Early Curricular Experiences with Nonnumeric Quantities, Evidence of an Enduring Perspective

In this study we explore possible long-term effects of an adaptation of the El'konin­-Davydov elementary grades curriculum, Measure Up or MU. The objectives for the study are to assess how students relate an equation of nonnumeric quantities to a length representation, and if former MU students develop and retain a perspective characteristic of the curriculum. Data were collected from thirteen former MU students and a group of fourteen peers who were instructed together with the MU students in identical middle and high school programs, but did not receive MU instruction. Findings show that former MU students reasoned about lengths as generalized quantities, applied a method for marking and labeling quantities, and justified a representation of relationships given by an equation. Implications are discussed for how a measurement context in elementary mathematics supports meaning making in the later study of algebra, particularly with regard to variables and multiple representations.