The new transdisciplinary nature of industrial product design should be appropriately addressed by post-secondary institutions and engineering schools in their curricula to ensure high quality of engineering design education and its applicability to industrial demands. To achieve this, a new transdisciplinary teaching methodology is required. This paper presents the results of a pilot trial of a new transdisciplinary teaching approach to engineering design education based on Bloom's Taxonomy and a comparative analysis of the cognitive game task performed by both professors and fours groups of students to investigate the differences in their design thinking. The approach included the knowledge component in the form of a lecture, a cognitive game task developed to map the design thinking of engineers, and administration of a modified sample design problem. The knowledge components consisted of a guest lecture on transdisciplinary engineering design and disciplinary differences. The cognitive task involved the formation of design activities and their placement along a general design process. The modification of the sample design problem involved the application of action verbs of Bloom's Taxonomy to create guiding steps to guide students' thinking while solving the problem. The results revealed a strong relation between engineering design activity and cognitive mental activity in both students and professors. The course instructors who piloted the new approach provided positive feedback finding it to be a "useful element" for the introduction of transdisciplinarity as well as for students' reflection on their design thinking. In addition, the application of Bloom's Taxonomy in design problems suggested potential improvements in students' performance on design tasks. The results of this study are applicable for the development of engineering design courses and transdisciplinary projects.