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This study aims to analyze the foundations and guidelines which current support the Mathematics syllabus suggested for the state of Sao Paulo in Brazil, regarding the introduction of irrationality as a concept. We tried to identify the relation between the suggestions as proposed by the syllabus implementation and other perspectives and researches that work with the same subject. This is a bibliographical/ documental study in which we will analyze the supporting resource called “Teacher’s Book” both under the perspective of syllabus theories and of some studies which focus on the Mathematical subject “Irrational Numbers”. By examining official syllabi papers in a general scope, we noticed some attention was given to Bishop’s Mathematical Enculturation (1997), although we also found gaps in the guidelines regarding incommensurability and line segment density.

Atual currículo de matemática do estado de São Paulo: Indicações para a introdução do ensino da ideia de irracionalidade