(2) Description of Technology Application:

Fully describe the technology application.
What technology is being used? How is it being used?
Who is responsible? Who is benefiting?
What processes or systems are in place to deliver this technology application?

One Mathematical Cat, Please! offers [beautiful math coming... please be patient] $\,237\,$ exercises—a complete Algebra I course, and essential concepts in Geometry and Algebra II. Each web exercise gives unlimited, randomly-generated, online and offline practice. The “in-a-nutshell” material on each web page forms the basis for the online exercise; at the bottom, students can click-click-click until they're sure that the concept is mastered. (They find out immediately if they're right or wrong.) Want more details than what is on the web page? For many of the exercises, you can click “read the text” for a thorough discussion, that looks a lot more like a “traditional” text book. Want to see how fast you're doing the problems? For [beautiful math coming... please be patient] $\,92\,$ of the exercises, you can time yourself—people with a competitive spirit can use the Algebra Pinball chart to see how they match up with the fastest users. (Just TRY to beat Rurika Oka's time of 2.1 seconds/problem for multi-step exponent law problems.) Need to leave the computer? With a click of a button, create a worksheet with solutions so you can keep working offline (you get a different one every time).

I've created tutorials and guided worksheets for GeoGebra, which is award-winning free software for exploring algebra, geometry, and calculus. When I taught an eight-week SAT prep course, I put it online. Want an entire, year-long course giving an introduction to HTML and Web Design? I developed this over the several years that I taught it at Miss Hall's School. Plus, I've been compiling the best math web sites for over a decade, and offer these to students in my “fun” column, for when they need a bit of a break.

The web site is totally free of cost, and it is freely-available to the world via the internet. My site is used by schools, students, teachers, home-schoolers, and older learners. It is used by industry and individuals—it's amazing how many hits come from the phrase percent increase and decrease. Many users are from course management system login pages (e.g., Moodle and Blackboard). In 2005, my site averaged only 342 unique visitors per month; by 2009, it averaged 20,517 unique visitors/month. In 2009, 80.1% of my visitors hit the “favorite” icon. More recently, 98.8% of users hit the favorite icon in February 2010.

I have high search engine rankings for many common phrases. For example, I just [September 14, 2010] went to Google and typed in ”function notation”—my site came up #1 out of 8,450,000 (results will vary).

Many of my web exercises are marked in the Table of Contents with a ♥, indicating that they require MathML (Math Markup Language) to correctly display the mathematics. “Correct display” means in a way comparable with textbook notation or the mathematical typesetting system TeX. (“TeX” is pronounced as “tech”; creator Donald E. Knuth offered it to the world in the mid-1980s, and it remains the worldwide standard for printed mathematics.) My use of MathML is what made my site rare among math educational web sites, for the decade from about 2000 to 2010. (With the advent of MathJax, people are finally starting to use MathML, perhaps without even knowing it!)

Here's a bit of history about MathML, and my association with it. In about 1998, the World Wide Web Consortium (W3C) released MathML, a standardized Mathematics Markup Language so that math could be put on web pages. Of course (as often happens) it took a while for the browsers to catch on, and there weren't really any usable browser implementations until about 2002. I personally didn't find out about MathML until the summer of 2004. I had spent years typing things like “Web TeX” and “TeX for the web” into search engines, thinking that someone must just be extending TeX to the web.

It ends up that there was a good reason that TeX wasn't “just being extended”. TeX is a presentation-only language; i.e., it can only describe how something looks—it can't encode meaning. For example, TeX can't distinguish between $\,d(h)\,$ (variable $\,d\,$ times variable $\,h\,$) and $\,d(h)\,$ (function $\,d\,$ acting on an input $\,h\,$). MathML, however, has the ability to encode this difference in meaning, making it far superior for searchable entities like the WWW.

MathML is natively supported in Firefox and Opera, but only in XHTML documents. For HTML files, MathML is only accessible on a PC with Internet Explorer and the (free and easy) MathPlayer plug-in; this is the environment that my users currently need for full functionality of my web site (until I get it all updated). This lack of across-the-board browser support is a real problem. Users deserve flawless, multi-platform, all-major-browser support. Right now, they see garbage (and a message saying what they can do about it) if they don't have the correct viewing environment. Even users who happen to come with a PC and Internet Explorer will rarely take the time to pause and download the (free and easy) MathPlayer plug-in. This is just the “glance-and-move-on” nature of the web. Think about your own browsing habits—if the first thing you click on requires a plug-in, do you immediately download it, or do you go on to the next search page entry? I know my answer.

But there is a solution! MathJax is an open source, Ajax-based math display solution designed with a goal of consolidating advances in many web technologies in a single definitive math-on-the-web platform supporting all major browsers. With MathJax (MathJax 1.0 was released in early August 2010), I am now able to get proper all-browser mathematical display in a way that makes the best current use of MathML, and which allows for easy transition to MathML as browsers evolve. With MathJax, I am able to make my 200+ existing web exercises available to EVERYONE, without plug-ins. I talk more about MathJax in Essay #3.

Who is responsible for this? Just me. Mathematics has been good to me, and this is my gift back to the mathematical community. I don't make any money from this site. I've developed it entirely on my own, over the past decade. At various times, I've paused and estimated the number of hours I've invested: conservatively, over $\,5000\,$ hours. This is like two and a half years of full-time work, squeezed in while working full-time.

While teaching, every spare daily hour, weekends, and vacations were spent on this work. An “easy” web exercise (nearly identical to something I've done before) takes about $\,10\,$ hours to code; new things can cause this to double. At the end of the $\,2009\,$ teaching year, I decided that if there's any chance of finishing the entire high school curriculum before I die, I need to work on it nearly full-time. My prior year in public school paid me well; I was able to save enough for a few months of “life bills” to enable my transition. So, I took a bold step, left teaching behind, and decided I was going to try and make a living with math-on-the-web.