Alternative Algorithms: Increasing Options, Reducing Errors

Abstract

An algorithm is “a finite, step-by-step procedure for accomplishing a task that we wish to complete” (Usiskin 1998, p. 7). Algorithms have served as a major focus of mathematics education in the United States for decades. Because school-based mathematics focuses on computation and estimation, the tasks of developing number sense, place-value understanding, and strategies for computing with algorithms remain of great importance to elementary school teachers. “The use of algorithms allows students to look at math as a process rather than as a question answer type activity … they can choose from their toolbox. Algorithms provide a comfort zone for some students and encourage students to pursue better ways as they get comfortable with them” (Mingus and Grassl 1998, p. 56).

A fresh look at research strategies in computational cognitive science: The case of enculturated mathematical problem solving

“…Already in learning simple operations, such as integer multiplication, some children may have difficulties grasping and using the standard algorithms (Fuson 2003). 24 These children may benefit from alternative algorithms for the operations, which often involve different manipulations of symbols in space (Carroll and Porter 1998;Randolph and Sherman 2001). Perhaps the best-known alternative to the standard long multiplication algorithm is the lattice (or tableau) multiplication method.…”

“…6). Problem solving strategies like lattice multiplication have been suggested as a tool for children with learning problems (e.g., Gurganus 2007) and the availability of different strategies for children is often seen as facilitating the learning process for students with different knowledge and skill levels (Fuson 2003;Randolph and Sherman 2001). But equally importantly, differences in the way methods are learned may be due to differences in the cultures in which the subjects are enculturated.…”