Children are Born Mathematicians Supporting Mathematical Development, Birth to Age 8

by Geist, Eugene

• ISBN13: 9780131116771
• ISBN10: 0131116770
• Edition: 1st
• Format: Paperback
• Copyright: 2008-02-01
• Publisher: Pearson

Summary

This brand new book for Early Childhood Mathematics Methods classes takes a comprehensive and chronological view of mathematics development in children, beginning at birth and going through the third grade. It offers specific teaching suggestions for each grade level based on the newly released NCTM (National Council of Teachers of Mathematics) standards. The new NCTM focal points for each grade are designed to help make mathematics teaching coherent and focused. Knowing what the two or three most important concepts are in each grade help teachers focus their teaching and their mathematics program. Using these standards can help teachers to use many different methods to reach their objectives rather than being tied to one specific method. This book takes a constructivist approach, meaning that children should be active learners and interact with other children in learning and constructing their knowledge. The author stresses that this process is at least as important as correct answers, as is comprehension of concepts. Teachers should focus on questioning and promoting mathematical thinking rather than simply getting the correct answer. Finally, the author encourages teachers to see math as a developmental process that children engage in as they grown and develop. The teacherrs"s role is to promote concept understanding and development through active experiences and questioning techniques in combination with teaching skills in developmentally appropriate ways.

Table of Contents

Children and Mathematics: A Natural Combination	p. 1
Chapter Objectives	p. 1
What is Emergent Mathematics?	p. 4
Promoting Emergent Math
Making a Difference as a Teacher	p. 7
Recent Findings in Teaching Mathematics	p. 9
Treating Children as Mathematicians	p. 11
Implications for Early Childhood Education
NCTM Principles, Standards and Curriculum Focal Points	p. 15
NCTM's Guiding Principles for School Mathematics
NCTM Standards for School Mathematics
NCTM and NAEYC Joint Statement on Mathematics
Curriculum Focal Points for Prekindergarten Through Grade 8
Putting the Pieces Together: The "3E" Approach	p. 28
Summary	p. 29
Web Sites	p. 31
Discuss and Apply What You Have Learned	p. 31
Building a Knowledge Base and Learning to Reflect	p. 35
Chapter Objectives	p. 35
Understanding Yourself	p. 36
The Process of Reflection
Dealing with Our Own Math Anxiety First
Teachers are Decision Makers	p. 40
A Lesson in Mathematics
Understanding Child Development	p. 43
The Behaviorist Approach
The Montessori Method
A Visual Approach to Learning Mathematics
The Constructivist Approach
NCTM and Theoretical Basis for Mathematics
Understanding Your Students	p. 57
Summary	p. 61
Web Sites	p. 62
Discuss and Apply What You Have Learned	p. 62
Diversity, Equity, and Individualized Instruction	p. 65
Chapter Objectives	p. 65
Nature and Nurture in the Mathematics Classroom	p. 66
Individualized Instruction	p. 67
Holding High Expectations for All Students
Socioeconomic Factors	p. 72
Overcoming SES Obstacles
Minority Student Achievement	p. 78
Children with Special Needs	p. 82
Creating Inclusive Environments
Gifted Students
English Language Learners and Linguistic Diversity	p. 90
Overcoming the Language Barrier
Gender Differences	p. 91
Accommodating Differences in Boys and Girls' Learning Styles
Standardized Testing and Gender Differences
Summary	p. 96
Web Sites	p. 97
Discuss and Apply What You Have Learned	p. 98
Creating a Constructivist Classroom	p. 103
Chapter Objectives	p. 103
The Child-Centered Curriculum	p. 104
Teachable Moments
Common Objections to the Child-Centered Approach
Preparation of the Child-Centered Environment	p. 115
Preparing the Environment
Designing Effective Educational Space
Materials	p. 118
Manipulatives
Textbooks and Math Series
What to Do Before the First Day	p. 123
Summary	p. 128
Web Sites	p. 129
Discuss and Apply What You Have Learned	p. 130
Infants and Toddlers	p. 132
Chapter Objectives	p. 132
What are Infants and Toddlers Like?	p. 133
What Mathematical Concepts Do Infants and Toddlers Learn?	p. 142
The Concept of "More"
The Concept of "One"
Making Relationships
Meeting Standards with Infants and Toddlers	p. 150
What Does an Infant and Toddler Learning Environment Look Like?	p. 155
Developmentally Appropriate Strategies and Activities for Infants and Toddlers	p. 157
Rhythm and Music
Blocks and Shapes
Everyday Activities
Manipulatives
Everyday Routines and Common Activities
Math Games
Supporting Emergent Mathematics	p. 163
Sample Infant and Toddler Lesson Plans	p. 163
Assessment	p. 171
Standardized vs. Authentic Assessment
Formal vs. Informal Assessment
Formative vs. Summative Assessment
Using Assessment with Infants and Toddlers
Summary	p. 174
Web Sites	p. 175
Discuss and Apply What You Have Learned	p. 176
Preschool Age	p. 180
Chapter Objectives	p. 180
What are Preschool Children Like?	p. 181
Physical Development
Cognitive Development
Emotional Development
Play
Developmental Milestones for Preschool Mathematics
What Mathematical Concepts do Preschool Children Learn?	p. 188
Mathematical Concepts in Preschool
Meeting Standards with Preschool Children	p. 201
General Mathematics Standards and Benchmarks for Preschool Mathematics
What Does a Preschool Mathematics Learning Environment Look Like?	p. 204
Developmentally Appropriate Strategies and Activities for Preschool-Age Children	p. 206
Sample Preschool Lesson Plans	p. 215
Assessment	p. 227
Summary	p. 230
Web Sites	p. 231
Discuss and Apply What You Have Learned	p. 232
Kindergarten and First Grade	p. 235
Chapter Objectives	p. 235
What Are K-1 Children Like?	p. 236
Physical Development
Cognitive Development
Social-Emotional Development
What Mathematical Concepts Do K-1 Children Learn?	p. 241
Encouraging Intellectual Autonomy
Mathematical Concepts in Kindergarten
Mathematical Concepts in First Grade
Meeting Standards With K-1 Children	p. 255
NCTM Focal Points
What Does a K-1 Mathematics Learning Environment Look Like?	p. 258
Developmentally Appropriate Strategies and Activities for K-1 Age Children	p. 261
Word Problems
Whole-Class Instruction
Math Games
Projects
Sample Kindergraten and First-Grade Lesson Plans	p. 269
Assessing Mathematics in K-1	p. 281
Summary	p. 286
Web Sites	p. 287
Discuss and Apply What You Have Learned	p. 287
Second and Third Grade	p. 291
Chapter Objectives	p. 291
What are Second and Third Graders Like?	p. 292
Physically
Cognitively
Socially-Emotionally
What Mathematical Concepts Do Second- and Third-Grade Children Learn?	p. 296
Base 10 and Place Value
Multiplication and Division
Linear Measurement
Learning Disabilities-Adhd, Dyslexia and Dyscalculia	p. 311
Meeting Standards for Second- and Third-Grade Children	p. 314
What Does a Second- and Third-Grade Mathematics Learning Environment Look Like?	p. 317
Developmentally Appropriate Strategies and Activities for Second-and Third-Grade Children	p. 318
Teaching Lessons and Problem Solving
Technology
Timed and Fluency Activities
Worksheets and Homework
Hands-On Materials and Manipulative
Sample Second- and Third-Grade Lesson Plans	p. 327
Assessing Mathematics in Second- and Third-Grade	p. 338
Summary	p. 341
Web Sites	p. 342
Discuss and Apply What You Have Learned	p. 343
Integrating Mathematics	p. 349
Chapter Objectives	p. 349
The Importance of Integration	p. 350
Integrating Math with Reading
Integrating Math with Science
Integrating Math with Social Studies
Integrating Math with Music
Integrating Math with Art
Physical Activity
Using the Project Approach	p. 370
Topic Selection
Summary	p. 373
Web Sites	p. 374
Discuss and Apply What You Have Learned	p. 375
Sample State Standards	p. 379
Index	p. 394
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