Second language learners benefit from exposure to level-appropriate grammar in interactive language use. While prompted frontier language models can usually produce target grammar structures, less resource-intensive models that can be run on device often fail in this task. We use sequential Monte Carlo (SMC) to steer dialogue turn generation in small lan- language models toward target grammar constructions from an expert-developed pedagogical resource. With a minimal set of hand-coded potential functions, SMC achieves near-perfect coverage of target grammar, enabling small models to outperform state-of-the-art results from models 140 times larger.
We also use code synthesis with frontier models to generate new potentials, showing that our method scales to hundreds of target grammar skills with no need for additional training or supervised data.