The Threshold Hypothesis

Cummins proposed that a bilingual child may have 'a threshold level of linguistic competence' (Baker, 1993, p.119).  The threshold hypothesis proposes the existence of a lower threshold (where bilingual proficiency should be sufficient to avoid any negative effects) and a higher threshold (where bilingual proficiency should be high to lead to cognitive growth) (Mohanty, 1994, p.50).

Language Awareness Hypothesis

Whorf suggests that individual's 'cognitive organization is primarily determined by the structure of their language and that speakers of different languages have different cognitive structures relative to their languages' (ibid, p.51).  Vygotsky (ibid, p.52) understands the relationship between bilingualism and cognition differently - he believes, that a bilingual child has the ability to see the language as one system among others and is thus aware of linguistic operations.  This view became known as language awareness hypothesis.