Interpretability Framework for LLMs in Undergraduate Calculus

TL;DR

This paper presents a new interpretability framework for analyzing LLM-generated solutions in undergraduate calculus, focusing on reasoning processes, stability, and conceptual correctness, to improve AI transparency in math education.

Contribution

It introduces a structured, quantitative approach combining reasoning flow extraction, semantic decomposition, and prompt ablation to diagnose LLM reasoning in mathematics education.

Findings

LLMs often produce fluent but conceptually flawed solutions

Reasoning patterns are sensitive to prompt phrasing and input variations

The framework enables fine-grained diagnosis of reasoning failures

Abstract

Large Language Models (LLMs) are increasingly being used in education, yet their correctness alone does not capture the quality, reliability, or pedagogical validity of their problem-solving behavior, especially in mathematics, where multistep logic, symbolic reasoning, and conceptual clarity are critical. Conventional evaluation methods largely focus on final answer accuracy and overlook the reasoning process. To address this gap, we introduce a novel interpretability framework for analyzing LLM-generated solutions using undergraduate calculus problems as a representative domain. Our approach combines reasoning flow extraction and decomposing solutions into semantically labeled operations and concepts with prompt ablation analysis to assess input salience and output stability. Using structured metrics such as reasoning complexity, phrase sensitivity, and robustness, we evaluated the model behavior on real Calculus I to III university exams. Our findings revealed that LLMs often produce syntactically fluent yet conceptually flawed solutions, with reasoning patterns sensitive to prompt phrasing and input variation. This framework enables fine-grained diagnosis of reasoning failures, supports curriculum alignment, and informs the design of interpretable AI-assisted feedback tools. This is the first study to offer a structured, quantitative, and pedagogically grounded framework for interpreting LLM reasoning in mathematics education, laying the foundation for the transparent and responsible deployment of AI in STEM learning environments.