MATH 165.01 Concepts of the Number System Spring 2007 Term Paper

The term paper is a project you will be working on throughout the semester. The topic is up to you but needs to be checked with me. Topics could be anything from the history of a mathematical concept to a current issue in math education. I expect that you will have found a topic by the end of February. A first draft is due on April 6. You will correct each other's drafts; the corrections are due on April 16. The final version of your paper is due on May 16, the last day of classes. As with your homework, you may hand in your paper early to be able to get feedback from me.

Here is a list of possible topics, but you should feel free to come up with your own ideas. The references are meant to provide starting points for your research.

• Reasoning and fallacies in fundamental mathematics taught in elementary school (L. Ma, Knowing and teaching elementary mathematics; choose one chapter to write about).
• How to define fractions in grade school (R. McCrory, Mathematicians and mathematics textbooks for prospective elementary teachers, Notices of the AMS, 53 (2006), pp. 20-29)
• Learning and teaching proofs (G. Harel & L. Sowder, Toward comprehensive perspectives on the learning and teaching of proof; G. Hanna, Proofs that prove and proofs that explain. In: G. Vergnaud, J. Rogalski, and M. Artigue (Eds.), Proceedings of the 13th Meeting of the International Group for the Psychology of Mathematics Education (pp. 45-51), PME, 1989)
• Mathematical awareness (start with any of the books by John Allen Paulos).
• Ethnomathematics (start with any of the books by Claudia Zaslavsky).
• History of number systems (H.-D. Ebbinghaus et al, Numbers, Springer-Verlag, 1990; B. Mazur, Imagining numbers, Farrar, Straus, and Giroux, 2003).
• History of certain numbers, e.g., 0 (C. Seife, Zero, Viking, 2000).
• The Math Forum Teachers' Place (concentrate on a specific activity or lesson plan)
• Mathnerds.com (write about this internet group--what they do, their philosophy, etc.)

"Philosophy is written in this grand book--I mean the universe--which stands continually open to our glaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures, without which it is humanly impossible to understand a single word of it."
Galileo Galilei (Il Saggiatore, 1623)

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