Strong and Weak Metaphors for Limits
Proceedings of the 27th International Conference for the Psychology of Mathematics Education, 3, page 397-404. Honelolu, Hawaii, (2003)Abstract
The metaphorical nature of first-year calculus studentsﾒ 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 significant role in their reasoning about limiting situations. In contrast, many of these studentsﾒ employed other non-standard metaphors, involving for example collapsing dimensions, to explore these situations and to build their emerging understanding of limit concepts.