Children Are Born Mathematicians: Supporting Mathematical Development, Birth to Age 8 » (1st Edition)

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 teacher’s role is to promote concept understanding and development through active experiences and questioning techniques in combination with teaching skills in developmentally appropriate ways.

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