Noticing is regarded as an important part of the process of learning new language, especially in acquisition-driven accounts of language learning, when learners at some point in their acquisition, notice their errors in production. Noticing will only occur when the learner is ready to take on the new language.
Example
A learner might make an error in the use of a preposition, but "notice" its correct use by another learner, or in an authentic text. This might allow them to begin to use it correctly.
In the classroom
In task-based work, part of the teacher's role will be to create the conditions under which learners can notice aspects of language use that are important for developing their interlanguage. This might be achieved by recording and listening to models of the task, or the learners production on the task. Learners talking informally in the classroom, will also be helping each other notice new language and understand how well they are using it via the feedback they are getting.
Further links:
https://www.teachingenglish.org.uk/article/lexical-approach-2-what-does-lexical-approach-look
https://www.teachingenglish.org.uk/article/analysing-language
https://www.teachingenglish.org.uk/article/content-language-integrated-learning
https://www.teachingenglish.org.uk/article/fairy-tales
https://www.teachingenglish.org.uk/article/homework
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