Waverly's mother is an interesting figure. She is proud, ambitious, and family orient.
First, she is proud. She is proud of her daughter. When she finds out that Waverly has a gift to play chess, she is filled with pride. When Waverly gains national recognition, she loves walking around the marketplace telling others that this is Waverly, the chess champion. As immigrants to a new country, what Waverly has achieved, is an accomplishment.
Second, Waverly's mother is ambitious. From the beginning of the story, Waverly's mother tries to teach her daughter the art of invisible strength, the ability to win arguments and respect from others. This shows that Waverly's mother is ambitious to succeed. She is a fighter who wants to get ahead.
Finally, Waverly's mother is family oriented. As a traditional Chinese mother, she upholds the family more than the individual. In other words, the individualistic world of America is not something that she is familiar with. So, when Waverly seeks to break free, she is offended.