## Math Subject Evaluation Rules

## MATHEMATICAL VERIFICATION DATA

When provided:
1. **Result CORRECT**: `factual_accuracy = 1.0`. Explanation wording issues go under `clarity_precision`, NOT `factual_accuracy`.
2. **Result INCORRECT**: `factual_accuracy = 0.0`, unless your own verification clearly confirms the answer is correct (extraction error).
3. **UNABLE TO VERIFY**: Fall back to your own reasoning.

Speak about the analysis as your own. Do NOT mention "SymPy" or "programmatic verification" in output.

When inline SVG is present, use SVG coordinates to mathematically verify geometric claims.

### Additional Math Verification Rules (Closed-Ended)

3. **If options analysis shows a distractor is accidentally correct**: Note this under `distractor_quality`.
4. **If options analysis shows NO option matches the computed answer**: This means all options are wrong -- set `factual_accuracy = 0.0`.

**Curriculum Context Note**: When curriculum specifies pedagogical distinctions (e.g., 3×4 vs 4×3 in early grade math), prioritize curriculum alignment over general equivalence.

**Conceptual Learning Context** (e.g., introducing multiplication to 3rd graders):
- A countable 3×4 array is APPROPRIATE scaffolding
- Even though students could "just count" instead of multiplying, this supports learning what multiplication means
- A "3 × 4 = ?" label on the array is also fine – the student still needs to compute
- Only "3 × 4 = 12" directly stated would be a problem (answer is literally given)

**Fluency/Mastery Context** (e.g., testing multiplication fact recall for 8th graders):
- The same countable array may be INAPPROPRIATE because:
  - 8th graders should already know 3×4
  - The array lets them bypass demonstrating that knowledge
  - This prevents identifying genuine knowledge gaps
- However, this requires clear curriculum evidence that fluency is being assessed

**Numeric Consistency (applies to images with explicit numbers/counts):**

When an image shows explicit numbers or countable objects:
- **Matching OR approximately matching the problem** → PASS (supports the problem)
- **Clearly labeled as a separate example** → PASS (conceptual scaffolding)
- **Shows the computation (e.g., "3 × 4 = ?")** → PASS (student still needs to compute)
- **Shows the answer directly (e.g., "3 × 4 = 12")** → May be a problem if this IS the question being asked
- **Contradicts the problem's numbers in a confusing way** → FAIL only if the mismatch would mislead students about what to calculate

**Examples - PASS:**
- "4 × 6 = ?" with a 4×6 array → PASS (scaffolding for conceptual learning)
- "4 × 6 = ?" with a labeled "4 × 6 = ?" on the array → PASS (student still computes)
- "Mia made 48 clay animals, divides into 6 groups" with photos of clay animals → PASS (illustrative/engaging - the exact count doesn't need to match)
- Question about multiplication with a decorative border of stars → PASS (neutral)

**Examples - FAIL:**
- "What is 3 × 4?" with an image showing "3 × 4 = 12" → FAIL (answer literally given)
- Multiplication fluency test (curriculum clearly states this) with countable arrays that let students bypass recall → May FAIL (trivializes for the specific pedagogical purpose)

**Important clarification**: Many good items can be solved from text alone (e.g., computing 48 ÷ 6). This is NOT a Mastery Learning failure if students still have to apply a procedure or reasoning step. Even if the image provides scaffolding rather than being strictly necessary, Mastery Learning can pass as long as the task requires thinking.

**Examples:**
- PASS: "48 ÷ 6 = ?" (requires computation, even if solvable from text alone)
- PASS: "Which fraction is equivalent to 2/4?" (requires understanding equivalence, not just recall)
- PASS: "Convert: 1 foot = ___ inches" when Difficulty Definition says "recalling a base equivalence" (curriculum-sanctioned recall)
