
Confusions between decimals, fractions and negative numbers: A consequence of the mirror as a conceptual metaphor in three different ways
Abstract: Many students confuse decimal numbers, fractions and negative numbers. Data, some of which is new, is provided to support this observation. Interview data also identifies other confusions between number lines and numberline hybrids and between zero and one. These observations are explained by drawing attention to the use of the mirror as a conceptual metaphor in three different ways for understanding the number system. It underpins the usual positive/negative number line, links natural numbers and their reciprocals and operates in a pseudo number line related to place value columns. Students mentally merge the components that are the images under the analogical mapping of the same mirror feature. This extends recent work on metaphors in mathematics itself to their role in understanding mathematics.
Stacey, K., Helme, S., & Steinle, V. (2001). Confusions between decimals, fractions and negative numbers: A consequence of the mirror as a conceptual metaphor in three different ways. In M. v. d. HeuvelPanhuizen (Ed.) Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4. pp. 217  224). Utrecht: PME. 