Competence. See Mathematical proficiency;

Strategic competence

“Complementary number-to-10” strategy, 218n

Composite units, 249n

Compound units, 249n

Computation, with rational numbers, 238

Computer-assisted-drawing (CAD) tools, 287

Computers

graphics on, 16, 269

instructional recommendations for using, 427

Conceptual understanding, 5, 10, 116, 136–137, 158–159, 380–382

and mathematical proficiency, 118–120

Concrete materials. See also Manipulatives not the same as physical, 426

Conditional probability, 292–293

Conditions, as aids to understanding, 127

Conference Board of the Mathematical Sciences, 397

Connections, supporting, 235–236

Content, 333–338, 350–356

and calculators, 354–356

and homework, 352–353

and manipulatives, 353–354

opportunities to learn, 333–335

planning, 337–338

and practice, 351–352

task selection and use, 335–336

Contexts

for instruction, 314

for learning, solving problems as providing, 420–421

meaningful, for word problems, 183–187

Conventional instruction, what can be learned from, 240–241

Cookie distribution problem, 376–377

Cooperative learning, 50, 344–349

Coordinating improvement efforts, in teaching mathematics in the U.S., 58–59

Council for Basic Education, 35

Council of Chief State School Officers, 52–53

Counting, 181

and the origins of the number concept, 159– 160

understanding and mastering, 161–162

Curriculum. See also Curriculum recommendations

decisions, 10–11, 410–424

guides and frameworks for, 34

mathematics, in U.S., 33–35

standards for, 34

Curriculum and Evaluation Standards for School Mathematics, 33–34, 36

Curriculum recommendations, 10–11, 410–424

building on informal knowledge, 410–411

developing algebraic thinking, 419

developing proportional reasoning, 417

expanding the number domain, 418

extending the place-value system, 416–417

giving students time to practice, 422–423

giving time to instruction, 422

improving materials for instruction, 421–422

learning about numbers, 412–413

learning number names, 411–412

learning numerical algorithms, 414

operating with single-digit numbers, 413

promoting algebra for all, 420

representing and operating with rational numbers, 415–416

solving problems as a context for learning, 420–421

using estimation and mental arithmetic, 415

using technology to learn algebra, 420

using the number line, 418

Cycle shop problem, 126

Czech Republic, levels of mathematics achievement in, 56

D

Data

analyzing, 290–291

describing, 289

learning to use, 288–291

organizing, 289–290

reading, 289–290

representations of, 290

Decimal system, 96.

See also Base-10

Derived number combinations, 188

Developing algebraic thinking, recommendation for, 419

Developing geometric reasoning, 284–288

reasoning about more advanced concepts, 287–288

reasoning about shape and form, 284–287

Developing mathematical proficiency, 8, 13–14, 246–247, 255–312, 432

acquiring measure concepts, 281–284

algebra for all, 279–280

from arithmetic to mathematics, 293–294

beginning algebra, 255–256

concept of negative numbers, 245

developing geometric reasoning, 284–288

developmental themes, 216–218

discontinuities in, 233–234