Connection between mathematical and visual approaches in engineering classes

摘要

It is essential that engineering students develop both quantitative and qualitative understanding of engineering concepts and principles. Although accuracy and reliability in solving quantitative problems is necessary, a qualitative understanding is required in applying concepts and principles to real-world problems, especially to innovative or unconventional ones. It becomes questionable whether the students have developed the adequate understanding of engineering principles if the students are not able to neither understand what underlies quantitative problem-solving procedures nor interpret the solution in physical form. In 12 years of teaching, it was my most frustrating experience to see many bright students in my structures classes, capable of solving complicated quantitative problems, fail to answer on seemingly simple qualitative questions. Engineering students in my classes seemed to pay more attention to problem solving technique without being attentive to the underlying concepts. Traditional engineering textbooks and lectures may have been pushing students toward problem-solving more than toward conceptual understanding. When engineering principles are reduced to a series of calculation without apparent link to physical phenomena of particular interest, they become miserably boring subjects. The engineering students must actively engage in procreative mental activity coupled with interpretation of personal observation and experience in order to develop the genuine understanding of engineering concepts and theories that underlies real-world phenomena. But if engineering students remain as passive listeners in classes, such activity is rarely induced. In an effort to find balance and connection, and increase awareness of the interrelationship between quantitative and qualitative understanding in structures classes, a unique teaching methodology has been developed and used in the classes. The content, sequence and rationale are described in this paper in some detail.