# Taxonomy-Targeted Error Generation for Quantitative Reasoning

arXiv: https://arxiv.org/abs/2605.29007 · HTML: https://mlsanity.com/paper/2605.29007/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 16 of its 42 references that are in the map.
- First posted on arXiv 27 May 2026.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 16 of 16)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [Measuring Coding Challenge Competence With APPS](https://mlsanity.com/paper/2105.09938/) (2021)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [WizardCoder: Empowering Code Large Language Models with Evol-Instruct](https://mlsanity.com/paper/2306.08568/) (2023)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [SciBench: Evaluating College-Level Scientific Problem-Solving Abilities of Large Language Models](https://mlsanity.com/paper/2307.10635/) (2023)
- [TheoremQA: A Theorem-driven Question Answering dataset](https://mlsanity.com/paper/2305.12524/) (2023)
- [Learning to Make MISTAKEs: Modeling Incorrect Student Thinking And Key Errors](https://mlsanity.com/paper/2510.11502/) (2025)
- [LLM-based Cognitive Models of Students with Misconceptions](https://mlsanity.com/paper/2410.12294/) (2024)
- [Error Classification of Large Language Models on Math Word Problems: A Dynamically Adaptive Framework](https://mlsanity.com/paper/2501.15581/) (2025)
- [A Benchmark for Math Misconceptions: Bridging Gaps in Middle School Algebra with AI-Supported Instruction](https://mlsanity.com/paper/2412.03765/) (2024)
- [Can LLMs Identify Gaps and Misconceptions in Students' Code Explanations?](https://mlsanity.com/paper/2501.10365/) (2024)
- [Can LLMs Model Incorrect Student Reasoning? A Case Study on Distractor Generation](https://mlsanity.com/paper/2603.15547/) (2026)

## Abstract (arXiv)

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.