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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
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Searching... | 30000010193614 | QA135.6 G44 2009 | Open Access Book | Book | Searching... |
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Summary
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 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.
Table of Contents
Chapter 1 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 |
Chapter 2 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 |
Chapter 3 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 |
Chapter 4 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 |
Chapter 5 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 |
Chapter 6 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 |
Chapter 7 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 |
Chapter 8 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 |
Chapter 9 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 |
Appendix Sample State Standards | p. 379 |
Index | p. 394 |