Let’s say that you (1) believe that direct instruction (i.e. explicit worked examples with a procedure followed by repeated practice) is key to instruction and that (2) as a mathematical goal, students should be able to solve problems that they have never seen before and are likely to get stuck on, at some point.
What would that classroom look like?
Well, you’d probably provide some explicit instruction at the beginning of class in how to solve a new problem. Except that, of course, there is no guaranteed procedure for solving new problems, so you’d probably be explicit that you’re modeling good moves that your students would practice using later. A worked example.
And then you’d probably give them a chance to work on a non-routine problem that uses some of the moves or strategies that you’ve explicated. Maybe a quick one in semi-whole group, so that students don’t reinforce a mislearned move and get feedback before trying a problem on their own.
And then you’d probably give practice. Except that practice with problem solving means getting stuck and then getting unstuck with some move, strategy or technique.
You’d give students feedback about how well students used the moves that you’ve explicitly taught.
Maybe I’m wrong, but this doesn’t sound so different to me from the classroom imagined by opponents of direct instruction.