What higher-order knowledge can make the difference between how well and how quickly one's students learn material?

Metacognition, the knowledge and regulation of one's own thinking, makes the difference in how well and quickly students learn.

Declarative knowledge (A) is knowing facts and information, not thinking about one's thinking.

Rote (B) is mechanical memorisation without understanding, not higher-order knowledge.

Procedural knowledge (D) is knowing how to perform tasks, not monitoring one's learning.

John Flavell coined metacognition, often described as thinking about thinking.

It includes metacognitive knowledge and metacognitive regulation such as planning and monitoring.