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{
    "pk": 31771,
    "title": "Assessing Conceptual Understanding of Arithmmetic Stucture and Language",
    "subtitle": null,
    "abstract": "We contend that the primary role of an\nillustration or physical manipulable for\nteaching mathematics is to help the learner\nunderstand the language of the mathematics\nby providing the learner with a referential\nsenr«ntics. Having taught this to subjects, w e\naddress the question of how to assess their\nunderstanding. Problem-solving performance,\nw e show, is insufficient by itself. A n\nassessment of students' m e m o r y for the\noriginal problem statement, and their ability to\nuse cues within the referential semantics is\ndemonstrated as a potential method.\nFourth graders (n=24) solved word algebra\nproblem after (a) training with a designed\nreferential semantics from a computer tutor\ncalled the Planner, (b) training with symbolic\nmanipulatives, or (c) receiving no training\n(control). Although pretest-posttest gains\nwere only moderately better for the Planner\ngroup than the symbol group, the former\nshowed reliably better ability to reconstruct the\nproblem statements after a 5-day delay. A\nparticular advantage for recall of algebraic\nrelations (as compared to assignments) was\nevident. Mental representation of relations has\nbeen singled out as a major obstacle to\nsuccessful word problem solving. The support\nthat a well-designed referential semantics\nplays in the formation and retrieval of\nappropriate mental structures for problem\nsolving are discussed, as are methods for\nassessing problem comprehension and\nconceptual change.",
    "language": "eng",
    "license": {
        "name": "",
        "short_name": "",
        "text": null,
        "url": ""
    },
    "keywords": [],
    "section": "Submitted Presentations",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/6q09331v",
    "frozenauthors": [
        {
            "first_name": "Baruch",
            "middle_name": "",
            "last_name": "Schwarz",
            "name_suffix": "",
            "institution": "Hebrew University",
            "department": ""
        },
        {
            "first_name": "Mitchell",
            "middle_name": "J.",
            "last_name": "Nathan",
            "name_suffix": "",
            "institution": "University of Pittsburgh",
            "department": ""
        }
    ],
    "date_submitted": null,
    "date_accepted": null,
    "date_published": "1993-01-02T00:00:00+06:00",
    "render_galley": null,
    "galleys": [
        {
            "label": "PDF",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/cognitivesciencesociety/article/31771/galley/22839/download/"
        }
    ]
}