MalruleLib: Large-Scale Executable Misconception Reasoning with Step Traces for Modeling Student Thinking in Mathematics
Xinghe Chen OpenStax, Naiming Liu, Shashank Sonkar University of Central Florida
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.
尚无 AI 解读，展示原文摘要
Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表