teaching - Should one offer to take over a lecture that the lecturer is struggling to teach?

Once upon a time in a lecture I attended, the lecturer had clearly not fully understood the material and was struggling to explain it. I was a student, but very knowledgeable about the topic, and had taught it many times in informal settings, so I felt silly just listening.

In the interest of the other attendees' learning, I considered offering to take over the lecture. However, I stopped myself, out of concern that the lecturer might feel humiliated, or think I'm questioning their authority more generally.

In such a situation, is it appropriate for a student to offer to teach a topic? What about other teaching staff who are attending? How would one politely suggest it, or otherwise deal with the situation?

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Related questions: From a student's perspective: offering alternative viewpoints on lecture content, handling unintelligible lecturers and handling lecturers who just read from the book. From a lecturer's perspective: teaching a class you've never taken.

Answer

Perhaps the best approach would be to ask leading questions that helps the lecturer head in the right direction. Or, offer an answer to a question that wasn't going well.

I've taught classes (especially ones that use complex libraries, such as parts of a game engine, that I wasn't a seasoned expert with), and have had students who had more experience with a specific topic chime in to the discussion with details I didn't know. It was great. I've also had students who were aggressive and conveyed arrogance and had them derail the class by setting up a me vs them dynamic. Not so great.

The most important thing is classroom dynamics: let the lecturer retain control (ie. facilitate the discussion) but you actively participate. The lecturer should be there to create a learning environment, not bestow knowledge on the class. You can make it clear you know the topic, and let them have you participate as much as they are comfortable.

Asking to "take over" would not go over well; offering your knowledge on bits and pieces and nudging the lecturer in the right direction through questions would be better.