The present work focused on developing teaching activities that would provide to the studentin initial teacher training, improving the ability of mathematical reasoning and hence a greaterappreciation of the concepts related to the golden section, the irrational numbers, and theincommensurability the demonstration from the reduction to the nonsensical. This survey isclassified itself as a field one which data collection were inserted within a quantitative andqualitative approach. Acted in this research, two classes in initial teacher training. These wereteachers and employees of public schools and local governments, living in the capital, inNatal Metropolitan Region - and within the country. The empirical part of the research tookplace in Pedagogy and Mathematics courses, IFESP in Natal - RN. The theoretical andmethodological way construction aimed to present a teaching situation, based on history,involving mathematics and architecture, derived from a concrete context - Andrea Palladio sVilla Emo. Focused discussions on current studies of Rachel Fletcher stating that the architectused the golden section in this village construction. As a result, it was observed that theproposal to conduct a study on the mathematical reasoning assessment provided, in teachingand activity sequences, several theoretical and practical reflections. These applications,together with four sessions of study in the classroom, turned on to a mathematical thinkingorganization capable to develop in academic students, the investigative and logical reasoningand mathematical proof. By bringing ancient Greece and Andrea Palladio s aspects of themathematics, in teaching activities for teachers and future teachers of basic education, it waspromoted on them, an improvement in mathematical reasoning ability. Therefore, this workcame from concerns as opportunity to the surveyed students, thinking mathematically. In fact,one of the most famous irrational, the golden section, was defined by a certain geometricconstruction, which is reflected by the Greek phrase (the name "golden section" becomesquite later) used to describe the same: division of a segment - on average and extreme right.Later, the golden section was once considered a standard of beauty in the arts. This isreflected in how to treat the statement questioning by current Palladio s scholars, regardingthe use of the golden section in their architectural designs, in our case, in Villa Emo
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