Dissertation/Thesis Abstract

Understanding less than nothing: Investigations into the representation of negative numbers
by Gullick, Margaret M., Ph.D., Dartmouth College, 2012, 278; 3508896
Abstract (Summary)

Little behavioral research, and less neural work, has examined how we process quantities like negative numbers, which are worth less than nothing and yet have value. The goal of this dissertation was to determine whether negative number processing is supported by the same brain regions as positive numbers across multiple mathematical levels and situations, thereby testing the flexibility of the mental number system in its ability to incorporate such abstract values.

We first examined adult responses to negative number comparisons. Negative comparisons demonstrated an increased positive-like distance effect, with decreasing response times and intraparietal sulcus (IPS) activity for comparisons farther apart than closer together, indicating utilization of basic number representation regions. This effect did not generalize to BC date processing, implying that larger negative numbers may not have a regular organization on the mental number line. We then explored the development of negative number processing. Both younger pre-instruction children and older post-instruction children demonstrated typical behavioral and neural distance effects to negative numbers. Across children, as age increased, the distance effect increased in the bilateral IPS, indicating increasing maturity in numeric processing; as task accuracy increased, the effect increased in only the left IPS, suggesting a shift from an approximate to a more exact representation of negatives' values. Last, we compared the brain activities evoked in negative and positive number arithmetic. Simple negative-operand problems demonstrated a positive-like operation-activity relationship in the inferior parietal lobule, but a reversed pattern in the angular gyrus. Arithmetic with negative numbers may be supported by the same regions as positive, but use of further problem transformation rules and strategies (such as "minus a negative is plus a positive") affects activity.

This dissertation thus explored several aspects of number processing in an effort to determine how negative numbers are understood. Participants used neural regions important in numeric processing when working with negatives, but also recruited extended areas and alternate strategies to support the unique features of negative numbers. The mental number system appears to be flexible enough to partially incorporate these abstract values worth less than nothing.

Indexing (document details)
Advisor: Wolford, George L.
Commitee: Ansari, Daniel, Shim, Won Mok, Tine, Michele T.
School: Dartmouth College
Department: Psychological and Brain Sciences
School Location: United States -- New Hampshire
Source: DAI-B 73/09(E), Dissertation Abstracts International
Subjects: Neurosciences, Cognitive psychology
Keywords: Cognitive neuroscience, Educational neuroscience, Negative numbers, Number processing, fMRI
Publication Number: 3508896
ISBN: 9781267348319
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