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1The Online mathematics course – Can it work? G. Donald Allen Department of Mathematics Texas A&M University College Station, TX 77843 Abstract. This paper contains discussion of four aspects of online course design and deployment for mathematics. Addressed are several of the most asked about issues of online courses. Included as well is a discussion of the issues pertaining to online mathematics presentation, typography and computation. General topics range from basic course design considerations such as content issues to advanced features such as streaming multimedia. The emphasis is on what can be done without extensive training. Because there are so many facets to course development, learning curves are unavoidable. Their number can be controlled but at the expense of scope. Overall the reader may view this article as a review of the terms, the features, and the software needed for creating and operating such a course. Web-based and Web-assisted courses The grand scope of an online course sweeps from creation of the course to interactivity to assessment. Since no one has more than a few years experience at online teaching, an essential part of course design is redesign. But, before the redesign must come the original course creation, and this prospect can be daunting. Many online courses have humble beginnings, just as Internet itself. Less than ten years ago the first online course homepages emerged; they contained basic information such as the text and syllabus and not much more. Most students didn’t use them; many didn’t even know they were there. Gradually instructors enhanced their course homepages by adding useful links and then homework assignments and labs. Those more adept at math-on-Web skills added practice exams and homework solutions. In the very early days, the LaTeX2HTML converter was widely used as the only alternative to massive math content on the Web. In recent times, alternatives have appeared, and together with the typography we have seen more and more course content with full math-on-Web features, graphics, animations, online assessment and interactivity. It is not uncommon to see course Websites with full streaming media lectures. (See [Oblinger, 1991], [Brusilovsky, 2000], and [Cunningham, Francis, 2001].) Today, few students will risk not looking at the course page for fear of missing essential course features. Today, many online courses are designed from the ground-up, the net result being a complete Internet-based mathematics course. This is not to say it will used for distance learning, which is another subject altogether. Aside from distance learning there is the important distinction between Web-based and Web-assisted courses. The former is a full measure more extensive and should be considered a complete package. The latter emphasizes certain aspects of the course, whether applets for interactivity or special examples, or even a bulletin board; Web assisted courses are best distinguished by the continuing presence of the lecture or classroom activity.2To create an online course, one must consider the scope of design, software tools, student deliverables, and security as major factors, each with multiple sub-factors. As for any educational publication, style is extremely important, and for the Web, especially so. See [Lynch, Horton, 1999]. Each should be considered thoughtfully, even though not all can be resolved right off. In this paper, we highlight a few of them. The scope of course design must address among others the content and interactivity issues. Content is the most important. One shortcut used by many authors is to use a print textbook as the sole source of mathematical content. Remarkably, irrespective of the modern mathematics textbook design, extensive editing, and multiply colored production, few are written for self-study. They are written to be the print-companions of the traditional lecture course. Indeed, it is for this traditional lecture/recitation environment that almost all textbook authors write. For the online course, over reliance on any textbook to convey mathematics content may well produce disastrous results. One alternative, that of writing the complete contents oneself, may require too much time and of course there is no guarantee of the results there. For additional discussion on tools and methods see [Bogley, Dorbolo, Robson, Sechrest, 1996, 1998] and [Robson, 1999]. However, a blend of a print text with personally generated supplements can work well. Consider the following three supplements. Generate a news-type page with full-rich mathematical content that is aimed at answering individual inquiries in a more general way for all students to read. This is relatively easy to produce and easy to maintain. Another is to post complete solutions to homework problems, and additional examples that illustrate some particular point. In both cases supply more than the usual detail found in the text. The third supplement, and a surprisingly important one, is posting practice exams. Students, it appears, have unusual tenacity about working these problems out. It may be that they feel that while homework has theoretical importance, practice exams have significant and practical importance. A lengthy practice exam may provide the student with an important learning instrument. Other methods including threaded discussions and chat rooms have merit, as well. These require continual monitoring, and that translates into additional, possibly substantial, instructor time. Interactivity Interactivity is the Internet buzzword these. What is it? And how can anyone put it into his or her Web-based course? A wide scope interpretation would define interactivity as anything that communicates with the student beyond mere text and static images. This includes animations – animated GIF images, for example. Animations, while simple to create for the web are not that easy to simulate in class. Most of us can remember trying to show our classes how the secant line may approach the tangent line by “moving” a fixed chalk line to the (chalk) tangent line. The result is not always convincing. With simple animations, these motions are both possible and effective. If the student cannot attend the lecture to see your simulated animation, he or she can see the real thing on the Internet. Well-crafted animations, and by the way brilliantly colored graphics, have a certain


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