America 2000, 34

American Federation of Teachers, 34–35

Arabic numerals, 18, 163, 166, 175n

Archimedes, 112–113n

Area interpretation of multiplication, 107

Area measure, 283

space-filling concept for, 283

Arithmetic. See also Mental arithmetic;

Single-digit arithmetic

abstract nature of, 74

and algebra, 256, 261

and geometry, 87–93

and mathematics, 293–294

multidigit, 121–122

number systems of, 72

paper-and-pencil, 20

preschool, 169

rules of, 73–75, 274, 280

Arithmetic operations, properties of, 73, 75–78

Arizona, exam passing rates in, 42

Arrays, rectangular, interpretation of multiplication, 77, 207–208

Assessment, 349–350

cut scores for, 42

high stakes, 41–42

internal and external, 39–40

of mathematics knowledge in the U.S., 35–36

of school mathematics in the U.S., 31, 39–44

of students, 349–350

Assessment Standards for School Mathematics, 34

Associative law, 75

Associativity of addition, 77

Automaticity, attaining, 351

Averages, 290

B

“Back to basics” movement, 115

Base-10

blocks, 96, 203, 221n

place-value system, 198

Beginning algebra, 255–256

Bird and worm problem, 129

Blocks

base-10, 96, 203, 221n

building, 106–110

Book purchase problem, 261

Borrowing, in subtraction, 204–205

Building blocks, number concepts as, 106–110

C

CAD. See Computer-assisted-drawing tools

Calculators, 45–46, 354–356

different types of, 100

four function, 100n

graphing, 269

instructional recommendations for using, 427

order-of-magnitude accuracy of, 247

recommendation for using, 427

scientific, 100n

use in Sweden, 355

Calculus, comprehending, 295n

California

standards for knowledge of mathematics, 34

textbook system in, 36

California State Board of Education, 50

Call for Change, A, 51

Canada, levels of mathematics achievement in, 56

Cardinal numbers, 160

Carrying, 203

Cases. See also Vignettes programs focusing on, 392–395

Central tendency, measures of, 289

CGI. See Cognitively Guided Instruction

Chance, learning about, 291–293

Children. See also Preschoolers’ mathematical proficiency

devising their own algorithms, 197

China

addition method in, 188

decimal system in, 175n

fractions in, 236

learning number names in, 164–168, 175n

Chocolate distribution problem, 266

Classroom discourse, 345–346

recommendation for managing, 425–426

Classroom vignettes. See Vignettes

Cognitive science, 117–118, 145n, 218n

Cognitively Guided Instruction (CGI), 389, 391– 392, 400n

Combinations. See Number combinations

Combinatorics, 109

Committee on Mathematics Learning, 2, 26

Communities

of learners, 344–345

of mathematics specialists, 397–398

of practice, 397–398

Commutativity

of addition, 75, 77

of multiplication, 77

Compare, problem types, 185

Comparing prices, teaching about, 326–327



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