(3) More Thorough Discussion of the Technology Application:

What obstacles are there?
How is technology being used to overcome these obstacles?
Is breakthrough technology being used?

As discussed in Essay #2, Math Markup Language (MathML) is the way of the future for mathematics on the World Wide Web. MathML is a way to describe mathematics for machine-to-machine communication, and is a product of the W3C Math working group. It can encode both presentation (how something looks) and content (meaning), and it is searchable. In some implementations, it can “read itself” to you, hence offering support for the visually impaired. It can be used, together with Javascript, to create randomly-generated math practice. Without MathML, math education on the web cannot evolve. With MathML, there is the capability to serve the online math needs of the nation and the world.

Up to now, spotty browser support has been the primary factor holding MathML back. Another obstacle to widespread MathML usage is that it is an extremely low-level language: to say something short (like [beautiful math coming... please be patient] $\,\displaystyle\frac{x^2}{3}\,$) requires a LOT:

This makes it difficult for web authors—it's verbose to type, and you can't easily look over the source code and discern the math that is there. Furthermore, MathML hasn't gotten sufficient exposure—math doesn't seem to make its way into the news very often.

After almost a decade of struggling with these first two difficulties—inconsistent browser support and unwieldly source code—a solution has emerged: MathJax. The name “MathJax” is a play on the “Ajax” technology that it uses (“Asynchronous Javascript And XML”). MathJax version 1.0 was released on August 4, 2010—you can't get much more “breakthrough” than this. Before that time, it had functional beta implementations available to the public, which allowed authors like me to start seeing what it can do.

MathJax solves the “unwieldly source code” problem by allowing authors to write in TeX syntax, which is concise, intuitive, and familiar. MathJax solves the browser/platform problems by offering various input/output “modules”: an author can (say) specify that the input source code is in TeX syntax, and the output should be either MathML (if the user's browser supports it) or HTML/CSS (a Javascript rendering of the math). While I'm updating my web exercises to MathJax, I'm also updating them to XHTML and CSS.

So, take a break from this essay and see what MathJax can do! Go in Firefox, Chrome, Opera, Safari, Internet Explorer. Go on a PC or on a MAC. You don't have to download any fonts or plug-ins. The math just works, and it is beautiful. Here are my updated files to date: pick a few that look interesting to you. Or, choose a few of my favorites:

In all these exercises, be sure to go to the bottom and click... click... click... to see how the online practice works. And, be sure to create some randomly-generated worksheets—these can be used for quizzes or practice away from the computer. If you want, take a look at the source code. If you've ever used TeX, you'll recognize everything.

Let me talk a bit about the advantages of my site over other math sites:

To conclude, it is potentially a very good time for math-on-the-web (done right) to get some publicity. There is currently high interest in national math standards, as opposed to the mosaic of state standards. Any set of standards can be mapped to my exercises, just as I have done for MCAS (Massachusetts Comprehensive Assessment System). I can fill in any gaps that present themselves. The result would be that students everywhere can have the unlimited, highly-credentialed practice they need to meet the challenge that national standards will provide.