Vision-language-action (VLA) and world-action models typically absorb unfamiliar manipulation tasks through additional robot data collection and policy optimization. This recurring retraining burden slows the acquisition of new behavior. We present Teach-and-Grow Learning (TGL), a training-free architecture that turns a few successful demonstrations into reusable robot skills. Task acquisition requires no gradient updates, fine-tuning, or reinforcement learning: pretrained model weights remain fixed as the robot expands its explicit knowledge. Teaching is an accelerator, not a precondition, because the agent can also drive the robot directly, and demonstrations mainly improve reliability. Our implementation uses OpenAI GPT-6 Astra for multimodal reasoning and Codex to connect the agent to robot tools. The agent identifies subgoals shared across demonstrations, expresses them as closed-loop Skill Blocks, and grounds each block in the current scene. Physical feedback guides the next action and any recovery. Verified behaviors enter a persistent Skill Library; Experience Memory records the conditions and repairs that inform later decisions. TGL reaches 99.9% mean success on four LIBERO suites and 92.4% on seven LIBERO-Plus perturbation categories. Controlled studies show that taught blocks persist and improve related-task execution under the same model weights and executors. We further formulate a scaling hypothesis that relates effective reusable experience to falling future-task error and teaching demand. Code and demonstration videos: https://tgl.changnie.top

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