Eric Knuth – författare

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.

In this volume, the authors address the development of students’ algebraic thinking in the elementary and middle school grades from curricular, cognitive, and instructional perspectives. The volume is also international in nature, thus promoting a global dialogue on the topic of early Algebraization.