Developing Essential Understanding Of Mathematical Reasoning For Teaching Mathematics In Prekindergarten Grade 8

Author : John K. Lannin,Amy B. Ellis,Rebekah Elliott
Publisher : National Council of Teachers of English
Page : 95 pages
File Size : 46,8 Mb
Release : 2011
Category : Effective teaching
ISBN : 0873536665

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Developing Essential Understanding of Mathematical Reasoning for Teaching Mathematics in Prekindergarten-grade 8 by John K. Lannin,Amy B. Ellis,Rebekah Elliott Pdf

How do your students determine whether a mathematical statement is true? Do they rely on a teacher, a textbook or various examples? How can you encourage them to connect examples, extend their ideas to new situations that they have not yet considered and reason more generally? How much do you know...and how much do you need to know? Helping your students develop a robust understanding of mathematical reasoning requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about mathematical reasoning. It is organised around one big idea, supported by multiple smaller, interconnected ideas - essential understandings.Taking you beyond a simple introduction to mathematical reasoning, 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.

Author : Janet H. Caldwell
Publisher : National Council of Teachers of English
Page : 85 pages
File Size : 47,5 Mb
Release : 2011
Category : Addition
ISBN : 0873536649

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Developing Essential Understanding of Addition and Subtraction for Teaching Mathematics in Prekindergarten-grade 2 by Janet H. Caldwell Pdf

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 organised 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. Essential Understanding Series topics include: 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

Author : Barbara J. Dougherty
Publisher : Unknown
Page : 60 pages
File Size : 46,7 Mb
Release : 2010
Category : Number concept
ISBN : 0873536290

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Developing Essential Understanding of Number and Numeration for Teaching Mathematics in Prekindergarten--grade 2 by Barbara J. Dougherty Pdf

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 organised 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 include: 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

Author : Ernest Paul Goldenberg,Douglas H. Clements,Barbara J. Dougherty
Publisher : National
Page : 90 pages
File Size : 53,5 Mb
Release : 2014-01-01
Category : Geometry
ISBN : 0873536657

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Developing Essential Understanding of Geometry and Measurement for Teaching Mathematics in Prekindergarten-grade 2 by Ernest Paul Goldenberg,Douglas H. Clements,Barbara J. Dougherty Pdf

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.

Author : Joanne Elizabeth Lobato,Amy B. Ellis
Publisher : Unknown
Page : 0 pages
File Size : 54,7 Mb
Release : 2010
Category : Curriculum planning
ISBN : 0873537890

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Developing Essential Understanding of Ratios, Proportions, and Proportional Reasoning for Teaching Mathematics in Grades 6-8 by Joanne Elizabeth Lobato,Amy B. Ellis Pdf

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.

Author : Thomas J. Cooney,Sybilla Beckmann,Gwendolyn M. Lloyd
Publisher : Unknown
Page : 109 pages
File Size : 47,6 Mb
Release : 2010
Category : Curriculum enrichment
ISBN : 0873536231

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Developing Essential Understanding of Functions for Teaching Mathematics in Grades 9-12 by Thomas J. Cooney,Sybilla Beckmann,Gwendolyn M. Lloyd Pdf

Are sequences functions? Why 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 organised 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.

Author : Richard Lehrer,Hannah Slovin,Barbara J. Dougherty,Rose Mary Zbiek
Publisher : Unknown
Page : 91 pages
File Size : 46,6 Mb
Release : 2014-06
Category : Geometry
ISBN : 087353669X

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Developing Essential Understanding of Geometry and Measurement for Teaching Mathematics in Grades 3-5 by Richard Lehrer,Hannah Slovin,Barbara J. Dougherty,Rose Mary Zbiek Pdf

How can you introduce terms from geometry and measurement so that your students’ vocabulary will enhance their understanding of concepts and definitions? What can you say to clarify the thinking of a student who claims that perimeter is always an even number? How does knowing what changes or stays the same when shapes are transformed help you support and extend your students’ understanding of shapes and the space that they occupy? 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 fundamental statistical concepts deeply. But what does that mean? This book focuses on essential knowledge for mathematics teachers about geometry and measurement. It is organized around three 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 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.

Author : Gary Kader,Tim Jacobbe,Patricia S. Wilson
Publisher : National
Page : 112 pages
File Size : 43,5 Mb
Release : 2013
Category : Mathematical statistics
ISBN : 087353672X

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Developing Essential Understanding of Statistics for Teaching Mathematics in Grades 6-8 by Gary Kader,Tim Jacobbe,Patricia S. Wilson Pdf

How does working with data in statistics differ from working with numbers in mathematics? What is variability, and how can we describe and measure it? How can we display distributions of quantitative or categorical data? What is a data sample, and how can we choose one that will allow us to draw valid conclusions from data? How much do you know? and how much do you need to know? Helping your students develop a robust understanding of statistics requires that you understand fundamental statistical concepts deeply. But what does that mean? This book focuses on essential knowledge for mathematics teachers about statistics. It is organised around four big ideas, supported by multiple smaller, interconnected ideas. Taking you beyond a simple introduction to statistics, the book will broaden and deepen your 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.

Author : Joanne Elizabeth Lobato,Amy B. Ellis,Randall Inners Charles
Publisher : National Council of Teachers of English
Page : 0 pages
File Size : 49,5 Mb
Release : 2010
Category : Curriculum planning
ISBN : 0873536223

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Developing Essential Understanding of Ratios, Proportions, and Proportional Reasoning for Teaching Mathematics in Grades 6-8 by Joanne Elizabeth Lobato,Amy B. Ellis,Randall Inners Charles Pdf

"A series for teaching mathematics."--P. [1] of cover.

Author : Carne Barnett-Clarke
Publisher : National Council of Teachers of English
Page : 83 pages
File Size : 41,5 Mb
Release : 2010
Category : Mathematics
ISBN : 0873536304

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Developing Essential Understanding of Rational Numbers for Teaching Mathematics in Grades 3/5 by Carne Barnett-Clarke Pdf

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 organised 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.

Author : Anonim
Publisher : Unknown
Page : 0 pages
File Size : 49,6 Mb
Release : 2024-05-19
Category : Electronic
ISBN : OCLC:1372385356

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Developing essential understanding of mathematical reasoning, PreK-gr. 8 by Anonim Pdf

Author : Maria L. Blanton
Publisher : Unknown
Page : 102 pages
File Size : 46,7 Mb
Release : 2011
Category : Algebra
ISBN : 0873536681

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Developing Essential Understanding of Algebraic Thinking for Teaching Mathematics in Grades 3-5 by Maria L. Blanton Pdf

Like algebra at any level, early algebra is a way to explore, analyse, represent and generalise mathematical ideas and relationships. This book shows that children can and do engage in generalising about numbers and operations as their mathematical experiences expand. The authors identify and examine five big ideas and associated essential understandings for developing algebraic thinking in grades 3-5. The big ideas relate to the fundamental properties of number and operations, the use of the equals sign to represent equivalence, variables as efficient tools for representing mathematical ideas, quantitative reasoning as a way to understand mathematical relationships and functional thinking to generalise relationships between covarying quantities. The book examines challenges in teaching, learning and assessment and is interspersed with questions for teachers’ reflection.

Author : Jennifer M. Bay-Williams,John J. SanGiovanni
Publisher : Corwin
Page : 265 pages
File Size : 50,9 Mb
Release : 2021-03-02
Category : Education
ISBN : 9781071818435

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Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8 by Jennifer M. Bay-Williams,John J. SanGiovanni Pdf

Because fluency practice is not a worksheet. Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. Real fluency involves reasoning and creativity, and it varies by the situation at hand. Figuring Out Fluency in Mathematics Teaching and Learning offers educators the inspiration to develop a deeper understanding of procedural fluency, along with a plethora of pragmatic tools for shifting classrooms toward a fluency approach. In a friendly and accessible style, this hands-on guide empowers educators to support students in acquiring the repertoire of reasoning strategies necessary to becoming versatile and nimble mathematical thinkers. It includes: "Seven Significant Strategies" to teach to students as they work toward procedural fluency. Activities, fluency routines, and games that encourage learning the efficiency, flexibility, and accuracy essential to real fluency. Reflection questions, connections to mathematical standards, and techniques for assessing all components of fluency. Suggestions for engaging families in understanding and supporting fluency. Fluency is more than a toolbox of strategies to choose from; it’s also a matter of equity and access for all learners. Give your students the knowledge and power to become confident mathematical thinkers.

Author : Gwendolyn M. Lloyd,Beth A. Herbel-Eisenmann,Jon R. Star
Publisher : National Council of Teachers of English
Page : 116 pages
File Size : 46,6 Mb
Release : 2011
Category : Effective teaching
ISBN : 0873536703

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Developing Essential Understanding of Expressions, Equations, and Functions for Teaching Mathematics in Grades 6-8 by Gwendolyn M. Lloyd,Beth A. Herbel-Eisenmann,Jon R. Star Pdf

Why do some equations have one solution, others two or even more solutions and some no solutions? Why do we sometimes need to ""switch"" the direction of an inequality symbol in solving an inequality? What could you say if a student described a function as an equation? How much do you know...and how much do you need to know? Helping your students develop a robust understanding of expressions, equations and functions requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about expressions, equations and functions. It is organised around five big ideas, supported by multiple smaller, interconnected ideas - essential understandings. Taking you beyond a simple introduction to expressions, equations and functions, 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.

Author : Wendy Ward Hoffer
Publisher : Heinemann Educational Books
Page : 0 pages
File Size : 40,5 Mb
Release : 2012
Category : Education
ISBN : 0325044341

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Minds on Mathematics by Wendy Ward Hoffer Pdf

Minds-on Mathematics explains the core elements of math workshop and provides detailed strategies for implementing the workshop structure, including Lesson Openers that engage students,Minilessons that model thinking and problem solving.