Preschool geometry : theory, research, and practical perpectives

Cover......Page 1
Preschool Geometry......Page 4
ISBN 9789460915994 (hardback)......Page 5
TABLE OF CONTENTS......Page 6
FOREWORD......Page 8
PART 1: STUDYING PRESCHOOL CHILDREN’S DEVELOPMENT OF GEOMETRICAL CONCEPTS......Page 10
1.1 THE NATURE OF CONCEPTS......Page 12
1.2 MATHEMATICAL CONCEPTS......Page 13
1.3 GEOMETRICAL CONCEPT FORMATION AND REASONING......Page 16
Level one: Visual reasoning and naming......Page 18
Levels 2 and 3: Critical and non-critical attributes......Page 20
Prototypes and concept formation......Page 22
Intuition and geometrical concept formation......Page 24
Are the van Hiele levels discrete?......Page 25
Developing three-dimensional concepts......Page 26
1.4 LOOKING AHEAD......Page 27
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......Page 28
2.1 IDENTIFYING TRIANGLES – ARE ALL EXAMPLES AND NONEXAMPLES CREATED EQUAL?......Page 29
2.2 REASONING ABOUT TRIANGLES......Page 34
2.3 BUILDING CONCEPT IMAGES IN LINE WITH CONCEPT DEFINITIONS: THE POWER OF A WORKING DEFINITION......Page 38
2.4 SUMMARY......Page 44
CHAPTER 3: THE CASE OF CIRCLES – WHEN THE CONCEPT DEFINITION IS INAPPROPRIATE FOR THE AGE OF THE CHILDREN......Page 46
THINKING ABOUT OTHER SHAPES......Page 52
PART 2: ENGAGING YOUNG CHILDREN WITH GEOMETRICAL TASKS......Page 54
4.1 ACADEMIC AND MATHEMATICAL TASKS......Page 56
4.2 DESIGNING MATHEMATICAL TASKS......Page 59
4.3 IMPLEMENTING MATHEMATICAL TASKS......Page 63
4.4 GEOMETRICAL TASKS FOR YOUNG CHILDREN: CURRICULA GUIDELINES......Page 66
4.5 SUMMARY......Page 68
CHAPTER 5: IMPLEMENTING GEOMETRICAL TASKS – SOME POSSIBLE SCENARIOS......Page 70
Implementing the One Shape at a Time task......Page 71
Possible scenarios when implementing the One Shape at a Time task......Page 72
Results of a study: Is this a pentagon? Why?......Page 76
Summarizing the One Shape at a Time task......Page 79
Implementing the What Do We Have Here? task......Page 80
Possible scenarios when implementing the What Do We Have Here? task......Page 81
5.3 SUMMARY......Page 85
6.1 EARLY PRESCHOOL......Page 86
6.2 ADDITIONAL TASKS DESCRIBED BY PRESCHOOL TEACHERS......Page 88
PART 3: GETTING READY TO TEACH GEOMETRY IN THE PRESCHOOL – PRESCHOOL TEACHER EDUCATION......Page 94
7.1 POSITION PAPERS, POLICY REPORTS, AND NATIONAL GUIDELINES: WHAT DO THEY RECOMMEND?......Page 96
7.2 THEORIES OF TEACHERS’ KNOWLEDGE......Page 100
7.3 CONCEPT IMAGE/CONCEPT DEFINITION – A THEORY OF MATHEMATICS KNOWLEDGE......Page 103
7.4 COMBINING A THEORY OF TEACHERS’ KNOWLEDGE WITH A THEORY OF MATHEMATICS KNOWLEDGE......Page 105
7.5 SUMMING UP......Page 108
8.1 BACKGROUND......Page 110
Assessing preschool teachers’ TMK and GMK regarding concept images......Page 111
Assessing and building teachers’ TMK and GMK regarding concept definitions......Page 113
Differentiating between subject matter knowledge (TMK and GMK) and KCT......Page 115
Building practitioners’ KCS regarding concept images of triangles......Page 117
Building preschool teachers’ KCT regarding concept definitions and concept images of triangles......Page 121
Summing up and looking ahead......Page 125
CHAPTER 9: TASKS IN THE PROFESSIONAL DEVELOPMENT OF PRESCHOOL TEACHERS......Page 128
Task two: Hierarchical relationships between figures......Page 129
Task 4: Responding to children......Page 130
Task 6: Describing three-dimensional geometric figures......Page 131
SUMMARY......Page 132
APPENDIX A......Page 133
APPENDIX B – HANDOUT FOR TASK 3......Page 135
APPENDIX C – HANDOUT FOR TASK 4......Page 136
APPENDIX C – TASK 5......Page 137
EPILOGUE......Page 138
REFERENCES......Page 140