Early Childhood Mathematics

by Sperry Smith, Susan

• ISBN13: 9780205454761
• ISBN10: 0205454763
• Edition: 3rd
• Format: Paperback
• Copyright: 2009-01-01
• Publisher: Allyn & Bacon

Summary

This NCTM Standards-based book encourages the teacher or future teacher to create an active learning environment that fosters curiosity, confidence, and persistence in children as they learn math. Because the knowledge of important mathematical relationships, number sense, and the ability to solve problems are three key ingredients to the successful acquisition of math in the early years, this book pays special attention to helping teachers foster those skills and ways of thinking. Features new to this edition include discussion of the No Child Left Behind legislation, teacher lesson plan websites in every chapter, a collection of blackline masters, and weekly assessment activities.

Table of Contents

Preface	vii
Acknowledgments	ix
Foundations, Myths, and Standards	1	(18)
Six Myths about Teaching Mathematics to All Children	1	(5)
Success for Every Child	6	(2)
Serving Children in Inclusive Settings	8	(1)
The Child Who Is Gifted	8	(1)
The Child with Learning Disabilities	9	(1)
The Child Who Is Cognitively Disabled (Children with Mental Retardation)	9	(1)
Where Are We Going--The NCTM Standards	10	(3)
Developmentally Appropriate Education: Creating the Best Learning Environment	13	(1)
Piaget, Vygotsky, Bruner, and Dienes	14	(5)
Summary	16	(1)
Fieldwork: A Clinical Log or Math Journal	16	(1)
More Activities and Study Questions	16	(1)
Links to Technology	17	(1)
References	17	(2)
The Language of Math	19	(17)
Developing Math Language Using Song and Verse	19	(1)
Developing Math Language through Children's Literature	20	(1)
Math Language and Older Children	21	(1)
Math Concepts Found in the Early Childhood Curriculum	22	(6)
The NCTM Process Standards: Writing with Math Words	28	(1)
The Symbols of Math	29	(1)
The Number Sentence	29	(7)
Summary	31	(1)
Ready-Set-Math	31	(3)
Fieldwork: A Clinical Log or Math Journal	34	(1)
More Activities and Study Questions	34	(1)
Classroom Equipment	34	(1)
Related Children's Literature	34	(1)
Links to Technology	35	(1)
References	35	(1)
Early Math Concepts: Matching, Classification, Comparing, and Ordering or Seriation	36	(18)
Matching	36	(7)
Early Classification---Creating Sets	43	(2)
Informal Learning around Home and School	45	(3)
Comparing	48	(1)
Ordering or Seriation	49	(5)
Summary	52	(1)
Fieldwork: A Clinical Log or Math Journal	52	(1)
More Activities and Study Questions	52	(1)
Classroom Equipment	53	(1)
Related Children's Literature	53	(1)
Links to Technology	53	(1)
References	53	(1)
Space and Shape	54	(21)
Space	57	(4)
Shape	61	(2)
Geometric Concepts in the Early Grades	63	(12)
Summary	70	(1)
Ready-Set-Math	70	(2)
Fieldwork: A Clinical Log or Math Journal	72	(1)
More Activities and Study Questions	72	(1)
Classroom Equipment	73	(1)
Related Children's Literature	73	(1)
Links to Technology	73	(1)
References	74	(1)
Pattern, Function, and Early Algebra	75	(16)
Pattern	75	(7)
Pattern in Music and Art	82	(1)
Functions in the Primary Grade Curriculum	83	(2)
Early Algebra	85	(6)
Summary	85	(1)
Ready-Set-Math	86	(2)
Fieldwork: A Clinical Log or Math Journal	88	(1)
More Activities and Study Questions	89	(1)
Classroom Equipment	89	(1)
Related Children's Literature	90	(1)
Links to Technology	90	(1)
References	90	(1)
Graphing	91	(15)
Topics for Graphing Experiences	92	(1)
The Challenge in Reading Graphs	93	(1)
Questions about Graphing	94	(1)
Early Experiences with Graphing	94	(6)
Choosing Categories That Avoid Hurt Feelings or Wanting to Be on the Winning Side	100	(1)
Probability	101	(5)
Summary	101	(1)
Ready-Set-Math	102	(1)
Fieldwork: A Clinical Log or Math Journal	103	(1)
More Activities and Study Questions	104	(1)
Classroom Equipment	104	(1)
Related Children's Literature	105	(1)
Links to Technology	105	(1)
References	105	(1)
Developing Number Sense	106	(24)
A Cultural Perspective	106	(1)
Counting: The Young Child Plays and Learns	107	(2)
Research and Today's Classroom	109	(1)
Piaget's Tests of Conservation	110	(1)
Guided Learning Activities	111	(3)
Counting-On Activities	114	(1)
Counting-Back Activities	115	(2)
From Counting to Part-Part-Whole Activities	117	(3)
Thinking in Groups	120	(1)
Reading and Writing Numerals	121	(1)
Fractions and Number Sense	122	(8)
Summary	124	(1)
Ready-Set-Math	124	(2)
Fieldwork: A Clinical Log or Math Journal	126	(1)
More Activities and Study Questions	127	(1)
Classroom Equipment	127	(1)
Related Children's Literature	127	(1)
Related Records and Tapes	128	(1)
Links to Technology	128	(1)
References	128	(2)
Problem Solving: Addition and Subtraction	130	(22)
Math Is Problem Solving	131	(1)
Choosing a Problem	131	(1)
General Kinds of Problems	132	(1)
Problem Posing	133	(1)
A Positive Environment	134	(1)
General Strategies	135	(4)
Cognitive Background Information for Teachers: Classes of Problems	139	(3)
Rules of Operation	142	(2)
Helping Children Write Their Own Problems	144	(1)
Using What Children Know to Learn the Facts	145	(7)
Summary	146	(1)
Ready-Set-Math	147	(1)
Fieldwork: A Clinical Log or Math Journal	148	(1)
More Activities and Study Questions	149	(1)
Classroom Equipment	149	(1)
Related Children's Literature	149	(1)
Links to Technology	150	(1)
References	150	(2)
Understanding Our Place Value System	152	(17)
Base-Ten	152	(2)
Multiple Conceptions of Place Value	154	(1)
Children's Natural Preferences	155	(2)
Manipulatives	157	(5)
Estimating and Rounding Larger Numbers	162	(2)
Assessing Children's Understanding of Place Value	164	(5)
Summary	164	(1)
Ready-Set-Math	165	(1)
Fieldwork: A Clinical Log or Math Journal	166	(1)
More Activities and Study Questions	167	(1)
Classroom Equipment	167	(1)
Related Children's Literature	167	(1)
Links to Technology	168	(1)
References	168	(1)
Measurement	169	(22)
Definition	170	(1)
Principles of Measurement	170	(1)
The General Method	171	(1)
The Young Child Plays and Learns	172	(1)
Two Measurement Systems	173	(1)
Difficulties in the Measurement Process	174	(2)
Guided Learning	176	(15)
Summary	185	(1)
Ready-Set-Math	185	(3)
Fieldwork: A Clinical Log or Math Journal	188	(1)
More Activities and Study Questions	188	(1)
Classroom Equipment	188	(1)
Related Children's Literature	189	(1)
Related Records and Tapes	189	(1)
Links to Technology	190	(1)
References	190	(1)
Problem Solving: Multiplication and Division	191	(18)
Definition	192	(1)
Readiness for Multiplication and Division	192	(1)
Children's Natural Strategies	193	(1)
Cognitive Background for Teachers: Classes of Problems	194	(4)
Remainders	198	(1)
Illustrations	198	(2)
Linking Problem Solving to Symbolic Representation	200	(1)
Rules of Operation	201	(1)
The Role of Zero	202	(1)
Helping Children Write Their Own Problems	202	(1)
Learning the Multiplication Facts	203	(6)
Summary	204	(1)
Ready-Set-Math	204	(3)
Fieldwork: A Clinical Log or Math Journal	207	(1)
More Activities and Study Questions	207	(1)
Classroom Equipment	207	(1)
Related Children's Literature	207	(1)
Links to Technology	208	(1)
References	208	(1)
Assessment	209	(17)
Assessment and Evaluation Defined	210	(3)
Curriculum Reform and Alignment	213	(1)
Assessment Strategies	213	(8)
Scoring Methods	221	(1)
Alternatives for Students in Inclusive Settings	221	(2)
Record Keeping	223	(3)
Summary	224	(1)
Fieldwork: A Clinical Log or Math Journal	224	(1)
More Activities and Study Questions	225	(1)
Links to Technology	225	(1)
References	225	(1)
Planning for Success: A Good Beginning	226	(14)
How Do I Get Started?	226	(5)
How Can I Involve Parents in My Program?	231	(1)
What Should I Do If My Students Have Had Only Rote Math Background?	232	(1)
How Can I Meet the Needs of Children from Diverse Backgrounds?	232	(2)
How Can I Use Technology to Enhance Learning?	234	(6)
Summary	237	(1)
Fieldwork: A Clinical Log or Math Journal	237	(1)
More Activities and Study Questions	237	(1)
Links to Technology	238	(1)
References	238	(2)
Thematic Units	240	(27)
All about Bears (Preschool)	240	(6)
The Circus (Preschool-Kindergarten)	246	(6)
Insects (Preschool-Kindergarten)	252	(7)
Peter Rabbit (First and Second Grade)	259	(8)
Appendixes	267	(8)
A: The More or Less Game	267	(1)
B: Algebraic Solution	267	(1)
C: Glyph Clowns	268	(1)
D: Ten Strips	269	(1)
E: Dot Cards	269	(1)
F: Five and Ten Frames	270	(1)
G: Bear Pond	270	(1)
H: First-Grade Mathematics Informal Assessment	271	(2)
I: Bingo Card	273	(1)
J: One Hundred Chart	273	(1)
K: A Curriculum Web	274	(1)
Index	275