Undergraduate Students’ Solutions of Modeling Problems in Algorithmic Graph Theory

Abstract

Graphs can be considered as useful mathematical models. Graph algorithms are a common part of undergraduate courses in discrete mathematics. Even though they have been successfully implemented in secondary curricula, little research has been dedicated to the analysis of students’ work. Within a discrete mathematics course for university students, several graph algorithms were introduced via their applications. At the end of the course, the students took a test focused, inter alia, on applications of the algorithms. The mistakes that occurred in 127 students’ solutions of three problems (the Chinese postman problem, the shortest path problem, and the minimum spanning tree problem) were categorized and compared. Surprisingly, no mistakes were identified in the mathematization of situations or in the interpretation of results with respect to the wording of the problem. The categories of errors varied regardless of the problem types. Hierarchical cluster analysis grouped together the students’ solutions for the Chinese postman problem and the minimum spanning tree problem. By means of nonparametric item response theory analysis, the Chinese postman problem was identified as the most problematic for students. Possible sources of this difficulty are discussed in more detail herein.

Keywords

• mathematics education
• discrete mathematics
• graph theory
• graph algorithms
• error pattern analysis