# A Benchmark for Math Misconceptions: Bridging Gaps in Middle School Algebra with AI-Supported Instruction

arXiv: https://arxiv.org/abs/2412.03765 · HTML: https://mlsanity.com/paper/2412.03765/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Dec 2024.

## Built on by (most cited first, 6 of 6)

- [Benchmarking the Pedagogical Knowledge of Large Language Models](https://mlsanity.com/paper/2506.18710/) (2025)
- [How well do Large Language Models Recognize Instructional Moves? Establishing Baselines for Foundation Models in Educational Discourse](https://mlsanity.com/paper/2512.19903/) (2025)
- [V-Math: An Agentic Approach to the Vietnamese National High School Graduation Mathematics Exams](https://mlsanity.com/paper/2509.12251/) (2025)
- [Can the current trends of AI handle a full course of mathematics?](https://mlsanity.com/paper/2507.21664/) (2025)
- [Cognitive-Uncertainty Guided Knowledge Distillation for Accurate Classification of Student Misconceptions](https://mlsanity.com/paper/2605.14752/) (2026)
- [Taxonomy-Targeted Error Generation for Quantitative Reasoning](https://mlsanity.com/paper/2605.29007/) (2026)

## Abstract (arXiv)

This study introduces an evaluation benchmark for middle school algebra to be used in artificial intelligence(AI) based educational platforms. The goal is to support the design of AI systems that can enhance learner conceptual understanding of algebra by taking into account their current level of algebra comprehension. The data set comprises 55 misconceptions about algebra, common errors, and 220 diagnostic examples identified in previous peer-reviewed studies. We provide an example application using a large language model, observing a range of precision and recall scores depending on the topic and experimental setup that reaches 83.9% when including educator feedback and restricting it by topic. We found that topics such as ratios and proportions prove as difficult for LLMs as they are for students. We included a human assessment of LLMs results and feedback from five middle school math educators on the clarity and occurrence of misconceptions in the dataset and the potential use of AI in conjunction with the dataset. Most educators (80% or more) indicated that they encounter these misconceptions among their students, suggesting the relevance of the data set to teaching middle school algebra. Despite varying familiarity with AI tools, four out of five educators expressed interest in using the data set with AI to diagnose student misconceptions or train teachers. The results emphasize the importance of topic-constrained testing, the need for multimodal approaches, and the relevance of human expertise to gain practical insights when using AI for human learning.