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In this paper, we describe the elements that characterize the teaching of Mathematics in the Ave María Schools, founded and run by Andrés Manjón in Granada between 1889 and 1923. He stood up for a peculiar model of integrated education, based on Christian values, and he also developed his own methodological principles, similar in many ways to those of the emerging École Nouvelle. The selection and analysis of several sources has allowed us to set his teaching of Mathematics within this pedagogical framework and has suggested us the idea that the strategies used by Manjón in order to teach Arithmetic and Geometry could be innovative at that time and, perhaps, valuable from the point of view of contemporary Didactics. [ABSTRACT FROM AUTHOR]