Direct Instruction Vs Problem-Based Teaching

I was recently at a conference that was heavily teaching problem solving tasks and problem solving techniques. I really enjoyed the conference, but it raised in me the question of what is the ideal relationship between direct instruction and problem-based teaching. Here our my thoughts in progress.

As I continue to think about this relationship I cam across this diagram from How People Lean, Brain, Mind, and School. 

 

They write p22: "Are some of these teaching techniques better than others? Is lecturing a poor way to
teach, as many seem to claim? Is cooperative learning effective? Do attempts to use computers (technology-enhanced teaching) help achievement or hurt it? 

This volume suggests that these are the wrong questions. Asking which teaching technique is best is analogous to asking which tool is best—a hammer, a screwdriver, a knife, or pliers. In teaching as in carpentry, the selection of tools depends on the task at hand and the materials one is working
with. Books and lectures can be wonderfully efficient modes of transmitting new information for learning, exciting the imagination, and honing students’ critical faculties—but one would choose other kinds of activities to elicit from students their preconceptions and level of understanding, or to
help them see the power of using meta-cognitive strategies to monitor their learning. Hands-on experiments can be a powerful way to ground emergent knowledge, but they do not alone evoke the underlying conceptual understandings that aid generalization. There is no universal best teaching practice.