About the Authors |
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xiii | |
Acknowledgements |
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xv | |
Foreword |
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xvii | |
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Introduction |
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xix | |
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1 The Learning Framework in Number for the Classroom |
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1 | (4) |
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Conceptual Understandings and Conventions of Mathematics |
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2 | (2) |
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4 | (1) |
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2 Professional Principles and Practices |
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5 | (14) |
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6 | (1) |
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CEC Standards for Professional Practice |
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7 | (2) |
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Adding It Up: Helping Children Learn Mathematics |
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9 | (3) |
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Standards for Mathematical Practice |
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12 | (3) |
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Principles to Actions: Ensuring Mathematical Success for All |
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15 | (3) |
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18 | (1) |
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3 Good Instruction for All Students |
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19 | (16) |
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Guiding Principles for Classroom Teaching |
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19 | (4) |
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Key Elements of Intensive One-to-One Instruction |
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23 | (7) |
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Dimensions of Mathematization |
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30 | (2) |
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Characteristics of Children's Problem Solving |
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32 | (2) |
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34 | (1) |
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4 Numeracy and Functional Mathematics |
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35 | (16) |
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What Is Functional Mathematics? |
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35 | (1) |
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Academic Standards and Functional Goals |
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36 | (1) |
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37 | (8) |
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45 | (2) |
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47 | (1) |
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48 | (2) |
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50 | (1) |
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5 Assessing Students with Disabilities |
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51 | (24) |
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51 | (1) |
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Administering Assessments |
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52 | (2) |
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Number Words and Numerals |
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54 | (4) |
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Counting, Addition, and Subtraction Strategies |
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58 | (3) |
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Structuring: Non-count-by-one Strategies |
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61 | (3) |
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Conceptual place value, addition, and subtraction to 100 |
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64 | (3) |
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Multiplication and Division |
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67 | (2) |
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69 | (4) |
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73 | (2) |
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6 Using the Learning Framework in Number to Write Individualized Education Programs |
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75 | (8) |
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Individualized Education Programs, the Learning Framework in Number, and the Teaching and Learning Cycle |
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75 | (2) |
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Sample Benchmarks or Objectives |
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77 | (5) |
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82 | (1) |
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7 Brain Research: Implications for Teaching and Learning Mathematics |
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83 | (14) |
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84 | (1) |
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The Neural Anatomy of the Neocortex |
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85 | (1) |
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85 | (1) |
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The Frontal Lobe and Working Memory |
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86 | (1) |
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The Parietal Lobe and Spatial-Numerical Reasoning |
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87 | (1) |
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Frontal-to-Parietal Shift |
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88 | (1) |
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Supporting Mathematical Development |
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88 | (4) |
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Maintaining Cognitive Demand |
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92 | (1) |
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Increasing Cognitive Demand |
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93 | (1) |
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Accommodations for Students with Limited Working Memory |
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93 | (1) |
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Developing New Structures and Addressing Dyscalculia |
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94 | (2) |
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Dimensions of Mathematizing |
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96 | (1) |
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96 | (1) |
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97 | (10) |
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97 | (3) |
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100 | (1) |
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Subitizing and Comparing Quantities |
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100 | (1) |
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Counting and Comparing Quantities |
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101 | (2) |
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Labeling a Quantity with a Number Word or Numeral |
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103 | (1) |
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Development of a Mental Number Line |
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103 | (3) |
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106 | (1) |
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9 Differentiating Instruction |
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107 | (16) |
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108 | (1) |
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Differentiating for Students' Diverse Ways of Thinking |
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109 | (2) |
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Five Teaching Practices to Differentiate Instruction |
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111 | (2) |
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More about Practice 2: Providing Purposeful Choices and Different Pathways |
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113 | (7) |
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Recommendations about Differentiating Instruction |
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120 | (2) |
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122 | (1) |
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10 Teaching Students with Disabilities |
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123 | (22) |
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Considerations for Assessment Accommodations and Modifications |
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126 | (1) |
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Considerations for Instructional Accommodations and Modifications |
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127 | (1) |
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Number Words and Numerals |
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127 | (1) |
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Counting, Addition, and Subtraction Strategies |
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128 | (2) |
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Structuring: Non-count-by-one Strategies |
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130 | (1) |
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Conceptual Place Value, Addition, and Subtraction to 100 |
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131 | (7) |
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Multiplication and Division |
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138 | (1) |
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139 | (4) |
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143 | (2) |
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11 The Constructivist as Teacher |
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145 | (10) |
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147 | (1) |
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Constructivism in Education |
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147 | (2) |
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Constructivist Teaching for Students with Disabilities |
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149 | (4) |
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153 | (2) |
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12 Supporting Students with Other Special Needs |
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155 | (14) |
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Students from Historically Marginalized and Systemically Underserved Groups |
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156 | (1) |
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Students Living in Poverty |
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157 | (1) |
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Homeless Students and Those in Temporary Housing Situations |
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158 | (1) |
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English Language Learners/English Learners |
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158 | (4) |
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Culturally Responsive Teaching |
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162 | (1) |
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163 | (1) |
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164 | (1) |
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Developing a Mathematical Mindset |
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165 | (1) |
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Math Recovery as a Vehicle for Improved Equity of Access to Quality Educational Opportunities |
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166 | (2) |
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168 | (1) |
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168 | (1) |
Glossary |
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169 | (12) |
References |
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181 | (16) |
Index |
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197 | |