ALGORITHMS: Through the Ages and Around the World

Webster's Collegiate Dictionary defines an algorithm as "a rule of procedure for solving a mathematical problem that frequently involves repetition of an operation. " (p. 22) The word “algorithm ” comes from the name of the 8th century Arab mathematician Mohammed al-Khowarizmi. He wrote two books, one about arithmetic and one about algebra, that explained the Hindu-Arabic numerals and methods of calculation. Readers of the Latin translations began to attribute the system to him and to call the new methods of calculation “algorismi. ” Over time the word became “algorithm, ” and came to mean an orderly, repetitive scheme. (Long, p. 186) The phrase “alternative algorithm ” refers to procedures different from those currently taught in most public school classrooms in the United States. Standard or traditional algorithms provide a first look at the four basic operations. As the numbers become very large or more difficult, alternative algorithms provide an interesting and generally, logically diverse, method of approach for students who are having trouble learning the basic school algorithms. Many alternative algorithms are found in the public domain and additional methods are being devised each day. Some references to Mathematics Education texts that contain various alternative algorithms are cited at the end of this paper. Here are some reasons why teachers should teach and use alternative algorithms in their classrooms: 1. Alternative algorithms accommodate different learning styles. 2. Alternative algorithms demonstrate that there IS more than just one way to solve a problem. 3. Alternative algorithms are fun! 4. Alternative algorithms provide a means so that we can appreciate the efforts of other people in other times and places