I teach L197 - Beginners' Chinese.
To be precise, it is Mandarin Chinese, 汉语 Hànyǔ(literally, Han language).
This is an important point. When people say they speak Chinese, they could mean they speak Cantonese, Hokkien, Hakka......
This page,
Varieties of Chinese, gives you an overview of the Chinese languages (Sinitic Languages).
Apart from Mandarin, there are Jin, Wu, Hui, Gan, Xiang, Min, Hakka, Yue, and Ping, and others.
Please don't call these 'dialects' of Chinese.
Read
Language Log » Mutual Intelligibility of Sinitic Languages (by Professor Mair) if you are curious about how various languages interact in China.
When I was growing up, I spoke Min at home with my family, and only used Mandarin socially. I still speak Min (Hokkien) with my family as my mother can't speak Mandarin.
There was a time while growing up I thought my 'mother tongue' was not an educated form of Chinese - how wrong (and misinformed) was I.
I'm pleased to be still able to communicate in Hokkien with my family, though occasionally I need to throw in quite a bit of Mandarin vocab into it.
What languages do you speak? What's your mother tongue?