The Language Acquistion Device (LAD) is Noam Chomsky's idea. His theory proposes that linguistic development in children is an innate process, the evidence for which comes from 'linguistic universals'. These are the similarities between completely different languages, for instance the basic structure 'subject-verb-object', and the ways we naturally acquire the ability to use grammatical constructions to make coherent sentences (this can all be summed up as 'everyone acquires language in a similar way'). The LAD itself is a vaguely defined abstract concept; essentially Chomsky believed that it is the inbuilt device that activates chilren's linguistic development when they are exposed to language in their environment (e.g. when they hear/interact with their adult carers).
You may have heard of Skinner, who proposed a Behaviourist theory of Language Acquisition based on Imitation and Reinforcment; he is Chomsky's main rival, and you can think of their two theories as 'opposites' (they aren't strictly opposite but it's a useful analogy). For example if you learnt about Skinner you would have learnt that his theory cannot explain why children are able to make up phrases that they have never heard before; Chomsky's theory can, as it accounts for the cognitive processes that underly development. That is, as children acquire an understanding of the structural rules of a language, they are able to string words together for themselves.
The Language Acquisition Support System (LASS) was Jerome Bruner's idea; he is another cognitive theorist, so you'll often see him mentioned alongside Chomsky, Piaget and Vygotsky. The LASS is the idea that caregivers support their children's linguistic development in social situations, by interacting and encouraging the child to respond (by pointing, asking questions). By experiencing good quality interaction with caregivers, children learn to take a more active role in social situations. The importance of Bruner's theory is highlighted by extreme cases of deprivation ('feral children'), where children who have not experienced interaction with caregivers early on in life have subsequent difficulties acquiring language later on. It is thought that there is a 'critical period', where if children do not experience caregiver interaction by a certain stage in development, their linguistic abilities will never develop fully. This is generally thought to be before the ages 5-6.
Vygotsky is another theorist who emphasises the idea of adult carers providing children with a 'model' for language use in everyday situations, i.e. children take in the language used by adults and will go on to apply it to thier own everyday situations. The model for language use provided intentionally by adults is referred to as 'scaffolding'.
Hope that was helpful, good luck.
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