Connecting the dots without the dots

A reader of Bridging Differences asks:

"Instructivist v constructivist? Can there be some common ground between the two?"

There is common ground by implication if you listen to constructivist rhetoric as in the excerpt below from the Association for Supervision and Curriculum Development (ASCD). For example, both schools of thought believe in asking students probing questions and in pressing them to explain their thinking. It only seems there is a gulf because all too often constructivists give the impression they invented asking students probing questions and pressing them to explain their thinking. For all I know, constructivists also claim they invented the recipe for apple pie.

Among the differences I can see is the role of the teacher. In addition to being an active listener and a coordinator and a manager and a facilitator, instructivists also want teachers to give explicit instruction.

From ASCD:
[What is the teacher's role in the constructivist classroom?
Narrator: A constructivist approach requires more of students—and teachers as well.

In addition to providing information, teachers must probe students' understandings, paying close attention to what they say and think and valuing their points of view. Teachers circulate more, talk more with students, asking them probing questions, pressing them to explain their thinking, encouraging them to draw conclusions.

Jacqueline Grennon Brooks: The teacher has a very proactive role. The teacher has a very intellectually rigorous role. The teacher has the role of being an active listener and a coordinator and a manager and a facilitator all at the same time. Because, while listening to what people are telling him or her, the teacher is formulating a plan of action.]

What is still shrouded in mystery as far as I am concerned is this whole issue of constructing knowledge rather than receiving it from others, e.g. from teachers and textbooks. What are the sources of external input if textbooks and explicit teacher instruction are out? It’s easy to proclaim that students learn best when they gain knowledge through exploration and active learning. But how does that work specifically in the various disciplines? OK, I can explore circles and pi, but how will I learn world history or geography or languages with hands-on materials instead of textbooks? How will I explain my reasoning, if I am not supposed to commit knowledge to memory? And why is reading a book or listening to the teacher and trying to understand the materials not active learning? What is learning if not something committed to memory? Why do constructivists disparagingly characterize a demonstration of learning residing in memory (where else would it reside?) as "regurgitation"?

Again from ASCD:
[The Definition of Constructivism
Constructivism is an approach to teaching based on research about how people learn. Many researchers say that each individual constructs knowledge rather than receiving it from others.

Although people disagree about how to achieve constructive learning, constructive teaching is based on the belief that students learn best when they gain knowledge through exploration and active learning. Hands-on materials are used instead of textbooks, and students are encouraged to think and explain their reasoning instead of memorizing and reciting facts. Education is centered on themes and concepts and the connections between them, rather than isolated information.]

Constructivists rail against committing factual knowledge to memory but are all for making connections. It's like trying to connect the dots without the dots.