320projects

Project Topics for Math 320, Fall 2005

The purpose of the project is for you to think about some mathematics outside of the textbook material that might be useful in an elementary classroom. The topic can either be one that you might actually teach to elementary school children, or simply one that helps you to understand and appreciate mathematics in a more concrete way. There are ideas listed below, but you are also encouraged to think of your own.

The project may be done individually or in pairs, but groups larger than two are not permitted. You are to write a short paper (2-3 pages) corresponding to the particular project. If you work as a pair, you need only write one paper, but the work should be shared equally. The hope is that each group will give a short presentation on their project, depending on how much time we have at the end of the semester.

You need to have your project topic chosen by Monday, September 12. You should talk to me at some point before this date!
The paper for the project is due Friday, November 11.
Presentations will be the last two weeks of class.

Possible ideas for the project include the following:
1. Read a work of mathematical fiction, such as:
       Uncle Petros and Goldbach's Conjecture, by Apostolos Doxiadis
       The Parrot's Theorem, by Denis Guedj
       The Man Who Counted, by Malba Tahan
       Arcadia or Rosencrantz and Guildenstern are Dead by Tom Stoppard (plays)
    Explain the role that mathematics plays in the story. Is this mathematics something that could be explained to elementary school children? Discuss the view of mathematics or mathematicians presented. In particular, do you think it is accurate?

2. Read a biography of a mathematician, such as:
       A Beautiful Mind, by Sylvia Nasar (Warning: the movie doesn't follow it well!)
       My Brain is Open, by Bruce Schechter (about Paul Erdős)
    What did you learn about mathematics and the life of a mathematician? What did you understand of the mathematics that this person did?

3. Read a children's mathematics book which presents basic mathematics in a creative way and/or more advanced mathematics in an accessible way, such as:
       The Adventures of Penrose the Mathematical Cat, by Theoni Pappas
       The Number Devil, by Hans Magnus Enzensberger
       The beginning chapter(s) of Indra's Pearls by David Mumford, et al.
       Books by Marilyn Burns (see http://home.blarg.net/~math/burnsbooks.htm)
    What did you learn about mathematics from reading this book? How could you use it in a classroom? Discuss one of the ideas presented.

4. Learn about an accessible theorem or mathematical idea, such as:
       The Monty Hall problem
       The Knights of the Round Table problem
       The Jordan curve theorem
       The four-color theorem
       Pascal's triangle
       Möbius strips
       The Königsberg Bridge problem
       The marriage problem
       Penrose tiles
       The Fibonacci numbers
       Fractals
       The birthday problem
       Fermat's Last Theorem
       Goldbach's Conjecture
       Different base systems
       The golden ratio and golden rectangle
       Magic squares
       Sets and Venn diagrams
    Explain the problem and how it works. What did you learn about mathematics? Would these ideas be useful in the classroom?

5. Read a book or article about teaching mathematics at the elementary level.
    What was the main idea of the book or article? Do you agree or disagree with the author's view of teaching? How might you use what you learned in this article in the classroom?

6. Chose a project from another math for elementary teachers book, a previous Math 320 course, or a children's textbook (I have some in my office). Some topics (that I have materials for) include:
       Base 6 arithmetic
       Math puzzles and games
       Choosing a number and talking about its various properties
       Designing boxes and other package designs
       Relating fractions and decimals
       Data, graphs, and patterns
       Teaching a child a mathematical concept they haven't learned yet
       See also ideas on www.proteacher.com or www.proteacher.net
    Do the project as given in the book. What did you learn from the project? What age group would the project be useful for?

Note: The ideas listed are highly subjective, in that most of the books are ones I own or have read, or projects I have found or have heard about from others for a similar class. You should not feel limited by them but are welcome to think of your own ideas as well.

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http://www.math.ksu.edu/~jbergner/math320f05projects.html Last updated: 25 August 2005