Multiple-choice questions (MCQs) are commonly used across all levels of math
education since they can be deployed and graded at a large scale. A critical
component of MCQs is the distractors, i.e., incorrect answers crafted to
reflect student errors or misconceptions. Automatically generating them in math
MCQs, e.g., with large language models, has been challenging. In this work, we
propose a novel method to enhance the quality of generated distractors through
overgenerate-and-rank, training a ranking model to predict how likely
distractors are to be selected by real students. Experimental results on a
real-world dataset and human evaluation with math teachers show that our
ranking model increases alignment with human-authored distractors, although
human-authored ones are still preferred over generated ones.

通过过度生成和排名方法，我们提出了一种新的方法来提高生成干扰项的质量，训练一个排名模型来预测干扰项被真实学生选择的可能性。在真实数据集上的实验结果和与数学教师的人工评估显示，我们的排名模型与人工编写的干扰项的一致性增加，尽管人工编写的干扰项仍然优于生成的干扰项。

使用超生成与评级提升数学多项选择题自动生成的效果

Improving Automated Distractor Generation for Math Multiple-choice  Questions with Overgenerate-and-rank

Automated feedback as students answer open-ended math questions has
significant potential in improving learning outcomes at large scale. A key part
of automated feedback systems is an error classification component, which
identifies student errors and enables appropriate, predefined feedback to be
deployed. Most existing approaches to error classification use a rule-based
method, which has limited capacity to generalize. Existing data-driven methods
avoid these limitations but specifically require mathematical expressions in
student responses to be parsed into syntax trees. This requirement is itself a
limitation, since student responses are not always syntactically valid and
cannot be converted into trees. In this work, we introduce a flexible method
for error classification using pre-trained large language models. We
demonstrate that our method can outperform existing methods in algebra error
classification, and is able to classify a larger set of student responses.
Additionally, we analyze common classification errors made by our method and
discuss limitations of automated error classification.

本研究通过使用预训练的大型语言模型，提出了一种灵活的错误分类方法，可以对更多的学生回答的数学问题进行分类，并分析了该方法的常见分类错误和自动错误分类的局限性。