It againsts Chinese law if you work on an F visa. But it is not a seldom case among foreigners in China, so, don't worry too much. But if you want to stay or work in China for longer time, you'd better apply for a work visa.

You may let the training school to support the documents for you to get a working visa, it is a better choice for you since F visa extension is not available now in Beijing.
For more information, you can e-mail or chat with me.

Hi Rebecca,
So many foreigners are in beijing, they hold the L visa , F visa, X visa or working visa. Most foreigners are holding F visa, but they also work here. sometimes, some one who is unlucky will be published.
You know, now the F visa can't be extended. If you have the company to sponsor you,you can do a working visa, it is affordable.you should prepare your personal documents and your company should prepare some documents such as business license.
For more information, we can discuss toghther.
I hope these information are helpful to you.
Best regards
Monica