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{
    "pk": 49482,
    "title": "Towards a curriculum for neural networks to simulate symbolic arithmetic",
    "subtitle": null,
    "abstract": "Understanding and operating on multi-digit numbers is a critical step in the development of mathematical skills and concepts. Empirical and computational modeling evidence suggests that multi-digit numbers are processed decomposed into units, tens, hundreds, etc. for magnitude comparison. Yet, there is currently no computational model to simulate multi-digit number arithmetic. Accordingly, we developed a neural network model with three interconnected modules reflecting single-digit additions, recognition of a carry-over, and decision-making. We then compared model performance after following two training curricula: i) a \\textit{ step-by-step} curriculum, where single-digit addition are trained before progressing to multi-digit problems and ii) an \\textit{all-at-once} curriculum, where all modules of the model were trained simultaneously. Our results indicated that only the \\textit{step-by-step} curriculum made the model learn multi-digit addition successfully as reflected by replicating empirical effects of carry-over and problem size. These findings highlight the importance of structured, incremental learning in both cognitive modeling and education.",
    "language": "eng",
    "license": {
        "name": "",
        "short_name": "",
        "text": null,
        "url": ""
    },
    "keywords": [
        {
            "word": "Education; Psychology; Learning; Computational Modeling; Neural Networks"
        }
    ],
    "section": "Papers with Poster Presentation",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/5dt3d93g",
    "frozenauthors": [
        {
            "first_name": "Samuel",
            "middle_name": "",
            "last_name": "Lozano",
            "name_suffix": "",
            "institution": "Complutense University of Madrid",
            "department": ""
        },
        {
            "first_name": "Markus",
            "middle_name": "",
            "last_name": "Spitzer",
            "name_suffix": "",
            "institution": "Martin-Luther University, Halle-Wittenberg",
            "department": ""
        },
        {
            "first_name": "Younes",
            "middle_name": "",
            "last_name": "Strittmatter",
            "name_suffix": "",
            "institution": "Princeton University",
            "department": ""
        },
        {
            "first_name": "Korbinian",
            "middle_name": "",
            "last_name": "Moeller",
            "name_suffix": "",
            "institution": "Loughborough University",
            "department": ""
        },
        {
            "first_name": "Miguel",
            "middle_name": "",
            "last_name": "Ruiz-Garcia",
            "name_suffix": "",
            "institution": "Complutense University de Madrid",
            "department": ""
        }
    ],
    "date_submitted": null,
    "date_accepted": null,
    "date_published": "2025-01-01T18:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "PDF",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/cognitivesciencesociety/article/49482/galley/37444/download/"
        }
    ]
}