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RESEARCH PRODUCT

The History of Algebra in Mathematics Education

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In this chapter, we analyse key issues in algebra history from which some lessons can be extracted for the future of the teaching and learning of algebra. A comparative analysis of two types of pre-Vietan languages (before 16th century), and of the corresponding methods to solve problems, leads to conjecture the presence of didactic obstacles of an epistemological origin in the transition from arithmetic to algebraic thinking. This illustrates the value of historic and critical analysis for basic research design in mathematics education. Analysing the interrelationship between different evolution stages of the sign system of symbolic algebra and vernacular language supports the inference that a particular sign system represents a significant step in the evolution of algebra symbolism when it permits calculations at a syntactic level. Such analyses provide elements to identify features of the algebraic in the translation processes from natural language to the algebraic code. In particular, these elements can be used as a basis to study pupils’ strategies when they solve word problems, and to conceive didactical routes for the teaching of solving methods of these problems. The examples discussed emphasise the importance of speaking of manifestations of the algebraic in the specific, in contrast to other perspectives that emphasise the nature of algebraic thinking in the general.