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

TL;DR

This paper presents a benchmark dataset of algebra misconceptions for AI educational tools, demonstrating its potential to diagnose student errors and support teacher training through AI integration.

Contribution

It introduces a new dataset of algebra misconceptions and evaluates AI models' effectiveness in identifying these misconceptions, highlighting the importance of human-AI collaboration.

Findings

LLMs achieved up to 83.9% precision and recall on misconceptions

Topics like ratios and proportions are particularly challenging for AI

Most educators see value in AI tools for diagnosing misconceptions

Abstract

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.