Contributors |
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xi | |
Foreword |
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xiii | |
Preface |
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xxv | |
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1 Introduction: How the Study of Neurobiological and Genetic Factors Can Enhance Our Understanding of Mathematical Cognitive Development |
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1 | (1) |
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Neurobiological Perspectives on Mathematical Cognitive Development |
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2 | (1) |
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Using Neuroimaging Methods to Study Children's Mathematical Development |
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2 | (1) |
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Mathematical Cognition and Development: Brain Structure and Function |
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3 | (4) |
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3 | (2) |
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5 | (2) |
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Brain Imaging Methods Used in Studying Mathematical Cognitive Development |
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7 | (2) |
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9 | (3) |
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11 | (1) |
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How Brain Imaging Can Advance Cognitive Theorizing |
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12 | (1) |
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Behavioral and Neuro-Genetics of Mathematical Cognition |
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13 | (3) |
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16 | (2) |
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Behavioral Genetics in the Age of Molecular Genetics and Neuroscience |
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18 | (1) |
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19 | (1) |
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19 | (8) |
Part I Neural substrates |
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2 Number Symbols in the Brain |
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27 | (2) |
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Which Brain Regions Are Engaged During the Processing of Numerical Symbols? |
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29 | (5) |
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Evidence from Comparison Tasks |
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29 | (1) |
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Response-Selection Confounds |
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30 | (1) |
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Evidence from fMRI Adaptation Studies |
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31 | (1) |
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Semantic or Perceptual Processing of Number Symbols in the IPS? |
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32 | (2) |
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Numerical Symbols in the Brain—Evidence from Developmental Studies |
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34 | (4) |
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Perceptual Representation of Number Symbols in the Brain |
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38 | (2) |
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Are Symbolic and Nonsymbolic Quantity Representations Linked in the Brain? |
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40 | (3) |
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Differences in Cardinal and Ordinal Processing of Number Symbols in the Brain |
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43 | (1) |
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Conclusions and Future Directions |
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44 | (2) |
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46 | (1) |
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46 | (5) |
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3 Neural and Behavioral Signatures of Core Numerical Abilities and Early Symbolic Number Development |
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51 | (2) |
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Two Systems for Nonverbal Numerical Cognition |
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53 | (4) |
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Parallel Individuation System |
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53 | (1) |
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Approximate Number System |
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54 | (1) |
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Behavioral Evidence for Distinct Systems of Numerical Cognition |
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54 | (3) |
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The Cognitive Neuroscience of Two Core Systems of Number |
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57 | (8) |
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Establishing the Neural Signatures of Two Systems |
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57 | (4) |
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Distinct Brain Mechanisms of Two Systems |
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61 | (1) |
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Continuity in Neural Signatures over Development |
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62 | (1) |
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Change in Core Numerical Processing over Development |
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63 | (2) |
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The Relationship Between Core Systems and Symbolic Number Abilities |
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65 | (5) |
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Approximate Number System and Symbolic Number and Mathematics Abilities |
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65 | (2) |
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The Relationship of Core Systems to Early Number Concept Development |
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67 | (3) |
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70 | (1) |
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71 | (1) |
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71 | (8) |
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4 A Neurodevelopmental Perspective on the Role of Memory Systems in Children's Math Learning |
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79 | (2) |
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Development of Memory-Based Strategies in Children's Mathematics Learning |
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81 | (2) |
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Declarative Memory and Its Development |
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83 | (1) |
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Medial Temporal Lobe Memory System |
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83 | (2) |
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Memory Processes in the Context of Mathematics Learning |
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85 | (1) |
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Children Engage the MTL Memory System Differently than Adults |
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85 | (2) |
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Individual Differences in Children's Retrieval Strategy Use are Associated with the MTL |
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87 | (1) |
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Decoding Brain Activity Patterns Associated with Counting and Retrieval Strategies |
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88 | (3) |
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Hippocampal-Prefrontal Cortex Circuits and their Role in Children's Mathematics Learning |
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91 | (2) |
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Longitudinal Changes in MTL Response, Representations and Connectivity Associated with Memory-Based Retrieval |
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93 | (5) |
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Why Adults May not Rely on MTL Memory Systems for Mathematics Performance and Learning |
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98 | (1) |
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99 | (1) |
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100 | (1) |
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100 | (9) |
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5 Finger Representation and Finger-Based Strategies in the Acquisition of Number Meaning and Arithmetic |
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109 | (1) |
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Fingers in Numerical and Arithmetic Processing |
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110 | (9) |
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The Role of Fingers and Finger Representation in Number Processing |
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110 | (2) |
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Neural Substrates for Hand and Number Processing |
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112 | (2) |
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Finger-Based Strategies and Finger Representation in Arithmetic |
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114 | (3) |
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Neural Substrates for Finger-Related Activation During Arithmetic Problem Solving |
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117 | (2) |
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Finger-Based Strategies and Operation-Specific Processes |
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119 | (9) |
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A Model Supporting Operation-Specific Processes |
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120 | (1) |
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Behavioral Evidence for Operation-Specific Processes |
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120 | (2) |
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Operation-Specific Neural Networks |
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122 | (1) |
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Operation-Specific Processes as a Consequence of Operation-Dependent Teaching Methods |
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123 | (1) |
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Operation-Dependent Finger-Related Activations |
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124 | (1) |
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Finger Counting, Cultural Influence, and Spatial-Numerical Relations |
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125 | (3) |
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128 | (4) |
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132 | (1) |
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132 | (9) |
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6 Neurocognitive Architectures and the Nonsymbolic Foundations of Fractions Understanding |
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141 | (2) |
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Fundamental Limitations of the Human Cognitive Architecture |
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143 | (1) |
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A Competing View: The Ratio Processing System |
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144 | (1) |
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How the RPS May Influence Fraction Learning |
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145 | (3) |
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Emerging Behavioral and Neuroimaging Evidence for RPS Model Predictions |
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148 | (6) |
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154 | (1) |
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Charting the Development and Architecture of the RPS |
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154 | (1) |
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Leveraging the RPS to Support Fraction Learning |
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155 | (2) |
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157 | (1) |
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158 | (1) |
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158 | (1) |
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159 | (6) |
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7 Developmental Dyscalculia and the Brain |
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165 | (1) |
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Developmental Dyscalculia |
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166 | (20) |
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Diagnosis of Developmental Dyscalculia |
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168 | (2) |
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What Neuroimaging Is Telling Us about Developmental Dyscalculia |
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170 | (3) |
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Neuronal Correlates of Developmental Dyscalculia |
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173 | (3) |
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Deficient Functional Networks |
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176 | (5) |
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Abnormal Neuronal Macro- and Microstructures |
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181 | (4) |
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185 | (1) |
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Conclusions and Future Directions |
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186 | (2) |
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188 | (7) |
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8 Neurocognitive Components of Mathematical Skills and Dyscalculia |
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195 | (2) |
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Accessing Quantity Representations |
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197 | (3) |
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Working Memory: The Role of Serial Order |
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200 | (8) |
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208 | (3) |
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Discussion and Conclusions |
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211 | (2) |
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213 | (6) |
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9 Individual Differences in Arithmetic Fact Retrieval |
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219 | (1) |
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Development and Measurement of Arithmetic Fact Retrieval |
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220 | (2) |
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Neurocognitive Determinants of Individual Differences in Arithmetic Fact Retrieval |
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222 | (8) |
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Numerical Magnitude Processing |
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224 | (3) |
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227 | (3) |
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Neural Correlates of Arithmetic Fact Retrieval |
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230 | (6) |
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Arithmetic Fact Retrieval in the (Developing) Brain |
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230 | (3) |
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Individual Differences in Brain Activity During Fact Retrieval |
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233 | (1) |
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Connections Between Areas of the Arithmetic Fact-Retrieval Network |
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234 | (2) |
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Conclusions and Future Directions |
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236 | (2) |
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238 | (7) |
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10 Transcranial Electrical Stimulation and the Enhancement of Numerical Cognition |
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245 | (5) |
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246 | (1) |
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247 | (1) |
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248 | (2) |
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Principles and Limitations of tES Experiments |
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250 | (5) |
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251 | (1) |
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Online and Offline Effects: Single Session and Training Studies |
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251 | (1) |
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252 | (1) |
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Choosing the Brain Region |
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252 | (1) |
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Size, Number, and Placement of the Electrodes |
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253 | (2) |
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Choosing the Type of Stimulation |
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255 | (1) |
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Evidence of tES-Induced Enhancement of Numerical Cognition |
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255 | (18) |
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255 | (5) |
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Symbolic and Magnitude Processing |
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260 | (7) |
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267 | (5) |
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All or Null? The Case of Nonsignificant Results |
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272 | (1) |
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Evidence of tES-Induced Enhancements in Dysfunctional Numerical Cognition |
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273 | (6) |
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273 | (3) |
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276 | (3) |
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279 | (6) |
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279 | (1) |
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280 | (2) |
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282 | (2) |
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284 | (1) |
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285 | (1) |
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286 | (13) |
Part II Genetic Influences |
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11 Individual Differences in Mathematics Ability: A Behavioral Genetic Approach |
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299 | (1) |
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Introduction to Quantitative Genetics |
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300 | (3) |
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Etiology of Individual Differences in Mathematics |
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303 | (3) |
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Etiology of the Links between Mathematics Ability and Other Traits |
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306 | (6) |
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Multivariate Genetic Designs |
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306 | (1) |
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Etiology of Relationships between Mathematics and Reading as well as Language-Related Skills |
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307 | (1) |
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Origin of Relationships between Mathematics and Spatial Ability |
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308 | (1) |
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Etiology of Relationships among Mathematical Subskills |
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309 | (1) |
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Overlap in Genetic Influences on Academic Subjects |
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309 | (1) |
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Genetic Effects Specific to Mathematics |
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310 | (1) |
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Etiology of Relationships between Mathematical Ability and Related Affective Factors |
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311 | (1) |
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312 | (1) |
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Molecular Genetic Studies of Mathematics |
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313 | (1) |
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Neurobiological Mechanisms |
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314 | (3) |
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317 | (1) |
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317 | (1) |
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317 | (8) |
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12 Genetic Syndromes as Model Pathways to Mathematical Learning Difficulties: Fragile X, Turner, and 22q Deletion Syndromes |
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325 | (3) |
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Why Focus on Fragile X, Turner, and 22q Deletion Syndromes to Study MLD? |
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326 | (1) |
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Contributions of Syndrome Research to Understanding MLD |
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327 | (1) |
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Syndromes as Models of MLD |
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328 | (20) |
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328 | (1) |
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329 | (1) |
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Chromosome 22q11.2 Deletion Syndrome |
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329 | (1) |
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MLD Frequency and Severity in Children with Fragile X, Turner, or 22q11.2 Deletion Syndromes |
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330 | (1) |
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Correlates as Indicators of Pathways to or Subtypes of MLD: Contributions and Limitations |
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331 | (1) |
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Correlates as Indicators of MLD Specificity in Fragile X, Turner, and 22q11.2DS |
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332 | (10) |
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Models of Relations Between Math, Executive Function, and Attention |
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342 | (3) |
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Syndrome Models Contribute to Understanding Neuro-Correlates of MLD |
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345 | (3) |
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348 | (2) |
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350 | (1) |
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350 | (9) |
Index |
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359 | |