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{
    "pk": 31703,
    "title": "Understanding Symbols: A Situativity-Theory Analysis of Constructinf Mathematical Meaning",
    "subtitle": null,
    "abstract": "We report analyses of the construction and\ninterpretation of mathematical symbols that refer to\nquantitative properties and relations of a physical\nsystem. Middle-school students solved problems that\ninvolved contracting tables, equations and graphs to\nrepresent linear functions of a device where blocks are\nmoved varying distances by turning a handle that\nwinds string around spools of different sizes. Previous\nresearch analyzed activities of reasoning about\nquantities of this system as attunement to constraints\nand affordances, a characterization of students' imphcit\nunderstanding of concepts of variable and linear\nfunctions. This report concerns activities of\nrepresenting quantitative properties and relations using\nmathematical notations. W e are developing analyses\nof constructing and interpreting tables, equations, and\ngraphs in terms of attunement to constraints and\naffordances of the represented system, the system of\nnotations, and relations between the constraints of the\nnotations and the represented domain. W e present\nexamples that illustrate concepts of semantic clumps,\ngroups, and morphisms; descriptive and demonstrative\nrepresentations; multiple referent domains; and\nconstructions of meaning in contributions to\nconversational discourse.",
    "language": "eng",
    "license": {
        "name": "",
        "short_name": "",
        "text": null,
        "url": ""
    },
    "keywords": [],
    "section": "Submitted Presentations",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/3pp891pj",
    "frozenauthors": [
        {
            "first_name": "James",
            "middle_name": "G.",
            "last_name": "Greeno",
            "name_suffix": "",
            "institution": "Stanford University",
            "department": ""
        },
        {
            "first_name": "Randi",
            "middle_name": "A.",
            "last_name": "Engle",
            "name_suffix": "",
            "institution": "Stanford University",
            "department": ""
        },
        {
            "first_name": "Laura",
            "middle_name": "K.",
            "last_name": "Kerr",
            "name_suffix": "",
            "institution": "Stanford University",
            "department": ""
        },
        {
            "first_name": "Joyce",
            "middle_name": "L.",
            "last_name": "Moore",
            "name_suffix": "",
            "institution": "Stanford University",
            "department": ""
        }
    ],
    "date_submitted": null,
    "date_accepted": null,
    "date_published": "1993-01-01T18:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "PDF",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/cognitivesciencesociety/article/31703/galley/22771/download/"
        }
    ]
}