I started reading How to Solve It by Polya (as one of my interests is education, particularly math education). Your professor's technique sounds like something straight from this book. Present a problem, ask the students for the next step. Guide them towards the solution (reference similar problems, maybe be explicit if they're way off).

By engaging them in a dialogue you keep them engaged and focused on the material (or at least more of them than in a straight "speak at them" lecture). And by giving them a chance to answer for themselves, you're encouraging them to think (rather than merely commit things to memory or similar).