{
  "id": "math.fractions.two-whole-numbers",
  "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.two-whole-numbers",
  "uuid": "dd52364b-0b0d-4ab8-a0f5-51bcb845f7fc",
  "version": "0.1.1",
  "status": "draft",
  "trust": "low",
  "title": "A fraction is two separate whole numbers",
  "statement": "A fraction is two whole numbers written one above the other, not a single number with its own size; the numerator and denominator can be read and handled separately.",
  "kind": "overgeneralization",
  "domain": "math.fractions",
  "about": [
    {
      "scheme": "CCSS",
      "code": "3.NF.A.2",
      "uri": "http://corestandards.org/Math/Content/3/NF/A/2/"
    },
    {
      "scheme": "CCSS",
      "code": "6.NS.C.6",
      "uri": "http://corestandards.org/Math/Content/6/NS/C/6/"
    }
  ],
  "level_band": [
    "primary",
    "middle"
  ],
  "locale": "en",
  "evidence_patterns": [
    {
      "item_shape": "place a fraction on a number line marked 0 to 10",
      "signature": "places the fraction at the numerator, the denominator, or their sum",
      "example": {
        "item": "Mark 3/4 on a number line from 0 to 10",
        "expected": "between 0 and 1, three quarters of the way",
        "response": "at 3 (or at 4, or at 7)"
      }
    },
    {
      "item_shape": "say which whole numbers a fraction lies between",
      "signature": "answers with the numerator and denominator themselves",
      "example": {
        "item": "Between which two whole numbers is 5/8?",
        "expected": "0 and 1",
        "response": "5 and 8"
      }
    }
  ],
  "discriminators": {
    "vs_slip": "A slip is one misplaced point. The belief is stable across fractions and shows in language: the learner describes 3/4 as 'three and four' or 'three out of four' but cannot say whether it is more or less than one.",
    "vs": {
      "math.fractions.number-line-whole-is-line": "Give a 0-to-1 line. Learners who treat the whole line as the unit place 3/4 correctly on a 0-1 line but not on a 0-2 line; learners with this belief fail both and place by the numerator."
    }
  },
  "relations": {
    "conflicts_with": [
      {
        "external": "http://corestandards.org/Math/Content/3/NF/A/2/",
        "label": "CCSS 3.NF.A.2: understand a fraction as a number on the number line"
      },
      {
        "external": "http://corestandards.org/Math/Content/6/NS/C/6/",
        "label": "CCSS 6.NS.C.6: understand a rational number as a point on the number line"
      }
    ],
    "resolved_by": [
      {
        "external": "http://corestandards.org/Math/Content/3/NF/A/2/",
        "label": "CCSS 3.NF.A.2: understand a fraction as a number on the number line"
      }
    ],
    "confusable_with": [
      "math.fractions.number-line-whole-is-line"
    ]
  },
  "alignments": [
    {
      "scheme": "CCSS",
      "code": "3.NF.A.2",
      "uri": "http://corestandards.org/Math/Content/3/NF/A/2/",
      "relation": "about"
    }
  ],
  "provenance": {
    "sources": [
      {
        "type": "paper",
        "citation": "Ni, Y., & Zhou, Y.-D. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist, 40(1), 27-52.",
        "doi": "10.1207/s15326985ep4001_3",
        "note": "Whole number bias: the components of a fraction are treated as independent natural numbers."
      },
      {
        "type": "paper",
        "citation": "Stafylidou, S., & Vosniadou, S. (2004). The development of students' understanding of the numerical value of fractions. Learning and Instruction, 14(5), 503-518.",
        "doi": "10.1016/j.learninstruc.2004.06.015"
      },
      {
        "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",
        "note": "Fraction magnitude understanding as the core of fraction knowledge; its absence underlies this belief."
      },
      {
        "type": "paper",
        "citation": "Mack, N. K. (1995). Confounding whole-number and fraction concepts when building on informal knowledge. Journal for Research in Mathematics Education, 26(5), 422-441.",
        "doi": "10.5951/jresematheduc.26.5.0422"
      }
    ],
    "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"
}