A hermeneutic study on demonstrations in the movement of modern mathematics

This research focuses on the meanings of mathematical demonstrations at the heart of the Modern Mathematics Movement (MMM) that took place in the 1960s, which is related to a scenario of reforms for the teaching of mathematics that began in the last years of the 19th century. During this period, when it was verified that the mathematics used in the sectors of industry and commerce was out of “tune” with that taught in schools, approaches were highlighted, among others that, based on demonstrations, led me to the need to understand how educators adhered to them in the teaching of the time. Thus, in the search for meanings for what the mathematical demonstration is in those circumstances, the following question emerged: What is this, the mathematical demonstration in MMM? In order to answer this question, I considered the readings of Martin Heidegger (1889-1976), Hans-Georg Gadamer (1900-2002) and Paul Ricoeur (1913-2005), with regard to the Hermeneutics developed by these philosophers. To this, I also reconciled the historical perspective outlined in the works of Husserl (1859-1938), in which history and historicity are thematized, as well as the description of the retrospective process for historical production through a phenomenological work. Some understandings about the meanings of the demonstrations in this study indicated that, in order to work in the classroom, teachers should employ a deductive approach, combined with a more precise and rigorous language, in teaching geometry. In addition, it was highlighted that those interested in the MMM established a proposal that was essentially based on the concepts of sets, relations and mathematical structures. (AU)