{
  "id": "math.decimals.longer-is-larger",
  "uri": "https://open-misconceptions.github.io/miscon-data/m/math.decimals.longer-is-larger",
  "uuid": "b9976592-9045-4327-8b17-485c7114d359",
  "version": "0.1.1",
  "status": "draft",
  "trust": "low",
  "title": "Longer decimal is larger",
  "statement": "A decimal with more digits after the point is a larger number, because the digits after the point make a bigger whole number.",
  "kind": "overgeneralization",
  "domain": "math.decimals",
  "about": [
    {
      "scheme": "CCSS",
      "code": "4.NF.C.7",
      "uri": "http://corestandards.org/Math/Content/4/NF/C/7/"
    },
    {
      "scheme": "CCSS",
      "code": "5.NBT.A.3",
      "uri": "http://corestandards.org/Math/Content/5/NBT/A/3/"
    }
  ],
  "level_band": [
    "primary",
    "middle"
  ],
  "locale": "en",
  "evidence_patterns": [
    {
      "item_shape": "compare two decimals where the shorter is larger",
      "signature": "chooses the decimal with more digits after the point",
      "example": {
        "item": "Which is larger, 0.5 or 0.25?",
        "expected": "0.5",
        "response": "0.25"
      }
    },
    {
      "item_shape": "order decimals of different lengths",
      "signature": "orders by the digits after the point read as whole numbers",
      "example": {
        "item": "Order from smallest to largest: 0.3, 0.125, 0.45",
        "expected": "0.125, 0.3, 0.45",
        "response": "0.3, 0.45, 0.125"
      }
    }
  ],
  "discriminators": {
    "vs_slip": "A slip is one wrong comparison. The belief is diagnosed by a consistent pattern on length-incongruent items and a justification such as 'twenty-five is more than five'.",
    "vs": {
      "math.decimals.shorter-is-larger": "Mirror belief. Include items where the longer decimal is larger (0.75 vs 0.8): longer-is-larger gets those right and shorter-is-larger gets them wrong."
    }
  },
  "relations": {
    "conflicts_with": [
      {
        "external": "http://corestandards.org/Math/Content/4/NF/C/7/",
        "label": "CCSS 4.NF.C.7: compare two decimals to hundredths by reasoning about their size"
      }
    ],
    "resolved_by": [
      {
        "external": "http://corestandards.org/Math/Content/4/NF/C/7/",
        "label": "CCSS 4.NF.C.7: compare two decimals to hundredths by reasoning about their size"
      },
      {
        "external": "http://corestandards.org/Math/Content/5/NBT/A/3/",
        "label": "CCSS 5.NBT.A.3: read, write and compare decimals to thousandths"
      }
    ],
    "confusable_with": [
      "math.decimals.shorter-is-larger"
    ]
  },
  "alignments": [
    {
      "scheme": "CCSS",
      "code": "4.NF.C.7",
      "uri": "http://corestandards.org/Math/Content/4/NF/C/7/",
      "relation": "about"
    },
    {
      "scheme": "CCSS",
      "code": "5.NBT.A.3",
      "uri": "http://corestandards.org/Math/Content/5/NBT/A/3/",
      "relation": "about"
    }
  ],
  "provenance": {
    "sources": [
      {
        "type": "paper",
        "citation": "Resnick, L. B., Nesher, P., Leonard, F., Magone, M., Omanson, S., & Peled, I. (1989). Conceptual bases of arithmetic errors: The case of decimal fractions. Journal for Research in Mathematics Education, 20(1), 8-27.",
        "doi": "10.5951/jresematheduc.20.1.0008",
        "note": "Whole-number rule for decimal comparison."
      },
      {
        "type": "paper",
        "citation": "Stacey, K., & Steinle, V. (1998). Refining the classification of students' interpretations of decimal notation. Hiroshima Journal of Mathematics Education, 6, 49-69.",
        "note": "Longer-is-larger classification and its sub-types."
      },
      {
        "type": "paper",
        "citation": "Durkin, K., & Rittle-Johnson, B. (2015). Diagnosing misconceptions: Revealing changing decimal fraction knowledge. Learning and Instruction, 37, 21-29.",
        "doi": "10.1016/j.learninstruc.2014.08.003"
      }
    ],
    "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"
}