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Grant
Proposal Summary
Project Director(s):
Melissa Heggen, Emily Buschang, and Joey Campbell Project Title:
The Mathematics of Minimalist Music
Total Budget Figure:
$2491.33
Our community is in a state of emergency
because our students have developed an aversion to the subject of
mathematics. The students show a general lack of interest in
mathematics and the traditional way it is taught in their schools. This
project originated by teachers seeking to connect with students on
common ground and use that common ground to engage students in
mathematics learning. The project we designed has students looking at
music compositions by the minimalist composer Steve Reich and analyzing
them mathematically. In doing so, students are more apt to develop
their mathematical knowledge and further extend the application of this
knowledge in new and real situations by gaining experience modeling and
applying mathematical concepts to musical compositions. Using music to
engage the student will recapture the average students lost interest in
math.
This project is intended for a Mathematical Models with Applications
course. Its four-week design allows both student and teacher to
introduce concepts in both math and music and allows students to
explore the intersection of these two subjects as they analyze
compositions mathematically looking for symmetry, permutations and
combinations.
After completing this project, it is our hope that
students will be able to develop their mathematical thinking and find
it easier to think about problematic situations outside of a classroom
mathematically. Also, it is our hope that students will retain their
mathematical knowledge for a longer period of time since they were able
to form their own understanding about math in the context that they
find interesting.
Description
The Mathematics of Minimalist Music Project
examines the mathematics
behind the music of Steve Reich (a modern minimalist composer). By
incorporating music into the math classroom our students will be more
connected to the concepts being introduced to them as opposed to the
traditional lecture format of teaching mathematical concepts. This
project will allow students to form their own understanding of advanced
mathematical concepts such as set theory, combinations, probability,
and symmetry.
This project uses music to gain student interest
and show students
that math can be found in music. During the first week of the four-week
course students are exposed to reading music, general music
appreciation, and minimalist music. This project assumes no formal
musical background. In fact, we see formal training as a potentially
harmful factor for students since it is highly unlikely that they have
ever been exposed to minimalist music and the techniques created for
analyzing music in this project will be foreign to the trained
musician. This first week is designed to peak student interest and have
them look into music they enjoy everyday in addition to hearing
minimalist music for the first time. After student interest is
maximized during the first week, we devote much of the second week to
mathematical concepts we can use to look at thee compositions and come
up with ways to explore them mathematically. Here we introduce set
theory, geometric permutations, rotations, and translations as well as
combinations and symmetry. Once the groundwork is laid through these
lessons students are now equipped with the tools necessary to examine
specific minimalist music compositions. Some play with instruments and
exploration of sound and the students can now come up with their own
mathematically charged compositions. Students will work together to
analyze pieces of music, and use what they have learned from each other
to create their own pieces, which will be performed at a recital at the
end of the project.
It is much more difficult to go back and unlearn
something which was
learned wrong, than it is to learn the right way from the very start.
As I stated earlier, student with a background for analyzing and
performing musical compositions might find this project an extra
challenge because the tendency to revert to what is already known might
skew their thought process necessary to analyze the compositions
presented in this course. But this can be easily overcome if students
are patient and rely not on their ability to analyze pieces musically
and rely on the mathematical knowledge accumulated in the second week
of the project to analyze the music.
It is important for students to relate in class work with their
everyday life. Extending what they learn through this course to music
they listen to everyday will help develop the student’s ability to
notice patterns or their ability to group similar objects into sets.
Music has captivated the hearts and minds of the majority of our
community, and this project exploits this interest to give students,
who find the traditional format of school mathematics a turn off, a new
avenue for exploring important mathematical concepts. This program
allows students the opportunity to explore math outside the traditional
sense and form their own mathematical understanding by using math to
describe and create works of art.
Rationale
Take a quick poll of the people walking down any street in America and
you will find that a disheartening proportion of our citizens view
mathematics as impossibly difficult, dry, and the source of anxiety in
their educational experiences. Those who have pursued their
mathematical studies past algebra, trigonometry, and calculus know that
it is in fact a highly creative and graceful art! While future
engineers may thrive in the algorithmic setting of a standard high
school mathematics course, most others will begin to develop a
life-long aversion to the subject.
This problem is more significant than it first may seem. Studies have
shown that mathematical aptitude often coincides with a creative,
artistic aptitude. Unfortunately, high school mathematics course
content and project topics typically are geared towards computation and
scientific applications. While many students enjoy such activities, a
significant student population – including many of those who may excel
in higher-level mathematics – can fail to be engaged by such
activities.
In this four-week project, designed for use in a
Mathematical Models with Applications course, students will not only be
exposed to elegant mathematics typically reserved for upper-division
and graduate level college students, but will also be given the
opportunity to explore intrinsic connections between mathematics and
music composition. It is reasonable to propose that most high school
students have an interest, at any level, in music. This interest will
be utilized as students seek out examples of set theory, combinatorics,
probability, and symmetry in the compositions of Steve Reich and begin
to see that mathematics can be found in unexpected places.
Potential Impact
This project is designed to satisfy and
expand on the general requirements of a Mathematical Models with
Applications course. Depending on the high school and the semester,
this class will be comprised of one teacher and between 15 and 30
students. The students will be a mix of sophomores, juniors, and
seniors. The only prerequisite for this class is Algebra I, and a
typical student in the class will not take additional math coursework
in the future. The academic and extracurricular interests of these
students are most likely in areas other than science, engineering, and
mathematics.
Exploring math through music will engage many of these students in ways
that a traditional approach might not. An atypically large proportion
of the students in a Mathematical Models with Applications may be
artistically gifted – either visually or musically. Both skills will
prove invaluable as students design ways to visually represent musical
patterns they have untangled from a composition.
Not only will this project satisfy the Knowledge and Skills objective
111.36.9, but will demonstrate to the students that they may possess
mathematically creative talents of which they were previously unaware.
They will complete the project with the understanding that the field of
mathematics is not a territory reserved only for the scientifically
minded, but in fact an elegant art where creativity and insight are the
most powerful tools.
Evaluation Plan
The students will be evaluated in several ways over the course of the
project. During the beginning of the project, participation will be a
large factor in their evaluation. Students will be asked to become
involved in the music that the class is studying. The music will be
analyzed for permutations, symmetry, and translations. The best way to
evaluate the students’ understanding of the presence of these
mathematical ideas in music is to have the students identify them. The
students also be evaluated on the written music assignments they will
be given. They will be graded on how well their composition follows the
given guidelines as well as on their creativity in the writing of the
music. A major part of the students’ evaluation on this project will
come from their analysis and presentation of a musical work by Steve
Reich. The method that the student developed to notate the sheet music
will be graded on its functionality. The analysis will be graded for
the student’s ability to identify the various mathematical principles
present within the music. The students will also be graded on the
progress they have made between the first presentation and the final
presentation.
Project Calendar
The calendar can be viewed by clicking here
Budget
| Item Description |
Unit Price |
Quantity |
Total |
| Personal CD Player |
$11.99 |
10 |
$119.90 |
| Memorex Boombox |
$44.99 |
1 |
$44.99 |
| CDs (Recorded) |
$13.98 |
10 |
$139.80 |
| Easy Media Creator 7 |
$99.99 |
1 |
$99.99 |
| 10 Pack Imation CD-RW Discs |
$10.00 |
5 |
$50.00 |
| Live performances |
$12.00 |
70 |
$840.00 |
| Standard Wirebound Manuscript Paper |
$3.95 |
50 |
$197.50 |
| Digidesign MBox Audio Interface |
$549.95 |
1 |
$549.95 |
| Sheet Music |
$10.00 |
10 |
$100.00 |
| Yamaha Keyboard |
$259.95 |
1 |
$259.95 |
| AA Batteries (4-pk) |
$5.95 |
15 |
$89.25 |
| Total: $2491.33 |
Staff Vitae
click name to view:
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