Figuring Out Fluency Ten Foundations For Reasoning Strategies With Whole Numbers
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Figuring Out Fluency--Ten Foundations for Reasoning Strategies With Whole Numbers
Because fluency practice is not a worksheet. Fluency in mathematics is more than basic facts or using algorithms. It is not about recall or speed. Real fluency is about choosing strategies that are efficient, flexible, lead to accurate solutions, and are appropriate for the given situation. Developing fluency is a matter of equity and access for all learners. The landmark book Figuring Out Fluency in Mathematics Teaching and Learning offered educators the inspiration to develop a deeper understanding of procedural fluency. It explained the seven Significant Strategies for fluency and offered a plethora of pragmatic tools for shifting classrooms toward a greater fluency approach. However, in order to become truly adept with these strategies, children must first have certain underlying foundational concepts and skills in place. Figuring Out Fluency-Ten Underlying Foundations for Reasoning Strategies with Whole Numbers explores the ideas that are essential to reasoning: Number Relationships; Subitizing and Decomposing; Distance to 10, 100, and 1,000; Counting and Skip-Counting; Properties of Addition and Its Inverse Relationship with Subtraction; Properties of Multiplication and Its Inverse Relationship with Division; Multiplying by 10s and 100s; Multiples and Factors; Doubling and Halving; and Computational Estimation. With this book, elementary teachers can Help children develop these foundational understandings, critical to reasoning and number sense. Leverage over 100 classroom-ready routines, centers, and games to develop these concepts both in first instruction, practice, and intervention. Download all of the needed support tools, game boards, and other resources from the companion website for immediate implementation Develop each and every students’ knowledge and power to become skilled and confident mathematical thinkers and doers.
Developing Mathematical Reasoning
Math is not rote-memorizable. Math is not random-guessable. Math is figure-out-able. Author Pam Harris argues that teaching real math—math that is free of distortions—will reach more students more effectively and result in deeper understanding and longer retention. This book is about teaching undistorted math using the kinds of mental reasoning that mathematicians do. Memorization tricks and algorithms meant to make math "easier" are full of traps that sacrifice long-term student growth for short-lived gains. Students and teachers alike have been led to believe that they’ve learned more and more math, but in reality their brains never get any stronger. Using these tricks may make facts easier to memorize in isolation, but that very disconnect distorts the reality of math. In her landmark book Developing Mathematical Reasoning: Avoiding the Trap of Algorithms, Pam emphasizes the importance of teaching students increasingly sophisticated mathematical reasoning and understanding underlying concepts rather than relying on a set rule for solving problems. Now, in this first companion volume, Developing Mathematical Reasoning: The Strategies, Models, and Lessons to Teach the Big Ideas in Grades K-2, she demonstrates how counting and additive strategies serve as the foundation for creating efficient, accurate, and flexible thinkers. Everyone is capable of understanding and doing real math. This book: Gives step-by-step guidance on how to teach the strategies, models, and big ideas that foster confidence and long-term success, preparing students for increasingly complex mathematical challenges Offers the "what to do" to teach counting, addition, and subtraction in ways that promote reasoning over rote memorization Provides practical tools such as problem strings, models, classroom routines, and discussion questions designed to implement reasoning-based practices Includes supporting resources for creating a classroom culture where students see math as figure-out-able and gain confidence as mathematical thinkers By addressing common misconceptions about math and providing practical strategies for teaching real math, this book shows that everyone can use the mathematical relationships they already know to reason about new relationships. In other words, everyone can math-even the very youngest students!
The Well-Rounded Math Student
Integrate a holistic approach to mathematics success with essential personal and social skills Teaching math is more than just numbers. It’s about shaping future-ready students who are not only academically strong but thrive socially and emotionally. Research shows that learning both intrapersonal and interpersonal skills helps students academically, and teachers play a crucial role in providing social-emotional support. The Well-Rounded Math Student helps mathematics teachers in Grades K-12 foster both their students′ academic prowess and their social and emotional development. Through the lens of the Standards for Mathematical Practice, the book emphasizes the importance of intentionally teaching and promoting intrapersonal and interpersonal skills, or "Next Generation" skills, alongside mathematical concepts. The authors provide step-by-step guidance on how small adjustments in lesson planning can have a profound impact on students′ growth. Providing teachers with a new lens to leverage in their planning as well as concrete ways to use their mathematics lessons to explicitly teach and reinforce social and emotional competencies, this book: Holds a strengths-based mindset and approach—for both teachers and students Highlights the importance of the science and the art of teaching to enhance social development, human connection, classroom management, and community within classrooms Stresses that the overarching goal of education is to help students become responsible adults who are ready for their future Includes a lesson planning guide, competency builder activities, vignettes of enhanced lessons across grade bands, reflection questions, and suggestions for taking action The Well-Rounded Math Student bridges critical intrapersonal and interpersonal elements to help educators create an environment where students excel in math and develop the life skills they’ll carry forever.