{"paper":{"title":"The Tutoring Effectiveness Index: Predicting LLM Math Tutor Quality from Four Conversation Signals","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CY","authors_text":"Shim Jaechang, Unggi Lee","submitted_at":"2026-05-28T23:55:33Z","abstract_excerpt":"Aligning large language models (LLMs) as math tutors typically demands costly reinforcement-learning (RL) training and external LLM judges. We ask whether a frozen model's internal reasoning signals can replace both. We propose the Tutoring Effectiveness Index (TEI), a training-free, judge-free four-signal index that combines a Schoenfeld-Verify keyword ratio, a math-step density, an ends-question rate, and a deep-reasoning gate from the Deep-Thinking Ratio (DTR) probe. Selecting from $N$ candidates with TEI (the TEI@$N$ rule) raises the improvement rate on pre-incorrect scenarios from $59.0\\%"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30666","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.30666/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}