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In this paper, we examine how differences in the academic and professional backgrounds of engineering teachers shape their personal relationship to the use of mathematics in engineering practices, and whether these differences affect some of their practices. The analyses herein are based on an institutional perspective and employ Chevallard's anthropological theory of the didactic (ATD). We interviewed two teachers in an engineering programme to identify specific elements of their practice that could be attributable to the mobilisation of knowledge and skills derived from their distinct academic backgrounds and experience. The results indicate that the teachers mobilise different tasks, techniques, and technologies in many of their practices, and that they take different approaches to using mathematics and applying rigour.

In this paper we analyse the introduction of irrational and real numbers in secondary textbooks, and specifically the propositions on how these should be taught, in a sample of Brazilian textbooks used in state schools and approved by the Ministry of Education. The analyses discussed in this paper follow an institutional perspective (using Chevallard's Anthropological Theory of Didactics). Our results indicate that the notion of irrational number is generally introduced on the basis of the decimal representation of numbers, and that the mathematical need for the construction of the field of real numbers remains unclear in the textbooks. It seems that textbooks used in secondary teaching institutions develop mathematical organisations which focus on the "practical" block.

In this paper we analyse the introduction of irrational and real numbers in secondary textbooks, and specifically the propositions on how these should be taught, in a sample of Brazilian textbooks used in state schools and approved by the Ministry of Education. The analyses discussed in this paper follow an institutional perspective (using Chevallard's Anthropological Theory of Didactics). Our results indicate that the notion of irrational number is generally introduced on the basis of the decimal representation of numbers, and that the mathematical need for the construction of the field of real numbers remains unclear in the textbooks. It seems that textbooks used in secondary teaching institutions develop mathematical organisations which focus on the practical block. [ABSTRACT FROM AUTHOR]