Teaching graph algorithms with Visage

Abstract

Combinatorial optimization is a substantial pool for teaching authentic mathematics. Studying topics in combinatorial optimization practice different mathematical skills, and because of this have been integrated into the new Berlin curriculum for secondary schools. In addition, teachers are encouraged to use adequate teaching software. The presented software package "Visage" is a visualization tool for graph algorithms. Using the intuitive user interface of an interactive geometry system (Cinderella), graphs and networks can be drawn very easily and different textbook algorithms can be visualized on the graphs. An authoring tool for interactive worksheets and the usage of the build-in programming interface offer new ways for teaching graphs and algorithms in a classroom.

Undergraduate Students’ Solutions of Modeling Problems in Algorithmic Graph Theory

“…Kuna and Turčáni [27] investigated how implementing interactive multimedia elements into discrete mathematics e-courses can provide an environment enabling students to better understand the given problems considering the fact that visualization can be interpreted as a way of reducing abstraction. Several topics of graph theory were taught using dynamic geometry systems [28], specially designed software [29][30][31], or e-learning courses [32][33][34]. Milková [35] provided software for pairing, subgraphs, isomorphism of graphs, and solving the minimum spanning tree problem and the shortest path problem.…”

“…Dijsktra's algorithm for solving the shortest path problem is also implemented in software developed by Dagdilelis and Satratzemi [36]. Despite Niman's idea [37] (p. 373) that graph theory "could constitute a plausible and exciting alternative in mathematics education" as early as primary level, it permeates school curricula very scarcely [30]. Several authors [38,39] have described their experiences of graph theory algorithms at secondary level; yet, it often happens that students encounter this topic no earlier than in undergraduate discrete mathematics courses.…”