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{
    "pk": 25824,
    "title": "Transitivity is Not Obvious: Probing Prerequisites for Learning",
    "subtitle": null,
    "abstract": "Empirical results from a fraction addition task reveal a\nsurprising gap in prior knowledge: difficulty applying the\ntransitive property of equality in a symbolic context. 13 out of\nthe 182 4th and 5th graders (7%) correctly applied the\ntransitive property of equality to identify the sum of two\nfractions in a step-by-step worked example. This difficulty\nwas robust to brief instruction on transitivity (after which\nperformance rose to 11%). Students’ demonstrated difficulty\nwith transitivity is surprising, especially because common\ninstructional techniques, such as worked examples, assume\nthat the learner understands this concept and where it applies.",
    "language": "eng",
    "license": {
        "name": "",
        "short_name": "",
        "text": null,
        "url": ""
    },
    "keywords": [
        {
            "word": "conceptual understanding; fraction addition;\nmathematical equality"
        }
    ],
    "section": "Papers",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/5vm450cr",
    "frozenauthors": [
        {
            "first_name": "Eliane",
            "middle_name": "Stampfer",
            "last_name": "Wiese",
            "name_suffix": "",
            "institution": "Carnegie Mellon University",
            "department": ""
        },
        {
            "first_name": "Rony",
            "middle_name": "",
            "last_name": "Patel",
            "name_suffix": "",
            "institution": "Carnegie Mellon University",
            "department": ""
        },
        {
            "first_name": "Jennifer",
            "middle_name": "K",
            "last_name": "Olsen",
            "name_suffix": "",
            "institution": "Carnegie Mellon University",
            "department": ""
        },
        {
            "first_name": "Kenneth",
            "middle_name": "R",
            "last_name": "Koedinger",
            "name_suffix": "",
            "institution": "Carnegie Mellon University",
            "department": ""
        }
    ],
    "date_submitted": null,
    "date_accepted": null,
    "date_published": "2015-01-01T18:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "PDF",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/cognitivesciencesociety/article/25824/galley/15448/download/"
        }
    ]
}