Representing Quantitative Information: Developmental and Neural Comparisons of Mental Magnitudes Open Access

Bonny, Justin William (2013)

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The ability to estimate and represent non-symbolic quantities is essential to cognition. Representations of non-symbolic quantities, known as mental magnitudes, are essential for quick judgments and have been found to be related to symbolic math skills. Mental magnitudes have been found to underlie all types of quantities, ranging from number to time to area. Despite the importance of mental magnitudes in cognition, the nature of these representations is unclear. Specifically, it is unclear whether there are shared mental magnitudes for different quantities, or, if mental magnitudes are specific for each quantity. In the present dissertation, I examine the specificity of mental magnitudes by comparing behavioral performance and neural signatures of two types of quantities, cumulative area and non-symbolic number.

In Study 1, I compared cumulative area and non-symbolic number by examining the developmental changes in each magnitude as well as the impact of different spatial arrangements on discrimination performance. Children (four- and six-year-olds) were presented with cumulative area and non-symbolic number stimuli either within a single spatial field (Experiment 1) or separated in two spatial fields (Experiment 2). Discrimination performance was lower for non-symbolic number when presented with spatially intermixed versus separated stimuli, but there was no difference in performance for cumulative area. Developmental analyses indicated that there was similar improvement in performance with age for both magnitudes regardless of spatial arrangement.

In Study 2, I compared the neural processing of cumulative area and non-symbolic number information using event-related potentials (ERPs). I compared the onset of ratio and congruity effects for cumulative area and non-symbolic number in the ERP waveforms when each magnitude was presented more or less independently each other. I found evidence of magnitude differences in the onset of each mental magnitude when presented independently (Experiment 1) and evidence of similarities when magnitudes were presented simultaneously (Experiment 2).

The results of both studies suggest there are partially overlapping representations for non-symbolic magnitudes. I provide a new framework to explain how partially overlapping representations are formed and contrast it to previous models of magnitude representation.

Table of Contents

Table of Contents

Chapter 1. General Introduction 1

1.1 Introduction to Study 1 12

Chapter 2. Study 1 19

2.1 Introduction 20

2.2 Experiment 1 31

2.3 Experiment 2 44

2.4 General Results: Comparing Both Experiments 54

2.5 General Discussion 61

Chapter 3. Discussion of Study 1 68

3.1 Introduction to Study 2 70

Chapter 4. Study 2 77

4.1 Introduction 78

4.2 Experiment 1 89

4.3 Experiment 2 121

4.4 Discussion 158

Chapter 5 Discussion of Study 2 171

Chapter 6 Dissertation General Discussion 172

6.1 Hypothesis for a Partially Overlapping Magnitude System 175

References 187

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