Automatic Diagnosis of Students' Misconceptions in K-8 Mathematics

K-8 mathematics students must learn many procedures, such as addition and subtraction. Students frequently learn "buggy'' variations of these procedures, which we ideally could identify automatically. This is challenging because there are many possible variations that reflect deep compositions of procedural thought. Existing approaches for K-8 math use manually specified variations which do not scale to new math algorithms or previously unseen misconceptions. Our system examines students' answers and infers how they incorrectly combine basic skills into complex procedures. We evaluate this approach on data from approximately 300 students. Our system replicates 86% of the answers that contain clear systematic mistakes (13%). Investigating further, we found 77% at least partially replicate a known misconception, with 53% matching exactly. We also present data from 29 participants showing that our system can demonstrate inferred incorrect procedures to an educator as successfully as a human expert.