  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.
