The Pedagogy of AI Mistakes: Fostering Higher-Order Thinking

As generative AI becomes increasingly integrated into higher education, its frequent errors and hallucinations, often seen as limitations, offer a unique pedagogical opportunity. By framing AI as a ``learning companion'' whose imperfect outputs prompt analysis, evaluation, and reflection, we argue that instructors can engage students in the fundamental processes of higher-order thinking. This paper presents a design-oriented study in which an AI-integrated syllabus in a \textit{database design} course deliberately leverages AI's limitations to foster critical thinking and higher-order cognitive skills aligned with Bloom's taxonomy of learning. Using a mixed-methods approach, we examine how structured interaction with AI-generated errors supports metacognitive engagement, reinforces disciplinary rigor, and relates to students' perceived AI literacy and subject-matter competency.