Final answer:
The family described is demonstrating cultural assimilation, which refers to the process of adopting a new culture and integrating into it. The family members are learning the language, adapting to the new culture, and the children are attending public school.
Step-by-step explanation:
The family described in the question is demonstrating cultural assimilation. Cultural assimilation is the process by which individuals and groups adopt the customs, language, and behavior of a new culture and integrate themselves into it.
In this case, the family members are learning the language, adapting to the new culture, and the children are attending public school, all of which are indicators of cultural assimilation.