Levenson / Tirosh / Tsamir Preschool Geometry

2011
ISBN: 978-94-6091-600-7
Verlag: SensePublishers
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 134 Seiten

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. Geometry is a key domain mentioned in many national curricula and may also support the learning of other mathematical topics, such as number and patterns. This book is based on the rich experience (research and practice) of the authors and is devoted entirely to the learning and teaching of geometry in preschool. The first part of the book is dedicated to children's geometrical thinking, building concept images in line with concept definitions, and the dilemmas that arise in the process. The second part focuses on geometrical tasks and their role in developing and assessing geometrical reasoning. 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. Written in a meaningful, yet enjoyable manner, any person who has an interest in the mathematics education of preschool children, be it parents, caregivers, teachers, teacher educators, and researchers, will find this book relevant.

Autoren/Hrsg.

Levenson, Esther

Tirosh, Dina

Tsamir, Pessia

Inhaltsverzeichnis

1;Preschool Geometry;3
1.1;TABLE OF CONTENTS;5
1.2;FOREWORD;6
1.3;PART 1: STUDYING PRESCHOOL CHILDREN’S DEVELOPMENT OF GEOMETRICAL CONCEPTS;8
1.3.1;CHAPTER 1: THEORIES AND RESEARCH RELATED TO CONCEPT FORMATION IN GEOMETRY;9
1.3.1.1;1.1 THE NATURE OF CONCEPTS;9
1.3.1.2;1.2 MATHEMATICAL CONCEPTS;10
1.3.1.3;1.3 GEOMETRICAL CONCEPT FORMATION AND REASONING;13
1.3.1.3.1;Level one: Visual reasoning and naming;15
1.3.1.3.2;Levels 2 and 3: Critical and non-critical attributes;17
1.3.1.3.3;Prototypes and concept formation;19
1.3.1.3.4;Intuition and geometrical concept formation;21
1.3.1.3.5;Are the van Hiele levels discrete?;22
1.3.1.3.6;Developing three-dimensional concepts;23
1.3.1.4;1.4 LOOKING AHEAD;24
1.3.2;CHAPTER 2: WHAT DOES IT MEAN FOR PRESCHOOL CHILDREN TO KNOW THAT A SHAPE IS A TRIANGLE? BUILDING CONCEPT IMAGES IN LINE WITH CONCEPT DEFINITIONS;25
1.3.2.1;2.1 IDENTIFYING TRIANGLES – ARE ALL EXAMPLES AND NONEXAMPLES CREATED EQUAL?;26
1.3.2.2;2.2 REASONING ABOUT TRIANGLES;31
1.3.2.3;2.3 BUILDING CONCEPT IMAGES IN LINE WITH CONCEPT DEFINITIONS: THE POWER OF A WORKING DEFINITION;35
1.3.2.4;2.4 SUMMARY;41
1.3.3;CHAPTER 3: THE CASE OF CIRCLES – WHEN THE CONCEPT DEFINITION IS INAPPROPRIATE FOR THE AGE OF THE CHILDREN;43
1.3.3.1;THINKING ABOUT OTHER SHAPES;48
1.4;PART 2: ENGAGING YOUNG CHILDREN WITH GEOMETRICAL TASKS;49
1.4.1;CHAPTER 4: MATHEMATICAL AND GEOMETRICAL TASKS: THEORIES AND RESEARCH;50
1.4.1.1;4.1 ACADEMIC AND MATHEMATICAL TASKS;50
1.4.1.2;4.2 DESIGNING MATHEMATICAL TASKS;53
1.4.1.3;4.3 IMPLEMENTING MATHEMATICAL TASKS;57
1.4.1.4;4.4 GEOMETRICAL TASKS FOR YOUNG CHILDREN: CURRICULA GUIDELINES;60
1.4.1.5;4.5 SUMMARY;62
1.4.2;CHAPTER 5: IMPLEMENTING GEOMETRICAL TASKS – SOME POSSIBLE SCENARIOS;63
1.4.2.1;5.1 TASK ONE: ONE SHAPE AT A TIME;64
1.4.2.1.1;Implementing the One Shape at a Time task;64
1.4.2.1.2;Possible scenarios when implementing the One Shape at a Time task;65
1.4.2.1.3;Results of a study: Is this a pentagon? Why?;69
1.4.2.1.4;Summarizing the One Shape at a Time task;72
1.4.2.2;5.2 TASK TWO: WHAT DO WE HAVE HERE?;73
1.4.2.2.1;Implementing the What Do We Have Here? task;73
1.4.2.2.2;Possible scenarios when implementing the What Do We Have Here? task;74
1.4.2.3;5.3 SUMMARY;78
1.4.3;CHAPTER 6: GEOMETRICAL TASKS IN PRESCHOOL: THE VOICE OF THE TEACHER;79
1.4.3.1;6.1 EARLY PRESCHOOL;79
1.4.3.2;6.2 ADDITIONAL TASKS DESCRIBED BY PRESCHOOL TEACHERS;81
1.5;PART 3: GETTING READY TO TEACH GEOMETRY IN THE PRESCHOOL – PRESCHOOL TEACHER EDUCATION;86
1.5.1;CHAPTER 7: CONCEPTUALIZING PRESCHOOL TEACHERS’ KNOWLEDGE FOR TEACHING GEOMETRY;87
1.5.1.1;7.1 POSITION PAPERS, POLICY REPORTS, AND NATIONAL GUIDELINES: WHAT DO THEY RECOMMEND?;87
1.5.1.2;7.2 THEORIES OF TEACHERS’ KNOWLEDGE;91
1.5.1.3;7.3 CONCEPT IMAGE/CONCEPT DEFINITION – A THEORY OF MATHEMATICS KNOWLEDGE;94
1.5.1.4;7.4 COMBINING A THEORY OF TEACHERS’ KNOWLEDGE WITH A THEORY OF MATHEMATICS KNOWLEDGE;96
1.5.1.5;7.5 SUMMING UP;99
1.5.2;CHAPTER 8: ENHANCING PRESCHOOL TEACHERS’ KNOWLEDGE FOR TEACHING MATHEMATICS;101
1.5.2.1;8.1 BACKGROUND;101
1.5.2.2;8.2 PROGRAM SEGMENTS;102
1.5.2.2.1;Assessing preschool teachers’ TMK and GMK regarding concept images;102
1.5.2.2.2;Assessing and building teachers’ TMK and GMK regarding concept definitions;104
1.5.2.2.3;Differentiating between subject matter knowledge (TMK and GMK) and KCT;106
1.5.2.2.4;Building practitioners’ KCS regarding concept images of triangles;108
1.5.2.2.5;Building preschool teachers’ KCT regarding concept definitions and concept images of triangles;112
1.5.2.2.6;Summing up and looking ahead;116
1.5.3;CHAPTER 9: TASKS IN THE PROFESSIONAL DEVELOPMENT OF PRESCHOOL TEACHERS;119
1.5.3.1;Task 1: Drawing examples and nonexamples;120
1.5.3.2;Task two: Hierarchical relationships between figures;120
1.5.3.3;Task 3: Sorting figures;121
1.5.3.4;Task 4: Responding to children;121
1.5.3.5;Task 5: Knowledge of children’s ways of thinking;122
1.5.3.6;Task 6: Describing three-dimensional geometric figures;122
1.5.3.7;SUMMARY;123
1.5.3.8;APPENDIX A;124
1.5.3.9;APPENDIX B – HANDOUT FOR TASK 3;126
1.5.3.10;APPENDIX C – HANDOUT FOR TASK 4;127
1.5.3.11;APPENDIX C – TASK 5;128
1.6;EPILOGUE;129
1.7;REFERENCES;131