Figure 1 Interplay of engineering knowledge to produce technology.

Most engineering curricula correctly emphasize these components; however, the emphasis is usually discrete, creating a series of distinct, unconnected elements. Disconnects arise if one component is emphasized at the expense of the others. At the lowest level of a curriculum, disconnects are evident when students are unable to connect conceptual and operational knowledge. For example, given a function , virtually any sophomore-level engineering student will compute the derivative with no difficulty. Change the context, however, to: “Given the function , if x is changed by some infinitesimal amount, what is the approximate corresponding change in ?” and even good students may struggle. This is especially true if the question is asked in an engineering course and not a mathematics course. Regardless of the context, students directly associate concepts with the course label. Although the concept of the derivative was probably presented in the context of a rate of change in a mathematics course, probably even in the context of an engineering example, many students will view it purely as a mathematical operation, devoid of any physical or applied interpretation. This is partly because they have not mastered enough engineering science to appreciate the mathematical formulation of engineering concepts. Once the mathematics course is completed, operational knowledge is usually retained, to some degree. Conceptual knowledge evaporates—if it was ever present. Consequently, engineering students may not see a connection between the concepts of preparatory mathematics courses and engineering courses. They cannot appreciate that mathematics is the language for representing and manipulating engineering concepts in an operational form. The situation is exacerbated when sophomore-level engineering science courses focus on problem solution, i.e., operational knowledge, with minimal emphasis upon conceptual or integral knowledge. Students are shown how without understanding why, consequently they are unable to generalize to do beyond the scope of the assigned problems.
To illustrate these observations, consider assignments and examinations for a typical sophomore engineering science course. Good textbooks are designed to present concepts in textual passages coupled with example problems that display operational details in solution strategies and methods. Students often complete reading assignments with little comprehension of concepts, and little attention to examplesunless they are similar to assigned homework problems. Typical problems again emphasize solution techniques, and with enough examples good students can reproduce the steps to solve specific types of problems, with little understanding of the underlying physical principles. Examinations, typically two or three for the entire course, are patterned after the homework, emphasizing solution techniques. Students usually prepare for an examination, not by carefully reading the text to ensure comprehension but by working as many problems as possible, in the hope that the examination problems will be similar. Based on the criteria of the course, students may excel based solely on their operational knowledge with virtually no conceptual or integrated knowledge.
Conceptual and operational knowledge should both be emphasized at every level of the curriculum. Incorporating integral knowledge at every level is not imperative, however. For example, a “traditional” curriculum, generally reserves integral-knowledge emphasis for design and capstone courses. The prerequisite courses are designed to help students achieve proficiency with conceptual and operational knowledge before placing an emphasis upon synthesis and integration. Emphasizing integral knowledge throughout the curriculum, however, helps to eliminate disconnects, enriches the overall educational experience, and encourages students to develop an early “engineering identity.” This is the approach embraced in the AE 2000.