{
  "id": "math.fractions.no-number-between",
  "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.no-number-between",
  "uuid": "a18f0879-fc85-4c07-8da5-d1e68e72c460",
  "version": "0.1.1",
  "status": "draft",
  "trust": "low",
  "title": "No number between neighbouring fractions",
  "statement": "Fractions come one after another like whole numbers, so between two fractions that are 'next to each other' there is no other number.",
  "kind": "overgeneralization",
  "domain": "math.fractions",
  "about": [
    {
      "scheme": "CCSS",
      "code": "6.NS.C.6",
      "uri": "http://corestandards.org/Math/Content/6/NS/C/6/"
    }
  ],
  "level_band": [
    "middle",
    "secondary"
  ],
  "locale": "en",
  "evidence_patterns": [
    {
      "item_shape": "ask how many numbers lie between two fractions",
      "signature": "answers none, or a small finite count found by listing",
      "example": {
        "item": "How many numbers are there between 1/5 and 2/5?",
        "expected": "Infinitely many",
        "response": "None"
      }
    },
    {
      "item_shape": "ask for a fraction between two given fractions with consecutive numerators",
      "signature": "says there is none, or gives one only by changing to a bigger denominator and then says that is the only one",
      "example": {
        "item": "Name a fraction between 3/7 and 4/7",
        "expected": "any of 7/14 ... e.g. 1/2",
        "response": "There isn't one"
      }
    }
  ],
  "discriminators": {
    "vs_slip": "A slip is failing to find one on a single item. The belief is a stated rule ('there's nothing between them') that survives being shown an example, or is repaired to 'there are a few, but not infinitely many'."
  },
  "relations": {
    "conflicts_with": [
      {
        "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/6/NS/C/6/",
        "label": "CCSS 6.NS.C.6: understand a rational number as a point on the number line"
      },
      {
        "external": "http://corestandards.org/Math/Content/4/NF/A/1/",
        "label": "CCSS 4.NF.A.1: explain why a fraction a/b is equivalent to (n x a)/(n x b)"
      }
    ],
    "specializes": [
      "math.fractions.two-whole-numbers"
    ]
  },
  "alignments": [
    {
      "scheme": "CCSS",
      "code": "6.NS.C.6",
      "uri": "http://corestandards.org/Math/Content/6/NS/C/6/",
      "relation": "about"
    }
  ],
  "provenance": {
    "sources": [
      {
        "type": "paper",
        "citation": "Vamvakoussi, X., & Vosniadou, S. (2004). Understanding the structure of the set of rational numbers: A conceptual change approach. Learning and Instruction, 14(5), 453-467.",
        "doi": "10.1016/j.learninstruc.2004.06.013",
        "note": "Discreteness of the rational number set as a synthetic model carried over from natural numbers."
      },
      {
        "type": "paper",
        "citation": "Vamvakoussi, X., & Vosniadou, S. (2010). How many decimals are there between two fractions? Aspects of secondary school students' understanding of rational numbers and their notation. Cognition and Instruction, 28(2), 181-209.",
        "doi": "10.1080/07370001003676603"
      },
      {
        "type": "paper",
        "citation": "Van Hoof, J., Verschaffel, L., & Van Dooren, W. (2015). Inappropriately applying natural number properties in rational number tasks: Characterizing the development of the natural number bias through primary and secondary education. Educational Studies in Mathematics, 90(1), 39-56.",
        "doi": "10.1007/s10649-015-9613-3"
      }
    ],
    "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"
}