\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2015a.00487}
\itemau{Kilhamn, Cecilia}
\itemti{Addition and subtraction of negative numbers using extensions of the metaphor ``arithmetic as motion along a path".}
\itemso{Winsl\o{}w, Carl (ed.), Nordic research in mathematics education. Proceedings from NORMA08 in Copenhagen, Denmark, April 21--25, 2008. Rotterdam: Sense Publishers (ISBN 978-90-8790-781-5/pbk; 978-90-8790-782-2/hbk; 978-90-8790-783-9/ebook). 17-23 (2009).}
\itemab
Summary: Negative numbers make up a domain of mathematics which is often considered difficult to teach and difficult to understand According to some researchers abstract mathematical concepts are understood through conceptual metaphors. Using the framework of conceptual metaphors developed by {\it G. Lakoff} and {\it R. E. N\'u\~nes} [``The metaphorical structure of mathematics: sketching out cognitive foundations for a mind-based mathematics", in: L. D. English (ed.), Mathematical reasoning, analogies, metaphors and images. Mahwah, NJ: Lawrence Erlbaum Associates. 21--89 (1997); Where mathematics comes from. How the embodied mind brings mathematics into being. New York, NY: Basic Books (2000; ME 2002f.04631)] a theoretical analysis is made of one of the characteristic metaphors for this domain in order to see what entailments an extension of the metaphor has. The analysis elicits three shortcomings of such an extension that might influence students' comprehension: loss of internal consistency, loss of external coherence and enforcement of properties or structure that are not part of the original source domain.
\itemrv{~}
\itemcc{F40}
\itemut{conceptual metaphors; negative numbers; rational numbers}
\itemli{}
\end