Understanding Mathematics for Young Children

A Guide for Foundation Stage and Lower Primary Teachers

Author: Derek Haylock,Anne D Cockburn

Publisher: SAGE

ISBN: 1446204979

Category: Education

Page: 272

View: 6273

'This book is the ideal way to dispel some of the fears which surround the subject area of mathematics and should be an essential part of the professional development library of every early years setting provider for children aged three and over' - Early Years Update 'A book that is both readable and rigorous. [Its] guidance will help teachers to make mathematics meaningful to young children. Throughout the book connections are made which relate language, symbols, concrete materials and pictures to the key ideas that are central to effective learning for the 21st century. This book will help teachers gain a depth of understanding that will make them confident in engaging children with real mathematical thinking' - Dr J.E. Anghileri, Senior Lecturer in Mathematics and Mathematics Education, Faculty of Education, University of Cambridge 'This is an updated version of a classic text which has been a best -seller among teachers and student teachers for many years. Being always strongly grounded in the classroom, it develops in a non-intimidating way teachers' own understanding of the mathematics they are teaching. Many insightful examples of children's thinking and appropriate activities help to illustrate the points. This is an essential book for teachers of Early Years and Key Stage 1' - Margaret Brown, Professor of Mathematics Education, King's College London, UK This is a fully revised version of the authors' successful and much-used book, Understanding Mathematics in the Lower Primary Years, updated to include the current Foundation Stage Curriculum and the new Primary Framework in England. The authors empower the reader to have a clearer understanding of the mathematical ideas behind the material they use in the classroom. They also show how children can be helped to develop an understanding of mathematics for themselves, rather than just learning recipes and routines with little meaning. Major themes are: - Understanding through making connections - Equivalence and transformation - Using and applying mathematics It is written for teachers and teacher trainees engaged in teaching mathematics to children aged 3 to 8 years. It is an essential student text and professional reference work for all teachers of children aged 3 to 8 years. Dr Derek Haylock is an education consultant and author, working in the field of mathematics education. His book Mathematics Explained for Primary Teachers has been a leader in the field for many years, with a third edition published in 2006. Dr Anne Cockburn is a Reader in the School of Education and Lifelong Learning at the University of East Anglia, Norwich. Watch the authors talking about their book here: YouTube
Posted in Education

Understanding Mathematics for Young Children

A Guide for Teachers of Children 3-7

Author: Derek Haylock,Anne D Cockburn

Publisher: SAGE

ISBN: 1526410001

Category: Education

Page: 336

View: 8511

Having a deep understanding of the mathematical ideas and concepts taught in the classroom is vital as a nursery or primary school teacher. In order for children to get to grips with these concepts, trainee teachers need to be aware of how they come to interpret and understand them. Now into its 5th edition, this essential book helps trainee teachers develop their own knowledge of key mathematical ideas and concepts for the nursery and primary classroom. Now focussing specifically on ages 3 - 7, it also supports trainees with several age-appropriate classroom activities. As well as updates to further reading suggestions and research focuses, this revised edition includes new content on: -Mastery in learning mathematics -Simple Fractions -Roman numerals -Money as a form of measurement
Posted in Education

Understanding Mathematics in the Lower Primary Years

A Guide for Teachers of Children 3 - 8

Author: Derek Haylock,Anne D Cockburn

Publisher: SAGE

ISBN: 9780761941040

Category: Education

Page: 238

View: 5596

New Edition of Best Seller! This is a fully revised and updated edition of the authors' successful and much-used book and was written for those who wish to have a clearer understanding of the mathematical ideas behind the material they use in the classroom.
Posted in Education

(K)ein Gespür für Zahlen

So bekommt man den Durchblick in Mathe

Author: Barbara Oakley

Publisher: MVG Verlag

ISBN: 3864157811

Category: Mathematics

Page: 352

View: 6773

Mathematik versteht man oder eben nicht. Der eine ist dafür natürlich begabt, dem anderen bleibt dieses Fach für immer ein Rätsel. Stimmt nicht, sagt nun Barbara Oakley und zeigt mit ihrem Buch, dass wirklich jeder ein Gespür für Zahlen hat. Mathematik braucht nämlich nicht nur analytisches Denken, sondern auch den kreativen Geist. Denn noch mehr als um Formeln geht es um die Freiheit, einen der vielen möglichen Lösungsansätze zu finden. Der Weg ist das Ziel. Und wie man zum richtigen Ergebnis kommt, ist eine Kunst, die man entwickeln, entdecken und in sich wecken kann. Die Autorin vermittelt eine Vielfalt an Techniken und Werkzeugen, die das Verständnis von Mathematik und Naturwissenschaft grundlegend verbessern. (K)ein Gespür für Zahlen nimmt Ihnen — vor allem wenn Sie sich in Schule, Uni oder Beruf mathematisch oder naturwissenschaftlich beweisen müssen — nicht nur die Grundangst, sondern stärkt Ihren Mut, Ihren mathematischen Fähigkeiten zu vertrauen. So macht Mathe Spaß!
Posted in Mathematics

Experiences in Math for Young Children

Author: Rosalind Charlesworth

Publisher: Cengage Learning

ISBN: 1111301506

Category: Education

Page: 528

View: 7757

EXPERIENCES IN MATH FOR YOUNG CHILDREN, 6th Edition, focuses on the developmental sequence of mathematics for young children and its integration with other content areas. For each mathematics concept presented, Charlesworth provides a picture of how the concept might be incorporated into music and movement, language arts, visual arts, science, and social studies for children from birth through age eight. Early education students learn about problem solving as the major means for constructing concepts with a balance of naturalistic, informal, and structured activities. Students are also prepared to put concepts into action with the assessment, instructional, and evaluation strategies provided in each unit. Finally, the text provides specific information about active approaches to mathematics, materials and resources for setting up learning centers, guidance on parental involvement, and Internet resources. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Posted in Education

Engaging Young Children in Mathematics

Standards for Early Childhood Mathematics Education

Author: Douglas H. Clements,Julie Sarama,Ann-Marie DiBiase

Publisher: Routledge

ISBN: 0805842101

Category: Education

Page: 474

View: 6032

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.
Posted in Education

Mathematical and Analogical Reasoning of Young Learners

Author: Lyn D. English

Publisher: Routledge

ISBN: 1135638691

Category: Education

Page: 236

View: 392

Mathematical and Analogical Reasoning of Young Learners provides foundational knowledge of the nature, development, and assessment of mathematical and analogical reasoning in young children. Reasoning is fundamental to understanding mathematics and is identified as one of the 10 key standards for school mathematics for the new millennium. The book draws on longitudinal and cross-cultural studies, conducted in the United States and Australia, of children's reasoning development as they progressed from preschool through the end of second grade. The multifaceted analysis of young children's development of mathematical and analogical reasoning focuses on individual learners, their learning environments, and the interaction between the two. The multidisciplinary team of authors present multiple perspectives and multiple methodologies, and provide valuable information on organizing and sustaining interdisciplinary and cross-cultural inquiry. Key issues addressed include: *the relationship between mathematical and analogical reasoning; *how changes in children's reasoning relate to the implicit instruction they receive in their classrooms; *analyses of the participating teachers' knowledge, beliefs, and practices with respect to mathematical and analogical reasoning of young learners; and *ways in which we might promote development of mathematical and analogical reasoning in young children. This volume is highly relevant for mathematics educators, researchers in mathematics education, educational psychologists, early childhood teachers, and others interested in mathematical development of young children, in particular, the development of their reasoning processes.
Posted in Education

Mathematics in the Early Years

Author: Juanita V. Copley

Publisher: National Council of Teachers of

ISBN: 9780873534697

Category: Education

Page: 230

View: 1020

This thought-provoking material shows that although children think differently from adults and although children construct their own informal mathematics, they are capable of surprisingly complex forms of mathematical thinking and learning. The book presents historical, theoretical and social pictures of early childhood mathematics; discusses the mathematics content essential to the young child's understanding and zooms in on mathematics for the young child from the panoramic view of mathematics for everyone.
Posted in Education

Math and Science for Young Children

Author: Rosalind Charlesworth

Publisher: Cengage Learning

ISBN: 1305686373

Category: Education

Page: 512

View: 8074

MATH AND SCIENCE FOR YOUNG CHILDREN, Eighth Edition, introduces readers to engaging math and science experiences for early childhood and early elementary education programs, and provides an organized, sequential approach to creating a developmentally appropriate math and science curriculum. The content aligns with key guidelines and standards: The National Association for the Education of Young Children's (NAEYC) Professional Preparation Standards (2010); Developmentally Appropriate Practice (DAP) guidelines; Common Core Mathematics Standards; and Next Generation Science Standards (NGSS). The book also addresses STEM/STEAM and the essential domains of child growth and development during the crucial birth-through-eight age range. A valuable resource for the student/future teacher, working professional, or involved parent, MATH AND SCIENCE FOR YOUNG CHILDREN emphasizes the interrelatedness of math and science and how they can be integrated into all other curriculum areas. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Posted in Education

Mathematizing

An Emergent Math Curriculum Approach for Young Children

Author: Allen C. Rosales

Publisher: Redleaf Press

ISBN: 1605543969

Category: Education

Page: 176

View: 7925

This proven, accessible approach to a curriculum presents a learner-centered approach to math education. Mathematizing provides both the emergent curriculum and professional development frameworks to help young children learn math throughout their everyday routine and to facilitate teachers' understanding of how to see and support children's math learning at every turn. With this book and its plentitude of case studies, illustrations, photographs, and documentation, the mathematizing adult can interpret children's interests and use that knowledge as a catalyst for creating meaningful and purposeful mathematical lessons and interactions.
Posted in Education

Early Childhood Mathematics Education Research

Learning Trajectories for Young Children

Author: Julie Sarama,Douglas H. Clements

Publisher: Routledge

ISBN: 1135592500

Category: Education

Page: 424

View: 4341

This important new book synthesizes relevant research on the learning of mathematics from birth into the primary grades from the full range of these complementary perspectives. At the core of early math experts Julie Sarama and Douglas Clements's theoretical and empirical frameworks are learning trajectories—detailed descriptions of children’s thinking as they learn to achieve specific goals in a mathematical domain, alongside a related set of instructional tasks designed to engender those mental processes and move children through a developmental progression of levels of thinking. Rooted in basic issues of thinking, learning, and teaching, this groundbreaking body of research illuminates foundational topics on the learning of mathematics with practical and theoretical implications for all ages. Those implications are especially important in addressing equity concerns, as understanding the level of thinking of the class and the individuals within it, is key in serving the needs of all children.
Posted in Education

Beweise und Widerlegungen

Die Logik mathematischer Entdeckungen

Author: Imre Lakatos

Publisher: Springer-Verlag

ISBN: 3663001962

Category: Mathematics

Page: 163

View: 7962

Posted in Mathematics

Children's Mathematical Thinking in Primary Years

Author: Julia Anghileri

Publisher: A&C Black

ISBN: 9780826479112

Category: Education

Page: 192

View: 2781

This popular Continuum series, intended chiefly for teachers and trainee teachers, places strong emphasis on practice but at the same time incorporates the latest research in the field. The book demonstrates a strong belief in the ability of children to learn, and in the ability of teachers to increase children's learning potential. The series authors are distinguished practitioners in their fields who write with authority, but without jargon. With the increasingly popular constructivist framework for learning, teachers are coming to recognize the limitations of taught procedures and to find ways to encourage children to generate their own knowledge and understanding in mathematics. The challenge for teachers is to promote an environment that encourages mathematical thinking in which pupils of all abilities are able to achieve their full potential. This text brings together experiences of teachers and researchers who examine the ways children work mathematically, in order to provide an enhanced learning environment within the classroom. It also addresses key issues in current maths teaching.
Posted in Education

Entwicklungspsychologie im Kindes- und Jugendalter

Author: Robert Siegler,Nancy Eisenberg,Judy DeLoache,Jenny Saffran

Publisher: Springer-Verlag

ISBN: 3662470284

Category: Psychology

Page: 688

View: 5375

Wer dieses Standardwerk liest, erhält einen umfassenden Überblick über einschlägige Theorien, moderne Forschungsmethoden und neueste Erkenntnisse zur Kindes- und Jugendentwicklung. Die einfache, klare Sprache sowie zahlreiche Illustrationen und Fallbeispiele machen die Lektüre des Lehrbuchs für Studierende der Entwicklungspsychologie zum echten Vergnügen. Tabellen, Schaubilder, Zusammenfassungen und Praxisbeispiele helfen dabei, den Stoff zu verstehen, zu strukturieren und zu verinnerlichen. Die Inhalte des Werkes gehen dabei teilweise deutlich über den klassischen Lehrstoff für Bachelor-Prüfungen hinaus und vermitteln ein vertieftes Verständnis dafür, wie die Entwicklung in unterschiedlichen Bereichen zusammenhängt, von welchen sozialen und gesellschaftlichen Rahmenbedingungen sie abhängt und wie die Entstehung von Problemen verhindert werden kann. Die Auseinandersetzung mit dieser Lektüre lohnt sich daher nicht nur für die Prüfungsvorbereitung im Bachelor- und Masterstudium. Auch wenn Sie bereits beruflich oder privat mit Kindern und Jugendlichen zu tun haben, wird Ihnen das Buch als wertvolles Nachschlagewerk dienen und immer wieder Lust machen, sich mit den Inhalten auseinanderzusetzen.
Posted in Psychology

Big Ideas of Early Mathematics

What Teachers of Young Children Need to Know

Author: Jeanine O'Nan Brownell,Jie-Qi Chen,Lisa Ginet,Erikson Institute. Early Math Collaborative

Publisher: Pearson

ISBN: 9780132946971

Category: Education

Page: 196

View: 8954

"The Big Ideas that convey the core concepts of mathematics are at the heart of this new book that gives early childhood educators the skills they need to organize for mathematics teaching and learning during the early years. For teachers of children ages three through six, the book provides foundations for further mathematics learning and helps facilitate long-term mathematical understanding. It's the perfect guide for those who want to focus their instruction on mathematics that is central, coherent, and rigorous. In it, readers see clearly why building early foundations in math matters, why teachers' understanding of foundational math matters, and why the methods used to teach it matter. Developed by the Erikson Institute's Early Math Collaborative team, the book groups the Big Ideas into nine chapter on topics that are familiar to early childhood teachers-sets, pattern and regularity, number, counting, operations, measurement, data analysis, shapes, and spatial thinking. The work is in keeping with the content strands identified by the National Council of Teachers of Mathematics (NCTM), and maps pathways to help teachers meet the Common Core State Standards for Mathematics." -- publisher website.
Posted in Education

Children's Mathematics

Making Marks, Making Meaning

Author: Elizabeth Carruthers,Maulfry Worthington

Publisher: SAGE

ISBN: 1847878814

Category: Education

Page: 280

View: 1970

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.
Posted in Education

Learning and Teaching Early Math

The Learning Trajectories Approach

Author: Douglas H. Clements,Julie Sarama

Publisher: Routledge

ISBN: 1134080719

Category: Education

Page: 380

View: 2847

In this important book for pre- and in-service teachers, early math experts Douglas Clements and Julie Sarama show how "learning trajectories" help diagnose a child’s level of mathematical understanding and provide guidance for teaching. By focusing on the inherent delight and curiosity behind young children’s mathematical reasoning, learning trajectories ultimately make teaching more joyous. They help teachers understand the varying levels of knowledge exhibited by individual students, which in turn allows them to better meet the learning needs of all children. Using straightforward, no-nonsense language, this book summarizes the current research about how children learn mathematics, and how to build on what children already know to realize more effective teaching. This second edition of Learning and Teaching Early Math remains the definitive, research-based resource to help teachers understand the learning trajectories of early mathematics and become quintessential professionals. Updates to the new edition include: • Explicit connections between Learning Trajectories and the new Common Core State Standards. • New coverage of patterns and patterning. • Incorporation of hundreds of recent research studies.
Posted in Education

Fünfter sein

Author: Ernst Jandl,Norman Junge

Publisher: N.A

ISBN: 9783407760050

Category: Children's stories

Page: 31

View: 9750

Fünf ramponierte Gestalten sitzen in einem dunklen Raum vor verschlossener Tür. Durch den Türspalt dringt nur ein klein wenig Licht. Und dann: Einer nach dem anderen verschwindet hinter der Tür, um anschließend vollständig und repariert wieder herauszukommen. "Wie gesagt: ein Lieblingsbilderbuch" Hilde Elisabeth Menzel, Süddeutsche Zeitung "Es gibt Bilderbücher, die braucht man nur einmal durchzublättern, und schon will man sie besitzen, räumt ihnen in Gedanken einen Ehrenplatz auf dem Regal der Lieblingsbücher ein. Mit einem solchen Bilderbuch haben wir es hier zu tun." Süddeutsche Zeitung "Das ganze Buch ist eine Pracht, höchste Empfehlungsstufe. Der Text ist beste Minimaldichtung. Die Bilder ein rechter Herzensbrecher.
Posted in Children's stories

Children and Number

Difficulties in Learning Mathematics

Author: Martin Hughes

Publisher: Wiley-Blackwell

ISBN: 9780631135814

Category: Psychology

Page: 212

View: 2466

The importance of learning mathematics is constantly stressed by educationalists and employers alike. Yet survey after survey shows that large numbers of children leave school lacking both competence and interest in mathematics. What is going wrong and what should be done about it? In Children and Number Martin Hughes proposes a new perspective on children's early attempts to understand mathematics. He describes the surprisingly substantial knowledge about number which children acquire naturally before they start school, and contrasts this with the difficulties presented by the formal written symbolism of mathematics in the classroom. He argues that children need to build links between their informal and their formal understanding of number, and shows what happens when these links are not made. Children and Number describes many novel ways in which young children can be helped to learn about number. The author shows that the written symbols children often invent for themselves are more meaningful to them than the symbols that they are taught. He presents simple number games for introducing children to mathematical symbols in ways they can appreciate and understand. Dr. Hughes also describes how the computer language LOGO can be adapted for young children, and shows the dramatic effect that LOGO can have on their mathematical understanding.
Posted in Psychology

Teaching Young Children Mathematics

Author: Sydney L. Schwartz

Publisher: Rowman & Littlefield Publishers

ISBN: 9781578867011

Category: Education

Page: 212

View: 6702

Children learn mathematics most effectively in contexts that are meaningful to them. In order to realize the potential of those contexts for fostering young children's mathematical learning, knowledge or mathematics as well as child development is the way to nurture and challenge children's thinking. Avoiding the debates surrounding "hands-on" learning vs. direct instruction, the author focuses on the value of different contexts for learning and illustrates ways to genuinely engage children as active learners. The work is rich with examples of children's interactions with each other and with adults as they utilize and extend their understanding of mathematics. Examples and guidelines for developing lessons and activities will be useful to educators and parents. Chapters explore such topics as: how we underestimate young children's mathematical capabilities; how appropriate sequencing of learning and building on prior knowledge will enhance understanding; what teachers, including parent-teachers, need to know; and high-stakes testing. This is a work that brings together the connections between knowing the basics and constructing knowledge in accessible and practical ways.
Posted in Education