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Feedback on student answers and even during intermediate steps in theirsolutions to open-ended questions is an important element in math education.Such feedback can help students correct their errors and ultimately lead toimproved learning outcomes. Most existing approaches for automated studentsolution analysis and feedback require manually constructing cognitive modelsand anticipating student errors for each question. This process requiressignificant human effort and does not scale to most questions used in homeworkand practices that do not come with this information. In this paper, we analyzestudents' step-by-step solution processes to equation solving questions in anattempt to scale up error diagnostics and feedback mechanisms developed for asmall number of questions to a much larger number of questions. Leveraging arecent math expression encoding method, we represent each math operationapplied in solution steps as a transition in the math embedding vector space.We use a dataset that contains student solution steps in the Cognitive Tutorsystem to learn implicit and explicit representations of math operations. Weexplore whether these representations can i) identify math operations a studentintends to perform in each solution step, regardless of whether they did itcorrectly or not, and ii) select the appropriate feedback type for incorrectsteps. Experimental results show that our learned math operationrepresentations generalize well across different data distributions.

Math Operation Embeddings for Open-ended Solution Analysis and Feedback