I am very interested in the psychology of learning. I was Googling around today to try to nail down the difference between associative learning and pattern recognition (there is a difference) and came upon this little gem (Kellman et al, 2010).
I have observed students learning through exposure to correct solutions without an explicit explanation but have not had a framework for understanding this process. From page 7:
Implicit pattern recognition versus explicit knowledge. Although PL may provide important scaffolding for explicit, verbalizable knowledge, PL itself need not involve explicit knowledge. PL changes the way a learner views a problem or representation; this idea of ‘‘mind as pattern recognizer’’ (Bereiter & Scardamalia, 1998) need not be accompanied by explicit facts, concepts, or procedures. In some domains, one might be able to demonstrate a ‘‘double dissociation’’ between PL effects and effects of con- ventional instruction. Whereas conventional instruction may lead to verbalizable knowledge but lagging pattern recognition and fluency, PL may produce the reverse. Such a clear division, although imaginable, may in practice be difficult to observe, because these forms of learning are normally synergistic, producing performance out- comes in which pattern recognition, facts, concepts, and procedures interact.
There is much more to this. One very interesting insight is that students using PL methods will be able to "see" the solution prior to being able to verbalized the rationale for the solution method.
Learning is a very weird process and that makes teaching hard.
Kellman, Philip J., Christine M. Massey, and Ji Y. Son. "Perceptual learning modules in mathematics: Enhancing students’ pattern recognition, structure extraction, and fluency." Topics in Cognitive Science 2.2 (2010): 285-305.
