MalruleLib: 大规模可执行的错误推理与步骤追踪用于数学学生思维建模
MalruleLib: Large-Scale Executable Misconception Reasoning with Step Traces for Modeling Student Thinking in Mathematics
AI总结：
MalruleLib通过可执行的错误推理和步骤追踪，建模数学学生思维，实现跨模板的误解预测与反馈。
摘要：
数学学习中的错误往往是系统性的：学习者应用了一种连贯但错误的程序，并在不同情境中重复使用。我们介绍了MalruleLib，一个以学习科学为基础的框架，将记录的误解转化为可执行的程序，基于67个学习科学和数学教育来源，并生成与错误规则一致的学生工作的逐步追踪。我们正式将一个核心学生建模问题定义为Malrule推理准确性（MRA）：从一个完成的错误中推断出误解，并预测学生在跨模板重新表述下的下一个答案。在九种语言模型（4B-120B）上，准确性从直接问题解决的66%下降到跨模板误解预测的40%。MalruleLib编码了101个错误规则，覆盖498个参数化问题模板，并为正确推理和错误规则一致的学生推理生成双路径追踪。由于错误规则是可执行的，而模板是可参数化的，MalruleLib可以生成超过一百万种实例，从而实现可扩展的监督和受控评估。使用MalruleLib，我们观察到跨模板退化率为10-21%，而提供学生步骤追踪提高了预测的准确性3-15%。我们发布MalruleLib作为教育AI的基础设施，用于在不同情境中建模学生程序，从而实现诊断和反馈，以针对潜在的误解。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
