Developing Essential Understanding Of Expressions Equations And Functions For Teaching Mathematics In Grades 6 8 PDF Download
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Author | : Gwendolyn M. Lloyd |
Publisher | : National Council of Teachers of English |
Total Pages | : 116 |
Release | : 2011 |
Genre | : Effective teaching |
ISBN | : 9780873536707 |
Download Developing Essential Understanding of Expressions, Equations, and Functions for Teaching Mathematics in Grades 6-8 Book in PDF, ePub and Kindle
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 | : Zandra De Araujo |
Publisher | : National |
Total Pages | : |
Release | : 2018-08 |
Genre | : Equations |
ISBN | : 9780873537353 |
Download Putting Essential Understanding of Expressions and Equations Into Practice in Grades 6-8 Book in PDF, ePub and Kindle
Author | : Gary Kader |
Publisher | : National |
Total Pages | : 112 |
Release | : 2013 |
Genre | : Mathematical statistics |
ISBN | : 9780873536721 |
Download Developing Essential Understanding of Statistics for Teaching Mathematics in Grades 6-8 Book in PDF, ePub and Kindle
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 | : Thomas J. Cooney |
Publisher | : |
Total Pages | : 109 |
Release | : 2010 |
Genre | : Curriculum enrichment |
ISBN | : 9780873536233 |
Download Developing Essential Understanding of Functions for Teaching Mathematics in Grades 9-12 Book in PDF, ePub and Kindle
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 | : John K. Lannin |
Publisher | : National Council of Teachers of English |
Total Pages | : 95 |
Release | : 2011 |
Genre | : Effective teaching |
ISBN | : 9780873536660 |
Download Developing Essential Understanding of Mathematical Reasoning for Teaching Mathematics in Prekindergarten-grade 8 Book in PDF, ePub and Kindle
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 | : Joanne Elizabeth Lobato |
Publisher | : National Council of Teachers of English |
Total Pages | : 0 |
Release | : 2010 |
Genre | : Curriculum planning |
ISBN | : 9780873536226 |
Download Developing Essential Understanding of Ratios, Proportions, and Proportional Reasoning for Teaching Mathematics in Grades 6-8 Book in PDF, ePub and Kindle
"A series for teaching mathematics."--P. [1] of cover.
Author | : Nathalie Sinclair |
Publisher | : National Council of Teachers of English |
Total Pages | : 95 |
Release | : 2012 |
Genre | : Education, Secondary |
ISBN | : 9780873536929 |
Download Developing Essential Understanding of Geometry for Teaching Mathematics in Grades 9-12 Book in PDF, ePub and Kindle
Why does it matter whether we state definitions carefully when we all know what particular geometric figures look like? What does it mean to say that a reflection is a transformation—a function? How does the study of transformations and matrices in high school connect with later work with vector spaces in linear algebra? How much do you know… and how much do you need to know? Helping your students develop a robust understanding of geometry requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about geometry. It is organised around four big ideas, supported by multiple smaller, interconnected ideas—essential understandings. Taking you beyond a simple introduction to geometry, 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. 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 | : Nathalie Sinclair |
Publisher | : National Council of Teachers of English |
Total Pages | : 96 |
Release | : 2012-01 |
Genre | : Critical thinking |
ISBN | : 9780873536912 |
Download Developing Essential Understanding of Geometry for Teaching Mathematics in Grades 6-8 Book in PDF, ePub and Kindle
Why are there so many formulas for area and volume, and why do some of them look alike? Why does one quadrilateral have no special name while another has several, like square, rectangle, rhombus, and parallelogram—and why are all these names useful? How much do you know … and how much do you need to know? Helping your students develop a robust understanding of geometry requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about geometry. It is organized around four big ideas, supported by multiple smaller, interconnected ideas—essential understandings. Taking you beyond a simple introduction to geometry, 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.
Author | : Albert Dean Otto |
Publisher | : National Council of Teachers of English |
Total Pages | : 84 |
Release | : 2011 |
Genre | : Division |
ISBN | : 9780873536677 |
Download Developing Essential Understanding of Multiplication and Division for Teaching Mathematics in Grades 3-5 Book in PDF, ePub and Kindle
Unpacking"" the ideas related to multiplication and division is a critical step in developing a deeper understanding. To those without specialised training, many of these ideas might appear to be easy to teach. But those who teach in grades 3-5 are aware of their subtleties and complexities. This book identifies and examines two big ideas and related essential understandings for teaching multiplication and division in grades 3–5. Big Idea 1 captures the notion that multiplication is usefully defined as a scalar operation. Problem situations modelled by multiplication have an element that represents the scalar and an element that represents the quantity to which the scalar applies. Big Idea 2 relates to the algorithms that problem solvers have invented - some of which have become “standard” - for multiplying and dividing. The authors examine the ways in which counting, adding and subtracting lead to multiplication and division, as well as the role that these operations play in algebraic expressions and other advanced topics. The book examines challenges in teaching, learning and assessment and is interspersed with questions for teachers’ reflection.
Author | : National Research Council |
Publisher | : National Academies Press |
Total Pages | : 265 |
Release | : 2005-01-28 |
Genre | : Education |
ISBN | : 0309089506 |
Download How Students Learn Book in PDF, ePub and Kindle
How Students Learn: Science in the Classroom builds on the discoveries detailed in the best-selling How People Learn. Now these findings are presented in a way that teachers can use immediately, to revitalize their work in the classroom for even greater effectiveness. Organized for utility, the book explores how the principles of learning can be applied in science at three levels: elementary, middle, and high school. Leading educators explain in detail how they developed successful curricula and teaching approaches, presenting strategies that serve as models for curriculum development and classroom instruction. Their recounting of personal teaching experiences lends strength and warmth to this volume. This book discusses how to build straightforward science experiments into true understanding of scientific principles. It also features illustrated suggestions for classroom activities.