Large language models (LLMs) are rapidly transforming knowledge work by improving the quality and efficiency of tasks such as writing, coding, and data analysis. However, their growing use in education has exposed a learning-performance paradox: while they can enhance short-term task performance, they may also undermine genuine learning, including cognitive growth, knowledge transfer, and metacognitive development. This paper addresses the question of how artificial intelligence should be designed and used to support learning rather than merely improve immediate outputs. We introduce the concept of AI learning companions, defined as adaptive, pedagogically informed, LLM-powered agents designed for integration into learning environments. We propose a framework for their design built on three interrelated foundations: a pedagogical foundation focused on how students learn with AI, an adaptive foundation focused on how AI learns about students, and a responsible design foundation ensuring systems remain transparent, accountable, inclusive, and secure. The framework is illustrated through five case studies spanning diverse educational contexts, levels, and tool designs, revealing both the promise and current limitations of existing tools. We conclude that there is a necessary shift away from LLMs designed for task-oriented performance, and beyond simply prompting them to act as tutors, toward deliberately developed AI learning companions that are pedagogically sound, adapt to their learners, and foster durable understanding, metacognitive growth, and learner agency.

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