Didatic trasnposition of irrational number concept in Portuguese textbooks from 1909 to 1963 - Dias, Marisa da Silva (2022)
The aim is to present the concept of irrational number in eleven Portuguese textbooks spanning the period from 1909 to 1963. Under the theoretical principles of didactic transposition, with a focus on teachable knowledge, and the bibliographic exploratory methodology, 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 a non-periodic infinite decimal fractions in textbooks of the 1950s and 1960s,as a definitive replacement of the notion contiguous classes. In general, the didactic explanations following the concept in the textbooks start from a particular case of square root of a number that is not a perfect square, along with a definition, by means of generalization, and few examples. Examples of transcendental numbers appear after 1954.