# The Art of Tessellation

When Jonathan first said the word “tessellation”, I immediately thought what on earth is he on about?! Yet, following this lecture I now understand that tessellation is something that surrounds us.

Tessellation is the arrangement of identical shapes that fit together perfectly to create a pattern. These shapes have to fit precisely beside one another, meaning they’ll leave no gaps. If we look closer at items that we come into contact with on a regular basis, such as chocolate, footballs and kitchen tiles, we can see that there are shapes such as hexagons, squares and triangles that are joined together to form tessellation.

But how does tessellation link into a classroom setting?

Tessellation can occur through two different types of shapes. The first are regular. These include squares, hexagons and equilateral triangles and therefore form a more simplistic tessellation, for example, in the form of chocolate squares. Regular shapes, unlike irregular, have the ability to interconnect as all the vertices meet one another and therefore create the sum of 360 degrees. The second are irregular shapes, these are shapes such as pentagons, octagons and isosceles and scalene triangles (Maths is Fun, 2018). These work similarly to regular shapes, however, the shapes must be cut and pasted to a different part of the shape to be able to interlock with the other identical shapes. An example of this is shown below in the creation of a horse.

A form of tessellation can particularly be seen in Islamic religion through mosaics and geometric patterns (Hames, 2017). Islamic art focus on the creation of stars through tessellation. For example, they particularly use equilateral triangles to create 6 to 12 points of stars. These represent and symbolise harmony and hum consciousness. These features can be introduced into a classroom. Using maths (tessellation) and interconnecting it with art is a great way of introducing a calm and settled environment to the classroom. Boaler (2009), states that completing tasks in different ways therefore allows children to see that there are different methods to learning maths and therefore maths can be enjoyable for everyone.

Liping MA’s idea of inter-connectedness is highlighted through the use of maths and art. By using a mixture of the two, children who feel anxious about maths will therefore find a task such as creating Islamic art, as a more relaxed approach to maths. For example, if they enjoy art they believe it is more about art than the maths. Furthermore, this will lead to their longitudinal coherence. This is because they will have the basic understandings of shapes and therefore children have a sound enough understanding to bring this information forward to more complex areas such as tesselation.

An example of a lesson that could be used for tessellation is multiplication to create stars. By finding the different digital roots e.g. 4 times 6 = 24 which therefore this simplifies to 2 + 4 = 6, you can start at a point in the circle and continue to connect to the following dots (answer). When completed the pupils can colour these in and therefore maths and art have been interconnected in a lesson, helping those who have a passion in art have a profound understanding of maths.

Example of tesselaltion star from the digital root of the 4 times tables.

Overall, tessellation is a great lesson to introduce differentiation within a classroom. It allows for both art and maths to be taught at the same time, making maths fun and achieveable for those suffering from maths anxiety. Tesslation links into our classroom setting through a number of different lessons and has a major link to pupils’ understanding of shapes. A basic concept of maths that is learnt thoroughly to bring forward. This lecture in particular is one that I will continue to revisit when teaching, as I have not only learnt how maths can be fun, but have learnt about a different culture in the process. Therefore, I think this topic could be integrated into the classroom in a number of ways such as a class topic or investigation task.

References:

Boaler, J. (2010). The Elephant in the Classroom: Helping Children Learn and Love Maths. London: Souvenir Press.

Giganti, P. (2010) Anatomy of an Escher Flying Horse. Available at:  https://www.youtube.com/watch?v=NYGIhZ_HWfg (Accessed on: 25th September 2018).

Hames, S. (2017). Tessellations in Islamic Art. Available at: https://classroom.synonym.com/tessellations-in-islamic-art-12085299.html. (Accessed on: 12th November 2018).

Ma, L. (2010) Knowing and Teaching Elementary Mathematics. (Anniversary Ed.) New York: Routledge.

Maths is Fun. (2018). Tesselation. Available at: https://www.mathsisfun.com/geometry/tessellation.html (Accessed on: 24th September).

Warner, M. (no date) Digital Root Patterns Available at: https://www.teachingideas.co.uk/number-patterns/digital-root-patterns (Accessed on: 26th September 2018).

## 1 thought on “The Art of Tessellation”

1. Derek Robertson

I love Escher’s work – so fascinating! When I was in 4th year as a teacher ed student I had an unannounced assessed visit (crit) that saw me teaching translational symmetry using Escher’s work as the context for exploring this. It went well, the children were fascinated by what they could do with this skill/knowledge. There is an exhibition of his work in The Hague if you ever find yourself near there. https://denhaag.com/en/location/9765/escher-in-the-palace