Torino GGB Day 2016

Aitzol Lasa, Sep 26, 2016

Torino - GeoGebra Day - 2016/10/06

Table of Contents

  1. Preliminary ideas
    1. Explorative, illustrative, demonstrative
  2. Childhood Education
    1. Larraintzar
    2. Aurkezpena
    3. Letrak osatu
    4. Irudi simetrikoak
    5. Orain, marraztu!
    6. Marrazki simetrikoak
    7. Osatu eredua
    8. Erdiak osatu
    9. Agurra
  3. Primary Education
    1. A plot for Laika
    2. Didactical obstacles and phenomena
    3. Students solve the activity
    4. Una parcela para Txuri / A plot for Laika
    5. Lasa, Wilhelmi & Belletich, 2014
  4. Secondary Education
    1. Long live triangles!
    2. Solving non-linear equations
  5. Conclusions
    1. Conclusions

1.

Preliminary ideas

  • 1. Explorative, illustrative, demonstrative

1.1.

Explorative, illustrative, demonstrative

Revista do Instituto GeoGebra de São Paulo, ISSN 2237- 9657, v.2 n.1, pp.52- 64, 2013
Lan honetan hainbat GeoGebra eraikuntza aurkezten dira, eta eraikuntza horiek guztiak diseinatuak izan dira triangeluen oinarrizko propietateak ikertzeko, Bigarren Hezkuntzako curriculumean oinarriturik. Alde batetik, eraikuntza horiei esker ikasgelako jarduera propietateetan zentratu daiteke, eta ez adibide isolatuetan. Bestetik, eztabaidatu egiten da zein neurritan lortzen den eraikuntza horiei esker indukzioaren eta dedukzioaren arteko langa igarotzea, azalpen hutsetik frogapen formalerako saltoa geometrian.
Explorative model
Moving points in the plane:[br][br][url=https://www.geogebra.org/m/Cvy84hyz#]https://www.geogebra.org/m/Cvy84hyz#[/url]
Illustrative model
What should have happened if Feynman would have Geogebra?[br][br][url=https://www.geogebra.org/m/wfjjKtBa#]https://www.geogebra.org/m/wfjjKtBa#[/url]
Demonstrative model
Pythagorean Theorem
Lema
Pythagorean Theorem
– Aitzol Lasa

2.

Childhood Education

  • 1. Larraintzar
  • 2. Aurkezpena
  • 3. Letrak osatu
  • 4. Irudi simetrikoak
  • 5. Orain, marraztu!
  • 6. Marrazki simetrikoak
  • 7. Osatu eredua
  • 8. Erdiak osatu
  • 9. Agurra

2.1.

Larraintzar

5 years-old children in a unitary school solve activities on vertical-axis symmetry
– Aitzol Lasa

2.2.

–

2.3.

–

2.4.

–

2.5.

–

2.6.

–

2.7.

–

2.8.

–

2.9.

–

3.

Primary Education

  • 1. A plot for Laika
  • 2. Didactical obstacles and phenomena
  • 3. Students solve the activity
  • 4. Una parcela para Txuri / A plot for Laika
  • 5. Lasa, Wilhelmi & Belletich, 2014

3.1.

A plot for Laika

An experience to work the isoperimetric inequallity in Primary Education (ages 8-9)
– Aitzol Lasa

3.2.

–

3.3.

–

3.4.

–

3.5.

–

4.

Secondary Education

  • 1. Long live triangles!
  • 2. Solving non-linear equations

4.1.

Long live triangles!

Dynamic models for trigonometry
A set of GGB constructions designed at UNITO.[br][br]Pubblicato in italiano:[br] "Lunga vita ai triangoli", [url=https://www.geogebra.org/book/title/id/cnKZVc6d#chapter/0]https://www.geogebra.org/book/title/id/cnKZVc6d#chapter/0[/url][br]Euskaraz eskuragarri:[br] "Triangeluen gorazarrea", [url=https://www.geogebra.org/book/title/id/Sg8UI8v8#chapter/0]https://www.geogebra.org/book/title/id/Sg8UI8v8#chapter/0[/url][br]Published in english:[br] "Long live triangles", [url=https://www.geogebra.org/book/title/id/oOGHNoq8#chapter/0]https://www.geogebra.org/book/title/id/oOGHNoq8#chapter/0[/url][br]Disponible en castellano:[br] "Elogio de los triángulos", [url=https://www.geogebra.org/m/d2exF80t#chapter/0]https://www.geogebra.org/m/d2exF80t#chapter/0[/url][br][br]
Belloso, 2016
– Aitzol Lasa

4.2.

–

5.

Conclusions

  • 1. Conclusions

5.1.

Conclusions

Three dimensions:
[i]1. [/i][i]Students progression on algebraization levels:[br] - Childhoord Education: dragging and moving points.[br] - Primary Education: generalized numbers, changing numerical values (from level 0 to level 2)[br] - Secondary Education: use of parameters (from level 3 to level 4).[br][/i][br][i]2. Integration of material supports, suitability of the learning process (treatment + conversion)[br][br]3. Influence of dynamic geometry software on the didactical contract (imitation contract - explorative model)[/i][br][br][br]
Algebraization levels
Suitability of the learning process
Influence on the didactical contract
– Aitzol Lasa

Information