{
  "abstract": "This paper presents a conceptual, cognitive-constructivist model for teaching the half-derivative. The model starts from a student's question and frames it as the problem of generalizing the familiar operation of differentiation. On a suitably chosen space of monomials, under the assumptions of linearity and of lowering the exponent by one half, the requirement that the operator applied twice give the ordinary derivative produces a recurrence for the coefficients. The freedom of normalization becomes visible, and an additional convention yields a formula compatible with the monomial rule of the Riemann-Liouville half-derivative. The domain of the operator and its relation to the Riemann-Liouville and Caputo operators are treated separately. The mathematical results rest on the author's earlier preprints; the contribution of this paper is their transformation into an instructional pathway organized in phases, with diagnostic questions, an analysis of typical errors, and comparative problems. The model is a design proposal: its effectiveness has not yet been established by systematic empirical research. The interactive Socratic implementation and the detailed diagnostics are the subject of Part II.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18932",
  "author_total": 1,
  "authors": [
    {
      "name": "Davit Kapanadze"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b7gt3v8d02apc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18932",
  "fulltext_url": null,
  "id": "b7gt3v8d02apc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18932",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.HO"
    ],
    [
      "openalex",
      "3304|Mathematics Education and Teaching Techniques"
    ]
  ],
  "openalex": "W7222254060",
  "pdf_url": "https://arxiv.org/pdf/2610.18932",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b7gt3v8d02apc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.18932",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18932"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.HO",
      "subfield": "general"
    }
  ],
  "title": "From a Student's Question to the Half-Derivative: A Constructivist Teaching Model - Part I",
  "title_text": "From a Student's Question to the Half-Derivative: A Constructivist Teaching Model - Part I",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/b7gt3v8d02apc",
  "venue": "arXiv",
  "versions": []
}