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Teaching Student-Centered Mathematics
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Table of Contents

Brief Table of Contents

Part 1: Establishing a Student-Centered Environment

1 Setting a Vision for Learning High-Quality Mathematics

2 Teaching Mathematics through Problem Solving

3 Creating Assessments for Learning

4 Differentiating Instruction

5 Teaching Culturally and Linguistically Diverse Children

6 Planning, Teaching, and Assessing Children with Exceptionalities

7 Collaborating with Families and Other Stakeholders Part 2: Teaching Student-Centered Mathematics 8 Fraction Concepts and Computation 9 Decimal Concepts and Computation 10 The Number System 11 Ratios and Proportional Relationships 12 Algebraic Thinking: Expressions, Equations, and Functions 13 Developing Geometry Concepts 14 Exploring Measurement Concepts 15 Working with Data and Doing Statistics 16 Investigating Concepts of Probability
Appendix A Common Core State Standards: Standards for Mathematical PracticeAppendix B Common Core State Standards: Grades 6-8 Critical Content Areas and Overviews Appendix C Mathematics Teaching Practices: NCTM Principles to Actions (2014) Appendix D Activities at a Glance: Volume III Appendix E Guide to Blackline Masters References Index
Detailed Table of Contents
Part 1: Establishing a Student-Centered Environment 1 Setting a Vision for Learning High-Quality Mathematics Understanding and Doing Mathematics How Do Students Learn? Teaching for Understanding The Importance of Students' Ideas Mathematics Classrooms That Promote Understanding 2 Teaching Mathematics through Problem Solving Teaching through Problem Solving: An Upside-Down Approach Mathematics Teaching Practices for Teaching through Problem Solving Using Worthwhile Tasks Orchestrating Classroom Discourse Representations: Tools for Problem Solving, Reasoning, and Communication Lessons in the Problem-Based Classroom Life-Long Learning: An Invitation to Learn and Grow 3 Creating Assessments for Learning Assessment That Informs Instruction Observations Questions Interviews Tasks Students' Self-Assessment and Reflection Rubrics and Their Uses 4 Differentiating Instruction Differentiation and Teaching Mathematics through Problem Solving The Nuts and Bolts of Differentiating Instruction Differentiated Tasks for Whole-Class Instruction Tiered Lessons Flexible Grouping 5 Teaching Culturally and Linguistically Diverse Students Culturally and Linguistically Diverse Students Culturally Responsive Mathematics Instruction Teaching Strategies that Support Culturally and Linguistically Diverse Students Assessment Considerations for ELLs 6 Planning, Teaching, and Assessing Students with Exceptionalities Instructional Principles for Diverse Learners Implementing Interventions Teaching and Assessing Students with Learning Disabilities Adapting for Students with Moderate/Severe Disabilities Planning for Students Who Are Mathematically Gifted 7 Collaborating with Families and Other Stakeholders Sharing the Message with Stakeholders Administrator Engagement and Support Family Engagement Homework Practices and Parent Coaching Part 2: Teaching Student-Centered Mathematics 8 Fraction Concepts and Computation Meanings of Fractions Partitioning and Iterating Fraction Equivalencies Comparing Fractions Understanding Fraction Operations Addition and Subtraction Multiplication Division Teaching Fractions Effectively Literature Connections 9 Decimal Concepts and Computation Extending the Place-Value System Connecting Fractions and Decimals Emphasizing Equivalence between Fractions and Decimals Comparing and Ordering Decimal Fractions Addition and Subtraction Multiplication Division Percents 10 The Number System Exponents Positive and Negative Numbers Operations with Positive and Negative Numbers Real Numbers Literature Connections 11 Ratios and Proportional Relationships Ratios Proportional Reasoning Covariation in Algebra Strategies for Solving Proportional Situations Teaching Proportional Reasoning Literature Connections 12 Algebraic Thinking: Expressions, Equations, and Functions Structure in the Number System: Connecting Number and Algebra Structure in the Number System: Properties Patterns and Functions Meaningful Use of Symbols Mathematical Modeling Algebraic Thinking across the Curriculum Literature Connections 13 Developing Geometry Concepts Developing Geometric Thinking Shapes and Properties Transformations Location Visualization Literature Connections 14 Exploring Measurement Concepts Foundations of Measuring Angles Area Volume and Capacity Literature Connections 15 Working with Data and Doing Statistics What Does It Mean to Do Statistics? Formulating Questions Collecting Data Analyzing Data: Graphs Analyzing Data: Measures of Center and Variability Interpreting Results Literature Connections 16 Investigating Concepts of Probability Introducing Probability Theoretical Probability and Experiments Sample Spaces and the Probability of Compound Events Simulations Common Misconceptions about Probability Literature ConnectionsAppendix A Common Core State Standards: Standards for Mathematical PracticeAppendix B Common Core State Standards: Grades 6-8 Critical Content Areas and OverviewsAppendix C Mathematics Teaching Practices: NCTM Principles to Actions (2014) Appendix D Activities at a Glance: Volume III Appendix E Guide to Blackline Masters References Index

About the Author

The late John A. Van de Walle was a professor emeritus at Virginia Commonwealth University. He was a mathematics education consultant who regularly gave professional development workshops for K-8 teachers in the United States and Canada. He visited and taught in elementary school classrooms and worked with teachers to implement student-centered math lessons. He co-authored the Scott Foresman-Addison Wesley Mathematics K-6 series and contributed to the Pearson School mathematics program, enVisionMATH. In addition, he wrote numerous chapters and articles for the National Council of Teachers of Mathematics (NCTM) books and journals and was very active in NCTM, including serving on the Board of Directors, as the chair of the Educational Materials Committee, and as a frequent speaker at national and regional meetings.


LouAnn H. Lovin is a professor of mathematics education at James Madison University (Virginia). She co-authored the first edition of the Teaching Student - Centered Mathematics Professional Development Series with John A. Van de Walle as well as Teaching Mathematics Meaningfully: Solutions for Reaching Struggling Learners, 2nd Edition with David Allsopp and Sarah Vaningen. LouAnn taught mathematics to middle and high school students before transitioning to pre-K-grade 8. For almost twenty years, she has worked in pre-K through grade 8 classrooms and engaged with teachers in professional development as they implement a studentcentered approach to teaching mathematics. She has published articles in Teaching Children Mathematics, Mathematics Teaching in the Middle School, and Teaching Exceptional Children and has served on NCTM's Educational Materials Committee. LouAnn's research on teachers' mathematical knowledge for teaching has focused most recently on the developmental nature of prospective teachers' fraction knowledge.
Karen S. Karp is at the School of Education at Johns Hopkins University-Baltimore, MD. Previously, she was a professor of mathematics education at the University of Louisville for more than twenty years. Prior to entering the field of teacher education she was an elementary school teacher in New York. She is also co-author of Elementary and Middle School Mathematics: Teaching Developmentally, Developing Essential Understanding of Addition and Subtraction for Teaching Mathematics in Pre-K-Grade 2, and numerous book chapters and articles. She is a former member of the Board of Directors of NCTM and a former president of the Association of Mathematics Teacher Educators (AMTE). She continues to work in classrooms to support teachers of students with disabilities in their mathematics instruction.
Jennifer M. Bay - Williams is a professor of mathematics education at the University of Louisville (Kentucky). Jennifer has published many articles on teaching and learning in NCTM journals. She has also coauthored numerous books, including Mathematics Coaching: Resources and Tools for Coaches and Leaders, K-12; Developing Essential Understanding of Addition and Subtraction for Teaching Mathematics in Pre-K-Grade 2; Math and Literature: Grades 6-8; Math and Nonfiction: Grades 6-8; and Navigating through Connections in Grades 6-8. Jennifer taught elementary, middle, and high school in Missouri and in Peru, and continues to work in classrooms at all levels with students and with teachers. Jennifer served as member of Board of Directors for TODOS: Equity for All, as president of AMTE, and as editor for the 2012 NCTM Yearbook.

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