This essay traces the history of two standards--estimation and mental calculation--devised by the National Council of Teachers of Mathematics (NCTM). It is hoped that the history of these standards will illustrate the difficulties encountered by other proposed standards and by the standards movement as a whole. The essay provides an overview of the national standards movement, its rise in the 1980s, and the evolving standards debate. It examines the rationale for the NCTM standards, arising from the recognition that most Americans could not solve simple math problems. It describes the need for proficiency in mental calculation and the command of math facts and basic operations in making such calculations. The document explains that many states quickly followed NCTM's lead in establishing standards, but notes that there were remarkable differences of interpretation among them. It details how California educators tried to implement the NCTM standards only to have their students perform abysmally on a national mathematics test, and how Maryland educators successfully pushed students to learn mathematical reasoning and the ability to solve novel problems. The essay recounts the politics surrounding the NCTM standards, parents' reactions to the changes, ways to measure skills in estimation and mental calculation, and other information. (RJM)