
Consulting
Services and
Programs Integrated Music and Mathematics Programs The connection of music and mathematics exists on many levels and has been explored by musicians and mathematicians for centuries. Yet, this connection is rarely present in schools to any meaningful extent. Now students can benefit from this fascinating and inspiring connection through interactive instructional units that open new pathways to deeper understanding of both mathematics and music concepts. Access is broadened for students of diverse intelligences and motivation and inspiration for the study of both mathematics and music is enhanced. The instructional units utilize an inquirybased pedagogy that serves as a model to inform teachers' overall teaching practice. All student learning outcomes are aligned with the National Council of Teachers of Mathematics (NCTM) Principles and Standards for School Mathematics. A standards alignment detail is forthcoming and will soon be added to the "student learning outcomes" presented in this page. Contents of this page:
To review a research project involving an integrated mathematics and music unit, click here to view "A Case Study of Teaching To Multiple IntelligencesMathematics and Music." The Standard ProgramThis program consists of two primary components with an optional third:
Classroom Instruction:

day

theme

math topics

music topics

activity
mode

1

Introduction, theme question, music and math definitions, history, student experience journal entries, "The Multiples of Drummers" The Mathematics of Polyrhythms 
counting, multiples, least common multiples, factors, ratio, patterns, problem solving 
beat,
rhythm, polyrhythms, phrasing, tempo, accents, performance

interactive, listening, ensemble performance calculating, graphing, journal writing, 
2

"Multiples of Drummers" (continued) How do musicians use LCMs? How can mathematics help us understand other cultures?  observing patterns, making conjectures, creating a rule for LCM 
phrase length, music of diverse cultures, elements of style

paper and pencil calculations, ensemble performance, listening, discussion 
3

Melody Graphs: "Name That Graph!" Writing and Singing Melodies as Graphs What do melodies look like?  graphs on 2 axes, qualitative story graphs, quantitative graphs, interpreting graphs  scales, sight singing, melodic contour, melodic and harmonic intervals, pitch 
interactive, singing, listening, graphing

4

"Functional
Composer"(variation) A Mathematical Solution to Writer's
Block 
functions, in/out tables, calculating and graphing transformations of graphs, symbolic representations (variable),  musical notation, music composition and melodic structure, ear training, transposition, modes, instrumental performance  interactive, listening, identifying and calculating, graphing, journal writing, instrumental performance 
5

"Functional
Composer" (continued) Class performances of math melodies 
linear equations and their graphs, transformations, problem solving  the major scale, music composition, instrumental performance 
listening, calculating, instrumental performance, reflectionjournal write and discussion 
Student Learning Outcomes
Learning outcomes for the unit are categorized according to knowledge, skill, habits of mind (reasoning, reflection, interpretation, etc.), affect and product. Elementary students are often able to achieve outcomes traditionally associated with grades 9 and 10 as a result of processing musical material in an algebraic language. The level of their mastery of these topics will vary in depth, applicabililty and retention, however a layer of understanding at this point of development fascilitates algebraic understanding in later grades. Return to this page in the future for correlation of the outcomes to the NCTM Principles and Standards for School Mathematics.
mathematics

music

interdisciplinary  
knowledge 
Students will know and have an understanding
of: 
Students will know and have an understanding
of: 
Students will
know and have an understanding that: the "subjects" they study in school are ultimately interconnected studying the connections between "subjects" can lead to deeper understanding of the real world. 
skill 
Students will be able to: 
Students will be able to: perform polyrhythmic beat patterns 

habits of mind 
Students
will: improve their ability to make conjectures from the observation of patterns learn to reflect on their learning process learn persistence in the problem solving process 
Students
will:  cultivate their artistic judgment with respect to musical decisions increase their awareness as to the subjective nature of artistic judgment listen with greater clarity and sensitivity 
Students
will: begin to seek connections between other disciplines they study generate a habit of inquiry to seek depth of understanding 
affect 
Students
will: gain confidence in their mathematical abilities become inspired to study mathematics gain an deeper appreciation for the ways that mathematics informs our lives see that mathematics is more than a tool, but a way to perceive beauty 
Students
will: gain an appreciation of diverse cultures through musical analysis gain confidence in their musical abilities gain a fresh perspective and open attitude to their musical art 
Students
will: discover new insights into the nature of creativity and the relationship between the work of scientists, mathematicians and artists. 
product 
Students
will create: polyrhythm graphs multiples tables for inductive analysis journal logs melodic contour graphs in/out tables 
Students will create: 
Program Customizing
The Standard Program can be customized for the specific needs of teachers, schools and/or districts to specify:
Parents can be invited to attend the staff workshops, or specialized workshops can be held for them. The topic of music and mathematics is especially interesting to people of all ages, and can provide an effective link to engage parents in the studies of their children. Adult education programs that mirror student programs serve to bring communities and schools together.