Praxeological Analysis of Real Numbers in Peruvian Secondary School Textbooks, 1961–1999

Yapo W.Q.; Acero E.R.R.; Flores F. · Revista Latinoamericana de Investigacion en Matematica Educativa (2026) · DOI: 10.12802/relime.2026.29.e445

Resumen

This study analyzes the presentation of real numbers in mathematics textbooks for secondary education in the Peruvian educational system published between 1961 and 1999. The introduction of irrational numbers, the definition of real number, the ostensive representations, and the associated praxeologies are examined through the Anthropological Theory of the Didactic. The corpus consisted of 25 textbooks organized into two periods: Traditional and Modern Mathematics. The results show that both periods prioritize operational definitions and visual representations focused on classification and geometric intuition, to the detriment of the theoretical foundations of the real continuum. A decoupling between praxis and logos is identified, where tasks and techniques are not articulated with technologies and theories that justify the structure of real numbers. It is concluded that strengthening the relationship between visualization, justification, and formalization is necessary for teaching real numbers.

Instituciones: Universidad Nacional del Altiplano