Human knowledge is inherently structured and interdependent: mastery of a concept requires prior mastery of its prerequisites, a principle formalized by Knowledge Space Theory (KST). While LLMs achieve strong performance on complex reasoning tasks, it remains unclear whether they exhibit coherent, human-like knowledge structure. We introduce a KST-grounded framework for evaluating LLM knowledge structure in mathematical reasoning, using it as a normative framework to analyze whether LLM behavior adheres to principled knowledge dependencies. Evaluating eight open- and closed-source LLMs against real human learners, we find that (1) LLMs do not adhere to human knowledge structure—they frequently violate knowledge dependencies and fail to leverage related knowledge provided in context to improve performance on dependent questions; (2) LLMs do not share a consistent knowledge structure among themselves, as reflected by low overlap in their knowledge distributions. Furthermore, these structural deficiencies remain largely invisible to accuracy-based and LLM-as-judge evaluations. Together, our results provide behavioral evidence that current LLMs knowledge does not follow a human-like structure.

Chatbots based on large language models offer cheap conversation practice opportunities for language learners. However, they are hard to control for linguistic forms that correspond to learners’ current needs, such as grammar. We control grammar in chatbot conversation practice by grounding a dialogue response generation model in a pedagogical repository of grammar skills. We also explore how this control helps learners to produce specific grammar. We comprehensively evaluate prompting, fine-tuning, and decoding strategies for grammar-controlled dialogue response generation. Strategically decoding Llama3 outperforms GPT-3.5 when tolerating minor response quality losses. Our simulation predicts grammar-controlled responses to support grammar acquisition adapted to learner proficiency. Existing language learning chatbots and research on second language acquisition benefit from these affordances. Code available on GitHub.

In this paper, we introduce a learning analytics framework to analyze the in-context learning (ICL) behavior of large language models (LLMs) through the lens of the Zone of Proximal Development (ZPD), an established theory in educational psychology. ZPD delineates the range of tasks a learner can accomplish with appropriate guidance but not yet independently. We adapt this concept to ICL, measuring the ZPD of LLMs based on model performance on individual examples in different settings. Furthermore, we propose an item response theory (IRT) model to predict the distribution of zones for LLMs. Our findings reveal a series of intricate and multifaceted behaviors of ICL, providing new insights into understanding and leveraging this technique. Finally, we demonstrate how our framework can enhance LLM in both inference and fine-tuning scenarios: (1) By predicting a model’s zone distribution, we selectively apply ICL to queries that are most likely to benefit from demonstrations, achieving a better balance between inference cost and performance; (2) We propose a human-like curriculum for fine-tuning, which prioritizes examples within the model’s ZPD. The curriculum results in improved performance, and we explain its effectiveness through an analysis of the training dynamics of LLMs.