Here at New Haven at the Sound School we want to integrate the Long Island Sound as a theme into our instruction, to make connections between the material taught in the classroom and what goes on in the Sound. The Sound School is one of the schools of choice offered to high school students by the New Haven Public Schools. Children may choose to come to one of these schools instead of the large, traditional high schools. Long Island Sound leads to topics such as marine biology, boats, and navigation. As a mathematics teacher I look for problems to share with my students. By looking at the methods of solution in one field we may find strategies for solving problems in other fields.
One topic I look forward to is naval architecture, the designing of ships. If we are going to look at boat design, we need to know some physics. What is a center of gravity? What is a center of buoyancy? How do levers work?
A. What Is a Unit?
A unit is the result of a New Haven Public School teacher’s participation in the Yale-New Haven Teachers Institute. The Institute provides an opportunity for New Haven public school teachers to write curricula with the assistance of a Yale faculty member and the resources of Yale University. The Institute runs various seminars related to the subjects one teaches. The units are the record of what one accomplished by being in the seminar. One applies in February and finishes by the first week of August.
When one writes a proposal, one has high expectations. “I’ll write an explanation that will make it obvious for any student.” After one has tried to do it one sees reality. “It doesn’t sound much different from the references.” Yes, that is how I learned that I had learned something. The explanations that seemed complicated at the start now make sense. Unfortunately, that means other students will have to put in the time just as I did. I didn’t find the magic explanation.
The seminar on aerodynamics was an opportunity to pursue some of the physics related to boats. Aerodynamics is a division of the larger field of fluid mechanics. The rules that apply to air, when the speeds are well below the speed of sound, also apply to water. It is only necessary to take into account the different properties of the media. Water is more dense and more viscous than air; both, however, are called fluids. The rules for floating boats and balloons are the same. The rules for submarines and airplanes are the same. Boats, however, work on the surface of the water producing free surface waves; this adds some problems that airplanes and submarines do not have to contend with.
B. How to Use This Unit
I want my students to see uses of mathematics. One way students can see uses of mathematics is by reading about engineering projects and their solutions.
I see this unit as something the student can read as a start on the subject. The unit may be broken into sections for reading, or the whole unit may be given to the class. I want discussion with the students on the writing: Is it clear? How could it be improved? What was left out? Did some source over-simplify the story? After dissecting this unit it will be their turn to write a report on some technological project.
Learning is a do-it-yourself job. The required work may not be enjoyable. I hope, however, the collateral readings will be enjoyable and fascinating.
I see the student projects centering on the history of engineering, ship building, naval architecture, and technology. Books that are readily available are the Time-LIFE Books,
Ships
, by Lewis et al. and Thomas C. Gillmer’s
Modern Ship Design
. Both are public library books.
The most important part of the process will be the discussion. Students are all too willing to sit passively as if they were jugs waiting to be filled up. I see the reading as the motivation for the discussion. If the books are interesting enough the students will be willing to share them with one another.
I use this material when we discuss variation in Algebra II. This unit itself mentions direct and inverse proportion. The naval architecture readings give examples of variation when they discuss laws of mechanical similitude, such as the wetted surface varies as the square of the length on the water line. There are other places that the unit could be used, but I need a starting place. If the students show interest, the project will expand.
