(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:
<math> <mrow> <mfrac> <mrow> <msup> <mrow><mi>x</mi></mrow> <mrow><mn>2</mn></mrow> </msup> </mrow> <mrow> <mn>3</mn> </mrow> </mfrac> </mrow> </math>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:
- Watch the math “melt” onto the page in Multi-step Exponent Law Practice.
- See dynamic graphics (JSXGraph) at work in
Area Formulas: Triangle, Parallelogram, Trapezoid.
At the top of the page, click the buttons to explore base/height pairs in a triangle.
Davide Cervone, the lead developer of MathJax, led me to JSXGraph as a solution to my dynamic graphics needs; it is a Javascript implementation of SVG (Scalable Vector Graphics), and it is amazing. - Explore the difference between precision and accuracy in Significant Figures and Related Concepts.
Let me talk a bit about the advantages of my site over other math sites:
- First and foremost, I offer dynamic, randomly-generated math, that looks the way it is supposed to look. There are lots of sites with static math content (mostly displayed with images). There are lots of sites that offer some great Java-based math games. There are lots of sites that use Javascript to do lower-level math that doesn't require any special math notation. There are lots of sites that offer a single printable worksheet or two. On my site, students will never run out of practice, and teachers will never run out of assessment materials.
- I offer students high-quality mathematics instruction—I have a Doctor of Arts degree in mathematics (a doctoral degree that emphasizes effective teaching). I have over 25 years of teaching, both at the college and high-school level. I've won numerous teaching awards. My vita is online, and you can read about my credentials there.
- One big advantage of what I offer to students is in its level of completeness. Even though I haven't yet finished what I want to do, I already have a complete Algebra I course, and enough Geometry and Algebra II for a “quick course” in each.
- The presentation is all in the same voice—mine. Because I'm the only author, there is a consistency in tone and language that is difficult to achieve in anything that is “pieced together” from a variety of sources.
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.