Assessing the Effectiveness of a Single Curriculum for a Group of Students with Different Mathematics Literacy

Abstract

In recent years, applicants to Azad universities are different than those in last years. This difference arose from the unequal ability in learning mathematics by students. Traditionally university students were K-12 graduates and because of severe competition to enter the university, they had equivalent math literacy. In contrast recent applicants to universities have been graduated from different majors in high school in different past years. Since passing more years after graduating from high school causes degradation in math literacy, this kind of applicants has more divergent math literacy. When having university students with more divergent math literacy, it may be required to have different syllabus for different students at the same course. In this paper we model the learning phases of a math course as a network in which the arcs are sub-topics and the logical precedence between arcs exhibits the prerequisite relation between sub-topics. The ability to accomplish the course is equal to pass all sub-topics. This problem can be modeled as finding the shortest path in a network with probabilistic arc lengths. Traditionally, finding the shortest path in a probabilistic network is done with PERT. Since PERT is known to be over optimistic, we have developed a new method to find a more realistic estimate for completion time in the network on sub-topics in a course.