How do LLMs decide what to teach next: by reasoning about a learner's knowledge, or by using simpler rules of thumb? We test this in a controlled task previously used to study human teaching strategies. On each trial, a teacher LLM sees a hypothetical learner's trajectory through a reward-annotated directed graph and must reveal a single edge so the learner would choose a better path if they replanned. We run a range of LLMs as simulated teachers and fit their trial-by-trial choices with the same cognitive models used for humans: a Bayes-Optimal teacher that infers which transitions the learner is missing (inverse planning), weaker Bayesian variants, heuristic baselines (e.g., reward based), and non-mentalizing utility models. In a baseline experiment matched to the stimuli presented to human subjects, most LLMs perform well, show little change in strategy over trials, and their graph-by-graph performance is similar to that of humans. Model comparison (BIC) shows that Bayes-Optimal teaching best explains most models' choices. When given a scaffolding intervention, models follow auxiliary inference- or reward-focused prompts, but these scaffolds do not reliably improve later teaching on heuristic-incongruent test graphs and can sometimes reduce performance. Overall, cognitive model fits provide insight into LLM tutoring policies and show that prompt compliance does not guarantee better teaching decisions.