Rethinking LLM-Judged Helpfulness as a Pedagogy Signal: A Pre-Registered Audit Across Tutor Models

LLM tutoring poses a measurement problem: can a general-purpose helpfulness rubric distinguish direct answer-giving from pedagogical guidance? We audit this signal in a pre-registered study. Within each of three tutor bases, we compare conversational and pedagogical policies instantiated with the same underlying model and paired with one fixed weak simulated student. Deterministic detectors measure answer leakage and next-turn independent work. Claude Opus 4.8 is the frozen, condition-blind primary judge. After the Opus scores were fixed, GPT-5.6 Sol was prospectively specified for a post hoc robustness audit of the same 1,179 confirmatory answer-phase tutor turns under the frozen helpfulness and pedagogy rubrics. On the primary base under Opus, the policies do not differ significantly in helpfulness but are perfectly rank-separated under the pedagogy rubric (Cliff's $|δ|{=}0.10$ vs. $1.0$). Across the two judges, pedagogy contrasts retain their direction where detected, whereas the helpfulness ordering is judge-contingent, reversing between judges on two of three bases. In an Opus-only ablation, seven primary-base policies span $2.3$ points in mean judged pedagogy within a $0.25$-point band of mean judged helpfulness. Separately, answer-revealing turns are followed by less independent student work on every base, a result that is judge-invariant by construction. In this controlled setting, general-purpose helpfulness is not a reliable pedagogy signal. Tutor evaluation should pair pedagogy-targeted rubrics with deterministic process measures.

Arithmetic Pedagogy for Language Models

We investigate whether methods of human mathematics pedagogy can guide the training of language models toward arithmetic reasoning. Building on the GASING method -- an Indonesian pedagogy that solves basic arithmetic through a left-to-right procedure aligned with the causal order of token generation -- we operationalize each operation as a computational procedure whose execution trace is serialized into natural-language Chain-of-Thought (CoT) supervision. A small GPT-2 decoder (86M parameters) with a syllabic-agglutinative TOBA tokenizer for Indonesian is trained from scratch on this data using only a next-token prediction objective, without reinforcement learning or reward-based optimization. Monitoring training reveals three distinct learning phases, and mechanistic analyses -- attention-masking interventions on the CoT information graph, residual-stream probing, and logit-lens inspection -- show that the model first internalizes a procedural pathway and subsequently develops an associative, ``mental-arithmetic'' capacity that retrieves intermediate results without explicit step-by-step computation. The trained model reaches over 80% accuracy on held-out problems and attains competitive performance against substantially larger language models, indicating that targeted, pedagogically grounded training can yield strong and economical arithmetic capability at small scale.