Amy Ellis – författare

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

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.

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.

Get a deeper understanding of teaching Statistics, Proof and Proving 9–12 with our concise and comprehensive Go-To Guide.Based on Developing Essential Understanding of Proof and Proving 9–12, this summary distills the key concepts and ideas into a quick-reference guide that's perfect forsupplementing your reading of Developing Essential Understanding of Proof and Proving 9–12,reviewing the basics before diving deeper into the subject,refreshing your knowledge and filling in gaps in your understanding, andidentifying areas where you need more information and want to learn more.Go-To Guides are designed to provide you with a thorough grasp of the mathematical ideas and principles needed to teach Statistics, Proof and Proving in grades 9–12, by focusing on the core concepts and relationships that underlie the subject.This Go-To Guide is perfect for those looking to:develop a deeper understanding of Statistics, Proof and Proving, 9–12,create targeted lessons and activities that meet the needs of students,anticipate common student misconceptions and errors,design effective assessments and evaluations, andenhance your own math knowledge and skills.Whether you're new to teaching Statistics, Proof and Proving, 9–12, or an experienced educator, our Go-To Guides will be your trusted resource for teaching with confidence and clarity.

It will appeal to students and scholars of public administration, public policy, public health, and education, as well as practitioners.