Teaching Student-Centered Mathematics

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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

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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