The Development of Algebraic Thinking A Vygotskian Perspective

Vygotsky asserted that the student who had mastered algebra had attained "a new higher plane of thought", a level of abstraction and generalization which transformed the meaning of the lower (arithmetic) level. He also affirmed the importance of the mastery of scientific concepts for the development of the ability to think theoretically, and emphasized the mediating role of semiotic forms and symbol systems in developing this ability. Although historically in mathematics and traditionally in education, algebra followed arithmetic, Vygotskian theory supports the reversal of this sequence in the service of orienting children to the most abstract and general level of understanding initially. This organization of learning activity for the development of algebraic thinking is very different from the introduction of elements of algebra into the study of arithmetic in the early grades. The intended theoretical ( algebraic) understanding is attained through appropriation of psychological tools, in the form of specially designed schematics, whose mastery is not merely incidental to but the explicit focus of instruction. The author's research in implementing Davydov's Vygotskian-based elementary mathematics curriculum in the U.S. suggests that these characteristics function synergistically to develop algebraic understanding and computational competence as well.