We propose a new way to assess certain short constructed responses to mathematics items. Our approach uses a pipeline that identifies the key values specified by the student in their response. This allows us to determine the correctness of the response, as well as identify any misconceptions. The information from the value identification pipeline can then be used to provide feedback to the teacher and student. The value identification pipeline consists of two fine-tuned language models. The first model determines if a value is implicit in the student response. The second model identifies where in the response the key value is specified. We consider both a generic model that can be used for any prompt and value, as well as models that are specific to each prompt and value. The value identification pipeline is a more accurate and informative way to assess short constructed responses than traditional rubric-based scoring. It can be used to provide more targeted feedback to students, which can help them improve their understanding of mathematics.

翻译：我们提出了一种评估数学题中特定简答题答案的新方法。该方法采用了一个流水线，用于识别学生答案中指定的关键数值。这使得我们能够判断答案的正确性，并识别出任何误解。随后，来自数值识别流水线中的信息可用于为教师和学生提供反馈。该数值识别流水线由两个微调的语言模型组成：第一个模型判断答案中是否存在隐式数值，第二个模型则识别关键数值在答案中的具体位置。我们既考虑了适用于任何问题及数值的通用模型，也考虑了针对特定问题及数值的专用模型。与传统基于评分标准的评估相比，该数值识别流水线是一种更准确且信息更丰富的简答题评估方式，可用于为学生提供更具针对性的反馈，从而帮助他们加深对数学的理解。