Contributors |
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xi | |
Foreword: Cognitive Foundations for Improving Mathematical Learning |
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xiii | |
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Preface |
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xxi | |
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1 Introduction: Cognitive Foundations for Improving Mathematical Learning |
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1 | (36) |
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1 | (1) |
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Brief History of Mathematics Intervention Studies |
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2 | (1) |
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Methodological Issues in Intervention Research |
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3 | (1) |
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3 | (2) |
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Fidelity of Implementation |
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5 | (1) |
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Diminishing Intervention Impacts Across Time (Fadeout) |
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5 | (2) |
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7 | (1) |
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What Are the Cognitive Foundations for Improving Mathematics Learning? |
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8 | (2) |
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Domain-General Components |
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10 | (4) |
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Domain-General Interventions |
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14 | (1) |
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Domain-Specific Components |
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15 | (1) |
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Domain-Specific Interventions |
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16 | (2) |
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Domain-Relevant Interventions |
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18 | (4) |
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Parental Influences on Child Cognition and Mathematical Learning |
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22 | (1) |
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A Brief History of Research on Parental Influences |
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23 | (1) |
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Research on Children's Home Numeracy Environment |
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24 | (1) |
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25 | (1) |
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25 | (1) |
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26 | (11) |
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2 The Effects of SES, Grade-Repeating, and IQ in a Game-Based Approximate Math Intervention |
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37 | (32) |
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37 | (1) |
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38 | (4) |
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Background for the Current Study |
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42 | (1) |
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Socioeconomic Status in Education |
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42 | (1) |
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Classroom Geometric and Arithmetic Abilities |
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42 | (1) |
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Approximate Number Abilities |
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43 | (2) |
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The Present Intervention Study |
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45 | (1) |
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Teachers' Responses to the Software |
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46 | (1) |
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Design of the Current Study |
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47 | (1) |
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48 | (4) |
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52 | (10) |
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Conclusions and Future Directions |
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62 | (3) |
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65 | (4) |
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3 Role of Play and Games in Building Children's Foundational Numerical Knowledge |
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69 | (22) |
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69 | (1) |
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Understanding of Numerical Magnitudes |
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70 | (1) |
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Integrated Theory of Numerical Development |
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70 | (5) |
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Numerical Magnitude Understanding in Early Childhood |
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75 | (1) |
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Play and Games in Mathematics Development |
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76 | (1) |
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Improving Children's Numerical Magnitude Knowledge Through Games and Play |
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77 | (6) |
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Preschool Programs Using Games and Play |
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83 | (1) |
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Conclusions and Future Directions |
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84 | (1) |
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85 | (6) |
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4 Understanding the Link Between the Approximate Number System and Math Abilities |
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91 | (16) |
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91 | (1) |
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92 | (1) |
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Training Studies Using "The Number Race" |
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92 | (3) |
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Nonsymbolic vs. Symbolic Training |
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95 | (1) |
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Training Specific Aspects of Nonsymbolic Number Processing |
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96 | (3) |
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Mechanisms Behind Long-Term ANS Training Improvements |
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99 | (3) |
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Conclusions and Future Directions |
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102 | (1) |
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103 | (4) |
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5 Mathematical Development in the Early Home Environment |
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107 | (36) |
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107 | (1) |
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Parent Math Language and Associated Outcomes |
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108 | (1) |
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108 | (9) |
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117 | (2) |
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119 | (1) |
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Gesture: An Additional Support for Children's Math Learning |
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120 | (1) |
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121 | (1) |
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122 | (2) |
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124 | (1) |
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125 | (1) |
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Parental Math Attitudes and Beliefs: Intergenerational Findings |
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126 | (1) |
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Intergenerational Effects of Math Anxiety |
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127 | (1) |
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Other Negative Attitudes Toward Math |
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128 | (2) |
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Summary: Parental Math Attitudes and Beliefs |
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130 | (1) |
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Conclusions and Future Directions |
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130 | (3) |
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133 | (1) |
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133 | (10) |
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6 From Cognition to Curriculum to Scale |
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143 | (32) |
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143 | (1) |
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The Curriculum Research Framework (CRF) |
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144 | (1) |
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The CRF and Early Mathematics |
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145 | (1) |
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145 | (1) |
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Category I A Priori Foundations |
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145 | (2) |
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Category II Learning Model and Learning Trajectory |
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147 | (15) |
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162 | (4) |
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Conclusions and Future Directions |
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166 | (1) |
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167 | (8) |
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7 Development of Mathematical Language in Preschool and Its Role in Learning Numeracy Skills |
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175 | (20) |
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175 | (1) |
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Connections Between Early Mathematics Development and General Language |
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175 | (1) |
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Difficulties in Both Domains |
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176 | (1) |
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Early Connections Between Mathematics and Literacy Skills |
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176 | (2) |
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Language Interventions and Mathematics Skills |
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178 | (1) |
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What is Content-Specific Mathematical Language? |
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178 | (1) |
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Correlational and Experimental Evidence on the Relations Between Mathematical Language and Mathematics Performance |
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179 | (3) |
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Interventions to Improve Mathematical Language |
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182 | (3) |
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185 | (1) |
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Mathematical Language and Numeracy Instruction |
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185 | (1) |
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186 | (1) |
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Mathematical Language Measures |
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187 | (1) |
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Developing Methods for Mathematical Language Instruction |
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187 | (1) |
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Conclusions and Future Directions |
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188 | (1) |
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188 | (7) |
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8 Early Numeracy Skills Learning and Learning Difficulties---Evidence-based Assessment and Interventions |
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195 | (20) |
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195 | (1) |
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Early Numeracy Skills are Important for Future |
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196 | (1) |
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Identifying Children at Risk for Mathematical Learning Difficulties |
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197 | (4) |
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Early Numeracy Interventions for Low-Performing Children |
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201 | (4) |
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Studies With ThinkMath Intervention Programs |
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205 | (3) |
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Conclusions and Future Directions |
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208 | (1) |
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209 | (6) |
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9 Improving the Mathematical Knowledge of At-Risk Preschool Children: Two Approaches to Intensifying Early Math Intervention |
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215 | (32) |
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The SES-Related Gap in Children's Early Mathematical Knowledge |
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215 | (2) |
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Potential for Early Curricular Intervention to Reduce the Math Cap |
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217 | (1) |
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The Pre-K Mathematics Intervention |
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218 | (2) |
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Effectiveness of the Pre-K Mathematics Intervention |
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220 | (1) |
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First Approach: Tutorial Interventions in Mathematics and Attention |
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221 | (2) |
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Study Design and Participants |
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223 | (2) |
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The Math Intervention: Pre-K Mathematics Tutorial |
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225 | (1) |
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The Attention Intervention |
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226 | (1) |
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Measures and Assessment Procedures |
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227 | (1) |
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228 | (2) |
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Summary of Findings From Tutorial Intervention Study |
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230 | (1) |
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Second Approach: Intensification by Providing 2 Years of Tier 1 Math Intervention |
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230 | (1) |
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Study Design and Participants |
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231 | (1) |
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The Math Intervention: Pre-Pre-K Mathematics and Pre-K Mathematics |
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232 | (2) |
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Measures and Assessment Procedures |
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234 | (1) |
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235 | (1) |
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236 | (1) |
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Effectiveness of the First Intervention Approach |
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236 | (1) |
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Effectiveness of the Second Intervention Approach |
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237 | (1) |
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Comparison of the Two Intervention Approaches for Very Low-Performing Children |
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237 | (1) |
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Conclusions and Future Directions |
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238 | (1) |
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Conclusion 1 Most Low-Performing Children Respond to Intensified Support in Mathematics |
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238 | (1) |
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Conclusion 2 A Residual Subgroup of Low-Performing Children Showed Low Response to Intensified Math Support; Research is Needed to Understand Why |
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239 | (1) |
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Conclusion 3 Public Preschool Programs Should Provide High-Quality, Intensive Math Support, But New Policies and Resources Are Needed |
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239 | (1) |
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240 | (1) |
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240 | (7) |
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10 The Use of Analogies in Mathematics Instruction: Affordances and Challenges |
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247 | (22) |
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Analogy and Analogical Reasoning in Mathematics |
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247 | (4) |
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Where Does the Analogy "Numbers are Points on the Line" Come From? |
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251 | (1) |
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Tapping Into Students' Understanding of the Dense Ordering of Rational Numbers |
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252 | (2) |
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Could the Number Line Support Students' Understanding of Density? |
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254 | (1) |
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Does the Number Line Have an Effect on Students' Reasoning About Density? |
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255 | (2) |
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Is Density More Accessible to Students in a Geometrical Rather Than in an Arithmetical Context? |
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257 | (4) |
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Using the "Numbers are Points" Analogy and the "Rubber Line" Bridging Analogy |
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261 | (3) |
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Conclusions and Future Directions |
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264 | (1) |
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265 | (4) |
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11 The Role of Visual Representations in Mathematical Word Problems |
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269 | (26) |
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Students' Natural Use of Visual Representations in Mathematics |
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270 | (6) |
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Embedding Visual Representations in Text |
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276 | (2) |
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Teaching Students to Create or Complete Diagrams as They Solve Problems |
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278 | (3) |
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Integrating Visual Representations With Text |
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281 | (3) |
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Schema-Based Instruction (SBI): Integrated Instruction in Word Problems and Visual Representations |
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284 | (5) |
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Conclusions and Future Directions |
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289 | (1) |
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290 | (5) |
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12 The Role of Cognitive Processes in Treating Mathematics Learning Difficulties |
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295 | (26) |
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Embedding Cognitive Training Within Explicit Skills Intervention to Facilitate Transfer to Academic Performance |
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297 | (1) |
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297 | (2) |
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Conceptual Model for Linking Language Comprehension and Our Approach to Explicit Skills Word-Problem Intervention |
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299 | (3) |
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302 | (1) |
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303 | (3) |
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Some Tentative Conclusions |
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306 | (1) |
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Allocating Varying Forms of Explicit Skills Intervention to Subgroups of Learners With Different Cognitive Profiles |
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306 | (1) |
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307 | (2) |
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Does Supported Self-Explaining Compensate for Limitations in Cognitive Processes? |
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309 | (3) |
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312 | (2) |
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314 | (2) |
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Implications for Practice |
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316 | (1) |
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Summary and Future Directions |
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316 | (1) |
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317 | (4) |
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13 Explanations and Implications of Diminishing Intervention Impacts Across Time |
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321 | (26) |
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321 | (1) |
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Patterns of Effects Across Time and Theories of Children's Mathematical Development |
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322 | (1) |
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Possible Explanations of Fadeout |
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323 | (14) |
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Implications for the Study of Children's Mathematical Development |
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337 | (2) |
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How can Researchers of Mathematical Cognition Help Produce Long-Lasting Effects? |
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339 | (4) |
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Conclusions and Future Directions |
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343 | (1) |
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343 | (1) |
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344 | (3) |
Index |
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347 | |