Very few learners actually "pick up" a language. They need comprehensible input (Krashen 1981), multiple opportunities to practice the second language at their level.
Simple exposure will not result in second language acquisition.
The only part of it children acquire faster is the social language and the pronunciations.
Younger children may seem to acquire the language faster, but remember that they have less language to actually learn in order to seem fluent with their peers.
Why? Would you? I know I wouldn't, and didn't when I moved overseas.
Most students will go through a silent stage where they are listening to others speak, trying to develop a receptive vocabulary and are watching how others interact socially.
It could very well be embarrassing for them to be forced to speak a language they do not yet know or understand. They will do it in their own time.
Speaking with peers is called our social language. This is very different from school language.
Social language can be developed with reasonable fluency in as little as 2-3 years.
School language, however, can take up to 7 or more years to develop.
School language involves rules, accuracy, is cognitively demanding and does not provide any face-to-face interactions to help the student make meaning.
Social language uses real language, is not cognitively demanding, and provides interaction for meaning
Most of these children are actually suffering from culture shock. People experience culture shock in a way that is similar to the stages of grief. In her book Getting Started with English Language Learners, Judie Haynes lists these stages as:
Honeymoon (showing excitement about a new life)
Rejection (there is too much to understand)
Regression (frustrations with communication and homesickness)
Integration (learning to deal with differences and finding ways to live in both cultures)
Acceptance (assimilation and adoption of mainstream culture at school while keeping home culture values)