sense intended by Finkel and Colaw), while clearly important for development of certain kinds of mathematical abilities, was in fact overestimated. Subsequent research shows us that a key to deeper understanding of mathematics (or any other intellectual discipline) by a much broader range of students is active involvement in their learning tasks. Solving problems from the Monthly or other journals is but one type of active learning, not necessarily the most productive one for most undergraduate mathematics students.
With widespread access to computers, the Internet, powerful computer algebra systems, and other modern technologies, the very concept of problem-solving has become much broader and more accessible, in ways that could not have been imagined 100 years ago. Nevertheless, Finkel and Colaw would be right at home with much of what they might see in a typical mathematics classroom today. JOMA's mission, in part, is to bridge that gap by making modern tools (especially soft ones -- as in software), curricula, and active learning environments more accessible to students and teachers everywhere.
Specifically, JOMA will take advantage of the World Wide Web to publish materials containing dynamic, full-color graphics, internal and external hyperlinks to related resources, Java applets, presentations based on MathML, SVG, and other XML markups, audio and video clips, and other web-based features. Indeed, many of these features are already apparent in this first issue. As a publication of MAA, we will concentrate on content for college level mathematical sciences, which we see as as overlapping to some extent with the upper-secondary and lower-graduate levels. Almost all undergraduate mathematics instruction is for students in other disciplines (justification), so JOMA will publish contributions from or about other disciplines as long as they have mathematical content that is accessible to undergraduates.