After years in the United States, she and her family are back in China. She tried an international school, a bilingual school and, now, a Chinese one for her two sons, and thinks the Chinese route works best. In order to ensure her children’s future here, if that’s what they want one day.

“If you want your kids to really learn the language, then elementary isn’t enough,” said Ms. Qiu, drawing on her own experiences as a child. She was 15 when she left for the United States with her 10-year-old sister. Today, “the difference is huge,” she said. Ms. Qiu is fluent in Chinese, including the written language. Her sister is not.

“You need the classical Chinese, know how it works, the forms and the structure of the language,” she said. “You have to understand not just the language but the whole cultural context. You have to know how the system operates.”

For her, the answer is another elite Chinese school. Like quite a few parents at Fangcaodi, she hopes her son, Oliver, passes highly competitive tests for the No. 4 High School, one of the best-regarded in the country.

It’s all a balancing act of enormous, often clashing factors — culture, identity and money, said Zhang Qiao, the mother of Natalie, a half-German fifth grader.

“The reality is that our children are living in two cultures,” said Ms. Zhang.

She has decided on the international stream of the state-run No. 80 High School. Chinese schools increasingly are offering international streams where students need a foreign passport to enter and where an International Baccalaureate curriculum may be offered.

For Ms. Zhang, unlike Ms. Ma or Ms. Qiu, money is an issue, as it is for many. Natalie spent some time at an international school in Beijing, but the cost was crippling. “It was my whole savings!” said Ms. Zhang. “I can’t do that.”