This paper identifies and discusses important school mathematics curriculum controversies in the United States of America, over the past 60 years. The first controversy considered here was the “New Math” , and the last is the Common Core State Standard for Mathematics. It summarizes the debates, the main actors, and their viewpoints. The second part of the paper investigates theoretical or research-based evidence related to the controversies. Finally, the last part of this paper investigates short-term and longer-term effects of movements with respect ro intended, implemented, and attained curricula