Small language models (SLMs) are increasingly proposed for educational use because they promise lower cost, offline deployment, and stronger data privacy. We report an exploratory evaluation of three sub-2B-parameter models on example-based decimal-arithmetic tutoring. Across structured interactions, all three produced fluent, confident output that masked unstable pedagogy and frequent mathematical errors even on elementary decimal addition and place-value tasks. Building on these observations, we describe an emerging interaction-based measurement framework intended to support more defensible readiness decisions about SLMs as math tutors.

This study evaluates whether three locally deployed small language models (LLaMA-3.2-1B, Qwen-2.5-0.5B, and Gemma-3-1B) can implement Socratic tutoring in Grade 6–8 mathematics. Using a rubric-based protocol across 72 sessions, results show that all models struggled to sustain guided inquiry, with Gemma performing best overall.