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MATH 165

Concepts of the Number System

Fall 2012

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 September. A first draft is due on October 29. You will correct each other's drafts; the corrections are due on November 5. The final version of your paper is due on December 14; you will need to turn it in on iLearn. 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 literacy (R. P. Moses, Radical equations, Beacon Press 2001; J. A. Paulos, Innumeracy, Vintage 1990).
  • 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)
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