Machine-Verifiable Item Models for Geometry Diagram Generation

Mei Chen; Gordon Stein

Machine-Verifiable Item Models for Geometry Diagram Generation

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Abstract

Geometry item creation is often slow, as every figure must be checked by hand. AI can draw figures, but they often look right yet are subtly wrong. We propose item generation where a LLM writes structured constructions and a geometry engine builds, checks, and scores diagrams automatically.

Anthology ID:: 2026.aimecon-main.75
Volume:: Proceedings of the Artificial Intelligence in Measurement and Education Conference (AIME-Con): Full Papers
Month:: October
Year:: 2026
Address:: Wyndham Grand Pittsburgh Downtown, Pittsburgh, Pennsylvania, United States
Editors:: Joshua Wilson, Christopher Ormerod, Magdalen Beiting-Parrish
Venue:: AIME-Con
SIG:
Publisher:: National Council on Measurement in Education (NCME)
Note:
Pages:: 666–672
Language:
URL:: https://aclanthology.org/2026.aimecon-main.75/
DOI:
Bibkey:
Cite (ACL):: Mei Chen and Gordon Stein. 2026. Machine-Verifiable Item Models for Geometry Diagram Generation. In Proceedings of the Artificial Intelligence in Measurement and Education Conference (AIME-Con): Full Papers, pages 666–672, Wyndham Grand Pittsburgh Downtown, Pittsburgh, Pennsylvania, United States. National Council on Measurement in Education (NCME).
Cite (Informal):: Machine-Verifiable Item Models for Geometry Diagram Generation (Chen & Stein, AIME-Con 2026)
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PDF:: https://aclanthology.org/2026.aimecon-main.75.pdf

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@inproceedings{chen-stein-2026-machine,
    title = "Machine-Verifiable Item Models for Geometry Diagram Generation",
    author = "Chen, Mei  and
      Stein, Gordon",
    editor = "Wilson, Joshua  and
      Ormerod, Christopher  and
      Beiting-Parrish, Magdalen",
    booktitle = "Proceedings of the Artificial Intelligence in Measurement and Education Conference ({AIME}-Con): Full Papers",
    month = oct,
    year = "2026",
    address = "Wyndham Grand Pittsburgh Downtown, Pittsburgh, Pennsylvania, United States",
    publisher = "National Council on Measurement in Education (NCME)",
    url = "https://aclanthology.org/2026.aimecon-main.75/",
    pages = "666--672",
    ISBN = "979-8-9983004-0-0",
    abstract = "Geometry item creation is often slow, as every figure must be checked by hand. AI can draw figures, but they often look right yet are subtly wrong. We propose item generation where a LLM writes structured constructions and a geometry engine builds, checks, and scores diagrams automatically."
}

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%0 Conference Proceedings
%T Machine-Verifiable Item Models for Geometry Diagram Generation
%A Chen, Mei
%A Stein, Gordon
%Y Wilson, Joshua
%Y Ormerod, Christopher
%Y Beiting-Parrish, Magdalen
%S Proceedings of the Artificial Intelligence in Measurement and Education Conference (AIME-Con): Full Papers
%D 2026
%8 October
%I National Council on Measurement in Education (NCME)
%C Wyndham Grand Pittsburgh Downtown, Pittsburgh, Pennsylvania, United States
%@ 979-8-9983004-0-0
%F chen-stein-2026-machine
%X Geometry item creation is often slow, as every figure must be checked by hand. AI can draw figures, but they often look right yet are subtly wrong. We propose item generation where a LLM writes structured constructions and a geometry engine builds, checks, and scores diagrams automatically.
%U https://aclanthology.org/2026.aimecon-main.75/
%P 666-672

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Markdown (Informal)

[Machine-Verifiable Item Models for Geometry Diagram Generation](https://aclanthology.org/2026.aimecon-main.75/) (Chen & Stein, AIME-Con 2026)

Machine-Verifiable Item Models for Geometry Diagram Generation (Chen & Stein, AIME-Con 2026)

ACL

Mei Chen and Gordon Stein. 2026. Machine-Verifiable Item Models for Geometry Diagram Generation. In Proceedings of the Artificial Intelligence in Measurement and Education Conference (AIME-Con): Full Papers, pages 666–672, Wyndham Grand Pittsburgh Downtown, Pittsburgh, Pennsylvania, United States. National Council on Measurement in Education (NCME).