Correct answer, wrong reason

Find the misconception hidden behind a correct answer.

Compare a learner’s answer and explanation, diagnose the rule behind a lucky answer, then verify a pre-authored synthetic replay response on a different problem.

Try the fixture No sign-in · precomputed from the tested fixture

One product.

One decision.

Visible evidence.

Interactive proof

Reveal the verified fixture.

These exact twenty labeled fraction cases are evaluated by product.py.

Learner response set

[
  {
    "id": "M01",
    "problem": "1/2 + 1/3",
    "answer": "5/6",
    "reasoning": "I added both numerators and both denominators, then changed it to 5/6.",
    "label": "ADD_BOTH_PARTS",
    "replay_problem": "1/2 + 1/2",
    "replay_answer": "1",
    "replay_reasoning": "Both halves make one whole."
  },
  {
    "id": "M02",
    "problem": "1/2 + 1/3",
    "answer": "5/6",
    "reasoning": "The common denominator is 6, so 3/6 + 2/6 = 5/6.",
    "label": "CORRECT",
    "replay_problem": "1/2 + 1/2",
    "replay_answer": "1",
    "replay_reasoning": "Both halves make one whole."
  },
  {
    "id": "M03",
    "problem": "1/2 + 1/3",
    "answer": "5/6",
    "reasoning": "The common denominator is 6, so 3/6 + 2/6 = 5/6.",
    "label": "CORRECT",
    "replay_problem": "1/2 + 1/2",
    "replay_answer": "1",
    "replay_reasoning": "Both halves make one whole."
  },
  {
    "id": "M04",
    "problem": "1/2 + 1/3",
    "answer": "5/6",
    "reasoning": "The common denominator is 6, so 3/6 + 2/6 = 5/6.",
    "label": "CORRECT",
    "replay_problem": "1/2 + 1/2",
    "replay_answer": "1",
    "replay_reasoning": "Both halves make one whole."
  },
  {
    "id": "M05",
    "problem": "2/3 + 1/4",
    "answer": "11/12",
    "reasoning": "I added both numerators and both denominators, then changed it to 11/12.",
    "label": "ADD_BOTH_PARTS",
    "replay_problem": "2/3 + 1/3",
    "replay_answer": "1",
    "replay_reasoning": "Three thirds make one whole."
  },
  {
    "id": "M06",
    "problem": "2/3 + 1/4",
    "answer": "11/12",
    "reasoning": "The common denominator is 12, so 8/12 + 3/12 = 11/12.",
    "label": "CORRECT",
    "replay_problem": "2/3 + 1/3",
    "replay_answer": "1",
    "replay_reasoning": "Three thirds make one whole."
  },
  {
    "id": "M07",
    "problem": "2/3 + 1/4",
    "answer": "11/12",
    "reasoning": "The common denominator is 12, so 8/12 + 3/12 = 11/12.",
    "label": "CORRECT",
    "replay_problem": "2/3 + 1/3",
    "replay_answer": "1",
    "replay_reasoning": "Three thirds make one whole."
  },
  {
    "id": "M08",
    "problem": "2/3 + 1/4",
    "answer": "11/12",
    "reasoning": "The common denominator is 12, so 8/12 + 3/12 = 11/12.",
    "label": "CORRECT",
    "replay_problem": "2/3 + 1/3",
    "replay_answer": "1",
    "replay_reasoning": "Three thirds make one whole."
  },
  {
    "id": "M09",
    "problem": "3/4 + 1/6",
    "answer": "11/12",
    "reasoning": "I added both numerators and both denominators, then changed it to 11/12.",
    "label": "ADD_BOTH_PARTS",
    "replay_problem": "3/4 + 1/4",
    "replay_answer": "1",
    "replay_reasoning": "Four fourths make one whole."
  },
  {
    "id": "M10",
    "problem": "3/4 + 1/6",
    "answer": "11/12",
    "reasoning": "The common denominator is 12, so 9/12 + 2/12 = 11/12.",
    "label": "CORRECT",
    "replay_problem": "3/4 + 1/4",
    "replay_answer": "1",
    "replay_reasoning": "Four fourths make one whole."
  },
  {
    "id": "M11",
    "problem": "3/4 + 1/6",
    "answer": "11/12",
    "reasoning": "The common denominator is 12, so 9/12 + 2/12 = 11/12.",
    "label": "CORRECT",
    "replay_problem": "3/4 + 1/4",
    "replay_answer": "1",
    "replay_reasoning": "Four fourths make one whole."
  },
  {
    "id": "M12",
    "problem": "3/4 + 1/6",
    "answer": "11/12",
    "reasoning": "The common denominator is 12, so 9/12 + 2/12 = 11/12.",
    "label": "CORRECT",
    "replay_problem": "3/4 + 1/4",
    "replay_answer": "1",
    "replay_reasoning": "Four fourths make one whole."
  },
  {
    "id": "M13",
    "problem": "1/5 + 1/2",
    "answer": "7/10",
    "reasoning": "I added both numerators and both denominators, then changed it to 7/10.",
    "label": "ADD_BOTH_PARTS",
    "replay_problem": "1/5 + 4/5",
    "replay_answer": "1",
    "replay_reasoning": "Five fifths make one whole."
  },
  {
    "id": "M14",
    "problem": "1/5 + 1/2",
    "answer": "7/10",
    "reasoning": "The common denominator is 10, so 2/10 + 5/10 = 7/10.",
    "label": "CORRECT",
    "replay_problem": "1/5 + 4/5",
    "replay_answer": "1",
    "replay_reasoning": "Five fifths make one whole."
  },
  {
    "id": "M15",
    "problem": "1/5 + 1/2",
    "answer": "7/10",
    "reasoning": "The common denominator is 10, so 2/10 + 5/10 = 7/10.",
    "label": "CORRECT",
    "replay_problem": "1/5 + 4/5",
    "replay_answer": "1",
    "replay_reasoning": "Five fifths make one whole."
  },
  {
    "id": "M16",
    "problem": "1/5 + 1/2",
    "answer": "7/10",
    "reasoning": "The common denominator is 10, so 2/10 + 5/10 = 7/10.",
    "label": "CORRECT",
    "replay_problem": "1/5 + 4/5",
    "replay_answer": "1",
    "replay_reasoning": "Five fifths make one whole."
  },
  {
    "id": "M17",
    "problem": "2/5 + 1/3",
    "answer": "11/15",
    "reasoning": "I added both numerators and both denominators, then changed it to 11/15.",
    "label": "ADD_BOTH_PARTS",
    "replay_problem": "2/5 + 3/5",
    "replay_answer": "1",
    "replay_reasoning": "Five fifths make one whole."
  },
  {
    "id": "M18",
    "problem": "2/5 + 1/3",
    "answer": "11/15",
    "reasoning": "The common denominator is 15, so 6/15 + 5/15 = 11/15.",
    "label": "CORRECT",
    "replay_problem": "2/5 + 3/5",
    "replay_answer": "1",
    "replay_reasoning": "Five fifths make one whole."
  },
  {
    "id": "M19",
    "problem": "2/5 + 1/3",
    "answer": "11/15",
    "reasoning": "The common denominator is 15, so 6/15 + 5/15 = 11/15.",
    "label": "CORRECT",
    "replay_problem": "2/5 + 3/5",
    "replay_answer": "1",
    "replay_reasoning": "Five fifths make one whole."
  },
  {
    "id": "M20",
    "problem": "2/5 + 1/3",
    "answer": "11/15",
    "reasoning": "The common denominator is 15, so 6/15 + 5/15 = 11/15.",
    "label": "CORRECT",
    "replay_problem": "2/5 + 3/5",
    "replay_answer": "1",
    "replay_reasoning": "Five fifths make one whole."
  }
]

The tested result is ready to inspect.

Reveal the expected decision generated by the product's deterministic acceptance fixture.

How it works

Small surface. Clear chain of proof.

Separate

Score the final answer independently from the learner’s causal explanation.

Diagnose

Map the explanation to a specific misconception, not a generic wrong label.

Replay

Verify the fixture’s pre-authored response to a different contrastive problem; mark RESOLVED only when both answer and reasoning are correct.

✓ Exact ground-truth recovery✓ Mathematically different replays✓ Reasoning-checked outcomes