id: 06418491
dt: a
an: 2015b.00617
au: Kilhamn, Cecilia
ti: Making sense of negative numbers through metaphorical reasoning.
so: Bergsten, Christer (ed.) et al., Perspectives on mathematical knowledge.
Proceedings of MADIF 6, the 6th Swedish mathematics education research
seminar, Stockholm, Sweden, January 29‒30, 2008. Linköping: Svensk
Förening för MatematikDidaktisk Forskning (ISBN 91-973934-5-2/pbk).
Skrifter vrån Svensk Förening för MatematikDidaktisk Forskning
(SMDF) 6, 30-40 (2009).
py: 2009
pu: Linköping: Svensk Förening för MatematikDidaktisk Forskning
la: EN
cc: F40
ut: negative numbers; conceptual metaphers; metaphorical reasoning
ci:
li:
ab: Summary: The concept of negative numbers is such an abstract concept that
it has been argued that it can only be understood through symbolic
reasoning. However, others argue that all mathematical concepts are
understood through metaphors. Previous research has identified three
important aspects of understanding negative numbers: direction and
multitude, proficiency in arithmetic operations, and the meaning of the
minus sign. This study further explores the theory of conceptual
metaphors and metaphorical reasoning by investigating the use of models
and metaphorical reasoning when dealing with negative numbers. The data
consists of test results from 99 students in the teacher training
program and follow-up group interviews. The results show that some
students’ difficulties seem to be a consequence of their use of
metaphorical reasoning using a metaphor that is insufficient. However,
metaphorical reasoning also seems to be helpful for students who are
aware of the limitations of the metaphor. Enlightened use of
metaphorical reasoning, i.e., being aware of the potentials and
constraints of models and metaphors, could therefore be described as a
fourth important aspect of understanding negative numbers.
rv: