Elementare Wege zur mathematischen Modellbildung : Fallbeispiele aus Biowissenschaften und Chemie

The role of mathematical models in high school education is often restricted to the application of model equations, or to fitting parameters. The modelling process is usually not a focus topic, and rarely the derivation of a model is discussed extensively. In the present thesis, using examples from biology and chemistry present approaches to modelling for various age groups on the high school level. In biology we develop conceptual models for the competition within one species, which are extracted from observations of competition in nature. These simple conceptual models can be transferred to stochastic models and simulation tools that allow experimentation and observation in silico. Evaluating the simulation results, requiring only tools from high school mathematics, yields, among others, the well-known Ricker model. A conceptual model for simple bimolecular chemical reactions allows the simulation and visualization of the systems behaviour. Again, high school mathematics is sufficient to analyse the simulation results and derive the mass action law for the equilibrium state. For both classes of examples we also develop a purely mathematical approach, using combinatorics. The mathematics used have exceed high school level, but are well within reach of first-year university level.The simulation-tools can be found under the following URL:www.matha.rwth-aachen.de/lehre/lehramtsausbildung/Tools.html

Grantor dc:publisher

Publikationsserver der RWTH Aachen University

Year dc:date

2006

Author dc:creator

• Gotzen, Bernd

Contributors dc:contributor

• Walcher, Sebastian

• info:eu-repo/classification/ddc/510
• Mathematik
• Mathematikunterricht
• Mathematisches Modell
• Modellierung
• Populationsmodell
• chemische Reaktionen
• Massenwirkungsgesetz
• modelling
• population-model
• chemical reactions
• mass action law

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

ger

Identifier

https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-123812%22

OAI identifier oai:identifier

oai:publications.rwth-aachen.de:62232