In accordance with the progressive knowledge-to-ability transformation laws, a hierarchical learning model composed of cognitive layer, application layer, and design layer was created and applied to college computer teaching. This model was used to facilitate the deep learning among students through the association establishment, step-by-step understanding, and comprehensive application of new and old knowledge. In the teaching design process, the “5-problem” teaching, which centered on “student–problem–activity–resource,” was conducted and applied to the “Small Private Online Course (SPOC) + flipped classroom.” The teaching result was assessed using the proposed hierarchical classification method. Results demonstrate that the improved teaching model remarkably enhances the ability of noncomputer major students to solve the practical problems encountered in their specialties by virtue of computational thinking through the data analysis of evaluation results and students’ survey feedback. The students obviously speak more highly of the improved teaching model than the traditional blended teaching in the aspects of teaching content organization, learning effect, integration degree with the specialty and satisfaction. The degree of their participation in the flipped classroom reached as high as 90%.