Ernst Bloch: esperança e educação em tempos de niilismo

This work aims give evidence of that The hope principle, the philosophical system devised by the German philosopher Ernst Bloch, in which hope assumes an ontological character, offers cognitive support that allows overcoming the void imposed by nihilism today, especially in the field of education. But while it offers cognitive support, it also presents a need that is fulfilled by an educational proposal based on a not-yet-conscious being. An education based on hope has four essential pillars: learning to know, learning to do, learning to be, learning to live together and, most of all, immerging into in the seas of uncertainty. In times when school is a promoter of certainties at the expense of uncertainties, education must not forsake the notion of the unpredictable and immeasurable, nor the need to find ways to enable better understanding of aspect related to the not-yet-be. The employed theoretical and methodological elements in this work paint a corpus through an interactive process in which layers of additional texts are subjected to analysis

A difícil aceitação dos números negativos: um estudo da teoria dos números de Peter Barlow (1776-1862)

The present study seeks to present a historico-epistemological analysis of the development of the mathematical concept of negative number. In order to do so, we analyzed the different forms and conditions of the construction of mathematical knowledge in different mathematical communities and, thus, identified the characteristics in the establishment of this concept. By understanding the historically constructed barriers, especially, the ones having ontologicas significant, that made the concept of negative number incompatible with that of natural number, thereby hindering the development of the concept of negative, we were able to sketch the reasons for the rejection of negative numbers by the English author Peter Barlow (1776 -1862) in his An Elementary Investigation of the Theory of Numbers, published in 1811. We also show the continuity of his difficulties with the treatment of negative numbers in the middle of the nineteenth century