When this concept was explained in our lecture, I did not fully understand. I feel this may happen many more times throughout the module as I familiarise myself with maths again. I decided to remain positive towards maths and explore the idea for myself until I both understood the how and the why. I think that I understand that there must be some element of mathematics within art. However I did not fully appreciate how interesting this is or exactly how it works. I have aways found maths intimidating and daunting. So my question for this week is; can I find the beauty in maths for myself?

Mark Warner (2015) discusses the idea that digital roots can provide a visual representation of the multiplication tables. As a visual learner, I found this helpful as I can link a mathematical concept to something almost artistic. I think that in the classroom, pupils who may struggle with the traditional learning methods of maths may find an exercise such as this helpful. I also now see the importance as it could be of benefit to children should they be able to identify and create patterns. This could bring forth the relevance of mathematics for children which is essential if they are to have the motivation to learn. Not only can I now appreciate how the digital roots work but I also can appreciate how clever it really is. Exploring times tables in this way would be an enjoyable and different experience for children whilst deepening and broadening their understanding of maths.

The National Centre for Excellence in the Teaching of Maths (2011) explains that creating art with maths must begin with an understanding of shape. My experience of observing shape taught was solely classifying and memorising the properties of shapes.  This is a good basis for understanding but should be explored further. Haylock (2007) explains ‘this process of classifying and naming leads to a greater confidence in handling shapes and a better awareness of the shapes that make up the world around us’. Exploring shape through art can bring relevance and a real life context which can solidify this learning for pupils.

Being able to tie together mathematics with art will highlight for children the importance and relevance of maths in daily life. I think it is important when learning maths to occasionally detach the concept from their traditional exercises and relate them to real life situations. Education Scotland (2018) highlight one of the key principles as relevance meaning this is essential to the curriculum. It is also a word I heavily associate with maths, bringing forward the relevance is key in my personal experience in order to give me the motivation.

I decided to explore interesting ways of intertwining art in maths to highlight the relevance of maths in what we see around us.

Architecture

                                            http://prettyarchitecture.tumblr.com

Using the example of architecture can show pupils how amazing maths and its uses can be. This is something I did not think about for myself but so much architecture is beautiful and would not be possible without maths. David Mumford (2006) states ‘the beauty of mathematics is very similar to the beauty one finds in abstract art or architecture, or in music’. Images such as these illustrate the beauty of mathematics. I think that making pupils feel inspired by mathematics could be a step in the direction of creating a more positive attitude towards maths.

Islamic Art

Creating Islamic art in classrooms can also be an interesting way of exploring maths. Salim Al-Hassani (2007) explains that ‘Girih designs feature arrays of tessellating polygons of multiple shapes, and are often overlaid with a zigzag network of lines’. This gave me some context for the concept of tessellation and an example of its use. I think that for teachers to have confidence and competence to teach maths, it is important for them to appreciate  the relevance of maths for themselves.

The Maths

It is all very well that I now can appreciate the maths in art but i still wanted to understand.

0 , 1 , 1 , 2 , 3 , 5 , 8 , 13 , 21 , 34 , ? , ? , ?..

I first of all wanted to know where the Fibonacci Sequence came from. Tyler Clancy (undated) states ‘first derived from the famous “rabbit problem” of 1228, the Fibonacci numbers were originally used to represent the number of pairs of rabbits born of one pair in a certain population’. Therefore a number sequence was used to tackle a real life problem. This gave me an idea of the importance of the Fibonacci Sequence. However, I was still thinking, why would this be important for me to know? Dan Reich (undated) further describes that the sequence spans so much further than it’s original purpose as it can be used in so many other contexts. This means that perhaps understanding the sequence could give me a wider and deeper understanding of mathematics which is an aim I have for myself throughout this module.

Fibonacci in Nature

The Fibonacci Sequence can be used to highlight patterns in nature. Dr Ronn Knott (2016) explains ‘on many plants, the number of petals is a Fibonacci number: buttercups have 5 petals; lilies and iris have 3 petals; some delphiniums have 8..’. This provides a basis for many lessons which can give maths a real life context. This also further develops a point made in my previous blog post about the necessity of highlighting relevance in maths. I can also see a positive to this as it can encourage exploration of maths and number. This is important in itself as I wanted to have a more positive attitude towards maths.

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Fibonacci in Art

Expanding on this point about encouraging children to explore the maths in the world, another example is art. This is all down to the ‘golden ratio’. Elaine Hom (2013) explains ‘The Golden ratio is a special number found by dividing a line into two parts so that the longer part divided by the smaller part is also equal to the whole length divided by the longer part’.

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Looking into images and seeing them as more than they are can motivate children to think deeper about maths and make discoveries for themselves.

Conclusion

I am beginning to see development of a deeper understanding as a key theme in the module. My own experience of mathematics left me with a profoundly surface level understanding of maths and I wish to give my pupils a richer experience. My research for this blog post has given me a new appreciation for maths and all of the beauty around us that would not be possible if not for maths. I also feel motivated to become more confident in the subject for myself because the love of maths in the future begins in the classroom.

References

Al Hassani, S. New Discoveries in the Islamic Complex of Mathematics, Architecture and Art. Available at:  http://www.muslimheritage.com/article/new-discoveries-in-islamic-complex. (Accessed: 27/9/18)

Education Scotland (2017) What is Curriculum for Excellence? Available at: https://education.gov.scot/scottish-education-system/policy-for-scottish-education/policy-drivers/cfe-(building-from-the-statement-appendix-incl-btc1-5)/What%20is%20Curriculum%20for%20Excellence (Accessed: 27/918)

Haylock, D. (2007) Mathematics Explained for Primary Teachers. London: Sage Publishers.

J. Hom, E. (2013). What is the Golden Ratio?. Available at: https://www.livescience.com/37704-phi-golden-ratio.html (Accessed: 5/10/18)

Knotts, R. (2016). The Mathematical Magic of the Fibonacci. Available at: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibmaths.html (Accessed: 6/10/18)

Mumford, D. (2006) as cited in CECM (undated). Mathematics belongs in a liberal education. Available at: http://www.cecm.sfu.ca/~pborwein/pborwein_resources/Architecture.pdf. (Accessed: 27/918)

NCTEM Admin (2011)  The Art of Mathematics. Available at: https://www.ncetm.org.uk/resources/18030. (Accessed: 27/9/18)

Reich, D. (undated) The Fibonacci Sequence, Spirals and the Golden Mean. Available at: https://math.temple.edu/~reich/Fib/fibo.html. (Accessed: 6/10/18)

Warner, M. (2015). Available at: https://www.teachingideas.co.uk/number-patterns/digital-root-patterns. (Accessed: 28th September 2018).