Helps develop a deeper understanding of indigenous people's mathematics and pedagogy. Explores native cultures and mathematics learning and discusses culturally relevant assessment and mathematics activities.

Changing the Faces of Mathematics: Perspectives on Indigenous People of North America (Changing the Face of Mathematics)

National Council Of Teachers Of Mathematics

Gerald R. Fast

NCTM

Written by an elementary teacher especially for teachers in the elementary grades (K 5) to help implement problem solving in the classroom, this book includes questions and answers designed to help address concerns parents may have with problem solving in the mathematics curriculum. It also includes information pertaining to classroom environment, warm-up activities, rubrics, and alternative forms of assessment, and allows room for experimentation with your own variations and comparison with classroom experiences.

Share and Compare: A Teacher's Story about Helping Children Become Problem Solvers in Mathematics

Larry Buschman

Figure This! CD-ROM: Math Challenges for Families

Unknown, Author

How do you refute the erroneous claim that all ratios are fractions? This book goes beyond a simple introduction to ratios, proportions, and proportional reasoning. It will help broaden and deepen your mathematical understanding of one of the most challenging topics for students and teachers to grasp. It will help you engage your students, anticipate their perplexities, help them avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing your students understanding of the topic. Essential Understanding Series topics: Number and Numeration for Grades Pre-K 2 Addition and Subtraction for Grades Pre-K 2 Geometry for Grades Pre-K 2 Reasoning and Proof for Grades Pre-K 8 Multiplication and Division for Grades 3 5 Rational Numbers for Grades 3 5 Algebraic Ideas and Readiness for Grades 3 5 Geometric Shapes and Solids for Grades 3 5 Ratio, Proportion, and Proportionality for Grades 6 8 Expressions and Equations for Grades 6 8 Measurement for Grades 6 8 Data Analysis and Statistics for Grades 6 8 Function for Grades 9 12 Geometric Relationships for Grades 9 12 Reasoning and Proof for Grades 9 12 Statistics for Grades 9 12

Developing Essential Understanding of Ratios, Proportions, and Proportional Reasoning for Teaching Mathematics: Grades 6–8

Amy Ellis

Rose Mary Zbiek

Joanne Lobato

Are sequences functions? What can t the popular vertical line test be applied in some cases to determine if a relation is a function? How does the idea of rate of change connect with simpler ideas about proportionality as well as more advanced topics in calculus? How much do you know... and how much do you need to know? Helping your high school students develop a robust understanding of functions requires that you understand mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about functions. It is organized around five big ideas, supported by multiple smaller, interconnected ideas essential understandings. Taking you beyond a simple introduction to functions, this book will broaden and deepen your mathematical understanding of one of the most challenging topics for students and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing students understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently.

Developing Essential Understanding of Functions for Teaching Mathematics in Grades 9–12

Gwendolyn Lloyd

Sybilla Beckmann Kazez

How do composing and decomposing numbers connect with the properties of addition? Focus on the ideas that you need to thoroughly understand in order to teach with confidence. The mathematical content of this book focuses on essential knowledge for teachers about numbers and number systems. It is organized around one big idea and supported by smaller, more specific, interconnected ideas (essential understandings). Gaining this understanding is essential because numbers and numeration are building blocks for other mathematical concepts and for thinking quantitatively about the real-world. Essential Understanding Series topics: Number and Numeration for Grades Pre-K 2 Addition and Subtraction for Grades Pre-K 2 Geometry for Grades Pre-K 2 Reasoning and Proof for Grades Pre-K 8 Multiplication and Division for Grades 3 5 Rational Numbers for Grades 3 5 Algebraic Ideas and Readiness for Grades 3 5 Geometric Shapes and Solids for Grades 3 5 Ratio, Proportion, and Proportionality for Grades 6 8 Expressions and Equations for Grades 6 8 Measurement for Grades 6 8 Data Analysis and Statistics for Grades 6 8 Function for Grades 9 12 Geometric Relationships for Grades 9 12 Reasoning and Proof for Grades 9 12 Statistics for Grades 9 12

Developing Essential Understanding of Number and Numeration for Teaching Mathematics in Pre-K–2

Science & Math

Barbara Dougherty

Alfinio Flores

Catherine Sophian

Everett,Louis

Mathematics

What is the relationship between fractions and rational numbers? Can you explain why the product of two fractions between 0 and 1 is less than either factor? How are rational numbers related to irrational numbers, which your students will study in later grades? How much do you know... and how much do you need to know? Helping your upper elementary school students develop a robust understanding of rational numbers requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about rational numbers. It is organized around four big ideas, supported by multiple smaller, interconnected ideas essential understandings. Taking you beyond a simple introduction to rational numbers, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing students understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently.

Developing Essential Understanding of Rational Numbers for Teaching Mathematics in Grades 3–5

William Fisher

Rick Marks

Sharon Ross

Carne Clarke

Teaching mathematics is a much broader endeavor than simply helping students to acquire skills and problem-solving strategies. Teachers also strive to develop motivation and positive dispositions toward studying mathematics-aspects that will have long-term effects on everything from students' confidence to do mathematics to their career choices. Each lesson in a mathematics classroom should take into account students' motivation level and dispositions and have as a goal the development of these affective characteristics.Explore a wide variety of perspectives on motivation and disposition as these concepts relate to mathematics teaching and learning. NCTM's seventy-third yearbook examines such elements as the demographic composition of a school; the role of movies, television and the Internet; and nontraditional pedagogy as means of promoting and influencing positive student and teacher dispositions. Motivation and disposition can arise from diverse sources and many factors can magnify-or diminish-both. The presence or lace of curiosity, ambition, parental influence, teacher encouragement, peer pressure and future goals-these and other elements play central roles. Against these realities, cumbersome rhetoric is less effective than concrete ideas for implementation-this book offers a perspective to the reader that reinforces action.

Motivation and Disposition

What is the relationship between addition and subtraction? How do you know whether an algorithm will always work? Can you explain why order matters in subraction but not in addition, or why it is false to assert that the sum of any two whole numbers is greater than either number? It is organized around two big ideas and supported by smaller, more specific, interconnected ideas (essential understandings). Gaining an understanding about addition and subtraction is essential as they are the foundation for students later learning of multiplication and division.

Developing Essential Understanding of Addition and Subtraction for Teaching Mathematics in Pre-K–Grade 2

Jennifer Bay-Williams

Janet Caldwell

Karen Karp

How can you build on young children's interactions with the world to develop their geometric thinking? What can you say to a student who claims that a diamond isn't a square because it "stands on a point"? How can knowing what does not change when shapes are transformed help you extend your students' thinking about the area of geometric figures? How much do you know ...and how much do you need to know? Helping your students develop a robust understanding of geometry and measurement requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about geometry and measurement. It is organized around four big ideas, supported by multiple smaller, interconnected ideas-- essential understandings . Taking you beyond a simple introduction to geometry and measurement, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students--and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing students' understanding of the topic. About the Series: Focus on the ideas that you need to understand thoroughly to teach confidently. Move beyond the mathematics you expect your students to learn. Students who fail to get a solid grounding in pivotal concepts struggle in subsequent work in mathematics and related disciplines. By bringing a deeper understanding to your teaching, you can help students who don't get it the first time by presenting the mathematics in multiple ways. The Essential Understanding Series addresses topics in school mathematics that are critical to the mathematical development of students but are often difficult to teach. Each book in the series gives an overview of the topic, highlights the differences between what teachers and students need to know, examines the big ideas and related essential understandings, reconsiders the ideas presented in light of connections with other mathematical ideas, and includes questions for readers' reflection.

Developing Essential Understanding of Geometry and Measurement for Teaching Mathematics in Pre-K–Grade 2

E.Paul Goldenberg

Douglas Clements

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