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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...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer Berlin Heidelberg
2022
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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. |
format | Online Article Text |
id | pubmed-8908952 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | Springer Berlin Heidelberg |
record_format | MEDLINE/PubMed |
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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