Abstract

DIAS, Marisa da Silva. Didactic transposition of irrational numbers in Portuguese textbooks from 1909 to 1963. Ensino em Re-Vista [online]. 2022, vol.29, e018.  Epub June 08, 2023. ISSN 1983-1730.  https://doi.org/10.14393/er-v29a2022-18.

The aim of this paper is to present the concept of irrational number in eleven Portuguese textbooks, spanning the period from 1909 to 1963. Under the theory of didactic transposition, with a focus on teachable knowledge, and as a bibliographic research, the main results provide definitions of irrational number as contiguous classes in textbooks in the 1910s; as a relation between incommensurable magnitudes in textbooks of the 1930s and early 1940s and as non-periodic infinite decimal fractions in textbooks of the 1950s and 1960s, as a definitive replacement of the notion of contiguous classes. In general, the didactic explanations following the concept presented in the textbooks start from a particular case of a square root of a number that is not a perfect square, along with a definition, by means of generalization, and a few examples. Examples of transcendental numbers appear after 1954.

Keywords : Irrational Number; Didactic Transposition; Textbook.

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