A steady stream of research has shown that many elementary school teachers have weak mathematical knowledge in some areas, including place value and fractions. Since a teacher's mathematical knowledge affects their students' performance, improving elementary school teachers' knowledge is critical. A better understanding of the mathematical misconceptions held by future (pre-service) elementary school teachers will help break this cycle. This article contributes to the understanding of this problem. As suggested by the Conference Board of the Mathematical Sciences (CBMS) report entitled, "The Mathematics Education of Teachers," many colleges now require several mathematics courses for pre-service elementary school teachers. But, because of a shortage of college mathematics educators these courses are often taught by mathematicians or mathematics educators (or sometimes graduate students) with little or no experience at the K-6 level. College instructors may find themselves under-prepared to anticipate the ways that their students, pre-service elementary school teachers, think of and engage the material. In this article, the authors present an analysis of the errors pre-service elementary school teachers tend to make as they solve mathematics problems. (Contains 8 figures.)