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These files are maintained strictly for historical reference, research, and recordkeeping purposes,
and the content has not been altered or updated since archiving.
Content on this site may not meet current digital accessibility standards.
If you require an alternative, accessible format of any information found on this site,
please contact Bruce Jones, bjones@ucsd.edu to request an accommodation.
The literature on understanding of integers notes a developmental
difference between a "two-attribute" and "single-attribute"
interpretation of negative number. Consider a child who places one hand
in a bucket of ice cold water and the other in a bucket of hot water,
and is asked "which bucket has warmer water?" The "two-attribute"
approach is characterized by dichotomous thinking, as in the bewildered
response, "This water isn't warm at all, it's cold!" As a later stage of
development hot and cold are realized as poles of a single dimension.
Seems like both of these perceptual frames are phenomenologically valid.
Maybe you're arguing from different frames.
David
Davis, R. B. & Maher, C. A. (1993). The reality of negative numbers. In
R. B. Davis & C. A. Maher (Eds.), Schools, mathematics, and the world of
reality (pp. 51-60). Boston, MA: Allyn and Bacon.