Agreement Is Not Validity: Cross-Model LLM Consensus in Diagnosing Student Failure Modes in K-12 Math Tutoring Dialogue

Abstract:In K-12 mathematics tutoring, student-tutor dialogue provides rich evidence of learners' problem-solving processes and sources of difficulty. Learning analytics research increasingly relies on large language models (LLMs) to extract such information from dialogue for a variety of downstream tasks, including knowledge tracing, behavioral modeling, and diagnosis of student reasoning errors. However, the validity of these model-generated interpretations remains insufficiently understood. In this exploratory study, we examine the validity of LLM classifications of five student failure modes in mathematics tutoring dialogue using an operational diagnostic codebook: uncertainty, misattribution, operator selection, conceptual gap, and procedural slip. Across models, human-LLM agreement was moderate (kappa = .524-.597), while cross-model agreement was substantially higher (kappa = .755-.781; alpha = .769). These findings show that cross-model agreement can create a misleading appearance of correctness, challenging the assumption that consensus among LLMs constitutes evidence of valid learner interpretation. For learning analytics, the implication is clear: scalable labeling is useful only if the inferred constructs are valid, and model consensus cannot substitute for independent evidence of that validity.

Submitted to LAK27 as a short paper. Currently under review

Computation and Language (cs.CL)

arXiv:2610.08703 [cs.CL]

(or arXiv:2610.08703v1 [cs.CL] for this version)

https://doi.org/10.48550/arXiv.2610.08703 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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