A theoretical model for the measure up program: relationships among logical reasoning and algebra preparedness

Abstract

The need to better prepare U.S. children for studying algebra and other high school mathematics is evidenced by studies of international student achievement. An ongoing issue in the field of mathematics education is to develop students' high-level thinking skills. It is believed that the mile-wide-and-inch-deep approach to curriculum and instruction is responsible for deficiencies in students' capabilities. The Measure Up elementary mathematics program was developed from the research and curriculum development conducted in Russia. The mathematics education research from El'konin-Davydov (Davydov, 1966) focused on the development of children's understanding of general and abstract concepts before teaching specific concepts. This builds from Vygotsky's (1978) work on the interplay of spontaneous and scientific concepts. The Russian work showed that students were capable of developing higher level thinking and were prepared for studying more advanced mathematics. Prior studies showed that students exiting the Measure Up program were better prepared for studying formal algebra than students who had other elementary mathematics programs. The goal of this study is to develop a statistical model, using theoretical implications from prior findings, to describe the relationships among Measure Up experience, age, prior achievement, logical reasoning capabilities, and algebra preparedness. Structural equation modeling revealed a direct and statistically significant impact from the Measure Up mathematics experience on algebra preparedness. Other findings include a statistically significant relationship between logical reasoning capabilities and algebra preparedness, and a nonsignificant direct relationship between prior achievement and algebra preparedness. The findings suggest that a mathematics program that develops children's logical reasoning capabilities also prepares them for a middle school Algebra I course. The findings from this study have implications for educators and curriculum developers who struggle with the trade-off between covering content for arithmetic manipulation skills on one hand and building conceptual understanding on the other.