Feedback on student answers and even during intermediate steps in their solutions to open-ended questions is an important element in math education. Such feedback can help students correct their errors and ultimately lead to improved learning outcomes. Most existing approaches for automated student solution analysis and feedback require manually constructing cognitive models and anticipating student errors for each question. This process requires significant human effort and does not scale to most questions used in homework and practices that do not come with this information. In this paper, we analyze students' step-by-step solution processes to equation solving questions in an attempt to scale up error diagnostics and feedback mechanisms developed for a small number of questions to a much larger number of questions. Leveraging a recent math expression encoding method, we represent each math operation applied in solution steps as a transition in the math embedding vector space. We use a dataset that contains student solution steps in the Cognitive Tutor system to learn implicit and explicit representations of math operations. We explore whether these representations can i) identify math operations a student intends to perform in each solution step, regardless of whether they did it correctly or not, and ii) select the appropriate feedback type for incorrect steps. Experimental results show that our learned math operation representations generalize well across different data distributions.
翻译:关于学生答案的反馈,甚至是在解决开放式问题的中间步骤中,学生对学生答案的反馈,是数学教育中的一个重要因素。这种反馈可以帮助学生纠正错误,最终导致学习结果的改善。学生自动化解决方案分析和反馈的大多数现有办法要求人工构建认知模型,并预测每个问题的学生错误。这一过程需要大量的人类努力,而不是与在家庭作业中使用的大多数问题和与这一信息无关的做法相比。在本文件中,我们分析学生逐步解决问题的解决方案程序,以便扩大为少数问题而开发的错误诊断和反馈机制,从而扩大为更多问题而开发的少量错误诊断和反馈机制。利用最近的数学表达编码方法,我们代表每个在解决方案步骤中应用的数学操作,作为数学嵌入矢量空间的过渡。我们使用包含学生解决方案步骤的数据集来学习数学操作的隐含和清晰的表达方式。我们探讨这些表达方式是否可以一)确定学生在每一个解决方案步骤中打算执行的数学操作,而不管他们是否正确,以及二)选择适当的反馈类型,用于不正确的数学操作。我们用不同的数学实验结果显示我们学习的数学操作。