Coaching Corner

# Know, Understand, and Do Mathematics

Essential Coaching Action 6 is to know, understand, and do mathematics. Coaching will focus on the mathematics content all teachers must know deeply in order to teach a grade level or course.

- Build mathematics content knowledge
- Grow strategies for incorporating mathematics process standards in lessons

This set of digital resources, designed and assembled with grant funding, help leaders engage teachers and administrators in dialogue around the 8 Standards for Mathematical Practice. The resources use classroom video to examine the practices in action.

Reproducible from NCSM Essential Action Series: Framework for Leadership in Mathematics Education for coaches and teachers/teams to plan for student learning using learning trajectories.

Listen to Nicholas Pyzik, Math Interventionist/Specialist K-5, Frederick County Public Schools, on how one math coach used a resource to help him transition from teacher to coach in the same building. He offer a school based professional learning group, using the resource Number Talks by Sherry Parrish to build trust with other teachers.

Listen to Damitra Newsome, Math Instructional Support Teacher, Howard County Public Schools, describe how she helped teachers collaboratively use evaluation and analysis tools to select worthwhile mathematics task, to prepare for the teaching of these tasks, and to reflect on their implementation and success. Because of this thoughtful and deliberate process, teachers witnessed increased student engagement and enthusiasm for mathematics.

This conversation highlights the notion of content coaching. Lucy West and Antonia Cameron share their ideas of how to coaching around the mathematics content.

NCSM has published a pair of books containing high quality tasks for classroom use. These tasks are linked to standards, include a launch activity and student work, and are meant as resources for teachers and leaders to use in the classroom.

NCSM has published a pair of books containing high quality tasks for classroom use. These tasks are linked to standards, include a launch activity and student work, and are meant as resources for teachers and leaders to use in the classroom.

This volume, paired by grade band from NCTM’s best-selling series, Developing Essential Understanding, transforms the way teachers understand mathematics. Each book helps teachers deepen and enrich their content knowledge of the big ideas. Learn to develop appropriate tasks, techniques, and tools for assessing students' understanding of the topics.

This must-have resource is widely acknowledged for helping teachers, coordinators, and college faculty deepen their understanding of the mathematical concepts they teach. Math Matters provides an in-depth study with 14 chapters covering number sense, computation, addition, subtraction, multiplication, division, fractions, decimals, percents, ratios, algebra, geometry, spatial sense, measurement, statistics, and probability. Over 100 activities give readers an opportunity to connect ideas, compare and contrast concepts, and consider how students understand the mathematics presented.

This volume, paired by grade band from NCTM’s best-selling series, Developing Essential Understanding, transforms the way teachers understand mathematics. Each book helps teachers deepen and enrich their content knowledge of the big ideas. Learn to develop appropriate tasks, techniques, and tools for assessing students' understanding of the topics.

With Fostering Geometric Thinking any math teacher can discover essential, practical ideas for helping students cultivate geometric habits of mind that lead to success in this crucial mathematical subject. The book focuses on rigorous, problem-based teaching that encourages students to deepen their thinking in three key geometric strands: geometric properties, geometric transformations and measurement of geometric objects.

This volume, paired by grade band from NCTM’s best-selling series, Developing Essential Understanding, transforms the way teachers understand mathematics. Each book helps teachers deepen and enrich their content knowledge of the big ideas. Learn to develop appropriate tasks, techniques, and tools for assessing students' understanding of the topics.

This popular text addresses the urgent need for curriculum materials that cross traditional boundaries to include many of the elements that are integrated in the teaching/learning enterprise: mathematics content, teacher understanding, student thinking, teaching methods, instructional activities, and assessment. The book pushes readers beyond the limits of their current understanding of rational numbers, challenging them to refine and explain their thinking–without falling back on rules and procedures they have relied on throughout their lives.

This volume is one of a series of books that support NCTM s Focus in High School Mathematics: Reasoning and Sense Making by providing additional guidance for making reasoning and sense making part of the mathematics experiences of all high school students every day.

- Developing Essential Understanding of Ratios, Proportions and Proportional Reasoning in Grades 6-8 (2011)

This volume is one of a series of books that support NCTM s Focus in High School Mathematics: Reasoning and Sense Making by providing additional guidance for making reasoning and sense making part of the mathematics experiences of all high school students every day.

In Thinking Mathematically, the same author team as Children's Mathematics: Cognitivly Guided Instruction, shows how Operations and Algebraic Thinking can be viewed as a unified field by understanding how children's intuitive strategies naturally draw upon the properties of operations and other algebraic concepts. This book shows how teachers can recognize and support children's use of the properties of operations and other algebraic concepts in a manner that deepens students' understanding of arithmetic and provides a solid foundation for learning algebra. This book also shows how teachers can increase their own knowledge of mathematics in the process of interacting with their children and reflecting about their practice.

This volume is one of a series of books that support NCTM s Focus in High School Mathematics: Reasoning and Sense Making by providing additional guidance for making reasoning and sense making part of the mathematics experiences of all high school students every day.

This highly anticipated follow-up volume to the landmark Children's Mathematics: Cognitively Guided Instruction addresses the urgent need to help teachers understand and teach fraction concepts. Fractions remain one of the key stumbling blocks in math education, and here Empson and Levi lay a foundation for understanding fractions and decimals in ways that build conceptual learning. They show how the same kinds of intuitive knowledge and sense making that provides the basis for children's learning of whole number arithmetic can be extended to fractions and decimals. Just as they did in Children's Mathematics and Thinking Mathematically, Empson and Levi provide important insights into children's thinking and alternative approaches to solving problems.

Focus on the ideas that you need to understand thoroughly to teach pre-K grade 2 students confidently.

Helping students develop an understanding of important mathematical ideas is a persistent challenge for teachers. In this book, one of a three-volume set, well-known mathematics educators Margaret Smith, Edward A. Silver, and Mary Kay Stein provide teachers of mathematics the support they need to improve their instruction. They focus on ways to engage upper elementary, middle school, and high school students in thinking, reasoning, and problem solving to build their mathematics understanding and proficiency. The content focus of Volume Three is geometry and measurement.

Helping students develop an understanding of important mathematical ideas is a persistent challenge for teachers. In this book, one of a three-volume set, well-known mathematics educators Margaret Smith, Edward A. Silver, and Mary Kay Stein provide teachers of mathematics the support they need to improve their instruction. They focus on ways to engage upper elementary, middle school, and high school students in thinking, reasoning, and problem solving to build their mathematics understanding and proficiency. The content focus of Volume One is rational numbers and proportionality.

Helping students develop an understanding of important mathematical ideas is a persistent challenge for teachers. In this book, one of a three-volume set, well-known mathematics educators Margaret Smith, Edward A. Silver, and Mary Kay Stein provide teachers of mathematics the support they need to improve their instruction. They focus on ways to engage upper elementary, middle school, and high school students in thinking, reasoning, and problem solving to build their mathematics understanding and proficiency. The content focus of Volume Two is algebra.

Elementary and Middle School Mathematics: Teaching Developmentally (7th ed.), by John A. Van de Walle, Karen Karp, and Jenny Bay-Williams, focuses on learning mathematics to teach mathematics. Twenty-three (23) chapters are divided into two major sections: • Teaching Mathematics: Foundations and Perspectives • Development of Mathematical Concepts and Procedures