What is the connection between first language acquisition in children and second language aquisition in adults ?

Excellent question!

The process of
language learning, in general, is the same when babies learn their first language, as when adults
learn a second language. However, the differences in brain function, amount of neurons, and
affective filters play a role in whether the learning will be successful or whether it will be
complicated in both cases.

Your premise asks to compare babies and
adults and how these two subjects would respond to learning their first and a second language,
respectively. Since we are not referring to a specific learning intervention, the first thing to
consider is the state of mind of the learner.

In the case of babies,
they are "clean slates". They have never been exposed to the sounds that would connect to a
meaning. They cannot scaffold, that is, add on to information that they already
know.

However, babies have the highest production of brain cells
which, with a low affective filter (with no bias or fears of learning) would enable them to
instantly create connections between sound and meaning. In all, a baby's process of first
language learning is natural and instinctive. It is proportional to the immense amount of brain
power that is developed at that age, the lack of emotional blockage that may prevent the
learning, and the willingness for learning that comes out of the natural curiosity of
babies.

Contrastingly, second language learning in adults is not an
inherent, nor natural process that comes as easily. This is not because we cannot naturally
process a second language, but because adults have learning barriers that may intervene with the
process itself.

Before adults can learn a second language, they
basically have to place themselves in the position of, you guessed it, babies! They have to clear
any bias or fear of learning, activate their natural curiosity, motivate themselves, and be open
minded- like babies are!

This being said, adults would learn quite
fast by immersing themselves in the second language. This way, all the senses would become
integrated in the learning, sending faster impulses to the brain. As a result, the adult mind
would make quick and accurate connections of
sound-meaning-symbol.

Therefore, it is the main task of any language
instructor to immerse and motivate students and learners to engage in the learning process and
enjoy it as naturally as possible.