Dr. Frank Gardella has experience teaching middle school, high school and college mathematics as well as serving as a supervisor of mathematics from grades K to 12. At present, he is Associate Professor of Mathematics Education and Mathematics at Hunter College where he teaches practicing elementary teachers who wish to become specialists and leaders in elementary mathematics teaching and curriculum. He has authored more than ten textbooks and twenty articles on mathematics and its teaching. This present work is based on his more than 30 years of experience working with elementary teachers and elementary mathematics specialists in the classrooms of public schools having students understand the meaning of the algorithms that are used to express mathematics.