Taxonomy-Targeted Error Generation for Quantitative Reasoning

Personalized tutoring, teacher preparation, and education research can benefit from worked errors annotated by the mechanisms that produced them. Authentic student errors with such cognitive labels are costly to collect and share, motivating the study of whether LLMs can generate taxonomy-targeted synthetic errors as complementary candidate material. We present a task-specific framework that generates errors targeted to a five-class Bloom-informed student-error taxonomy. A Generation Agent (GA) drafts a candidate erroneous solution conditioned on a target class, and an Examination Agent (EA) judges whether the draft is incorrect and class-consistent. The framework yields a reusable recipe for building class-stratified synthetic error datasets where authentic student corpora are unavailable. As a secondary diagnostic, targeted error generation is substantially harder than free-form incorrect-answer generation, and answer-grounding contributes more than expanded examples or external textbook content.