Standard algorithms

In elementary arithmetic, a standard algorithm or method is an efficient manual method of computation which yields one correct answer, and has been traditionally taught over a long period of time. These methods vary somewhat by nation and time, but generally include carrying, borrowing, long division, and long multiplication using a standard notation, and standard formulas for average, area, and volume. Manual methods do exist for procedures such as square root and even more sophisticated functions, but have fallen out of the general mathematics curriculum in favor of calculators (or tables and slide rules before them).

This has recently fallen out of favor with the introduction of the 1989 NCTM standards-based mathematics which favors deep understanding over rote memorization of standard methods, or teaching only one method to arrive at one correct answer. It is believed by many that the development of sophisticated calculators has made manual calculation obsolete, and traditional methods have created failure among many students, particularly women and minorities in the United States, and equity should be made one of the primary goals of a mathematics education. Some researchers such as Constance Kamii have suggested that elementary arithmetic, as traditionally taught, is not appropriate in elementary school. Many first editions of textbooks written to the original 1989 standard such as TERC deliberately committed and actively discouraged teaching or application of any standard method, instead devoting class and homework time to cutting, pasting, singing music, circling groups of tally marks, and coloring in 100s or 10,000s charts.

However, the NCTM in more recent revisions has re-emphasize the learning of basic math facts and standard methods. Many new editions of standards-based texts do present standard methods and basic skills. However, many texts which followed the original guidelines continue to be used by many school districts, and continue to draw fire from parents and community members, some of whom advocate a return to traditional mathematics.