
06294992
j
2014c.00605
Gonz\'alezMart\'{\i}n, Alejandro S.
Giraldo, Victor
Souto, Alexandre M.
The introduction of real numbers in secondary education: an institutional analysis of textbooks.
Res. Math. Educ. 15, No. 3, 230248 (2013).
2013
Taylor \& Francis (Routledge), Abingdon, Oxfordshire; British Society for Research into Learning Mathematics (BSRLM)
EN
F53
U23
real numbers
irrational numbers
textbook analysis
praxeology
mathematical organisation
doi:10.1080/14794802.2013.803778
Summary: 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.