Implementation of ‘Aesthetical Geometry’ (SOI-EXT-185)

Geometry is an integral part of the curriculum on a global scale as it is a learning object where students can engage in inquiry learning process and develop skills and competences. Cultural heritage is a basic component of each country, as it includes all values from past to future. In other words is treasure through the years.

  • But, what is the way that students learn geometrical concepts and in which way they construct and transform geometrical concepts?
  • How can we engage students to get familiar with cultural heritage?
  • Can we implement interdisciplinary learning scenarios with geometry for developments students 21st skills through cultural heritage?

The implementation of the teaching scenario ‘Aesthetical Geometry’ replies to this questions, as the teaching of geometry is based on the examination and analysis of the characteristics of the material objects of the digital cultural heritage Europeana. Specifically, the students explored their geometric properties in space and level, searched for the correlations and how they are presented on these basic theorems and propositions of geometry.

Most importantly, students themselves, creators and solvers of geometry and algebra problems on the objects of digital heritage, express their creativity, use their innovative and critical thinking, and their ability to process and use information and the skill ‘learning by doing’.

The implementation context

The learning scenario was implemented in distance learning for 40 students aged 16-17 years of 1st and 2nd grade of Evangelika Model High School of Smyrna, in Athens Greece (using the facility of Scientix on line meeting room).

Digital cultural heritage of Europeana was used to repeat basic geometric concepts/theorems and propositions of the Euclidean geometry and stereometry. The examination of the two and the three (space) dimensions of the objects is justified by the content of the curriculum of the two different grade of classes.

At the cognitive level:

Students were asked for i) recognize and apply their knowledge of geometry on the objects of digital cultural heritage and ii) on the other hand to describe with details the cultural context of the object (where it is located, what it describes and why you consider it important for cultural heritage).

Except for learning objects, I focus on development i) critical thinking ii) ICT literary: collection and analyze information iii) creativity iv) problem-solving.

Finally, this scenario is i) a teaching tool for the promotion and understanding of geometry through the various art forms, through different contexts of cultural heritage. ii) is an evaluation tool of the students’ geometric thinking levels (Optical skills, Verbal skills, Design skills, Logical skills, Implementing skills).

The narrative

Preparation:

I asked students to search for digital heritage objects from Europeana in order to work with their classmates (by distance with on line collaboration tools) and prepare a short presentation:

  1. on the one hand they have to explain the cultural context
  2. on the other hand they have to analyze in detail the properties of quadrilaterals and solids, theorems and applications of geometry (taught).

I gave them suggestions i) on the criteria for searching for content ii) copyright, so that each item also mentions the corresponding report of the creator or source.

Online meeting (2 hours)

A) The students presented their work: https://bit.ly/2RPNBR2

Examples:

B) I presented i) the basic features of the Europeana network

ii) the influence of geometry on various art forms (architecture, painting, sculpture) from ancient Greece to modern industrial times, through the selection of digital objects of Europeana.

iii) I gave advice on digital tools https://www.geogebra.org/graphingthat can be used to calculate the volume and surface area of geometric objects.

C) In addition to the proposed activities of the scenario is i) that students were asked to formulate an algebraic or geometric problem based on the geometric features of the objects they had chosen ii) to use digital GeoGebra tools to design-present geometric theorems and suggestions.

Example:

  • The suggested sources of the script were not used, but the students were given a choice, based on their interests to express their creativity.
  • The schedule of activities cannot be compared to what the scenario suggests, as the teaching was carried out remotely and the students were given preparation work.

Learning outcomes

Before the implementation of learning scenario, I evaluate students’ knowledge of cultural heritage

Results: https://bit.ly/2VE58wJ

I mentioned that they did not know the different fields included in cultural heritage (most of them gave as example Acropolis, or Parthenon), but they think that it is very important to learn about it.

After implementation I asked for self –evaluate the skills that they develop through the learning activities:

Results: https://bit.ly/34MxGbo

High scores of their results have i) Intercultural understanding ii) analysis of information iii) critical thinking. Moreover, I evaluate their views of this innovative learning approach: I learned geometry from real objects; I got familiar with the cultural heritage through geometry; The approach of geometry in the aspect of cultural heritage was; The cultural heritage with the approach of geometry was.

Results: https://bit.ly/3cu3Dba

Objects of cultural heritage could be used not only as teaching tools and include them in curricula of geometry, as students: i) recall prior knowledge ii) development visualization or imaging process for representing objects in the space, explaining a proposal, systematically investigating a complex state or verifying different geometric situations, or checking some cases using representations (eg numbers, images, diagrams, symbols).

The results highlight that the teaching methodologies have to improve including connections with real world, as students had difficulties to expand their knowledge. Mostly, art or in general cultural heritage objects in increased students’ creativity and motivate them in in learning geometry.

Teaching outcomes

The investigation of geometric properties in architectural creations, paintings, sculptures, famous mosaics we hope to eliminate the prejudice that mathematics has nothing to do with the real world. The historical tour of the world of geometry and its applications will present and reveal a world of unknown beauty where the accuracy of reasoning and surprises meet creativity and efficiency. The need to examine the connection between the concepts of art and mathematics is also highlighted by the growing interest in Europe, in museums and in education in general, on this subject.

The combination of cultural heritage with STEM lesson is a challenge for the educational community with many additional values in teaching and learning process. Cultivating a spirit of inquiry, promoting inclinations, strengthening interests, learning ways to organize strategies and methods to solve problematic situations, the ability to select and compose material, develop collaboration and engage in a constructive and fruitful dialogue between students are among the curriculum educational goals for all students, regardless of their performance.

Expansions:

  • The use of new technologies to create modern digital art makes it necessary to take advantage of the properties of educational software for the presentation, construction and examination of artistic constructions, where they confirm the strong influence of mathematics on art.
  • It could be used as activity for distance learning.

CC BY 4.0: the featured image used to illustrate this article has been found on Europeana Collections and provided by the Wellcome Collection.

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