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The AMATYC Review Fall 2005, Vol.27, No.1 |
The Battle of the Zero Divisors Patricia Hale and Charles Hale |
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Patricia Hale is an associate professor of mathematics starting her sixth year of teaching at California State Polytechnic University, Pomona. She teaches mathematics courses primarily for elementary and secondary preservice teachers. Her interests include mathematics education, group theory, and women in mathematics. E-mail: phale@csupomona.edu Charles Hale is a lecturer in the mathematics department at California State Polytechnic University, Pomona. His interests are mathematics education, mathematics history and non-Euclidian geometries. Additionally, he likes to water-ski, camp, hike and eat, not necessarily in that order. Lastly, he is the proud father of Jessica, who has been accepted to Stanford's graduate program. E-mail: crhale@csupomona.edu |
| The mathematical reasons that we cannot divide by zero are not easy for most students to understand; in fact, even those students who have more than just a basic understanding of algebraic concepts still have difficulty. This is most problematic for college students who are prospective teachers since they need to develop a deep understanding of division because both national and state standards usually require these topics be taught to elementary school children. Unfortunately, many of our prospective teachers are never given the opportunity to develop a deep understanding of the reasons why division by zero is undefined; what indeterminate means in this setting; and what is meant when we say a solution does not exist because it would approach infinity. In this paper we give examples of prospective teacher's understanding of division by zero and a particular model that has helped our college students come to an understanding of why division by zero is undefined. | |