Maths is a difficult subject to study, that’s why it is important for teachers to ask themselves, how can they make maths more entertaining? How can they make it something which is enjoyed rather than something which is a textbook subject? I have always believed maths to be a textbook subject as it was all that I have ever experienced. When I was in school, I was never given the opportunities to explore maths in any other subject or outside the classroom, therefore our input on maths outdoors was very eye opening.

What we carried out in this input is one of many ways in which teachers could use to teach maths outdoors and help their pupils to understand maths from a different perspective. In this input we looked at how we could measure a tree by using an isosceles triangle, however, I don’t think many children or adults would ever look at trees and associate them to maths, well I certainly never would; this outlines the lack of creativity shown within my maths education.

What can children gain from Maths outdoors?

Early years careers, (2015) state that by “taking maths outside, it refreshes the subject,” it can help to move away from traditional textbook learning and can show children an entire new and creative dimension to maths which they are not fully aware about. (Early years careers, 2015). (National Centre for Excellence in the Teaching of Mathematics, 2008) also state that they believe that “every young person should experience the world beyond the classroom as an essential part of learning and personal development, whatever their age, ability or circumstances.”

Thus, maths outdoors should be recognised as important in order to help children’s development; as working on maths outdoors can encourage children to make different “links between feelings and learning” (NCETM, 2008). NCETM, (2008) outline that these links can help to influence the decisions and choices we make, thus they enable young individuals to “transfer learning experienced outside to the classroom and vice versa”. Therefore, by working outdoors children could gain information about the subject that they would have never gained from inside the classroom.

By going outside of the classroom, children can gain more opportunities compared to within the classroom because outdoors can provide “authentic or experiential learning” this is where learners can actually experience what they are learning, this cannot always happen in the classroom. This can facilitate improved access to the key “pathways to learning”; for example, Visual, Auditory and Kinaesthetic. Teachers could use this to their advantage to help their pupils learn new information in the most appropriate and beneficial way for them. (National Centre for Excellence in the Teaching of Mathematics, 2008)

How can children engage with maths outdoors more?

There are so many different forms of resources which can be used inside a classroom when completing maths, however there is actually an unlimited amount of resources which can be used outside. This is because the “natural environment can be used as resources in maths activities as well as bought in resources” (Early years careers, 2015). Therefore, teachers should make use of all the exciting outdoor resources when doing maths activities to encourage engagement, by only using pencils, papers and clipboards outside the engagement may lack because they use these so much inside.

It is important to note that resources are not always objects, as within our input we were measuring trees, we did use a form of apparatus when properly estimating the measurements but we also used ourselves to help measure the trees. We used our sight to see the top of the tree whilst bending over, this then helped us to know where to measure from. Teachers should make the most of the outdoor space and use the pupils to calculate their own findings as this wouldn’t happen all the time in the classroom.

Teachers will know that the outdoor environment will provide different opportunities, thus they should “apply creative and imaginative tasks in which the children can apply knowledge they already have to the real world” (Early years careers, 2015). For example, a creative outdoors activity could be kite making where they have to find outdoor materials to make their kite. By making their activities relevant, they will be more interested and therefore more engaged with what they are doing.

Within schools, maths can be seen as a sit-down activity, I believe this should change in order to remove this negative stigma of maths and appreciate all of its different elements indoors and outdoors. Thus, to engage with maths outdoors more, teachers should work together to make outdoor learning more regular within the school day. (University of Plymouth, 2016) For example, teachers could adapt their lesson plans to work in both indoors and outdoors conditions, this will then give children the opportunity to experience maths in different exciting ways and not only describe it as a textbook subject but understand that “learning mathematics outside the classroom is not enrichment, it is at the core of empowering an individual’s understanding of the subject” (NCETM, 2008). Therefore, with the support and creative ideas from teachers, not only should the level of engagement increase but it could help to increase a child’s confidence when understanding different mathematical content.

References
Early Years Careers. (2015). The importance of taking maths outdoors – Early Years Careers. [online] Available at: http://www.earlyyearscareers.com/eyc/early-years-practice/the-importance-of-taking-maths-outdoors/ [Accessed 23 Nov. 2018].

National Centre for Excellence in the Teaching of Mathematics. (2008). Learning Maths Outside the Classroom. [online] Available at: https://www.ncetm.org.uk/resources/9268 [Accessed 23 Nov. 2018].

University of Plymouth. (2016). TRANSFORMING OUTDOOR LEARNING IN SCHOOLS. [online] Available at: https://www.plymouth.ac.uk/uploads/production/document/path/7/7634/Transforming_Outdoor_Learning_in_Schools_SCN.pdf [Accessed 23 Nov. 2018].

When I learnt that we were going to be doing an input on Maths and Music, I was confused, to me these two subjects have nothing in common with each other. I was fascinated to see what we were going to be focusing on.

I love music but have never had any luck with playing any instruments. My music knowledge is nowhere as good as my fathers’, but I can still appreciate most genres of music. Music is a subject I never really took that much from within School and during my MA1 placement I didn’t witness any music lessons. Thus, I feel I didn’t receive the most exciting music education. So, before this input I was slightly worried I wouldn’t know of any musical terms which may have been quite obvious.

To begin with, we were shown a quote by Marcus du Sautoy (2011) which stated, “Rhythm depends on arithmetic, harmony draws from basic numerical relationships, and the development of musical themes reflects the world of symmetry and geometry. As Stravinsky once said: “The musician should find in mathematics a study as useful to him as the learning of another language is to a poet. Mathematics swims seductively just below the surface.” After reading this quote, I somewhat understood that Mathematics could have different functions; I could recognise how different harmonies could be associated with “numerical relationships” because when playing music every individual has to count to make sure they are in time with the music playing. From this, I was slightly more open-minded and didn’t think it was such an abnormal concept. (Sangster, P, 2018)

Within the input, we were asked to write down as many different links between Maths and Music that we could think of; (my mind went black) so I only could think of the number of beats within a piece of music. I knew myself, that there was going to be many more links which were not as obvious as my suggestions; however, I didn’t realise how many links there could be. I did recognise the musical terms, I just simply would have never linked Maths to these musical terms. That’s when it dawned on me just how much value the subject of Maths had within Music.

Some of the links we were shown:
• Note values/rhythms
• Beats in a bar
• Tuning/Pitch
• Chords
• Counting songs
• Fingering on music
• Time signature
• Figured bass
• Scales
• Musical Intervals
• Fibonacci sequence

When looking at these links, some are reasonably recognisable or obvious. Although I wanted to learn more about the Fibonacci sequence.

I soon discovered that the Fibonacci sequence “is one of the most famous formulas in mathematics” (Live Science, 2018) which was originally found by Leonardo Pisano Bigollo, who was famously known as Fibonacci. It is a sequence of numbers where each number within the sequence is the sum of the two numbers which come before it. The sequence goes as 0,1,1,2,3,5,8,13,21,34 and this sequence is continuous; the “mathematical equation describing it is Xn+2= Xn+1 + Xn”. For example, if we take the number 21, it is in the sequence that the two preceding numbers equal 21 (8+13). (Live Science, 2018)

When looking at a keyboard the numbers in the Fibonacci sequence can be seen. For example, there are thirteen keys along a keyboard “in the span of a full octave which consists of eight white keys and five back keys that are arranged in groups of two and three along the keyboard”. (PQ, 2016) Fibonacci numbers can also be seen in “the notes that make up musical scales” (PQ, 2016), for instance, the Pentatonic scaled consists of five notes, the Diatonic scales is made up of eight notes and the Chromatic scale has thirteen notes. It appears that the foundation of chords are made up from the 1st, 3rd, and 5th notes in any scale; and all three of these numbers are Fibonacci numbers. (PQ, 2016) This video below demonstrates the Fibonacci sequence in a musical context.

Throughout my research of Maths in Music, I discovered Pythagoras who was historically known as a mathematician and a musician. I already knew that Pythagoras was best known for “his Pythagorean Theorem, which states that in any right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (A2 + B2 = C2).” (History of Music Theory, undated)

However, I wasn’t aware that he ever had a connection to music. He held the idea that “everything in the universe” was connected to maths and numbers. He felt the same way about music, he viewed music as “the unifying principle of Harmonia, which he regarded as a divine principle that brings order to chaos and discord.” (History of Music Theory, undated) Pythagoras also believed that music could remove stress and he also arranged specific songs “to be played at the end of the day to relieve day to day stress levels”. In addition, he thought that there were particular genres of music which suited to the time of day and to the seasons throughout the year. (History of Music Theory, undated)

Overall, before this input and before any of my research I was so oblivious to the different functions that Maths has in relation to Music. There has been a connection between Maths and Music for at least 2000 years, and I am only learning of it now. That says something doesn’t it? I believe that there is not enough emphasis on Mathematics within Music in Education. I have learnt so much about this concept and think it is useful to know the different links between the two subjects.  Every child should be shown the different applications which mathematics has to everyday real-life situations. For example, they should recognise that Maths is not a boring adding sums activity but that “it can be a challenging, exciting and fascinating subject” (Saloni, 2010).

Teachers should try to encourage children to understand how Mathematics is used in a greater context, for example, by bringing music “into mathematical teaching” (Saloni, 2010), they can show how exciting and versatile Maths can be. For example, teachers could implement Pythagoras’ theory of music within the classroom to remove any stress and create a peaceful atmosphere. This could therefore make Mathematics more relevant, entertaining and joyful for children; and also remove the negative attitudes towards Maths from an early age and instead encourage them to indulge within the musically mathematical world and enjoy the many different opportunities and activities that it brings.

References

History of Music Theory. (undated). Pythagoras: Music, Geometry and Mathematics | History of Music Theory. [online] Available at: http://www.historyofmusictheory.com/?page_id=20 [Accessed 4 Nov. 2018].

Live Science. (2018). What Is the Fibonacci Sequence?. [online] Available at: https://www.livescience.com/37470-fibonacci-sequence.html [Accessed 4 Nov. 2018].

PQ, R. (2016). Music and the Fibonacci Sequence. [online] Dubspot Blog. Available at: http://blog.dubspot.com/fibonacci-sequence-in-music/ [Accessed 4 Nov. 2018].

Saloni, S. (2010). An Exploration of the Relationship between Mathematics and Music. [ebook] University of Manchester. Available at: http://eprints.ma.man.ac.uk/1548/1/covered/MIMS_ep2010_103.pdf [Accessed 4 Nov. 2018].

Sangster, P. (2018). ‘Discovering Maths: Music and Mathematics’. [Powerpoint presentation]. ED21006: Discovering Mathematics. Available at: https://my.dundee.ac.uk/webapps/blackboard/content/listContent.jsp?course_id=_58988_1&content_id=_5173832_1&mode=reset [Accessed 4 Nov. 2018].
Schwab, G. (2012). Fibonacci sequence in music.

Videos used

Available at: https://www.youtube.com/watch?v=2pbEarwdusc&feature=youtu.be [Accessed 4 Nov. 2018].
Du Sautoy, M. (2011). ‘Listen by numbers: music and maths’ Guardian. Available at: http://theclassicalsuite.com/2011/06/listen-by-numbers-music-and-maths-via-guardian/ [Accessed 4 Nov. 2018].

I always saw Maths as an important subject, an important subject to be passed not enjoyed. When I was in school there was a complete lack of enjoyment within this subject, there was no creativity within the provided work, it was very much copying questions from a textbook. This procedural approach didn’t ensure the understanding of the different topics; my class and I could remember each topic as we worked on them, although by the stage we moved on to another topic, we couldn’t properly remember the correct information. This then triggered negative attitudes towards mathematics creating an intense and uncomfortable environment to work in which immediately affected my confidence levels.

My experience in school is a common one, as a big problem within schools and for children is that maths can be portrayed as something which is hard to do but is expected to be completed. This automatically complicates the subject and thus children internalise this thought which ultimately will affect their feelings towards maths as well as their work. Moreover, children can begin to believe maths is a subject you can or cannot do, if you fall in either category the sense of enjoyment is somewhat lost. For example, if a child feels they cannot carry out mathematical work their motivation and confidence could be limited, equally if a child is reaching their targets, there can be pressure to continuously meet these or higher, and if fails occur this could also impact their confidence levels and sense of self-worth. Both ways display that maths can be seen to be something which is too hard to do or something which is required to be passed. (Fleming, 2018)

For pupils in secondary schools, Maths is a subject which is ‘required’ for employment and university so pupils may only focus on passing this subject because it is seen as a necessity. Therefore, pressure on pupils will increase and their opinions of the subject can be more negative because it is the subject itself which is causing the stress and discomfort that pupils may feel. Teachers will also feel the pressure to ensure that their pupils are prepared for their exams; ultimately the excitement of maths has faded due to this overwhelming amount of pressure to achieve a grade C or above.

Therefore, there needs to be more of a focus on removing the negative stimulus around maths and instead promote a positive attitude towards the subject at an early age. By doing this, at an early age, it can give more opportunities for teachers to be creative and portray to children that mathematics is much more than numbers and is a subject which should be enjoyed. Enjoying maths will help with understanding and therefore help individuals gain more awareness of how it is used in everyday life.

Schools must ensure they are hiring teachers who enjoy and are passionate about maths. Within a classroom the teacher should be a role model and lead their class with enthusiasm and motivation by utilising a consistent positive approach towards maths which focuses on stimulating self-worth and confidence around the subject. Therefore, teachers should ensure they lead by example and influence pupils not to view maths as something procedural but something which provides enjoyment. For example, teachers could make maths more creative by using songs or rhymes as this can make “it easy for children to develop mathematically”. (Pound, 2008, p.7) By using music at an infant age it can also help children to remember information. (Pound and Harrison, 2003) Thus by inserting rhymes and songs in early childhood, it is more likely for children to remember what they have been taught because it was easier and more enjoyable to learn. Equally, if children are gaining a proper understanding of each topic in maths, they will be capable of effectively moving on to another topic and continue to build upon their previous knowledge. (Fleming, 2018)

To remove this negative stimulus and promote enjoyment there should be more active involvement of parents as this has a huge effect on their children’s learning and development. Research has “highlighted over two decades the importance of parents’ interest and involvement in their child’s mathematical thinking and understanding”. (Pound, 2008, p.9) This research portrays that making maths easier and more enjoyable “relies heavily on getting parents involved and making maths more relevant to children’s everyday lives”. (Pound, 2008, p.9) If parents are able to influence enjoyable maths upon their children at a young age, for example through providing “educational toys and activities which promote their maths skills” (ETL Learning, undated) children may instead internalise the feeling that maths is enjoyable rather than an impossible and difficult subject.

Overall, it is important that a positive approach to mathematics is applied and influenced to children by their teachers, parents and the whole school community as “if we are to support children in becoming autonomous learners and responsible citizens then it is the role of educators to ensure that children feel as comfortable with numbers as they do with words”. (Pound, 2008, p.5) Thus, if negative opinions of mathematics decreased and there were more supportive, creative and less pressuring teachers promoting positivity, children may feel more comfortable in a mathematic learning environment and perform to the best of their ability whilst enjoying what they are doing.

ETL Learning (undated). The Importance of Teaching Math in the Early Years – ETL Learning. [online] Available at: https://www.etllearning.com/resources/the-importance-of-teaching-math-in-the-early-years/ [Accessed 1 Oct. 2018].

Fleming, G. (2018). Why Math Is So Hard. [online] ThoughtCo. Available at: https://www.thoughtco.com/why-math-seems-more-difficult-for-some-students-1857216 [Accessed 1 Oct. 2018].

Pound, L. (2008). Thinking and learning about mathematics in the early years. London: Routledge.

Pound, L. and Harrison, C. (2003) Supporting Musical Development in the Early Years. Buckingham: Open University Press Cited in Pound, L. (2008). Thinking and learning about mathematics in the early years. London: Routledge.