The purpose of this study was to investigate 6th-grade students' use of equations to describe and represent problem situations prior to formal instruction in algebra. Ten students were presented with a series of similar tasks in 6 different problem contexts representing linear and nonlinear situations. The students in this study showed a remarkable ability to generalize the problem situations and to write equations using variables, often in nonstandard form. Although students were often able to write equations, they rarely used their equations to solve related problems. We describe students' preinstructional uses of equations to generalize problem situations and raise questions about the most appropriate curriculum for building on students' intuitive knowledge of algebra.
Jane O. Swafford, Professor, Department of Mathematics, Mail Code 4520, Illinois State University, Normal, IL 61790-4520; firstname.lastname@example.org
Cynthia W. Langrall, Assistant Professor, Department of Mathematics, Mail Code 4520, Illinois State University, Normal, IL 61790-4520; email@example.com