Developing Essential Understanding Of Statistics For Teaching Mathematics In Grades 9 12

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Developing Essential Understanding of Statistics for Teaching Mathematics in Grades 9-12

Roxy Peck,Robert Gould,Stephen J. Miller
Developing Essential Understanding of Statistics for Teaching Mathematics in Grades 9 12 Book PDF

Author : Roxy Peck,Robert Gould,Stephen J. Miller
Publisher : National
Page : 122 pages
File Size : 55,5 Mb
Release : 2013
Category : Effective teaching
ISBN : 0873536762

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Developing Essential Understanding of Statistics for Teaching Mathematics in Grades 9-12 by Roxy Peck,Robert Gould,Stephen J. Miller Pdf

How does a statistical model differ from a mathematical model? What are the differences among the sample distribution, the sampling distribution, and the population distribution? In an experiment, what effect does the sampling method have on the results? What are the implications of the use of processes of random selection and random assignment? Can a small sample yield accurate estimates of population parameters? This book examines five big ideas and twenty-four related essential understandings for teaching statistics in grades 9–12. The authors distinguish mathematical and statistical models, explore distributions as descriptions of variability in data, focus on the fundamentals of testing hypotheses to draw conclusions from data, highlight the importance of the data collection method, and recognise the need to examine bias, precision, and sampling method in evaluating statistical estimators. Recognising that analysing data is an important part of understanding the world, the authors discuss the growth of students’ ideas about statistics and examine challenges to teaching, learning, and assessment. They intersperse their discussion with questions for teachers’ reflection.

Developing Essential Understanding of Statistics for Teaching Mathematics in Grades 6-8

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

Author : Gary Kader,Tim Jacobbe,Patricia S. Wilson
Publisher : National
Page : 112 pages
File Size : 41,6 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.

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

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

Author : Thomas J. Cooney,Sybilla Beckmann,Gwendolyn M. Lloyd
Publisher : Unknown
Page : 109 pages
File Size : 55,9 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.

Developing Essential Understanding of Geometry for Teaching Mathematics in Grades 9-12

Nathalie Sinclair,David Pimm,Melanie Skelin
Developing Essential Understanding of Geometry for Teaching Mathematics in Grades 9 12 Book PDF

Author : Nathalie Sinclair,David Pimm,Melanie Skelin
Publisher : National Council of Teachers of English
Page : 95 pages
File Size : 45,7 Mb
Release : 2012
Category : Education, Secondary
ISBN : 0873536924

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Developing Essential Understanding of Geometry for Teaching Mathematics in Grades 9-12 by Nathalie Sinclair,David Pimm,Melanie Skelin Pdf

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.

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

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

Author : Joanne Elizabeth Lobato,Amy B. Ellis,Randall Inners Charles
Publisher : National Council of Teachers of English
Page : 0 pages
File Size : 54,9 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.

Putting Essential Understanding of Statistics Into Practice in Grades 9-12

Terry Crites,Roy Thomas St. Laurent
Putting Essential Understanding of Statistics Into Practice in Grades 9 12 Book PDF

Author : Terry Crites,Roy Thomas St. Laurent
Publisher : Unknown
Page : 0 pages
File Size : 52,8 Mb
Release : 2015
Category : Mathematical statistics
ISBN : 0873537378

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Putting Essential Understanding of Statistics Into Practice in Grades 9-12 by Terry Crites,Roy Thomas St. Laurent Pdf

Focuses on the specialized pedagogical content knowledge that you need to teach statistics effectively in grades 9-12. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with statistics.

Developing Essential Understanding of Expressions, Equations, and Functions for Teaching Mathematics in Grades 6-8

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

Author : Gwendolyn M. Lloyd,Beth A. Herbel-Eisenmann,Jon R. Star
Publisher : National Council of Teachers of English
Page : 116 pages
File Size : 48,6 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.

Developing Essential Understanding of Addition and Subtraction for Teaching Mathematics in Prekindergarten-grade 2

Janet H. Caldwell
Developing Essential Understanding of Addition and Subtraction for Teaching Mathematics in Prekindergarten grade 2 Book PDF

Author : Janet H. Caldwell
Publisher : National Council of Teachers of English
Page : 85 pages
File Size : 51,9 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

Developing Essential Understanding of Number and Numeration for Teaching Mathematics in Prekindergarten--grade 2

Barbara J. Dougherty
Developing Essential Understanding of Number and Numeration for Teaching Mathematics in Prekindergarten grade 2 Book PDF

Author : Barbara J. Dougherty
Publisher : Unknown
Page : 60 pages
File Size : 47,6 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

Developing Essential Understanding of Multiplication and Division for Teaching Mathematics in Grades 3-5

Albert Dean Otto
Developing Essential Understanding of Multiplication and Division for Teaching Mathematics in Grades 3 5 Book PDF

Author : Albert Dean Otto
Publisher : National Council of Teachers of English
Page : 84 pages
File Size : 41,7 Mb
Release : 2011
Category : Division
ISBN : 0873536673

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Developing Essential Understanding of Multiplication and Division for Teaching Mathematics in Grades 3-5 by Albert Dean Otto Pdf

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.

Putting Essential Understanding of Ratios and Proportions Into Practice in Grades 6-8

Travis Olson,Melfried Olson,Hannah Slovin
Putting Essential Understanding of Ratios and Proportions Into Practice in Grades 6 8 Book PDF

Author : Travis Olson,Melfried Olson,Hannah Slovin
Publisher : National Council of Teachers of English
Page : 0 pages
File Size : 41,8 Mb
Release : 2015
Category : Ratio and proportion
ISBN : 0873537173

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Putting Essential Understanding of Ratios and Proportions Into Practice in Grades 6-8 by Travis Olson,Melfried Olson,Hannah Slovin Pdf

Focuses on the specialized pedagogical content knowledge that you need to teach ratios and proportions effectively in grades 6-8. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with ratios and proportions.

Principles and Standards for School Mathematics

Anonim
Principles and Standards for School Mathematics Book PDF

Author : Anonim
Publisher : Unknown
Page : 20 pages
File Size : 44,9 Mb
Release : 2000
Category : Mathematics
ISBN : 0873534840

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Principles and Standards for School Mathematics by Anonim Pdf

This easy-to-read summary is an excellent tool for introducing others to the messages contained in Principles and Standards.

Developing Essential Understanding of Mathematical Reasoning for Teaching Mathematics in Prekindergarten-grade 8

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

Author : John K. Lannin,Amy B. Ellis,Rebekah Elliott
Publisher : National Council of Teachers of English
Page : 95 pages
File Size : 46,6 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.

Key Ideas in Teaching Mathematics

Anne Watson,Keith Jones,Dave Pratt
Key Ideas in Teaching Mathematics Book PDF

Author : Anne Watson,Keith Jones,Dave Pratt
Publisher : Oxford University Press
Page : 270 pages
File Size : 55,7 Mb
Release : 2013-02-21
Category : Education
ISBN : 9780199665518

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Key Ideas in Teaching Mathematics by Anne Watson,Keith Jones,Dave Pratt Pdf

International research is used to inform teachers and others about how students learn key ideas in higher school mathematics, what the common problems are, and the strengths and pitfalls of different teaching approaches. An associated website, hosted by the Nuffield Foundation, gives summaries of main ideas and access to sample classroom tasks.

Helping Children Learn Mathematics

National Research Council,Division of Behavioral and Social Sciences and Education,Center for Education,Mathematics Learning Study Committee
Helping Children Learn Mathematics Book PDF

Author : National Research Council,Division of Behavioral and Social Sciences and Education,Center for Education,Mathematics Learning Study Committee
Publisher : National Academies Press
Page : 52 pages
File Size : 52,6 Mb
Release : 2002-07-31
Category : Education
ISBN : 9780309131988

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Helping Children Learn Mathematics by National Research Council,Division of Behavioral and Social Sciences and Education,Center for Education,Mathematics Learning Study Committee Pdf

Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we’re teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre--kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society.