The role of conceptual integration and simple dynamic scenarios in the meaning construction of the mapping in mathematics
The role of conceptual integration and simple dynamic scenarios in the meaning construction of the mapping in mathematics

Summary/Abstract: Over the last two decades the impact of conceptual metaphor and conceptual blending on mathematics has been extensively researched (Lakoff & Núñez, 2000; Fauconnier & Turner, 2002; Turner, 2005; Núñez, 2006; Alexander, 2011; Turner, 2012; Danesi, 2016; Woźny, 2018). This paper examines the manner in which simple dynamic scenarios allow, through the process of conceptual integration, for multiple ways of constructing the meaning of a mathematical mapping. The paper analyses selected fragments extracted from two popular academic mathematics textbooks to ascertain how the authors use a number of simple dynamic scenarios to explain the concept. The paper then demonstrates how these dynamic scenarios help to avoid the problem of circularity of the (static) formal definition of the mapping. The results of the study indicate that conceptual blending may account for the flexibility of mathematics and its effectiveness in modelling the world around us.

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