Modeling Mathematical Ideas

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Chapter 1: Developing Strategic Competence through Modeling Mathematical Ideas 1.1 Developing Strategic Competence through Modeling Mathematical Ideas 1.2 Promoting Math Proficiency and Mathematical Practices 1.3 Problem Solving and Mathematical Modeling in the Elementary and Middle Grades 1.4 Multiple Representations and Strategies as Tools to Cultivate Visible Thinking in Mathematics 1.5 Importance of Understanding the Vertical Learning Progression to Deepen Students' Mathematical Understanding 1.6 Technology Integration in Problem Solving 1.7 More Related Rich Problems to Explore Chapter 2: Setting Math Norms to Promote Math Reasoning and Modeling 2. 1 Developing Persistent Problem Solvers with a Productive Disposition towards Math 2.2 Unpacking the Mathematics for Deeper Conceptual Learning 2.3 Choosing Worthwhile Tasks through Cognitive Demand Analysis 2.4 Promoting the Core Teaching Practices through Research Lessons 2.5 Integration Technology and Connecting to the Learning Progression 2.6 Assessing Students Understanding through a Problem-based Task Chapter 3: Engaging in Mathematical Modeling in the Elementary and Middle Grades 3.1 Math Modeling in the Elementary and Middle Grades: What are the building blocks? 3.2 Mathematical Modeling through Unstructured Real-World Problems 3.3. Lesson Study Focus on the Mathematical Modeling: Traffic Jam 3.4 Promoting the 21st Century Skills 3.5 Technology Integration in Problem Posing and Problem Solving 3.6 A Related Rich Problem to Explore Chapter 4: Modeling Math Ideas with Numbers and Operations 4.1 Lesson Study Vignette: Prime and Composite Numbers 4.2 Visible Thinking in Math: Using Multiple Representations 4.3 Zooming in on the Learning Progression of Numbers and Operations 4.4 Teaching Strategies: Using Math Happenings 4.5 Connecting Procedural Fluency and Conceptual Understanding 4.6 Technology Integration in Problem Solving 4.7 More Related Rich Problems to Explore Chapter 5: Modeling Math Ideas with Patterns & Algebraic Reasoning 5.1 Lesson Study Vignette - Growing Staircase problem 5.2 Visible Thinking in Math: Using a Modeling Math Mat 5.3 Patterns and Algebra: Zooming in on the Learning Progressions 5.4 Teaching Strategies: Promoting the Algebraic Habits of Mind 5.5 Lesson Vignette: What Would You Choose? Analyzing Change in Number Patterns 5.6 Technology Integration in Problem Solving 5.7 More Related Rich Problems to Explore Chapter 6: Modeling Math Ideas with Equations and Inequalities 6.1 Lesson Study Vignette: Setting a Math Learning Agenda 6.2 Zooming in on the Learning Progressions for Algebra 6.3 Visible Thinking in Math: Naming, Sequencing and Connecting Math Strategies 6.4 Teaching Strategies: Using Misconceptions to Repair Understanding &Looking for Efficiency 6.5 Technology Integration in Problem Solving 6.6 More Related Rich Problems to Explore Chapter 7: Modeling Math Ideas with Fractions 7.1 Lesson Study Vignette: The Unusual Baker 7.2 Visible Thinking in Math: Assessing Student Learning through Classroom Artifacts 7.3 Zooming in on the Learning Progressions: Fractions 7.4 Implementing mathematical tasks that promote reasoning and problem solving 7.5 Teaching Strategies, Using Representations and Overcoming Common Misconception 7.6 Technology Integration in Problem Solving 7.7 More Related Rich Problems to Explore Chapter 8: Modeling Math Ideas with Fraction Computation 8.1 Lesson Study Vignette: Stuffed with Pizza- Adding fractions 8.2 Visible Learning in Math- Using Tools to Prove their Thinking 8.3 Learning Progression in Fraction Operations 8.4 Lesson Study Vignette: Share My Candy 8.5 Teaching Strategies: Strategy mapping on the board plan 8.6 Use of students' diversity of strategies as pedagogical content tools 8.7 Technology Integration in Problem Solving 8.8 More Related Rich Problems to Explore Chapter 9: Modeling Math Ideas with Ratio and Proportional Reasoning 9.1 Lesson Study Vignette: The Leaky Bathtub 9.2 Zooming in on the Learning Progressions on Proportional Reasoning 9.3 Visible Thinking in Math: Using Representational models for proportional reasoning 9.4 Lesson study vignette: The Cathedral Problem 9.5 Deepening Teacher Knowledge and their Strategic Competence 9.6 Promoting Reasoning to Rich tasks 9.7 Technology Integration in Problem Solving 9.8 More Related Rich Problems to Explore Chapter 10: Pulling it all Together: Strengthening Strategic Competence through Modeling Mathematics Ideas 10.1 Practice-based Activities to Focus on Models and Modeling within our Standards 10.2 Modeling Math with Tools and Representations 10.3 Understanding Conceptual and Interpretative Models of Math Ideas 10.4 Modeling Math through Problem Solving and Problem Posing Tasks 10.5 Mathematical Modeling through Unstructured Real-World Problems 10.6 Strengthening Strategic Competence for Modeling Mathematical Ideas Appendix References

Jennifer Suh is associate professor in the Graduate School of Education, College of Education and Human Development, George Mason University. Dr. Suh teaches mathematics methods courses in the Elementary Education Program and mathematics leadership courses for the Mathematics Specialist Masters and PH.D Programs. She directs the Center for Outreach in Mathematics Professional Learning and Educational Technology, COMPLETE, a joint center between the College of Education and the College of Science. Her research focuses on mathematics teacher development while using Lesson Study to develop pedagogical mathematics knowledge across the continuum from pre-service teachers to mathematics teacher leaders; Children's development of mathematical meaning and models by building understanding and representational fluency; Problem-based Learning Environments to promote equitable access to 21st century skills: Creativity, Critical Thinking, Communication and Collaboration for diverse student populations in STEM disciplines. Padmanabhan Seshaiyer is professor of mathematical sciences and serves as the Director of the STEM Accelerator Program and the Center for Outreach in Mathematics Professional Learning and Educational Technology (COMPLETE) at George Mason University in Fairfax, Virginia. During the last decade, he has initiated and directed a variety of educational programs including graduate and undergraduate research, K-12 outreach, teacher professional development, and enrichment programs to foster the interest of students and teachers in mathematical modeling and STEM at all levels. He is also actively involved in multiple global initiatives and training programs that engage students, teachers and faculty to develop innovative STEM-based solutions to real-world problems.

Modeling mathematical ideas offers teachers a practical guide to
leading third- through eighth-grade students to develop strategic
competence and to use models to solve cognitively demanding
tasks.... A few main strengths of the book are the insights
provided to readers about the implementation of the tasks and the
inclusion of a variety of models that students use when solving the
tasks.... The content of this book will help educators become
skillful teachers of modelers and of the mathematical content
associated with each task. The book is a good choice for teachers
looking to implement modeling into their classroom. This is also a
great resource for a preservice math methods course. * Teaching
Children Mathematics *

The authors of Modeling Mathematical Ideas deconstruct the concepts
of models and modeling, both from a mathematical perspective and a
pedagogical perspective. Through a variety of examples from real
research lesson experiences, called Lesson Study Vignettes, the
authors bring to life the concepts and principles of models and
modeling. Pre-service and practicing teachers will find the text is
filled with multiple representations and technology examples, rich
illustrations of students' work, in-depth modeling exemplars, and a
variety of engaging and real world problems to pursue. A must-read
for any instructor who wants to become an expert on models and
modeling! -- Patricia S. Moyer-Packenham, PhD, Professor,
Mathematics Education, Director, Mathematics Education and
Leadership Programs, Utah State University

This book is a great resource for mathematics teachers and
professional development providers. The concepts are clearly
presented using both classic and novel real-world problems to
highlight the process of mathematical modeling through problem
solving. The lesson study vignettes and student-work samples are
great ways to generate discussions among teachers because they
illustrate how teachers and students think about the concepts and
engage in classrooms. I will definitely use this book in my
mathematics methods courses and workshops! -- Dorothy Y. White,
PhD, Associate Professor of Mathematics Education, University of
Georgia

Modeling Mathematical Ideas provides strong support for how to help
students develop strategic competence in K-8 mathematics. The
lesson study vignettes, student work examples, discussion of the
mathematics, suggestions for student solution sharing, and the many
rich tasks makes this a pragmatic resource for individual teachers,
as well as groups of teachers engaging in their own lesson studies!
-- Jennifer M. Bay-Williams, PhD, University of Louisville

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