A recast is a technique used in language teaching to correct learners' errors in such a way that communication is not obstructed.
Recasts are used both by teachers in formal educational settings, and by interlocutors in naturalistic language acquisition.
Sometimes, the teacher will repeat the words back to the student, usually with different intonation or form, or as a question, so that the recasting appears as a continuation of the conversation: For example, in German: Here, the teacher has corrected the student's incorrect positioning of the infinitive "haben" and their declension of the indefinite article "ein".
The teacher will correct the student's errors but also extend the learning by adding additional words or phrases.
A further example, in English: In this example the teacher is making the correction to the student's speech (adding a "to") but also extending the learning by asking a question.