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Can music-making help your pupils
understand mathematical concepts such as fractions, ratios and
probability? In autumn 2005, creative arts charity, Create, sent
four professional musicians to maths classrooms to find out. In
this article, Create's founders - Nicky Goulder and Samantha Lodge
- reveal how maths books and marimbas can go hand-in-hand.
Introduction
If you're a maths teacher, the thought of thirty children all
playing tambourines and bongo drums may not immediately appeal, but
does music-making have the potential to help your pupils understand
mathematical concepts such as fractions, ratios and probability?
Eager to explore this possibility, Create launched its pioneering
cross-curricular maths and music project, Count the Beat, in
October 2005. This involved four of Create's leading professional
musicians taking music and maths workshops to 150 pupils (aged 9 to
11) at two primary schools in South East London.
Project Background
The motivation behind every Create project is to give individuals a
chance to be creative, develop valuable life skills (such as
teamwork, listening and communication), become more confident and
have fun! Since its foundation in July 2003, Create has run a great
number of music projects in schools across the UK and, when you run
as many music projects as Create, the parallels between maths and
music are never far from your mind. Beats in a bar, for instance,
translate into fractions, note lengths into ratios and symmetry is
used to create harmonies and texture. The more music projects we
ran, the more we thought about how we could consciously draw out
these parallels and use music-making as a tool to aid teachers to
communicate key mathematical principles.
We were further inspired by Dr Gordon Shaw's seminal 1999 study
that identified a causal relationship between musical training and
improved numerical ability. Taking place in Los Angeles, the study
compared the maths test results of children who had been given
piano lessons with those who had received traditional maths
teaching assisted by the use of computer programs. Dr Shaw found
that pupils who had piano lessons saw a significant improvement in
their maths skills - particularly with regards to ratios and
fractions . For Dr Shaw, this served to highlight the connection
between pupils' music-making and their grasp of mathematical
principles: "The learning of music emphasises thinking in space and
time ... when children learn rhythm, they are learning ratios,
fractions and proportion" (Dr Shaw, Neurological Research, 1999).
It was funding from Citigroup Foundation that finally allowed us to
put our plans to take musicians into maths classrooms in motion
and, in 2005, Count the Beat was born.
The Project
We embarked upon this project with two main aims: to help teachers
deliver the Maths Curriculum in fun and imaginative ways; and to
introduce children to the creative potential of maths. Our overall
vision was to achieve a sense of seamless learning by bringing
together supposedly separate areas of the curriculum. Activities
began on 4 October 2005, when we took a team of four musicians to
Key Stage 2 pupils at Lewisham Bridge School and Lucas Vale Primary
School. It was a new area for us all, so we couldn't wait to see
what the children and teachers would make of it!
Each session started with the class teacher delivering a brief
lesson on a key mathematical principle, such as fractions, angles,
ratios, measurement or probability. The rest of the session was
spent bringing these principles to life through a range of creative
music activities.
"Practical application of any theory
is always good to reinforce an idea. Using music to teach maths is
excellent both for maths and music ... the maths comes alive and
the composition of music is more clearly understood." (Create
musician)
A workshop that
had children transforming fractions upon a number line into a
musical score was particularly effective in highlighting the
connection between these two disciplines. Leading on from the
teacher's lesson on fractions, the musicians asked the class to
create a number line of twenty units. They then divided the class
into small groups, giving each group a different instrument to
play. One group, for example, had xylophones, another had African
djembe drums. Each group was then given three fractions that they
had to plot on a number line. Once they had completed this task,
one of the musicians began to clap a steady beat and asked the
first group to beat their instruments when their fraction came up.
To illustrate, let's say that this group had been given the
fractions $\frac{2}{10}$, $\frac{3}{4}$ and $\frac{4}{5}$. This
would mean that they would hit their given instruments on the 4th,
15th and 16th beats. After each group had practised playing their
fractions on their own, the musicians helped the children to bring
these different rhythms together to create a class musical
score.
The activities that followed developed the number line/musical
score link to allow children to put their own creative stamp on the
music-making. Each group was given the opportunity to work
alongside one of our musicians to create their own rhythms using a
variety of instruments. The children then had a chance to put their
knowledge of fractions to the test by mapping their own individual
rhythms (each differentiated by a different colour pen) onto a
group number lines which, again, acted as a musical score. As well
as giving children a chance to place fractions in a
temporal-spatial context, this exercise was fantastic at opening
children's eyes to the creative possibility of maths. It showed how
maths can be so much more than a "right" or "wrong" answer.
Children who had perhaps struggled with the subject in the past
were suddenly using mathematical principles to create something
they were proud of, and that gave them a huge boost of
confidence.
"By counting rhythm and learning the
timing of beats, we have really seen an improvement in the pupils'
mathematical ability ... the kids have loved this creative way of
learning!" (Deputy Head of Lewisham Bridge School, Julia Holmes,
speaking on behalf of the school's educators)
The Count the Beat activity that proved most popular with the
pupils that took part was the one geared towards instilling the
principles of probability. Here, the focus was less on the direct
relationship between maths and music, and more on how music can
provide children with fun and memorable ways of revising their
maths curriculum and vocabulary.
"It makes maths more fun and
easier. You're learning and you're also enjoying it!" (Year 5 pupil
at Lucas Vale Primary School)
For this game, our musicians asked the participants to divide
themselves into six groups, each of which was given the task of
creating a probability-inspired chant (for example: "It's unlikely
that Wigan will win the Premiership"). The groups then created
rhythms and movements to accompany their chants. Once this had been
completed, a musician stood in front of them all with a giant
fluffy dice and gave them one rule: they could sing their chant as
loudly as they wished, but only if the dice landed on their group's
number. This exercise made the pupils subject to the laws of
probability, as one group might get to chant ten times whilst
another was forced into silence for the whole piece. Desperate to
bring the roof down with their chant, the unfairness of probability
quickly hit home!
Summing Up
Let's return to the question with which we began: does
music-making have the potential to help your pupils understand
mathematical concepts such as fractions, ratios and probability?
Create's Count the Beat experience highlights two ways in which
music-making can aid your pupils' understanding: firstly, it can
provide a fun and imaginative way of familiarising children with
maths topics and vocabulary; secondly, there are direct parallels
between the skills needed to succeed in the maths and music
classrooms that can be drawn out to reinforce each other.
Music-making is also a brilliant means of demonstrating how
mathematical principles can be applied in creative contexts and we
certainly feel that our activities geared towards pupils'
exploration of this were a particularly successful element of the
project.
"The gains from this project have
been wide reaching, from improved retention of mathematical
vocabulary to increased self confidence, from a greater
understanding of rhythm to a greater understanding of fractions,
from an improvement in listening skills to greater knowledge of
musical instruments. It is hard to separate the musical gains from
the mathematical gains, but isn't that what learning should look
like, seamless?" (Head of Lewisham Bridge School, Sue Sarna, and
Head of Lucas Vale Primary School, Alexandra Hardy)
The first year of Count the Beat was
a fantastic experience and our musicians are looking forward to
building on the project's successes when we return to Lewisham
Bridge and Lucas Vale schools in the autumn and spring terms of
this new academic year.
Inspired?
If you feel inspired by this
article, why don't you try out some of the Count the Beat
activities described above in your own maths classroom!
Whilst a team of professional
musicians and an extensive collection of percussion instruments
are, of course, a big bonus, both the number line/musical score
activity and the probability exercise can be adapted to your own
maths classroom. Pencils can be drummed on table-tops for instance
and yogurt pots can be filled with rice to make maracas.
With the number line activity, you
might want to start by getting the children to create a simple
number line of twenty units (you can make it harder once they've
got the hang of it!). Then divide the class into three groups and
give them each a simple set of fractions (for example one group
could have $\frac{1}{2}$, $\frac{3}{10}$, $\frac{1}{5}$, another
$\frac{1}{4}$, $\frac{2}{5}$, $\frac{8}{10}$ and the last
$\frac{19}{20}$, 1, $\frac{3}{5}$). You don't need to worry if it
doesn't make a great rhythm at first; in fact that could be worked
into the exercise. You could then get them working in small groups
to plot fractions that make a rhythm they like better.
Good luck!!
For more inspiration, visit www.createarts.org.uk