Developing Essential Understanding – serie
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14 produkter
14 produkter
Developing Essential Understanding of Ratios, Proportions, and Proportional Reasoning in Grades 6-8
Häftad, Engelska, 2010
220 kr
Skickas inom 5-8 vardagar
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 include:Number and Numeration for Grades Pre-K-2Addition and Subtraction for Grades Pre-K-2Geometry for Grades Pre-K-2Reasoning and Proof for Grades Pre-K-8Multiplication and Division for Grades 3-5Rational Numbers for Grades 3-5Algebraic Ideas and Readiness for Grades 3-5Geometric Shapes and Solids for Grades 3-5Ratio, Proportion and Proportionality for Grades 6-8Expressions and Equations for Grades 6-8Measurement for Grades 6-8Data Analysis and Statistics for Grades 6-8Function for Grades 9-12Geometric Relationships for Grades 9-12Reasoning and Proof for Grades 9-12Statistics for Grades 9—12
Developing Essential Understanding of Functions for Teaching Mathematics in Grades 9-12
Häftad, Engelska, 2010
238 kr
Skickas inom 11-20 vardagar
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.
220 kr
Skickas inom 5-8 vardagar
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-2Addition and Subtraction for Grades Pre-K-2Geometry for Grades Pre-K-2Reasoning and Proof for Grades Pre-K-8Multiplication and Division for Grades 3-5Rational Numbers for Grades 3-5Algebraic Ideas and Readiness for Grades 3-5Geometric Shapes and Solids for Grades 3-5Ratio, Proportion and Proportionality for Grades 6-8Expressions and Equations for Grades 6-8Measurement for Grades 6-8Data Analysis and Statistics for Grades 6-8Function for Grades 9-12Geometric Relationships for Grades 9-12Reasoning and Proof for Grades 9-12Statistics for Grades 9-12
220 kr
Skickas inom 5-8 vardagar
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.
Developing Essential Understanding of Addition and Subtraction for Teaching Math in PreK-Grade 2
Häftad, Engelska, 2011
231 kr
Skickas inom 11-20 vardagar
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-2Addition and Subtraction for Grades Pre-K-2Geometry for Grades Pre-K-2Reasoning and Proof for Grades Pre-K-8Multiplication and Division for Grades 3-5Rational Numbers for Grades 3-5Algebraic Ideas and Readiness for Grades 3-5Geometric Shapes and Solids for Grades 3-5Ratio, Proportion and Proportionality for Grades 6-8Expressions and Equations for Grades 6-8Measurement for Grades 6-8Data Analysis and Statistics for Grades 6-8Function for Grades 9-12Geometric Relationships for Grades 9-12Reasoning and Proof for Grades 9-12Statistics for Grades 9-12
Developing Essential Understanding - Mathematical Reasoning in Grades Pre-K- Grade 8
Häftad, Engelska, 2011
238 kr
Skickas inom 11-20 vardagar
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.
Developing Essential Understanding - Multiplication and Division for Teaching Math in Grades 3-5
Häftad, Engelska, 2011
220 kr
Skickas inom 5-8 vardagar
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.
Developing Essential Understanding of Algebraic Thinking for Teaching Mathematics in Grades 3-5
Häftad, Engelska, 2011
238 kr
Skickas inom 11-20 vardagar
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.
Developing Essential Understanding of Expressions, Equations, and Functions for Teaching Math in Grades 6-8
Häftad, Engelska, 2011
220 kr
Skickas inom 5-8 vardagar
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 Statistics for Teaching Mathematics in Grades 6-8
Häftad, Engelska, 2013
238 kr
Skickas inom 11-20 vardagar
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 Proof and Proving for Teaching Mathematics in Grades 9-12
Häftad, Engelska, 2012
231 kr
Skickas inom 11-20 vardagar
What is the difference between “proof” in mathematics and “proof” in science or a court of law? In mathematics, how does proof differ from other types of arguments? What forms can proof take besides the traditional two-column style? What activities constitute the process of proving? What roles do examples play in proving? Can examples ever prove a conjecture? Why does a single counterexample refute a conjecture?How much do you know…and how much do you need to know?Helping your students develop a robust understanding of mathematical proof and proving requires that you understand this aspect of mathematics deeply. But what does that mean?This book focuses on essential knowledge for teachers about proof and the process of proving. It is organised around five big ideas, supported by multiple smaller, interconnected ideas—essential understandings. Taking you beyond a simple introduction to proof and the activities involved in proving, 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 Statistics for Teaching Mathematics in Grades 9-12
Häftad, Engelska, 2013
220 kr
Skickas inom 5-8 vardagar
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 Geometry for Teaching Mathematics in Grades 6-8
Häftad, Engelska, 2012
513 kr
Skickas inom 11-20 vardagar
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.
Developing Essential Understanding of Geometry for Teaching Mathematics in Grades 9-12
Häftad, Engelska, 2012
220 kr
Skickas inom 5-8 vardagar
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.