Creating Your Own Rock Band

Grant Proposal for the “Rock Band” project

Project Summary

             Without providing context, mathematics becomes a boring and disengaging topic for today’s students.  Unfortunately this occurs too often in too many classrooms and has contributed to a national education crisis. This project, designed by future teachers attempting to make a connection with students using a playful subject, provides this needed context and meaning. The project we designed has students looking at a variety of topics related to music including the way it sounds, music theory’s mathematical origins, and the business side of starting a band. This project is intended for an Algebra II course.  Its six-week design allows a variety of ideas to emerge from these and other musical topics.

            Students work in groups that operate as a team to complete their project. Students are responsible for documenting their work and presenting their findings to the class at the end of the project. After completing this project, students will gain a sense of how mathematics permeates many different aspects, even if all they want to do is grow up to be a rock star.

Description

            The six-week project begins by exploring the origins of mathematics in Western civilization.  The ancient Pythagoreans, who introduced the fields of math and numbers into the Western world, discovered mathematical relationships through examining the harmonics of musical sound. Students will learn about their achievements while discovering the same mathematical properties the Pythagoreans found.

         The next section elaborates on the introductory topics by letting students analyze the properties of a vibrating string, conducting qualitative and quantitative experiments in much the same fashion that Pythagorus did.  Students will formulate their own theories about the relationship of pitch to length of the string, and then compare their conclusions to those of Pythagorus. The project continues with a survey of the subject of acoustics.  The mathematics of acoustics is extremely high-level, and is not within the scope of this project, but students will be able to recognize key concepts when they see them, and develop an understanding of the key principles involved. Students will then embark on a study of sound volume.  Using both simple mechanical demonstrations and operational use of sound pressure detection equipment, students will learn to relate sound power with audible changes in volume using a logarithmic scale.  They will then use their findings to make conclusions regarding appropriate music volume, and the sensitivity of the human ear at various levels.   This portion of the lesson concludes with a section on tinitus awareness and prevention, elaborated by a guest speaker in the health profession.

            Another section of the project lets students get creative with designing a stage set for a rock concert. We take this opportunity to examine conic sections through the context of stage lighting. Several key mathematical concepts emerge from conic sections – specifically, parabolas. Students will examine the equation of the parabola in more detail by looking at the general, vertex, and standard equations. They will see how changing certain parameters affect a parabola’s graph.  The students use graphing calculators to explore these changes.  By the end of the lessons on conics, students will be able to identify the general equation for a conic section, describe the principle of the directrix and focus of a parabola, and describe the effect of transformations on a graph.

            Not only will students discover mathematical concepts such as logarithms and parabolic functions from lessons utilizing music and sound, they will create a cost-effective business model to help local emerging musicians make the transition to successful music artists. A local band would be used to drive motivation for this portion of the project. The band would visit the class to introduce the portion of the project to explain what type of help they need. They again would visit at the end of the project to select which model they like best after groups present to them their solution. Furthermore, students could potentially work with the organizers of the SXSW music festival - a weeklong event that gives emerging artists a chance to showcase their music - to create a webpage displaying the business models they have developed. This work would be available to any band seeking help.

Rationale

            Studies conducted in recent years have identified “Project Based Instruction” as more effective than traditional education.  In a 3-year study, Jo Boaler (2002) found that students involved in project based instruction score higher on problems involving conceptual and analytical thought, as well as those demanding direct recall and application of mathematical techniques.  Moreover, researchers at SRI International found that students using technology in their projects outperformed those that did not.

            Project Based Instruction incites students to tie their mathematical knowledge to other disciplines by applying what they have learned to real world problems.  As such, it heightens student awareness of the culture they live in and the people with whom they share it.  Students in Austin have a unique opportunity to become culturally involved in the local music scene because of the city’s reputation as the “Live Music Capital of the World”.

            In short, the vital need for realistic contexts and practical applications become more and more evident to members of the education community.  This project serves this end amply and explicitly.  Students will be able to develop an intrinsic interest and motivation in their work by directly relating it to the needs and concerns of the music community.  They will have a direct impact on the artists who choose to adopt their business models, and labor under a sense of responsibility and measurable consequence far beyond their own grades and academic careers.  For many, these are features never before likened to the mathematics classroom.

Potential Impact

             Musicians in the Austin area dedicate a large fraction of their energy to the composition and performance of their music.  For many, the promotion and distribution of their work, as well as knowledge of the audience for whom they play are secondary considerations only incidental to their profession.  It is left to an entirely different class of professional persons: managers, producers, sound and lighting technicians, and executives, to make vital decisions in these areas.  Without an understanding of the mechanics underlying the final production and delivery of their work, many artists can develop cynical or resigned attitudes, with regard to marketing, advertising, technical specifications, and popular consumption.

            In the course of this project, students will explore the mathematical models and principles that form the technical and business end of music production.  Many will be led to question and reform their own pre-conceived notions of the music industry, how excellent performances are achieved, how assets are understood and developed, and how the artists are eventually rewarded for their work.  By project’s conclusion, the students will form their own conclusions with regard to the optimal practices and procedures that can be taken by independent aspiring artists, and present their recommendations and models to artists in their area. 

            The products that they make will have an enduring value long after the project has concluded, and has the potential to significant contribute to the prevalent music scene in Austin.  Given the requisite facilities, technology, encouragement, and guidance, it is only a matter of time until the positive effects of this project are manifest.

Evaluation Plan

             Each team will develop an annotated portfolio. These will be used as the main form of assessment as it provides a collection of all aspects of the project. This will be augmented by a final presentation. To assist the students in completing their portfolios, we will periodically expect documented problem solutions from them. Furthermore, each student will keep diagnostic learning logs. This will be the main form of individual assessment. These logs will allow students to return to previous work and revise it before presenting their final portfolio. We will review these periodically. If there are concepts that some students display a better understanding than others, then we will set aside time for those students to present this understanding.

            To begin the project, however, we will have the students create concept maps that serve two purposes. First, it will allow us to see where the students have misconceptions about the math behind creating a rock band. Second, it will give them a structure that can be augmented throughout the project.  We believe that with these assessment techniques, we will set up the students for success both on the group level and on the individual level.

Project Calendar

 
         Mon                    Tue                         Wed                      Thurs                        Fri

Budget

Vernier LabPro Interface                                   $220.00                    10                        $1980.00

Vernier Microphone                                            $37.00                    10                          $333.00

Vernier LoggerPro Site License                         $159.00                     1                           $159.00

*TI 83 Plus Graphing Calculators                         $99.98                    30                          2999.40

*Office Supplies                                                  $50.00                     1                             $50.00

Subtotal                                                                                                                          $5521.40

* Funding from school or district                                                                                    -$3049.40

Total                                                                                                                              $2472.00