@inproceedings{chen-etal-2026-malrulelib,
    title = "{M}alrule{L}ib: Large-Scale Executable Misconception Reasoning with Step Traces for Modeling Student Thinking in Mathematics",
    author = "Chen, Xinghe  and
      Liu, Naiming  and
      Sonkar, Shashank",
    editor = "Liakata, Maria  and
      Moreira, Viviane P.  and
      Zhang, Jiajun  and
      Jurgens, David",
    booktitle = "Proceedings of the 64th Annual Meeting of the {A}ssociation for {C}omputational {L}inguistics (Volume 1: Long Papers)",
    month = jul,
    year = "2026",
    address = "San Diego, California, United States",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/ingest-acl/2026.acl-long.690/",
    pages = "15112--15138",
    ISBN = "979-8-89176-390-6",
    abstract = "Student mistakes in mathematics are often systematic: a learner applies a coherent but wrong procedure and repeats it across contexts. We introduce MalruleLib, a learning-science-grounded framework that translates documented misconceptions into executable procedures, drawing on 67 learning-science and mathematics education sources, and generates step-by-step traces of malrule-consistent student work. We formalize a core student-modeling problem as Malrule Reasoning Accuracy (MRA): infer a misconception from one worked mistake and predict the student{'}s next answer under cross-template rephrasing. Across nine language models (4B - 120B), accuracy drops from 66{\%} on direct problem solving to 40{\%} on cross-template misconception prediction. MalruleLib encodes 101 malrules over 498 parameterized problem templates and produces paired dual-path traces for both correct reasoning and malrule-consistent student reasoning. Because malrules are executable and templates are parameterizable, MalruleLib can generate over one million instances, enabling scalable supervision and controlled evaluation. Using MalruleLib, we observe cross-template degradations of 10 - 21{\%}, while providing student step traces improves prediction by 3 - 15{\%}. We release MalruleLib as infrastructure for educational AI that models student procedures across contexts, enabling diagnosis and feedback that targets the underlying misconception."
}