Music and Numeracy

Abstract

The links between music and mathematics have been of interest since the Pythagoreans, who deliberated over the connections between musical intervals and ratios. Recent research suggests that content and concepts are common across learning areas and making the links for students by teaching them together can be hugely beneficial ‘…the greatest impact of interdisciplinary learning seems to be in the potential for making connections: across disciplines, between individuals, and with the wider world’ (Bazinet & Marshall in General Music Today 28(3):5–11, 2015).

Full text

Music and Numeracy
Jane Law
Introduction
The links between music and mathematics have been of interest since the
Pythagoreans, who deliberated over the connections between musical intervals and
ratios (Pesic, 2013). Recent research suggests that content and concepts are com-
mon across learning areas and making the links for students by teaching them
together can be hugely beneficial ‘…the greatest impact of interdisciplinary
learning seems to be in the potential for making connections: across disciplines,
between individuals, and with the wider world’(Bazinet & Marshall, 2015). It is the
author’s opinion that each person has some level of ability to be creative using
music to express themselves. Research for many decades has supported the
importance of music education in encouraging creative expression. Panther and
Aston (1970: 9) articulate this belief:
we must also cultivate the artist with ourselves, for each one of us has something of that
child-like innocence which is the characteristic of the artistic mind, which draws fresh
inspiration from familiar things and expresses feelings in words, actions, visual symbols or
music.
This chapter aims to support teachers engaging with their students in quality,
classroom activities which enable concurrent development of musical and mathe-
matical concepts. In order to facilitate this aim the chapter presents: (i) a specific
definition of classroom music, (ii) research-based evidence of children’s innate
capacities for identifying with music and building competencies in transference of
learning from short term to long term memories (iii) notions of musical pedagogy
J. Law (&)
University of Newcastle, Newcastle, NSW, Australia
e-mail: jane.law@newcastle.edu.au
©Springer Nature Singapore Pte Ltd. 2018
M. Sellars (ed.), Numeracy in Authentic Contexts,
https://doi.org/10.1007/978-981-10-5736-6_14
317

(iv) the integration of numeracy and music and (v) a discussion regarding the
development of numeracy skills through engagement with classroom musical
activities.
What is Classroom Music?
There are a number of definitions to consider in terms of music teaching and
learning in schools. The Australian Curriculum: The Arts, defines the musical roles
that students will occupy when they learn music in the primary classroom.
Making in Music involves listening, imitating, improvising, composing, arranging, con-
ducting, singing, playing, comparing and contrasting, refining, interpreting, notating,
practising, rehearsing, presenting and performing. Responding in Music involves students
being audience members listening to, enjoying, reflecting, analysing, appreciating and
evaluating their own and others’musical works. (The Revised Draft Australian Curriculum:
The Arts Foundation to Year 10, 2013: 93.)
For the purposes of this chapter, classroom music is defined by the author as the
process whereby a class of students is introduced to the concepts of music (rhythm;
pitch; dynamics and expression; form and structure; timbre and texture) through a
variety of learning activities that involve listening, singing, playing, moving and
organising sound. This definition of classroom music does not include additional
(or co-curricular) musical activities that occur in primary and secondary schools
such as choirs, instrumental ensembles and musical theatre.
Concepts of Music—Australian Curriculum Assessment and Reporting
Authority (2013: 136–140)
Rhythm: (including tempo and metre): the organisation of sound and silence
using beat, rhythm and tempo (time)
Pitch: the relative highness or lowness of sound. Pitch occurs horizontally (as
in a melody) and vertically (as in harmony)
Dynamics and expression: the relative volume (loudness) and intensity of
sound and the way that sound is articulated and interpreted
Form and structure: the plan or design of a piece of music described by
identifying what is the same and what is different and the ordering of ideas in
the piece
Timbre: the particular tone, colour or quality that distinguishes a sound or
combinations of sounds
Teaching music in the primary classroom is not about detailed instruction in the
skills necessary to play an orchestral instrument to a high level, nor is it about
discovering, amongst a class of students, musical prodigies to be then nurtured and
318 J. Law

developed. It is about enabling all students to be creative, using music to express
themselves and in this case, improving their numeracy capabilities at the same time.
Research-Based Evidence Regarding Music and the Brain
The benefits for students that result from engaging in musical processes and skills
have been well documented. Jeanneret (2013), summarised and compiled these
findings for the Victorian Parliament’s inquiry into the extent, benefits and potential
of music education. Amongst the findings she identified were the following. They
were sourced from various disciplines including education, psychology, music and
neuroscience and are particularly relevant for this context.
•A larger corpus collosum, which allows for a high number and faster
synapses (messages) to travel from one side of the brain to the other
(Peretz & Zatorre, 2005).
•A larger motor cortex where planning and voluntary motor functions are
controlled (Peretz & Zatorre, 2005).
•More highly developed neurofilaments which leads to faster and more
synchronised neural firings (Hannon & Trainor, 2007).
•A denser auditory cortex (Janata et al., 2002) and grey matter (Gaser &
Schlaug, 2003), and thus respond to auditory stimuli more effectively and
have the capacity to store more information.
•Significantly higher abilities in memory, including short and long term
memory retention and retrieval (Dunbar, 2009; Jonides, 2008).
•A more highly developed executive function which is the ability to reg-
ulate our cognitive and emotional responses (Bialystok & DePape, 2009;
Posner, 2008).
•More developed geometrical skills (Hannon & Trainor, 2007).
•More highly developed neural pathways (Ball, 2008; Trainor, 2008; Wills,
2007).
Research carried out at Melbourne University also focusses on the effects of
musical activity on brain activity and development:
There are now over 100 neuroimaging studies showing that music activates multiple brain
networks during music listening, responding and performance. As a result, when we
compare musicians and non-musicians there are substantial differences in size, shape,
density, connectivity, and functional activity that occur extensively throughout the musi-
cian’s brain…The brain can change in response to music and [there is a] broad range of
cognitive processes and behaviors this may impact. Powerful amongst these is the ability of
music to prime the brain for future learning, whilst more broadly promoting our individual
and social wellbeing. (Wilson, 2013:1)
Music and Numeracy 319

Music activities can also contain the following ideas and tasks.
•Rhythm activities that provide opportunities to explore pattern, develop
algebraic expression and explore equations in addition.
•Musical activities that have the potential to support learning in basic
mathematical memory activities such as number facts, timetables and
other mathematical skills related to repeat rehearsal for instant recall.
•Interactions with a form of written music called graphic notation which
present occasions during which spatial and geometric concepts can be
strengthened.
•Opportunities for students to use musical structures in order to create their
own compositions can link with a range of mathematical concepts, e.g.
lapsed time, pattern in numbers or even fractions.
Notions of Musical Pedagogy
There are a number of theoretical approaches to teaching music in the primary
classroom, however a classroom teacher with a love of music, but not necessarily
years of formal music training, needs to find an approach that is flexible and able to
be integrated with other curriculum areas.
Foremost among the approaches suitable for a primary classroom, that focus on
active music making and high student engagement are as follows:
•The Orff (Schulwerk) Approach
•The Kodaly Method
•The Dalcroze Method.
In this chapter, it is suggested that the pedagogical approach which is most
valuable for general primary teachers aiming to integrate numeracy and music is the
Orff–Schulwerk approach. The Orff approach is the most promising for teachers
who are seeking ways of integrating instruction because as the name suggests, the
320 J. Law

Orff approach is not a methodology or a lineal, sequential series of lessons, con-
cepts or graded steps. It is not a method with a predetermined progression of ideas.
Orff–Schulwerk activities present prospects of appropriate development of ideas,
of experimentation, of improvisation and innovation without the rigidity of the
learning sequences found in other, more formal approaches. For example this
approach has, as one of its central platforms, the concept of rhythm. Rhythm in
movement, speech and music.
This approach is activity based. Students learn music by actually doing it. They are engaged
in the learning process by experiencing, experimenting, creating, improvising and partic-
ipating in different musical activities. It is this approach that can facilitate problem solving
skills and strategies while nurturing creativity and self-expression. Creating and improvi-
sation is embedded in the Orff approach and these types of activities require students to
think divergently. Divergent and creative tasks are known to require certain areas of the
brain to coordinate the thinking. These are areas that do not work together during the
completion of convergent tasks. Creativity is often thought of, incorrectly, as a special
quality that individual innately possess, not as a competency that can be developed
(Hardiman, 2010b).
Improvisation has also been shown to contribute positively to the brain’s cre-
ative capacity. Deasy (in Hardiman, 2010b: 233) identified some positive learning
behaviours that could be fostered by students engaging in the arts. These included:
•Persistence in sustaining concentrated attention to a task
•Symbolic understanding by using multiple modes to communicate
•Resilience in overcoming frustration and failure
•Engaged learning through absorption in content
•Collaborative learning as a member of group processes for acquiring and
manifesting knowledge.
•The brain is ‘wired’to seek out patterns and relationships (Hardiman,
2010a), both of which are vital to understanding mathematical foundations
and musical composition.
•The positive learning behaviours that are associated with students
engaging in the arts are able to impact positively in other areas of cur-
riculum, including numeracy.
Music and Numeracy 321

Interdisciplinary Learning—Numeracy and Music
Integration of music and numeracy (or mathematics) lessons into one process
makes perfect sense, especially in the Orff–Schulwerk approach to music education.
However, whichever music/numeracy approach or approaches teachers use in their
classroom must be underpinned by sound mathematical understandings embedded
as numeracy capacities. This does not imply that students must first have formal
mathematical knowledge in order to create music, in fact it may be quite the
reverse. Some important findings on the links between classroom music and
numeracy are found in research about the arts. The significant ‘Champions of
Change—The Impact of the Arts on Learning’(Fiske, 1999) was carried out at
Columbia University and published in 1999. This seminal research focussed, in
part, on the links between rich in-school arts learning and academic success.
A diverse methodology was used combining standardised tests, paper and pencil
inventories, a self-description questionnaire and a teacher perception scale. Over
two thousand children in public schools in New York, Connecticut, Virginia and
South Carolina were involved in this study.
This research, although encompassing all the arts, points to the particular
importance of music in four of the seven sections of the report. Many aspects of
music in schools including curriculum implications were highlighted. The results of
the study revealed that the children who had received ‘high exposure to an arts rich
curriculum’scored significantly higher in:
•creative thinking abilities of fluency, originality, elaboration and resistance to
closure
•general capabilities such as expression, risk taking and imagination
•perceptions of themselves as mathematics learners (Fiske, 1999:54–55).
322 J. Law

Growing interest in the links between numeracy (mathematics) and music has
led to recent exploratory research which investigated the way teachers have inte-
grated music and mathematics. (Song, Capraro, & Tilman, 2013) indicated that
integrating music/mathematics lessons had a positive effect. Forty-six students from
grade 1 and grade 3 participated in music composition and playing activities while
investigating mathematics learning in such areas as patterning, subtraction, frac-
tions and addition.
After 5 weeks, the study showed:
•Music can connect to mathematics in a range of content areas.
•Students demonstrated statistically significant improvements in almost all
assessments of mathematical ability.
•The lessons facilitated students engagement and motivation (Song et al., 2013:
14–15).
Conclusion
These studies indicate the positive impact of integration of music and mathematics.
This integration impacts both student’s perceptions of mathematics and their per-
ceptions of themselves as learners of mathematics. However, it also the increase in
the creative thinking, expression, imagination and risk taking that could be the most
significant for the future of these students and their children (Bazinet & Marshall,
2015; Fiske, 1999; Hardiman, 2010b; Song et al., 2013).
•Numeracy competencies are found in music, irrespective of the peda-
gogical approach implemented
•Tasks that combine numeracy competencies and music can be progres-
sively developed to involve a range of symbolic representation and
mathematical competencies in number, space, pattern and algebra.
Music and Numeracy 323

The Learning Task - Foundaon
Students echo rhythm paerns and devise their own body percussion
rhythm paerns.
Students find collecons of familiar objects to establish an understanding of
numbers to 20.
Students imitate rhythm paerns in order to represent the number 4 and
other larger numbers to 20.
Differenaon
The task can be differenated when
students make their own rhythm paern for
a number under 10. Students can then make
rhythms for larger numbers.
Australian Curriculum
Mathemacs Outcomes
ACMNA002
Connect number names, numerals
and quanes, including zero, inially
up to 10 and then beyond.
Numeracy Links
Understanding that the arrangement of
objects does not affect how many there
are.
Strategies to include learners with oral
backgrounds
This task uses rhythm to enable students to
understand the concept of numbers. It
supports students of oral backgrounds by
using exclusively pictures and rhythm. The
teacher would not be giving wrien or even
verbal ‘instrucons’ but using gestures and
sound to teach the number concept.
Authenc Assessment strategies
Observing students as th ey acvely
engage with the lesson will enable
targeted product analysis. Recording
students as they demonstrate their
rhythm paerns can be invaluable as
a tool to communicate with parents.
The recordings are evidence of
student aainment and can
contribute to digital porolios for
each student.
Variaons for students from diverse
social contexts
Students can illustrate their chosen number
by collecng objects representave of their
culture. Students can be encouraged to
bring items from home and these objects
can be used when repeating the lesson to
encompass larger and more complex
numbers.
Including ATSI perspecves
All students can work non-verbally in the
acvity based hand-on tasks. The class
can ulize objects from their tribal culture
to form collecons of objects for use with
the enre class. The inclusion of ATSI
parents or teaching assistants would be
advantageous.
Australian Curriculum Music Outcomes
Develop aural skills by exploring and
imitang sounds, pitch and rhythm paerns
using voice, movement and body
percussion (ACAMUM080)
324 J. Law

Foundation
Music/numeracy lesson Resources
The aim of this lesson is for students to
imitate, count and devise ‘body percussion’
rhythm patterns
Students devise their own body percussion
patterns for even numbers under 10
HINT
Body Percussion consists of clapping,
clicking, hitting thighs (called patchen) and
stamping
1. Teacher claps 4 times—students copy
2. Teacher—How many claps?
3. Teacher stamps twice then claps
twice—students copy
4. How many stamps and how many claps?
Students count as teacher repeats two
stamps and then two claps*
5. How many sounds did we make
altogether?
6. Teacher claps 6 times—students copy
7. Teacher—How many claps?*
8. Teacher stamps 6 times—students copy
9. Teacher—How many stamps?*
10. Teacher claps 3 times and stamps
3 times—students copy
11. How many claps and how many stamps?
Students count as teacher repeats three
stamps and then three claps
12. Students choose number 2, 4, 6 or 8 and
make their number by clapping and
stamping**
13. Students demonstrate their numbers. Each
group demonstrate their combinations**
For each body percussion rhythm, students
count the number of claps, stamps and
shoulder pats
HINT
Teacher may also demonstrate using
percussion instruments, e.g. woodblock hit
three times then a drum three times
HINT
Let the students choose their own number.
This is a good differentiation strategy
Music and Numeracy 325

The Learning Task – Year One
Students echo body percussion paerns and create their own paerns to
solve simple addion problems.
Students analyse sound paerns, write and record addion sentences.
Differenaon
The task can be differenated by students
selecng their own addion sentences, at
appropriate levels, to represent with body
percussion sounds.
Australian Curriculum
Mathemacs Outcomes
Represent and solve simple addion
problems using a range of strategies
including on, paroning and
rearranging parts - ACMNA015
Numeracy Links
Develop a range of mental strategies for
addion problems.
Strategies to include learners with oral backgrounds
This task uses rhythm to enable students to understand the
concept of numbers.
Using flash card to write number sentences should be
approached when students have had extended experience
with rhythmic representaon of addion if accompanied by
lots of repeon, acon, performance and responses to
link the wrien with the acvity, then with the symbolic
representaon of number and the symbolic representaon
of acon (+, - , =)
Authenc Assessment strategies
Recordings of students performing rhythm paerns
provide assessment data for both Mathemacs and
Music.
The number sentence flash cards provide a
worksample that can form the basis of teachers’
anecdotal records.
Variaons for students from diverse
social contexts
Picture books can be used to introduce
this lesson to reflect students’ social
contexts.
Including ATSI Perspecves
Focus on where the students would need to
use these number sentences in t he world
outside the classroom, be sensive to the
code changing from tradional numeracy to
western, abstract, symbolic rep resentaon.
Engage though narrave and story- telling.
Use tradional ATSI clapping scks to
perform the rhythms instead of using body
percussion.
Australian Curriculum Music outcomes
Develop aural skills by exploring and
imitang sounds, pitch and rhythm paerns
using voice, movement and body
percussion (ACAMUM080)
Imitang pitch and rhythm paerns to
develop aural recognion skills, for
example, echo clapping.
326 J. Law

Year 1
Music/numeracy lesson Resources
The aims of this lesson are for students to
•Echo body percussion patterns
•Create their own body percussion
patterns
•Write sound patterns using number
algorithms
Body Percussion consists of clapping,
clicking, hitting thighs (called patchen) and
stamping
1. Teacher (Clap, patchen, patchen, clap)
2. Students echo the body percussion
(BP) pattern
3. Students and teacher count the sounds
while performing the BP pattern again
4. Teacher/students analyse the pattern of
sounds performed by the teacher. How
many of each type of sound? How many
sounds altogether? (2 claps plus 2 patchen
are 4 sounds altogether)*
5. Teacher (Clap, clap, stamp, stamp)
6. Students echo
7. Students and teacher count the sounds
while performing the BP pattern again*
8. Teacher/students analyse the BP pattern
performed by the teacher. How many of
each type of sound? How many sounds
altogether? (2 claps plus 2 stamps are 4
sounds altogether)*
9. Repeat with other numbers to 10
10. In pairs students choose a number and
make up a BP pattern. How many BP
patterns can they devise for their number?
11. Each group chooses a BP pattern to
demonstrate to the class. How can we
write this BP pattern down with
numbers?*
12. Flash cards can be used to record addition
sentences
HINT
Some students cannot click their fingers.
Students can pretend by making an
approximation of the movement. In some
circumstances, it may be appropriate to
substitute another sound (e.g. shoulder tap)
HINT
Students will benefit from many repetitions of
step 4
Music and Numeracy 327

The Learning task – Year Two
Students use 2D shapes as graphic notaon to construct a sound scape.
Students draw representaons of regular and irregular two-dimensional
shapes to form an art work.
Students assign each shape a sound that relates to a characterisc.
A student leader constructs a composion using the shapes.
Differenaon
Introducing the concepts of dynamics and
speed to step 6 enables the leader to vary
the music he/she is creang a sound scape.
A greater number of shapes used in the art
work challenges more able students.
The level of complexity can also be increased
by using irregular shapes.
Australian Curriculum
Mathemacs Outcomes
Describe and draw two-dimensional
shapes, with and without digital
technologies - ACMMG042
Numeracy Links
Idenfying key features of squares,
rectangles, triangles, kites, rhombuses and
circles, such as straight lines or curved lines,
and counng the edges and corners.
Strategies to includelearners withoral
backgrounds
This task uses graphic notaon to link a two-
dimensional shape to an appropriate musical
sound.
The pedagogical strategies are based around
oral discussions, music and visual arts. These
pedagogies are highly appropriate for
students with oral backgrounds, most
especially in acons, repeons, narrave
and response to suggested acons and
direcons
Authenc Assessment strategies
Sustained Academic Dialogue (SAD)
conferences with students either
individually or in groups can focus on:
•The qualies of the sounds
chosen
•The characteristics of the shapes
chosen when construcng art
work.
Variaons for students from diverse
social contexts
Students from diverse social contexts will
bring a rich background of experiences that
will enable creave selecon of symbol s
and shapes.
The student led pedagogical approach is
demonstrably effecve in engaging
students with behavioural challenges,
diverse learning needs, different social
experiences, interests and creave
capacies
Including ATSI perspecves
Traditional ATSI symbols can be used by the
class to construct the art work in a
subsequent lesson. Differences between
shapes in the first lesson and shapes in the
second lesson can be discussed. However,
as most tradional art does not involve
angles, as it may be that the studen ts
actually find the default posion
themselves.
Australian Curriculum Subject
outcomes
Create composions and perform music to
communicate ideas to an audience
(ACAMUM082)
Choosing and combining sounds to create
composions.
328 J. Law

Year Two
Music/numeracy lesson Resources
Graphic notation
Graphic notation is the representation of music using
visual symbols. The symbols can represent any of the
music concepts (Pitch, Tone Colour, Dynamics, Rhythm,
Structure). Graphic notation scores can be very simple
(as in the lesson below) graduating to more and more
complex as students develop their understanding of
musical notation and composition
The aims of this lesson are for students to
•Experiment with 2D shapes to construct a visual
pattern*
•Experiment with a range of environmental sounds
in the classroom and/or playground
•Use the 2D shapes as graphic notation to construct
a sound pattern*
1. Draw three different 2D shapes on the board so that
they take up much of the space and intersect in
different ways, e.g.
2. Divide the class of students so that each group ‘owns’
a particular shape
3. Each group explores their classroom environment to
find a sound they like and can all play together, e.g.
ruler slapping the desk, metal chair legs hit by a
pencil, paper being scrunched
4. The teacher (or a student) takes a metre ruler and drags
it across the board crossing over the shapes
5. Whenever the leader’s pointer crosses the shape’s
perimeter the groups make their sound
6. The leader can vary the speed, stop and even travel
along the perimeter lines (so that a continuous sound
is made)
7. Students (individually or in groups) create their own
piece of music by drawing shapes on art paper and
deciding what sounds are assigned to each shape. The
sounds can represent a place or story, e.g. a storm at
sea or a school athletics carnival
Representations of regular and irregular
two-dimensional shapes and their names around the
classroom. Drawing implements, paper
Whiteboard or electronic Smart Board
HINT
This activity can also be done effectively on a
blackboard, whiteboard or with butchers’paper
NOTE
The concept of perimeter is not taught in this lesson
HINT
In step 2:
Group 1—Oval
Group 2—Quadrilateral
Group 3—Pentagon
Metre ruler or another suitable pointer
Art paper and drawing implements
Music and Numeracy 329

The Learning Task – Year Three
Students link mulplicaon to rhythm paerns and use a stamp to indicate
the process of mulplicaon.
Body Percussion is used as a tool for expressing the concept of
mulplicaon.
Body Percussion consists of clapping, clicking, hing thighs (called patchen)
and stamping.
Differenaon
The introducon can be differenated in
many ways by accessing a variety of backing
tracks from you tube. The examples given
are based around the musical genre of
‘blues’, however other genres are available
to be used. Multiplicaon algorithms can be
increased in difficulty and other symbols e.g.
(represented by hands).
Australian Curriculum
Mathemacs Outcomes
Explore and describe number paerns
resulng from performing
mulplicaon ACMNA081
Numeracy Links
Idenfying examples of number paerns
Strategies to include learners with oral
backgrounds
The emphasis in this lesson on performing a wide
variety of rhythms will boost student involvement
and interest.
Addional scaffolding should be provided to
enable students to devise a method of wring
/recording their mulplicaon paerns. These may
be drawings or simple symbols. Movement,
repeon and channg are also part of the highly
developed cognive learning strategies for
students with oracy backgrounds
Authenc Assessment Strategies
Aer selecting a mulplicaon
algorithm from those displayed
around the classroom, each student
explores a variety of rhythmic body
percussion paerns that illustrate the
algorithm. Students can demonstrate
the rhythmic paern to the teacher or
submit the assessment in wri ng by
devising a method of writing down
their rhythmic paern.
Variaons for students from diverse
social contexts
Students bring a rich variety of rhythmic
backgrounds to this lesson. Body
percussion is a folk tradion of countries
that include Ethiopia (armpit music) and
Spain (flamenco).
Explore the cultural backgrounds of
students in this area and involve
community members to perform rhythms
that reflect their social and cultural
backgrounds. Special needs students may
need support.
Including ATSI perspecves
This lesson is very appropriate for ATSI
students as tradional aboriginal singing is
oen accompanied by hand clapping or
thigh clapping and buocks-slapping. The
class can acknowledge these acons as part
of various cultural heritages
Further informaon can be retrieved from:
hp://aboriginalart.com.au/didgeridoo/inst
ruments.html
Australian Curriculum Music Outcomes
Develop aural skills by exploring, imitang
and recognising elements of music
including dynamics, pitch and rhythm
paerns (ACAMUM084)
Singing learnt pitch and rhythm paerns
and varying elements of music within them
to create different effects, for example,
singing faster or slower, repeang phrases.
330 J. Law

Year Three
Music/numeracy lesson Resources
The emphasis in this lesson is for the students
to keep a regular beat while imitating teacher
devised body percussion patterns
Students also devise their own body
percussions to accompany a backing track
(see suggested backing tracks)
In step 5, the sound of a stamp is used as a
multiplier and students answer by clapping
the correct number
1. Listen to the backing track, clap the beat
2. Teacher performs simple Body Percussion
patterns for the students to copy, e.g. clap,
clap, clap, click
3. Perform the Body Percussion patterns to
the backing track
4. Student volunteers make up short patterns
to the backing track and teach the other
students, e.g. patchen, patchen, clap
5. Teacher introduce the concept that a stamp
means to multiply*
6. Teacher—four claps, stamp, two claps*
7. Students clap back the answer (8)*
8 Teacher—three claps, stamp, five clicks*
9. Students clap back the answer (15)*
10. Once the students understand the concept
this activity can be done to a backing
track
11. Choose 4 students to lead. Each student
takes it in turn to ‘ask the number
question’*
12. Each of the 4 student leaders asks the
number question then the rest of the class
claps the answer back*
13. The student leaders can point to the group
that is to answer the question
https://www.youtube.com/watch?v=9H2oY_
85q8U
https://www.youtube.com/watch?v=
y1ueWz4-Hkk
https://www.youtube.com/watch?v=
hZWNb5AZDWk
https://www.youtube.com/watch?v=
Dxo2bEX45KI
HINT
Before choosing the students to lead, ask all
the students in the class to make up 2 of their
own body percussion patterns
HINT
Insist that the students make up very simple
body percussion patterns. This activity does
not work if complex patterns are tried before
the concepts are understood
Music and Numeracy 331

The Learning Task – Year 4
Students learn and sing the song “One Bottle of Pop.” They discuss the
number of beats in each bar of the song and invesgate some possible
number sequences e.g. starng on 3 and increasing by 3’s.
Another version of the song: hps://www.youtube.com/watch?v=_je-
rbBgOLo
Differenaon
The song ‘One Bole of Pop’ is made up of 3
different secons. Each secon can be
taught separately with appropriate
rhythmical acvies for each secon.
Improvising a harmony part to fit with any of
the three secons of this song encourages
less adherence to the melody and more
creavity when singing.
Australian Curriculum
Mathemacs Outcomes
Invesgate number sequences
involving mulples of 3, 4, 6, 7, 8, and
9 ACMNA074
Numeracy Links
Recognising that number sequences can be
extended indefinitely
Strategies to include learners with oral
backgrounds
Construct different lyrics for the same tune –
especially effecve if the class has just been
on an excursion or has enjoyed a popular
whole school event such as a sports carnival
or students have come to the class from
various backgrounds and experiences –
singing is culturally inclusive and can be part
of language development and memorising
for students with oracy backgrounds. Any
words in mulpole languages can be sung in
the lyric variaon
Authenc Assessment Strategies
Record students singing – as a class
and/or in groups.
Students use the audio-visual
recordings to evaluate their
performance. The criteria used to
evaluate the performance should be
jointly constructed and agreed by the
class.
Variaons for students from diverse
social contexts
The involvement of parents as partners in
this lesson enables them observe their
children being successful. Students who
have behavioural challenges can oen
respond to:
•Being selected as a leader (ensure that
the student is successful here!)
•Being selected to provide the stamps
(it will also appeal to kinaesthec
learners.)
Engaging with lyrics that reflect their own
understanding and language use, code or
register- allows students to create meaning
ATSI consideraons
All students can develop lyrics that reflect
this cultural group. A list of names of items
in appropriate ATSI language can be used to
construct the song e.g. ‘One loaf of nulai
(bread in Awabakal), two loaves of nulai,
three loaves of nulai, four loaves of nulai.
Source:
hp://www.miromaa.org.au/shop/product
s/language-resources/item/awabakal-
bushtucker-poster.html?category_id=4
Australian Curriculum Music Outcomes
Pracse singing, playing instruments and
improvising music, using elements of music
including rhythm, pitch, dynamics and form
in a range of pieces, including in music from
the local community (ACAMUM085)
Rehearsing and performing music in unison
and with accompaniment paerns.
332 J. Law

Year Four
Music/numeracy lesson Resources
In this lesson students practise singing, using
elements of music–rhythm and pitch. They
investigate number sequences involving
multiples of 3 and recognise that multiples of
3 can start from any number
1. Learn the song ‘One Bottle of Pop’
2. This song can also be sung as a round
where the class is divided into three
sections and each begin after the
words—‘Seven bottles of pop!’
3. Number the beats in the song ‘One Bottle
of Pop’as follows:
12 3
One Bottle of Pop
45 6
Two Bottles of Pop
78 9
Three Bottles of Pop
10 11 12
Four Bottles of Pop
13 14 15
Five Bottles of Pop
16 17 18
Six Bottles of Pop
19 20 21 22
Seven Bottles of Pop
4. Investigate the number sequence starting
on 3 and increasing by 3. Put a red circle
around all the numbers in this sequence
(3, 6, 9, etc.)*
5. Students sing the song and clap on the
numbers with red circles*
6. Investigate the number sequence starting
on 1 and increasing by 3 by put a green
circle around this number sequence
(1, 4, 7, etc.)*
7. Students sing the song and stamp on the
numbers with green circles*
8. Half the class sings and the other half claps
on the number sequence increasing by 3,
starting on 3 (red)*
9. The other half of the class sing,
accompanied by the rest of the students
stamping on the number sequence
increasing by 3 starting on 1 (green)*
https://www.youtube.com/watch?v=u-
TdsmPHjo0
HINT
The song ‘One Bottle of Pop’is in groups of
3. Songs in groups of 4 can also be used:
•Miss Mary Mac
•Old Macdonald
•Ging Gang Gooli
•Boom Chicka Boom
•Agadoo
All these songs are available to download on
YouTube but be careful of the advertisements
if you are using YouTube to teach the songs
to your students
HINT
This activity can form the basis of a great
assembly item
Music and Numeracy 333

The Learning task – Year Five Mulples
In this lesson students improvise and experiment with combinaons of non-
tuned percussion sounds to create and accompaniment to a number chant.
Students revise mulples of 8 then generate number paerns. These
number paerns are turned into musical composions by assigning sounds
to each digit from 0 to 9.
Differenaon
The number paern used in this lesson was
based on the mulples of 8. The lesson can
be differenated by using easier or more
difficult number paerns. A range of musical
sounds can be ulized. Sources of sounds
can range from environmental sounds
(classroom taps hit with rulers); tuned
percussion (xylophones or metalaphones);
or unusual voiced sounds.
Australian Curriculum
Mathemacs Outcomes
Describe, connue and create
paerns with fracons, decimals and
whole numbers resulng from
addion and subtracon. ACMNA107
Numeracy Links
Using diagrams to create paerns involving
Strategies to include learners with oral
backgrounds
This task uses different sounds to enable
students to understand the concept of
mulples of a number. It reinforces that
numbers are paerns that can be played
with and manipulated. This can be enhanced
by movement, channg repeon of
paerns and visual representaons of
numbers that are not Hindu- Arabic
mathemacal symbols
Authenc Assessment Strategies
Each student group perform their
mulples music for the class.
As the teacher is recording anecdotal
records of the performance, the rest
of the class complete a feedback sheet
where they idenfy:
•The mulple used
•The next three mulples
•Their favourite sounds etc.…
Variaons for students from diverse
social contexts
Explore the un-tuned percussion
instruments used in a variety o f diverse
cultural backgrounds e.g. Indonesia, Sudan,
Egypt and China and the simpler
instruments that were tradionally used by
Australian selers. What are the bole top
scks called, also the bod hran, spoons, gum
leaves, other types of drums as these are
very basic and made from literally anything
– bucket bands, steel bands, bush bands etc
Including ATSI perspecves
Tradional ATSI musical instruments (or
replicas) can be used by the class to make
the sounds for each digit from 0 to 9.
Students can use these when construcng
their own music:
•Clapscks, Boomerang Clapscks,
Percussion Tube, Rasp, Rale,
Bullroarer.
Australian Curriculum Music Outcomes
Rehearse and perform music including
music they have composed by improvising,
sourcing and arranging ideas and making
decisions to engage an audience.
(ACAMUM090)
Improvising and experimenng with
combinaons of sounds and technologies
to create moods and atmospheres.
334 J. Law

Year Five
Music/numeracy lesson Resources
In this lesson students improvise and
experiment with combinations of non-tuned
percussion sounds to create and
accompaniment to a number chant
1. Generate a number pattern chant using the
multiples of 8 starting from 8 to 8, 16, 24,
32, 40, 48 56 64 72 80, 88, 96*
2. Assign a non-tuned percussion sound to
each digit from 0 to 9 e.g.
0 = Tambourine
1 = Bells
2 = Triangle
3 = Large Drum
4 = Small Drum
5 = Sticks
6 = Guiro
7 = Castanets
8 = Cabasa
9 = Cow Bell
3. Give the above non-tuned percussion
instruments to students
4. Teacher chants the multiples of 8 while the
relevant percussion instruments ‘play’, the
numbers*
5. Teacher (or student) chants the multiples of
8 again with a backing track while the
percussion instruments are played*
6. Students form friendship groups, select
another number and find multiples of
another number, (this step can be
differentiated to suit the ability of the
students), and form their own musical
composition Students discuss timbre of
different non-tuned percussion instruments
to help inform their instrument selection
7. Students can find a rhythmic backing track
on YouTube (see link)
HINT
After the first section of the lesson and brief
demonstration of the concepts, this lesson is
constructed to enable student exploration
The role of the teacher is to encourage and
enable not direct
Students explore the relevant multiple pattern
display the patterns using musical sounds
HINT
Displaying the number patterns on a
blackboard or whiteboard gives students who
are less confident the ability to fully
participate
HINT
Students swap percussion instruments then
repeat step 5. This can be done a number of
times to really ensure a depth of
understanding
https://www.youtube.com/watch?v=22m
WUkAi0PI
https://www.youtube.com/watch?v=HiWh
PNtDuQ0
Music and Numeracy 335

The Learning Task – Year Six
Improvisaon and experimentaon is enabled by the ulizaon of prime
and composite numbers to form a musical structure.
Student friendship groups construct a musical composion based on prime
and composite numbers.
Students dissect the musical composion and discuss the prime and
composite numbers represented.
Differenaon
Sound sources used in this lesson should be
differenated and enab le students to choose
from: voiced sounds (e.g. beat box),
environmental sounds (classroom taps hit
with rulers), non-tuned percussion sounds
and body percussion sounds.
Australian Curriculum
Mathemacs Outcomes
Idenfy and describe properes of
prime, composite, square and
triangular numbers ACMNA122
Pedagogical Strategies
Understanding that some numbers have
special properes
Strategies to include learners with oral backgrounds
As the students make musical representaons of number
paerns they are exploring their personal meanings and
understandings of mathemacs concepts. It is valuable, as a
concluding acvity, for these and all the other students in
the class to talk about the decisions that were made in the
construcon of the music and the reasons why those
decisions were made and to record these in ways that are
personally meaningful.
Authenc Assessment Strategies
Sustained Academic Dialogue (SAD)
conferences with students either
individually or in groups can focus on:
•Students definions of prime and
composite numbers
•The musical mbre of the sounds
chosen in their musical composions.
•Classifying numbers as prime or
composite.
Variaons for students from diverse
social contexts.
Music can be a movator for all students
including those with special needs. Music is
also part of all cultures and social classes. It
enables many of them to parcipate in a
whole class lesson. Students who need
addional support to fully parcipate can
select instruments that allow them to
produce a sound. All students can use their
own music preferences and socially diver se
musical knowledge to enable their
creavity.
Including ATSI perspecves
Tradional ATSI musical instruments – or
replicas can be used by the class when
playing their prime or composite numbers:
•Clapscks, Boomerang Clapscks,
Percussion Tube, Rasp, Rale, Bullroarer.
•Folded leaf whistle, hollow log struck with
a small sck, Didgeridoo (tradionally
only played by men in very few
indigenous groups in Australia)
Australian Curriculum Music Outcomes
Rehearse and perform music including
music they have composed by improvising,
sourcing and arranging ideas and making
decisions to engage an audience.
(ACAMUM090)
Improvising and experimenng with
combinaons of sounds and technologies
to create moods and atmospheres.
336 J. Law

Year Six
Skeleton music/numeracy lessons Resources
This lesson uses prime and composite numbers to
construct a rhythmic composition. Prime and composite
numbers form a structure to enable a musical
composition to be created where every student
contributes
A class composition is constructed in this lesson where
each group of students is responsible for one part of the
musical composition
This lesson can be repeated so that the teacher is a
mentor or guide and the students explore other number
patterns
1. Divide the students into six groups and ask each
group to make up one sound that they will all perform
together. To ensure variation in the sounds, teachers
may assign each group a different type of sound e.g.
a. Tuned Percussion
b. Non-tuned Percussion
c. Environmental Sounds
d. Metal sounds
e. Body Percussion Sounds
f. Vocal Sounds
2. Explore the composite and prime numbers to 100 by
assigning the numbers as follows
a. Group 1—Prime Numbers to 100
b. Group 2—Composite numbers with a factor
of 4–100
c. Group 3—Composite numbers with a factor
of 3–100
d. Group 4—Composite numbers with a factor
of 7–100
e. Group 5—Composite numbers with a factor
of 9–100
f. Group 6—Composite numbers with a factor
of 8–100
3. Each group explores the type of sound that they could
play
4. Each group makes their sound on ONLY their
assigned numbers*
5. The teacher count from 1 to 20 and groups has make
their sound on their assigned numbers*
6. The teacher (or student leader) establishes a beat by
clicking fingers and counts from one to 30 while other
students perform*
7. Teacher or student leader establishes the beat but does
not count out loud. Students listen to the combination
of sounds and rhythms as they play*
8. Class discussion:
a. How can this class composition be improved?
b. Can dynamics be added?
c. Does any group wish to change their sound?
9. The class composition can be performed any number
of times and then recorded
Whiteboard or electronic Smart Board
Tablets, Computers or paper
Non tuned percussion instruments (if appropriate)
HINT
Voiced sounds can be any type of sounds that you can
make with the voice or throat. See link—https://www.
youtube.com/watch?v=CPKq9sDIs2M
HINT
This activity can be concluded with a reflective activity
where the students reflect on the musical composition
produced
Music and Numeracy 337

The Learning Task – Year Seven
Students use their understanding of Prime, Composite, Square and
Triangular Numbers to construct a musical composion.
Differenaon
Development of a variety of musical sounds
can reflect a specific event or environment
e.g. a storm.
Students should aempt to record their
music so that others can reproduce it.
Students can choose to invesgate any
group of prime, composite, square and
triangular numbers, even very large numbers
e.g. numbers over 10 000.
Australian Curriculum
Mathemacs Outcomes
Idenfy and describe properties of
prime, composite, square and
triangular numbers ACMNA122
Numeracy Links
Understanding that some numbers have
special properes
Strategies to include learners with oral
backgrounds
Give students with oral backgrounds more
me to understand requirements of the
lesson. This is especially important if the
lesson uses a pedagogy which is not teacher
directed.
Begin the lesson with a visual acvity that
involves the targeted concepts e.g. prime,
composite, square and triangular numbers.
Authenc Assessment Strategies
Students develop an electronic or
paper porolio that reflects the
development of their:
•Understanding of the musical
terms
•Exploraon of types of sound
•Contribuon to the final group
Variaons for students from diverse social contexts.
Construct a mind map to introduce the lesson. Give each child a
number of scky notes and ask them to add informaon about
prime, composite, square and triangular numbers to the mind
map.
Students can use any informaon source to help them revisit the
concepts. They can also use their different ways of calculaon and
making meaning that reflects the cultural and social backgrounds.
Including ATSI perspecves
Relate prime numbers to a real-world situaon that
illustrates the differences in ways of thinking about
numeracy, e.g. having a BBQ where there are 101 people
and they have to sit at tables in even groups. What would
you do? Allow the students to construct and deconstruc t
a scenario several mes to facilitate learning. Have a
‘yarn-up’, draw pictures and make a physical model.
Australian Curriculum Music Outcomes
Develop musical ideas, such as mood, by
improvising, combining and manipulang
the elements of music (ACAMUM093)
338 J. Law

Music: Year Seven
Music/numeracy lesson Resources
This lesson uses different types of numbers to form a
rhythmic composition. The lesson revises the concepts of
Prime, Composite, Square and Triangular Numbers
1. In friendship groups students explore body percussion,
environmental and non-tuned percussion sounds. They
list 3 examples of sounds in each category and choose
one favourite
2. Each friendship group is given a set of numbers:
a. Group 1—Square numbers to 100
b. Group 2—Triangular numbers to 100
c. Group 3—Prime numbers to 100
d. Group 4—Composite numbers with a factor of 7–100
e. Group 5—Composite numbers with a factor of 8–100
f. Group 6—Composite numbers with a factor of 2–100
3. The teacher or student leader establishes a beat by
clicking fingers (or playing the beat on a non-tuned
percussion instrument) and while counting from
one to 20
4. All groups play on their assigned numbers
5. Discussion regarding the patterns discovered. Who plays
on 20? Why? Is there a number that all students play on?
Why or Why not?*
6. All groups play together while the teacher/student leader
counts to 30*
7. All groups play together while the teacher/student leader
beats to 40 (without saying the number)*
8. Perform this again (to 50) with a backing track*
Whiteboard or electronic
smartboard
Tablets, Computers or paper
Non-tuned percussion
instruments (if available)
https://www.youtube.com/
watch?v=NuqH7_vFNRg
https://www.youtube.com/
watch?v=NuqH7_vFNRg
References
Aston, P., & Paynter, J. (1970). Sound and silence: Classroom projects in creative music. London,
UK: Cambridge University Press.
Australian Curriculum Assessment and Reporting Authority. (2013). Revised draft Australian
curriculum: The arts foundation to year 10. ACARA Sydney.
Ball, P. (2008). Science and music: Facing the music. Nature,453(1792), 160–162.
Bazinet, R., & Marshall, A. (2015). Ethnomusicology ethnomathematics, and integrating
curriculum. General Music Today, 28(3), 5–11. doi:10.1177/1048371315573566.
Bialystok, E., & DePape, A. (2009). Musical expertise, bilingualism and executive functioning.
Journal of Experimental Psychology: Human Perception and Performance,35(2), 565–574.
Dunbar, K. N. (2009). Arts education, the brain and language. Learning, Arts and the Brain
(pp. 81–104). The Dana consortium Report on Arts and Cognition.
Fiske, E. (1999). Champions of change: The impact of the arts on learning. Retrieved from http://
www.eric.ed.gov/contentdelivery/servlet/ERICServlet?accno=ED435581.
Gaser, C., & Schlaug, G. (2003). Brain structures differ between musicians and non-musicians.
The Journal of Neuroscience,23(27), 9240.
Music and Numeracy 339

Hannon, E., & Trainor, L. (2007). Review: Music acquisition: Effects of enculturation and formal
training on development. Trends in Cognitive Sciences,11, 466–472. doi:10.1016/j.tics.2007.
08.008.
Hardiman, M. (2010a). The creative-artistic brain. In D. Sousa (Ed.), Mind, Brain and education:
Neuroscience implications for the classroom (pp. 227–248). Bloomington IN: Solution Tree
Press.
Hardiman, M. (2010b). the creative-artistic brain. In D. Sousa (Ed.), Mind, brain and education:
Neuroscience implications for the classroom. Bloomington, IN: Solution Tree Press.
Janata, P., Birk, R., Van Horn, J. D., Leman, M., Tillerman, B., & Baharucha, J. (2002). The
cortical topography of tonal structures underlying Western music. Science (New York, NY),298
(5601), 1095–9203.
Jeanneret, N.J. (2013). Inquiry into the extent, benefit and potential of music education in
Victorian schools, 5–6. Retrieved 26/09/2017 from: http://www.parliament.vic.gov.au/images/
stories/committees/etc/submissions/Music_Ed_Inquiry/196_Neryl_Jeanneret_16022013_pdf
Jonides, J. (2008). Musical skill and cognition. Learning, Arts and the Brain (pp. 11–17). The
Dana consortium Report on Arts and Cognition.
Peretz, I., & Zatorre, R. (2005). Brain organization for music processing. Annual Review of
Psychology,56,89–114.
Pesic, P. (2013). Euler’s musical mathematics. The Mathematical Intelligencer, 35(2), 35–42.
Posner, M., Rothbart, M. K., Sheese, B. E., & Kieras, J. (2008). Howe arts training influences
cognition. Learning, Arts and the Brain (pp. 1–11). The Dana consortium Report on Arts and
Cognition.
Song, A., Capraro, M., & Tillman, D. (2013) Elementary teachers integrate music activities into
regular mathematics lessons: Effects on students’mathematical abilities. Journal for Learning
Through the Arts, 9(1), 109–127. Retrieved from http://files.eric.ed.gov/fulltext/EJ1018326.pdf.
Trainor, L. (2008). The neural roots of music. Nature,453(1795), 598–599.
Wills, J. (2007) The neuroscience of joyful education. Educational Leadership Online, Summer,
64. Retrieved 26/09/2017 from: http://www.ascd.org/publications/educational-leadership/
summer07/vol64/num09/The-Neuroscience-of-Joyful-Education.aspx.
Wilson, S. (2013). From the Proceedings of the 2013 Research Conference Australian Council for
Education Research. Melbourne, Australia: How the Brain Learns.
Author Biography
Jane Law has been a school principal, music consultant and director for the NSW Department of
Education. She has led curriculum implementation in schools and written educational material for
organisations such as Music Count Us In and Sydney Symphony Orchestra. Jane is currently
teaching Numeracy, Literacy and Music at Newcastle University.
340 J. Law