Children are Born Mathematicians: Supporting Mathematical Development, Birth to Age 8 by Eugene Geist

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Developed to address the new NCTM focal points, which use a chronological approach to thinking about what should be taught in early childhood mathematics.  The book views mathematics as a developmental and constructive process in which the teacher acts as an instructor and facilitator.  The book takes a “3 E” approach to thinking about how math is presented to each age group.  For infants and toddlers, best introduced and presented through interaction with the environment so designing a mathematically active and interactive classroom should be the focus.  For Preschool and Kindergarten children, mathematics is best learned through experiences with materials or projects in the classroom.  For grade school children, more traditional educational experiences become more developmentally appropriate in combination with environment and experience.

 

The approach is to see math as a developmental process that children engage in as they grow 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.

  • Focus on Standards based mathematics education--Using standards can help teachers to use many different methods to reach their objectives rather than being tied to one text book series.
  • Focus on children's mathematics development rather than on skill and drill--Mathematics is best introduced to children if the teacher understands how children think and grow generally and mathematically.  This book focuses in depth on the mathematical development of the child and how to introduce developmentally appropriate mathematics programs.
  • NCTM Focal Points are central to teaching mathematics--The new NCTM focal points for each grade are designed to help make mathematics teaching coherent and focused in schools.  This book uses those focal points as a guide to teaching in each grade level.  Knowing what are the two to three most important concepts in each grade helps teachers focus their teaching and mathematics program.
  • A constructivist perspective as well as an acceptance of skills practice--This book takes a constructivist perspective to learning mathematics.  This means that children should be active learners and interact with other children in learning and constructing their knowledge.  Process is at least as important as correct answers and, for teachers, questioning and promoting mathematical thinking is at least as important as learning how to produce correct answers.  Comprehension of concepts is more important than just getting correct answers.
  • Focuses on Mathematics from Birth--This is the only book to include infants and toddlers as active learners of methematics.  A lot of construction and active learning is taking place in the infant and toddlers environment and mathematics can be supported even in the very young.  Just as literacy is promoted from birth, so too can math.

Chapter 1    Children and Mathematics:  A Natural Combination

                    What is Emergent Mathematics?

                    Making a Difference as a Teacher

                    Recent Findings in Teaching Mathematics

                    Treating Children as Mathematicians

                    NCTM Principles, Standards and Curriculum Focal Points

                    Putting the Pieces Together:  The "3E" Approach

                    Summary

                    Web Sites

                    Discuss and Apply What You Have Learned     

Chapter 2    Building a Knowledge Base and Learning to Reflect

                    Understanding Yourself

                    Teachers are Decision Makers

                    Understanding Child Development

                    Understanding Your Students

                       Summary

                    Web Pages

                    Discuss and Apply What You Have Learned     

Chapter 3    Diversity, Equity, and Individualized Instruction

                    Individualized Instruction

                    Socioeconomic Factors

                    Minority Student Achievement

                    Children with Special Needs

                    English Language Learners and Linguistic Diversity

                    Gender Differences

                        Summary

                    Web Pages

                    Discuss and Apply What You Have Learned     

Chapter 4    Creating a Constructivist Classroom

                    The Child-Centered Curriculum

                    Preparation of the Child-Centered Environment

                    Materials

                    What to Do Before the First Day

                      Summary

                    Web Pages

                    Discuss and Apply What You Have Learned     

Chapter 5    Infants and Toddlers

                    What are Infants and Toddlers Like?

                    What Mathematical Concepts Do Infants and Toddlers Learn?

                    Meeting Standards with Infants and Toddlers

                    What Does an Infant and Toddler Learning Environment Look Like?

                    Developmentally Appropriate Strategies and Activities for Infants and Toddlers

                    Supporting Emergent Mathematics

                    Sample Infant and Toddler Lesson Plans

                    Assessment

                      Summary

                    Web Pages

                    Discuss and Apply What You Have Learned     

Chapter 6    Preschool Age

                    What Are Preschool Children Like?

                    What Mathematical Concepts Do Preschool Children Learn?

                    Meeting Standards with Preschool Children

                    What Does a Preschool Mathematics Learning Environment Look Like?

                    Developmentally Appropriate Strategies and Activities for Preschool Age Children

                    Sample Preschool Lesson Plans

                    Assessment

                      Summary

                    Web Pages

                    Discuss and Apply What You Have Learned     

Chapter 7    Kindergarten and First Grade

                    What Are K-1 Children Like?

                    What Mathematical Concepts Do K-1 Children Learn?

                    Meeting Standards with K-1 Children

                    What Does a K-1 Mathematics Learning Environment Look Like?

                    Developmentally Appropriate Strategies and Activities for K-1 Age Children

                    Sample Kindergarten and First-Grade Lesson Plans

                    Assessing Mathematics in K-1

                      Summary

                    Web Pages

                    Discuss and Apply What You Have Learned     

Chapter 8    Second and Third Grade

                    What Are SEcond and Third Graders Like?

                    What Mathematical Concepts Do Second and Third Grade Children Learn?

                    Learning Disabilities - ADHD, Dyslexia and Dyscalculia

                    Meeting Standards for Second and Third Grade Children

                    What Does a Second and Third Grade Mathematics Learning Environment Look Like?

                    Developmentally Appropriate Strategies and Activities for Second and Third Grade Children

                    Sample Second- and Third-Grade Lesson Plans

                    Assessing Mathematics in Second and Third Grade

                      Summary

                    Web Pages

                    Discuss and Apply What You Have Learned     

Chapter 9    Integrating Mathematics

                    The Importance of Integration

                    Using the Project Approach

                      Summary

                    Web Pages

                    Discuss and Apply What You Have Learned    


Appendix - Sample State Standards

 

 

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