It depends entirely on how many people you're teaching. If you're sitting in a lecture hall full of 250 students, asking continual questions is just not going to get any response. No-one wants to embarass themselves in front of an audience that large. You'll just slow down the lecture while you pause and listen to a stony 10 second silence every couple of minutes. I've had lecturers do this, and it's extremely frustrating.

Personally, I don't mind lecturers "telling" the answers straight away. Obviously give motivation and lead into it rather than just delivering it with no introduction, but I've found a lot of problems are simply too large or too non-obvious to take a straw poll from the class.

The best teachers I've had have been:

(i) Really bloody good at their subject. My probability lecturer (the Field's medallist Tim Gowers), when presenting the proof of Stirling's approximation, said something along the lines of "now, the normal method for proving this bit is a bit complicated, and on my cycle in this morning I thought 'There must be an easier way', when the following struck me. Now, I've never written this down before, so hopefully it works...", and of course laid out a simplification of a famous proof that worked perfectly. Inspirational. (See http://gowers.wordpress.com/2008/02/01/removing-the-magic-fr...)

(ii) Incredible elucidators. The ability to take a complex concept and pick exactly the right words or metaphors to explain it is a powerful ability.

I feel these criteria are far more important than asking the audience questions. You need both -- I've been taught by plenty of talented mathematicians who had no idea how to teach, and certainly a handful of great teachers who simply didn't have the aptitude to really grasp the more complex topics.

Agree. Asking questions in a class of 250 students is counter productive. But, here in India, it's against regulations in many colleges to have classes larger than 60 students. So, perspective :)

taught 300 students in Kabul, Afghanistan at one go (English Class) - what we did was we had PowerPoint, we had a microphone (connected to a mixer and JBL speakers) - and everyone had a sheet so they can follow the lessons, even had think-pair-share (using the PowerPoint as prompts) - had 5 of these classes going at the same time in Kabul University and 1 at the Kabul Polytechnic simultaneously. So you could ask 300 students all at the same time if you set it up properly :)

Judah Schwartz, my physics professor at MIT, used to end each lecture by saying "Comments? Questions? Puzzles?"

Usually there would be dead silence from the class.

And then he would say "I don't believe you." And he waited for someone to ask a question.