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• Teaching graph algorithms with Visage

  35-50

  Andreas Fest

  Ulrich Kortenkamp

  Views:

  29

  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.

• The role of representations constructed by students in learning how to solve the transportation problem

  129-148

  Gordana Stankov

  Zoltan Pap

  Sanja Maravić Čisar

  Views:

  107

  The purpose of the research presented in this paper was to study the role of concrete and table representations created by students in learning how to solve an optimization problem called the transportation problem. This topic was learned in collaborative groups using table representations suggested by teachers in 2021. In 2022, the researchers decided to enrich the students’ learning environment with concrete objects and urged the students to use them to present the problem to be solved. The students did it successfully and, to be able to record it in their notebooks, they constructed a table representation by themselves without any help from their teacher. After that, they managed to solve the problem by manipulating the objects. At the same time, each step in the solution was presented with changes in the table. The students were assessed before (pre-test) and after collaborative learning (test) in both academic years. The pre-test results were similar, but the test results were better in 2022. Therefore, it can be concluded that using concrete and table representations constructed by students in learning how to solve transportation problems makes collaborative learning more constructivist and more effective than when they use only table representations suggested by their teachers.

  Subject Classification: 97M10, 97M40

• Algorithmics of the knapsack type tasks

  37-71

  Csaba Pătcaş

  Klára Ionescu

  Views:

  27

  We propose a new kind of approach of the teaching of knapsack type problems in the classroom. We will remind you the context of the general knapsack-task and we will classify it, including the two most popular task variants: the discrete and the continuous one. Once we briefly present the solving algorithm of the continuous variant, we will focus on the solving of the discrete task, and we will determine the complexity of the algorithms, looking for different optimizing possibilities. All these issues are presented in a useful way for highschool teachers, who are preparing students in order to participate in different programming contests.