Tangram: an Ancient Educational Material (LS-GR-267)
This learning scenario explores tangram as educational material. Initially, students research mathematics textbooks and identify the thematic areas using tangram. They then research the Europeana Collections information on tangram, and in particular the ancient Greek mathematicians Pythagoras and Archimedes who devised tangram. They then discover tangram’s relation to the proof of geometrical problems such as Pythagorean Theorem. As a final activity, some students design and construct Pythagoras tangram, Archimedes “ostomachion” or tangram, while others create their own tangram inspired by the material from the Europeana Collections.
Working with Europeana
The LS intends to help students learn through interdisciplinarity in the direction of the STEAM method. For the implementation of the learning scenario, the Europeana Collections are used for the development of research skills, information utilization, critical thinking and creativity. Through collaboration, inquiry-based methodologies, and the use of digital tools, students explore the subject, they learn and expand their knowledge, concerns, and skills.
Students also realize the role of important people and their ideas. They recognize that the development of science and art takes place in different places and by different people whose thinking creates culture.
Implementation
The lesson has an interdisciplinary scope which is based on objectives from 3 different subjects, included in the 6th grade of primary school Greek curriculum.
- Mathematics: there is a proposal to use tangram to prove the Pythagorean theorem.
- History: students are invited to research the history of tangram in connection with different times and people, the geometric theorem of Pythagoras, and the tangram of Pythagoras and Archimedes as educational material.
- Art: students are invited to design and construct tangram and to think and discuss similarities with painting streams.
Initially, the introduction to the topic can take place in the schoolbook, provided by the teacher and students will discuss it (Pythagorean theorem and proof by tangram). The discussion will mainly focus on mathematics and art. Afterwards, students search the Europeana Collections for pictures of the Pythagorean theorem, tangram and other mathematicians such as Archimedes, who designed and constructed their own tangram. Students can also use Historiana.
Then students work to understand the relationship between Pythagorean theorem and tangram. They try to prove the Pythagorean theorem (the square of the hypotenuse equals the squares of the other two sides) by using the pieces of tangram. They can use material such as tangram, triangle, etc or the digital tools on GeoGebra.
Subsequently, observing several texts, images and presentations, students work in groups, to create the timelines and presentation for the Pythagorean theorem and tangram. Students can use Prezi and Timetoast.
Finally, students create their own tangram, inspired by geometric art or new art trends. They try to transform the cut pieces of tangram (based on the relation between Pythagorean theorem and tangram). The groups present their designs in the classroom and get feedback from the other students.
Conclusion
The result of this learning scenario application was our students’ interest in learning. The connection of different disciplines to art was a pleasing effect. For the implementation, they used web 2.0 tools in the computer lab. Our students worked during breaks in the computer lab to complete their task.
Students creating their tangram
In addition, it was a priority to guide and assist my students in using the Europeana Collections. Here are some tips on how to build new web tools with digital tools or simple materials. Finally, they exchanged experiences, feelings and ideas and how they could connect with Europeana.
Achievements
Here is a collection of my students’ activities:
Timetoast: Pythagorean theorem: an interesting history
GeoGebra: Tangram – Pythagorean Theorem
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The featured image used to illustrate this article has been found on Europeana Collections and belongs to the public domain.