|
||||||||||||||||
|
||||||||||||||||
The following HTML text is provided to enhance online readability. Many aspects of typography translate only awkwardly to HTML. Please use the page image as the authoritative form to ensure accuracy. 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 geometry, 87–93 and mathematics, 293–294 multidigit, 121–122 number systems of, 72 paper-and-pencil, 20 preschool, 169 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 place-value system, 198 Beginning algebra, 255–256 Bird and worm problem, 129 Blocks 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 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 multiplication, 77 Compare, problem types, 185 Comparing prices, teaching about, 326–327
|
|
|||||||||||||||
