Gabriel Poesia

Assessing Mathematics Misunderstandings via Bayesian Inverse Planning (@ Cognitive Science 2020)

Anna N. Rafferty, Rachel A. Jansen, Thomas L. Griffiths


This paper describes a probabilistic model of how students go about solving algebra problems step-by-step. They encode students' ability to successfully apply algebraic operations on equations as a latent vector $\theta$. Then, their model specifies $p(D|\theta)$: how likely is the student to arrive at equation $D$ (say, from the previous step where they had equation $e$) given that their ability is $\theta$. Given this model, they apply inverse planning to obtain $p(\theta|D)$ - given the observations of what a student did, they estimate their ability $\theta$.