Standard Algorithms

In elementary

arithmetic Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th ...

, 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 exchanging, regrouping,

long division In arithmetic, long division is a standard division algorithm suitable for dividing multi-digit Hindu-Arabic numerals (Positional notation) that is simple enough to perform by hand. It breaks down a division problem into a series of easier steps ...

, and

long multiplication A multiplication algorithm is an algorithm (or method) to multiply two numbers. Depending on the size of the numbers, different algorithms are more efficient than others. Efficient multiplication algorithms have existed since the advent of the de ...

using a standard notation, and standard formulas for

average In ordinary language, an average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list (the arithmetic mean). For example, the average of the numbers 2, 3, 4, 7, ...

area Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or ''plane area'' refers to the area of a shape A shape or figure is a graphics, graphical representation of an obje ...

, and

volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). The de ...

. Similar methods also exist for procedures such as

square root In mathematics, a square root of a number is a number such that ; in other words, a number whose ''square'' (the result of multiplying the number by itself, or  ⋅ ) is . For example, 4 and −4 are square roots of 16, because . E ...

and even more sophisticated functions, but have fallen out of the general mathematics curriculum in favor of calculators (or

tables Table may refer to: * Table (furniture), a piece of furniture with a flat surface and one or more legs * Table (landform), a flat area of land * Table (information), a data arrangement with rows and columns * Table (database), how the table data ...

and

slide rules The slide rule is a mechanical analog computer which is used primarily for multiplication and division, and for functions such as exponents, roots, logarithms, and trigonometry. It is not typically designed for addition or subtraction, which ...

before them). The concepts of

reform mathematics Reform mathematics is an approach to mathematics education, particularly in North America. It is based on principles explained in 1989 by the National Council of Teachers of Mathematics (NCTM). The NCTM document ''Curriculum and Evaluation Standa ...

which the

NCTM Founded in 1920, The National Council of Teachers of Mathematics (NCTM) is a professional organization for schoolteachers of mathematics in the United States. One of its goals is to improve the standards of mathematics in education. NCTM holds an ...

introduced in 1989 favors an alternative approach. It 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. Students' alternative algorithms are often just as correct, efficient, and generalizable as the standard algorithms, and maintain emphasis on the meaning of the quantities involved, especially as relates to place values (something that is usually lost in the memorization of standard algorithms). The development of sophisticated calculators has made manual calculation less important (see the note on square roots, above) and cursory teaching of traditional methods has created failure among many students. Greater achievement among all types of students is among the primary goals of mathematics education put forth by

. Some researchers such as

Constance Kamii Constance Kamii is a Swiss-Japanese-American mathematics education scholar and psychologist. She is a professor in the Early Childhood Education Program Department of Curriculum and Instruction at the University of Alabama in Birmingham, Alabama. ...

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 discouraged teaching of any particular method, instead devoting class and homework time to the solving of nontrivial problems, which stimulate students to develop their own methods of calculation, rooted in number sense and place value. This emphasis by no means excludes the learning of number facts; indeed, a major goal of early mathematical education is procedural fluency. The

in recent revisions has made more explicit this need for learning of basic math facts and correct, efficient methods. Many new editions of standards-based texts do present standard methods and basic skills. However, the original guidelines continue to draw fire from well-meaning parents and community members, some of whom advocate a return to

traditional mathematics Traditional mathematics (sometimes classical math education) was the predominant method of mathematics education in the United States in the early-to-mid 20th century. This contrasts with non-traditional approaches to math education.Mathematics education {{Education-stub