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How can you introduce terms from geometry and measurement so that your students’ vocabulary will enhance their understanding of concepts and definitions? What can you say to clarify the thinking of a student who claims that perimeter is always an even number? How does knowing what changes or stays the same when shapes are transformed help you support and extend your students’ understanding of shapes and the space that they occupy? How much do you know … and how much do you need to know? Helping your students develop a robust understanding of geometry and measurement requires that you understand fundamental statistical concepts deeply. But what does that mean? This book focuses on essential knowledge for mathematics teachers about geometry and measurement. It is organized around three big ideas, supported by multiple smaller, interconnected ideas—essential understandings. Taking you beyond a simple introduction to geometry and measurement, 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.
Focuses on the specialized pedagogical content knowledge that you need to teach geometry and measurement effectively in grades 3-5. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with geometry and measurement.
Do your students suppose that 1/3 is greater than 1/2, since 3 is greater than 2? Do they believe that having “halves” means having two, and only two, congruent “pieces” of a whole? What tasks can you offer—what questions can you ask—to determine what your students know or don’t know—and move them forward in their thinking? This book focuses on the specialised pedagogical content knowledge that you need to teach fractions effectively in grades 3–5. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with fractions—not only in their current work, but also in higher-level mathematics and a myriad of real-world contexts. Explore rich, research-based strategies and tasks that show how students are reasoning about and making sense of fractions. Use the opportunities that these and similar tasks provide to build on their understanding while identifying and correcting misunderstandings that may be keeping them from taking the next steps in learning.
Do your students believe that division "doesn't make sense" if the divisor is greater than the dividend? Explore rich, researched-based strategies and tasks that show how students are reasoning about and making sense of mulitplication and division. This book focuses on the specialised pedagogical content knowledge that you need to teach multiplication and division effectively in grades 3-5. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with these computations - not only in their current work, but also in higher-level maths and a myriad of real-world contexts. Explore rich, research-based strategies and tasks that show how students are reasoning about and making sense of multiplication and division. Use the opportunities that these and similar tasks provide to build on their understanding while identifying and correcting misunderstandings that may be keeping them from taking the next steps in learning. About the Series: You have essential understanding. It’s time to put it into practise in your teaching. The Putting Essential Understanding into Practice Series moves NCTM’s Essential Understanding Series into the classroom. The new series details and explores best practises for teaching the essential ideas that students must grasp about fundamental topics in mathematics - topics that are challenging to learn and teach but are critical to the development of mathematical understanding. Classroom vignettes and samples of student work bring each topic to life and questions for reader reflection open it up for hands-on exploration. Each volume underscores connections with the Common Core State Standards for Mathematics while highlighting the knowledge of learners, curriculum, understanding into practise, instructional strategies and assessment that pedagogical content knowledge entails. Maximise the potential of student-centred learning and teaching by putting essential understanding into practise.
"A series for teaching mathematics."--P. [1] of cover.
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 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
"This book is a game changer! Strengths-Based Teaching and Learning in Mathematics: 5 Teaching Turnarounds for Grades K- 6 goes beyond simply providing information by sharing a pathway for changing practice. . . Focusing on our students’ strengths should be routine and can be lost in the day-to-day teaching demands. A teacher using these approaches can change the trajectory of students’ lives forever. All teachers need this resource! Connie S. Schrock Emporia State University National Council of Supervisors of Mathematics President, 2017-2019 NEW COVID RESOURCES ADDED: A Parent’s Toolkit to Strengths-Based Learning in Math is now available on the book’s companion website to support families engaged in math learning at home. This toolkit provides a variety of home-based activities and games for families to engage in together. Your game plan for unlocking mathematics by focusing on students’ strengths. We often evaluate student thinking and their work from a deficit point of view, particularly in mathematics, where many teachers have been taught that their role is to diagnose and eradicate students’ misconceptions. But what if instead of focusing on what students don’t know or haven’t mastered, we identify their mathematical strengths and build next instructional steps on students’ points of power? Beth McCord Kobett and Karen S. Karp answer this question and others by highlighting five key teaching turnarounds for improving students’ mathematics learning: identify teaching strengths, discover and leverage students’ strengths, design instruction from a strengths-based perspective, help students identify their points of power, and promote strengths in the school community and at home. Each chapter provides opportunities to stop and consider current practice, reflect, and transfer practice while also sharing · Downloadable resources, activities, and tools · Examples of student work within Grades K–6 · Real teachers’ notes and reflections for discussion It’s time to turn around our approach to mathematics instruction, end deficit thinking, and nurture each student’s mathematical strengths by emphasizing what makes them each unique and powerful.
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
This easy-to-read summary is an excellent tool for introducing others to the messages contained in Principles and Standards.