Medicine. It is something we all hate but without a doubt something we all have to take at some point in our lives. However, mathematical knowledge is something you and any medical professional need to have before administering any kind of medicine.

For some medicines it is quite easy to follow the dosage intrusions, for example with paracetamol you are advised to take between 1 and 2 500mg tablets every 4 hours within a 24 hour period. This means that the maximum does of paracetamol for an adult is 8 500mg tablets in 24 hours, ensuring there is the advised 4 hour cap between (NHS Paracetamol for Adults, No Date).  In order to prescribe yourself with paracetamol you must have mathematical knowledge about quantities, so how many is 2  and also a good understanding of time. To stop yourself from overdosing you will need to know how long 4 hours is, as well as figuring at what time these 4 hours will have past for you to take another does, if you require it.

For children, paracetamol dose are different to adults as the dosage changes by age and children receive their paracetamol through a liquid syrup. This image from NHS Paracetamol for Children shows the different ages and the dosage that goes with this.

Even though you receive a measuring spoon with liquid paracetamol, it is not known what age the child who is going to be taking it is and so it standard to give a 5ml spoon with a 2.5ml on the other end. This mean that if you child is 8 – 10 years they will require 7.5ml, you need to know to give them a 5ml dose and then 2.5ml, straight after each other in order to make that required does of 7.5ml. Similarly, with a 10ml does you need to know to give the child two 5ml dose in order to make a 10ml. This mathematical knowledge is essential to ensure that you do not give the child an overdose and they end up in a serious condition.

When a patient is in hospital they trust the medical professionals to help them get better and so this also means that they trust that the medical professionals have sufficient mathematical knowledge to ensure they are not given an overdose or not enough medication to help them feel better.

Some of the data medical professionals have to record look a bit like this:

Now I’m not going to pretend I know what these charts mean or what they can predict purely because I’m studying to be a teacher and not a medical professional. However, what I do know is that it requires a lot of mathematical knowledge to be able to create these charts, furthermore it is essential that the medical professionals have a deep understanding of what the maths is telling them and be able to interpret this into a diagnosis such as high blood pressure.

Medical professionals often have to use a person height and weight to calculate how much of a specific medicine they can receive (Hothersall, 2016). For example, say I am in hospital and require some medication, the dosage I receive based on my height of 4ft 11 and a weight of 7 stone will be smaller a smaller dose than someone who is 6ft 10, weighing 11 stone. If I was to be given the same dose of this specific medicine as the person who is 6ft 10 weighing 11 stone, it is most likely I will become more ill than what I was originally (Hothersal, 2016).

In the future I plan to take a greater interested in administering medicine and how much mathematical knowledge it requires to do so. I have been fascinated by the variety of areas of mathematics that can be used in medicine and I would like to deepen my understanding of this.

References:

Hothersall, E (2016) Numeracy: Every contact counts (or something) [PowerPoint Presentation]. ED21006 Discovering Mathematics. Available at: https://mydundee.ac.uk  (Accessed on: 13th November 2017)

NHS Paracetamol for Adults (Not Date). Available at: https://beta.nhs.uk/medicines/paracetamol-for-adults (Accessed on: 13^th November 2017)

NHS Paracetamol for Children (No Date). Available at:  https://beta.nhs.uk/medicines/paracetamol-for-children (Accessed on: 13^th November 2017)

Are maths and music connected? This is a question I never thought I would ask myself and the answer was even more surprising… yes, they are!

At first I must say that I did not see the link between the two. In my opinion I view maths as a very structured subject. It has set formulas and for each question only one set answer, something in which music is not. Music, to me, is a way to express your feelings and emotions; it is free for you to do what you like with, you are free to make your own styles, there is not set structures and not set answers. However, even though musicians do create their own music they use maths to help them develop, express and communicate their ideas (Shah, 2010)

There are many aspects mathematical knowledge that musicians use when playing and creating music, one of the simplest aspects is being able to count, for example a musician needs to be able to count the number of beats in a bar. A musician also uses their mathematical knowledge when looking at rhythm, scales, intervals, patterns, symbols, time signatures, overtones and pitch (American Mathematical Society, 2017).

Maths is not only used to help musicians to create and play music, it is also used to help them to tune and play their instruments. Mathematics is able to explain how strings vibrate at certain frequencies and that sound ways are used to describe these mathematical theories (Shah, 2010).

However, it is not just string instruments such as violins and cellos that use their frequencies to help with tuning and playing, a pianist will also do this. But the maths is not always enough and so a pianist will use the frequencies along with their knowledge of the sound of the keys in order to tune the piano (Sangster, 2017).

Seeing first-hand the ways in which maths and music connect is something I have enjoyed. This has made me consider the possibility of using music as a way of explaining mathematical concepts such as patterns and sequences in my teaching practice. I believe that doing this well bring an element of enjoyment as well as a large amount of engagement from pupils as this would be an interactive activity that could be used with a variety of ages and stages within the primary school.

References:

American Mathematical Society (2017) Mathematics & Music Available at: http://www.ams.org/samplings/math-and-music (Accessed on: 6th November 2017)

Sangster, P. (2017) Discovering Maths: Music and Mathematics [PowerPoint Presentation]. ED21006 Discovering Mathematics. Available at: https://mydundee.ac.uk  (Accessed on: 6^th November 2017)

Shah, S. (2010) An Exploration of the Relationship between Mathematics and Music. Available at: http://eprints.ma.man.ac.uk/1548/1/covered/MIMS_ep2010_103.pdf (Accessed on: 6^th November 2017)

I have never really been overly enthusiastic about maths and I have most defiantly never been enthusiastic about art. The two as individuals give me much anxiety and I often believe the myth that your either good at maths or literacy, the two never hold the same value. I also had this view towards art and so, when I realised we were going to be receiving a lecture on maths and art together, I must say I felt a strong sense of dread. However, I was amazed and how simply maths and art could be connected. My original thoughts were that we would be using our mathematical knowledge to create large portraits, how one would do this I do not know.

Piet Mondrian is one artist who bring maths and art together. He was famous for creating geometric abstract pieces of work (Piet Mondrian 1877 – 1944, no date). This abstract style he created was quite simple, he would create a grid of black and white horizontal lines on white paper. The black lines would create a variety of different sized squares and rectangles which he coloured in using only 3 primary colours; he called this piece of art Neo – Plasticism (Piet Mondrian 1877 – 1944, no date).

A mathematician whose work has artistic connections was Fibonnaci. Fibonnaci created different sequences, one of his most famous was the golden spiral.  Fibonnaci created a mathematical sequence that if you start at 1 and add the two numbers before it you will create the Fibonnaic’s sequence (Meinser, 2015). Doing this myself I found that the sequences goes in the order of 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 etc. Fibonnaci discovered that using this sequence as dimensions for squares he would be able to create a perfect spiral inside of them; today this spiral is known as the golden spiral (Meinser, 2015).

The golden spiral can be seen most of all in nature. FIbonnaci’s sequence can be seen in sunflower seeds, pinecones and pineapples (Meinser, 2015).

“Is God a mathematician? Certainly the universe seems to be reliably understood using mathematics. Nature is mathematics. The arrangements of seeds in a sunflower can be understood using Fibonacci numbers. Sunflower heads, like those of other flowers, contain families of interlaced spirals of seeds – one spiral winding clockwise, the other counter clockwise. The number of spirals in such heads, as well as the number of petals in flowers, is very often a Fibonacci number.”

(Pickover, 2009, p.100)

https://www.youtube.com/watch?v=iEnR8zupK0A

A progression from Fibonnaci’s golden spiral was that from using this sequence a golden ratio could be determined for line segments. This special ratio will appear when a line is spilt into two segments. We divide a line into two segments so that the ratio of the whole segment to the longer part is the same as the ratio of the longer part to the shorter part (Pickover, 2009, p.112).  The ratio is determined by using the formula:

(a + b) / b = b/a

The golden ratio is 1.61803, however not every line segment will equate to this, it will only occur if the numbers used appear in Fibonacci’s Sequence.

I started off by creating my own golden spiral, then by using the dimensions of the rectangular boxes and substituting these into the golden ratio formula I was able to determine the golden ratio. I also done this using the dimensions for my Mondrian drawing, however I was unable to determine the golden ratio in these, meaning that the dimensions did not occur in FIbonnaic’s sequence.

Maths is often used when creating patterns. Maths can be used to determine the length of the line or the size of the boxes within a pattern. One example of this is fractals, a fractal is a never ending pattern which is self-similar across different scales (Robb, 2017).

I went into the lecture on maths and art with the feeling of dread and came out in amazement. I had no idea about the variety of ways that maths could be linked with art and that I could do it. I now feel passionate about bringing maths and art together and it is something I plan on researching further to take with me onto to placement and in my career as a teacher to ensure that children do not feel the same feeling of dread I first had when I saw the title Maths and Art.

References:

Meisner, G (2015), Spirals and the Golden Ratio, Available at: https://www.goldennumber.net/spirals/ (Accessed on: 27^th October 2017)

Pickover, C. A. (2009) The Math Book From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics. London: Sterling.

Piet Mondrian 1877 – 1944, (No Date),  Available at: http://www.tate.org.uk/art/artists/piet-mondrian-1651 (Accessed on: 27^th October 2017)

Robb, A (2017) ‘Maths and Art’, [PowerPoint Presentation], ED21006 Discovering Mathematics, Available at: https://mydundee.ac.uk (Accessed on: 27^th October 2017)