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The emergence of large-scale generative artificial intelligence (AI) presents significant challenges for effective human interaction. A cognitive gap exists between established, human-centric problem-solving frameworks and the ad-hoc, unstructured methods currently used to prompt these AI systems. This paper introduces and formalizes Aiming Thinking (AT), a metacognitive framework designed to bridge this gap. We propose a three-level hierarchy of cognition to position AT as a Level 3 metathinking that structures human-AI collaboration. The framework is operationalized through four distinct pillars—Targeting, Trajectory Design, Sequencing, and Calibration—and a practical library of 20 actionable interaction patterns. We demonstrate the universality and utility of the framework by systematically mapping nine established thinking frameworks (e.g., Computational Thinking, Design Thinking, Critical Thinking) to the principles and patterns of AT. The result is a formal, teachable methodology that moves beyond intuitive prompting to enable more deliberate, reliable, and sophisticated human-AI co-creation.