I can’t quite believe that first semester is drawing to an end and that the Discovering Mathematics module is now over. I can truly say that I have thoroughly enjoyed my time and have learned a great amount about the world of maths surrounds me. I have also learned the extreme importance of having a profound understanding of fundamental maths, which I will ensure I have before I complete university. So that when I have my own class, I can give the children in my class the best opportunity to reach their full potential.
From learning about how Fibonacci’s golden sequence and ratio occurs in many aspects of nature, music, art and I am sure, many other things… To learning about the history and mathematical concepts behind logistics, sport, statistics and even gambling! I will be sure to use many of the different activities we took part in through out the module in my own lessons. All the workshops were engaging and encouraged us to research and discover even more!
At the beginning of the module I was very worried about my maths anxiety holding me back with my teaching, however, this module has not only given me the confidence in my own abilities but it has also made me realise that teaching maths isn’t all about the complicated maths equations that scare me! I look forward to continuing my maths journey throughout university and beyond.. I will forever be reminded about this module with all the maths I see in my everyday life!
I can tell I won’t be very popular when I keep asking people… “did you know there’s actually maths behind that?!”
But what can I do when mathematics really is EVERYWHERE!!
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.
