Using straightforward, practical language, early math experts Douglas Clements and Julie Sarama show how learning trajectories help teachers understand children's level of mathematical understanding and lead to better teaching. By focusing on the inherent delight and curiosity behind young children's mathematical reasoning, learning trajectories ultimately make teaching more joyous: helping teachers understand the varying levels of knowledge exhibited by individual students, it allows them to better meet the learning needs of all children.

Whether physical or virtual, commercial or home-made, manipulatives are a powerful learning tool to help students discover and represent mathematical concepts. Mastering Math Manipulatives includes everything you need to integrate math manipulatives--both concrete and virtual--into math learning.

Classroom Ready-Rich Math Tasks for Grades 2-3 details research- and standards-aligned, high-cognitive-demand tasks that will have your students doing deep-problem-based learning. These ready-to-implement, engaging tasks connect skills, concepts and practices, while encouraging students to reason, problem-solve, discuss, explore multiple solution pathways, connect multiple representations, and justify their thinking. They help students monitor their own thinking and connect the mathematics they know to new situations.

Project-Based Learning in the Math Classroom (Grades 3-5) explains how to keep inquiry at the heart of mathematics teaching. This book: Outlines basic teaching strategies, such as questioning and exploration of concepts. Provides advanced strategies for teachers who are already implementing inquiry-based methods. Includes practical advice about strategies the authors have used in their own classrooms.

Teaching math in a student-centered way changes the role of the teacher from one who traditionally "delivers knowledge" to one who fosters thinking. Most importantly, we must ensure our practice gives each and every student the opportunity to learn, grow, and achieve at high levels, while providing opportunities to develop their agency and authority in the classroom which results in a positive math identity.

Responding to the linguistic and cultural diversity of the U.S. K-12 student population and an increasing emphasis on STEM, this book offers a model for professional development that engages teachers in transformative action research projects and explicitly links literacy to mathematics and science curriculum through sociocultural principles.

This book, inspired by the Julia Robinson Mathematics Festival, aims to engage students in mathematical discovery through fun and approachable problems that reveal deeper mathematical ideas. Each chapter starts with a gentle on-ramp, such as a game or puzzle requiring no more than simple arithmetic or intuitive concepts of symmetry. Follow-up problems and activities require intuitive logic and reveal more sophisticated notions of strategy and algorithms.

This book aims to advance ongoing debates in the field of mathematics and mathematics education regarding conceptions of argumentation, justification, and proof and the consequences for research and practice when applying particular conceptions of each construct. Through analyses of classroom practice across grade levels using different lenses - particular conceptions of argumentation, justification, and proof - researchers consider the implications of how each conception shapes empirical outcomes.

Sandy Atkins is a popular math consultant who works with schools across the country. Builds mathematical language and provides examples for developing conceptual depth of math key ideas. Emphasis on problem solving, attending to precision, and making and critiquing arguments that supports the Common Core State Standards Mathematical Practices New edition contains applications for digital instruction and new connections for English language learners (ELLs).

Second edition contains new sections on kidwatching, planning, and questioning, and a new study guide. Offers practical templates and anchor charts you can use immediately.

Based on the bestselling Guided Math in Action, this practical book offers 16 lessons, taught in a round of 3-concrete, pictorial and abstract. The lessons are based on the priority standards and cover fluency, word problems, fractions and place value.

Giving students opportunities to read like mathematicians as they explore content has the potential to move their thinking and understandings in monumental ways. Each chapter presented in this volume provides readers with approaches and activities for pairing a young adult novel with specific mathematics concepts.

Learn how to differentiate math instruction to help all students be successful learners in the secondary mathematics classroom. Featuring 89 new questions, this revised edition uses two powerful and universally applicable strategies-Open Questions and Parallel Tasks-to help teachers differentiate instruction with less difficulty and greater success.

Contains easy-to-implement activities for fourth grade guided math groups.

Discover new and exciting ways to teach STEM content through the arts in your early childhood program with this innovative and comprehensive guidebook. Chapters feature playful activities divided by age band that bridge early academic learning and social, emotional, physical, and mental development with active engagement in the arts.

In the face of complex local and global problems, there is a critical need to prepare PK-12 students to be innovative, resilient problem-solvers and well-equipped STEM-literate citizens. With focus upon integrated content, college and career readiness, authentic problems, and action-oriented pedagogies, integrative STEM education provides a promising approach to address this challenge.

Eco-Mathematics Education strives to show how everyone can experience the embedded connection between mathematics and the natural world. The authors' sincere hope is that by doing so, we can radically change the way we come to understand mathematics, as well as humanity's place in the ecosystem. The book hopes to accomplish this by providing in-depth lesson plans and resources for educators and anyone interested in teaching and learning mathematics through an ecological aesthetic perspective.

A follow-up to the popular book Design, Make, Play (2013), this volume combines new research, innovative case studies, and practical advice from the New York Hall of Science (NYSCI) to define and illustrate a vision for creative and immersive learning, focusing on STEM learning experiences that are truly equitable and inclusive, and that foster learners' agency.

Design effective, learner-driven math interventions with this accessible and thought-provoking guidebook. Learn how to set up instruction to promote participation and understanding, plan purposeful, targeted tasks, develop student thinking, and create tools to assess student work in a way that measures learning, not just performance.

The selected and adapted set of lessons incorporated in this series were chosen from NCTM's Navigations series, with particular emphasis given to incorporating the Mathematics Teaching Practices in NCTM's Principles to Actions: Ensuring Mathematical Success for All.

This book explores what it means to teach modeling. In part I, the authors discuss mathematical modeling broadly and allow you to explore the student practices and perspectives involved, how modeling can empower students, and classroom communities that support modeling. In part II, the authors launch you on your journey of becoming a teacher of modeling by illustrating features of modeling that are evident in the classrooms of teacher who engage their students in modeling and by sharing specific strategies for making modeling a part of your own classroom practices. In part III, they examine the complementary perspectives of mathematical and statistical models, the role of modeling in the secondary mathematics curriculum, and the role of technology in supporting modeling.

This book explores what it means to teach modeling. In part I, the authors discuss mathematical modeling broadly and allow you to explore the student practices and perspectives involved, how modeling can empower students, and classroom communities that support modeling. In part II, the authors launch you on your journey of becoming a teacher of modeling by illustrating features of modeling that are evident in the classrooms of teacher who engage their students in modeling and by sharing specific strategies for making modeling a part of your own classroom practices. In part III, the authors share wisdom from other teachers who have engaged in this journey and invite you to join in the modeling community.

There are many topics within the scope of the secondary school mathematics curriculum that are clearly of a motivational sort, and because of lack of time they are usually not included in the teaching process. This book provides the teacher 125 individual units - ranging from grades 7 through 12 - that can be used to enhance the mathematics curriculum.

Designed for all teachers, this book provides a wealth of materials and resources to support the needs of learners, aged 6 to 14 years, who have difficulty with maths and number. Packed full with 220 activities and 55 games, the author provides you with a complete toolkit to enable you to understand dyscalculia and implement practical and innovative strategies to use in the classroom or at home.

"This timely volume brings together a range of international scholars to analyse cultural, political, and individual factors which contribute to the continued global issue of female underrepresentation in STEM study and careers."

"Guided Math Lessons in First Grade provides detailed lessons to help you bring guided math groups to life. Based on the bestselling Guided Math in Action, this practical book offers 16 lessons, taught in a round of 3-concrete, pictorial and abstract. The lessons are based on the priority standards and cover fluency, word problems, operations and algebraic thinking, and place value."

"Guided Math Lessons in Second Grade provides detailed lessons to help you bring guided math groups to life. Based on the bestselling Guided Math in Action, this practical book offers 16 lessons, taught in a round of 3-concrete, pictorial and abstract. The lessons are based on the priority standards and cover fluency, word problems, operations and algebraic thinking, and place value."

This book explores the key concepts of middle school mathematics such as fractions, negative numbers, arithmetical operations, variables, the coordinate plane, and measurement formulas. It also highlights the rarely examined notions of the tree of mathematics and language of mathematics. The practical content knowledge is scaffolded using the history of the concepts in mathematics of various cultures around the world.

Geometry, of all the branches of mathematics, is the one that is most easily visualized by making something. However, it is all too easy to reduce it to reams of formulas to memorize and proofs to replicate. This book aims to take geometry back to its practical roots with 3D printed models and puzzles as well as demonstrations with household objects like flashlights and paper towel tubes.

Mathematics for Social Justice: Focusing on Quantitative Reasoning and Statistics offers a collection of resources for mathematics faculty interested in incorporating questions of social justice into their classrooms. The book comprises seventeen classroom-tested modules featuring ready-to-use activities and investigations for college mathematics and statistics courses.

Math Hour Olympiads is a non-standard method of training middle- and high-school students interested in mathematics where students spend several hours thinking about a few difficult and unusual problems. When a student solves a problem, the solution is presented orally to a pair of friendly judges. Discussing the solutions with the judges creates a personal and engaging mathematical experience for the students and introduces them to the true nature of mathematical proof and problem solving.

Numeracy for All Learnersis a wide-ranging overview of how Math Recovery® theory, pedagogy, and tools can be applied meaningfully to special education to support learners with a wide range of educational needs.

This book brings together research from mathematics education and instructional design to describe the development and impact of online environments on prospective and practicing teachers' learning to teach mathematics.

Whether you are a teacher looking for ways to strengthen the math learning in your early childhood classroom, an educator in a community of practice who wants to learn more about teaching math in developmentally appropriate ways, or a teacher-educator who wants to offer students an easy-to-use reference and guide for helping young children develop their math competencies and skills, this text will help you make math learning a fun and worthwhile activity in your setting.

This groundbreaking book looks at the development of mathematical thinking in infants and toddlers, with an emphasis on the earliest stage, from zero to three, when mathematical thinking and problem solving first emerge as natural instincts.

Bridging a gap in the literature by offering a comprehensive look at how STEM teacher education programs evolve over time, this book explores teachHOUSTON, a designer teacher education program created to respond to the lack of adequately prepared STEM teachers in Houston and the emerging urban school districts that surround it.

This book, with nine carefully described model projects, gives detailed examples of how much math can be taught as part of engaging projects. Created with the elementary school grades in mind, these mathematics-focused units are classroom-tested and address the Common Core State Standards for Mathematics.

The abundance of data on the failure of Black students in mathematics has contributed to mainstream beliefs of a racial hierarchy of mathematics ability in America. This perception has not only shaped attitudes and behaviors of educational practitioners, but it has contributed to the alienation of many students from the community of 'doers of mathematics.'

"Learn how to help K-8 students who struggle in math. Now in its second edition, this book provides a variety of clear, practical strategies that can be implemented right away to boost student achievement."

This innovative STEAM guide will help general and special education teachers to increase effective instruction with adolescents (grades 5-10). The authors show teachers how to link STEM concepts with popular fiction and film selections as a catalyst to launch student interactions, discussions, projects, and investigations. This approach will promote problem solving and reasoning skills by initiating the scientific process, rather than simply presenting established facts.

When distance learning is the "new normal," educators know that rich remote math teaching involves more than direct instruction and endless practice problems. Teaching Math at a Distance offers the support, clarity, and inspiration teachers need to provide all students with deep learning and academic growth.

Active engagement is the key to learning. You want your students doing something that stimulates them to ask questions and creates a need to know. Teaching Mathematics Through Games presents a variety of classroom-tested exercises and activities that provoke the active learning and curiosity that you hope to promote.

Using Mathematics to Understand the World presents a theory about the development of children's quantitative reasoning and reveals why and how teaching about quantitative reasoning can be used to improve children's mathematical attainment in school. It describes how learning about the analytical meaning of numbers is established as part of mathematics at school but quantitative reasoning is emphasized less even though it is increasingly acclaimed as essential for thinking mathematically and for using mathematics to understand the world.

Getting the right answers in maths is only half the problem. Understanding why what you're doing works is the part that often stumps students and teachers alike. The essential guide for mathematics teachers and those training to teach, Yes, but why? answers all your questions, and sheds light on the hidden connections between everything in mathematics at school.

Everything a child does has mathematical value--these words are at the heart of this completely revised and updated third edition of The Young Child and Mathematics. Grounded in current research, this classic book focuses on how teachers working with children ages 3 to 6 can find and build on the math inherent in children's ideas in ways that are playful and intentional.

"This book contains a carefully selected and adapted set of lessons from NCTM's Navigations series, with a special emphasis on incorporating the Effective Mathematics Teaching Practices in NCTM's Principles to Actions. Teachers of 3-5 students can use these activities to engage their students in exploring, thinking, connecting, discussing, justifying, and advancing in their mathematical understanding and confidence."

Drawing on narratives from hundreds of Black, Latinx, and Indigenous individuals, Ebony Omotola McGee examines the experiences of underrepresented racially minoritized students and faculty members who have succeeded in STEM. Based on this extensive research, McGee advocates for structural and institutional changes to address racial discrimination, stereotyping, and hostile environments in an effort to make the field more inclusive.

This book examines the current state of the field of mathematics pre-service teacher education through the theme of borders. Borders are ubiquitous; they can be used to define, classify, organize, make sense of, and/or group. Chapters include the following topics: explorations of mathematics across topics (e.g., geometry, algebra, probability) and with other disciplines (e.g., science, the arts, social sciences); challenging gender, cultural, and racial borders; exploring the structure and curriculum of teacher education programs; spaces inhabited by teacher education programs (e.g., university, community); and international collaborations and programs to promote cross-cultural sharing and learning.

"Catalyzing Change in Middle School Mathematics calls for all stakeholders involved in the teaching of mathematics to middle school students to critically examine the following: The identity and agency of students in middle school by being developmentally responsive while also creating and supporting a learning environment that takes into account each and every student's unique background, experience, cultural perspectives, traditions, and knowledge."

Chasing Aces in Middle Grade Math proves that math can be fun and demonstrates how useful it is throughout our lives. Using the game of disc golf, teachers will discover new ways to incorporate math problems in, and out, of the classroom.Students will be introduced to math, science, and technology concepts that will require them to think outside the box.

"Benefits of early learning in science and math include the following: (a) It leads to social-emotional development and fewer challenging behaviors; (b) it supports the development of a mind-set that includes curiosity, communication, persistence, and problem solving; (c) it contributes to gains in other subjects by supporting literacy and language development and better reading comprehension and writing skills; and (d) it includes subjects that can engage students from varying backgrounds, including English language learners."

Sometimes it is believed that students aren't smart enough to master mathematics or that mathematics is just too difficult for all but the chosen few. This book offers an alternative explanation: Students' difficulties in mathematics can best be understood and explained social scientifically. That is, Learning Theories, Agents of Socialization, and more generally, cultural and social milieu, are relevant in trying to understand individuals' ideas about mathematics.

Engage students in mathematics using growth mindset techniques The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the kindergarten-grade level through visualization, play, and investigation.

"Math educators always seek great problems and tasks for the classroom, and this collection contains many that could be used in various grades. By using this book, the reader will understand ways that great problems can be used to encourage student participation and to promote powerful mathematical ideas. In addition, suggestions for how problems can be presented in the classroom will provide professional development to teachers in the form of effective routines for promoting problem solving."

"S3D: Fostering and Improving Small-Group, Student-to-Student Discourse specifically focuses on small-group discourse in the secondary mathematics classroom. This professional resource guides teachers through a two-phase process to enhance the student-to-student talk in small groups."

"Science education's two-fold challenge is clear: Schools need to (1) align their curricula with contemporary state standards and (2) meet the growing demand for STEM education. What's not as clear: how to meet the challenge if your school doesn't have the right instructional materials. STEM, Standards, and Strategies for High-Quality Units is designed to address both these needs.

"Activity Gems for the PK-2 Classroom is a collection of select tasks from the National Council of Teachers of Mathematics Navigations series that embody the research-informed, effective teaching practices described in Principles to Actions. The tasks illustrate how the selected activities provide opportunities for students to develop the mathematical understanding and proficiency that we value as goals for all students."

This book provides classroom activities for elementary and middle school based on National Assessment of Educational Progress project items.

The twenty-nine cases, written by teachers describing real situations and actual student thinking in their classrooms, provide the basis of each session's investigation of specific mathematical concepts and teaching strategies. Reading and discussing the cases under the guidance of the facilitator actively engages seminar participants in their own learning enterprise.