Distributed Representation of Misconceptions

Tutoring systems deployed at scale present an opportunity to reinvigorate the study of how misconceptions or partial understanding develops in a wide range of STEM domains by connecting to critical pedagogical theories from the learning sciences by way of a distributed representation of the learner. Using answer sequence data from three Khan Academy exercises, we generate high-dimensional vector representations of incorrect student answers using a model of distributed representation more commonly applied to natural language. After clustering wrong answers in the learned vector space, we use these clusters as the basis for analysis of student misconceptions with a quantitative comparison to manual coding and a deeper qualitative discussion based on a constructivist framework. The result is a demonstration of how big data from conventional tutoring systems can act as a bridge to more critical pedagogies from the learning sciences via a distributed, connectionist model of student concept formation.

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