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Children Are Born Mathematicians : Supporting Mathematical Development, Birth to Age 8,9780131116771
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Children Are Born Mathematicians : Supporting Mathematical Development, Birth to Age 8



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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 Combinationp. 1
Chapter Objectivesp. 1
What is Emergent Mathematics?p. 4
Promoting Emergent Math
Making a Difference as a Teacherp. 7
Recent Findings in Teaching Mathematicsp. 9
Treating Children as Mathematiciansp. 11
Implications for Early Childhood Education
NCTM Principles, Standards and Curriculum Focal Pointsp. 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" Approachp. 28
Summaryp. 29
Web Sitesp. 31
Discuss and Apply What You Have Learnedp. 31
Building a Knowledge Base and Learning to Reflectp. 35
Chapter Objectivesp. 35
Understanding Yourselfp. 36
The Process of Reflection
Dealing with Our Own Math Anxiety First
Teachers are Decision Makersp. 40
A Lesson in Mathematics
Understanding Child Developmentp. 43
The Behaviorist Approach
The Montessori Method
A Visual Approach to Learning Mathematics
The Constructivist Approach
NCTM and Theoretical Basis for Mathematics
Understanding Your Studentsp. 57
Summaryp. 61
Web Sitesp. 62
Discuss and Apply What You Have Learnedp. 62
Diversity, Equity, and Individualized Instructionp. 65
Chapter Objectivesp. 65
Nature and Nurture in the Mathematics Classroomp. 66
Individualized Instructionp. 67
Holding High Expectations for All Students
Socioeconomic Factorsp. 72
Overcoming SES Obstacles
Minority Student Achievementp. 78
Children with Special Needsp. 82
Creating Inclusive Environments
Gifted Students
English Language Learners and Linguistic Diversityp. 90
Overcoming the Language Barrier
Gender Differencesp. 91
Accommodating Differences in Boys and Girls' Learning Styles
Standardized Testing and Gender Differences
Summaryp. 96
Web Sitesp. 97
Discuss and Apply What You Have Learnedp. 98
Creating a Constructivist Classroomp. 103
Chapter Objectivesp. 103
The Child-Centered Curriculump. 104
Teachable Moments
Common Objections to the Child-Centered Approach
Preparation of the Child-Centered Environmentp. 115
Preparing the Environment
Designing Effective Educational Space
Materialsp. 118
Textbooks and Math Series
What to Do Before the First Dayp. 123
Summaryp. 128
Web Sitesp. 129
Discuss and Apply What You Have Learnedp. 130
Infants and Toddlersp. 132
Chapter Objectivesp. 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 Toddlersp. 150
What Does an Infant and Toddler Learning Environment Look Like?p. 155
Developmentally Appropriate Strategies and Activities for Infants and Toddlersp. 157
Rhythm and Music
Blocks and Shapes
Everyday Activities
Everyday Routines and Common Activities
Math Games
Supporting Emergent Mathematicsp. 163
Sample Infant and Toddler Lesson Plansp. 163
Assessmentp. 171
Standardized vs. Authentic Assessment
Formal vs. Informal Assessment
Formative vs. Summative Assessment
Using Assessment with Infants and Toddlers
Summaryp. 174
Web Sitesp. 175
Discuss and Apply What You Have Learnedp. 176
Preschool Agep. 180
Chapter Objectivesp. 180
What are Preschool Children Like?p. 181
Physical Development
Cognitive Development
Emotional Development
Developmental Milestones for Preschool Mathematics
What Mathematical Concepts do Preschool Children Learn?p. 188
Mathematical Concepts in Preschool
Meeting Standards with Preschool Childrenp. 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 Childrenp. 206
Sample Preschool Lesson Plansp. 215
Assessmentp. 227
Summaryp. 230
Web Sitesp. 231
Discuss and Apply What You Have Learnedp. 232
Kindergarten and First Gradep. 235
Chapter Objectivesp. 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 Childrenp. 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 Childrenp. 261
Word Problems
Whole-Class Instruction
Math Games
Sample Kindergraten and First-Grade Lesson Plansp. 269
Assessing Mathematics in K-1p. 281
Summaryp. 286
Web Sitesp. 287
Discuss and Apply What You Have Learnedp. 287
Second and Third Gradep. 291
Chapter Objectivesp. 291
What are Second and Third Graders Like?p. 292
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 Dyscalculiap. 311
Meeting Standards for Second- and Third-Grade Childrenp. 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 Childrenp. 318
Teaching Lessons and Problem Solving
Timed and Fluency Activities
Worksheets and Homework
Hands-On Materials and Manipulative
Sample Second- and Third-Grade Lesson Plansp. 327
Assessing Mathematics in Second- and Third-Gradep. 338
Summaryp. 341
Web Sitesp. 342
Discuss and Apply What You Have Learnedp. 343
Integrating Mathematicsp. 349
Chapter Objectivesp. 349
The Importance of Integrationp. 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 Approachp. 370
Topic Selection
Summaryp. 373
Web Sitesp. 374
Discuss and Apply What You Have Learnedp. 375
Sample State Standardsp. 379
Indexp. 394
Table of Contents provided by Ingram. All Rights Reserved.

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