ICME 13, TSG 46: Growth and Modelling with KUMULATOR

H.-J. Elschenbroich. GeoGebra Institut NRW, Jul 12, 2016

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

Table of Contents

  1. Intro
    1. Start
    2. Schule oder Hochschule?
    3. Modelling and Simulation of dynamic systems
    4. Heinrich Winter
    5. Kumulator - The idea
    6. What's the number?
  2. One State: Growth
    1. Types of growth
    2. Linear growth: water
    3. Linear growth
    4. Exponential growth: alga
    5. Exponential growth
    6. Limited growth
    7. Logistic growth: sunflower
    8. 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. Start
  • 2. Schule oder Hochschule?
  • 3. Modelling and Simulation of dynamic systems
  • 4. Heinrich Winter
  • 5. Kumulator - The idea
  • 6. What's the number?

1.1.

Start

[size=200][b]Growth and Modelling with KUMULATOR [br][/b][i][br]Hans-Jürgen Elschenbroich[/i][/size]
[size=200]A graphical and calculation-free approach.[br][color=#1551b5]www.geogebra.org[b]/m/CDUYBbvk [/b][/color][/size]
– H.-J. Elschenbroich. GeoGebra Institut NRW

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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2.

One State: Growth

Growth

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

2.1.

Types of growth

[size=150][size=200][color=#000000]Two approaches:[br][list][*]explicit (solving differential equations): Function.[br][/*][*][b]cumulative [/b](calculating step by step): Graph. [/*][/list][br]Four characteristic kinds of modelling growth:[br][list][*]linear[/*][*]exponential[/*][*]limited[/*][*]logistic[/*][/list][/color][/size][/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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2.8.

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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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