Preschool geometry : theory, research, and practical perpectives PDF
Preview Preschool geometry : theory, research, and practical perpectives
PRESCHOOLGEOMETRY Preschool Geometry Theory, Research, and Practical Perspectives By EstherLevenson TelAvivUniversity,Israel DinaTirosh TelAvivUniversity,Israel and PessiaTsamir TelAvivUniversity,Israel SENSEPUBLISHERS ROTTERDAM/BOSTON/TAIPEI AC.I.P.recordforthisbookisavailablefromtheLibraryofCongress. ISBN978-94-6091-598-7(paperback) ISBN978-94-6091-599-4(hardback) ISBN978-94-6091-600-7(e-book) Publishedby:SensePublishers, P.O.Box21858,3001AWRotterdam,TheNetherlands www.sensepublishers.com Thisbookhasbeenreviewedbyindependentpeerreviewers,whorecommendedpublication. Printedonacid-freepaper Allrightsreserved©2011SensePublishers Nopartofthisworkmaybereproduced,storedinaretrievalsystem,ortransmittedinanyformor byanymeans,electronic,mechanical, photocopying,microfilming,recordingorotherwise,without writtenpermissionfromthePublisher,withtheexceptionofanymaterialsuppliedspecificallyforthe purposeofbeingenteredandexecutedonacomputersystem,forexclusiveusebythepurchaserof thework. TABLE OF CONTENTS Foreword ............................................................................................................... vii PART ONE: Studying Preschool Children’s Development of Geometrical Concepts Chapter 1: Theories and Research Related to Concept Formation in Geometry ...... 3 Chapter 2: What Does It Mean for Preschool Children to Know That a Shape Is an Image? Building Concept Images in Line with Concept Definitions ........... 19 Chapter 3: The Case of Circles: When the Concept Definition Is Inappropriate for the Age of the Children ............................................................. 37 Thinking about Other Shapes ............................................................................... 43 PART TWO: Engaging Young Children with Geometrical Tasks Chapter 4: Mathematical and Geometrical Tasks: Theories and Resarch .............. 47 Chapter 5: Implementing Geometrical Tasks: Some Possible Scenarios ............... 61 Chapter 6: Geometrical Tasks in Preschool: The Voice of the Teacher ................. 77 PART THREE: Getting Ready to Teach Geometry in the Preschool – Preschool Teacher Education Chapter 7: Conceptualizing Preschool Teachers’ Knowledge for Teaching Geometry ............................................................................................................ 87 Chapter 8: Enhancing Preschool Teachers’ Knowledge for Teaching Mathematics ........................................................................................................ 101 Chapter 9: Tasks in the Professional Development of Preschool Teachers ......... 119 Epilogue ......................................................................................................... 129 Referencess ......................................................................................................... 131 v FOREWORD Recently the issue of early childhood mathematics has come to the fore and with it the importance of teaching geometrical concepts and reasoning from a young age. Research has not only demonstrated that young children can learn mathematics but that children’s mathematics knowledge and reasoning should be actively promoted from an early age (Clements & Sarama, 2007). Specifically, geometry is not only in and of itself a key domain but it may also support the learning of other mathematical topics, such as number and patterns. Developing geometrical reasoning, progressing from visual to descriptive and analytical reasoning may go hand in hand with developing the ability to form well defined concepts in other domains as well. Unfortunately, young children with little mathematics knowledge tend to fall further behind their peers each year. Compounding this problem, early knowledge of mathematics is often seen as a predictor of later school success (Jimerson, Egelnad, & Teo, 1999). With this in mind, it is not surprising to find increased calls for improving early childhood mathematics education, including the learning of geometrical concepts. At a recent 2009 Conference of European Research in Mathematics Education, a new working group in Early Years Mathematics was established in response to increased calls for research regarding mathematics learning and mathematics teacher education in the early years (ages 3-8). A joint position paper published in the United States by the National Association for the Education of Young Children (NAEYC) and the National Council for Teachers of Mathematics (NCTM) stated that “high quality, challenging, and accessible mathematics education for 3- to 6- year old children is a vital foundation for future mathematics learning” (NAEYC & NCTM, 2002, p. 1). Further evidence of concern for preschool mathematics education may be seen in the rise of national curricula in various countries which now make specific and sometimes mandatory recommendations for including mathematics and geometry as part of the preschool program. For example, in England, the Statutory Framework for the Early Years Foundation Stage (2008) states precise goals related to learning geometrical concepts during these years. In the US, the Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics (NCTM, 2006) specifically mention that children should be able to identify and describe a variety of two- and three-dimensional shapes presented in a variety of ways and use geometrical concepts when recognizing and working on simple sequential patterns or when analyzing a data set. Yet, geometry and spatial thinking are often ignored or minimized in early education (Sarama & Clements, 2009). Thus, there is an urgent need for the early childhood education community to improve geometry education in preschool. This book is devoted entirely to the learning and teaching of geometry in preschool. The first part of the book is dedicated to children’s geometrical vii FOREWORD thinking; the second part focuses on geometrical tasks; the third part focuses on teaching geometry to young children. Each of the three parts is structured in a similar manner, beginning with general theory and research, continuing with specific examples related to those theories, and moving on to elements of actual practice. Part one is a study of preschool children’s conceptualization of geometrical figures. As such, it begins with a review of theories and research related to concept formation in geometry. It then discusses more specifically the building of concept images in line with concept definitions, and how children’s knowledge may be both assessed and promoted. It also discusses dilemmas that arise in the process. The second part of the book is devoted to geometrical tasks. It reviews the general structure and different elements of mathematical tasks and moves on to specifically discuss aspects of geometrical task design and implementation with young children. The second part also offers a review of several geometrical tasks implemented with young children and their role in developing and assessing geometrical reasoning. The third part of this book focuses on teaching geometry to young children. Taking into consideration that preschool children may attend a variety of day-care facilities or may be entirely home schooled, this part begins with theories and research related to the knowledge necessary for anyone who wishes to teach geometry to young children. It then continues with how this knowledge may be promoted, through, for example, professional development, and how this knowledge may then be put into practice. It also offers suggestions for tasks which may be implemented during professional development. For whom did we write this book? First of all, we believe that this book will contribute greatly to preschool caregivers and teachers. Often, these practitioners receive little or no preparation for teaching mathematics to young children (Ginsburg, Lee, & Boyd, 2008). Yet, as we mentioned above, according to many national guidelines and curricula, they are responsible for teaching geometry in their classes. This book offers both a theoretical review as well as practical suggestions for how the teacher may promote geometrical learning in preschool. We also believe that this book will contribute to teacher educators, responsible for the professional development of both prospective and practicing preschool teachers. For the research community, each part of this book not only offers a review of previous research related to that section, but also raises many questions which point to the need for additional research. In general, any person who has an interest in the mathematics education of preschool children, be it parents, caregivers, formal, and informal educators, will find this book relevant. As you read this book, you may view it as an odyssey, an intellectual wandering and eventful journey, of learning and teaching geometry with preschool children. It is not a book to be read through in one sitting. It is a book to linger over, to take the time and contemplate the different examples and situations illustrated throughout. We hope that you will also find this book an eventful journey. viii PART 1 STUDYING PRESCHOOL CHILDREN’S DEVELOPMENT OF GEOMETRICAL CONCEPTS This book is concerned with geometry in the preschool. In order to begin discussing how geometry might be introduced to young children and the kinds of tasks and activities which might promote geometrical thinking, it is necessary to first review how children develop geometrical thinking. The first chapter is dedicated to studying preschool children’s development of geometrical concepts. We begin with an overview of theories related to how children acquire geometrical concepts and research concerned with developing geometrical thinking. We then focus on two-dimensional figures, examining separately the nuances and challenges associated with different shapes. Finally, we discuss three-dimensional figures. The second and third chapters discuss how preschool children may come to build concept images in line with concept definitions.
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