One of the best "side effects" of active learning is that students develop metacognition - self-awareness of their own learning and problem-solving approaches. Metacognition supports mathematical problem-solving because students with good metacognitive skills can better analyze and adjust their own problem-solving approaches or abandon ones that are not fruitful. Thus metacognition transfers to other settings - it's a lifelong learning habit. A metacognitive classroom has a rich mathematical culture where students are behaving like mathematicians, examining claims and asking for justifications. Alan Schoenfeld demonstrates this link in his classic article on metacognition and problem solving and suggests four ways to foster metacognition in your own classroom.
(Shared by Sandra Laursen, UC Boulder).
