Abstract:A comparison of the development of algebra in Davydov’s elementary mathematics curriculum with the approach to algebra advocated by the National Council of Teachers of Mathematics in the US reveals striking differences. Rather than developing algebra as a generalization of number, Davydov’s curriculum develops algebraic structure from the relationships between quantities such as length, area, volume, and weight. The arithmetic of the real numbers follows as a concrete application of these algebraic generalizations. The instructional approach, while similar to constructivist teaching methodology, emanates from a very different theoretical perspective, namely, the findings of Vygotsky and Luria that cognitive development is enabled by overcoming obstacles for which previous methods of solution prove inadequate. In a study in which the entire three-year elementary curriculum of Davydov was implemented in a US school setting, children using the curriculum developed the ability to solve algebraic problems normally not encountered until the secondary level in the US.