<p>The growing emphasis on engineering education in K-12 STEM curricula highlights the importance of engineering design as a core component. International standards define engineering design thinking by identifying essential elements, while national documents and reports on K-12 education attempt to outline its diverse components. However, existing theoretical frameworks describe the key aspects of the engineering design process but have tended to overlook the theoretical mechanisms underlying it. To address this gap, this study introduces a cognitive based theoretical framework for engineering design thinking, the Inquiry for Engineering Design and Optimization (iEDO) framework. This framework emphasizes scientific thinking and science inquiry as the essential underlying cognitive based mechanism for modeling and integrating the engineering design process and its critical elements under a cohesive theoretical basis. Using the iEDO framework, we deconstructed and evaluated existing models of K-12 engineering design. Additionally, the iEDO-assessment framework was applied to analyze and adapt the Technology and Engineering Literacy (TEL) test items from the National Assessment of Educational Progress (NAEP). The adapted test items were administered to 100 Chinese high school students, yielding significant insights and results about the utility and validity of the iEDO based assessment. The iEDO framework establishes clear relationships among the elements of engineering design thinking and their roles within the design process. It provides practical pathways for assessing engineering design thinking and serves as a theoretical guide for advancing K-12 engineering education.</p>