The teaching number sense series focuses on the critical role that number sense plays in students' developing mathematical understanding. Number sense encompasses a wide range of abilities, including being able to make reasonable estimates and to think and reason flexibly.

The teaching number sense series focuses on the critical role that number sense plays in students' developing mathematical understanding. Number sense encompasses a wide range of abilities, including being able to make reasonable estimates and to think and reason flexibly.

Just as athletes stretch their muscles before every game and musicians play scales to keep their technique in tune, mathematical thinkers and problem solvers can benefit from daily warm-up exercises. Jessica Shumway has developed a series of routines designed to help young students internalize and deepen their facility with numbers. The daily use of these quick five-, ten-, or fifteen-minute experiences at the beginning of math class will help build students' number sense. Students with strong number sense understand numbers, ways to represent numbers, relationships among numbers, and number systems. They make reasonable estimates, compute fluently, use reasoning strategies (e.g., relate operations, such as addition and subtraction, to each other), and use visual models based on their number sense to solve problems. Students who never develop strong number sense will struggle with nearly all mathematical strands, from measurement and geometry to data and equations. In Number Sense Routines, Jessica shows that number sense can be taught to all students. Dozens of classroom examples -- including conversations among students engaging in number sense routines -- illustrate how the routines work, how children's number sense develops, and how to implement responsive routines. Additionally, teachers will gain a deeper understanding of the underlying math -- the big ideas, skills, and strategies children learn as they develop numerical literacy.

This unique book represents another concerted research effort concerning Chinese mathematics education, with contributions from the world's leading scholars and most active researchers. The book presents the latest original research work with a particular focus on the "teaching" side of Chinese mathematics education to a wide international audience. There are mainly three sections in the book. The first section introduces readers to a historical and contemporary perspective, respectively, on traditional mathematical teaching in ancient China and on how modern Chinese mathematics teachers teach and pursue their pre-service training and in-service professional development. The second section presents studies investigating a wide range of issues at both the macro- and micro-levels on how Chinese mathematics teachers teach mathematics. The third section focuses on Chinese mathematics teachers, investigating issues about their knowledge, belief, teacher training and professional development. Like its predecessor, "How Chinese Learn Mathematics: Perspectives from Insiders," this book is a must for educational researchers, practitioners, and policy-makers who are interested in knowing more about mathematics teaching, teachers, teacher education and professional development concerning Chinese teachers and learners.Contents: Focusing on Chinese Mathematics Teaching, Teachers and Teacher Education: An Introduction"Historical and Contemporary Perspectives: "The Wisdom of Traditional Mathematical Teaching in China "(DAI Qin and CHEUNG Ka Luen)" How Chinese Teachers Teach Mathematics and Pursue Professional Development: Perspectives from ContemporaryInternational Research "(FAN Lianghuo, MIAO Zhenzhen and MOK Ah Chee Ida)" "Understanding the Chinese Ways of Teaching Mathematics: " Mathematics Teaching in a Chinese Classroom: A Hybrid-Model Analysis of Opportunities for Students' Learning "(HUANG Rongjin, MILLER L Diane and TZUR Ron)"Achieving Coherence in the Mathematics Classroom: Toward a Framework for Examining Instructional Coherence "(WANG Tao, CAI Jinfa and HWANG Stephen)" Elementary School Teachers' Instruction in Measurement: Cases of Classroom Teaching of Spatial Measurement in Taiwan "(HUANG Hsin-Mei E)" Pedagogical and Curriculum Potentials of Homework: A Case Study about Geometric Proofs in Shanghai "(FANG Yanping)" Teaching Calculation of Time Intervals: Comparing Mathematics Competence of Students in Macau, Hong Kong and the Netherlands "(LI Titus Siu Pang)" Teaching Number Sense via Interactive Multimedia in a Primary School in Taiwan "(YANG Der-Ching, CHEN Pei-Chieh, TSAI Yi Fang and HSIEH Tien-Yu)"Teaching Geometrical Theorems in Grade 8 Using the "Shen Tou" Method: A Case Study in Shanghai "(DING Liping, JONES Keith and ZHANG Dianzhou)" Implementation of Objectives Based on the Curriculum Standards: A Case of Teaching Using Letter to Represent Number at a Chinese Primary School in Chinese Mainland "(HUANG Xingfeng, YANG Jinglei and LI Shiqi)" Chinese Project-based Classroom Practices: Promoting Students' Engagement in Mathematical Activities "(XU Binyan and ZHU Guangtian)"A Large-Scale Video Survey on Taiwanese Fourth-Grade Classrooms of Mathematical Teaching Behaviors "(LEE Yuan-Shun and LIN Fou-Lai)" Features of Exemplary Lessons under the Curriculum Reform in Chinese Mainland: A Study of Thirteen Elementary Mathematics Lessons "(MA Yunpeng and ZHAO Dongchen)" Qingpu Mathematics Teaching Reform and Its Impact on Student Learning "(GU Lingyuan, YANG Yudong and HE Zhenzhen)""Chinese Mathematics Teachers, Teacher Educati

This volume emerges from a partnership between the American Federation of Teachers and the Learning Research and Development Center at the University of Pittsburgh. The partnership brought together researchers and expert teachers for intensive dialogue sessions focusing on what each community knows about effective mathematical learning and instruction. The chapters deal with the research on, and conceptual analysis of, specific arithmetic topics (addition, subtraction, multiplication, division, decimals, and fractions) or with overarching themes that pervade the early curriculum and constitute the links with the more advanced topics of mathematics (intuition, number sense, and estimation). Serving as a link between the communities of cognitive researchers and mathematics educators, the book capitalizes on the recent research successes of cognitive science and reviews the literature of the math education community as well.

This teacher resource offers a detailed introduction to the Hands-On Mathematics program (guiding principles, implementation guidelines, an overview of the processes that grade 2 students use and develop during mathematics inquiry), and a classroom assessment plan complete with record-keeping templates and connections to the Achievement Levels outlined in the?WNCP Mathematics Curriculum. The resource also provides strategies and visual resources for developing students? mental math skills. The resource includes: Mental Math Module 1: Patterns and Relations Module 2: Statistics and Probability Module 3: Shape and Space Module 4: Number Concepts Module 5: Number Operations Each module is divided into lessons that focus on specific curricular outcomes. Each lesson has materials lists activity descriptions questioning techniques problem-solving examples activity centre and extension ideas assessment suggestions activity sheets and visuals

This teacher resource offers a detailed introduction to the Hands-On Mathematics program (guiding principles, implementation guidelines, an overview of the processes that grade 1 students use and develop during mathematics inquiry), and a classroom assessment plan complete with record-keeping templates and connections to the Achievement Levels outlined in the Ontario Mathematics Curriculum. The resource also provides strategies and visual resources for developing students' mental math skills. The resource includes: Mental Math Strategies Unit 1: Patterning and Algebra Unit 2: Data Management and Probability Unit 3: Measurement Unit 4: Geometry and Spatial Sense Unit 5: Number Sense and Numeration Each unit is divided into lessons that focus on specific curricular expectations. Each lesson has materials lists, activity descriptions, questioning techniques, problem-solving examples, activity centre and extension ideas, assessment suggestions, activity sheets, and visuals required.

Mathematics and Science education have both grown in fertile directions in different geographic regions. Yet, the mainstream discourse in international handbooks does not lend voice to developments in cognition, curriculum, teacher development, assessment, policy and implementation of mathematics and science in many countries. Paradoxically, in spite of advances in information technology and the “flat earth” syndrome, old distinctions and biases between different groups of researcher’s persist. In addition limited accessibility to conferences and journals also contribute to this problem. The International Sourcebooks in Mathematics and Science Education focus on under-represented regions of the world and provides a platform for researchers to showcase their research and development in areas within mathematics and science education. The First Sourcebook on Asian Research in Mathematics Education: China, Korea, Singapore, Japan, Malaysia and India provides the first synthesized treatment of mathematics education that has both developed and is now prominently emerging in the Asian and South Asian world. The book is organized in sections coordinated by leaders in mathematics education in these countries and editorial teams for each country affiliated with them. The purpose of unique sourcebook is to both consolidate and survey the established body of research in these countries with findings that have influenced ongoing research agendas and informed practices in Europe, North America (and other countries) in addition to serving as a platform to showcase existing research that has shaped teacher education, curricula and policy in these Asian countries. The book will serve as a standard reference for mathematics education researchers, policy makers, practitioners and students both in and outside Asia, and complement the Nordic and NCTM perspectives.

This sixth volume, in the series of yearbooks by the Association of Mathematics Educators in Singapore, entitled Learning Experiences to Promote Mathematics Learning is unique in that it focuses on a single theme in mathematics education. The objective is for teachers and researchers to advance the learning of mathematics through meaningful experiences.Several renowned international and Singapore scholars have published their work in this volume. The fourteen chapters of the book illustrate evidence-based practices that school teachers and researchers can experiment with in their own classrooms to bring about meaningful learning outcomes. Three broad themes, namely fundamentals for active and motivated learning, learning experiences for developing mathematical processes, and use of ICT tools for learning through visualizations, simulations and representations, shape the ideas in these chapters. The book makes a significant contribution towards the learning of mathematics. It is a good resource for mathematics teachers, educators and research students.

This must-have resource provides the theoretical groundwork for teaching number sense. Authored by Chris Shore, this e-book empowers teachers with the pedagogy, lessons, and detailed instructions to help them implement Clothesline Math in K-12 classrooms. Detailed, useful tips for facilitating the ensuing mathematical discourse are also included. At the elementary level, the hands-on lessons cover important math topics including whole numbers, place value, fractions, order of operations, algebraic reasoning, variables, and more. Implement Clothesline Math at the secondary level and provide students with hands-on learning and activities that teach advanced math topics including geometry, algebra, statistics, trigonometry, and pre-calculus. Aligned to state and national standards, this helpful resource will get students excited about learning math as they engage in meaningful discourse.