Abstract
Vygotsky asserted that the student who has mastered algebra attains “a new higher plane of thought” (Vygotsky 1986, p. 202), a level of abstraction and generalization that transforms the meaning of the lower (arithmetic) level. The development of this higher (algebraic) plane of thought not only precedes the development of arithmetic but becomes a major focus of the child’s elementary education. It is characterized by orienting children to the most abstract and general level of mathematical understanding from the beginning of their formal schooling. This orientation to theoretical structure is mediated by the mastery of psychological tools which are not encountered as incidental to the solution of particular problem types but are instead the focus of explicit instruction. It is further characterized by the development of an adequate conceptual base, the incorporation of principles of dialectical logic, and the ascent from the abstract to the concrete in the development of conceptual content.
This chapter is a revised version of an article published in ZDM—International Reviews on Mathematical Education, 37(1), 16–22. DOI 10.1007/BF02655893.
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Schmittau, J. (2011). The Role of Theoretical Analysis in Developing Algebraic Thinking: A Vygotskian Perspective. In: Cai, J., Knuth, E. (eds) Early Algebraization. Advances in Mathematics Education. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17735-4_5
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