I've been sending out a lot of emails to ESL job advertisements placed in the classifieds section of The Beijinger.com ... many of these employers assume that I'm in Beijing, and want me to come in for an interview there. Oftentimes, upon revealing the fact that I am not yet there (still in America), they seem to lose interest.
Yes, the ones who want to recruit from overseas generally do not advertise in the Beijinger. They advertise on overseas recruiting sites. There's a list in this article:
http://wikitravel.org/en/Teaching_English Web search will turn up many more.
For China-specific sources, check the job listings section here and subscribe to mailing lists at TEFLChina.org
Generally, I'd say a first-time teacher will be better off being recruited from abroad. You might get met at the airport, taken for dinner, and delivered to a lovely apartment, or you might get poor directions on how to reach your place by cab, and find it crappy when you get there. However, either is better than several weeks in a hotel you have to pay for. More generally, coping with China is a lot easier with some help from a Chinese-speaker.
Also, jobs that recruit abroad are more likely to provide a proper visa (absolutely essential!) and perks like housing and annual airfare home (nice!). These is not entirely certain in jobs recruiting abroad or entirely absent in those recruiting locally, but the trend runs that way.
Can you broaden your search? With a Math & Economics degree, are there jobs you might get in foreign trade or business analysis or some such? Are there cities other than Beijing you might consider? There's a whole thread here somewhere on people's preferences.