Large Language Models (LLMs) are highly effective at learning from extensive offline datasets but face significant challenges when acquiring complex knowledge dynamically in online scenarios. Traditional training paradigms, based on supervised or reinforcement learning, reflect a Piagetian view of independent discovery and rely on vast data and sparse feedback, limiting their adaptability. Inspired by Vygotsky’s sociocultural theory, this study investigates whether structured pedagogical interactions can enhance the efficiency of online learning in LLMs. We introduce a novel training method where a learner LLM engages in structured teaching dialogues with a knowledgeable LLM teacher to learn a synthetic taxonomy. The trained learner then applies this knowledge in downstream tasks, specifically tested in the challenging and well-known 20 Questions Game. These dialogues not only convey new external knowledge but also actively guide the learner in testing and refining its understanding. Our approach complements internal reasoning methods and prompt engineering: rather than relying on self-generated chains of thought or manually tailored inputs to refine the understanding and response to a single request, it introduces enriched and reusable task-specific knowledge through automatically structured pedagogical interactions. Unlike fine-tuning or few-shot learning, our method introduces novel domain knowledge without altering model weights or requiring explicit task examples. Our results show that the AI pedagogy strategy combining teacher explanations with learner-driven questions leads to better acquisition and application of knowledge compared to direct access to structured data. This highlights the potential of pedagogically guided interactions to enhance post-training learning and advance the development of more adaptable and human-aligned collaborative AI systems.