(4) Evidence of Contribution:

How do you know that your application of technology is having a beneficial impact?
Please provide data or evidence to support your claims.

My web server ( supplies AWStats for my domain, and I summarize parts of this data online.
Every month, AWStats reports the number of unique visitors.
In 2005, I averaged 342 unique visitors/month.
In 2009 (my last full year), I averaged 20,517/month.
Here are the data points for the five full years they have been available:

(year, average number of monthly unique visitors)

Let [beautiful math coming... please be patient] $\,t\,$ denote time. To make numbers manageable, let $\,2005\,$ correspond to [beautiful math coming... please be patient] $\,t=1\,$ (hence $\,2009\,$ is $\,t=5\,$), and do an exponential regression on these five data points. I obtained the function [beautiful math coming... please be patient] $\,y = (118.5)(2.858)^t\,$ with a very nice fit (see below); so this is approximately exponential growth with a base close to $\,3\,$. Exponential growth is hard to maintain for very long, but if this trend continues, then in $\,2010\,$ I would be averaging $\,64{,}579\,$ visitors per month, which is about $\,2153\,$ visitors per day.

(Interesting observation. My daily hits for September 13–15, 2010 have been: 1505, 1530, 1484. This is with only about one-quarter of my files updated to MathJax.)

One indicator of “worthiness” is how many users hit the “favorite icon” to bookmark a page.
In 2009, 80.1% of my users hit the favorite icon.
Here are the figures for the first few months of 2010:
January: 96.2% hit favorite icon
February: 98.8% hit favorite icon
March: 107.6% hit favorite icon (that is, on average, users hit the favorite icon more than once; say on several different pages)

Another indicator of worthiness is testimonials and guestbook entries from my users. I offer testimonials here (I obtained permission before posting any names and comments). Here are some snapshots from this page:

email from Carolyn Melo, Subject Area Coordinator, Secondary Math, Pennsylvania Leadership Charter School, USA

... we are a cyber charter-school, so having something like this is a god-send...

... I absolutely love the book—it is the one I would love to have written if I were going to write a math book. I am always sending people to the site to look it over.
email from Jose E. Revelo, a father in Southern California, USA:
I love your site... And wish I would have had a teacher like you!!

... I found your site through and love it. I have reviewed your first 13 sections of Algebra I and really see the light. So much so, that I am helping my 8th grader see that it is easy. You just have to learn the language and know the rules!! Your presentation is so crystal clear; that everything I should have known way back when is amazingly easy for me to comprehend today. I love doing the exercises, and then helping my son. Because of you, he will never struggle with any of these concepts, or have the same inadequate feelings I had. When he comes to me, I review your site and then have a GREAT time helping him.

... I am sure you have been told that you have a great gift from God! What a blessing!!
selections from email correspondence with Kara C., a home-schooling mother in Atlanta, Georgia, USA:
... Thanks to a Google search, I found One Mathematical Cat. Suddenly, math was fun again! The children actually looked forward to the lessons. They were encouraged and I could see the puzzled, dazed look in their eyes fading away.

... I've been piecing together curricula for myself, and others, for a number of years and I've found very few people that offer educational material that is so complete and well formatted...
a series of emails from Naomi Laeuchli, a home-schooled American living in Vienna, Austria:
... I have tried several online Algebra courses for my math and have always been confused after the first few sections, yours is the best I have ever found, remaining clear, even after it gets into some of the harder material.

... Also I always enjoy the links you have to other sites with interesting math facts and such.

... Your course explains everything in-depth and always has everything written out so clearly.

... The course is indeed very easy to use without a teacher, I have never had to get help from either my parents or my brother (who actually knows something about math), I've always been able to figure it out, based solely on the lessons.

Just a few months ago, I put a Guestbook on my site. People seem more willing to leave a guestbook entry than to email me directly. Here is a sampling of recent comments:

Dick Illyes (East Central Illinois):
You never know what amazing knowledge the next day, or hour, will bring. This certainly qualifies.

Thanks for all the ingenuity.
Alexandra (U.S.): I learn math fairly well, just not always in ways other people learn math. When my textbook gave me three sentences on reciprocals, that did not do it, and I quickly became confused. I did a Google search and found a couple of sites, but they helped very minimally. Your explanation, however, helped much more. It was simple, explained both the fractions and whole numbers, and not only do I think I've got the hang of it, I know that I do because of the interactive problems. There are other interactive sites, but so many of them cost money or just don't explain things well. This site is fantastic!

Thank you so much for the time and effort you put into this. And, doubtless, money as well... I know how much hosting, bandwidth and the like costs... yowch! So, thank you again. Your site is a blessing to me!
Ken J. Winkleman (Boise, Idaho):
What a fantastic website! Thank you so much for putting this together. I am a gentleman in his fifties who needs to brush up on and improve his math skills. This is the perfect way to do it.
George (Castro, Egypt): THIS IS GREAT!!!! I'm 17 and in algebra 1 and this is helping me get heads above the competition. I feel like a baller now. You rock!!!! OneMathematicalCat drives me wild.

Finally, my search engine rankings are high for many common phrases involving math. From my sitemeter, I can see where my users come from: if they come from a search engine, I can see what they typed in, and where my site ended up in the search results. Here are some results in the last five minutes of when I typed this [September 17, 2010]:

Google, "function notation", 1 of 8,420,000
Google, "subtraction of signed numbers", 2 of 99,600 (the MathPage was #1)
Google, "weekly compounding", 6 of 507,000
Bing, "function notation", 2 of 5,240,000 (PurpleMath was #1)

For historical interest, I've kept track of some sample search engine results throughout the years (although I haven't added anything new in a long time).

I hope this illustrates that my site is truly reaching and helping a wide variety of people: students, teachers, older learners, home-schoolers, and more.