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...without thinking about the implied knowledge. Because previous knowledge experience can facilitate the acquisition of knowledge, an approach to facilitate the learning process is to identify concepts that are familiar to the students as the basis for teaching new concepts. Applying the learning strategies exemplified in concept mapping, this approach focuses on adding links in the concept map. Additional links make it easier for students to learn and retain information (Clough and Kauffman, 1999).
Within the engineering curriculum, engineering economy educators have noted a lack of significant change in engineering economy courses and textbooks over many decades (Hartman, 1999), the need to reduce rote calculations (Eschenbach, 1999; Hartman, 1999), and the corresponding need to increase the attention to design and/or decision-making activities (Eschenbach, 1999; Hartman, 1999; Peterson, 1965). Instructional methods that reduce the time necessary for students to master the rote calculations allow for additional time to focus on design and decision-making. As in other engineering courses, technologies such as spreadsheets and computers have provided productivity improvements in the past. Surveys (Needy et al., 2000) have shown that a variety of traditional instructional methods are in current use. The focus of this article, however, is on an instructional approach that builds on the student's experience and knowledge to improve learning.
The remaining sections describe an approach to teaching engineering economy based on the concept of moments from statics and mechanics of materials and analytical results of this approach. Although the concept of moments is familiar to engineering students, the linkage between the moments concept and engineering cash flows is not demonstrated or articulated in modern engineering economy textbooks or publications. In 1990, Strong (1990) used the concept of moments to explain bond duration. In a follow-up commentary, Hayes (1993, p. 346) noted that principles of physics do not apply "to an abstract concept such as present worth. There is no corresponding financial principle to equilibrium in statics." However, this article demonstrates that equivalence can be thought of as the corresponding financial principle to equilibrium in statics. Preliminary results indicate that using the moments concept in teaching engineering economy provides for a more efficient utilization of credit hours.
ENVIRONMENT
The Department of Industrial and Systems Engineering at Tennessee Technological University offers two courses in engineering economy. Course outcomes for the three--credit hour course, ISE 3100, are presented in Table 1. Course outcomes for the two--credit hour course, ISE 3110, are outcomes a through e from Table 1.
The three-credit ISE 3100 is required for industrial engineering students and, until recently, for mechanical engineering students; it is an elective for electrical engineering students. The two-credit ISE 3110 is required for civil engineering and now mechanical engineering students. Although these students may opt to take the three-credit course, most of them enroll in the two-credit course. All students are in the same class, but the two-credit course meets for approximately two thirds of the semester. With the exception of industrial engineering students, most of the students in both courses are seniors. Of 271 students in nine sections taught over the past 6 years, 89% of the students had completed the statics course prior to taking the engineering economy course, and another 5.5% of students, mostly industrial engineering majors, were concurrently enrolled in statics and engineering economy. Electrical and computer engineering majors represented the majority of the remaining 5.5% who did not take statics before taking engineering economy.
The textbook in use at the time of this study was Engineering Economic Analysis, 8th and 9th editions, by Newnan et al. (2002, 2004). Chapters 3 and 4 of the text present calculations based on algebraic expressions for the relationships between present worth, future worth, or annual payments as a function of interest rate and number of compounding periods. For a basic equation with four parameters (e.g., P, A, F, i, or n), it is intuitive for engineering students that three of these parameters must be specified in order to solve for an unknown (i.e., one equation and one unknown). These problems may be solved without much thought about the implied knowledge.
After students are familiar with the basic calculations, equivalence is introduced. The concept is typically taught by presenting numerous applications of the definition. It is apparent that there is a different rate of learning and therefore ability to apply this concept. As students become familiar with equivalence, errors as well as the time needed to solve these problems decrease. Chapters 5 and 6 address the present worth and the annual uniform payment analysis, respectively. Chapters 7, 8, and 9 address other before-tax alternative selection methods.
Prior to the fall 2003 semester, a traditional approach had been used to teach the ISE 3100 and 3110 courses. However, beginning with the fall 2003 semester, chapters 3 through 9 were presented using concepts of moment equations from statics and chapters 5 and 6 were covered simultaneously and presented as extensions to the moment equations concept. The following sections detail the approach.
CONCEPTS OF MECHANICS
Moment equations may be developed by assuming clockwise as positive and recalling that a moment about a point is defined as the sum of the...
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