I think by cognitivism, you are referring to cognitive psychology which is the scientific study of the mind. This is different to social psychology, where the focus is on a person’s sense of identity and group behaviour. The use of social psychology in language teaching can be seen in humanistic approaches. Cognitive psychology is evident in behaviourist methodology; techniques such as drilling and in course books such as the Streamline series.
Cognitive psychologists study processes such as language, memory, reasoning and problem solving. Research tends to look at cognitive abilities that can be applied to large groups rather than individual differences. One influence in cognitive psychology is behaviourism. Behaviourists focus on what is visible rather than what is in the mind. So they look at stimuli and responses; they believe that learning a language is a case of learning responses to stimuli. For example, the stimulus “how are you?” often elicits the response “I’m fine thanks”. Behaviourists also believe strongly in the use of rewards to reinforce good behaviour. Rewards include praise, giving points and gold stars.
I hope this has answered your question. Please write in again if you have any further questions.