This is by far the best mathematics teaching resource book that has been written in many years. It is an easy read of only 115 pages with many practical classroom and teacher examples. The best part is it was NOT written by a single author from a single point of view. It was written by multiple authors who are all recognized as some of the best math education experts in the field right now.

To get so many math education experts to agree on anything tells you the power of this book. Best of all it is research based. The last 20 pages of the book lists all the research that was used to write and justify what is said in the book! It can be downloaded from http://www.nctm.org for only $4.99.

Principles to Actions: Ensuring Mathematical Success for All offers guidance to teachers, specialists, coaches, administrators, policymakers, and parents:

Builds on the Principles articulated in Principles and Standards for School Mathematics to present six updated Guiding Principles for School Mathematics

Supports the first Guiding Principle, Teaching and Learning, with eight essential, research-based Mathematics Teaching Practices

Details the five remaining Principles—the Essential Elements that support Teaching and Learning as embodied in the Mathematics Teaching Practices

Identifies obstacles and unproductive and productive beliefs that all stakeholders must recognize, as well as the teacher and student actions that characterize effective teaching and learning aligned with the Mathematics Teaching Practices

## #2 - Taking Action: Implementing Effective Mathematics Teaching Practices in Grades 9-12

by Melissa Boston, Frederick Dillon, Margaret Smith, and Stephen Miller

Are you ready to take your teaching to the next level? Taking Action: Implementing Effective Mathematics Teaching Practices in Grades 9–12 offers a coherent set of professional learning experiences designed to foster teachers’ understanding of the effective mathematics teaching practices and their ability to apply those practices in their own classrooms. The book examines in depth what each teaching practice would look like in a high school classroom, with narrative cases, classroom videos, and real student work, presenting a rich array of experiences that bring the practices to life.

Chapters are sequenced to scaffold teachers’ exploration of the effective mathematics teaching practices and furnish activities and materials for hands-on learning experiences around each individual teaching practice and across the set of the eight effective practices as a whole. Specific examples of each practice are presented in context, providing real-life instantiations of what the practice “looks” and “sounds” like in the classroom, with a careful analysis that links the practice to student learning and equity.

The reader is invited to personally engage in two types of activities that run throughout the book: Analyzing Teaching and Learning, in which tasks or situations are presented to the reader to consider, work out, and reflect on, and Taking Action in Your Classroom, in which concrete suggestions are provided for exploring specific teaching practices in the classroom. Tools, such as a lesson plan template, a task analysis guide, and five practices for orchestrating productive discussions are offered to assist teachers in applying the ideas discussed in the book to their own practices.

#### Other Great Books

by John Hattie, Douglas Fisher, Nancy Frey, Linda M. Gojak, Sara Delano Moore, William Mellman

Rich tasks, collaborative work, number talks, problem based learning, direct instruction…with so many possible approaches, how do we know which ones work the best? In Visible Learning for Mathematics, six acclaimed educators assert it’s not about which one―it’s about when―and show you how to design high impact instruction so all students demonstrate more than a year’s worth of mathematics learning for a year spent in school.

That’s a high bar, but with the amazing K 12 framework here, you choose the right approach at the right time, depending upon where learners are within three phases of learning: surface, deep, and transfer. This results in "visible" learning because the effect is tangible. The framework is forged out of current research in mathematics combined with John Hattie’s synthesis of more than 15 years of education research involving 300 million students.

Chapter by chapter, and equipped with video clips, planning tools, rubrics, and templates, you get the inside track on which instructional strategies to use at each phase of the learning cycle:

Surface learning phase: When―through carefully constructed experiences―students explore new concepts and make connections to procedural skills and vocabulary that give shape to developing conceptual understandings.

Deep learning phase: When―through the solving of rich high cognitive tasks and rigorous discussion―students make connections among conceptual ideas, form mathematical generalizations, and apply and practice procedural skills with fluency.

Transfer phase: When students can independently think through more complex mathematics, and can plan, investigate, and elaborate as they apply what they know to new mathematical situations.

To equip students for higher level mathematics learning, we have to be clear about where students are, where they need to go, and what it looks like when they get there. Visible Learning for Math brings about powerful, precision teaching for K 12 through intentionally designed guided, collaborative, and independent learning.

There are also these two books in the series. I have not read them but if there are even close to as good as the mathematics version, I am sure they are great:

Visible Learning for Literacy, Grades K-12: Implementing the Practices That Work Best to Accelerate Student Learning by Douglas Fisher, Nancy Frey, John Hattie

Visible Learning for Science, Grades K-12: What Works Best to Optimize Student Learning by John T. Almarode, Douglas Fisher, Nancy Frey, John Hattie

## #4 - Mathematical Mindsets: Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching by Jo Boaler

Mathematical Mindsets provides practical strategies and activities to help teachers and parents show all children, even those who are convinced that they are bad at math, that they can enjoy and succeed in math. Jo Boaler―Stanford researcher, professor of math education, and expert on math learning―has studied why students don't like math and often fail in math classes. She's followed thousands of students through middle and high schools to study how they learn and to find the most effective ways to unleash the math potential in all students.

There is a clear gap between what research has shown to work in teaching math and what happens in schools and at home. This book bridges that gap by turning research findings into practical activities and advice. Boaler translates Carol Dweck's concept of 'mindset' into math teaching and parenting strategies, showing how students can go from self-doubt to strong self-confidence, which is so important to math learning. Boaler reveals the steps that must be taken by schools and parents to improve math education for all. Mathematical Mindsets:

Explains how the brain processes mathematics learning

Reveals how to turn mistakes and struggles into valuable learning experiences

Provides examples of rich mathematical activities to replace rote learning

Explains ways to give students a positive math mindset

Gives examples of how assessment and grading policies need to change to support real understanding

Scores of students hate and fear math, so they end up leaving school without an understanding of basic mathematical concepts. Their evasion and departure hinders math-related pathways and STEM career opportunities. Research has shown very clear methods to change this phenomena, but the information has been confined to research journals―until now. Mathematical Mindsets provides a proven, practical roadmap to mathematics success for any student at any age.

by Margaret (Peg) S. Smith, Mary K. (Kay) Stein

Learn the 5 practices for facilitating effective inquiry-oriented classrooms

Anticipate what students will do—what strategies they will use—in solving a problem

Monitor their work as they approach the problem in class

Select students whose strategies are worth discussing in class

Sequence those students’ presentations to maximize their potential to increase students’ learning

Connect the strategies and ideas in a way that helps students understand the science learnedThis book presents and discusses an framework for orchestrating mathematically productive discussions that are rooted in student thinking.The 5 Practices framework identifies a set of instructional practices that will help teachers achieve high-demand learning objectives by using student work as the launching point for discussions in which important mathematical ideas are brought to the surface, contradictions are exposed, and understandings are developed or consolidated. By giving teachers a road map of things that they can do in advance and during whole-class discussions, these practices have the potential for helping teachers to more effectively orchestrate discussions that are responsive to both students and the discipline.

by Jennifer Cartier, Margaret Schwan Smith, Mary Kay Stein, Danielle Ross

Robust and effective classroom discussions are essential for providing students with opportunities to simultaneously engage in science practices while learning key science content. Using numerous examples and science learning tasks, the authors show how teachers can plan the lesson to encourage students to not only learn science content but employ disciplinary practices as well. This volume outlines the five practices teachers need for facilitating effective inquiry-oriented classrooms:

Anticipate what students will do—what strategies they will use—in solving a problem

Monitor their work as they approach the problem in class

Select students whose strategies are worth discussing in class

Sequence those students’ presentations to maximize their potential to increase students’ learning

Connect the strategies and ideas in a way that helps students understand the science

The 5 Practices framework identifies a set of instructional practices that will help teachers achieve high-demand learning objectives by using student work as the launching point for discussions in which important scientific ideas are brought to the surface, contradictions are exposed, and understandings are developed or consolidated.

by Marian Small, Amy Lin

We know that Differentiated Instruction (DI) helps all students to learn. Yet DI challenges teachers, and nowhere more than in mathematics. In this new book, written specifically for secondary mathematics teachers, the authors cut through the difficulties with two powerful and universal strategies that teachers can use across all math content: Open Questions and Parallel Tasks.

Showing teachers how to get started and become expert with these strategies, this book also demonstrates how to use more inclusive learning conversations to promote broader student participation. Strategies and examples are organized around Big Ideas within the National Council of Teachers of Mathematics (NCTM) content strands. With particular emphasis on Algebra, chapters also address Number and Operations, Geometry, Measurement, and Data Analysis and Probability, with examples included for Pre-Calculus.

To help teachers differentiate math instruction with less difficulty and greater success, this resource:

Underscores the rationale for differentiating secondary math instruction.

Provides specific examples for secondary math content.

Describes two easy-to-implement strategies designed to overcome the most common DI problems that teachers encounter.

Offers almost 300 questions and tasks that teachers and coaches can adopt immediately, adapt, or use as models to create their own, along with scaffolding and consolidating questions.

Includes Teaching Tips sidebars and an organizing template at the end of each chapter to help teachers build new tasks and open questions.

Shows how to create a more inclusive classroom learning community with mathematical talk that engages participants from all levels.

by Marian Small

We know that differentiated instruction helps all students to learn. Yet DI challenges teachers, and nowhere more than in mathematics. Now math education expert Marian Small cuts through the difficulties with two powerful and universal strategies that teachers can use across all math content: Open Questions and Parallel Tasks.

Showing teachers how to get started and become expert with these strategies, Small also demonstrates more inclusive learning conversations that promote broader student participation. Specific strategies and examples for each grade band are organized around the National Council of Teachers of Mathematics (NCTM) content strands: Number and Operations, Geometry, Measurement, Algebra, and Data Analysis and Probability.

To help K-8 teachers differentiate math instruction with less difficulty and greater success, this resource:

Underscores the rationale for differentiating math instruction.

Describes two universal, easy-to-implement strategies designed to overcome the problems that teachers encounter.

Offers almost 300 questions and tasks that teachers and coaches can adopt immediately, adapt, or use as models to create their own.

Includes Teaching Tips sidebars and an organizing template at the end of each chapter to help readers build new tasks and open questions.

Shows how to create a more inclusive classroom learning community with mathematical talk that engages participants from all levels.

by Dr. Spencer Kagan, Miguel Kagan

The book that started it all—is completely revised! Why would the Kagans update a classic that has sold nearly half a million copies? The answer: So much has changed! Cooperative Learning today is different. This new book presents today's most successful cooperative learning methods.

The Kagans make it easier than ever to boost engagement and achievement. You'll still find all the practical and proven Kagan Structures, including Numbered Heads Together, RoundTable, and Three-Step Interview—direct from the man who invented cooperative learning structures. And there's still plenty of ready-to-do teambuilding and class building activities to make your class click. But in this expanded edition, you will find new step-by-step structures, hundreds of helpful management tips, many more teacher-friendly activities and forms, and up-to-date research on proven methods.

You hear how schools have used Kagan Cooperative Learning to boost academics, close the achievement gap, improve student relations, and create a more kind and caring school community. After decades of training and working with hundreds of thousands of teachers, Kagan has refined and perfected the most widely used and respected form of cooperative learning ever. The Kagans make it easy for you to dramatically increase engagement and achievement in your class!

by Dina Kushnir

A cooperative learning book specifically for high school mathematics teachers. Includes a rich array of activities for all levels of high school mathematics. You receive half a dozen Kagan cooperative learning structures: Line-Ups, Mix-Pair-Rally Coach, Mix-N-Match, Inside-Outside Circle, Rally Coach, RoundTable.

For each structure you receive numerous activities and black-line masters for Pre-Algebra, Algebra 1, Geometry, Algebra 2, Trigonometry, and Pre-Calculus. Activities for fractions, geometry definitions, graphs, probability, algebraic expressions, word problems, slope, angle, proofs, equations, functions, parabolas, and much, much more. Nearly 300 activities in all! Your students will work together successfully with these proven cooperative structures. Working together, your students enjoy math more and learn more.

by Francis M. Fennell, Beth McCord Kobett, Jonathan A. Wray

Mathematics education experts Fennell, Kobett, and Wray offer five of the most impactful and proven formative assessment techniques you can implement―Observations, Interviews, "Show Me," Hinge Questions, and Exit Tasks― every day. You’ll find that this palette of classroom-based techniques will truly assess learning and inform teaching.

This book gives you a concise, research-based, classroom-dedicated plan with lots of tools to guide your daily use of The Formative 5. K-8 teachers will learn to

Directly connect assessment to planning and teaching

Engineer effective classroom questioning, discussions, and learning tasks

Provide success criteria and feedback that moves students forward

## #12 - Making Sense of Math: How to Help Every Student Become a Mathematical Thinker and Problem Solver

by Cathy L. Seeley

In Making Sense of Math, Cathy L. Seeley, former president of the National Council of Teachers of Mathematics, shares her insight into how to turn your students into flexible mathematical thinkers and problem solvers. This practical volume concentrates on the following areas:

Making sense of math by fostering habits of mind that help students analyze, understand, and adapt to problems when they encounter them.

Addressing the mathematical building blocks necessary to include in effective math instruction.

Turning teaching "upside-down" by shifting how we teach, focusing on discussion and analysis as much as we focus on correct answers.

Garnering support for the changes you want to make from colleagues and administrators.

Learn how to make math meaningful for your students and prepare them for a lifetime of mathematical fluency and problem-solving.

Read The Things People Say About Math by Bill Reed.