Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence provides a rationale for focal points for each grade level, prekindergarten - 8.

Children in prekindergarten focus on counting and gradually master the essential one-to-one matching of an object to a number. By the end of second grade, they can represent one, two and three digit numbers, understand simple fractions and apply a variety of facts and strategies to add and subtract skilfully. This book supports this progression by inviting students to count and order ducklings in a line, compute the total cost of several items on a menu and play a variety of games that reinforce their understanding of number, addition and subtraction.

Shows teachers and other educators how they can incorporate NCTM's Curriculum Focal Points for PreK-8 into their current mathematics curricula. The book provides practical ideas for bringing focus to mathematics learning and instruction in the classroom. Intended as a professional development tool, it presents self and group reflection tasks, sample student work, a sample state mathematics curriculum organised around the Focal Points and other tools that teacher educators can use with the preservice teachers in their classes.

Focus in Grade 2: Teaching with Curriculum Focal Points describes and illustrates learning paths for the mathematical concepts and skills of each grade 2 Focal Point as presented in Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics. It includes representational supports for teaching and learning that can facilitate understanding, stimulate productive discussions about mathematical thinking and provide a foundation for fluency with the core ideas. This book also discusses common student errors and misconceptions, reasons the errors may arise and teaching methods or visual representations to address the errors. Because learning paths cut across grades, some discussion of related Focal Points at grades 1 and 3 have been included to describe and clarify prerequisite knowledge and show how the grade 2 understandings build on what went before. Focus in Grade 2, one in a series of grade-level publications, is designed to support teachers, supervisors and coordinators as they develop and refine the mathematics curriculum.

A comprehensive guide to helping all learners focus and reach their potential through brain-centered management and teaching strategies! Includes a full-color, innovative teaching poster with fascinating facts about the brain!

Based on extensive research conducted by the authors, Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2, is designed to help classroom teachers understand, monitor, and guide the development of students' reasoning and sense making about core ideas in elementary school mathematics. It describes and illustrates the nature of these skills using classroom vignettes and actual student work in conjunction with instructional tasks and learning progressions to show how reasoning and sense making develop and how instruction can support students in that development. Students who can make sense of mathematical ideas can apply those ideas in problem solving, even in unfamiliar situations, and can use them as a foundation for future learning. Without them, students are reduced to rote learning, often experiencing frustration and failure. But what do reasoning and sense making during learning and teaching look like? Each chapter of Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2 explores a different topic that young children encounter in mathematics, demonstrating with actual student work and classroom dialogue how their mathematical knowledge and reasoning ability move through "levels of sophistication" or learning progressions: After opening with a discussion of the nature of reasoning and sense making and their critical importance in developing mathematical thinking, chapter 1 examines how young students attempt to make sense of the concepts of place value and length measurement. Chapter 2 focuses on how early childhood instruction can engage students in mathematical reasoning while helping them construct a rich sense of number and operations. Chapter 3 identifies core algebraic ideas and shows how students can engage with these ideas in ways that not only deepen their understanding of arithmetic but also lays the foundation for the future study of algebra. Children's reasoning and sense making as they decompose and compose geometric shapes--including reasoning about area--is examined in chapter 4. The use of learning progressions to understand students' reasoning and to guide their sense making with appropriate teaching is also discussed. Not just a theoretical discussion, the book also provides specific suggestions for related instructional activities for each topic. Supplementary online resources can be accessed at NCTM's More4U website. Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2 will be a valuable and practical addition to your professional library.

Do your students have the incorrect idea that addition “makes numbers bigger” and subtraction “makes numbers smaller”? Do they believe that subtraction is always “taking away”? 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 specialized pedagogical content knowledge that you need to teach addition and subtraction effectively in prekindergarten–grade 2. 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 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 addition and subtraction. 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. You have essential understanding. It’s time to put it into practice 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 practices 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 reaction 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, instructional strategies, and assessment that pedagogical content knowledge entails. Resources and tasks are available at nctm.org/more4U.

Discover new, practical methods for teaching literacy skills in your early childhood classroom. Has teaching early literacy skills become a stumbling block to getting your preschool students kindergarten ready? Break out of the tired “letter of the week” routine and learn how to transform your lessons with fun and effective techniques. Teach Smarter: Literacy Strategies for Early Childhood Teachers will equip teachers to infuse every aspect of their teaching with exciting hands-on literacy teaching methods that engage students and help them build authentic connections with books, so that 100% of their students will have a strong literacy foundation and will be fully prepared for success in kindergarten and beyond. Respected author Vanessa Levin, veteran early childhood educator and author of the “Pre-K Pages” blog, breaks down the research and translates it into realistic, actionable steps you can take to improve your teaching. Features specific examples of teaching techniques and activities that engage students in hands-on, experiential learning during circle time, centers, and small groups. Offers a simple, four-step system for teaching literacy skills, based on the foundational principles of early literacy teaching Demonstrates how to build your confidence in your ability to get 100% of your students ready for kindergarten, long before the end of the school year Understand the problems with traditional literacy teaching and identify gaps in your current teaching practice with this valuable resource.

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