This is the first in a series of issue briefs to be written for The Center for Comprehensive School Reform and Improvement during 2006. A longstanding tenet of American education--one built into the very fabric of teacher training and licensure--is that elementary teachers need only general teaching skills and that having a caring personality is sometimes more important than how much math (or science or history) a teacher knows. In the lower grades, so the reasoning goes, even adults who have weak math skills themselves simply need to be sure they know enough to teach a given concept or skill. An important new study published last year suggests that this conventional wisdom is very, very wrong. The study revealed that a teacher's own mathematical knowledge has a substantial impact on student learning even at the first-grade level, a finding that left even the researchers themselves "modestly surprised." Teaching mathematics effectively depends on a solid understanding of the material. Teachers must be able to do the mathematics they are teaching, but that is not sufficient knowledge for teaching. Effective teaching requires an understanding of the underlying meaning and justifications for the ideas and procedures to be taught and the ability to make connections among topics. Fluency, accuracy, and precision in the use of mathematical terms and symbolic notation are also crucial. Well-designed instructional materials, such as textbooks, teachers' manuals, and software, may provide significant mathematical support, but they cannot substitute for highly qualified, knowledgeable teachers. (Contains 14 endnotes.) [This document was produced by The Center for Comprehensive School Reform and Improvement, administered by Learning Point Associates in partnership with the Southwest Educational Development Laboratory (SEDL) and WestEd, under contract with the Office of Elementary and Secondary Education of the U.S. Department of Education.]