This story of implementation is based on the learning scenario “Symmetrical ART” created by Rafael Montero, a teacher from Spain. The students involved were 16-17 years old (11th grade) and they had already had prior knowledge of Europeana resources as we were using them during our lessons in the past. The learning scenario was implemented in maths and physics on-line lessons during the school closure due to Covid-19 outbreak.
From the original learning scenario, I decided to implement these topics:
- Recognize the presence of geometric transformations in nature and art. We explored the Europeana web portal and found lots of interesting examples of maths in natural forms and art pieces. We discussed if the book of Nature is written in a mathematical language and if maths transformations are intentionally used in architecture.
- Identify the key elements of the symmetry axis, centres of rotation, rotation amplitude, etc. We analyzed famous artworks to identify some transformations that students were already used to recognize in a cartesian plane or calculus.
- Discuss the role of symmetry in the history of physics research. I underlined that the 20th century is called a “symmetry century” because the Noether’s theorem (1918) that promotes the study of symmetries from artistic, mathematics and physics point of view was proven (example 1 example 2 example 3).
Can maths help when analyzing art?
The starting point of our activities was a geometric transformation and its meaning in maths. Students got familiar with the definition that could be found in their books and found out how symmetry, translation, rotation, flip symmetry, etc. were often used by artists in their artworks. The students were very curious to find a link between arts and maths. One of them said:
“Sometimes during maths lessons, we talked about art and how artists used maths but never during art lessons we used maths concepts to analyze artworks!”
The wonders of (a)symmetry in physics
Then, students compared the symmetry definition in maths and physics and they found some artworks where the concepts of maths and physics were recognizable. They searched for an example of symmetry in physics, using their book (the conservation law of momentum, energy and angular momentum). Students focused on asymmetry, they were interested in the time concept because major philosophers and physicists agreed that this is one of the most intuitive examples of asymmetry in Nature. Basic laws of physics are confirmed forward or backwards in time, but we perceive just one-time flow direction: to future.
Finding fascinating examples on Europeana
We found lots of materials in Europeana Collections that supported this idea. The most suggestive is this one. The final conclusion made by students was that “due to transformation it is impossible to notice changes but symmetry is what remains unchanged and preserved in evolution”.
This learning scenario encouraged my students to recognize the link between maths, physics and arts and to overcome the old vision of division between these subjects. I encouraged them to use Europeana Collections to find more examples of symmetry and asymmetry in arts and nature.
With this learning scenario, students had an opportunity to work in groups, present their work through web conference and acquire public speaking skills. In future, we would love to make a presentation with lots of pictures of symmetry and asymmetry in nature and, maybe, present it in a bigger event.
Did you find this story of implementation interesting? Why don’t you read about the related learning scenario?
Symmetrical ART created by Rafael Montero
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