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While computer and communication technologies have provided effective meansto scale up many aspects of education, the submission and grading ofassessments such as homework assignments and tests remains a weak link. In thispaper, we study the problem of automatically grading the kinds of open responsemathematical questions that figure prominently in STEM (science, technology,engineering, and mathematics) courses. Our data-driven framework formathematical language processing (MLP) leverages solution data from a largenumber of learners to evaluate the correctness of their solutions, assignpartial-credit scores, and provide feedback to each learner on the likelylocations of any errors. MLP takes inspiration from the success of naturallanguage processing for text data and comprises three main steps. First, weconvert each solution to an open response mathematical question into a seriesof numerical features. Second, we cluster the features from several solutionsto uncover the structures of correct, partially correct, and incorrectsolutions. We develop two different clustering approaches, one that leveragesgeneric clustering algorithms and one based on Bayesian nonparametrics. Third,we automatically grade the remaining (potentially large number of) solutionsbased on their assigned cluster and one instructor-provided grade per cluster.As a bonus, we can track the cluster assignment of each step of a multistepsolution and determine when it departs from a cluster of correct solutions,which enables us to indicate the likely locations of errors to learners. Wetest and validate MLP on real-world MOOC data to demonstrate how it cansubstantially reduce the human effort required in large-scale educationalplatforms.

Mathematical Language Processing: Automatic Grading and Feedback for Open Response Mathematical Questions