This paper will discuss three areas in which I have recommendations for future development of WebCT: the browsers supported, the quiz tool, and the math functions for calculated quiz questions, and will provide some late-breaking-news on rendering of mathematics in browsers. One year ago, the paper "Mathematics in WebCT II" was presented at the Second International WebCT Conference in Athens, Georgia, USA. In that paper I looked at two broad categories: static content and interactive content. While software version numbers have increased, this information is largely still current.
Faculty and students continue to use two types of authoring environments for mathematics, markup languages and palette driven interfaces. TeX and LaTeX are the most commonly used markup language and the Microsoft Equation Editor or its parent MathType is the most frequently used palette driven interface.
The document types currently rendered by browsers and browsers with plugins include:
The WebEQ Math Viewer by Design Science can render MathML that has been enclosed within viewer applet tags.
MathType 5, to be released in July/August 2001 by Design Science, together with Word 97, 2000, or XP, can produce all these document types. In addition, equations can be numbered left or right and linked references to equations can be inserted. Many users will find the MathType translation of Word to HTML superior to Word's built-in translation. Design Science is also working on an Internet Explorer 5.5 plugin called the MathPlayer, which will likely be released in the fall of 2001. The MathPlayer uses Microsoft "element behaviors" and is very closely integrated with Internet Explorer. It is intended to handle all MathML 2.0 markup, both presentation and content.
Mozilla is an open-source web browser, designed for standards compliance, performance and portability. Netscape has released Netscape 6.1 Preview Release 1, its commercial browser based on Mozilla 0.9.1. A version of Mozilla is available with MathML 2.0 support. The Web site MathML for Mozilla (Sidje, 2001) contains information on XHTML, authoring with MathML, and the fonts used with MathML.
In recent email correspondence, Paul Topping of Design Science writes:
"Internet Explorer and Mozilla currently disagree on the MIME type with which an XHTML page containing <math> elements should be served. Right now, that is the only thing stopping a single page being rendered in Mozilla and IE 5.5 with MathPlayer."
Let us assume that some future version of Netscape will support MathML or that WebCT will extend its browser support to include Mozilla. Then WebCT users will want to be able to create a single XHTML page containing MathML and have that page rendered by both Netscape/Mozilla or by Internet Explorer/MathPlayer. At the moment Mozilla requires that such a document carry the XML extension and be served as text/xml. This has a negative impact on WebCT users. Mozilla will render an XML document using the WebCT single page tool, but not as a page in a WebCT content module. If the XML document source is pasted into an organizer page textbox, a quiz question textbox, a discussions message textbox, or a mail message textbox, the MathML elements will not be correctly rendered. For backward compatibility, Mozilla should allow the document to carry the HTML extension and be served as text/html. The WebCT mathematics community needs to be vocal on this issue. In this regard Paul Topping made the following statement.
"I have no idea what the prospects for a solution are. The issue upsets us involved in MathML so much, I have to keep away from it to maintain sanity. I think it is best that potential consumers of MathML, rather than software vendors that are seen as profitting from MathML, to raise a ruckus and demand that the issue get resolved."
I also questioned Bill Hammond of the Department of Mathematics and Statistics, The University at Albany, Albany, NY on this issue. Here are his remarks.
"And much as I hate to say it, on this question, I believe that Mozilla (temporarily, I hope) appears to be obstinate. I think that, as things are today, an XML-aware browser should be able to deal with namespace extensions of HTML (the way web pages with math need to be marked up, but much more general than just the particular namespace extension for MathML) when served through HTTP as either text/html or text/xml. Other content types may arise that need to be added to this pot. W3C's Amaya behaves this way. If such pages are served as text/html in a way that is documented in section 5 of the XHTML 1.0 spec (http://www.w3.org/TR/xhtml1), then they degrade correctly in old browsers (the math is not decipherable), but the rest of the HTML survives."
Paul Topping and others on the WebCT mailing list recently discussed the 'size problem' associated with the display of mathematics using images, Netscape plugins, applets, or object tags. Here are Paul's comments.
The plugins that Microsoft refers to are not so-called 'Netscape plugins' or Java applets that do suffer from the 'size problem'. They use an entirely different technology Microsoft calls 'behaviors' and does not suffer the size problem. My company, Design Science, is working on such a plugin. We call it MathPlayer and have already demonstrated early versions of it. Using the behavior mechanism, our MathPlayer software becomes a very closely integrated part of Internet Explorer."
My recommendation to the WebCT development team is to support both Netscape 6.1 and the corresponding stable milestone of Mozilla beginning with WebCT 3.7.
MathML and WebEQ
The WebEQ Math Viewer applet from Designer Science looks like it may be one of the best ways to view an HTML document which contains MathML markup for the near term. Waterloo Maple Inc. announced on June 7, 2001 that Maple 7, to be shipped on June 29, 2001, will use WebEQ technology to incorporate MathML 2.0. The Maple 7 press release contains the following statement.
"Maple 7s implementation of MathML 2.0 is the most comprehensive in the industry. It allows for the translation of Maple-based documents to full MathML 2.0 for display on browsers and for translation into native formats by other applications. Maple 7 takes advantage of the WebEQ component by Design Science to view mathematics on standard browsers."
The WebEQ Math Viewer and the WebEQ Math Viewer for Maple are free downloads. I downloaded both for experimentation. Using WebCT 3.5 SE, Netscape 4.77, and Internet Explorer 5.5 (with the May 24, 2001 security patch which fixes the download problem), I pasted this test page into a quiz textbox, a organizer page textbox, a mail textbox, and a discussions textbox. I also put it into a content module. Everything worked as expected except for the mail and discussions textboxes. An error message is produced by the APPLET MathML tags. I passed along a recommendation to WebCT.com that the list of tags acceptable in a mail and discussions textbox be extended to include these tags. Rick Herding replied by saying that, "I've forwarded your suggestion on to Product Development who inform me that we'll likely be examining WebEQ for 3.7, and that it is indeed currently a project under consideration for 3.7. 3.7 is currently scheduled for release this October."
Using the WebEQ suite from Design Science, a web page containing equations can be created in two steps. The first step (and final step when browsers are able to handle MathML directly) is to insert MathML into your web page using the WebEQ Equation Editor. The second step is to run the Page Wizard on the file produced in step one. The Page Wizard wraps an APPLET tag around the MathML and computes appropriate height and width attribute values. If you have the WebEQ Math Viewer installed in your browser, you will be able to view the page.
Users of Maple 7 will have an alternative authoring environment. Maple 7 will have an option to export to HTML containing MathML 2.0 and APPLET tags suitable for viewing with the WebEQ Math Viewer for Maple.
The WebEQ technology is not perfect. It has the same vertical and horizontal alignment problems you see in HTML documents that have inline equations inserted as images, because, like the IMG tag, the APPLET tag also has height, width, and align attributes. To make life more difficult, the rendering of the align attribute is also browser dependent. The height and width values define the dimensions of a "bounding box" into which the equation is drawn. Here is an example from the Design Science web site that suffers from vertical alignment problems. These can be partially corrected by adjusting the dimensions of the bounding boxes. Here is an example from the Maple web site that suffers from bounding boxes that are generally not wide enough, causing some characters at the beginning and end of equations to be clipped. In both examples the calculated dimensions of the bounding boxes are not optimum.
Take a look at the source of the test page mentioned above. The PARAM tag name/value pairs control the look of the equation. The align and valign values control the horizontal and vertical placement within the bounding box. The size value controls the equation font size. If the controls value is set to "true", then right clicking on the equation will open a dialog box that will allow the user to adjust the size of the equation.
Respondus came out of beta testing in January 2001 and is the first offline WebCT quiz generation tool (Windows only) that provides for mathematical equation input. Respondus has a number of useful features including:
The Respondus Equation Editor is similar to the Microsoft Equation Editor. Both of these products can be replaced by the more powerful parent product MathType. The Respondus Equation Editor outputs an image file. Positioning of displayed equations is satisfactory, but the positioning of inline equations sometimes is not. Future versions of Respondus are likely to support WebEQ and MathML.
WebCT permits the archiving of a question database, but not a quiz. The quiz archiving feature of Respondus fills a gap in WebCT making it easy to move a quiz from one WebCT course to another. I recommend that WebCT, through its commitment to IMS and SCORM, implement an open specification for storing quizzes and question databases.
WebCT 3.x implements the Perl core functions abs and int along with atan2, sin, cos, exp, log, and sqrt for use in calculated quiz questions. The code base for Cobalt, the next major release of WebCT, is being rewritten in Java, which contains a Math class consisting of 20 functions. Visual Numerics has long been known for providing scientific software to business, industry, and education. Visual Numerics is currently making available the Java Numeric Library 1.0 for free download. The Web page (http://www.vni.com/products/wpd/jnl/) states the following:
"Visual Numerics believes that Java has the potential to become the ubiquitous cross-platform Numeric Computing programming language. Visual Numerics intends to use its expertise to propose and implement a Numeric API for Java called JNL, A Numeric Library for Java. JNL gives you the most important numerical functions missing in Java: a numerical type class; Complex; and three categories of numerical functions classes -- the special functions class, the linear algebra classes and the statistics class. All classes use double precision floating point as the underlying float type."
The special functions class currently contains 14 functions while the statistics class contains 17 functions.
Development in the area of numerical computing in Java is being coordinated by the Java Grande Forum web site contains the following statements:
"Java has potential to be a better environment for Grande application development than any previous languages such as Fortran and C++. The goal of the Java Grande Forum is to develop community consensus and recommendations for either changes to Java or establishment of standards (frameworks) for Grande libraries and services."
The JavaNumerics page provides a focal point for information on numerical computing in Java. This is an activity of the Java Grande Forum Numerics Working Group, chaired by Ron Boisvert and Roldan Pozo.
I recommend that the Visual Numerics JNL be incorporated into Cobalt.
Calculated Quiz Question Recommendation
Calculated quiz questions are currently limited to a single numerical answer. I concur with the suggestions of several users that the flexibility of multiple answers is needed. This might be accomplished in two ways: by providing for multiple answers within a calculated question or extending the scope of calculated question variables to the entire quiz.
MAA, MathDL, and JOMA
The Mathematical Sciences Digital Library (MathDL) is an online resource managed by the Mathematical Association of America (MAA) with funding by the National Science Foundation. The Library is hosted by the Math Forum. The site provides online resources for both teachers and students of collegiate mathematics, including a new MAA publication, the Journal of Online Mathematics and its Applications (JOMA), a catalog of mathematics commercial products, complete with editorial reviews, reader ratings and discussion groups and an online collection of mathematics instructional material with authors' statements and reader reviews. JOMA will take advantage of the World Wide Web as a publication medium for materials containing dynamic, full-color graphics; internal and external hyperlinks to related resources; Java applets; MathML, SVG, and other XML markups; audio and video clips; and other web-based features. JOMA will publish innovative, class-tested, web-based learning materials, articles on design and use of online materials, original research articles on student learning via online materials and other technology-rich environments, surveys of existing online materials, high-quality "mathlets" (self-contained, dynamic, single-purpose learning tools), and other articles on related subjects, with particular emphasis on applications.
In the first issue of JOMA (January 2001), Tina Straley, MAA Executive Director, made the following statements in her article "JOMA Welcome."
"The National Science Foundation has created a program entitled the Science, Mathematics, Engineering, and Technology Education Digital Library, administered by the Division of Undergraduate Education. The national digital library will be a linked system of sites devoted to online resources in undergraduate education. A user will be able to enter any node on the system and access other sites. The content area sites will be primarily discipline-specific. Each site will have its own character and interpretation of a digital library, but search data will be consistent so that a visitor to any part of the library may search the entire library."
"In the first round of funding, three disciplinary areas were funded, one of which is the MAA Mathematical Sciences Digital Library. We are partnering with the MathForum, a subsidiary of WebCT, which is designing and hosting our site. The expertise and experiences of MAA and MathForum are a perfect combination to bring to you high quality educational materials on-line."
"The national digital library will address some difficult issues in order to realize the full potential of the World Wide Web as an educational resource. Although there is an enormous amount of material freely available on the web, there is no quality control and no organization."
In WebCT 3.x, any document can be put into a content module, not just HTML documents. Suppose your course My-Files contains the PDF document objectives.pdf. To add this to a content module, do the following: Content Module -> Designer Options -> Add File -> Go -> Browse -> select objectives.pdf -> Pick -> Add -> Edit titles -> Go -> replace (untitled) with Objectives -> Update.
How your WebCT server and browser combination will handle this document will depend on the Mime type settings of the server, and your browser settings. It is no longer necessary to use an auxiliary HTML file as was explained in "Mathematics in WebCT II."
This study was sponsored by the Southeastern University and College Coalition for Engineering Education (SUCCEED) and the Pilot Laptop Program, College of Engineering and Science, Clemson University.
1 William F. Moss, Department of Mathematical Sciences, College of Engineering and Science, Clemson University.