Active supervision of the problem-solving process. Covers Schoenfeld's control layer, Ann Brown's self-regulation moves, planning-monitoring-evaluating cycle, time budgeting, strategy switching, and the "what am I doing and why?" check. Use continuously alongside any solving activity to avoid wandering, dead ends, and unproductive grinding.
Metacognition is thinking about your thinking. In problem solving, it is the supervisor process that interrupts execution to ask: "Am I still on the right track? Is my current activity the best use of this moment? Do I need to reconsider?" Schoenfeld's research on mathematical problem solving shows that novices who grind for 20 minutes on a dead end outperform instantly when taught to pause every 2-3 minutes and check. This skill is the catalog of the checks.
Agent affinity: brown-ps (self-regulation, reciprocal teaching), schoenfeld (control layer), polya-ps (review phase)
Concept IDs: prob-problem-representation, prob-adaptive-management, prob-uncertainty-management, prob-trial-error-iteration
Metacognition decomposes into three phases:
These run nested inside problem solving, not alongside it.
Goal: Set the meta-level frame for the solving session.
Operations:
A solver who starts without a plan is already in a dead end.
Goal: Continuously check that the current activity is the right activity.
The core check — every 2-5 minutes, ask:
If any of the four questions produces "I don't know," stop and figure it out before continuing.
Progress indicators:
If all three are no, you are grinding.
Stall indicators:
When stall indicators appear, switch strategies or escalate (ask for help, consult a resource, take a break).
Goal: After solving, extract the lesson.
Operations:
Evaluation is what converts a one-time win into a transferable skill.
Ann Brown's work on reciprocal teaching identified four metacognitive moves that learners can be explicitly taught:
These move problem solving from passive to active, and from implicit to inspectable.
Schoenfeld videotaped experts and novices solving the same math problem and analyzed their use of time. Typical results:
Novice:
Expert:
The expert spends less total time (20 vs 19 minutes) but allocates differently. The novice's 18 minutes of execution include 15 minutes of wandering on the first strategy. Explicit control would have saved most of it.
Rule of thumb:
If execution is eating 90% of the budget, metacognition has failed.
When to switch:
How to switch:
A student is solving an integral by substitution. They have tried two substitutions, neither of which simplifies the integrand. They have spent 12 minutes.
Monitoring check:
Strategy switch:
Without the metacognitive check, the student would have tried a third substitution and wasted another 5 minutes.