Design of an international bridge program for engineering calculus

A large university in the southwest U.S. established a bridge program for incoming freshmen to increase success in engineering calculus and retention in engineering majors. The program was initially grant-funded but became institutionalized because of continued success. Participants in the program who were at high risk of failure in mathematics, based on the mathematics placement exam (MPE), performed as well in their first semester as their peers who had scored higher on the (MPE). The program was fully online, consisting of practice problems, quizzes, example videos, textbook, and required time with a live tutor (online). The original program spread the 36 hours of tutoring over six weeks, and the revised program compressed it into three weeks. The content of the program was used as a basis of a face-to-face bridge program at an engineering school in the western Asia. The same MPE and cut score were used at both campuses. However, the program was adapted from a fully online to a fully face-to-face program. In addition, different educational experiences for the students in the western Asia were taken into account in the teaching strategies implemented. Students in the western Asia campus were somewhat stronger in symbolic manipulation and use of formulas to solve standard problems. However, they had little experience with problems in a real-life context. The instruction on the same mathematics content involved hands-on activities designed to deepen understanding of mathematics concepts, laying a stronger foundation on which to build calculus knowledge and skills. Students were presented with real-life data and asked to work collaboratively to analyze and find a function to model the data. They learned how to utilize a graphing calculator to aid their understanding of the relationship between graphs and their equations and find solutions to problems that did not lend themselves to traditional algebraic manipulation. In the second year of the program, additional time was allotted to the program, making room to add another small component. Because spatial visualization is so important in engineering, activities were added to support improvement in this area. Students explored spatial relationships of 3-D objects through a drawing task, paper models, and computer simulations. Through the development of these two bridge programs that addressed primarily the same mathematics content to support engineering calculus concepts and skills, we can see the possibilities to adapt a program to different groups of students to achieve greater success. This paper describes the design, similarities, and differences of these programs along with quantitative data results.