Build a lasting foundation for math proficiency right from the start
The "math" is on the wall: unless we can instill in our youngest mathematicians a solid understanding of number sense, they have little hope of mastering the more rigorous fractions and algebra that lie ahead. A key piece is identifying precisely where K-3 students are likely to struggle, then intervening with smart, targeted instruction. Thats where Witzel and Riccominis Building Number Sense Through the Common Core fits in.
Grounded in research-supported instruction with aligned assessments to ensure comprehension, this essential resource provides:
Teaching strategies that build number sense skills, including quantity and cardinality, numeral/number recognition, fact fluency, math language, and more Adaptations for students with specific needs, including English learners and students with disabilities, based on an RTI approach Guidance on measuring number sense through assessments and preparing students for standardized testing User-friendly charts, tables, and sample math problems for planning curriculum and lessons
Discover strategies that enable your students to develop a fundamental sense for numbers and create a lasting foundation for math proficiency!
"The authors describe how each common standard should be taught, which makes this a quick and immensely useful resource. Ive already begun using the strategies with my fellow teachers." Deborah Gordon, Third-Grade Teacher Madison School District, Phoenix, AZ
"This is an evidence based, accessible manual on how, why, and what to teach. Well written with effective examples and scenarios to illustrate key points, this book should be read by anyone interested in improving outcomes for children in mathematics." Annmarie Urso, Assistant Professor State University of New York at Geneseo
Arvustused
"With the adoption of the Common Core State Standards, this is the perfect resource! Ive already begun using the strategies in the book with my fellow third grade teachers! The author describes how each standard should be taught, which makes this such a quick and immensely useful resource!" -- Deborah Gordon, Third Grade Teacher "This book reminds us of the need for rigorous and appropriate math education and then gives us the wherewithal to do such. It has great stores, wonderful examples, and will greatly help pre-service instruction as well as K-12 education. There absolutely needs to be more emphasis on math instruction in schools, and this book will lead the way!" -- David Bateman, Professor of Special Education "Witzel and Riccomini have demystified mathematics instruction! Building Number Sense is an evidence based, accessible manual on how to, why to, and what to teach in regards to the very foundation of mathematics understanding - number sense. Well written with effective examples and scenarios to illustrate key points, anyone interested in improving outcomes for children in mathematics should read this." -- Annmarie Urso, Ph.D.
| Acknowledgments |
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ix | |
| About the Authors |
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xi | |
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1 Introduction to the Characteristics of Number Sense |
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1 | (10) |
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1 | (1) |
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Turning Around Math Achievement |
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2 | (2) |
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4 | (2) |
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The Common Core State Standards |
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6 | (1) |
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The CCSS and Elements of Number Sense |
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7 | (1) |
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8 | (1) |
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9 | (2) |
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2 Redefining Mastery Through Long-Term Planning |
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11 | (18) |
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How to Prepare Children for Mathematics Understanding |
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11 | (2) |
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13 | (3) |
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Horizontal (Grade-Level) Planning |
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16 | (3) |
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19 | (2) |
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KIT Framework to Support What Is Being Taught |
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21 | (1) |
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22 | (4) |
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26 | (1) |
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Expectations and Differentiation |
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26 | (2) |
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28 | (1) |
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3 Assessment and Progress Monitoring of Number Sense |
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29 | (16) |
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Four Main Purposes of Assessments |
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30 | (2) |
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32 | (4) |
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Error Pattern Analysis to Guide Instruction |
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36 | (1) |
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Conducting Error Analysis |
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37 | (2) |
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New Generation of Assessments |
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39 | (2) |
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Critical Issues for Educators |
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41 | (1) |
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42 | (1) |
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43 | (1) |
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43 | (2) |
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4 Counting, Number Identification, and Early Addition and Subtraction |
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45 | (26) |
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47 | (6) |
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53 | (1) |
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53 | (4) |
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Early Addition and Subtraction |
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57 | (9) |
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Interventions for Students Struggling With Addition and Subtraction |
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66 | (1) |
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67 | (1) |
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68 | (1) |
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69 | (2) |
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5 Building Computation Systems Through Place Value |
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71 | (38) |
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The Place Value Imperative |
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72 | (5) |
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77 | (3) |
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Decomposition of Place Value |
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80 | (9) |
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Intervention for Place Value |
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89 | (1) |
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90 | (1) |
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90 | (1) |
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90 | (3) |
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6 Multiplication and Division |
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93 | (1) |
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93 | (2) |
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Multiplication Difficulties |
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95 | (5) |
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Setting Multiplicative Foundation |
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100 | (1) |
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Moving Into Multiplication |
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101 | (2) |
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The Relationship Between Multiplication and Division |
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103 | (1) |
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104 | (1) |
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Intervention for Multiplication Fluency and Automaticity |
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105 | (2) |
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107 | (2) |
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7 Applications in Algebra, Geometry, and Measurement |
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109 | (14) |
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110 | (2) |
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112 | (1) |
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Connections to the Common Core |
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112 | (3) |
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Building Through Geometry and Measurement |
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115 | (6) |
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121 | (1) |
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121 | (2) |
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8 Using Math Language to Solve Problems |
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123 | (14) |
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126 | (8) |
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134 | (1) |
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135 | (2) |
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9 Mathematical Vocabulary and the Development of Early Mathematicians |
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137 | (20) |
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Vocabulary and Mathematical Proficiency |
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138 | (1) |
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Difficulties Students Experience With Mathematical Vocabulary |
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139 | (3) |
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General Approaches and Techniques to Teaching Mathematical Vocabulary |
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142 | (1) |
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Activities for Teaching Math Vocabulary |
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143 | (8) |
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151 | (4) |
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155 | (2) |
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10 The Next Steps to Teaching Number Sense |
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157 | (10) |
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157 | (2) |
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159 | (3) |
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162 | (1) |
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Social Studies and Science |
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162 | (2) |
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164 | (1) |
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164 | (3) |
| Index |
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167 | |
Bradley S. Witzel, PhD, is an award-winning teacher and professor who works as an associate professor and education program coordinator at Winthrop University, the flagship education college for the state of South Carolina. As a classroom teacher, and before that as a paraeducator, he worked in multiple settings teaching mainly math and science to high-achieving students with disabilities. Dr. Witzel has written five books, including the best-selling Response to Intervention in Math through Corwin, as well as several dozen book chapters, research and practitioner articles, and training manuals. He has also produced six education videos and several hundred conference and workshop presentations. He is a selected member of the Governing Board of the Southeast Regional Educational Laboratory (REL), funded by the Institute of Education Sciences (IES), and of the Smarter Balanced Assessment Consortium (SBAC) Accessibility and Accommodations work group. Dr. Witzel currently serves as the editor of Focus on Inclusive Education through the Association for Childhood Education International (ACEI) and recently served as a panelist on the IES practice guide Assisting Students Struggling with Mathematics and as an invited reviewer of the final report from the National Mathematics Advisory Panel. Most importantly, he is a father of two, husband of an educator, and son of two educators.
Paul J. Riccomini is an experienced classroom teacher, author, mathematician, and leading special education expert. Dr. Riccomini began his career as a dual-certified general education mathematics teacher of students with learning disabilities, emotional and behavioral disabilities, and gifted and talented students in Grades 712. He taught mathematics to both general and special education students in inclusive settings. He is coauthor of the best-selling Response to Intervention in Math (Corwin, 2009) book and is an associate professor of education at the Pennsylvania State University. His teaching experiences required him to have both strong content knowledge in mathematics and to develop and maintain strong collaborative relationships with both general and special educators. As a former middle and high school mathematics teacher, he knows firsthand the challenges faced by students who struggle in mathematics and recognizes the importance of early mathematics development. He hopes the writing of this book will assist teachers in their efforts to develop young mathematicians.
Dr. Riccomini provides professional development in schools across the nation. His dynamic presentations offer research-validated practices that focus on the development of improved instructional practices for all students. Dr. Riccominis written work includes numerous research and practitioner articles for students with and without learning disabilities, including one of the first books to address Response to Intervention in the area of mathematics. Additional publications he coauthored include three Tier 2 Interventions for the areas of fractions, integers, and simple equations.
Marla Larson Herlong, MEd, earned her bachelor of science in early childhood and her master of education in curriculum and instruction with a concentration in mathematics at Winthrop University in South Carolina. An experienced classroom teacher, she has taught a wide variety of students from kindergarten through second grade. A popular speaker, she has presented several workshops and conference sessions in the areas of math intervention strategies, integrating content, teaching math through problem solving, data-driven assessments, and increasing student engagement. She is currently working on deconstructing assessments and aligning curriculum maps for the Common Core State Standards. Marla was born and raised in California and currently resides in Aiken, South Carolina, with her husband and daughter.
, MEd, earned her bachelor of science in early childhood and her master of education in curriculum and instruction with a concentration in mathematics at Winthrop University in South Carolina. An experienced classroom teacher, she has taught a wide variety of students from kindergarten through second grade. A popular speaker, she has presented several workshops and conference sessions in the areas of math intervention strategies, integrating content, teaching math through problem solving, data-driven assessments, and increasing student engagement. She is currently working on deconstructing assessments and aligning curriculum maps for the Common Core State Standards. Marla was born and raised in California and currently resides in Aiken, South Carolina, with her husband and daughter.
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