{
  "id": "math.fractions.subtract-across",
  "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.subtract-across",
  "uuid": "f9b8d0fd-1f46-47ac-8fc7-d4923e7ef2c8",
  "version": "0.1.1",
  "status": "draft",
  "trust": "low",
  "title": "Subtracting fractions across numerators and denominators",
  "statement": "Fractions are subtracted by subtracting the numerators and subtracting the denominators.",
  "kind": "overgeneralization",
  "domain": "math.fractions",
  "about": [
    {
      "scheme": "CCSS",
      "code": "5.NF.A.1",
      "uri": "http://corestandards.org/Math/Content/5/NF/A/1/"
    }
  ],
  "level_band": [
    "primary",
    "middle"
  ],
  "locale": "en",
  "evidence_patterns": [
    {
      "item_shape": "subtract two fractions with unlike denominators",
      "signature": "difference numerator = a - c and difference denominator = b - d for a/b - c/d",
      "example": {
        "item": "3/4 - 1/2 = ?",
        "expected": "1/4",
        "response": "2/2 (= 1)"
      }
    },
    {
      "item_shape": "subtract two fractions with like denominators",
      "signature": "subtracts denominators to get zero and cannot finish, or writes the numerator difference over 0",
      "example": {
        "item": "3/5 - 1/5 = ?",
        "expected": "2/5",
        "response": "2/0 (or 'impossible')"
      }
    }
  ],
  "discriminators": {
    "vs_slip": "Like-denominator items are diagnostic: the bug produces a zero denominator and the learner stalls. A slip does not.",
    "vs": {
      "math.fractions.add-across": "Same mechanism for the other operation. Most learners with one have the other; test both."
    }
  },
  "relations": {
    "conflicts_with": [
      {
        "external": "http://corestandards.org/Math/Content/5/NF/A/1/",
        "label": "CCSS 5.NF.A.1: add and subtract fractions with unlike denominators"
      }
    ],
    "resolved_by": [
      {
        "external": "http://corestandards.org/Math/Content/5/NF/A/1/",
        "label": "CCSS 5.NF.A.1: add and subtract fractions with unlike denominators"
      }
    ]
  },
  "alignments": [
    {
      "scheme": "CCSS",
      "code": "5.NF.A.1",
      "uri": "http://corestandards.org/Math/Content/5/NF/A/1/",
      "relation": "about"
    }
  ],
  "provenance": {
    "sources": [
      {
        "type": "paper",
        "citation": "Siegler, R. S., Thompson, C. A., & Schneider, M. (2011). An integrated theory of whole number and fractions development. Cognitive Psychology, 62(4), 273-296.",
        "doi": "10.1016/j.cogpsych.2011.03.001"
      },
      {
        "type": "paper",
        "citation": "Braithwaite, D. W., Pyke, A. A., & Siegler, R. S. (2017). A computational model of fraction arithmetic. Psychological Review, 124(5), 603-625.",
        "doi": "10.1037/rev0000072"
      },
      {
        "type": "book",
        "citation": "Ashlock, R. B. (2010). Error Patterns in Computation: Using Error Patterns to Help Each Student Learn (10th ed.). Allyn & Bacon."
      }
    ],
    "origin": "llm-drafted",
    "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."
  },
  "history": {
    "changelog": [
      {
        "version": "0.1.1",
        "date": "2026-09-05",
        "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."
      }
    ]
  },
  "license": "CC-BY-4.0"
}