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Mathematical modelling and discrete mathematics: opportunities for modern mathematics teaching

Discrete mathematics and mathematical modelling, along with the educational discourse surrounding these, have many connections. However, ways that the educational discourse on discrete mathematics can benefit from the inclusion of examples of mathematical modelling and the accompanying discussion ar...

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Autores principales: Greefrath, Gilbert, Siller, Hans-Stefan, Vorhölter, Katrin, Kaiser, Gabriele
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8908952/
https://www.ncbi.nlm.nih.gov/pubmed/35291444
http://dx.doi.org/10.1007/s11858-022-01339-5
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author Greefrath, Gilbert
Siller, Hans-Stefan
Vorhölter, Katrin
Kaiser, Gabriele
author_facet Greefrath, Gilbert
Siller, Hans-Stefan
Vorhölter, Katrin
Kaiser, Gabriele
author_sort Greefrath, Gilbert
collection PubMed
description Discrete mathematics and mathematical modelling, along with the educational discourse surrounding these, have many connections. However, ways that the educational discourse on discrete mathematics can benefit from the inclusion of examples of mathematical modelling and the accompanying discussion are currently under-researched. In this paper, we elaborate on the educational potential of examples of mathematical modelling based on the usage of methods from discrete mathematics, with a focus on secondary education. We first describe vertex-edge graphs as possible topics of discrete mathematics that are accessible at school level within modelling lessons. Secondly, in the context of a case study, we describe modelling activities with students at the end of lower-secondary education, using a classical problem of discrete mathematics originating from the Königsberg bridge problem. The students’ solution processes for this optimisation problem based on graph theory are described. Their approaches are examined referring to the phases of the modelling cycle, using the method of qualitative content analysis. We studied in particular the extent to which students use concepts related to vertex-edge graphs in specific sub-phases of the modelling process. The analysis allows the required sub-competences of modelling to be identified and the connection of these competences with discrete mathematics to be worked out. On the basis of this analysis, educational opportunities of teaching discrete mathematics and mathematical modelling are assessed. Overall, we point out the possibilities and opportunities for using examples from the field of discrete mathematics to acquire modelling competences and to foster the linkage of mathematical modelling and discrete mathematics at school level.
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spelling pubmed-89089522022-03-11 Mathematical modelling and discrete mathematics: opportunities for modern mathematics teaching Greefrath, Gilbert Siller, Hans-Stefan Vorhölter, Katrin Kaiser, Gabriele ZDM Original Paper Discrete mathematics and mathematical modelling, along with the educational discourse surrounding these, have many connections. However, ways that the educational discourse on discrete mathematics can benefit from the inclusion of examples of mathematical modelling and the accompanying discussion are currently under-researched. In this paper, we elaborate on the educational potential of examples of mathematical modelling based on the usage of methods from discrete mathematics, with a focus on secondary education. We first describe vertex-edge graphs as possible topics of discrete mathematics that are accessible at school level within modelling lessons. Secondly, in the context of a case study, we describe modelling activities with students at the end of lower-secondary education, using a classical problem of discrete mathematics originating from the Königsberg bridge problem. The students’ solution processes for this optimisation problem based on graph theory are described. Their approaches are examined referring to the phases of the modelling cycle, using the method of qualitative content analysis. We studied in particular the extent to which students use concepts related to vertex-edge graphs in specific sub-phases of the modelling process. The analysis allows the required sub-competences of modelling to be identified and the connection of these competences with discrete mathematics to be worked out. On the basis of this analysis, educational opportunities of teaching discrete mathematics and mathematical modelling are assessed. Overall, we point out the possibilities and opportunities for using examples from the field of discrete mathematics to acquire modelling competences and to foster the linkage of mathematical modelling and discrete mathematics at school level. Springer Berlin Heidelberg 2022-03-10 2022 /pmc/articles/PMC8908952/ /pubmed/35291444 http://dx.doi.org/10.1007/s11858-022-01339-5 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Original Paper
Greefrath, Gilbert
Siller, Hans-Stefan
Vorhölter, Katrin
Kaiser, Gabriele
Mathematical modelling and discrete mathematics: opportunities for modern mathematics teaching
title Mathematical modelling and discrete mathematics: opportunities for modern mathematics teaching
title_full Mathematical modelling and discrete mathematics: opportunities for modern mathematics teaching
title_fullStr Mathematical modelling and discrete mathematics: opportunities for modern mathematics teaching
title_full_unstemmed Mathematical modelling and discrete mathematics: opportunities for modern mathematics teaching
title_short Mathematical modelling and discrete mathematics: opportunities for modern mathematics teaching
title_sort mathematical modelling and discrete mathematics: opportunities for modern mathematics teaching
topic Original Paper
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8908952/
https://www.ncbi.nlm.nih.gov/pubmed/35291444
http://dx.doi.org/10.1007/s11858-022-01339-5
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