Starting this month, I.T. alumni will go to elementary and junior high schools all over Minnesota for the first part of the construction project. The students will cut and paint 1620 triangular panels, each approximately one yard across, which will eventually make up the globe.
One May 4, the students will come to the university put all the panels together to build the earth. The construction will involve a bicycle powered hydrolic lift, enabling the students to be responsible for every part of the project.
This new world project is a quite interdisiplinary effort, calling for interaction between engineers, such as organizer Bryan Beaulieu, elementary and junior high teachers, students, I.T. alumni, and, as you might expect by the newsgroup choice, geometers.
Stuart Levy of the Geometry Center got involved with the project because in order to use flat material to build a sphere, someone needs to calculate the geodesic structure. I spoke to Mr. Levy this afternoon about the project. He gave me some of the particulars of working on this applied project. It is quite intriguing, especially since it is somewhat rare for engineers and geometers to work together, so concerns such as strength of construction and size of panel are easy to forget.
The material used is a thin plastic which comes in one yard sheets. In order to maximize the stability of the globe, it was best for the panels to be triangles. Under these conditions, Mr. Levy came up with the following triangulation scheme: starting with an iscosohedron, split the faces nine-fold, slightly raising each of the new triangles to give a closer approximation of the sphere. Use two successive applications of this process to get the proper size of panels.
After designing the triangulation and underlying structure of the earth, the next step was projecting maps onto each of the panels. The students will use these maps to paint the panels with rivers, other geography, as well as political boundaries. This involved choosing the best projection to use, which turns out to be the stereographic projection. In order to make a map which is larger than one panel, a better choice of projection is one which unrolls the surface onto a tangent plane while preserving arclength. On a larger map, the stereographic projection distorts size in a distracting way.
This program is an exciting way to bring people of all ages and many diciplines together for a common purpose. If you are in the area on May 4, come to campus to watch the final construction of the world.
From usenet Sun Apr 04 13:47 PD 1993 Path: forum.swarthmore.edu!uunet!cdp!doversherhs From: Dover-Sherborn High School <firstname.lastname@example.org> Newsgroups: geometry.pre-college Date: 04 Apr 93 13:47 PDT Subject: Re: Geometry Projects Message-ID: <email@example.com> References: <firstname.lastname@example.org> Sender: Notesfile to Usenet Gateway <email@example.com> Nf-ID: #R:firstname.lastname@example.org:-1417078536:cdp:1800700003:000:15982 Nf-From: cdp.UUCP!doversherhs Apr 4 13:47:00 1993 Lines: 347
April 4, 1993
Dear Geometry Forum Readers,
This is a fairly long entry. It includes: I. a project design outline and project evaluation criteria II. students' project proposals and questions - first draft III. the classes' regular evaluation model
If you have the time and interest the we would like your responses to all three, but particularly to the project proposals. Any ideas, resources, questions, and constructive criticism are welcome.
Our audience will include the entire community - each year the school sponsors a day when students exhibit their best work for teachers and parents.
Please address any comments to the students.
Keith Grove Mathematics Teacher-Dover Sherborn High School, Dover, MA
I. Geometry Projects - Design and Evaluation
When writing your proposal, please address the following list of considerations. Feel free to list and address other considerations as you discover them.
Ideas to keep in mind when designing your project.
1. What will your product look like? (identify the characteristics of your project) - Who is your audience? - What do you intend to do with your product? - How do you intend to present your product?
2. Questions to consider: - What is your project's relationship to geometry? - Consider the usefulness of your results. - What are the possibilities of using your results?
3. Develop a time line for your project.
4. Decide which members of your team will perform each tasks.
Evaluation Criteria: 1. creativity 2. meaning or relevance of the results to your lives 3. general interest 4. attention to detail 5. neatness of presentation 6. choice of presentation 7. accuracy
II. Students' Proposals and Questions - First Draft
Children's Toys: Kristen, Elise, and Tracy We propose to make two children toys. The toys will consist of different geometric shapes made of different materials. Is there a place where we can get any materials for the toys? If the toys are successful we propose that we try the toys out on the little kids in the child development center (in our school) and try to send them to a toy manufacturer. We hope these toys amuse the children and please them.
Pool Table: Rajiv, Jim, Becky, and Andrew We are going to show the relevance of geometry in the game of pool. We are going to show how reflection is the major factor of playing pool. we can teach the viewing audience of the eduation of pool in form of a video.
Scale Model Auditorium: Rajiv, Jim, Becky, and Andrew We are going to construct a model of the new Boston Garden and how we would envision it. We will show the geometry of building an auditorium in scale and proportions.
Sailing: Van I would like to use geometry to design a sailboat of same sort. I'm looking for some of the basic principles of sailboat design. I'll try to make a small model of the boat I design. I would also like to know what materials are easily available and easy to use to make a small model. I would like to find out some of the formulas used in sailboat design to possibly use.
Construction of a Geodesic Dome: Judd, Alex, Carey We will attempt to construct a Geodesic Dome. It is planned to be around eight feet high and eight feet in diameter. We will construct it with a wood frame and ply wood floor with linoleum supported by cement blocks to prevent rotting. The frame will be covered midway with plywood and midway to the top with Plexiglas. In the end, this will be used as a small greenhouse. The purpose of this project is to experiment with the geometry of construction. This will be worked with until the first week in June. Our progress on this structure will be videotaped and photographed to show the different stages. The materials we will need are the following: tools, screws, nails, 8 small hinges, 2 X 4's, plywood, 10 cement blocks, Plexiglas, linoleum. Please respond to this message with any ideas, pictures, or materials that can help us fulfill our ideas for the project. If you do have materials that you are willing to donate, please leave your phone number or call (508) 785-1561; ask for Judd.
Gingerbread Village: Krista and Sara We want to make a gingerbread village. We'll build small gingerbread houses. We're going to name all the geometric figures that apply to our house. We'll build it with candy and gingerbread that have unique and different shapes. Afterwards, we'll show our village to the class and let the class eat it. We were wondering if any other people had the same idea as us in doing this project.
Video of Boston Trip: Danielle, Erin and Alissa We are working on a trip to Boston.(20 miles away) We will go into Boston with a video camera. Our goal is to plan a field trip to Boston for our class. We will go in before to plan the day and time it. In doing that we will also video tape the geometry we see in the specific sites we want to visit in Boston. Hopefully, we will find informed people at the specific sites to interview. We are considering visiting: Omni Theater, Boston Garden, State House, Faneuil Hall, Cheers, and Back Bay (architecture). My friend will accompany us through the Back Bay, as someone informed of the architecture. We will then present the video to the class, so they see the geometry. The next step is to propose a field trip to our headmaster. We will also need to find chaperones, because we will be taking the T in Boston. We hope that we will physically be able to show our class the geometry of Boston. Basically, we are asking what you would suggest we look for as the non-obvious geometric things in Boston.
Telecommunication: Stephanie, Jen, and Lynn Study and learn about telecommunication. Start conversations with geometry students from foreign countries. We want to find out how geometry is related to telecommunication. What is cyberspace?
Photography and Painting: Hilary, Dan, C.C., and Stephanie We are sophomores at Dover Sherborn High School and are studying geometry. We are creating a project dealing with paintings and photographs and trying to apply it to geometry. We want to make a book with paintings and photographs and analyze them using geometry concepts. Has anyone done a project similar or has any suggestions? If you have any please respond.
Aspects of Telecommunication: Charlie, David, and Tom How it works? What it is? How dimensions are crossed in telecommunications? How cyberspace is defined? I want to pose a question of how geometry is related to telecommunications ... in general, and specific ways? Some other questions I might want to pose would be: How geometry is related to sensory depravation tanks? What are several alternate dimensions? How does cyberspace relate to virtual reality?
Photography: Joe and Eric For our project we are examing the geometric shapes around the school building. By taking picture and examining the architecture we want to learn more about the engineering of this school. We would like to see if you have any more ideas of geometric areas in the school to look at? Are there any parts of a building such as this which are less obvious in examing engineering?
Sound Maps (1): Paul, Rachel, Noah, Amy, Emily We have different ideas about location of where to do our sound maps. In the hallway during school and recording what we hear from which direction we hear it. (with eyes closed) Also in downtown Dover, or the roof of one of our houses, and in the woods. On our recordings on paper, that are not 3-D, we will draw the sounds on translucent paper (tracing) and put them together so they over-lap. We would also make a 3-D model (from a coat hanger as a mobile) creating an image of real life. These all would include location of sounds, origins of sounds, and color coded volume.
Sound Maps (2): Paul and Noah We are going to listen to music at different tones, places and we will experiment with different angles of the speakers and what the different angles result in. We will map out the bass tones, treble tones and how the sounds differ at different places in the room.
Geometry Relativity: Dan My project is basically geometric relativity in normally appearing occurrences, especially through the use of photography. Using this medium I hope to focus on factors such as distance, length, dimension, angles, and shadowing. From there I would consider and compare geometric consequences and causes in these images.
Snowboards: Alex, Eric, and Tim In our project we will be connecting the shape and construction of a snowboard with geometry or at least trying to. Also we would like to consider the physics of the speed and momentum used to jump and carve down a hill (carving is a way of turning that will be more explained in depth during our project). We are having some trouble with the physics aspect of our project. If anyone has any ideas to help us, it would be greatly appreciated. Thank you.
III. Regular Class Evaluation Model
Goals of the assessment process:
Students will eagerly anticipate assessment tasks as opportunities to produce something useful - a plan, a portfolio, a report, or results of an investigation.
The assessment process is a means to ... tell us where we are ... develop habits of mind ... set ourselves up for better results in the future ... develop more interesting problems ... develop vocabulary ... tell us how well we are working together. ------------------------------------------------------------------- I. Mathematical Problem Solving, Reasoning & Connections ........ 1 2 3 4 5 %I'm using, with increasing confidence, problem-solving approaches to investigate and understand mathematical content. %I'm aware of the strategies I'm using to solve problems. %If necessary, I change or modify my strategy in the middle of my work. %I understand what I'm doing -- I'm not just going through the motions. %I have mastered the material. %I'm making and evaluating mathematical conjectures and arguments. %The work I do reminds me of work I've done before. %I think about whether my answers make sense. %I can give reasons for choosing the strategies I use. %I eventually get most of my work correct. %I am able to explain the rationale for each answer.
II. Mathematical Communication ..................................1 2 3 4 5 %I discuss mathematical ideas and make convincing arguments. %I reflect on and clarify my thinking about mathematical ideas. %I understand what is discussed in class. %I can explain my thoughts and strategies in class. %I ask questions for clarification and I ask "What if ... ?" questions. %I participate to the best of my ability.
III. Mathematical Disposition ...................................... 1 2 3 4 5 %I'm developing personal self-confidence and a disposition to seek, evaluate, and use quantitative and spatial information in solving problems and in making decisions. %I'm developing flexibility, perseverance, interest, curiosity, and inventiveness. %I feel like I'm doing well in class. %I'm better now at solving math problems than I was in September. %I work hard to solve math problems. %I try more than one idea before I give up on hard problems. %I seek out differences of opinion. %I make sure others mastered the material. %I avoid interrupting. %I avoid put-downs. %I actively listen.
IV. Small Group ............................................................... 1 2 3 4 5 %We establish effective procedures for accomplishing our work. %Everyone understands the purpose of our tasks. %Everyone stays on task. %Everyone works together on the same problem. %Each question is understood by everyone. %Each person contributes her or his ideas. %Everyone understands and takes a turn explaining. %We actively listen to each other. %We seek out differences of opinion. %We encourage each other to participate. %We express support and acceptance of each other. %We have fun!
V. Class ............................................................................ 1 2 3 4 5 %TIME CONSIDERATIONS %Are you on time each day? %Are others in the class on time each day? %Does class start promptly? %Is class time being used effectively? %PREPARATION FOR CLASS %Are you prepared for class each day? %Are others prepared for class each day? %ACTIVE LISTENING %Are you listening to the other members of the class? %Do you feel heard by the other members when you speak? %PARTICIPATION %Are you participating in group problem solving discussions? %Are other members participating in group problem solving discussions? %UNDERSTANDING %Do you understand the class discussions? %Does every member of the class understand the discussions? %RESPECT %Do you respect your own behavior and attitude? %Do you feel your contributions are respected? %Do you respect the contributions of others? --------------------------------------------------------------- %Your base-line numbers were negotiated at the end of the preceding term. At the end of this term we will negotiate in each category. ----------------------------------------------------------------- Journal Entries: %Please answer the following questions at the end of the term: %What do you do particularly well? %What, if anything, hinders your success? %What could you do differently to have greater success?
%Do you perform at least one of the following roles or tasks for the class? Which one(s) and what is your evidence? Organizer - makes lists, gives directions, lines up materials. Encourager - shows enthusiasm for people's ideas. Idea Person - comes up with a lot of suggestions, or with one very good one. Good Humor Person - keeps the activity fun by making funny remarks in a way that keeps people enjoying what they're doing. Cooperator - responds to organizers, who can't get anything done unless there are good cooperators in the group. Listener - listens intently when people give ideas, so there is a sense of calm and concentration in the group. Stick-to-itive Person - when the going gets tough, these people stick in there and keeps thinking, listening, trying, concentrating. Problem-finder - contributes by seeing what's wrong with the way the group is solving the problem. Detail-detective - notices little things in the instructions or in the problem-solving method that are important to pay attention to. Clarifier - uses words well to explain what other people don't understand. Includer - makes sure everybody gets a chance to talk.
%How do you feel about yourself as a math student? Explain why you feel that way. What would the rest of us see that would correlate with what you are feeling about yourself? %Are you comfortable with the procedures and the leadership of the class?
Small Group Questions: %How are procedures for solving the problems established? %How is leadership established in the group? What forms did it take? %Does everyone's ideas get heard and used? %What effect does time have on your group process? %What is most frustrating about the experience of working in groups? %What kinds of contributions do people make? (roles played, forms of participation, styles of communication) %What helped the conversation? What hindered the conversation? %What do you want to say or do in the group that you don't say or do? %What territory does the conversation cover? %What questions aren't asked? What isn't discussed? What is passed over too quickly? %From whom do you feel the most support in the group? How is that support given? How important is it to feel supported by others in the group?
If thisP.sS. If this comes through as scrambled as it appears on my screen - I will try again. ... Keith