Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-24T17:24:26.506Z Has data issue: false hasContentIssue false
  • English
  • Français

Geometrical theorems about conservation of area for use in classroom activities

Published online by Cambridge University Press:  17 February 2021

Moshe Stupel ,
Shula Weissman  and
Idan Tal
Moshe Stupel
Affiliation:
Gordon and Shaanan Academic Colleges, Haifa, Israel
Shula Weissman
Affiliation:
Shaanan Academic College, Haifa, Israel
Idan Tal
Affiliation:
Kibbutzim Academic College of Education, Tel-Aviv, Israel
Get access Rights & Permissions [Opens in a new window]

Extract

Five geometrical tasks demonstrating the interesting property of conservation of area that may be used in the mathematics classroom are presented. The initial premise is proved and then changes in attributes are investigated using dynamic geometric software to show that in the cases demonstrated there is conservation of area or specific ratios. These demonstrations illuminate the hidden beauty in mathematics and constitute an intellectual stimulus for discovering additional properties.

Type
Articles
Information
The Mathematical Gazette , Volume 105 , Issue 562 , March 2021 , pp. 61 - 69
Check for updates
Copyright
© The Mathematical Association 2021

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Wassie, Y. A. and Zergaw, G. A., Capabilities and contributions of the dynamic math software, GeoGebra: A review. North American GeoGebra Journal, 7(1) (2018) pp. 68–86.Google Scholar
Libeskind, S., Stupel, M. and Oxman, V., The concept of invariance in school mathematics. International Journal of Mathematical Education in Science and Technology (U.K.) 49(1), (2018) pp. 107–120.10.1080/0020739X.2017.1355992CrossRefGoogle Scholar
Weissman, S., Sigler, A. and Stupel, M., Increasing the use of the area for enriching the toolbox of problem solving and proofs in mathematics, Far East Journal of Mathematical Education 18(1), (2018) pp. 1–20.CrossRefGoogle Scholar
Coxeter, H. S. M. and Greitzer, S. L., Geometry revisited (19). MAA (1967).CrossRefGoogle Scholar
Stupel, M. and Ben-Chaim, D., Using multiple solutions to mathematical problems to develop pedagogical and mathematical thinking: A case study in a teacher education program. Investigations in Mathematics Learning Journal of Research Council for Mathematics Learning, 9(2), (2017) pp. 86–108.CrossRefGoogle Scholar