Children Doing Mathematics provides a reliable and up to date review of the substantial recent work in children' mathematical understanding. The authors also present important new research on children's understanding of number, measurement, arithmetic operation and fractions both in and out of school. The central theme of Children Doing Mathematics is that there are crucial conditions for children's mathematical learning. Firstly, children have to come to grips with conventional mathematical systems. Secondly, but equally important, they have to be able to present mathematical knowledge in a way that solves problems. The book also discusses how mathematical activities and knowledge involve much more than what is currently viewed as mathematics in the school curriculum. Most recent work illustrates how children can be successful in mathematical activities outside school whereas they fail in similar activities in the classroom. Through these two underlying themes the authors bring together discussions on conventional mathematical learning and on real life mathematical success. In so doing, they also highlight new and better ways of analysing children's abilities and of advancing their learning in school.

Noting that young children are capable of surprisingly complex forms of mathematical thinking and learning, this book presents a collection of articles depicting children discovering mathematical ideas, teachers fostering students' informal mathematical knowledge, adults asking questions and listening to answers, and researchers examining children's mathematical thinking. The chapters are: (1) "Why Do We Teach Young Children So Little Mathematics? Some Historical Considerations" (Balfanz); (2) "Children's Ways of Knowing: Lessons from Cognitive Development Research" (Sophian); (3) "The Sociology of Day Care" (McDill and Natriello); (4) "Cultural Aspects of Young Children's Mathematics Knowledge" (Guberman); (5) "Ready To Learn: Developing Young Children's Mathematical Powers" (Greenes); (6) "The Development of Informal Counting, Number, and Arithmetic Skills and Concepts" (Baroody and Wilkins); (7) "Geometric and Spatial Thinking in Young Children" (Clements); (8) "Rational-Number Learning in the Early Years: What Is Possible?" (Hunting); (9) "Young Children Doing Mathematics: Observations of Everyday Activities" (Ginsburg, Inoue, and Seo); (10) "Cognitively Guided Instruction in One Kindergarten Classroom" (Warfield and Yttri); (11) "Supporting Students' Ways of Reasoning about Patterns and Partitions" (McClain and Cobb); (12) "The Effective Use of Computers with Young Children" (Clements); (13) "Making Connections: A 'Number Curriculum' for Preschoolers" (Shane); (14) "Within Easy Reach: Using a Shelf-Based Curriculum To Increase the Range of Mathematical Concepts Accessible to Young Children" (Nelson); (15) "Teaching Mathematics through Musical Activities" (Kim); (16) "The Boston University--Chelsea Project" (Greenes); (17) "The Outdoors as a Context for Mathematics in the Early Years" (Basile); (18) "Using Storybooks To Help Young Children Make Sense of Mathematics" (Hong); (19) "Movement, Mathematics, and Learning: Experiences Using a Family Learning Model" (Coates and Franco); (20) "Math in Motion" (Goodway, Rudisill, Hamilton, and Hart); (21) "Assessing the Mathematical Understanding of the Young Child" (Copley); (22) "Improving Opportunities and Access to Mathematics Learning in the Early Years" (Padron); (23) "What To Do When They Don't Speak English: Teaching Mathematics to English-Language Learners in the Early Childhood Classroom" (Weaver and Gaines); (24) "Involving Parents of Four- and Five-Year-Olds in Their Children's Mathematics Education: The FAMILY MATH Experience" (Coates and Thompson); (25) "Perspectives on Mathematics Education and Professional Development through the Eyes of Early Childhood Administrators" (Weber); and (26) "Early Childhood Mathematics in Japan" (Hatano and Inagaki). (Each chapter contains references.) (KB)

The third edition of Reys’ Helping Children Learn Mathematics is a practical resource for undergraduate students of primary school teaching. Rich in ideas, tools and stimulation for lessons during teaching rounds or in the classroom, this edition continues to provide a clear understanding of how to navigate the Australian Curriculum, with detailed coverage on how to effectively use Information and Communications Technology (ICT) in the classroom. This is a full colour printed textbook with an interactive eBook code included. Great self-study features include: auto-graded in-situ knowledge check questions, video of teachers demonstrating how different maths topics can be taught in the classroom and animated, branched chain scenarios are in the e-text.

Drawing on their many years' experience of teaching children 3 to 8 years, the authors explain the development and range of young children's mathematical marks and representations.

Visit the author's own website here! Children's Mathematics Network 'In Case Study 5 (a grassroots 'Children's Mathematics Network group') the initiative supported the participants in their professional change by giving them a space for the detailed and joint consideration of children's mathematical thinking. Another significant feature of this initiative is its focus on careful consideration and analysis of children's mathematics, and the ways in which professionals can support and encourage the children's mathematical thinking and reasoning... The standard of the mathematical understanding, thinking and reasoning that the displays revealed was far higher than the specified curriculum objectives for children of this age...' - Researching Effective CPD in Mathematics Education (RECME) project: (NCETM, 2009) 'The review also plays great score by play-based learning of a mathematical nature, and makes specific recommendations regarding early mark-making as a precursor to abstract mathematical symbolism'. Section 115 features children's mathematical graphics and emphasises: 'The role of mark-making in children's cognitive development is set out in the taxonomy (Carruthers and Worthington, 2006)'. The report recommends that 'local authorities, leaders, managers and head teachers should provide a culture with a significant focus on mathematical mark-making' and 'a learning environment that encourages children to choose to use their own mathematical graphics to support their mathematical thinking and processes' - The Williams Maths Review: (DCSF, 2008) `At the very heart of the success of the book is the authors' ability to see mathematics through young children's eyes by listening to and reflecting on the constant efforts made by children to make sense of their world. This is a liberating book which proposes that the teaching of mathematics could and should be a highly creative and enjoyable proceess' - Branwen Llewelyn Jones, Early Years Consultant at PACE Ltd / TACTYC 'Ground breaking... To single out any one chapter would be unfair because there is something thought-provoking and inspirational throughout. If you want to expand your understanding upwards and outwards then get a copy soon' - Times Educational Supplement 'I first read Children's Mathematics, Making Marks, Making Meaning a couple of years ago and it had an immediate impact on my own thinking and teaching, and the work I do with trainee teachers. I'm sure you will find it compelling reading too. I think it has the potential to change, in a fundamental way, how we think about early mathematical development' - Lynne McClure, Editor, Math Co-ordiator's File, Mathematics Association 'In their exceptionally readable and informative book, Children's Mathematics, Making Marks, Making Meaning Carruthers and Worthington (2006) draw attention to one of the main goals of early years teaching, that is, to help children make links between the mathematics they have already encountered (and continue to engage with) at home and the more abstract mathematics of the school. These authors suggest that by encouraging children to represent mathematical ideas in their own ways and, crucially, by talking to the pupils about the marks they have made, we are given a "window" onto their thinking that may otherwise be inaccessible' - Liz Pumphrey, NRICH This book draws on the authors' many years of teaching children aged three to eight years and also on their extensive research with children in the home, nursery and school. The authors explain the development and range of young children's mathematical marks and visual representations, showing how children make mental connections between their own early marks and subsequent abstract mathematical symbolism, and go on to develop their own written methods. Combining theory and practice, this acclaimed book demonstrates how children's own mathematical graphics are highly creative and show deep levels of thinking. The authors show how this is the key to success in school mathematics and to higher levels of achievement. The authors are winners of TACTYC's (2003) Jenefer Joseph Award for the Creative Arts (3 - 8) - awarded for their innovative work with children on mathematical graphics.

Eminent scholars from around the globe gathered to discuss how educational systems would change if the prevailing principles of constructivism were applied to three major aspects of those systems -- knowledge and learning, communication, and environment. This volume provides documentation of the proceedings of this important meeting - - the Early Childhood Action Group of the Sixth International Congress on Mathematics Education. This international assembly, representing such diverse disciplines as mathematics and math education, epistemology, philosophy, cognitive science, psycholinguistics, and science education, is the first to examine early childhood mathematics education from constructivist and international perspectives in addition to formulating recommendations for future work in the field.

Includes bibliographical references (pages 395-406) and index.

Teaching Young Children Mathematics provides a comprehensive overview of mathematics instruction in the early childhood classroom. Taking into account family differences, language barriers, and the presence of special needs students in many classrooms throughout the U.S., this textbook situates best practices for mathematics instruction within the larger frameworks of federal and state standards as well as contemporary understandings of child development. Key topics covered include: developmental information of conceptual understanding in mathematics from birth through 3rd grade, use of national and state standards in math, including the new Common Core State Standards, information for adapting ideas to meet special needs and English Language Learners, literacy connections in each chapter, ‘real-world’ connections to the content, and information for family connections to the content.

Engaging Young Children in Mathematics: Standards for Early Childhood Mathematics Education brings together the combined wisdom of a diverse group of experts involved with early childhood mathematics. The book originates from the landmark 2000 Conference on Standards for Pre-kindergarten and Kindergarten Mathematics Education, attended by representatives from almost every state developing standards for young children's mathematics; federal government officials; mathematicians; mathematics educators; researchers from mathematics education, early childhood education, and psychology; curriculum developers; teachers; policymakers; and professionals from organizations such as the National Conference of Teachers of Mathematics and the National Association for the Education of Young Children. The main goal of the Conference was to work collectively to help those responsible for framing and implementing early childhood mathematics standards. Although it has its roots in the Conference, the expanded scope of the standards and recommendations covered in this book includes the full range of kindergarten to grade 2. The volume is organized into two main parts and an online appendix (http://www.gse.buffalo.edu/org/conference/). Part One, Major Themes and Recommendations, offers a framework for thinking about pre-kindergarten - grade 2 mathematics education and specific recommendations. Part Two, Elaboration of Major Themes and Recommendations, provides substantive detail regarding young students' understandings of mathematical ideas. Each Part includes five parallel subsections: "Standards in Early Childhood Education"; "Math Standards and Guidelines"; "Curriculum, Learning, Teaching, and Assessment"; "Professional Development"; and "Toward the Future: Implementation and Policy." As a whole the book: * presents comprehensive summaries of research that provide specific guidelines for standards, curriculum, and teaching; * takes the recent reports and recommendations for early childhood mathematics education to the next level; * integrates practical details and research throughout; and * provides a succinct, but thorough review of research on the topics, sequences, and learning trajectories that children can and should learn at each of their first years of life, with specific developmental guidelines that suggest appropriate content for each topic for each year from 2-year-olds to 7-year-olds. This is an indispensable volume for mathematics educators, researchers, curriculum developers, teachers and policymakers, including those who create standards, scope and sequences, and curricula for young children and professional teacher development materials, and students in mathematics education, early childhood trainers, teacher educators, and faculty in mathematics education.

Essential guide for teaching children aged 3-7, developing knowledge of key mathematical ideas and concepts in the nursery and primary classroom.