This is a must-read for those wondering why they cannot continue to teach as they have in the past. Because the research literature did not cover what mathematical knowledge students have, James Stigler undertook fieldwork to learn more about students’ understanding of basic mathematics, and student perceptions of what they believe it means to do mathematics. This essay, by James W. Stigler, Karen B. Givvin, and Belinda J. Thompson, was published in MathAMATYC Educator, Vol. 1, No. 3. May 2010.