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Math on the Web: A Status Report
July, 2001
Focus: Distance Learning
by Robert Miner and Paul Topping, Design Science, Inc.
The six months since the last Status Report have seen steady incremental
improvement in support for Math on the Web. There has been some progress with
browser support, and more activity with authoring tools. However, some of the
most notable developments have been in the area of support for math in
distance learning tools.
In this volume of the Status Report, we begin with a
brief survey of
what people are doing with math and science communication on the Web, and the
techniques they are using to do it. We will then take a look at some notable
Math on the Web news and announcements from the
last six months. Finally, we end by taking a closer look at what has been
happening in the distance learning
arena.
The problem of communicating Math on the Web is really no different than
communicating math via other media. Namely, authoring and displaying
mathematical notation is difficult. On top of that, the Web is a dynamic medium,
where users can interact with rich media documents in sophisticated ways. This
introduces a whole new layer of challenges and possibilities for engaging,
interactive communication between authors and readers.
In spite of the fact that math and science communication on the Web requires special skills and tools, along with a healthy dose of ingenuity,
this has not stopped people from taking advantage of the
Web's potential. Many innovative Web sites, some new, some old, show what is
possible with today's technology.
New Resources for Students
One thing the Web is doing is greatly expanding the resources available to
students. "Math Help" sites abound, often with tutors or moderators that answer
questions posted by students. Others offer study and enrichment materials aimed
at parents and mentors. Another interesting kind of site seeks to give students
ways to help each other. For example,
ThinkQuest [1] was
created for fourth graders by fourth graders to work on word problem
skills. Enabling this kind of
interaction between students from around the globe is something that is hard to
conceive of on a wide scale without an enabling technology like the Web.
New Ways for Students and Teachers to Interact
There has been tremendous growth in Web sites and services for coordinating
interactions between teachers and students over the Web. Interaction over the
Web offers a compelling blend of the thoughtfulness of written communication,
and the immediacy and informality of spoken communication. The partial anonymity of
interacting through the Web can have a liberating effect on shy students who
might otherwise be too reticent to fully engage with learning. For adult
learners, the ability to work at one's own pace and schedule can create an
opportunity for ongoing training and education in situations where the pressures
of everyday life won't permit more traditional pedagogical methods.
Distance learning is a very large area, but broadly speaking, distance
learning platforms from various vendors generally seek to provide frameworks in
which teachers can easily set up a class Web site where students and teachers
can then interact. Such frameworks provide ways for teachers to post materials
and announcements, message boards, real-time whiteboards, email, and
other communication services, as well as online testing and assessment in some
cases. Several distance learning vendors have recently taken steps to support math in
their product offerings. See our Focus:
Distance Learning section below for more details.
New Ways of Presenting Math
On the Web, documents don't have to be static. Web material can engage readers in a host of new ways, from embedding
rich media such as sound and video, to interacting with readers through
simulations, animations, and "live text" that alters in response to a reader
request to see information in a different form, or in more detail.
One of the most exciting new technologies for dynamic mathematics is the World Wide Web Consortium's (W3C) Recommendation for
Scalable Vector Graphics (SVG) [2]. SVG
is an XML-based markup language that describes 2D graphics, rather like
PostScript. It is displayed by a browser plug-in, and the scene can be modified
on the fly from within a Web page by using JavaScript, for example. You can see
some great examples of how this emerging technology can be used to explain
mathematical concepts from
Integre Technical Publishing [3].
New Tools for Research
Many projects are
underway to make research publications available online to facilitate faster and
more complete exchange of information between researchers around the world. While getting research articles online has been a major focus for some years,
as the amount of information online has grown, the ability to find relevant
material has become more and more important. While traditional searching and
indexing techniques can do a lot, searching scientific material presents special
challenges. One innovative research project seeking to address this
problem is the SearchFor
initiative [4] at the University of Nice and INRIA Sophia-Antipolis, run by
Marc Gaëtano and Stéphane Dalmas.
They have built a prototype search engine that knows about math. Thus, for
example, searching for x + y will also find y + x,
when appropriate. Using these search techniques together with inference rules,
it may soon be possible to answer questions such as "Is
 ?" by
searching the world's research literature. The result would not only be the
answer (which in this case might be more easily found by simply graphing the
function numerically) but also a pointer to where the proof of the
answer could be found.
Many Technologies, None Perfect
While the promise of the Web for scientific communication is great, technical
problems still remain. The thread that ties together all attempts to use the Web
for math and science is the need to put mathematical notation in Web pages.
There are basically four strategies for publishing technical material to the Web
today, none without drawbacks.
Non-HTML Formats
The simplest way to publish a technical document created in a format that
natively supports math (e.g. Adobe PDF, TeX/DVI files, Word documents) is to
put the document online as is. This has the significant advantage that the
author retains total control over the formatting. But it also has significant
disadvantages: it requires the reader to have the software to display
that format on his or her machine, and such documents can only be
superficially integrated into the rest of the Web. Using Adobe's PDF format
minimizes the software problem, since the Acrobat Reader is widely available.
But the integration with the rest of the Web remains problematic. Most
research articles are currently put online using this technique.
Browser-native HTML
- At the other end of the spectrum, one can choose to use only the
mainstream browsers' native HTML capabilities. That generally means images of
equations for complicated material, or a combination of text, symbols, fonts,
tables and stylesheets for more elementary material. The big advantage of this
method is that it reaches the widest audience by far. It places almost no
burden on the reader to obtain additional software, such as browser plug-ins. However, the downsides
are that the quality tends to be
lower, and such documents are quite difficult to author and maintain.
This technique is most widely used for more elementary, expository educational
material.
Although there are limits to what is economically viable, the best thing
for the math and science community, obviously, is for mainstream browsers to
add more support for native math rendering. The most important activity to
watch in this area is the ongoing work on
MathML in Mozilla [5].
However, there is some possibility of greater style support for math in future
versions of the W3C's Cascading Style Sheet (CSS) specification.
HTML with Components
- Even if native math support eventually makes its way from Mozilla into
Netscape's browser, it is clear that mainstream browsers cannot build in all
the dynamic math capabilities the math and science community might eventually
need, not to mention features desired by other groups with specialized
interests. For this reason, a great deal of work has been done on techniques
for integrating special purpose components into Web pages. Browser support for
component technologies such as applets, plug-ins and behaviors continue to
mature, while several vendors now make various kinds of components for dynamic
math and science Web pages.
The main disadvantage of the component approach to putting math and science
on the Web is that it requires readers to install specialized components into
their browsers. Also, authoring pages that make use of such components is
generally quite difficult. A final factor that has hampered broader adoption
of this strategy is that components have generally not
integrated very seamlessly into the surrounding page, usually requiring ad
hoc techniques for every browser. Therefore, the difficulty of creating
pages that are robust across many browsers and operating systems has been
substantial.
It is clear that this approach ultimately has, by far, the greatest
potential for facilitating the creation of engaging, dynamic,
high-functionality math and science content on the Web. It also has the
advantage of competition, since component architectures are of necessity
standards-based, with components coming from many vendors. At present,
however, because of the technical nature of authoring, this technique has
mostly been limited to professionally developed and maintained Web sites and
pages created by commercial authoring systems.
Server-side Programming
- One of the main difficulties in choosing a strategy for dealing with math
in Web pages is that the criteria for what is best are typically controlled
more by the reader than the author. If a reader is browsing a page using an
old copy of Netscape on a Mac, a very simple browser-native HTML strategy is
going to work best, while a reader with the latest version of
Internet Explorer with a raft of specialized components and helper
applications installed will most likely want content which takes advantage of
the more sophisticated component-based HTML strategy.
The only real viable strategy to deal with this conundrum is programming
the Web server to determine what kind of browser the reader is using, so that
it can then send a page customized to work best in that environment. The advantage of this technique is obvious
— readers get the highest quality, most
engaging and dynamic version of a page that their browsers are capable of
supporting. The downside is that server-side programming is quite difficult,
and requires more access to the server software than is feasible to give a large
number of authors. In other words, server-side programming requires expert
knowledge and access; hence, it is generally limited to professionally
developed and maintained sites.
Standards are Paving the Way to Better Solutions
While many in the math and science community have long been frustrated by the
lack of a clear and effective strategy for putting math on the Web, if one steps
back a bit, several important trends become visible that are cause for optimism.
A Clear Winner: HTML + Components
First of all, when thinking about the future of Math on the Web, the first
and the last of the strategies discussed in the previous section can be ignored.
Like a modest baseline level of unemployment in a healthy economy, there will
always be a place for putting non-HTML documents online in their native formats.
For one thing, the sheer mass of legacy documents in the world gives value to
the ability to share them directly in their native format. Also, in many
situations all that is wanted or that is appropriate is the electronic
transmission of paper documents. But apart from special narrow communities with
a strong vested interest in a particular format, such as TeX, it is clear that
the mainstream of electronic communication lies with the Web.
Similarly, the expedient of server-side programming to customize content for
different browsers is currently so important mostly as a short-term consequence
of the explosive growth of the Web. The issue of backward compatibility is
inherent in computer software, and a large part of what software vendors do for
their customers is try to shield them from the worst aspects of the problem. In
general, the requisite server-side programming to handle backward compatibility
with older browsers has already begun migrating into the infrastructure of the
Web, and will likely become increasingly transparent to casual authors. Indeed,
in many of the distance learning systems we will be looking at in more detail
later in this report, some degree of server-side adapting of content to browsers
is already built in. Increasingly, authors will be able to interact with
higher-level Web management software that takes care of the gritty details of
browser compatibility for them.
Consequently, the future of Math on the Web is really tied up with
browser-native HTML and component-based extensions to it. While proprietary
systems occasionally claim to solve the problem of Math on the Web by creating a
parallel, proprietary, Web-like architecture, the success and pervasiveness of
the Web is already so total, these efforts simply aren't credible in the long
term. While they may appear to be attractive "complete solutions" in the very
near term without any messy integration problems, in the long term they are apt
to be expensive mistakes.
The HTML Platform
The groundwork for powerful browser-native HTML capabilities, together with a
flexible, component-based extension mechanism, has been slowly but steadily
emerging over the last five years, in large part as a result of the standards
process taking place at the World Wide Web Consortium. While to mainstream users
the technical details are a confusing alphabet soup of new technologies
— HTML, XML, XSL, DOM, CSS, SVG, MathML and
so on — one by one these W3C Recommendations
and related standards have mapped out an architecture for a powerful, extensible
way of communicating via rich, dynamic Web documents.
That framework, which taken altogether we call the "HTML Platform," has made
great strides in the last year or two, and is finally getting to the point where
it is sufficient for math and science communication. In particular, there has
been substantial progress on component embedding technologies in the last year
or so. In response to the technical advances, a component architecture workshop
is currently being organized at W3C to set about creating the standards
necessary to insure robust, cross-platform implementation of these promising new
techniques. Most veteran standards activity watchers in
the math software community now agree that enough pieces of the HTML Platform
are really there and fit together well enough to start building what we have
always wanted to build.
MathML in Browsers is Important but not Everything
One part of the HTML Platform deserves special attention from the math and
science community. MathML 1.01 [6]
and
MathML 2.0 [7] are
the W3C Recommendations for encoding mathematics for the Web. When MathML was
first adopted in 1998, there was a backlash of frustration when MathML failed to
be the "silver bullet" that suddenly made math work right in browsers. However,
the real success of MathML has been more behind the scenes. The mere existence
of MathML has had a substantial influence on the ultimate shape of the HTML
platform. In working out how different markup languages, style mechanisms, and
component architectures should all fit together in the HTML platform, there were
many occasions where there was a temptation to choose a simpler, more
text-oriented design, instead of a more complicated and powerful design that
could accommodate mathematics as well. Because of MathML, those pitfalls have
largely been avoided.
At last count, there were 18 MathML implementations in various released
products and tools. While it remains frustrating that the last thing of all to
fall into place is sufficient browser support for the HTML Platform to do the
math, it is indubitably on the way. Internet Explorer 6 and Mozilla 1.0, when
they are released later this year, will both have far superior native and/or
component-based support for math than ever before. We look forward to seeing
what people will have managed to do with MathML technology by the time the next
Status Report comes out.
The last six months have seen quite a bit of MathML adoption activity. The
following sampling of news items highlights some of the more notable events.
- MathML 2.0 Recommendation Adopted.
MathML 2.0 [7] was adopted as a
W3C Recommendation on February 21, 2001. The main improvements over MathML 1.0
are a much improved listing of mathematical characters newly standardized by
the Unicode consortium, a DOM interface, extensions to MathML content markup, and
provisions for equation numbering in presentation markup.
- Rechartering of
W3C Math Working
Group [8].
The W3C announced it would renew the Math Activity on June 9, 2001. The new
Working Group will be working on maintaining the MathML2.0 Recommendation,
continuing liaison with other W3C working groups and other standards bodies,
and more generally continue the task of facilitating the use of mathematics on
the Web.
- Maple 7 Adds MathML Support, Incorporates WebEQ. On June 7, 2001,
Waterloo Maple announced [9]
that it will introduce enhanced Web math functionality using WebEQ technology
from Design Science. The new functionality will be an integral part of Maple
7, slated to begin shipping on June 29. Maple 7 will feature a comprehensive
MathML 2.0 implementation, providing import and export of MathML-encoded math
expressions, as well as the ability to save Maple worksheets in HTML+MathML
format for display in Web browsers.
- Blackboard Licenses WebEQ. Blackboard, Inc. concluded licensing
arrangements with Design Science in March, 2001 for incorporating WebEQ math
editing and display technology into their e-Learning products. As of this
writing, details as to
when math support will be available within Blackboard have not yet been
announced.
- WestWords [10] Announces
Plans for MathML Support in MathMonarch. MathMonarch, the
content transportability tool for math publishing, is keeping pace with Design
Science's development of MathML features. MathMonarch 4.0 converts Microsoft
Word documents containing MathType equations into its intermediary language, WWdoc, which is
then imported directly into Quark with the PowerMath or Mathable extension
loaded. The resulting Quark files can then be exported back out to WWdoc,
which can then be imported back into Microsoft Word with MathType. MathMonarch
is extending its capabilities to the MathML environment by combining the
ability to transport design information, as well as content. Both
are crucial to display math correctly on the Web.
- MathML Support in Mozilla Matures. Work on adding native MathML
support to the Mozilla Open Source browser has progressed substantially over
the last six months. While MathML support is not enabled in routine nightly
builds of Mozilla, precompiled binary versions of Mozilla with MathML and SVG
support turned on are available from several sources [11].
The current version is 0.9.1. The commercial Netscape 6 browser is based on
Mozilla version 0.6, without MathML support.
- Design Science Releases MT Extra Font under Open Source License.
Fonts are a key issue for enabling MathML generally, both in Mozilla as well
as potential future versions of the commercial Netscape browser. As an open
source project, Mozilla can only bundle open source fonts with it for
distribution. However, without fonts, MathML support will not work, and
consequently, fonts are a major obstacle to turning on MathML support by
default. To address this problem, Design Science announced in February that it
had released its MT Extra font under an Open Source license with the specific
goal of helping Mozilla get to the point of turning on MathML support by
default.
- IBM Techexplorer 3.1 Released. IBM released version 3.1 of its
Techexplorer scientific browser in June, 2001. The new version offers full
MathML 2.0 support, as well as support for Internet Explorer 5.5 behaviors.
- MathML to Braille Converter Announced. Taking advantage of MathML's
ability to encode mathematical semantics in a structured way, a MathML-to-Braille
converter, called
BraMaNet [12], was released early this year.
It has a user-friendly Visual Basic interface and can be used together with
MathType to translate Microsoft Word documents into Braille for printing. Other related projects are investigating ways of combining MathML, and a speech
rendering technology called VoiceXML, to further enhance the accessibility of
mathematics.
- Beta: MathType 5.0 with MathPage Technology. This new version
of Design Science's MathType equation editor adds an important new feature:
the ability to save Microsoft Word documents containing equations into Web
pages that really work. The equations and math symbols can be embedded in the
Web page as either GIF images (for maximum browser compatibility) or as MathML
2.0. MathType 5.0 is in beta test. Final release is expected in August, 2001.
- Beta: WebEQ 3.0. This new version of WebEQ, Design Science's
Java-based suite of tools for building dynamic math Web pages, features
improved and more intuitive editing, content MathML generation, customizable
user interfaces, powerful new scripting capabilities for programmers using
the DOM, sophisticated math line-breaking of long expressions, and MathML 2.0
support.
- Coming: MathPlayer. Design Science is working on a software
component that will enable Microsoft's Internet Explorer Web browser to
display MathML. It is based on Microsoft's Behavior technology and will work
with Internet Explorer 5.5 or later. It is planned that a version of
MathPlayer be available free-of-charge to anyone requiring MathML display.
Release is expected in Fall, 2001.
What is Distance Learning?
According to the USDLA (United States Distance
Learning Association [13]), distance learning is "the acquisition of knowledge
and skills through mediated information and instruction. Distance learning
encompasses all technologies and supports the pursuit of life long learning for
all. Distance learning is used in all areas of education including Pre-K through
grade 12, higher education, home school education, continuing education,
corporate training, military and government training, and telemedicine." The Web
is a perfect medium for distance learning. It enables the delivery of
educational materials within seconds to anyone with access to a computer. And
since science, engineering, and technology play such a crucial role in our
modern economy, the ability to work with mathematical notation is an important
component of distance learning over the Web.
Besides education in colleges and universities, the U.S. military is also very
interested in distance learning. In 1997, the Advanced Distributed Learning
(ADL) [14] initiative was created to "ensure access to
high-quality education and training materials that can be tailored to individual
learner needs and made available whenever and wherever they are required." The
ADL organization is responsible for producing SCORM (Sharable Content Object
Reference Model), a set of standards that define a Web-based learning content
model.
The distance learning market is expected to grow to $5.2 billion by 2004
according to Frost & Sullivan [15] (as quoted by
the Federal Learning Technology Resource
Center [16]). There are many companies already in this growing field and more are
entering it all the time. Colleges and universities are also looking seriously
at becoming vendors of distance learning services as a way to extend their reach
and as an important source of revenue (see
"EduCAUSE president discusses future of distance learning in education"
[17]).
Where Does Math Fit into Distance Learning?
Although most distance learning content does not contain mathematical
notation, lack of it limits the utility of distance learning whenever there is a
strong technical component to the material. Many college departments have at
least some material that makes use of math.
Mathematical notation may appear in online material in much the same
way as it does in traditional educational materials. However, there are a few
applications that are of special interest to the distance learning marketplace:
- Courseware — This includes materials
containing static math (technical papers and tutorials) as well as dynamic
math (interactive pages demonstrating a mathematical or scientific concept).
- Assessment (testing) — Math notation is used
in the presentation of test questions. In addition, students can use
interactive entry of math (using tools like Design Science's
Equation Input Control [18], for example) to answer questions. The use of
MathML to represent answers enables automated evaluation of correctness. Also,
it enables the variable names and numbers to be algorithmically
customized on a per-student basis to prevent cheating.
- Course-oriented Bulletin Boards — The
Internet enables students and teachers to communicate as never before, without
the restrictions imposed by the traditional professors' office hours. In this
application, students and teachers post messages to a Web-based bulletin
board. MathML allows mathematical notation to be part of such
communication.
Progress in Distance Learning
There are many companies and organizations involved in providing distance
learning products and services. Although this marketplace continues to grow by
leaps and bounds, it is just now maturing to the point where the ability to
handle mathematical notation is becoming an important requirement. Below, we
list some highlights in this growing trend. In most cases, we have quoted
representatives of each organization directly. We apologize in advance for this
list being somewhat Design Science-centric but this is the work with which we
are most familiar.
In March of this year, Design Science concluded a license agreement with
Blackboard Inc. that allows it to use WebEQ technology in its future products.
We expect the company to release more details as they become available.
Blackboard Inc.
http://www.blackboard.com
"We develop curriculum, including software and print materials, for
high-school level mathematics. Currently, our main products are Algebra I,
Geometry and Algebra II. We sell directly to high schools, who use our materials
as the main class curriculum. Students typically spend 40% of their class time
in a computer lab using our software and 60% of the time in the classroom, doing
projects and activities based on our print materials.
"The software is based on research done at Carnegie Mellon into how students
learn mathematics. It traces students' actions in a problem-solving activity,
providing hints when necessary. In addition, the software tracks students'
growth in knowledge throughout the school year. It forms a model of each
student's strengths and weaknesses and then selects problems for each student to
solve based on that student's skill profile. This 'knowledge tracing' enables
students to work at their own pace. They receive more problems if they are
having difficulty and need to master each section of the curriculum before
moving on.
"Our products were initially developed in Lisp and are in the process of being
ported to Java (the interfaces are all in Java; Algebra 1 has a Java back-end as
well; the others use a Lisp back-end). We use WebEQ to display formatted
mathematical expressions in all of our interfaces (including problem text,
symbolic algebra tools, spreadsheets, etc.).
"Our products are not currently accessible over the Web; students use them in a
lab at the school. We are currently piloting a new course, Quantitative Literacy
through Algebra, which is a college-level course using the same technology. For
this course, we've configured the software to save student records over the
internet."
Steve Ritter, Ph.D.
Senior Cognitive Scientist
Carnegie Learning, Inc.
http://www.carnegielearning.com
IQMind.com
IQMind.com is a Singapore-based education service provider that offers
software and hardware services to schools in Asia. These services include
software applications that are aimed at improving productivity of teachers and
administrators, and enhancing communication, collaboration and interaction among
students, teachers and parents, hardware infrastructure, and enrichment/training
programs.
"Distance learning for IQMind.com entails students doing their assignments
from home (e.g. weekends, holidays, etc.). Most of the time, students will engage
the teachers directly in school. Design Science's WebEQ product has been
integrated with IQmind's e-learning platform, specifically in the area of online
quiz and assessment, so that teachers can present their questions in a seamless
manner. No longer do they have to cut-and-paste mathematical symbols and
equations from Word documents or other specimens in the process of creating
questions for students to tackle in an online realm.
"The real benefit is the dilution of manual effort on the part of teachers.
WebEQ is very easy to use and requires no rocket-science methodology to unravel.
The time taken to piece all these symbols together in the past is now channeled
towards the creation of more value-added questions and solutions."
Jansen Lim
IQMind.com
(originally at http://www.iqmind.com)
Prometheus uses Design Science's WebEQ technology to allow courseware
developers to incorporate math in online courses and to allow students to
incorporate math in discussion areas.
Prometheus
George Washington University
http://www.prometheus.com
Question Mark
"Question Mark assessment software enables educators and trainers to write,
administer and report on assessments via PCs, local area networks, the Internet
and intranets.
"Many users of Question Mark wish to include mathematical and scientific
equations within questions, and it's now possible for authors to enter or paste
equations as MathML into questions as they write them. Question Mark then uses
Design Science's WebEQ MathViewer applet to display these within the student or
participant's browser.
"The advantages to authors of using MathML is that it is easy to author, and
much easier to manage and edit than a separate GIF or JPEG graphic file, which
is the most obvious alternative mechanism. Good questions take a long time to
write and check, and people want them to have lasting value. A strong advantage
of using MathML rather than a proprietary solution is that questions should be
usable into the long term future, even if technology changes.
"The advantage to Question Mark of using WebEQ is that it works on all major
browsers and seamlessly displays maths equations within questions. It's easy to
deploy within the package and users can simply create MathML using WebEQ itself
or another tool, and put them within questions, and they then run and display
correctly without the user needing to set up or deploy anything.
"For a demonstration of Question Mark displaying MathML with WebEQ, see
http://www.questionmark.com/links/tryit.htm."
John Kleeman MA MBCS C.Eng
Managing Director
Question Mark Computing Ltd.
http://www.questionmark.com
Wiley has two products, eGrade and Math Machina for Calculus, both of which
use Design Science's WebEQ technology. eGrade is available now, Math Machina is
a future product.
"Wiley eGrade is a software product that allows instructors to assign
homework and assessments to students in technical disciplines. It gives
instructors the ability to create and modify questions and exams that are
mathematically rich. One can create questions from multiple choice to
fill-in-the-blank to matching and essay questions. Algorithmic problems are
available as well as multi-stepped problems.
"The program is ideal for distance learning programs in that it addresses a
variety of needs, from self-paced practice for students to fully proctored
online testing. Students are given automatic feedback and grades are recorded in
the instructor's grade book. It is also well suited for homework which is graded
automatically. This product is offered in conjunction with several Wiley
textbooks in math, physics, chemistry and engineering.
"Math Machina for Calculus is a Web-based, intelligent software tutorial for
calculus. Math Machina solves and documents calculus problems in real-time.
Students supply solutions in step-by-step detail for a wide variety of calculus
problems. The student's answers are then analyzed and graded. Math Machina is
able to also automatically solve problems and reveal the detailed step-by-step
answers. This intelligent software supports extensive graphical activities to
aid in the understanding and use of calculus concepts.
"Math Machina employs algorithms that use the rules of algebra and calculus to
solve calculus problems. The algorithms produce customized content to document
'how' and 'why' problem steps progress as they do, inserting specific pieces
from the student's own problem into examples steps. The software also links to
pages of the student's calculus book where the relevant content is covered."
Ruth Baruth
John Wiley & Sons, Inc.
http://he-cda.wiley.com/WileyCDA/Section/id-107234.html
The Future of Distance Learning Technology
The future for distance learning is very bright. As success in education is
crucial for the health of our society and as society becomes more global and
less local, demand for technology that connects students with educators and
educational material will only increase. Within the context of this report, we
see two trends:
1. There will be a continuing move away from static math to dynamic math in
distance learning materials. It is well known that students learn more quickly,
and with less pain, when concepts can be demonstrated interactively. MathML
enables interactivity in mathematics. Currently, most dynamic math materials
must be created "by hand", requiring the author to have knowledge in several
programming languages and Web technologies. We expect this situation to change
with the advent of interactive, point-and-click authoring tools for dynamic math
content. Design Science is very active in this area.
2. To date, distance learning has largely been directed at providing
educational materials to those who cannot attend face-to-face classes. In the
future, we see the technologies employed in distance learning used for all kinds
of learners, not just distance learners. In no way should this be taken to
indicate that the value of face-to-face student-teacher interaction is
diminishing. Instead, interactive online materials free the teacher to spend
more time with students. The power of interactive content enhances, rather than
replaces, face-to-face teaching.
[1] Math for Kids - A Medieval Problem-Solving Adventure, http://tqjunior.thinkquest.org
(originally at
http://tqjunior.thinkquest.org/4471/Default.htm).
[2] Scalable Vector Graphics,
http://www.w3.org/TR/SVG/.
[3] Integre Technical Publishing, interactive examples (no
longer available -- originally
at http://www.integretechpub.com/examples/interactive/index.html#svg).
[4] Searching Mathematics with SearchFor, Gaëtano, Marc (marc.gaetano@sophia.inria.fr),
Dalmas, Stéphane (stephane.dalmas@sophia.inria.fr),
originally at http://www.mathmlconference.org/Talks/dalmas/.
[5] MathML in Mozilla Project,
http://www.mozilla.org/projects/mathml.
[6] MathML 1.01,
http://www.w3.org/TR/REC-MathML/.
[7] MathML 2.0,
http://www.w3.org/TR/MathML2.
[8] W3C Math Working Group Charter,
http://www.w3.org/Math/Documents/Charter2001.html.
[9] Maple Press Release,
http://www.maplesoft.com/whats_new/news_releases/web_eq.html.
[10] WestWords, Inc., makers of MathMonarch,
http://www.westwordsinc.com.
[11] Mozilla download site,
http://www.mozilla.org
[12] BraMaNet: An XSL Style Sheet that translates MathML (Presentation tags
only) into French Mathematical Braille,
http://handy.univ-lyon1.fr/projets/bramanet/.
[13] United States Distance
Learning Association (USDLA),
http://www.usdla.org.
[14]
Advanced Distributed Learning (ADL),
http://www.adlnet.org/.
[15] Frost & Sullivan,
http://www.frost.com.
[16] Federal Learning Technology Resource
Center, http://www.fed-training.org.
[17]
"EduCAUSE president discusses future of distance learning in education",
(originally at http://www.news.cornell.edu/Chronicles/5.4.00/EduCAUSE-DL.html).
[18]
Equation Input Control,
(originally at
http://www.dessci.com/en/products/webeq/default.htm#inputcontrol, since replaced
by MathFlow Components at
http://www.dessci.com/en/products/mathflow)
Mailing List
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