Standard algorithms

For computer algorithms, see List of algorithms.

In elementary arithmetic, a standard algorithm or method is a specific method of computation which is conventionally taught for solving particular mathematical problems. 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. Similar methods also 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).

The NCTM standards-based mathematics introduced in 1989 favors an alternative approach which proposes a deeper understanding of the underlying theory instead of memorization of specific methods will allow students to develop individual methods which solve the same problems. Supporters of this model believe that the development of sophisticated calculators has made manual calculation less important and traditional methods have created failure among many students, particularly women and minorities in the United States. They propose greater equity in achievement 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.