Beyond Accuracy: Alignment and Error Detection across Languages in the Bi-GSM8K Math-Teaching Benchmark

Recent advancements in LLMs have significantly improved mathematical problem-solving, with models like GPT-4 achieving human-level performance. However, proficiently solving mathematical problems differs fundamentally from effectively teaching mathematics. To bridge this gap, we introduce the Bi-GSM8K benchmark, a bilingual English-Korean dataset enriched with teacher solutions, student solutions, and annotations marking students’ initial errors. This dataset is designed to evaluate two core capabilities of LLMs: (1) measuring similarity between student and teacher solutions, and (2) identifying the initial error point in student solutions. Our method achieves high agreement with human judgments, with Pearson 0.89 and Spearman 0.88 on English, and Pearson 0.89 and Spearman 0.87 on Korean. It also offers significantly lower latency and resource usage than commercial APIs, demonstrating strong computational efficiency. In the error detection task, open-source models achieved approximately 86% accuracy, with performance within 10% points of commercial LLMs API, suggesting strong practical potential. Our key contributions include the open-source release of Bi-GSM8K, novel evaluation metrics, and comparative analyses of LLM performance across languages.