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Mathematical modelling and discrete mathematics: opportunities for modern mathematics teaching
Gilbert Greefrath1, Hans-Stefan Siller2, Katrin Vorhölter3
1University of Münster, Münster, Germany.
ZDM : the International Journal on Mathematics Education
|March 16, 2022
Summary
This study explores how discrete mathematics, specifically vertex-edge graphs, can enhance mathematical modeling education in secondary schools. Integrating these concepts improves students
Area of Science:
- Mathematics Education
- Discrete Mathematics
- Mathematical Modelling
Background:
- The relationship between discrete mathematics and mathematical modeling is recognized, yet its educational applications, particularly in secondary education, remain underexplLored.
- Existing research lacks sufficient focus on how incorporating mathematical modeling examples can enhance the teaching and learning of discrete mathematics concepts.
Purpose of the Study:
- To explore the educational potential of mathematical modeling examples rooted in discrete mathematics.
- To investigate the integration of discrete mathematics methods into secondary school modeling lessons.
- To analyze students' development of modeling competencies through discrete mathematics applications.
Main Methods:
- Utilized vertex-edge graphs as a key topic in discrete mathematics suitable for secondary school modeling.
- Conducted a case study involving lower-secondary students applying graph theory to the Königsberg bridge problem.
- Employed qualitative content analysis to examine students' solution processes and their engagement with modeling cycle phases and graph theory concepts.
Main Results:
- Students engaged in modeling activities using graph theory concepts to solve an optimization problem.
- Analysis identified specific sub-competencies in mathematical modeling and their connection to discrete mathematics.
- The study revealed opportunities for fostering modeling skills through discrete mathematics.
Conclusions:
- Integrating discrete mathematics, particularly graph theory, offers significant potential for developing students' mathematical modeling skills.
- The Königsberg bridge problem serves as an effective tool for teaching discrete mathematics and modeling concepts.
- Further research and curriculum development are needed to fully leverage the synergy between discrete mathematics and mathematical modeling in education.
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