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Yes, but usually it is pretty bad for the learning experience, if the teacher stumbles and needs time for himself to figure things out. It can work out to become a deep lesson, if the student is highly motivated and the teacher good at explaining his thought processes - otherwise the student will stand aside and get bored and loose interest, as the problem is way beyond his level to understand.

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But sometimes, watching a teacher work through a problem can actually demystify the process

In college, I took a discrete math course with the world's most unprepared, distractible professor. It was incredible. He would come in with nothing planned in particular, we could ask about concepts from the textbook and he would invent a problem on the spot. Then he'd run through various problem-solving strategies until one worked. I learned so much about how a mathematician thinks from this class.

This was in sharp contrast to my calculus classes where the results were basically thrown at you fully-formed. If you're lucky, you might get to walk through a proof with the professor, but you're never going to see how they mentally navigate the search space.

Sounds great, much better than rote drugery imo!

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