# 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).

# Discovering Maths in Me

When choosing my elective, I had to think rationally about what would have the most influence on my future career. Maths was the one subject that leapt out at me on the elective list. But not in a good way. I, like many other people, associate the word ‘maths’ with fear, horror, failure and disappoint. I eventually chose this elective, as I wanted to change this thinking and my feelings about maths.

Teachers can be placed in a difficult position. If they don’t understand or like a subject they cannot pass this on to their pupils. As many lecturers said during placement “faking it, till you make it” is vital. If we don’t fake our confidence within a subject and our teaching, then the children will see through this and adopt the same attitudes. Kelly and Tomhave (1985) found that primary school teachers have the ability to transmit their own anxiety about maths to their pupils. This, multiplied by 20-33 pupils, has the ability to influence children from age 5 to adulthood, which could have a detrimental effect on their future careers and their own children.

Maths plays a prominent part in our everyday activities, from reading bus timetables, to working out when to set an alarm. If children begin to believe that they can’t do maths, then easy everyday activities can become a difficulty. I remember telling two of my high school maths teachers that maths was impossible and I didn’t understand anything. The first, told me that maths wasn’t for everyone and maybe more English based subjects were my forte. The second, broke it down for me. He asked me if I could read a clock, count money, organise my day. All of which I agreed to. He then told me that maths is not just ‘find the equation’ or Pythagoras, but it was simple concepts that we take for granted. As teachers, we have to break maths into different components, to show children the everyday uses of maths to highlight to them that they CAN do maths.

A study carried out by the university of Cambridge shows that anxiety in any subject can prevent progression in learning. Having your mind tell you that you cannot do something can be one of the most detrimental things. Children need to know that they can improve and they can do maths. One factor that may knock a child’s confidence is always being told they’re wrong. Adults have a responsibility to tell children that it’s fine to get things wrong and it is just a learning curve that they can overcome. Teachers in particular need to be careful about constantly using a cross beside wrong answers or using the dreaded red pen. Instead, helping a child understand step by step where they went wrong and reassuring them that they can do maths, will hopefully prevent maths anxiety. Therefore, their confidence will maths can flourish in everyday uses and in the classroom.

Overall, my main goal with discovering maths is to develop a positive relationship with the subject and finally believe that I can do maths to develop my skills as a teacher.

References:

Cne.psychol.cam.ac.uk. (2018). The Relationship Between Maths Anxiety and Maths Performance — Centre for Neuroscience in Education. [online] Available at: https://www.cne.psychol.cam.ac.uk/the-relationship-between-maths-anxiety-and-maths-performance [Accessed 15th September].

Schwarzer, D., Bloom, M. and Shono, S. (2006). Research As A Tool for Empowerment. Greenwich, Conn.: Information Age Pub., p.4.