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ICME 13, TSG 46: Growth and Modelling with KUMULATOR
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1. Intro
- Start
- Schule oder Hochschule?
- Modelling and Simulation of dynamic systems
- Heinrich Winter
- Kumulator - The idea
- What's the number?
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2. One State: Growth
- Types of growth
- Linear growth: water
- Linear growth
- Exponential growth: alga
- Exponential growth
- Limited growth
- Logistic growth: sunflower
- Logistic growth
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3. Two or three States: Dynamic Systems
- Modelling chemical equilibrium
- Pipettes
- Modelling an epidemic
- Change rates instead of matrices
- Spread of an epidemic
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4. Finally
- Conclusion
- References
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ICME 13, TSG 46: Growth and Modelling with KUMULATOR
H.-J. Elschenbroich. GeoGebra Institut NRW, Jul 12, 2016
A graphical and calculation-free approach. www.geogebra.org/m/CDUYBbvk
Table of Contents
- Intro
- Start
- Schule oder Hochschule?
- Modelling and Simulation of dynamic systems
- Heinrich Winter
- Kumulator - The idea
- What's the number?
- One State: Growth
- Types of growth
- Linear growth: water
- Linear growth
- Exponential growth: alga
- Exponential growth
- Limited growth
- Logistic growth: sunflower
- Logistic growth
- Two or three States: Dynamic Systems
- Modelling chemical equilibrium
- Pipettes
- Modelling an epidemic
- Change rates instead of matrices
- Spread of an epidemic
- Finally
- Conclusion
- References
Start
Growth and Modelling with KUMULATOR
Hans-Jürgen Elschenbroich
A graphical and calculation-free approach.
www.geogebra.org/m/CDUYBbvk
Types of growth
Two approaches:
- explicit (solving differential equations): Function.
- cumulative (calculating step by step): Graph.
- linear
- exponential
- limited
- logistic
Modelling chemical equilibrium
Two test tubes, with a blue liquid and a clear liquid.
Two pipettes to transfer liquids.
I. Grafenhofer, V. Klöckner
Conclusion
- Easy and calculation-free modelling of elementary dynamic systems
- Shifts the perspective from the state to the change rate
- Simple and clear diagram
- No differential equations necessary
- Calculation step by step, graphical output.
- Learning Environment for students, enables exploring & discovering
- Well suited for school, easy to use in maths classes and in science classes!
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