Discovery process in mathematics class: abductive, inductive and deductive reasoning

Abstract

In this paper, we present and analyze some results of a research carried out at the Universidad Pedagógica Nacional during the years 2010 and 2011. In this study we characterize the different forms of reasoning used by a group of prospective mathematics teachers to address some activities related to rational and irrational numbers. The theoretical approach used for the development of research incorporates some aspects of Peirce’s theory of scientific method and mathematical reasoning, which can interpret the arguments developed by students in the resolution of the different task and discuss the results of other studies that are assigned to the same line of research, such as the proposed Cañadas and Castro (2007) about conjecture process. As a result of this work we obtain the characterization and classification of different forms of reasoning employed in the process of mathematical discovery and examples of each of these.