Prior to studying discovering mathematics I believed maths to be only about numbers. However following the module, I now understand it is much more than that, it is everything and it is definitely an art form. Mathematics is prominent in many aspects of music such as beats in a bar , notation value ie crotchets and semi quavers etc, tempo and in tablature, the list is infinite.

For those who are unfamiliar with tablature or tab it is a form of musical notation that refers to instrument fingering rather than musical pitches (big guitar , no Date) . For example:

This picture shows musical notation indicating pitch and so requires the guitarist to know where each note is represented on the guitar fret. However the bottom line is the tabs. Tablature tells the individual where to put their fingers so the first note would be open first string as it tells the reader no fingers on fret but to play open first string once, the second note would then be first finger first fret first string played once.

I used to believe those who played tablature to play music were much like artist whos work was made using dot to dot. I didn’t think it required much if any understanding of music. However I recently decided to try playing tab and I think it is possibly the best decision I have made in terms of my musical progression. I already had a conceptual understanding of music or so I believed I recently tried to learn hotel California on guitar however there are quite a lot of sharps and flats in the music and I was struggling to remember it all so I tried using tabs and found it be alot easier. I didn’t need to keep reminding myself where the sharps were as the notation told me where to put my fingers. I learnt to play the song reasonably quick after this I just needed to perfect the pace.  Which brings me to my next point; pacing.

A disadvantage of tablature is that because there is no notes without truly knowing the song or understanding the notation above it indicating the pitch you have no way of determining the speed of the song or the dynamics (how loud a note is played) . However, as I learned to play music before I did tablature I used the notations to help me determine the speed of the song. I also knew that by looking at the start of the music where it tells me how loud to play the song using something I believe could be defined as algebra.

These letters represent more than just their face value they dictate a song massively (Angela ,2018). I believe that the understanding and appreciation of pupils learning about dynamics will increase their appreciation of the beauty of algebra.

In addition to this I used to believe that the f note was first finger first string just because it just was however after comparing the notation to the tablature I noticed the links between the two. I used to wonder why the  g note  was third finger first fret first string and not first finger second fret first string after all G does follow F in the alphabet ?  Tablature has helped me understand by comparing the two it is because there is a semi tone between f and g which Is f sharp and that Is why the second threat first string is f sharp not g.

So this begs the question so what?

I believe that by learning tablature my horizons have been broadened in terms of music as having an understanding of both tablature and notation I have developed a conceptual understanding of music, understanding not only the how but also the why of music. Learning music through the use of numbers have furthered my understanding of a mathematician and a musician and I would love for pupils in my future classes to have the opportunity to experience this and so I will to the best of my abilities ensure I teach maths and music together in hope that both experiences are enlightening and enjoyable for pupils.

Can mathematics be used to allow pupils to explore the world around them and even the entire universe? We often tell our pupils to aim for the stars, but would this metaphor be even more effective if pupils knew exactly how far away these stars actually are?  Many young children I spoke to on placement told me that when they grew up they wanted to be astronauts. However amongst the children that told me this many said they did not like mathematics. Astronomy is a subject that fascinates and engages people of all ages. The idea of an infinite number of galaxies and other planets is extremely interesting.  So can we captivate children’s interest by showing them that within astronomy there is not only an infinite universe to explore but also mathematics? Can we as professionals show children that Space like everything has a story and show them that within this story there is mathematics.

The majority of people are aware that there are many stars in the universe (about ten thousand million million million stars or 10^22).  Numbers are extremely prevalent in space and astronomy and this allows for discussion opportunities with children so that they do not even realise they are doing mathematics. This therefore allows  them to experience maths in a different way that isn’t just from textbooks and is fun engaging and most importantly something they actually can enjoy doing . Boaler (2010) believes that children find mathematics to be boring ,scary and uninteresting. This attitude is vastly spread throughout Scotland It is often referred to as maths anxiety. I argue partially it exists as a result of many children  not being taught that mathematics is more than just numbers.  Mathematics to me is a story told in a variety of different ways. A story communicated in a secret language that is waiting to be decoded with understanding and equations.  Children are constantly trying to decode the world around them why not show them how to do this using mathematics?

In addition to this another example of mathematics in astronomy is a light year; this refers to the distance that light can travel in a year. Light travels at 3.8 x 10^8  metres per second  and there are 365 days in a year,  However  before we do our equation we must first ensure we are using the same units.  we can do this by working out how many seconds there are in a year

365 x 24 (hours in a day) x 60( minutes in an hour)  x 60  (seconds in a minute)

= 31, 536,000

Following this we then use the distance speed and time formula we teach in schools

d = s/t

substitute in

3.8 x 10^8 x 31, 536,000

9,460,000,000,000 kilometres

Therefore light travels 9,460,000,000,000 kilometres in a year.

This concept alone incorporates many of the mathematical concepts covered in the mathematics curriculum for example measurement , distance speed and time,  decimals etc . Hopefully children will be able to form links between what they have learnt in mathematics and see the relevance of it.

To conclude I believe that astronomy offers children with an amazing opportunity to explore mathematics in a completely unique and fun way. I believe it offers a rich and diverse range of  mathematics such as measurement , distance, speed, time and multiplication and many more. Arem(2010) believes that children have the right to enjoy mathematics and question why we do things in maths. He believes that by allowing this we can help children overcome maths anxiety. Therefore I believe it is extremely important to use astronomy to assist children overcome maths anxiety. The universe has so much to offer and will continue to be explored by many for hundreds even thousands of years I know for certain it is something that I look forward to exploring with my class both in relation to the science and  maths behind it.

Arem, C. (2010). Conquering math anxiety. 3rd ed. Australia: Brooks/Cole Cengage Learning.

Boaler, J. (2010) The elephant in the classroom: Helping children learn and love maths. London: Souvenir Press.