Making Connections Between Mathematics and Music:
prospective Teachers’ Experiencing the Mathematics in
Drumming
NCTM Regional Conference
Baltimore, MD
Anne Marie Marshall, PhD
Lehman College
CUNY
Ryan Bazinet, PhD
John Jay College
CUNY
WELOME!
 Introductions
 Our story
 The lesson
 Do some drumming!
 What “we” learned
 Questions and conversations
Turn and Talk
 How are mathematics and music connected?
EDE 715: Children’s
Concepts of Mathematics in
Grades 1-6
 Exploration of the ways that children develop an understanding
of mathematical literacies in family, neighborhood, and school
settings. Approaches to formal and informal documentation
and assessment of children’s development in mathematics. Use
of media and technology as appropriate within an integrated
curriculum. Fieldwork in early childhood settings with diverse
populations, integrative seminar, development of an academic
portfolio.
Mathematics in the
Community Unit
 In peer groups, you will be asked to identify a setting outside of
the classroom that would provide a meaningful context for
students to explore mathematics. This could be, but is not limited
to, a museum, community based center or cultural organization.
 Visit the site and create an integrated mathematics unit that
situates the trip, and describe how the context and
mathematics would be relevant to students.
 Mathematics must be in accord with the Common Core State
Standards and to students living in a large urban community.
The Unit
 Phase 1: Prepare for and attend the trip
 Site selection
 Pre-visit prep (web, coordinators/docents)
 Logistics (accommodations, travel, cost)
 Rationale
 Phase 2: Planning the unit
 5-day unit
 Integrated content
 1 Fieldtrip
Rationale for the Assignment
1. Connections across content, across disciplines
-NCTM Connections Process Standard.
2. Ethnomathematics / Culturally relevant
-mathematics is not a culture-free discipline
3. Understanding mathematics in a different way
-when mathematics is placed in a relevant context, it has meaning for students.
4. Preparing for changing state of schools, loss of specialists
-arts education is being challenged by budget cuts and ]as pressure to improve
test scores in “core” subjects.
Integrating content in the
classroom
 Research indicates that using an interdisciplinary curriculum
provides opportunities for more relevant, less fragmented, and
more stimulating experiences for learners (Frykholm &
Glasson, 2005; Koirala & Bowman, 2003).
In the past, units have
included...
 Trips to Pizzerias (measurement, fractions)
(Students will watch chefs make pizza, Celebrate with pizza)
 Trips to Grocery Stores/Corner Stores (money)
(Students will receive $ and need to purchase food for a party)
 Trips to the Park (looking for shapes)
(Take a shape walk through the park to see as many shapes as possible)
 Trips to the Zoo (collecting data, story problems)
(Keep track of how many zebras, monkeys, elephants you see. Create story problems)
But the integration has been superficial.
So….
Our Study Questions
 How does experiencing an integrated lesson impact prospective
teachers’ understanding of content and how to integrate
curriculum?
 What are necessary components of learning about integrating
curriculum that help support transfer to practice? Which are the
most important?
The Study…
 1 mathematics educator, 1 ethnomusicologist
 Co-teach an integrated math/music lesson, focusing on
points in the lesson where math and music are integrated
 After the lesson, students reflected on the experience and
students created integrated math/music lessons
 Integrated Lesson
 Student reflections
The Math and Drumming
Lesson
 Who has ever played an instrument?
 In what ways do you think math and music are
related?
 Listen to examples of drumming
 Drumming Notation- Mathematics
 Students play drums
 Reflection on the experience
Turn and Talk
What are all the ways math and
music are connected?
How does music use math?
How are mathematics and
music connected?
Students said…
 Timing- counting beats
 Adding/taking away beats
 Patterns
 Grouping
 Measuring how long to play a beat
 Symbols
 Adding/subtracting
 BPM (beats per min) rate
Listen…
 What do you notice about the drumming in each song?
 Try to describe the beats and rhythms you hear in each
song.
 How does the music make you feel?
EXAMPLE A
EXAMPLE B
EXAMPLE C
Example A: Indonesia
Example B: Nigeria
Example C: Zuccotti Park
Turn and Talk
 Why do you think different songs sound
different?
 In what ways do drums make songs sound
different?
 How can you describe how drumming is
different in different songs?
How could you represent the
beats in a song?
Western Notation
TUBS Notation
Time Unit Box System
x
x x x
x x x x x x x x x x
Pa
pa do / gun
gun ta / go do pa do / go ta go do
What’s a Polyrhythm?
 Polyrhythms are produced by dividing a measure in two or
more different ways simultaneously and are related to
fractions and the least common multiple/greatest common
divisor.
 For example, if one drum is to play 3 equal beats in the same
space of time, as another drum is to play 2 equal beats, we
must divide the measure up into 6 beats (or a multiple of 6).
This division of 6 beats between 2 drums has clear connections
to understanding and experiencing factors, multiples, and
fractions.
Visual Representation of
3 against 2 Polyrhythm
Polyrhythm Exercise
Bell Pattern:
X
X
O O
X
O O
kon
kon
ko - lo
kon
ko - lo
Triple Pattern:
X X X O O O X X X O O O
3
+
3
+
3
+
X
X
3
+
Duple Pattern:
X
2
X
+
2
X
+
2
+
2
+
2
X
+
2
+
How are mathematics and
music connected?
Students said…
 Timing- counting beats  Symbols
 Multiplication
 Adding/taking away
beats
 Shape
 Division
 Adding/subtracting
 Notation
 Size
 Factors
 Patterns
 Grouping




 BPM (beats per
Measuring how long to min)/rate
play a beat
 Magnitude
Time signature
 Fractions
Pitch
 Part/whole
Loudness
Homework:
1.
Complete a reflection
2.
Design a lesson that includes the
integration of music and
mathematics. You can choose to
highlight any of the areas we talked
about this afternoon or use any new
ideas you may have.
Q1: What did you learn
about math and music?
Students responded…
 new techniques to incorporate math and music  music is not just sound. It is organized. It takes
knowledge. It has length, speed, intensity.
 learned about other cultures/music from other
 I was surprised to see that Math and Music have
cultures
so much in common.
 math is a subject in life, it is related to everything
 I learned that as much as I listen to music on a
daily basis, I really don’t know anything about it.
 incorporate math in fun and meaningful ways
 integrating math and other subjects makes
students think about math in the real world
 math and music have patterns, shape, symbols,
notation
 gives them practical approaches to learning
and using mathematics
 Music uses fractions, parts & wholes
 helps students to answer the question “When
are we ever going to use this?”
 helps students enjoy math
 math lives everywhere
 segments and counting is what actually gives us
music
 language of drumming
 easier to integrate subjects than I previously had
thought
 I learned about drum circles and what they are
used for.
Q2: What did you learn
about integrating subjects?
Students responded…
 best way is through an interactive lesson
 it is important to let students speak about what they
already know and then work with that as a
foundation.
 there are many ways to integrate math and other
subjects
 easy to find ways that math can be integrated with
different disciplines
 integrating math and another discipline can make
math more enjoyable for those who do not ‘like’
math
Q3: What new questions do
you have?
Students responded…
 What would be the next step after this lesson?
 What other areas can music be integrated with?
 How can you utilize instruments if you have little
or no access to them?
 When integrating math and other subjections,
how would you assess the students?
 Would this have been an easy lesson to do with
only one instructor instead of two?
Lessons Included
 Students will sing ‘Twinkle Twinkle Little Star” to look at patterns
 Students will show how words repeat (patterns) in “Bah Bah Black Sheep”
 Students will use measures to connect notes to fractions (whole note, half note,
quarter note, etc)
But….
 Students will listen to a song about shapes on YouTube and then talk about shapes
 Students will listen to an audio tape song connected with the book, “One Elephant
Went Out to Play”
 Students will sing “The Hokey Pokey” while ‘putting in a shape’
Now what?
 How does experiencing an integrated lesson impact prospective
teachers’ understanding of content and how to integrate
curriculum?
 What are necessary components of learning about integrating
curriculum that help support transfer to practice? Which are the most
important?
Questions and Comments
Thank you!
Anne Marie Marshall
Ryan Bazinet
anne.marshall@lehman.cuny.edu
rbazinet@jjay.cuny.edu