---
name: math-progress-monitor
description: Metacognitive check-ins during problem solving - detects when to pivot or persist
---
# Math Progress Monitor
## When to Use
Trigger on phrases like:
- "am I on the right track"
- "is this approach working"
- "I'm stuck"
- "should I try something else"
- "verify my progress"
- "check my reasoning"
- "is this getting too complicated"
Use mid-work to assess whether to continue, pivot, or decompose (Schoenfeld's metacognitive control).
## Process
Run a structured progress assessment:
### 1. Inventory attempts
**Ask:** "What have you tried so far?"
- List each approach
- Order by when attempted
- Note time spent
### 2. Extract learnings
**Ask:** "What did each attempt tell you?"
- Even failures provide information
- What was ruled out?
- What patterns emerged?
### 3. Complexity check
**Ask:** "Is complexity growing faster than expected?"
- Warning signs:
- More terms than you started with
- New variables appearing
- Calculation getting messier
- Normal: complexity stays flat or decreases
### 4. Spot-check verification
**Ask:** "Can you verify any intermediate results?"
- Run numerical examples
- Check limiting cases
- Dimensional analysis
### 5. Decomposition check
**Ask:** "Is there a simpler sub-problem to solve first?"
- Identify dependencies
- Find stepping stones
- Reduce scope
### 6. Sunk cost assessment
**Ask:** "What would abandoning this approach cost?"
- Time already spent (irrelevant)
- Insights that transfer (relevant)
- Probability of success if continue
## Key Questions to Ask
1. What have you tried? (inventory)
2. What did you learn? (extract)
3. Is it getting simpler or harder? (complexity)
4. Can you check a piece? (verify)
5. What's the smallest step? (decompose)
6. Should you pivot? (decide)
## Output Format
```
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]
```
## Example Interaction
```
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?
```
## Co-activates
When user is stuck, suggest:
- **math-intuition-builder** - reset understanding
- **math-model-selector** - if framework was wrong
- **math-mode** - for verification computations
- **Relevant domain skill** - for alternative approach
