The representation of negative numbers: Exploring the effects of mode of processing and notation

Abstract

The representation of negative numbers was explored during intentional processing (i.e., when participants performed a numerical comparison task) and during automatic processing (i.e., when participants performed a physical comparison task). Performance in both cases suggested that negative numbers were not represented as a whole but rather their polarity and numerical magnitudes were represented separately. To explore whether this was due to the fact that polarity and magnitude are marked by two spatially separated symbols, participants were trained to mark polarity by colour. In this case there was still evidence for a separate representation of polarity and magnitude. However, when a different set of stimuli was used to refer to positive and negative numbers, and polarity was not marked separately, participants were able to represent polarity and magnitude together when numerical processing was performed intentionally but not when it was conducted automatically. These results suggest that notation is only partly responsible for the components representation of negative numbers and that the concept of negative numbers can be grasped only through that of positive numbers.

Keywords:

• Negative numbers
• Notation
• Numerical processing
• Automaticity

This research was supported by the Israeli Science Foundation Grant 825/00 to J.T. We wish to thank Zohar Bar and Boaz Tzur for help in running Experiments 1 and 2. Experiment 2 was run by Keren Maymon-Schreiber in partial fulfilment of the requirements for an MA degree in Psychology.