The study investigates the use of LLMs as teachable agents for programming education. It introduces AlgoBo, an LLM-based tutee chatbot, and TeachYou, an LBT environment for algorithm learning. The Reflect-Respond pipeline restrains LLMs' knowledge to initiate "why" and "how" questions for effective knowledge-building. Mode-shifting guides conversations through thought-provoking questions. The study confirms the effectiveness of the prompting pipeline in configuring AlgoBo's problem-solving performance. A user study with 40 algorithm novices shows that AlgoBo's questions led to knowledge-dense conversations. Design implications, cost-efficiency, and personalization of LLM-based teachable agents are discussed.
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