The Literary Genre of Tales in Teaching Irrational Numbers
Abstract
The school mathematical discourse of teachers in class occurs to communicate abstract concepts to students. In mathematics classes, when teaching some concepts, due to their level of abstraction, metaphors or literary figures of speech are used as a mental tool in the cognitive dimension to establish connections between concepts. Mathematical concepts, such as negative integers and rational numbers, can be taught using metaphors to relate them to ordinary concepts acquired through experience in particular contexts. However, there are concepts, such as infinity or irrational numbers, whose level of abstraction is so low that it is complicated to find concrete concepts to build a metaphor to explain them. This article shows the results of qualitative research aimed at determining the effectiveness of using a little story instead of a metaphor to teach the topic of irrational numbers. This strategy using the literary genre of fairy tales to explain the topic of irrational numbers at the university education level and its positive results constituted the main novelty of this study. This strategy generated a-didactic situation as part of a didactic strategy based on the theory of didactic situations for teaching irrational numbers to students in a first-semester fundamental mathematics course for engineering careers. To determine the effectiveness, a test was designed and applied before and after taking the students to participate in the teaching situations supported by the tale, a teaching guide, and a kit of didactics material. There was a positive evolution in the level of knowledge about the characteristics of the mathematical concept under study. The results contribute to the teaching of irrational numbers and the research field of mathematics education. The tale strategy constitutes a way of generating a-didactic situation required when the theoretical framework of research is the theory of didactic situations.
Keywords: a-didactic situation, didactic situation, irrational numbers, tale’s literary genre, theory of didactic situations.
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