Mathematics for Young Children

by Shaw, Jean M.; Blake, Sally

• ISBN13: 9780024097644
• ISBN10: 0024097640
• Edition: 1st
• Format: Paperback
• Copyright: 1997-06-03
• Publisher: Pearson

Summary

Appropriate for undergraduate and graduate courses in teaching mathematics in the primary grades or in early childhood. Intended for pre-service and in-service teachers, this book discusses how mathematics should be taught to children ages three to eight. Based on ideas from effective practice, the book supports the importance of quality early education and the need for better mathematics for all children. Organized in two parts, the first part describes the need for and nature of mathematics reform, discusses how young children learn, and how educators can plan and implement activities. Multi-faceted approaches to assess learning are also addressed in part one. The second part of the text focuses on mathematics topics and ways to facilitate young children's learning.

Table of Contents

Chapter 1 A New Vision of Mathematics for Young Children	1	(20)
Why Do We Need a New Vision of Mathematics for Young Children?	4	(1)
What is the New Vision of Mathematics for Young Children	4	(2)
Who Has Supported the New Vision of Mathematics for Young Children? Who Must Work to Implement the New Vision?	6	(1)
How Can the New Vision of Mathematics for Young Children Be Implemented?	7	(10)
Problem Solving	8	(1)
Communicating Mathematically	9	(3)
Reasoning	12	(2)
Making Mathematics Connections	14	(3)
When Will the New Vision of Mathematics Education for Young Children Be Implemented?	17	(1)
Parallel Reform Efforts in Science Education	17	(1)
Summary	18	(1)
Applications: Thinking and Collaborating	18	(1)
References	19	(1)
Selected Children's Books	20	(1)
Chapter 2 Developmental Expectations in Math	21	(22)
Developmentalism and Constructivism	22	(4)
Influences on Developmental Theories	26	(12)
Jean Piaget	26	(6)
Zoltan P. Dienes	32	(4)
Maria Montessori	36	(2)
General Implications of Constructivist Theories	38	(1)
Planning for Developmental Levels	39	(2)
Mathematics Development	40	(1)
Summary	41	(1)
References	41	(2)
Chapter 3 Mathematics Standards and Developmentally Appropriate Practice	43	(22)
Developmentally Appropriate Practice	44	(8)
Background	45	(1)
National Association for the Education of Young Children	45	(2)
Principles and Implications	47	(5)
NCTM Professional Standards	52	(9)
Principles for Teaching	53	(4)
Classroom Environment	57	(1)
Teacher Evaluation	58	(2)
Professional Development	60	(1)
Mathematical Assumptions for Teaching	61	(1)
Summary	62	(1)
References	63	(2)
Chapter 4 Helping All Children Learn Mathematics	65	(22)
Equity Issues in Mathematics	67	(8)
Gender Issues	68	(3)
Cultural Influences	71	(2)
Socioeconomic Environment	73	(2)
Building Parents' and Families' Understanding of Their Roles in Equity Issues	75	(4)
Involving Parents in Mathematical Programs	77	(1)
Activities for Involving Parents	78	(1)
The Classroom Environment	79	(4)
Teaching Methods	79	(2)
Thematic Units	81	(2)
Summary	83	(1)
Applications: Thinking and Problem Solving	84	(1)
References	85	(2)
Chapter 5 Assessment and Evaluation	87	(24)
Purposes and Uses of Assessment and Evaluation	89	(2)
Techniques for Formative Assessment and Evaluation of Children's Work	91	(11)
Observation	92	(1)
Questioning and Discussion	93	(2)
Anecdotal Records	95	(1)
Interviews	96	(1)
Written Work and Drawings	97	(2)
Performances and Problem Solving	99	(1)
Children's Self-Assessment and Evaluation	100	(2)
Techniques for Summative Assessment and Evaluation of Children's Work	102	(5)
Projects and Products	102	(1)
Portfolios	103	(3)
Tests	106	(1)
Changing Assessment and Evaluation Techniques	107	(1)
Summary	108	(1)
Applications: Thinking and Collaborating	108	(1)
References	109	(2)
Chapter 6 Problem Solving and Reasoning	111	(24)
What Is Problem Solving?	113	(1)
What Is Reasoning?	114	(6)
Types of Reasoning	116	(4)
Reasoning and Young Children	120	(1)
Sorting and Classifying	120	(3)
Developing Problem-Solving Strategies	123	(4)
Developing Problem-Solving and Reasoning Situations	127	(5)
Plan for Success	127	(1)
Praise Risk-Taking	128	(1)
Use Nonjudgmental Responses	129	(1)
Small-Group Cooperative Work	130	(2)
Summary	132	(1)
Applications: Thinking and Collaborating	132	(1)
References	133	(1)
Selected Children's Books	134	(1)
Chapter 7 Numeration and Number Sense	135	(26)
Developing Number Ideas and Number Sense	137	(1)
Materials for Developing Children's Understandings of Numeration and Number Sense	138	(2)
Numeration and Number Sense Topics for Young Children	140	(17)
Counting	140	(3)
Number Concepts and Number Sense	143	(2)
Comparing Sets and Numbers	145	(1)
Cardinal and Ordinal Numbers	146	(1)
Numbers, Numerals, and Number Names	146	(2)
Place Value	148	(5)
Fractions and Decimals	153	(2)
Estimating with Numbers	155	(2)
Summary	157	(1)
Applications: Thinking and Collaborating	157	(1)
References	158	(1)
Selected Children's Books	159	(2)
Chapter 8 Operation Concepts and Skills	161	(24)
Operations and Operation Sense	163	(10)
Presenting and Developing Meanings of Operations	173	(5)
Addition	173	(1)
Subtraction	174	(1)
Multiplication	175	(2)
Division	177	(1)
Basic Facts	178	(2)
Multidigit Operations	180	(2)
Summary	182	(1)
Applications: Thinking and Collaborating	182	(1)
References	183	(1)
Selected Children's Books	184	(1)
Chapter 9 Working with Data and Probability	185	(24)
Developing Statistical Thinking	186	(2)
Materials for Involving Children in Working with Data and Probability	188	(1)
Gathering, Organizing, and Displaying Data	189	(2)
Sources of Data	191	(1)
Graphs for Young Children	192	(8)
Real Graphs	194	(1)
Picture Graphs	194	(2)
Bar Graphs	196	(1)
Circle Graphs	197	(2)
Line Graphs	199	(1)
Interpreting Data	200	(2)
Discussing Data	200	(1)
Writing About Data	201	(1)
Simple Statistics	201	(1)
Probability	202	(4)
Summary	206	(1)
Applications: Thinking and Problem Solving	206	(1)
References	207	(1)
Selected Children's Books	208	(1)
Chapter 10 Geometry	209	(24)
Geometry for Young Children	212	(1)
Materials for Involving Young Children in Geometry	212	(1)
Theory for Teaching Geometry to Young Children	213	(4)
The van Hieles Model	213	(3)
Del Grande's Aspects of Spatial Perception	216	(1)
Geometry Topics for Young Children	217	(12)
Geometry in the World	217	(2)
Positions and Paths	219	(1)
Three-Dimensional Figures	220	(2)
Two-Dimensional Figures	222	(6)
Congruence and Symmetry	228	(1)
Summary	229	(1)
Applications: Thinking and Collaborating	229	(2)
References	231	(1)
Selected Children's Books	231	(2)
Chapter 11 Measurement	233	(26)
Measurement for Young Children	235	(1)
More Principles for Teaching Measurement	236	(1)
Materials for Involving Children in Measurement	237	(2)
Exploring Measurement Attributes	239	(17)
Length	239	(3)
Area	242	(1)
Capacity	243	(2)
Volume	245	(1)
Weight	246	(2)
Time	248	(4)
Temperature	252	(2)
Angles	254	(2)
Summary	256	(1)
Applications: Thinking and Collaborating	257	(1)
References	258	(1)
Selected Children's Books	258	(1)
Appendix A Suppliers of Mathematics Education Materials Suitable for Young Children	259	(2)
Appendix B Mathematics Autobiography	261	(2)
Index	263