First of all, understand that every educator makes mistakes. A mistake in and of itself does not disqualify you from the profession of teaching. However, intellectual humility requires us to apologize when we become aware of that mistake. This is actually a good thing for students to hear and hopefully internalize and emulate when they make their own mistakes.
Kaplowitze et. al.’s Race Dialogues has a 5 step method called ReAACT for issuing an apology (92–93) where that is appropriate:
- Reflect on the situation
- Acknowledge your mistake
- Change your behavior
Thank your students/peers for helping you learn.