Successful Human-Robot Teaching assumes alignment between robot processing needs and human teaching intent. To better understand this alignment, this work seeks to uncover the underlying logic that humans intuitively apply when teaching. Through an exploratory, bottom-up study with N=34, participants observing two distinct robot Reinforcement Learning (RL) scenarios, we analyze 204 intuitive teaching responses across early, middle, and late learning phases. Results reveal that teaching decisions consist of a nuanced, interconnected network of Triggers (situational catalysts), Objectives (subjective teaching targets), Signals (communicative acts), and Strategies (high-level governance) in which teachers spontaneously adopt diverse roles, acting as coaches, engineers, or designers and prioritize different objectives. Based on these results, we introduce the TOSS Framework, which conceptualizes Human-Robot teaching as a procedural loop between robot behavior and human teaching actions, in which human teaching decisions are modeled as Trigger-Signal responses modulated by teaching Objectives and Strategies. It provides future research with an openly accessible dataset and a theoretical foundation for a) understanding teaching decisions and b) simulating realistic oracles as well as c) designing human-centered teaching settings and novel robot learning algorithms that go beyond the constraints of current robot learning settings.

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