Metacognitive check-ins during problem solving - detects when to pivot or persist
Trigger on phrases like:
Use mid-work to assess whether to continue, pivot, or decompose (Schoenfeld's metacognitive control).
Run a structured progress assessment:
Ask: "What have you tried so far?"
Ask: "What did each attempt tell you?"
Ask: "Is complexity growing faster than expected?"
Ask: "Can you verify any intermediate results?"
Ask: "Is there a simpler sub-problem to solve first?"
Ask: "What would abandoning this approach cost?"
Progress Assessment:
Status: [On track / Hitting resistance / Should pivot]
Attempts Summary:
1. [Approach] -> [Outcome/Learning]
2. [Approach] -> [Outcome/Learning]
Complexity Check:
- Expected: [what should this look like]
- Actual: [what it actually looks like]
- Verdict: [Normal / Warning / Abandon]
Verification Points:
- [Intermediate result to check]
- [Numerical test case]
Recommendation:
[Continue / Modify approach / Switch strategy / Decompose / Get more info]
If Pivoting:
- Alternative: [specific new approach]
- Why it might work: [reasoning]
User: I've been trying to evaluate this integral for an hour
Claude: Let's do a progress check.
Q1: What have you tried?
> u-substitution with u = sin(x), then integration by parts twice.
Q2: What did each tell you?
> Substitution made it longer. Parts created a cycle.
Q3: Complexity now vs start?
> Much worse. Started with 3 terms, now have 8.
Complexity Check:
- Expected: Should simplify or stay similar
- Actual: 3 terms -> 8 terms after 2 techniques
- Verdict: WARNING - likely wrong approach
Let me verify an intermediate step...
[Runs sympy on original integral]
This integral has closed form using:
- Beta function (special function)
- Or contour integration
Recommendation: PIVOT
Your algebraic approaches won't simplify this pattern.
Alternative Approach:
1. Recognize: integral of sin^m(x) * cos^n(x)
2. Use Beta function identity
3. Or convert to complex exponentials
Related Skills:
- complex-analysis/contour-integrals
- numerical-methods/numerical-integration
Would you like the Beta function approach, or get a numerical answer first to verify?
When user is stuck, suggest: