The aim of this paper is to demonstrate that in spite of some superficial similarities the current mathematics reform in the US based on constructivist principles differs substantially from mathematical education based on Vygotskian cultural-historical theory (V.V. Davydov's mathematics program), and to illustrate the manner in which Davydov's program virtually obliterates the conceptual-procedural division that has fueled the current "math wars". Both constructivism and Davydov's approach emphasize the active character of students' acquisition of mathematical concepts. Constructivists, however, begin the instructional process from the children's pre-existent concepts while Vygotskians reorient it toward acquisition of what Vygotsky defined as "scientific" rather than "spontaneous, everyday" concepts. A three-year study of the implementation of Davydov's elementary mathematics program in a school setting in the US found that the American children overcame the initial challenges of the program, consistently resolved computational errors conceptually, and finally demonstrated the ability to solve high school level mathematics problems. The curriculum appeared to foster the development of theoretical thinking, an explicit goal of Davydov's program, which constitutes its major value and educational significance. (Contains 9 figures.)