Proceedings of the Annual Meeting of the Cognitive Science Society

Fraction arithmetic is a challenging topic for students. Past work has found that many errors can be accounted for by alimited number of malrules, reflecting both execution errors and incorrect strategies (Braithwaite, Pyke, and Siegler 2017).We develop an inverse planning model for fraction arithmetic that computes students’ affinity for particular malrulesbased on their problem solutions. Inverse planning models people’s choices when solving problems, and has been used tomodel data from solving algebraic equations and playing educational games. The output of the fraction arithmetic inverseplanning model gives a more detailed assessment of a student’s knowledge than the number of problems she answerscorrectly, and does not require human interpretation of students’ solutions. Applying the model to the two datasets inBraithwaite et al. (2017) and inferring tendencies to use two specific malrules shows that its output is consistent withmanual annotations of students’ strategies.