Contents

               Editorial
Articles

1.            iMath, an Online Future for Mathematics,  Stephen M. Hunt

2.   What Do We Do Until MathML?, G. Donald Allen
3.   Announcements

Editorial

What do Mozart and I have in common?  

Indeed, in our own times Mozart and I are both  “techies.”   It all began in 1698.  After hundreds of attempts by dozens of craftsmen, the Italian instrument maker Bartolmeo Cristofori finally solved all the problems inherent in making a harpsichord with hammers.  The result was the creation of a new instrument – soon called the piano -  with a dynamic range that completely eclipsed the harpsichord.  The new sound excited the public and it was an instant success.   Here was a powerful new tool, virtually untouched by anyone.  Rules for composing and performance did not exist.  The first explorers with the new piano technology, which included Mozart, would have the greatest impact.  

At first, the piano was an experimental and expensive technology.  By the time Mozart (1757 – 1791) was a youngster, these technical problems of mass-producing the piano had been solved and it became widely available.  Mozart adopted the piano, composing hundreds of works for this new instrument - the hi-tech piano.  Hayden began his career composing for the harpsichord and ended it composing for the piano. So important was this new instrument that the greatest composers, including no less than Ludwig von Beethoven, wrote extensively for it.   Eventually it surpassed the violin as the instrument of choice for concert soloists. 

Does this story sounds familiar?  In the normal course of events, the new technology displaces the old; the new idea supplants the old; the new device replaces the old.  It may not even be the case that the old is bad or does not work.  In time, the old passes in favor of the new.  This is the case before us - in education.  With qualified and capable teachers in ever-greater demand, and without the resources to stimulate greater production, institutions are turning to an expensive but effective alternative: technology enhanced learning.  Call it what you will, distance education, Web-assisted instruction, Web-based learning, or computer based training, the technology, the idea, the device all wrapped in one is here to stay. 

Make no mistake; with available resources the best way to teach is face-to-face tutorials with gifted and talented teachers.  This system produced Isaac Newton, Plato, and Archimedes.   However, modern institutions and contemporary priorities cannot sustain this kind of education for the many reasons we all know.

So, what is better: uncertified and unqualified teachers porting knowledge as best they can?  Or a hi-tech and in this case, an online alternative?

iMath, an Online Future for Mathematics

Dr Stephen M. Hunt

Director

Internet Math Consortium

steve@imath.org

http://www.imath.org

At the turn of the millennium the advent of the printing press was identified as the most significant innovation in the previous 1000 years.  Many aspects of our society today could not have evolved without print.  Some would argue that the Internet is going to have an even greater impact on the way we work and communicate.  John Chambers, CEO of Cisco Systems predicts that education will become a much larger user of the Internet. 'The next big killer application of the Internet is going to be education.  Education over the Internet is going to be so big it is going to make e-mail usage look like a rounding error.'  (NYT, November 99)

Print led to the evolution of universal math notation that today distills centuries of mathematical development.  The 'printed' page as a medium is also evolving, proto-types of electronic 'paper' have been developed and some anticipate that the process of putting ink to paper will be entirely replaced by electronic mechanisms.  Clearly, the electronic format(s) for encoding math will need to accommodate this move to a diversity of electronic forms.  The issue is not unique to math and a general solution to the problem of encoding data into portable electronic formats has emerged as a generalization of HTML (HyperText Markup Language).  The solution is called XML (eXtensible Markup Language).  MathML was the first XML vocabulary and it addresses the issue of encoding math notation.

Math educators face a tension in working with the notation mathematicians use to elegantly represent abstract ideas.  Do we teach concepts or representations?  When you ask a student to explain a math concept like a derivative, they very likely will show you how to compute the derivative. Much of what we teach today is how to calculate and these calculations are expressed using notation.  Whether we have the balance between concepts and calculations right or not is a topic for constant debate, but what is clear is that today students must master math notation if they are going to learn math.

Today the main tool we have for working with math notation is pen & paper. In the future, we may use similar tools, but in an electronic form. While we wait for handwriting and other technologies to emerge the keyboard has arisen as at least a bridge technology.  The first tools for communicating electronically focused on simple character processing.  These tools did not represent math in a useful form.  In order to edit math we don't just want information about how to paint a superscript or exponent on the screen, we want to identify what the base of the exponent is.  This requires a higher level processing of the data, one that is done by interpreting or inferring tags (like those used in HTML) within the character stream.  The tagging of data or the addition of metadata or information about the data has a universal application.  A uniform tagging model allows one application to process the data exported by another unknown application.  The ability for different applications to work with a common data model is a key rationale for XML.

There are various work-arounds for the lack of support for math notation within common applications.  Specialist applications and languages have evolved.  TeX gives the math author the power to dictate precisely the appearance of printed math.  About 25% of math papers are delivered to publishers as TeX.  Although no popular word processor implements a math editor, MathType licenses a math expression editor component to some of these vendors (Microsoft Office products, for example).  About 50% of math papers are delivered to publishers in this form.

Now, the Web is set to overtake print as a form for publishing and is revolutionizing communications in general.  Unfortunately, neither of these workarounds translate well into MathML.  TeX for example, does not require the author to bind the exponent to the base, and so it is not possible to translate all TeX into MathML.  Word saves a document as a Web page, but it turns the math into images.  So, neither TeX nor Word provide a solution for moving a math document to the Web as MathML.  Without appropriate structure, as provided by MathML, the document cannot be edited or processed by other applications.  Moreover, for universal educational use, the tools for communicating math must be free and easy to use.

As John Chambers' quote highlights, education is poised to become a huge user of the Internet/Web.  And, as math users and educators we wonder: Where is the math?  Will math continue to exist as a second class add-on to mainstream applications?  What would be the implications for the evolution of math and math education in such a world?  The Web has led to a knowledge explosion in other fields; what about math?

The good news is that math is a first class citizen of XML.  MathML was the first XML application and there are now open tools that are universally and freely available for communicating math within the Internet/Web.  No longer do you need to use specialist applications and syntaxes or components that do not integrate seamlessly with your document editor.  Now, you can effortlessly and painlessly author an open document with math and transmit this document with all its structure to others to read or edit.

As we move from print to electronic forms, new opportunities arise.  In a print form you could not dynamically edit the printed page and create your own derivative notes.  You could not easily annotate or comment on the page and send this fragment to a colleague as email.  You could not work collaboratively with others on the page.

Visit any online math course (except iMath's) and you will see educators struggling to do some of these things in their courses.  They will publish their notes and provide references to resources on the Web.  The class will use email, discussion forums, whiteboards, instant messaging, audio and video.  The math will be present in the pages as images.  The email, discussion and messaging tools are all limited to text.

Both instructors and students are a little overwhelmed with all the technology and applications used in these online courses.  There is no a priori reason for the features needed in an online course to be separated into so many different applications.  It creates multiple issues for both instructors and students who want to focus on content, not technology.

What caused this mess and what perpetuates it?  The answer is partly history and partly proprietary interest.  Fortunately education doesn't need to be constrained by either.  When Berners-Lee designed the early Web it was a new medium for communication, two-way communication.  You were never meant to look at markup.  Through visual tools you would send and receive pages that could include links to other pages.  The Mosaic browser and NCSA Web server crystallized the linked document publishing part of the world Berners-Lee had defined resulting in the notion that Web pages were only to be browsed. Publishing is significant, but it is way behind general communication. Education is clearly not just interested in students browsing Web pages. Education is about learning.  And learning is a dynamic process which involves being able to question and discuss, not just digest information - and the richer the information they can interact with, the better the learning experience.

Education benefits from the convergence of the various modes of communication to XML and the availability of appropriate tools.  Convergence means that email is no longer unstructured text that can be anonymously sent into the network in search of a possible destination.  Instead, it is just an XML vocabulary, a structured document where both author and recipient are authenticated and delivery happens in real time.  Convergence to XML enables MathML as part of general communication.

The Internet provides an avenue for the delivery of course materials and communications between course participants.  The four core Internet components that can be used to support a course are one-to-one messaging (e.g. email & instant messaging), collaborative discussions (e.g. discussion boards & chat), publishing (e.g. documents you publish or others publish) and storage (e.g. maintaining private course documents).

iMath redefines traditional data models and protocols underlying email, news, chat (and Web) as XML.  The unification of data models and protocols within XML leads to what is called the Unified Internet. Through the use of the Unified Internet tasks that previously required a multitude of tools are simply, elegantly and economically accomplished in a single setting.  Everything is authored as a Web page and these pages can be sent to others, discussed, published or stored - all simply and directly from within a single tool.  When the pages are received or viewed by another user they can be edited and commented on, then returned or stored independently of your desktop.  Everything on the Web becomes an editable resource.  If you don't like looking at the banner ad, delete it!  When you read this article on the Web, you can insert comments on the parts that interest you and introduce links to related resources.  In this way you can evolve your own Webs of personalized resources, on any topic.

The reason iMath moved towards the Unified Internet is to enable math communication.  Within the Unified Internet math can now be represented in messaging, discussions and the Web.  The use of a Web editor, not just a browser, together with a Web server that supports messaging, discussions, publishing and storage - is a necessary enhancement in order to resolve the problem of math communication.  It is also the right context for education. Education is not interested in a one-way Web.  Students are not just consumers of information.  Students and instructors need to be able to edit the information they acquire, discuss and collaborate with others, and publish and store Web information, independent of their physical location.

iMath has implemented the Unified Internet and made it available free for individual use (http://www.imath.net).  The iMath solution involves a Web editor who supports math, the back-end Web server which supports communication and course templates appropriate for math courses.  Instructors are using iMath as support infrastructure for their courses. An example is Barbara Gentry's (Parkland College) Beginning Algebra course.  To review this course, go to http://www.imath.net and register for a free iMath account.  Account information will be sent to your email address.  When you download iMath follow the link to the Beginning Algebra course.

The course has a home page that is used as the main point of contact between the instructor and students.  The home page includes an introduction to the course, information about the instructor and the timetable, course delivery information, the protocols for communicating with the instructor and other students and a syllabus. Links off the home page go to study requirements, the class schedule, the grading formula, an archive of announcements, the class list and a discussion space.

This type of structure is typical of course management systems.  However, other systems use forms to process parameters and resources supplied by an instructor and then build the course site.  This design arose because in the early days of the Web instructors would otherwise have needed to author HTML by hand, writing out the HTML tags.  On the other hand, iMath is a visual editor, creating a Web page is not an issue for instructors or students.  Both students and instructors can now freely communicate, collaborate and publish rich Web pages.  And, there is an important side effect - the course is not bound to a single course management application, since the page is not built dynamically from parameters.  The page begins as a Web page and evolves as a Web page under the full control of the author.

The class list provides an introduction to each student for the benefit of the other students and instructors.  Each student account allows pages to be stored privately, published, discussed, sent and received.  Students don't just read Web pages.  They can author and edit pages, and send these pages to others either privately or publicly.

The syllabus is divided into units.  Each unit represents a lesson. Associated with a unit are six components:  reading, notes, study guide, quiz, exercises, assignment.

The reading provides the background source material for the unit.  It may include a reference to texts or links to other Web sites, and even cross-references to readings or notes from earlier units.  Instructors write these materials within iMath in the same simple, intuitive way that any other page is created.  Pages are published directly to the course account.  It's simple, direct, and straightforward.

Students can collect the quizzes and assignments individually. When completed they are sent directly to the course account.  Every transaction is time stamped and authenticated, so everyone is accountable for his or her communications.  The instructors can comment liberally within the students' work.  When the work has been graded it can be sent back to the students' account.

In addition, the Beginning Algebra course uses an automatic protocol provided by iMath that enables the student to self-grade their quizzes and assignments.  The instructor audits the graded work prior to assigning the grade.  Usually when a server protocol is implemented it is done in a closed and proprietary way.  iMath however abstracts the server processing as an open XML protocol.  This approach is of paramount importance if the course is to remain portable and not bound to a single proprietary application.  By reducing interactions to XML transactions, iMath makes the course and course-processing model portable, exportable, and open to other applications.

The catalyst for much of iMath's design has been a group of instructors who have struggled with the limitations of existing systems.  These instructors are moving their courses from one-way Web solutions like WebCT and Blackboard to iMath.  They have spent hundreds of hours filling out forms, clicking buttons and sending their materials to a closed, database-driven applications which irreversibly captured their data - these systems do not provide a full export capability.  So, when iMath is asked to re-implement a Blackboard course we have to implement various parts of the course from scratch.  If Blackboard adhered only to open specifications, then we would merely need to import the course.

Although IMS (IMS - Instructional Management System, see http://www.imsproject.org) was an attempt to eliminate this type of proprietary binding, the released spec is incomplete and the IMS vendors have been implementing their own proprietary extensions.  The conflict between the IMS specification and extensions mirrors the tension between Web standards and browser extensions or 'browser wars'.  The incompatibilities between browsers are estimated to represent about 25% of the cost of Web site development.  For educators using the current Web/IMS solutions the cost is going to be much higher.  It's not just a matter of tweaking HTML - moving an entire course from Blackboard to WebCT involves fresh implementation work.  When the course is available as open XML protocols the transfer becomes automatic.

Internet and Web implementations have not supported math.  The IMS-related solutions add another layer of issues related to their use of forms, discussion modes, quiz models and the lack of integration with open computation and visualization.

Effectively using the Internet and Web for math courses requires more than just the browser being able to display math notation.  Online courses benefit from a Unified Internet - a single framework for all forms of communication.  For courses to be portable they need to implement only open XML protocols.  Commercial browsers are moving to XML and if they implement the full design they will be able to embed iMath seamlessly.  The browsers are unlikely to provide implementations that support all XML vocabularies. Rather, specialists will maintain the components for highly technical or unique vocabularies. The iMath Consortium provides the math components to enable the XML protocols of interest to math education.

The Beginning Algebra course (register for free at http://www.imath.net) described above more efficiently and effectively implements Internet/Web support in a way that complements the way most math educators deliver their off-line courses.  The addition of self-grading adds an enhanced learning activity.  This is possible because the protocol of checking in solutions, grading and auditing the graded work, can be handled quickly, cheaply, and without increasing the load on an instructor.

Another dimension provided by an Internet system is the delivery of dynamic reports (based on open protocols), which provide instant feedback to the instructor as to how students are engaging the course.  Armed with this information an instructor can dynamically modify their program to target student-learning issues.  iMath provides the support, design skill and implementation capability to educators to enable them to implement their approach to an online math course.  The iMath solution is developed in a form that is open, portable and available to all math educators.

iMath and the Unified Internet enable you to do what you are doing today, more efficiently while delivering a more effective learning experience for students.  iMath and the Unified Internet do not replace the need for an instructor.  They allow existing practices to be implemented more effectively and provide valuable enhancements.

Using the Unified Internet several new opportunities arise for education.  Just as students can work collaboratively, both with each other and with instructors, so also instructors can work collaboratively with students and other instructors to evolve materials.  An online course can also be a context for the evolution of course materials.  The Unified Internet provides the infrastructure for the distributed evolution of knowledge.  In the end the distinction between instructors and students will blur.  We will all be students; some will provide guidance, but we will all be learning.

There is no barrier to entry to the Unified Internet.  iMath is free for individual use and to small institutions.  iMath also offers an economical per user per course solution.  Your institution can affiliate with iMath to influence the evolution of open math infrastructure and also receive an unlimited license to iMath reference implementations and support for the use of iMath across your entire institution.  Anyone can get access to iMath and communicate with others.  If you want to use iMath in a course then you don't need to worry about software installations or servers.  For a low per student per course price you can use iMath and the hosted imath.net servers. Affiliation is a way of partnering with iMath and receiving support across your institution in your deployment of online courses.  The iMath Consortium is emerging as a diversified group of educational and commercial institutions committed to providing open math infrastructure for the benefit of education and users of math.  We invite you and your institution to get involved.

About the Author

Stephen M. Hunt (BSc(Hons), PhD, DipEd, BTh) pioneered the use of the Web for interactive math.  In 1995 he initiated the formation of the World Wide Web Consortium (W3C) Math Working Group (http://www.w3.org/math).  In 1999 he founded the Internet Math Consortium (http://www.imath.org).

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What Do we Do Until MathML?
G. Donald Allen
Department of Mathematics
Texas A&M University
College Station, TX 77843-3368

Abstract

Not withstanding the emergence of iMath, just discussed in the preceding article, many will still ask the question: How do we put mathematics on the Web? Arguably the most important issue for mediated technology developers of online mathematics courses, it has at this time no clear answer. Only the promise of MathML seems certain. This tagged language, which will be compatible with normal HTML browsers, is the definitive answer. The only problem is that the major browsers do not yet support MathML. In the interim, the question remains as to how we put mathematics on the Web.   While it seems that only Netscape (and not IE) has extant plans to implement MathML, the first ever conference entirely dedicated to MathML,  MathML International Conference 2000,  is scheduled for  October 20-21, 2000, Urbana-Champaign, IL, USA.

Introduction

The obvious extension of HTML (HyperText Mark up Language) is MathML, which means Mathematics Mark up Language. This extension, completely specified by W3C, makes the display of mathematics on normal HTML pages a reality. To date it has been implemented by a couple of browsers but not the "Big Two," Netscape and Internet Explorer. If you ask someone "when" will Netscape have it, the inevitable answer is "soon." For official information about MathML, see the W3C Math Activity Statement of the W3C Math Working Group.

Remarkably, the same answer "soon" to the question "when" has been given for at least three years. It was then that this author began work on WebCalC – online calculus. Indeed, when we began work on WebCalC, this was one our top three issues that needed resolution. To put high quality mathematics display on the Web takes some effort and MathML answers almost all of them. Of course the natural recourse is to assume that MathML is almost here and wait/prepare for it. Our decision was to get top quality mathematics up there and to make it look good, not just for other mathematicians, but for students that have little patience for less than first rate computer productions. Thus another approach was required.

Here is one theory upon which many developers of online mathematics have proceeded. Prepare materials in TeX or LaTeX and convert them to MathML when the time is right. Assume TeX/LaTeX-to-MathML converters will be available concurrently. An alternative theory requires the use MSWord or Word Perfect with MathType. But what can be done with the TeX files until the time comes? Let us note emphatically that both these provisional solutions do not lend themselves easily to any sort of interactivity. Indeed, interactivity is at this time is a difficult feature to implement with most of the text tools.

Tools for Math Display

In this short article we will discuss alternatives to MathML, many of which have value even if MathML was available tomorrow. Several types of various categories are in use today. First we list the categories:

• CAS engines (Maple, Mathematica, MathCad, MATLAB)

• Plug-ins (Tech Explorer)

• Converters (Latex2html, T_TH, MSWord, Wordperfect, MathType, WebEQ)

• Special browsers (Scientific Notebook, Amaya, e-Lite)

• Other

Other tools exist. This list is by no means exhaustive.

Descriptions

Computer Algebra Systems (CAS) have been around for a long time. The dream of every first year college student for a program that can take derivatives, compute integrals, and solve equations symbolically whenever possible, is here. Slowly, the power of these programs has increased to the point now that they are serious research tools in most of science and mathematics. Both Maple and Mathematica are pure CAS engines of considerable power and growing complexity that also have mathematical display capabilities. They can be used over the Internet. But … the file types are proprietary, and the programs themselves are their own browsers. Editing in Maple is particularly difficult. However, Maple will save files as HTML documents. You can even include math symbols. All mathematical expressions are converted to GIF files. However, some considerable practice for proficiency is required. MathCad, which uses the Maple kernel, is similar. Display of virtually everything is superior to the others, but file sizes can be large. Another product from MathSoft is StudyWorks, a low cost yet powerful alternative to any of the big four CAS engines with some nifty Web features. MATLAB is more a research and high perfomance numerical analysis tool than a Web page generator. Costs for all four, Maple, Mathematica, MathCad, MATLAB, are substantially more than a top quality "Office" package. For example, the retail cost of Maple 5.1 is at least $500. The others are priced comparably. Education pricing and street discounts are available, however. Cost continues to be an important factor for many institutions.

IBM markets Tech Explorer, a browser plug-in that reads TeX and LaTeX files directly and displays them within your browser, be it Netscape or IE. The latest version is very robust, doing an excellent job of accurately parsing complex TeX documents. It is inexpensive. At only $25, it must be considered a bargain. But there is a bonus. Tech Explorer, Professional version, is also a MathML converter. You can see your TeX converted or it can real MathML files directly. If only Netscape or Microsoft would make a deal with IBM, the next versions of these browsers would be there!

(LaFlamme and Nicholson have used TechExplorer and Java effectively in this linear algebra package offered through the University of Calgary. Here is some information about couse. URL: http://www.ucalgary.ca/UofC/events/pubaff/Gazette/Archives/Jan24-00/math.htm)

A more basic plug-in that seems to be just about ubiquitous is Adobe Acrobat. Users can download the reader at no cost; it self-installs and the browser launches when a link to a PDF file is encountered. The creator must buy the software, Adobe’s Distiller to create the acrobat file (~$200). After some experimentation with fonts, the page creator can generate documents easily viewable and printable from any browser with excellent resolution. The United States government makes extensive use of Acrobat files and for good reason. Any file is displayed exactly as it appears when created. With Distiller installed, the user may print to the PDF format by selecting the PDF printer. For more complex files, it may be better to first save them to a postscript file and then distill them. To do this the user must install a postscript printer and then print to a file with this printer. Use of course this PS (postscript) extension. As an example, this author installed the HP LaserJet 5P (postscript) printer directly from the Add Printer icon.

File sizes tend to be large, however. As well, hyperlinks are difficult to insert. Moreover, PDF documents do not lend themselves easily or at all to other HTML and particularly Java constructs. In sum, PDF is a great format for pure content on the Web, but not much else. That’s just what it was designed for.

For several years now, the mathematician’s war-horse of math display over the Web has been LATEX2HTML, the LaTeX  to HTML converter. This program, which is freely available, will parse a LaTeX file and convert the `math parts' to GIF images and the text part to standard HTML and finally combine them altogether into a HTML document viewable on any browser. Some limitations to the volume of math has it will handle have been noted – though this is more an inconvenience than a limitation. It only processes basic LaTeX; macros are ignored, and this is a true limitation. It is free; it is very widely used particularly among mathematicians, physicists, and engineers. However, to run it you need both LaTeX and LATEX2HTML installed on your Unix-based system. There are also free versions of LaTeX for all platforms. Like PDF, interactivity is not simple, requiring insertion after each modification.   A similar converter is TeX4ht.  A highly configurable TeX-based authoring system, it produces graphic images for mathematics as well for producing hypertext. It interacts with TeX-based applications through style files and postprocessors, leaving the processing of the source files to the native TeX compiler. Therefore, TeX4ht is compatible with Plain TeX, LaTeX and AMS style files.

T_TH

Another T_EX  to HTML translator is  T_TH. Unlike LATEX2HTML, it will translate either the Plain or LaTeX macro packages.  is  T_TH produces more compact web documents than other converters, because it translates the equations into HTML using DIV and Table tags, instead of converting them to images.   It may well be the fastest and most convenient approach, with the extra benefit is that document structure such as footnotes, lists, cross-references and sectioning, is automatically included with internal hyperlinks. T_TH uses native symbol fonts, which means that T_TH created pages can be viewed on Netscape 4.0 and later “right out of the box.”  It is available for all platforms including versions of, Unix, Windows, and MacOS. 

Here is a comparison between the output of T_EX, the lingua franca of mathematics typesetting and T_TH:

T_EX output:

T_TH output:

Please ignore the relative widths; it is the mathematics that is of interest.  We “cheated” just a bit here.  The T_EX file was compiled using PCTeX specifying Windows system fonts, the same fonts that are used by T_TH.  Had this not been done, that is had we used standard Computer Modern fonts, the T_EX output would appear much lighter.  As is apparent, however, the mathematics of the T_TH converter is very readable but not quite up to professional standards.

We would be remiss in not mentioning that there are many, many more math rendering to Web programs.  Among the categories are browsers such as Amaya, which is sponsored by W3C and is free, and e-Lite, a Java-based commercial offering from IceSoft in collaboration with WebEQ. Hutchinson has written an excellent review of them, showing how they compare with each other and with Netscape rendered T_TH.

Both Microsoft Word and Word Perfect have equation editors and both have conversion to HTML capabilities. In both cases the conversions of the math portions are getting better and better. The principle of conversion however is the same as for LATEX2HTML. Math segments are converted to gif images, the result displayed on a standard HTML page. A definite advantage is that the word processors can already access much of the power of HTML in and of themselves. This means heading and other HTML features are available without the user needing to know the many TAGS of HTML. In fact this document was created using MS Word and then converted to HTML – with some post-processing. A disadvantage is that the equation editors themselves are in comparison to T_EX, clumsy to use. The cost is right as most folks have ready access to one of these powerful word processors. Note: the ordinary HTML conversion of a MSWord document of even simple construction is rather complicated and tricky to edit after the fact. It is recommended that if your document is intended for the Web, you should construct it from the ground up in an HTML editor - like Dreamweaver, FrontPage, HotMetal, or many others.

MathType™ by Design Science is a powerful interactive tool that generates mathematical notation for all types of print and web-based technical documents. MathType's built-in MathML  translator converts mathematical expressions created with MathType and Equation Editor (Equation Editor is the junior version of MathType that comes with Microsoft Office, Corel WordPerfect and many ther Windows and Macintosh products), to MathML.  Once you select a translator, create expressions with MathType's easy-to-use nterface, then copy and paste, or drag and drop expressions into a MathML document -- MathType converts the equations to MathML on the fly.

Scientific Notebook, with the Maple kernel inside, is a word processor, CAS, and Internet browser all in one. The base file type is LaTeX, though a somewhat proprietary version. However, it can read and display simple LaTeX files, though often some adjustments are necessary. It can perform complex mathematics just like Maple, and since it doubles as a browser, the files are viewable directly over the Internet. The cost is reasonable. At $70, it is difficult to get more program in a single box. Mathematics is simple to produce using either buttons, pull down menus or keyboard shortcuts. In fact, we have typically had complete novices creating their own documents of nearly any mathematical complexity within an hour. Tables and matrices are transparently simple to create and manipulate. Files sizes, excluding graphics, are no larger than LaTeX files. Graphics can be built on the fly or stored in vector (wmf) or compressed bitmap (bmp or gif) formats. If one needs to get a lot of math on the Web and quickly, Scientific Notebook is a way to do it. The defect, like that described above, is that it is a special program that users need to buy. There is a free viewer version that has no CAS engine, and consequently the implications of that. One drawback is that it reads only T_EX files. So, other HTML documents must be viewed in another browser.

Under the category of other we offer a totally graphic alternative. Based on the fact that most screens have a resolution of 72-96 dpi, it is possible to make entire sections of the document as images. Here is the idea. Compile your T_EX /LaTeX (or other word processor/spreadsheet program) document and display it on your screen. This can apply as well to spreadsheets, word processors, graphics programs, and the like. Using a screen capture program slice it up into paragraph size pieces and import or paste them into the display page of an HTML editor. For example, the Corel screen capture program can make the screen shots and save them in sequentially numbered files. The HTML editor import image function can be used to reconstruct the page piece by piece. Alternative, some HTML editors (e.g. Adobe Page Mill) will permit a paste directly from the pasteboard, creating GIF images and sequentially numbering them. This combination of three programs, T_EX + Screen Capture + HTML editor, is a powerful combination that allows the full use of HTML features such as frames, it displays anything at screen resolution, and it’s quick. Internal links within document snippets must be accomplished through image maps, a possible problem. Also, the page does not print well. However, it is simple to add a link to the Acrobat version of the page. An early example, a brief history of Pi is at this link. (You will note that it is set in a frame structure, with the main body part almost all graphic images. Certain flaws in the design of mixing layers and graphics not in layers ililustrate some fine points of design.)

Advantages are many. One gets a fully functional page with mathematics on it, where it is supposed to be. Between the graphic images, normal HTML text can be placed. Using layers, other graphics such as buttons can be placed next to or even on top of the text graphics. Using site maps, parts of graphics can contain links or other HTML functionality.  By cutting the page into several pieces, rather than an entire page at one time, the full functionality of HTML can be utilized.  Disadvantages are many, as well. The pages do not print very well, though this could be considered an advantage by developers desirous of protecting their pages from copying. Very special care must be taken to account for various screen resolutions. For example, a screen displaying 800 x 600 pixels will give a very much different look to the one displaying 1024 x 768 pixels. Become accustomed to using your monitor at various resolutions during development.

All these possibilities are well tested.  There are many more, most of which can be found at the W3C Website.  It would be wonderful if we knew that MathML was just about here, perhaps with the next release of IE or Netscape.  This prospect is very dim; rumors are that Microsoft has no current plans whatever for implementation of MathML now or anytime soon.  Netscape is said to have implementation plans sometime around version 6.5, if then.   In the meantime, if you need to make a decision, the best advice is to select a method that is robust and easily converted in the future.

URL’s of organizations mentioned in this article:
W3C MathML - http://www.w3.org/Math/
Amaya - http://www.w3.org/Amaya/
e-Lite - http://www.icesoft.no/
IBM TechExplorer – http://www-4.ibm.com/software/network/techexplorer/
Scientific Notebook – http://www.mackichan.com/msifacts.html
Maple - http://www.maplesoft.com/
Mathematica - http://www.wolfram.com/
MathType - http://www.mathtype.com/
Latex2HTML - http://www.geom.umn.edu/~ross/webtex/webtex/
TTH - http://hutchinson.belmont.ma.us/tth/mml
WebEQ - http://www.webeq.com

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Announcement and New Products

1.      ICTCM – 2000.  The annual ICTCM conference is scheduled this year November 16-19 in Atlanta, Ga. There you will find the state of the art teaching-with-technology people.  Talks will all phases of classroom technology from Java JavaScript applications to using calculators to teach math. Specialists in the major CAS engines, Derive, Maple, and Mathematica, experts with TI and Casio calculators, and an assortment of tutorial sessions will all be available.  See http://www.ictcm.org/ for more information.

2.      ODE Architect, a suite of software tools designed for use in an introductory differential equations course.  Available from John Wiley and Sons, Inc., it from John Wiley and Sons, Inc., it comes neatly packaged with a companion text and accompanying CD. The text contains a introduction, a tutorial, and a collection of modern applications of differential equations. A highlight of the package is a number of explorations that allow the reader to broaden his or her understanding through interaction with the ODE Architect software.  The collection of references is excellent, pointing readers to published papers.  The ODE Architect is actually several packages in one, including the multimedia ODE Architect. Here you will find a number of learning modules with names like Nonlinear Systems, Compartment Models, and Chaos and Control. Each module employs sound, video, animation, and a host of pedagogical techniques designed to introduce important and interesting applications of differential equations.

3.      MathType 4 has just been released from Design Science, Inc.  MathType is an intelligent mathematical equation editor designed for personal computers.  This version works as usual with Microsoft Word and Corel Word Perfect, and constitutes the full upgrade of the onboard equation editors for both word processors.  A potentially very useful feature of this version is that it exports as MathML and as LATEX. Conversion to HTML is vastly improved in MathType 4.   It is available for the MacOS or Windows operating systems. 

4.      ActivStats, a product of Addison-Wesley-Longman,  is a software package that teaches basic statistics using a multimedia approach. The software can be run on either a PC or a Macintosh, provided that QuickTime 3 or higher is already installed and the computer has a 2X CD-ROM drive. It is designed to run from the CD itself, but it can be installed on the hard drive. Interactivity is the key approach to learning statistics using ActivStats. After a topic is introduced, the lesson is presented in the format of a QuickTime movie. An increasingly prominent feature in many software packages is a web resources connection. This feature for ActivStats is very good, with every page containing (Internet) links to additional.  In this way, the program allows the student to explore the world of statistics online.

5.      StudyWorks III Mathematics by MathSoft is a software package very similar to its big brother  MathCad, also published by MathSoft.  Though this software was developed for high school students, it is powerful enough to handle undergraduate mathematics through the calculus sequence.  The package can be used to communicate electronically with distance-learning college algebra students and is recommended it to anyone interested in giving students a first experience with computer algebra software.  Among the advantages that StudyWorks III Mathematics offers are that it is easy to learn, is inexpensive (about $30), and has impressive built-in resources.

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Call for manuscripts.

We are interested in articles for one of the following sections.   Article should be interesting but brief: 500-1200 words.  Longer articles will be considered on an individual basis.

·        Vision. The focus is on the future: what may happen, what certainly will happen, and what will not happen as technology advances into learning and education.

·        Case Studies.  Especially important are examples of technology application that really work in the classroom.  Data is important here

·        Commentary.  Timely observations and opinions on the use of technology to enhance Mathematics and Science education.

·        Faculty development.  How are faculty supported, trained, and encouraged in the integration of technology into Mathematics and Science education?  How are faculty rewarded – or should be rewarded.    

·        Book and Software Reviews.  With the ever-accelerating pace of hardware and software development, and with the continuing application of technology in the classroom, it is more important than ever to keep in touch with new methods and software.

·       Letters to the editor.  If some technology issue is significant, or if some point in an article is noteworthy, this section allows feedback for the editors or readers.

Send your article to any member of the editorial board for review.

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We gratefully acknowledge the support of the Department of Mathematics at Texas A&M University for preparation costs.