Category Archives: 3.1 Teaching & Learning

What do you mean there is maths in music?

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Music has always been a special part of my life. Ever since I was born I have grown up surrounded in the wonderful world of music. My grandad was a trombone player, conductor and music teacher, my uncle is currently a professional trombone player for the RTE orchestra in Dublin and of course the biggest influences in my life; my mum a horn player and my dad a principle cornet player in a championship brass band. My whole childhood I was taken along to band practises, concerts and contests… I was always blown away by the talent of the people sat in front of me but sadly I never took an interest in playing an instrument myself, one of my biggest regrets! I always wonder “why?” but after seeing the time and commitment my parents had to put in, it must have put me off which is a shame because the reason they were so committed and hard-working, was because of the love and passion they had for playing music. “ Oh, well.. Jacqueline is the singer and dancer of the family” my mum always told her friends from band when they asked why I wasn’t playing an instrument yet. I really did love singing, oh and I can’t forget my attempt at playing (more like memorising) the keyboard for my higher music exam, they managed to bag me an A (I hope it was more the singing!), so I couldn’t have been too bad! I can’t forget the help my mum gave me with the theory either, she wouldn’t be happy if I never mentioned that!

 

So, even after having so many encounters with music, when I was told we had a lecture on maths and music, I questioned it. How much maths is there really in music? Well, a quote we were given in the lecture was a revelation! Connecting music and maths finally made sense to me:

 

“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.”  (Marcus du Sautoy, 2011)

 

There are many connections:

 

  • Note values/rhythms –
  • Beats in a bar- being able to divide bars in to numerous fractions of beats in a bar
  • Tuning/Pitch
  • Chords
  • Counting songs
  • Fingering on music
  • Time signature
  • Figured bass
  • Scales
  • Musical Intervals
  • Fibonacci sequence

 

Many of these actually have quite an obvious link with maths when you really think about it.

 

 

Music and ‘golden sequence’:

 

Another, perhaps less known, but important, link between maths and music is the ‘Fibonacci sequence’. The Fibonacci sequence is a special series of numbers formed by using the sum of the previous two numbers to get the next number within the sequence. The sequence looks like this: 0,1,1,2,3,5,8,13,21 and so on…

 

If we look at a piano keyboard we can see that the chromatic scale consists of 13 notes. The diatonic scale is composed of 8 notes and the pentatonic scale, 5 notes. In addition to this, the basic chord structures used in music consist of a triad of notes. These are the first, third and fifth notes in the common ‘diatonic’ scale.

 

I thoroughly enjoyed the mathematics and music workshop… firstly because it reminded me of my love for music but, more importantly, it taught me that something that I have been immersed in my whole life has, in fact, got a lot to do with music which I had never really thought about until that point! It made me consider all the other things in my life that probably has some sort of maths behind it that I haven’t discovered… yet! I am looking forward to teaching music in the future with enjoyable activities where the children can really see the impact maths has on music.

 

Mathematics and creativity?

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Maths AND creativity??

I know! two words you would never normally put together. Maths is usually a subject people associate with lessons that involve worksheet upon worksheet where your answer can either be right or wrong. Where is the fun in that? No wonder so many children hate maths when they are stuck doing the same boring lessons. But maths CAN be fun and creative! This was proven in the two workshops we had in the discovering mathematics module that focused on the creative side of maths.

In Eddie’s workshop, we looked at teaching creative maths in geometry. For example, teaching about shapes by using tessellation. A tessellation (or tiling) is a repeating pattern of shapes that fit perfectly together without any overlaps or gaps. There are different types of tessellations: regular, semi-regular, and then other tessellations of circular, curved, irregular shapes that mathematicians cannot agree on how to name. Tessellations of CONGRUENT shapes, are called monohedral tessellations. The word monohedral basically means ‘one’ – mono and ‘shape’ – hedral.  Regular tessellations are made up of only one regular shape repeated, whilst semi-regular tessellations are made up of two or more regular shapes tiled to create a repeating pattern. The regular shapes that tessellate are: squares, hexagons and equilateral triangles. ALL triangles and quadrilaterals also tile but they are not ‘regular’ shapes and often have to be rotated to make them fit together.

Tessellations are a great for connecting maths and art together. Many historic paintings were made using tessellations and by showing some examples of these to a class, it would be a great way to engage the children in the lesson immediately. They probably wouldn’t even think it was a maths lesson! I thoroughly enjoyed this workshop and creating my own tessellation with Caitlin. Creating patterns with the different shapes and colours whilst also making sure everything fitted together perfectly was a fun challenge and is a lesson I will use in the future. It allows the children to fully experiment with 2D shapes instead of just looking at them in a textbook.

 

Getting into the child-like spirit with paw patrol plates and colourful paints!

The beginning of our masterpiece! figuring out how we wanted our tessellation to fit together and what pattern we wanted it to create.

The final product! unfinished and not very neat.. but I love the way it would have been if we had more time to finish it.

Maths anxiety in children

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Maths anxiety

Heart beats faster and faster. Sweaty palms. Puzzled and confused. Everyone has some type of fear or anxiety. Imagine how you would feel when being faced with a maths question that leaves you in this state, the cause? Maths anxiety.

What is maths anxiety?

Maths anxiety is defined by Mark H. Ashcraft (2002) as ‘a feeling of tension and anxiety that interferes with the manipulation of numbers and the solving of mathematical problems in ordinary life and academic situations’. This shows that people not only suffer from anxiety when faced with a maths question, but due to the maths affecting aspects of our everyday lives, it can affect some people constantly. Now, of course everyone can have a different level of anxiety and it doesn’t always stop some people from doing well in maths. It is also possible to conquer maths anxiety and I will mention some of the ways teachers and parent can help children who suffer from it.

Does maths anxiety affect performance?

Well to this I ask: What came first, the chicken or the egg?

Random question, I know! But this theory can be applied to maths anxiety and performance in maths. And of course, there isn’t a clear-cut answer for this either. What came first? Ma (1999) provides evidence that people who suffer from maths anxiety are more likely to perform more poorly during assessments than those who do not suffer from it. Where it gets confusing is that we don’t know which caused which. Anxious thoughts could be what causes poorer performance in maths or it could be that struggling with maths causes anxious thoughts about mathematics. I personally feel it is my difficulty with maths that has stemmed my anxiety and this can be traced back to primary as there are some fundamental area of maths that I never got to grips with which meant anything that was built on top of these area as I got older I was anxious about and had no confidence. However, others may experience it the other way around for example if they go to school with a fear of maths from listening to people at home being negative about it, this may affect the from the start.

 

How will I defeat maths anxiety in my future classes?

 

Involvement: Ensuring parents are actively involved in helping their child with maths is proven to improve children’s success with maths. If a child sees their parent has a good relationship with maths, this will help them to have a better perception of it.

 

Positivity: As a teacher, I will ensure I use positive language surrounding maths and children’s abilities. Making sure children are not under pressure to answer questions they may not be confident about in front a whole class so that anxious feelings and loss of confidence never happen. I will also make sure to celebrate improvements and give assurance for any struggles they may have.

 

Fun and relevant lessons: Making lessons fun and relevant will allow children to realise that maths isn’t just a subject you need to learn for school. Highlighting that it is all around us in our everyday lives will motivate children to put more effort in to learn. Active lessons eg. groups competing against one another are great ways for children who are less confident working individually to learn from their peers. As there are no specific children in the spotlight it allows them to enjoy the activity without worry. Even adapting lessons around specific children’s interest eg. football or dancing, will engage them more and make them want to learn. Making sure to eliminate gender stereo types for future jobs by showing both genders achieving any many professions.

 

 Building knowledge slowly: Rote learning is often looked down on these days, however, I am someone who wishes I did learn some of the basics by rote to ensure they were instilled in my mind. Timetables were always an aspect of maths I never knew ‘off by heart’ and it caused to struggle with many other aspects of maths that depended on confidence with times tables. Therefore, with my class I would ensure that children are confident in fundamental maths so that building further knowledge isn’t daunting. Going slow doesn’t mean a child is bad at maths but it ensures they have thorough understanding before moving on which will, in the long run, make them more confident.  

 

Mistakes are allowed! Children must realise that maths is not all about getting every answer correct all the time. The process of solving the problem is just as important. My maths exams in school are what taught me about the importance of this, as one maths question could be worth 5 marks and within those 5, the correct answer was only worth 1 mark. Maths is about being able to process problems and being able to apply these skills to many different questions within maths or even real-life situations. The more pressure a child puts on their self to always be right, the more anxious it will cause them to be. It is also a good way to show all the alternative ways there are to find an answer to one question and all of them are correct if it leads you in the right direction.

8 Practical Ways to Conquer Your Child

(Taken from www.MathsInsider.com)

 

As a committed, professional developing teacher at university, I am determined to work hard over the next few years and freshen up my maths skills to ensure my past and current feelings of maths anxiety do not affect the children in my classes. After writing this blog post I have already given myself an open mind and confidence in myself that I can do it! I want to teach children, the way I have mentioned above, to be confident in maths concepts and problem solving with the hopes that anxiety will never affect them.

 

References

 Ashcraft (2002). MATH ANXIETY: PERSONAL, EDUCATIONAL, AND COGNITIVE CONSEQUENCES. Current Directions in Psychological Science 181-185.

Ma (1999). A META-ANALYSIS OF THE RELATIONSHIP BETWEEN ANXIETY TOWARD MATHEMATICS AND ACHIEVEMENT IN MATHEMATICS. Journal for Research in Mathematics Education, 30(5). 520-40.

Mukisa, C. (2017). 8 Practical Ways to Conquer Your Child’s Math Anxiety | Maths Tips From Maths Insider. [online] Maths Tips From Maths Insider. Available at: http://www.mathsinsider.com/conquer-math-anxiety/ [Accessed 25 Oct. 2017].

the Guardian. (2017). The fear of all sums: how teachers can help students with maths anxiety. [online] Available at: https://www.theguardian.com/teacher-network/2015/nov/17/how-teachers-help-students-maths-anxiety [Accessed 25 Oct. 2017].