prekindergarten, 142

principle, 135

socioeconomic variation on tasks of, 103

standards of learning, 230, 231

subitizing and, 132, 134, 141, 142, 146, 150, 151, 155

teaching-learning paths, 129, 130, 131, 132-134, 135, 139, 140, 141, 142, 147, 148, 150, 169

truly operational cardinal number, 166

Charge to committee, 1, 10-13

Child Care Development Fund, 303

Child Development Associate, 292, 303, 318

Child-initiated experiences, 226, 227, 247-248, 250, 298, 352

Chutes and Ladders, 238 n.3, 251

CLASS framework, 235-236

Classroom Assessment Scoring System, 234, 236, 237, 243-244, 299

Classroom context for instruction.

See also Grade 1;

Kindergarten;

Mathematics instruction;

Preschool programs

emotional support, 236

generalized teaching strategies, 241-242

instructional opportunities, 235

instructional supports, 237

kindergarten, 239-242

mathematics content, 235, 237-242

noninstructional activities and time, 235

organization and management, 236-237

prekindergarten, 237-239

teacher-child interactions, 235-237

Classroom Observation of Early Mathematics Environment and Teaching, 270-271, 272

Cognitive flexibility, 83

Cognitive foundations for early learning

behavioral and attentional regulation and, 82-84, 85

cardinality, 63, 71

fraction representations, 61

measurement, 61, 79-82, 84-85

number understanding, 60-71, 84

pattern finding, 69, 83

Piaget’s theories, 60, 70, 72, 79-80, 155-156

preverbal number knowledge, 60-66

proportional relations, 61, 82

spatial thinking and geometry, 61, 71-79, 84, 192-193

universal starting points, 59-60, 85, 95, 96, 104

van Heile’s theories, 77

Cognitively Guided Instruction, 314

Colorado, 229

Comparisons, 30-31, 53, 97

additive, 23, 33, 34, 231, 351

Competence and performance.

See also Cognitive foundations for early learning;

Learning disabilities;

Number understanding or number sense

activities in daily lives and, 100, 102-104, 113

automaticity, 128

committee conclusions, 332-335

English language learners, 100-101

experiences and learning opportunities

and, 100, 103-105, 333-334

family role, 101-105, 113, 333-334

fluency, 7, 25, 111, 125, 128, 138, 141, 145, 153, 154, 156, 157, 158, 159, 160, 166, 169, 250, 352

gender and, 98-99

individual variations in, 127-128, 154, 157, 334-335

international comparisons, 184, 192, 273

language/cultural influences, 98, 106-110

parents’ knowledge and beliefs and, 102

race/ethnicity and, 99-100

socioeconomic status and, 1-2, 70, 96-98, 103, 104-105, 334-335

Composing/decomposing activities, 248

addition/subtraction situations, 23, 32-33, 45-46, 51, 133, 231

decimal system, 45-46

defined, 352

groups of groups, 49

groups of groups of groups, 50

and mathematical connections across content areas, 39-40, 45-46, 48-49, 50, 194

and measurement, 35, 39-40, 46, 202, 206, 207, 360

and multiplication/division, 45, 51-52

numbers, 23, 32-33, 45, 48, 49-50, 154, 157, 161, 164-165, 194, 231

operations, 45

reasoning processes, 35, 45-46, 179

Front Matter (R1-R12)

Summary (1-4)

Part I: Introduction and Research on Learning (5-6)

1: Introduction (7-20)

2 Foundational Mathematics Content (21-58)

3 Cognitive Foundations for Early Mathematics Learning (59-94)

4 Developmental Variation, Sociocultural Influences, and Difficulties in Mathematics (95-120)

Part II: Teaching-Learning Paths (121-126)

5 The Teaching-Learning Paths for Number, Relations, and Operations (127-174)

6 The Teaching-Learning Paths for Geometry, Spatial Thinking, and Measurement (175-222)

Part III: Contexts for Teaching and Learning (223-224)

7 Standards, Curriculum, Instruction, and Assessment (225-288)

8 The Early Childhood Workforce and Its Professional Development (289-328)

Part IV: Future Directions for Policy, Practice, and Research (329-330)

9 Conclusions and Recommendations (331-350)

Appendix A: Glossary (351-358)

Appendix B: Concepts of Measurement (359-362)

Appendix C: Biographical Sketches of Committee Members and Staff (363-370)

Index (371-386)