Contributors |
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xiii | |
Foreword: Mathematical Cognition, Language, and Culture: Understanding the Links |
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xv | |
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Preface |
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xxi | |
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1 Introduction: Language and Culture in Mathematical Cognitive Development |
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1 | (30) |
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1 | (1) |
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A Brief Historical Review of Research on the Roles of Language and Culture in Mathematical Cognition |
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2 | (1) |
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Specific Linguistic Levels of Influence on Numerical Processing |
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3 | (9) |
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Lexical: The Composition of Number Words |
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3 | (2) |
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Semantic: The Meaning of Words |
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5 | (2) |
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Syntactic: The Grammatical Structure of Languages Beyond Word-Level Influences |
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7 | (1) |
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Phonological: The Structure and Sequencing of Speech Sounds |
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8 | (1) |
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Visuo-Spatial-Orthographic: Conventions for Writing and Reading Directions of Languages |
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8 | (1) |
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Conceptual: Conceptual Properties of Language |
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9 | (2) |
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Other Language-Related Skills: Verbal Working Memory and Other Cognitive Skills Related to Language Representations |
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11 | (1) |
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A Key Question Driving Research on Numerical Development |
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12 | (2) |
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How Do Children Learn the Meaning of Number Words? |
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12 | (2) |
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Other Considerations in Studying Linguistic Influences on Numerical Processing |
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14 | (3) |
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Language and Number in the Brain |
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14 | (1) |
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Domain-General and Domain-Specific Influences of Bilingualism on Cognition |
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15 | (2) |
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The Role of Culture in Mathematical Cognition |
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17 | (5) |
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Five Myths of Cultural Psychology |
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19 | (3) |
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Disentangling Linguistic and Cultural Influences on Numerical Processing and Mathematics Achievement |
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22 | (1) |
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23 | (1) |
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24 | (7) |
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2 Analogical Mapping in Numerical Development |
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31 | (18) |
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31 | (1) |
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Analogical Mapping in Integer Learning |
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32 | (1) |
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Acquisition of Natural Numbers |
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32 | (1) |
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Analogical Mapping in Acquiring Natural Numbers |
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33 | (2) |
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Problems With the Current Account of Analogical Mapping in Integer Learning |
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35 | (4) |
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Analogical Mapping in Magnitude Estimation |
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39 | (1) |
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Analogical Mapping in Estimation: Evidence From the Flexibility and Interdependence of Estimates |
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40 | (3) |
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Analogical Mapping in Estimation: The Role of Ordinality |
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43 | (1) |
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Other Evidence of Analogy as a Source of Representational Changes |
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44 | (1) |
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45 | (1) |
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45 | (4) |
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3 Linguistic and Experiential Factors as Predictors of Young Children's Early Numeracy Skills |
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49 | (24) |
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Number Language and Early Numeracy Performance |
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52 | (1) |
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Comparisons of Counting Across Languages |
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53 | (7) |
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English- Vs Chinese-Speaking Canadian Children |
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53 | (1) |
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English- Vs French-Speaking Canadian Children |
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54 | (3) |
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English-Speaking Canadian Vs Spanish-Speaking Mexican Children |
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57 | (2) |
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Turkish- and Chinese-Speaking Canadian Children |
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59 | (1) |
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Correlation Vs Causation in Comparisons Across Languages |
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60 | (1) |
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Other Approaches to Exploring Language Effects |
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60 | (7) |
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English-Speaking Children Learning to Speak French |
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61 | (2) |
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Training Study I: Guided Practice Counting for English-and Turkish-Speaking Children |
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63 | (3) |
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Training Study II: Structured Counting Practice for English-Speaking Children |
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66 | (1) |
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67 | (2) |
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69 | (1) |
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69 | (3) |
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72 | (1) |
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4 Effects of Mathematics Language on Children's Mathematics Achievement ana Central Conceptual Knowledge |
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73 | (26) |
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Mathematics Language and Achievement |
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74 | (12) |
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75 | (2) |
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Cognitive Organization of Numbers |
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77 | (2) |
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Numerical Language and Estimation of Numerical Magnitudes |
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79 | (1) |
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Relation of Numerical Language to Mathematics Achievement |
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80 | (1) |
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Place-Value Understanding |
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80 | (2) |
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Numerical Language and Instructional Methods |
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82 | (1) |
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83 | (1) |
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Terms for Geometric Shapes |
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84 | (2) |
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Mathematics Achievement, Central Conceptual Knowledge, and Numerical Language |
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86 | (7) |
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Development of Core Conceptual Knowledge |
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86 | (2) |
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Cultural Comparisons of Central Conceptual Knowledge and Specific Skills |
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88 | (5) |
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93 | (1) |
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94 | (5) |
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5 How Does the "Learning Gap" Open? A Cognitive Theory of Nation Effects on Mathematics Proficiency |
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99 | (32) |
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The Traditional Approach: Differences in Input, Differences in Output |
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100 | (4) |
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Quantity of Math Instruction |
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101 | (1) |
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Quality of Math Instruction |
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101 | (1) |
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Quality of Teacher Knowledge |
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102 | (1) |
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Cultural Differences in Math Attitudes |
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102 | (1) |
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Beyond Habits of Highly Successful Educational Systems |
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103 | (1) |
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A Cognitive Theory on How the Learning Gap Opens |
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104 | (11) |
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Why Numerical Magnitude Judgments? |
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105 | (1) |
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Varieties of Numerical Magnitude Judgments |
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106 | (5) |
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Connections Between Numerical Magnitude Judgments and Math Proficiency |
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111 | (2) |
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Cross-National Differences in Numerical Magnitude Judgments |
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113 | (2) |
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Do Numerical Magnitude Judgments Mediate Nation Effects on Math Proficiency? |
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115 | (5) |
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Comparing Sets and Numbers: U.S. Vs Chinese Children |
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117 | (1) |
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Estimating the Placement of Sets and Numbers on a Number Line: U.S. Vs Chinese Children |
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118 | (1) |
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Approximately Adding Sets and Numbers: U.S. Vs Chinese Children |
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118 | (1) |
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Cognitive Mechanisms of Nation Effects on Mathematics Proficiency |
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119 | (1) |
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120 | (2) |
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122 | (1) |
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122 | (7) |
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129 | (2) |
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6 Mathematical Skills of Children With Specific Language Impairments: Testing Developmental Theory |
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131 | (14) |
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131 | (1) |
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Background to Specific Language Impairment |
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132 | (2) |
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132 | (1) |
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132 | (1) |
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Mathematical Attainments of Children With SLI |
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133 | (1) |
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Linguistic and Nonlinguistic Contributions to Mathematical Development |
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134 | (4) |
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The Approximate Number System |
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134 | (1) |
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The Importance of Number Symbols |
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135 | (1) |
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The Integration of Symbolic Representations |
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135 | (1) |
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Natural Language as a Support for Learning Number Meanings |
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136 | (1) |
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137 | (1) |
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138 | (1) |
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Evidence From Children With Specific Language Impairments (SLI) |
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138 | (2) |
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Challenges Presented by the Number Word Sequence and Transcoding |
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138 | (2) |
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Effects of Cognitive Factors |
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140 | (1) |
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140 | (1) |
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141 | (4) |
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7 Arithmetic in the Bilingual Brain |
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145 | (28) |
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145 | (1) |
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Bilingualism and Retrieval of Mathematical Facts |
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146 | (18) |
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How Bilinguals Process Arithmetic |
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146 | (1) |
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Relevant Models of Mathematical Cognition |
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147 | (3) |
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Behavioral Evidence From Bilinguals as Tests of the TMC and ECM Models |
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150 | (2) |
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Review of Brain Evidence in Bilingual Arithmetic Processing |
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152 | (12) |
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Conclusions and Future Directions |
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164 | (3) |
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167 | (6) |
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8 Linguistic Traces in Core Numerical Knowledge: An Approach From Bilingualism |
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173 | (24) |
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173 | (1) |
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174 | (2) |
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Language and Symbol Acquisition |
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176 | (2) |
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Bilingualism as a Window to Numerical Cognition |
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178 | (3) |
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181 | (1) |
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The Language of Learning Mathematics |
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181 | (5) |
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New Evidence: Bilingual Dyscalculia |
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186 | (4) |
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190 | (1) |
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191 | (1) |
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191 | (5) |
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196 | (1) |
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9 Early Number Knowledge in Dual-Language Learners From Low-SES Households |
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197 | (32) |
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197 | (1) |
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Does Bilingualism Matter for Early Numeracy? |
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198 | (2) |
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Ways for Young Children to Represent Numbers |
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200 | (6) |
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The Innate, Approximate Number System |
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200 | (2) |
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202 | (4) |
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206 | (1) |
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206 | (15) |
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What We Measured and What We Found |
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207 | (11) |
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Overall Conclusions of the Study |
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218 | (3) |
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221 | (1) |
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222 | (7) |
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10 How Culturally Predominant Reading Direction and Number Word Construction Influence Numerical Cognition and Mathematics Performance |
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229 | (28) |
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229 | (1) |
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Effects of Reading Direction |
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230 | (11) |
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232 | (6) |
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238 | (2) |
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Summary of the Effects of Reading Direction |
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240 | (1) |
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Effects of Number Word Construction |
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241 | (8) |
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243 | (1) |
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Number Word Inversion and the Carry Effect in Addition |
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244 | (1) |
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Carry Effect and Mathematical Performance |
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244 | (1) |
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Effects of Reading Direction and Number Word Construction Can interact |
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245 | (2) |
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Compatibility Effect and Mathematical Performance |
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247 | (1) |
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Summary of Effects of Number Word Construction |
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248 | (1) |
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Conclusions and Future Directions |
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249 | (1) |
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250 | (1) |
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250 | (7) |
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11 Language, Culture, and Space: Reconstructing Spatial-Numerical Associations |
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257 | (18) |
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Verbal Components of Language-Related Spatial-Numerical Associations |
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258 | (5) |
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Do Space-Number Associations Require Directional Harmony? |
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258 | (3) |
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Longstanding Cultural Habits or Recent Experience? |
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261 | (2) |
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Non-Verbal Language-Related Behavior and Spatial-Numerical Associations |
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263 | (6) |
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264 | (1) |
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265 | (2) |
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267 | (2) |
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Evolutionary Predispositions to SNARC |
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269 | (1) |
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270 | (2) |
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272 | (3) |
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12 Cultural Processes in Elementary Mathematics: Studies in a Remote Papua New Guinea Community |
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275 | (22) |
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Dichotomous Approaches to Analyzing Relations Between Culture and the Development of Numerical Understandings |
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275 | (2) |
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Intrinsic Relations Approaches to Analyzing Relations Between Culture and the Development of Numerical Understandings |
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277 | (5) |
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Cultural Dimension of the Framework: A Focus on Collective Practices |
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277 | (5) |
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The Interplay Between Cultural and Developmental Processes in Mathematical Understandings: A Program of Research in Remote Oksapmin Communities |
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282 | (12) |
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282 | (1) |
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Studies Conducted in 1978 and 1980. Form-Function Shifts in Children's Developing Use and Knowledge of the Body System |
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283 | (1) |
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Studies of Unschooled Children's Use of the Body System: A Focus on Ontogeny of Numerical Representations With the Body System |
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284 | (5) |
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Studies on Children Attending School in 1980: A Focus on Genetic Processes in Form-Function Relations in Collective Practices of Schooling |
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289 | (5) |
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294 | (1) |
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295 | (2) |
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13 Numeration Systems as Cultural Tools for Numerical Cognition |
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297 | (24) |
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297 | (1) |
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Properties of Numeration Systems and Their Implications |
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298 | (9) |
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300 | (1) |
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300 | (1) |
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Dimensional Representation |
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301 | (1) |
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302 | (1) |
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303 | (3) |
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306 | (1) |
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Inconsistencies Between Representational Systems |
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307 | (6) |
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Learning the Verbal System |
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308 | (1) |
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309 | (1) |
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310 | (2) |
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Possible Benefits of Inconsistencies and Mismatches |
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312 | (1) |
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313 | (3) |
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316 | (1) |
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316 | (5) |
Index |
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321 | |