The metaphorical nature of first-year calculus students' reasoning about limit concepts is explored using an instrumentalist approach. Analysis of written and verbal language reveals that, while these students used motion terminology profusely when discussing limits, it was typically not intended to signify actual motion and did not play a…

Situated within the framework of the conceptual metaphor theory (Lakoff & Johnson, 1999), this study investigated young children's understanding of metaphorical extensions of spatial motion. Metaphor was defined as a conceptual-linguistic mapping between a source and a target domain. The study focused on metaphors that are structured by the source…