# Artists and Mathematics? Who knew.

You wouldn’t quite believe the vast amount of things mathematics relates to, we constantly hear people say, ‘you need math in everyday life’, however the concepts that spring to mind are money, percentages, date and time and so on.

But if I was to tell you artists use mathematics, what would you say to that?

I know for a fact that before one of our Discovering Math inputs I would have argued that this statement was false.  However, knowing what I know now, I can agree that mathematics really is involved in nearly everything we do.

During this particular input, we focused on the way our own faces are proportioned and would you believe it, our face is wholly based on mathematical formulae. Without these mathematical measurements our face would not be split up equally.

Johnathon helped us unpick the different levels and stages portrait artists go through in order to assemble a correct and accurately proportioned drawing of a face.  I wouldn’t say I am a particularly creative person and art has never been one of my strong points, so this has never really crossed my mind.  I had heard that our eyes are positioned half way down our face but that was about the only ratio I was aware of.  As I continued to draw I was more amazed as each ratio and measurement was revealed, who knew so much mathematics was involved in such art and artistry.

The first task we were asked to carry out involved us doing a freehand drawing of a face.  This brought on a few giggles from those in the class as art was maybe not everyone’s strong point.  A small sense of that dreaded ‘art anxiety’, however we carried on with the task wondering when the math part would join us.  We were asked to look around the room and examine one another’s free hand drawings and that was when it became clear to us that none of these drawings were proportional.  Johnathon then attempted to get us to try and find some common measurements with our own faces.  We determined that, our eyes are half way down our head, the width of our face is about five eyes wide and the bottom of our nose is halfway between our eyes and the bottom of our chin.

Nowadays through the use of social media we are bombarded with ‘beautiful’ / ‘perfect’ people all the time.  We all aspire to look like the celebrity’s we follow as we see them all over our screens and magazines.  We feel these people have beauty and there is a pressure within our society to look our best all the time.  But what are we really judging ourselves on, are we judging ourselves through mathematical concepts?

The ‘perfect’ face is based upon the ‘golden ratio’.  Obviously not every face is perfectly proportioned, and this is where discussion is invoked. It can be said that the way we see beauty is based upon a mathematical scale, a more proportioned face is often seen to us as a more attractive person (Meisner, 2012).

So, when we are asked to focus on our face carefully we notice some basic measurements and without these standard measurements our face would have no structure. But do we look deeply into this? Probably not.  Let’s break some of this down and see for ourselves what true beauty looks like using mathematics.

• The pupils should be in line with the outer corners of your lips
• The tops of the ears should be in line with the centre of your eyes with the bottom of the ears being in line with the bottom of your nose
• The outer edge of each nostril to be in line with the inner corner of each eye
• The middle of your chin should be in line with middle of the upper lip
• The tops of the ears to be in line with the centre of your eyes with the bottom of the ears being in line with the bottom of your nose

Dr Stephen Marquardt was the man who revealed that our faces can be split up into different segments and managed to determine the different measurements that are involved in giving us the most attractive face (Meisner, 2014).

This can be furthered studied when looking into the work of plastic surgeons. Surgeon De Silva focuses upon the use of the golden ratio and measures beauty by this.  He takes the mathematical formula and calculates the precise measurements for his clients faces in line with the formula in an attempt to give them the ‘best’ outcome (Letzter, 2016).  This is echoed by Hardy (2016) who also argues that these mathematical concepts are a good indication for plastic surgery.  As we age or put on/lose weight the dimensions of our faces change again, our eyes may begin to droop, wrinkles may appear and therefore plastic surgeons arrange many thorough consultations and use these mathematical formulae to try and determine the best look for their patients.

“Our perception of beauty is based on the ratio proportions of 1.618. As the face comes closer to this ratio, it becomes perceptibly more beautiful” (Dr Maryam Zamani, citied in Hardy, 2016).  This helps detail the significance of the golden rule, it gives us our sense of beauty as we see it.

From looking at our own drawings in the lecture it was clear to see that the majority of us had improved from our first free hand portrait to our attempt when considering the mathematical dimensions and proportions.  Without mathematics these scales could not be implied, and the understanding of the scale and proportion would not be achieved.  By focusing on the groupings of the face and relating it to the cosmetic world it is clear to see that beauty, art and mathematics can be interlinked.

References

Hardly, L. (2016) The precise formula for a beautiful face. Available at: https://www.raconteur.net/healthcare/the-precise-formula-for-a-beautiful-face(Accessed: 31 October 2018).

Letzter, R. (2016) A plastic surgeon used a golden mathematical ratio to ‘prove’ this is the most beautiful person in the world. Available at: http://uk.businessinsider.com/the-golden-ratio-really-has-nothing-to-do-with-beauty-2016-7?r=US&IR=T(Accessed: 31 October 2018).

Meisner, G. (2014) Facial Analysis and the Marquardt Beauty Mask.  Available at: https://www.goldennumber.net/beauty/(Accessed: 31 October 2018).

Meisner, G. (2012) The Human Face and the Golden Ratio. Available at: https://www.goldennumber.net/face/(Accessed: 31 October 2018).

# Shape IS important.

Shapes, they are all around us.  From the tiles on our wall to the food that we eat. They are a basic mathematical concept we learn from the early stages of school that surround us every day.  Even the ability groups we fall into are named based on our basic shapes to help reinforce these each day – squares, circles and so on

When discussing the use of shape, we focused upon the art of tessellation.  This is the repetition of a shape that fits together seamlessly over a surface area with no cracks (How did Tessellation Transform from Method to Art?, 2016).  Tessellation can be seen everywhere, whether that be on the floor we walk on, the food we eat, that nature surrounding us or the world cultures we learn.

There are different forms of tessellation; regular, semi-regular and other. With regular tessellation there are only three possible outcomes, squares, triangles and hexagons and only one of those regular shapes is repeated to create the piece of art.  Semi-regular tessellation uses two or more regular shapes to create the tiling, with these there are only eight products.  The other tessellation can use many different shapes, including curves (mathisfun, 2018).

Nature is a complex matter; however, we must look at the mathematical link it has.  Look at the example of the bee’s honeycomb, bees want to store the most amount of food possible, so they have to think logically about the shapes they use.  Therefore, bees use tessellation.  If we were to place circles together repeatedly, we would have gaps hence why the hexagon is the used shape in honeycomb as replicating this shape next to each other leaves no gaps. Hexagons are one of the most intricate interlocking shapes (Bees and Maths, undated).  This is a prime example of tessellation being used in nature and our ever day surroundings.

Many cultures use this art to form beautiful designs, an example of this would be Islamic art. There are three main principles of Islamic art, this involves calligraphy, arabesque and geometry.  Calligraphy is significant due to the importance of writing within the Islamic faith, the use of writing is used within building designs and decorations.  Geometry is at the heart of Islamic design; the use of shape and patterns cover many surfaces.  The use of the geometric shapes relates to spiritual doings and nature (Hussain, 2009).

I feel that it is of high importance to educate our future pupils with the real-life link of maths to their surroundings.  Mathematics has a fine link to many aspects of our life, including art.  It is essential to make connections to other curricular areas involving mathematics as this is a fundamental principle of mathematics and it is significant through our learning (Ma, 2010).  I therefore believe sharing the creativeness of mathematics and their links will benefit children’s future learning.

References

Bees and Maths (undated) Available at: https://lifethroughamathematicianseyes.wordpress.com/2014/06/13/bees-and-math/(Accessed: 5 November 2018).

How did Tessellation Transform from Method to Art? (2016) Available at: https://www.widewalls.ch/tessellation-mathematics-method-art/(Accessed: 5 November 2018).

Hussain, Z. (2009) Introduction to Islamic art. Available at: http://www.bbc.co.uk/religion/religions/islam/art/art_1.shtml(Accessed: 5 November 2018).

Ma, L. (2010) Knowing and teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States. Available at: https://ebookcentral.proquest.com/lib/dundee/detail.action?docID=481154. (Accessed: 5 November 2018).

Maths is Fun (2018) Tessellation.  Available at: https://www.mathsisfun.com/geometry/tessellation.html(Accessed: 5 November 2018).

# What are the chances?

As I continue my journey through this module my eyes are continually being opened to new and exciting information and concepts. Who knew maths could be so interesting? The more I hear, the more relevant maths becomes, whereas my previous ideas about math never went any further than ‘I’ll never use that, why am I learning it?’, when really mathematical concepts surround us at all times.

So, what is probability?  It is in simple terms the measure of how likely a specific event will take place or not (E’s&O’s, 2018).  A simple example of this would be the flipping of a coin. Most of us have done this to help us decide who will do something when we know nobody wants to.  The whole “heads or tails, heads I win” scenario.

Now we probably never consider this being related to anything mathematical, we just do it and that is that.  However, the likelihood of flipping heads or tails is 50/50 therefore some math is involved but in a very simple form.  If we take another example, like the throwing of a dice for instance, it follows the exact same form, except this time there are 6 different outcomes, so if we wanted to roll a 6 the probability of us landing on it, is a 1/6 probability (mathsisfun, 2018).

Throughout recent inputs with both Johnathon and Eddie, they have sparked further discussion about the way our brains think about ‘randomness’ and I realised it is something I had never really considered before. However, when I thought more about it, I realised that they were correct.

As a species, we tend to think that even randomness must follow some sort of pattern. We cannot seem to get our heads around the fact that if we rolled a dice 4 times we could get a 4 every time or if we flipped a coin 7 times, we could get 7 heads in a row. We tend to think it is about time we rolled another number, or it is time for a different outcome but we must understand that every time we flip that coin it is the same 50/50 chance each time therefore with real randomness there is no one applying an order, only we as humans do this (Bellos, 2010).

So, let’s take a look at a chance game show, ‘Monty Hall Problem’.  In this game you are given the choice of three doors. Two doors have a goat behind them and one has a car, the prize everyone is waiting for.  You will be asked by the host which door you want to choose.  You pick one and then the game show host will open one of the doors you did not choose, revealing a goat.  From this you will be asked whether you want to stick or switch from the door you first picked, leaving you with a 50/50 chance? Well no, that is not the case.

It’s not? Why? Well initially, when all the doors were closed, and you were asked to choose one, there was a 1 in 3 chance of you choosing the door with the winning car.  Consequently, there is now a 2 in 3 chance that the prize is behind one of the closed doors.  When the gameshow host reveals a goat from one of the doors, we know that the car is not there, therefore the probability now only lies with the last door, meaning the chance of you picking the car is 2 in 3.  Hence why in reality you are twice as likely to win the prize by switching from your original door (betterexplained, undated).

In 2015, 66% of Scotland’s population gambled, that is over half of Scotland that have been involved in sort form of gambling (gamblingcommision, 2016) including playing the lottery, online gambling and casino venue gambling. However, what people do not know is that the casinos and slot machines are out to get you. The odds are stacked up against you and they understand human thinking as outlined above. When we gamble, we are losing money.  Even when we think we’re winning, it is usually us just breaking even (nfattc, undated).

Is gambling worth it? Whether it is gambling in its simplest form or whether we are doing it for big money in casinos, gambling is designed to have us lose. A way in which to overcome and beat gambling is simply by, you guessed it, using MATHS.  If you can work out the probability of you winning you are giving yourself a boost and a better chance to leave with the prize you desire. However, the only way to really win and beat the system is not to gamble.

References

Bellos, A. (2010) Humans find the concept of randomness very hard to understand, and this can get us into big trouble. Randomness fools us all.  Available at: https://www.dailymail.co.uk/home/moslive/article-1334712/Humans-concept-randomness-hard-understand.html(Accessed: 30 October 2018).

Better Explained (undated) Understanding the Monty hall problem. Available at: https://betterexplained.com/articles/understanding-the-monty-hall-problem/#!parentId=5766(Accessed: 30 October 2018).

Education Scotland (2018) Curriculum for excellence: numeracy and mathematics experiences and outcomes.  Available at: https://education.gov.scot/Documents/numeracy-maths-eo.pdf(Accessed: 30 October 2018).

Gambling Commission (2016) Levels of problem gambling in Scotland. Available at: https://www.gamblingcommission.gov.uk/news-action-and-statistics/Statistics-and-research/Levels-of-participation-and-problem-gambling/Levels-of-problem-gambling-in-Scotland.aspx(Accessed: 30 October 2018).

Maths is Fun (2018) Probability. Available at:https://www.mathsisfun.com/data/probability.html(Accessed: 30 October 2018).

NFATTC (no date) Why gamblers never win. Available at: http://www.nfattc.org/why-gamblers-never-win/(Accessed: 30 October 2018).

# Math Anxiety.

Math as far as I can remember has always been a daunting subject for me.  Throughout my time at high school anytime I entered the math classroom this sudden fear would hit, the fear of the unknown, the fear of not being able to do the work.  And no matter how hard I tried I could not get out this mindset, year on year the anxiety growing. Haylock and Thangata (2007) discuss the anxieties people face within this subject that often leads them to underperforming.  The classroom setting and the way of assessing pupils work also plays a role in developing this feeling of panic and stress.  Therefore, as a student teacher I want to change my outlook, so I can create fun and understanding ways to teach the subject to pupils, so they achieve a profound understanding of math.

When the year of my National 5 exams finally came, the math exam was fast approaching, and my attitude of math had not changed.  It felt impossible, I spent my days going into the school to try and tackle old math papers with my teacher and friends with no positive results.  Results day came, and I found out I had failed, my anxieties with math only got worse.

I did however struggle along and manage to leave school with my National 5 math qualification.

Although I know and understand math is used in my day to day life, I’m still left stressed when faced with any math problems or the prospects of enjoying teaching math in the primary school and making it fun and relatable to the pupils within my class, so they do not grow up with a hatred towards the subject.

So now, in my second year of university, I decided to take on this module in order to change my views, mindset and open up to new ideas and learn the ‘why’ in maths and not just the ‘how’.  In school we would have a quick discussion and a few on the board examples then turned to a textbook to work on our own through multiple pages of the same sums.  Ford et al. (2005, cited in Haylock and Manning, 2014) furthers this by detailing that pupils who struggle in math begin to only understand math when following a structure or a set of rules, meaning when faced with anything new or something worded in an unfamiliar way difficulty creeps in, this impacting how they work in the classroom setting.  Whereas Johnathon is helping me understand that we as educators must make math relatable and teach it in creative way to block out any negativity towards these lessons and allow children to understand problems even when they are faced with them in a different form.

Overall, I understand the importance of math and how it is used in all our everyday lives even without us noticing it.  I feel that in time, with the help of this module my outlook will change and my barrier with this subject will come down and I will not avoid all math situations and find problems less challenging in the future.

References

Haylock, D. and Manning, R . (2014) Mathematics Explained for Primary Teachers. London: SAGE.

Haylock, D. and Thangata, F. (2007) Key Concepts in Teaching Primary Mathematics. London: SAGE.

# RME, what is it all about?

When reflecting upon my previous understanding of RME it became clear to me that my knowledge didn’t really stretch past stories of jesus , easter or christmas ! In primary school that is all i remember  touching on, maybe an odd visit from the minister or a trip down to the local church.

High school didn’t really touch upon much either , i guess from there i only really remember touching on euthanasia.

So from these past few inputs it has finally became clear to me from seeing and touching many different religious artefacts that there is more to RME than jesus.  They have helped me understand other religions on a much wider scale and helped to provoke different discussions and feelings from each individual in the room.

From seeing the way artefacts can bring value to a lesson i feel teaching RME like this to children in my future classes will benefit them in many ways to form a stronger knowledge and become more engaged and open minded about religions.

During our Tdt time, me and a couple of other girls looked at Hinduism and some of the clothes woman and men in this religion wear , one of the girls then found out how Hindu woman apply their Sari and i wore it.  I think allowing children to take part in activities like this will definitely help widen their religious understanding.

# Resource Workshop

On Tuesday last week during our Values Lesson the class was split up into five different groups, with each group being handed a large envelope, including a number of resources.  The lecturer informed us we must come up with an idea of a helpful and resourceful tool for somebody just starting out on the course at the University.  From there we were to present our idea then go on to create it with the resources in front  of us.

Our group came up with the idea of a colourful timetable as none of us had found it easy trying to follow the complicated timetable.  We had many different resources within our envelope, including pencils, pens, coloured paper, elastic bands, post it notes etc.  It was also clear to us, group one had many materials like us when they shared their idea.

As we continued to hear other groups ideas it came to our attention they maybe didn’t have as much materials as us and struggled more to come up with an idea but we didn’t take any more notice to it and carried on with the task given.  It was clear to us that as Brenda (the lecturer) observed the class, she looked unhappy with the other groups and was paying them little attention which caused us to feel rather uncomfortable with a much more tense atmosphere and left us wondering why she seemed so angry and annoyed – you started to hear mutters around the class of everyone wondering why Brenda was so annoyed , we had never seen her before either so was a strange first impression to receive.

As she went on to score the groups we started to catch on that the way she was acting was all an act and she was doing this on purpose.  It made us all feel uneasy to begin with.  But this act was put in place to help us learn and realise the inequalities that are still vibrant in the classroom between the teachers and the children.

Those with more are seen as more important therefore given far more attention than those with less , this should never happen as each child should be given the attention and support that they require no matter what they have.  If anything, those with less, may possibly need more guidance.  Teachers need to be observant of all children in their care, and support each child with what they need, leading us to see how truly important equality is within the classroom and what a big role it truly plays.

Also after our group caught on to the act we realised we maybe should have given our resources to the groups who had less as we didn’t use every item we were given, but instead we just got on with what we had to do and didn’t think about those who didn’t have as much.  We just let them struggle on and watched Brenda help us and ignore them.

It definitely made me realise you have to pay attention to everybody and give everyone a fair chance or they will fall behind as we can too easily become oblivious to other peoples struggles.

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