Anderson, 24, had been missing since shortly after the March 11 earthquake. Her family, of Midlothian, Va., was notified Monday that her body was discovered about 240 miles north of Tokyo, in the city of Ishinomaki, where she taught English for the past 2 1/2 years. She is believed to be the first American casualty from the disasters in Japan.
"That's what she would have wanted," Julz said on CBS' "The Early Show." "She would have wanted Japan to rebuild and become a beautiful country again. We're going to do everything in her name to get Japan back to where it should be."
After the quake, Anderson made sure students had been picked up from elementary school by their parents. She was last seen biking away from the school, shortly before the tsunami hit, according to reports.
Jean Anderson said the way her daughter died was emblematic of the life she lived.
"Taylor was a warm, kind human being and thought a lot about others," she said on CBS. "And her last acts on Earth were helping somebody else, so that pretty much sums up who she was."
Students had called her daughter their favorite teacher, Anderson said.
"They had warm, kind things to say about her," Jean Anderson said. Taylor "connected to them."
"I was very proud of her," her mother said.
In addition to teaching grade schoolers, Taylor Anderson also helped older Japanese adults learn conversational English, her mother said. She met with them once a month to work on American phrases.
She connected with not just her students, younger and older, but also neighbors and her fellow teachers in the Japan Exchange and Teaching Programme, her mother and sister said.
"She touched so many lives over there," Julz Anderson said on "The Early Show. "She just could create a bond of friendship that not many people could do. She was so sincere. She was always willing to help."
Anderson was busy, planning trips and weekend activities, her sister said. "Just going beyond teaching, she had an enthusiasm for life that truly affected others," Julz said. "She was a person that people wanted to travel with because she made it such a good time."
"She took advantage of everything that was in front of her," she said.
Anderson began learning Japanese in sixth grade and minored in Asian Studies, according to reports. She graduated in 2008 from Randolph-Macon College in Ashland, Va.
"Taylor was a cheerful and enthusiastic student who, from her very earliest days at Randolph-Macon, had a dream to teach English in Japan," Todd Munson, an associate professor of Asian studies at the college, told the Richmond Times-Dispatch. "I am comforted by the knowledge that she was able to achieve that dream, even if the remainder of her life was cut so short."