ICME TSG 43 Growth and Modelling with KUMULATOR

H.-J. Elschenbroich. GeoGebra Institut NRW, Jul 29, 2016

[b]A graphical and calculation-free approach.[/b] [color=#1551b5][b]www.geogebra.org/m/kGp8dnfp#[/b][/color]

Table of Contents

  1. Intro
    1. The Problem
    2. Kumulator - The idea
  2. One State: Growth
    1. Linear growth: water
    2. Linear growth
    3. Exponential growth: alga
    4. Exponential growth
    5. Limited growth
    6. Logistic growth: sunflower
    7. Logistic growth
  3. Two or three States: Dynamic Systems
    1. Modelling chemical equilibrium
    2. Pipettes
    3. Modelling an epidemic
    4. Change rates instead of matrices
    5. Spread of an epidemic
  4. Finally
    1. Conclusion
    2. References

1.

Intro

  • 1. The Problem
  • 2. Kumulator - The idea

1.1.

The Problem

[b][size=150]Exploring growing like logistic Growth at the School there a two hurdles:[br]- solving differential equations [/size][/b]
[br]
[b][size=150]- or using very special flow Charts.[/size][/b]
[br]
– H.-J. Elschenbroich. GeoGebra Institut NRW

1.2.

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2.

One State: Growth

Growth

  • 1. Linear growth: water
  • 2. Linear growth
  • 3. Exponential growth: alga
  • 4. Exponential growth
  • 5. Limited growth
  • 6. Logistic growth: sunflower
  • 7. Logistic growth

2.1.

Linear growth: water

[size=200][color=#000000]The change rate is constant.[/color][/size]
– H.-J. Elschenbroich. GeoGebra Institut NRW

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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3.

Two or three States: Dynamic Systems

  • 1. Modelling chemical equilibrium
  • 2. Pipettes
  • 3. Modelling an epidemic
  • 4. Change rates instead of matrices
  • 5. Spread of an epidemic

3.1.

Modelling chemical equilibrium

[size=200][color=#000000]Two test tubes, with a blue liquid and a clear liquid.[br]Two pipettes to transfer liquids.[/color][/size]
[b]I. Grafenhofer, V. Klöckner[/b]
– H.-J. Elschenbroich. GeoGebra Institut NRW

3.2.

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3.3.

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3.4.

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3.5.

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4.

Finally

  • 1. Conclusion
  • 2. References

4.1.

Conclusion

[list][size=200][color=#000000][*]Easy and calculation-free modelling of elementary dynamic systems[/*][*]Shifts the perspective from the state to the change rate[br][/*][*]Simple and clear diagram[/*][*]No differential equations necessary[/*][*]Calculation step by step, graphical output.[br][/*][*][size=200][b]Learning Environment [/b]for students, [/size][size=100][size=200]enables exploring & discovering[/size][/size][/*][*][size=100][size=200]Well suited for school, e[/size][/size]asy to use in maths classes and in science classes![br][/*][/color][/size][/list]
– H.-J. Elschenbroich. GeoGebra Institut NRW

4.2.

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