According to Lev Vygotsky –

Concept: Vygotsky's sociocultural theory holds that cognitive development is fundamentally a social and cultural process. Higher mental functions develop through social interaction, and language is the primary psychological tool that mediates and organises thought — first as social speech shared with others, later internalised as “inner speech” that drives independent thinking.

Application: Applying this to the statement in the stem, “language plays an important role in cognitive development of children” is precisely Vygotsky's central claim — that language is not a mere by-product of thought but an active tool that shapes it.

Cross-check — the other statements belong to different theorists, not Vygotsky:

• ‘Children learn language through a language acquisition device’ is Noam Chomsky's nativist account of language acquisition, built around an innate, biologically pre-wired language module — a different theorist and a different mechanism from Vygotsky's social-tool account.

• ‘Children's cognitive development occurs in stages’ is Jean Piaget's stage theory (sensorimotor → preoperational → concrete operational → formal operational), which treats development as a fixed, age-linked sequence rather than a socially mediated process.

• ‘Maturation of schemas leads to cognitive development’ is also Piaget's framework, where schemas mature through assimilation and accommodation — again a constructivist, not a sociocultural, mechanism.

Result: The statement matching Vygotsky's sociocultural view — that language plays an important role in children's cognitive development — is the one consistent with his theory; the official CTET January 2021 Paper II answer key confirms this as the keyed response.