Math Teaching in Practice Series – serie

What mathematics truly matters for student success in middle and high school? Can we really declutter the content while accomplishing more?Too often, secondary mathematics instruction is cluttered with disconnected procedures, jargon, and "drill-and-kill" computational practice. This approach hands students a huge pile of tiny puzzle pieces where students never build or even see the picture of the puzzle on the box, leading to confusion and fragile thinking that unravels the moment a memorized formula is forgotten. This book, co-published with the National Council of Teachers of Mathematics, draws upon mathematics education research and offers an alternative that prioritizes fundamental understandings.Drawing on over a century of combined experiences, including an NSF-funded project involving over 300 educators, this book identifies five fundamental understandings that serve as a bedrock for student thinking in grades 6–12. By centering on these core ideas, teachers can reduce clutter in both content and student thinking by elevating sense-making and meaning. The authors provide practical examples and show how unleashing student thinking pays off in amazing ways.This book guides teachers and instructional coaches to reimagine the mathematics they teach and to bring it to life in the classroom. The five fundamental understandings act as big puzzle pieces that support students to accomplish bigger things with mathematics. Whether you are a veteran educator or a preservice teacher, this book helps create a robust, mathematical environment in which every student can experience the joy of true sense-making.Book Features:Five Fundamental Understandings: Identifies essential mathematical ideas—including measurement, comparisons, proportional relationships, equivalence, and graphical representations—to help teachers prioritize what matters most for student success.What Really Matters: Describes how the fundamental understandings unleash student thinking.The Math Attic: Recommends the mathematical clutter that can (and should) be de-prioritized in light of the five understandings.High-Profile Expertise: Authored by a team of experts and award-winning educators.

What mathematics truly matters for student success in middle and high school? Can we really declutter the content while accomplishing more?Too often, secondary mathematics instruction is cluttered with disconnected procedures, jargon, and "drill-and-kill" computational practice. This approach hands students a huge pile of tiny puzzle pieces where students never build or even see the picture of the puzzle on the box, leading to confusion and fragile thinking that unravels the moment a memorized formula is forgotten. This book, co-published with the National Council of Teachers of Mathematics, draws upon mathematics education research and offers an alternative that prioritizes fundamental understandings.Drawing on over a century of combined experiences, including an NSF-funded project involving over 300 educators, this book identifies five fundamental understandings that serve as a bedrock for student thinking in grades 6–12. By centering on these core ideas, teachers can reduce clutter in both content and student thinking by elevating sense-making and meaning. The authors provide practical examples and show how unleashing student thinking pays off in amazing ways.This book guides teachers and instructional coaches to reimagine the mathematics they teach and to bring it to life in the classroom. The five fundamental understandings act as big puzzle pieces that support students to accomplish bigger things with mathematics. Whether you are a veteran educator or a preservice teacher, this book helps create a robust, mathematical environment in which every student can experience the joy of true sense-making.Book Features:Five Fundamental Understandings: Identifies essential mathematical ideas—including measurement, comparisons, proportional relationships, equivalence, and graphical representations—to help teachers prioritize what matters most for student success.What Really Matters: Describes how the fundamental understandings unleash student thinking.The Math Attic: Recommends the mathematical clutter that can (and should) be de-prioritized in light of the five understandings.High-Profile Expertise: Authored by a team of experts and award-winning educators.

How can teachers move beyond surface-level coverage of math standards to focus on what truly matters for student understanding?This book, co-published with the National Council of Teachers of Mathematics (NCTM), provides a transformative approach to K–8 mathematics instruction. Rather than treating standards as a fixed checklist of skills to be executed, internationally recognized expert Marian Small demonstrates how to treat them as professional texts that require thoughtful interpretation. By uncovering the "big ideas" behind the standards, educators can move beyond surface-level coverage to foster deeper mathematical thinking and lasting student understanding.Drawing on decades of classroom experience, this resource helps teachers translate teacher-facing standards into student-centered learning experiences. Small introduces a framework that shifts the focus from micro-level procedures to macro-level concepts, ensuring that students prioritize reasoning and connections over rote alignment. With examples spanning across grades K–8, the book illustrates how the same standard can be interpreted in multiple ways to shape how students learn and demonstrate their knowledge.This guide also reimagines the role of evaluation through asset-driven assessment. By framing tasks and questions that emphasize what students do know and can explain, teachers can provide more meaningful opportunities for student voice in the math classroom. Whether you are a classroom teacher, coach, or instructional leader, this book offers the tools necessary to design powerful instruction that surfaces conceptual understanding for every learner.Key Features:A Proven Framework: Learn a systematic way to look at math standards in terms of broader educational goals and the foundational ideas upon which they are based.Asset-Driven Assessment: Gain strategies for designing assessments that prioritize student voice and focus on what students understand and can explain.Conceptual Task Design: Access practical guidance on creating questions and tasks that surface deep reasoning rather than just procedural fluency.K–8 Grade Span Support: Explore numerous examples across many domains and grade levels that show how big ideas develop as students progress.Alignment With Mathematical Practices: Discover how to naturally attend to mathematical practices while teaching core content standards.

How can teachers move beyond surface-level coverage of math standards to focus on what truly matters for student understanding?This book, co-published with the National Council of Teachers of Mathematics (NCTM), provides a transformative approach to K–8 mathematics instruction. Rather than treating standards as a fixed checklist of skills to be executed, internationally recognized expert Marian Small demonstrates how to treat them as professional texts that require thoughtful interpretation. By uncovering the "big ideas" behind the standards, educators can move beyond surface-level coverage to foster deeper mathematical thinking and lasting student understanding.Drawing on decades of classroom experience, this resource helps teachers translate teacher-facing standards into student-centered learning experiences. Small introduces a framework that shifts the focus from micro-level procedures to macro-level concepts, ensuring that students prioritize reasoning and connections over rote alignment. With examples spanning across grades K–8, the book illustrates how the same standard can be interpreted in multiple ways to shape how students learn and demonstrate their knowledge.This guide also reimagines the role of evaluation through asset-driven assessment. By framing tasks and questions that emphasize what students do know and can explain, teachers can provide more meaningful opportunities for student voice in the math classroom. Whether you are a classroom teacher, coach, or instructional leader, this book offers the tools necessary to design powerful instruction that surfaces conceptual understanding for every learner.Key Features:A Proven Framework: Learn a systematic way to look at math standards in terms of broader educational goals and the foundational ideas upon which they are based.Asset-Driven Assessment: Gain strategies for designing assessments that prioritize student voice and focus on what students understand and can explain.Conceptual Task Design: Access practical guidance on creating questions and tasks that surface deep reasoning rather than just procedural fluency.K–8 Grade Span Support: Explore numerous examples across many domains and grade levels that show how big ideas develop as students progress.Alignment With Mathematical Practices: Discover how to naturally attend to mathematical practices while teaching core content standards.

How can teachers help students overcome persistent struggles with fractions? Fractions Unlocked, co-published with the National Council of Teachers of Mathematics, provides a research-based answer by shifting instruction away from traditional part-whole models toward a measurement-based approach grounded in unit fractions. Fractions represent one of the most persistent challenges in mathematics education. Despite their critical importance as a foundation for algebra and advanced mathematics, many students struggle to develop a meaningful understanding of fraction concepts and operations. Fractions Unlocked offers teachers a transformative approach to instruction. Drawing on decades of research and classroom experience, the authors show how understanding fractions as numbers with magnitude can transform student learning. This book provides a clear roadmap for instruction, prioritizing conceptual meaning over rote memorization to help students build a deep, connected understanding of how fractions work. This essential resource equips elementary and middle school teachers and coaches with instructional strategies and research-based activities to put these ideas into immediate practice. Book Features: Analysis of student work and "Spotlights on Student Thinking" to help teachers interpret and build on student strategies and explanations.In-depth development of the number line as a central tool for understanding fractions as numbers with magnitude.Purposeful use of representations (fraction strips, drawings, number lines, contextual situations, and symbolic notation) to make fraction concepts, relationships, and operations visible.Tools, tasks, and discussion prompts, along with instructional sequences, that support implementation of meaningful and connected fraction instruction.Teaching takeaways that synthesize the key ideas of each chapter.