The significance of symmetries 

Symmetries are connected to the human cognitive history. All civilizations that flourished on the planet, even those that had no interactions with each other, developed the same symmetries in decorative arts (translation, reflection, glide- reflection, and rotation). This means that symmetries constitute a universal language, maybe the first kind of representation of abstract geometrical thinking. 

Symmetries are connected to the human cognitive history. All civilizations that flourished on the planet, even those that had no interactions with each other, developed the same symmetries in decorative arts (translation, reflection, glide- reflection, and rotation). This means that symmetries constitute a universal language, maybe the first kind of representation of abstract geometrical thinking. 

Dr. Stanislas Dehaene, cognitive neuroscientist and professor at the Collège de France, argues that what differentiates the human mind and makes it unique are the innate geometric intuitions it possesses. 

Wizzle is a "serious game" with applications in Education

Symmetries are the foundations and background of geometric thinking. Fundamental propositions of geometry can be derived through simple contemplation on symmetry issues. The axiomatic foundation of the equality of geometric shapes, as achieved by Euclid, is accomplished through moving and fitting, though without revealing that fitting can be achieved through the fundamental isometries of translation, reflection, and rotation.

All definitions and properties of geometric shapes can be described and summarized by symmetries. Wizzle incorporates and visualizes the mathematical ideas of symmetries, and makes it easy for the learners to understand the regularities in geometric problems. So, students can see what the experienced eye of a mathematician can perceive, and they don’t need to use the complex symbolic language of mathematics. As a hands-on learning tool, Wizzle is valuable for educators and students, suitable for learners with dyslexia and for refugee students who struggle with language, promoting inclusion. 

Wizzle was based on the Educational Practice titled "Isometries, from Art to Geometry" which received the seal of quality for Best Educational Practice, won 1st place in the 2nd Open Educational Practices Competition, and is published in PHOTODENTRO-National Aggregator of Educational Content.

On this page, proposals for the educational utilization of wizzle will be published, educational practices that use it, and ongoing research papers on wizzle. 

Conference papers

Wizzle was presented at the following conferences: 

"The utilization of the theory of geometric transformations in the teaching of Euclidean Geometry. A proposal based on the new Curriculum Programs", Proceedings of the 1st Conference on Mathematics and their Teaching, Greek-French School “Kalamari”, March 2024. ISBN: 978-618-82332-3-2

A mathematical game of thought and creativity", 38th Panhellenic Conference on Mathematical Education "Contemporary Approaches and Applications of Mathematics in Education and Sciences", Hellenic Mathematical Society, November 2023. ISBN: 978- 960-7341-48-8

"Isometries from Art to Geometry - An educational practice for utilizing digital educational material". European Conference "Digital Transformation for Educational Innovation and Inclusion", of the European Project Augmented Assessment, Aristotle University of Thessaloniki, November 2023. ISBN: 978-618-84619-4-9

"History of Mathematics & Art. The utilization of an authentic mathematical problem in the pilot implementation of the New Curriculum Programs." 13th International Week Dedicated to Maths 2023, Hellenic Mathematical Society, April 2023. ISBN:978-618-83724-4-3

Upcoming

"Exploring meta-tilings and isometries using the mathematical game Wizzle. An approach to Geometric Transformations within the framework of the pilot implementation of the new Curriculum Programs." 14th International Week Dedicated to Maths 2024, Hellenic Mathematical Society, April 2024.