How Students Learn Mathematics in the Classroom (2005) / Chapter Skim
Currently Skimming:
Index
Index
Pages 237-256
The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.
From page 237... ...
597 Index This index includes the text of the full vet sion of How SfudenfsLeatn: Hisfoty, Mathematics, and Science, which can be found on the C19 attached to the back cover A Absolute difference, 311 Absolute thinkmg as additive, 311 Access to someone who saw for himself and te2cchook c aims and the nature of sources, 93 Accounts, 59 61 of Colombian voyages, 192-193 diffe ant ideas about h storical, 38 39 h stoncal, 59 61 substantiated, 87 Actions at a distance explonog similarities and differences between, 492 493 Activity Al worksheet, 483 Adams, John, 185 Adaptive teasonmg, 218 Addi,.g It Up, 218, 233, 241 Additive reason fig, 311, 321 absolute thinking as, 311 Add essmg preconceptions, 399 403 Advantage selective, 542 Adventu e sense of, 71 A ten sine inst uctiona approaches, 321322 An encdll Association for the Advancement of Science guide nes of, 398 textbook eview by, 16 Analogs of number rep esentations that ch d en c m actively explo e hands on, 292-296 Rosen a y's Magic Shoes game, 295296 Skating Pa ty game, 292-295 Analogy to al de stamd the benchmark experience, 489 490 Ancient views of the Ea th as flat or roumd, 196 197 the Atlas Fa nese, 196 the sto y of E accost lot es and the Ea th's ci cumference, 196 197 Anglo-Saxons, 117 Anselm, st, 46 A guments inadequacies in, 403 Ashby, Rosa yn, 79 178, 591 Assessment centered, 415 Assessment centered c assroom envi onments, 13, 16 17, 267, 290, 292, 555-558 examples of students' critiques of thei own Darwinian explamations, 558
|
From page 238... ...
595 INDEX sample exam question, and consistency between models, 557 Assessment systems DIAGNOSER, 513 Assessments See also Self-assessment formative, 16 17, 193 preinst at loll, 495 "reflective," 412 Assumptions substantive, 127 At as Fan use, 194, 196 Authonty, 135 Award cards, 293 Awareness of how you a e thinking, 135 B Bain, Robe t B 23, 179 213, 591 Balzac, Hol ore de, 236 Balrv,, Tr, 578 Ba ton, Keith, 45, 160 Beakers a new approach to rations -number learn ng, 322-324 Bede, st, 58 Bell jar expenment, 4 4, 489 Benchmark lessons, 493-501, 512n weighing in a vacuum, 480 483 Black box approaches, 519 520 "Bbstoffl", 298 Boorstin, Daniel, 198 Bradford, Wi am, 84 88, 96, 108 111 Bramsfo d, John D, 1-28, 217-256, 397419, 569 592 Brendan, st, 71, 82 83, 128 164, 171 he ieving historica fi ms when people in t em hchave as we won d, 151 the deficit past, 154 155 exp anation of words in the sto y, 132-133 fmding out what kind of sto y it is, 150 164 gad for evidence on, 173-174 the question, 128 the sh inking past, 160 161 the sto y, 128 133 thin ding from inside the sto y, 144 150 thin dn8 from outside the sto y, 138144 voyage of, 130 132 workmg d rigs out for on selves, 133-138 Budging from al de standing magmetic action at a distance to al de standing g avxational action at a dixamce, 508 510 "Bridg rig context," 324, 359 Bnefmg sheets, 87, 91 and textbook c aims and dhe natu e of son ces, 88 89 Bui ding conceptual unde stamding, procedunal fluency, and connected knowledge, 364 369 3-slot schema for grapEmg a line, 370 371 developmental model for lea n ng functions, 365-366 level 0, 364, 367 level 1, 367-368 level 2, 368 level 3, 369 Building on chi d en's cur ent umderstmdings, 267-279, 359 364 admmiste ing and sco ing dhe Number Knowledge Test, 271 mental coumcmg ne st uctu e, 276 Number Knowledge Test, 268 269 unde standings of 4-year olds, 270 273 unde standings of 5-year olds, 273274 unde standings of 6-year olds, 274 277 unde standings of 7-year olds, 277278 unde standings of 8-year olds, 278 279 Bui ding esou cefu, self- egu atmg problem solve s, 371-373 an mtegnated umderstand ng of functions, 372 C Cambridge Histo y Project, 177n Canada teaching histo y in, 151 "Camd es" (umt)
|
From page 239... ...
INDEX 599 Carey, Susan, 592 Ca tier, Jennifer L, 23, 515-565, 592 Ca toons, 143, 145 146, 148, 546 549 Peamuts, 309 sequencing activity, 546 547 Case, Robbie, 23 Causa mode s to accoumt for patterns providing students with oppo unities to develop, 524 Causes, 49 54 explo ing the logic of the situation, 50-51 modeling, 562n as necessary conditions, 53 "underlying,' 35 Cent al conceptua st uctu e hypothesis bidimensiona, for number, 279 dependence of futu e learn rig on the acquisition of this st uctu e, 264 265 impo lance of st uctu e to success u performance on a ange of tasks, 262-263 for whole number, 261-262, 275 Change, 43 46, 61 di Action of, 44 la ge-sca e patterns of, 68 pace of, 44 as prog essive, rational, and limited in time, 45 Cheese and the Worms, 185 Children engaging their emotions and captu ng thei imagination, embedding knowledge const acted m thei hopes, fea s, and passions, 296 298 exposing to major fomms of number rep esentation, 283-288 as "natu al" scientists, 421 Ch d en passing the Number Knowledge Test and measu es of ant m Eric learning and ac ievement, 265 and numerical t amsfer tests, 263 Ch d en's Math World project, 219, 223, 227, 229, 231, 236, 241 Ch d en's thinking af er inst action, 338 340 China teachmg of mathematics m, 15-16, 18-19 Christian geog aphy, 200 Ci cle Land, 286 287 Claims backing up, 58 Classroom environments genetic inquiry m, 529-534 principles of learning and, 586 588 Classroom environments that suppo t learning with unde standing, 555560 assessment cente ed classroom environments, 13, 16 17, 267, 290, 292, 555-558 community-cente ed classroom environments, 13, 17-20, 301, 559-560 knowledge cente ed classroom envi onments, 13-16, 267, 284, 292, 555, 587 learner cente ed c ass oom envi onments, 13-14, 266, 292, 555 Clumping infommation, 69 Codes c acking, 335 Cogmttive Tutor A gebra, 355, 391 Colombian Evposhtion, 208 Columbus' voyages, 189 193, 195, 199, 204 205, 207-20R, 587 Common p econceptions about mathematics, 220 222 as "foDowmg ules" to gua antee cor ect answers, 220 221 as leaming to compute, 220 on y some people have the ability to "do math," 221-222 Community centered classroom environments, 13, 17-20, 301, 415, 559-560 learn ng with understandmg, 559-560 o gamizmg knowledge around co e concepts, 18 19 Comparing number worlds and control g oup outcomes, 304 Competence developed by students, I Comp ehensive Test of Basic Ski Is, 412 Computing wtth percent, 329 Concepts substantive, 61 65 Concepts of History and Teaching Approaches (Project CHATA)
|
From page 240... ...
600 INDEX Conceptua chamge, 400 403 student conceptions of knowledge gene ation and justification in science, 402 403 Conceptua explanations without conceptual umderxamding, 578 Conceptua st uctu e bidimensiona cent al, for number, 279 cent a, for whole number, 261-262, 275 Conceptua unde standmg, 218 of light, 423 424 Conceptua ization chid en's problems with, 137 Connected knowledge, 15-16 Conquest of Paradise, 208 Consistency internal and external, 518 between models, 557 Constitution, 61 Context evidence in, 167 Continuity, 44 "Controlled experiments," 402 Core concepts, 589 organizing knowledge around, 18-19 orgamzing procedu al knowledge amd ski Is a ow d, 19 Come, Michael Felice, 90 Cowmre intuitive" intuitions in history, 33, 42 Counting schema, 272 Counting wo ds as the c octal link between the world of quantity and the world of fo ma symbols, 280 281 order of, 274 Con se outcomes, 181 Cu nculum mandates in, 181 from Modelmg for Us de standing in Science Education, 555, 559 "openings" m, 245 Cu nculum for moving students th Hugh the model, 373-375 example lessons, 375-389 learning slope, 378 381 learning y-intercept, 381-384 operating on y = x', 384 389 sample computer screen, 386 suggested cu ncubr sequence, 376 377 two different student solutions to an open ended problem, 385 Cut-and-paste, 167 Cycles of investigation development of commumxy knowledge across cyc es of investigation, 460 development of conceptua frameworks for light, 462 467 in guided-mquiry science, 427 suppo tmg learn rig through, 460 467 D Dances ruith Woltes(fim) , 151 Danvin, Charles, 542-545, 550-551, 556, 573 Danvin's model of Nate al selection in high school evolution, 540 554 attending to significant disciplinary knowledge, 543-544 attending to student knowledge, 544 545 ca toon sequencing activity, 546 547 explanation written by students on the monarch/viceroy case, 553 ion action, 545-554 laying the groundwork, 545-549 us de standing, 550 552 Data trite pretation of, 403 Data tables from initial reco ding and with evisions for analysis, 445 Debugging em p has iz fig, 2 39- 240 Decimals, 332-334 magnitude and order in decimal numbers, 333-334 and stopwatches, 332-333 Decisions as to what knowledge to teach, 259267, 281-282 Deficit past, 154 155 Dependence, 234, 352 Desigm of lost action bndg rig lost uctional activities, 231 learn rig envi onments and, 12-20 Development of con fllWnf y knowledge across cyc es of investigation, 460
|
From page 241... ...
, 467 community knowledge from the second cycle of investigation (fi st-1 and i, 464 community knowledge from the thi d cycle of investigation (secondhand) , 465 Development of mathematical proficiency, 232-236 inaccessible algonthms, 236 lost action to suppo t mathematics proficiency, 233-236 a learning path from children's math worlds for single digit addition and subtraction, 234-235 Developmental model fo Iffimmg fimctions, 365-366 DIAGNOSER assessment system, 513 Diagmosing preconceptions in physics, 404 Diagmostic assessment, 491 492 Diagmostic questions, 478 Dialogue intema and external, as suppo t for metacogmrion, 241 Di action of c ange, 44 Disciplinary knowledge, 32 attending to sign ficant, 543-544 "second order," 61 Disconfirmation, 415 Discrepant events providing students with oppo tumries to expenence, 571-573 Discussion guided, 579, 582 DiSessa, And ea.
|
From page 242... ...
176 Fuson, Ka en C, 23, 217-256, 593 Future eal-world experience, 390 G Galapagos to toises, 558 GCK 5~e Genetics Construction Kit General ideas, 162 General mean ng of slope, 363 Genera izing and textbook c aims and the natu e of sou ces, 102 107 Genetics, 516 540 attending to students'existing knowledge, 517-526 metacognition and engaging students m reflective scientific practice, 538 540 simple dominance homework assigmment, 539 student inquiry in, 526 538
|
From page 243... ...
Stan ey, 177n Halsall, William Formsby, 87 Help seeking and giving, 241-242 Heuristic for teaching and learning science th ough guided inqui y, 427 455 cyc e of love Ligation m guidedmqui y science, 427 data tables from Nodal recording and with evasions for ama ysis, 445 engage phase, 428 434 fou th gnade s' initial ideas about light, 431 investigate phase, 438 443 investigative setup fo studymg how ight mteracts with solid objects, 437 prepa e-to-investigate phase, 434 438 prepa e-to-repo t phase, 443 448 repo t phase, 448 455 `~H(ev) ", 187 Higher o der knowledge st UCtu e, 276 Hixorica accoumrs, 59 61 di ferent ideas about, 38 39 not copies of the past, 62 63 "problematizing," 184 188 Hixorical evidence, 134 Hixorical fi ms, 151 Hixorical lines of thinking, 182 Hixorical problems t ansforming topics and oh ectives mto, 181-199 Hixo y 29-213 applymg the principles of How P ople Learn in teaching high school histo y, 179-213 "counte intuitive" mtuitions in, 33, 42 "domg," 32, 48 implications for plannmg, 164-176 periods m, 42 43 putting panciples into practice, 79178 the rea ity test, 80 84 sign ficance in, 45 that "works," 65-72 unde standing, 31-77 workmg with evidence, 84 119
|
From page 244... ...
604 INDEX I Histo y amd eve yday ideas, 33 61 diffe ences in the power of ideas, 36 37 groumds for caution, 40 41 ideas we need to add ess, 41 61 the prog ession of ideas, 37 40 understandmg the past and us de standing the disciplme of histo y, 34 35 "Histo y-as-account," 187-188, 203 "Histo y-as event," 187, 203 "Histo y considerate" learn rig environments design fig, 199 209 dhe g eat intenuption in En opean geographic knowledge, 200 201 with tools for historical thinking, 199209 History of the DeeRne and Fall of the Roman Empire, The, 57 Hider, Ado f, 34 35, 59 60, 586 Holt, John, 218 How Pe'2PIe Learn: Brain, Mind, Experi wee, and School, 1, 25, 31-32 cautions in, 199 design cl araaenst~a described in, 12-13, 20 22, 257-258, 359 key findmgs of, 79 80, 171-173, 176 resea ch summarized in, 241 violating principles of, 319 How P opie L arn framework, 411 415 assessment centered, 415 community centered, 415 knowledge centered, 414 learner cente ed, 414 reflective assessment in ThinkerTools 412 413 Humor en ivening lea n rig and helping bui d positive elationships widh students, 501 Ideas, 41 61 accoumrs, 59 61 cause, 49 54 chamge, 43 46 empadhy, 46 49 evidence, 54 58 prog ession of, 37 40 providmg students with oppo tunities to make public, 524 "second o der," 32-33 time, 41 43 Inaccessible algondhms, 236 Information, 41, 124, 166 "c umping," 69 findmg, 121 from histo y, 499 from the histo y of science, 499 inqui y based, 470n sto ing in memo y, 180 Inheritance meiotic processes goveming, 528 Initial models providmg students with oppo tunities to revise in light of anomalous data amd in tesPonse to c itiques of others, 524 Inqui y based information, 470n Inst uction, 545-554 to suppo t mathematical proficiency, 233-236 Instruction in ational number, 319-340 alternative inst uctiona approaches, 321-322 ch d en's dhinking af er inst uction, 338 340 cu nculum ove view, 325 fractions and mixed rep esentations of national numbers, 334 337 introduction of decima s, 332-334 introduction to pe cents, 325-332 knowledge network, 340 pie cha ts and a pa t-whole mterp etation of rationa numbe s, 320 321 pipes, tubes, amd beake s, 322-324 Inst uction dhat suppo ts metacogmrion, 239 242 emphasizmg debugging, 239 240 internal and external dialogue as suppo t for metacognition, 241 seeking and giving help, 241-242 Inst uctional nes of dhmking, 182 Intellectua roles for students to adopt, 436 Internal consistency, 518 Internal mignation, 68 Interp etation ancho ing dhemes in historica, 186 of data, 403
|
From page 245... ...
INDEX 605 Interpreting son ces m context and textbook c aims amd the natu e of son ces, 100 Lntuitions m histo y ~counterintuitive," 33, 42 Lnvented procedu es, 329 Lnvestigate phase, 438 443 Investigative setup for studying how light interacts with solid objects, 437 I ving, Wash 112011, 208 Isolation evidence in, 167 Italy inst action about payment for work, 66 67 J Japan teacher professions development in, 244 Jasper Woodbu y senes, 391 Jeffe son, Thomas, 62 63 Johnson, Lyndon, 62 Jonassen, David, 181 Judgments avoiding exp easing, 498 K Kalchman, Mindy, 23, 217-256, 351-393, 593 Knowledge See also Pnor umderstandmgs bui ding lea n rig paths amd networks of, 258 connected, 15-16 discipline y, 32, 543-544 handed down th ough gene ations, 93-94 mampu atmg factual, 79 80 Swatch sto ical," 32 organized, 462 "second order," 32-33 see et, 72 student, 258, 544 545 of what it means to "do science," 403 407 Knowledge centered crass ooll1 envi omments, 13-16, 267, 284, 292, 414, 555, 587 Knowledge c aims in genetics, assessing, 523 Knowledge networks, 340 new concepts of numbe s and new applications, 312-316 new symbols, meanings, and presentations, 313-314 reconceptualizmg the unit and operations, 315 the subconst acts, 314 315 w de standing nulllbe s as multiplicative elations, 316 "Knowledge packages," 588n Knowledge that shou d he taught, 259 267 cent al conceptual st uctu e hypothesis, 262-265 ch d en passing the Number Knowledge Test, 263, 265 measu es of a it metic learning amd achievement, 265 llW1 encal t ansfer tests, 263 Koedinger, Kemmeth R 351-393, 593-594 K aus, Pamela, 23, 401, 475-513, 594 KWL cha ts, 199, 428 430 L Lama ck, Jean Baptists de, 550, 573 La son, Ga y, 217 Learner cente ed class oom envi onments, 13-14, 266, 292, 414, 555 Learn ng an active p ocess, 476 humor en ivening, 501 Learning envi onments and the desi~,m of mstruction, 12-20 assessment cente ed classroom environments, 13, 16 17, 267, 290, 292, 555-558 community-cente ed classroom environments, 13, 17-20, 301, 559-560 knowledge cente ed c ass oom envi onments, 13-16, 267, 284, 292, 555, 587 learner cente ed c ass oom envi onments, 13-14, 266, 292, 414, 555 perspectives on, 13 Learn ng goa s for prekinde ga ten th ough g ade 2, 284 285
|
From page 246... ...
606 INDEX Lea ning paths of knowledge building, 258 from child en's math worlds, for single digit addition and subtraction, 234 235 Learning principles engaging rest lent preconceptions, 569-575 organizing knowledge a ound core concepts, 575-577 pnncip es of learning and class oom environments, 586 588 pu ling th Cads, 569 590 revisiting the th Be, 567-590 suppo ring metacognition, 577-586 Learr[u g nations number, 341-343 metacoEmition, 342 network of concepts, 341-342 prior al de s[andulgs, 341 Lea llUlg with umderstamding, 559 560 suppo ring knowledge use in new situations, 7 Leather boats, 139 141 Lee, PeterJ, 23, 31-178, 576, 594 Lesson Study Resea ch Group, 244 Lif e and Voyages of Christopher Colu mbus, The, 208 "Light catchers," 437 See also Study of ight Linkage of forma mathematical w de sta 1dwg to informs reason ng, 354 355 Liommi, Lee, 2, 4 See also Fish sto y Logic of the situation explo ing, 50 51 Lowenthal, David, 185 M Ma, Lipmg, 15-16, 18 19, 577-578 Magic Shoes game, 295-296 MaEmetism analogy to g avity, 508 Magmtude in decimal numbers, 333-334 of gnavitationa force, 501-508 MaEmusson, ShirleyJ, 421 474, 594 M magement of student activities, 435 M mdates cunicuar, 181 Mamipu ation of factua knowledge, 79 80 Maps, 86, 140 141 conceptual, 188 Marfan's synd on e, 533 Math words, 230 Mathematical proficiency, 218 adaptive reasonmg, 218 conceptual understandmg, 218 procedu al fluency, 218 productive disposition, 218 strategic competence, 218 Mathematica thi kers buiding, 258 Mathematica undenstanding, 217-256 computation without comprehension, 218 developing mathematical proficiency, 232-236 learn ng to use student thinking in teacher video c ubs, 244 lesson study cyc e, 244 a metacogmtive approach ff ab mg studffnt se f-mowtommg, 236 243 suggested eadmg list fo tffchffs, 256 teachers as cuniculum desiEmffs, 245 teachers engagmg studffnts' p econceptions, 219 231 undenstanding equi mg factua knowledge and conceptua hameworks, 231-236 Mathematics, 215-393 as ahout quanthty, not about numbens, 280 as "fohowing ules" to guanantee cor ect answers, 220 221 fostenog the development of whole number sense, 257-308 as leaming to compute, 220 pipes, tubes, amd beakens in, 309 349 teach ng and learn ng fimctions, 351393 Mathematics mst uction in China, 15-16, 18 19 Mayflower, The arnval of, 84, 87, 90, 92-95 Medawa, Peter, 406 Media tec nica and passive, 496 Meiotic processes goveming mberitance, 528
|
From page 247... ...
, 516, 548 cu ncu a from, 555, 559 Models, 402 403 consistency between, 557 of progression in ideas about evidence, 166 167 providmg students with oppo tunities to revise in light of anomalous data and in esponse to critiques of others, 524 Mona ch/viceroy case Da winian explanation w xten by students on the, 553 Monitoring See also Self-monitormg metacognitive, 10 "Monster-f ee zone," 295 Moss, Joan, 23, 309-349, 595 Motion of projectiles explainmg, 511 Multiple st ategies, 223-227 allow ng, 223-227 engagmg xudentst problem-solving st ategies, 225-227 th ee subt action methods, 224 Multiplicative operators, 315 Multiplicative reason ng relative thmking as, 311 MUSE SeeModeling for Understanding in Science Education Myste y sense of, 71 "Myste y Ohject Challenge," 329 N Nanative accounts providmg students with, 573-575 National Council of Teache s of Mathematics (NCTM) , 221, 241, 259 standa ds f om, 305
|
From page 248... ...
608 INDEX National Can ice urn for Hitxoy, 177n National Resea ch Coumci, 1, 218, 221, 233 guidelines of, 398 National Sconce Education Standands, 455, 561 Native Americans, 41, 82 83, 98, 105-106 NCTM Sac National Council of Teachers of Mathematics Necessary conditions causes as, 53 Neighbo hood Number Lme, 295 Networks of concepts, amd national number, 341-342 of knowledge, bui ding, 258 New conceptualizations umderstandmg numbers as mu tip icative relations, 316 New ideas development of, 470n New ules discovermg, 588 New symbols meanings, and epresentations, 313314 "Noth fig" happening, 43 Number Knowledge Test, 260, 264, 267269, 271, 279, 304 305 admmiste ing and scoring, 271 Number wo Ids, 282 302 ffncounagmg the use of metacoEmitive processes to faci irate knowledge const action, 300 302 engaging child en's emotions and capturing their imagination, 296 298 exposing children to water forms of number epresentation, 283-288 the five forms of rep esentation amd the lands m which they appea, 286 learning goals for prekinde ga ten th ough g ade 2, 284 285 providing analogs of number rep esentations that children can actively explore hands on, 292296 providing oppo unities for chi d en to acqui e computations fluency as well as conceptua al de standing, 298 300 providmg opporhmities to link the "world of quantity" with the "world of coming numbers" and the "world of formal symho s," 288 292 Number Worlds program, 262, 283, 287288, 292, 296, 300, 302-303 Numenc al sue s, 372 o Oh ect land, 284 286, 288 "One world" evolution, 169 "Openmgs" m the cuniculum, 245 Oppo tumities to develop causal models to account for pattems, 524 to experience discrepant events that a low them to come to terms with the sho tcomings in thei everyday models, 571-573 to make ideas public, 524 providmg students with, 523 524 to revise initia mode s m ight of amomalous data amd m esponse to critiques of others, 524 to sea ch for patterns in data, 524 to use patterns in data amd models to make p edictions, 524 to use prior knowledge to pose problems and genenate data, 523524 Oppo tummies for chi d en to acqui e computations fluency as well as conceptual understanding, 298 300 Sky land Blastoff activity, 298 299 Oppo unities for students to suggest and test related hypotheses in elaboration activities, 484 489 love ted cylinder in a cylinder of water, 485 486 love ted glass of water, 484 485 leaky bottle, 4 6 water and al in a st aw, 486 488 weighmg" an oh act m a fluid medium, 488 489 Oppo tummies to li k the "world of quamrity" with the "world of counting numbers" and the "world of formal symbols," 288 292 Minus Mouse, 290 291
|
From page 249... ...
, 122 Po y, John, 84 85, 90, 97, 100 104, 106 108 Positive relationships humor helping to bui d with students, 501 Possible Worlds, 4 6 Power explanato y and predictive, 518 Pteconceptions, 1, 55, 399 403 ahout people, society, and how the world works, 127-128 conceptual change, 400 403
|
From page 250... ...
tools, 573-575 Preconceptions about how we know about the past, 121-123 common student assumptions about how we know of the past, 123 dangers of what appears to be fami iar, 122 P edictive power, 518 P einst action assessments, 495 P epare-[o mvestigate phase, 434 438 Prepa e-to-repo t phase, 443 448 Principles of HOOP People Learn applied to teaching high school history, 179213 designing a "history considerate" learn rig envi onment, 199 209 t amsforming topics and objectives into hi itorica problems, 181-199 Prior umderstandmgs development of physica concepts m infancy, 4 engaging, 4 5 of light, 425 misconceptions about momentum, 5 providing students with oppo tumries to use to pose problems and genenate data, 523-524 and nations number, 341 P Able SOIVffS building, 258 "Problematizing' h stoncal accounts, 184 188 Procedu a fluency, 218 Productive disposition, 218 Prohciency mathematical, 218 Prog ess, 44 45 Prog ession of ideas, 37 40 di ferent ideas about h stoncal accounts, 38 39 Prog essive chamge, 45 Project CHATA See Concepts of History and Teaching Approaches Projectiles explainmg motion of, 511 Propo tion, 234, 340 Pump Algebna Tutor See Cognitive Tutor A gebna Q Quantity, 234 schema for, 272 Question Poser, 300-301 Question ng and explaming m high school science suppo tmg metacognition, 582-583 Questions, 128 diagnostic, 478 at the heart of using evidence, 124 mamy as yet unanswered, 492 teachers modelmg for students, 477 Quotient interpretation, 314 R Rationa change, 45 Rationa number, 341-343 metacogmrion, 342 network of concepts, 341-342 prior umderst mdings, 341 Rationa -number lea n ng and the knowledge network, 312-316 metacogmrion amd national number, 319 new concepts of numbe s and new applications, 312-316 and the p inciples of HOEV Peop) e Learn, 312-319 studentst errors and misconceptions based on previous learn ng, 316 319
|
From page 251... ...
INDEX 611 Real-world expenence cunent amd fate e, 390 Real-world words, 230 Rea ty test, 80 84 7-year gap," 82 Reciprocal teaching, 11 Reconceptua icing the unit and operations, 315 Reco der, 435 Reflective assessments, 412 in TbinkerToo 5, 412 413 Regrouping subt action with, 18 19 Relative thinkmg as multiplicative, 311 Relativism, 176 Reliability, 126 Religious practices, 113-118 Repo ter, 301 Repo ring phase, 427, 44t 455 Rep esentations, 372 anchoring themes in histoncal, 186 Reproductive success, 542 Revolution, 61 S Sagan, Ca 1, 194, 196 197 Sales, lii kpatack, 208 schemes 2-slot amd 3-s 01, 370 coming amd quantity, 272 Schools Counci Histo y Project, 40, 177n Science, 395-565 developing understanding through model-based inqui y, 515-565 guided inqui y m the science c east 0111, 475-513 information from the histo y of, 499 leavmg many questions as yet unanswe ad, 492 teachmg to promote the development of scientific knowledge and reasoning about light at the elements y school level, 421 474 unit on the natu e of g avity and its effects, 477-511 Science classrooms guided inqui y m, 475-513 Scientific inqui y and How Prlplc Leant, 397 419 add easing p econceptions, 399 403 diagnosmg preconceptions in physics, 404 the HOEU People Lt~atn framework, 411415 knowledge of what it means to "do science," 403 407 Scientific method misconceptions about, 414 Scissors-amd-paste approach and lezlb ok c aims and the natu e of son ces, 94 Ste~fn~hers, Thu(fim) , 151 Second cycle of mvestigation community knowledge from, 4 4 Second-hand investigation, 455 459 "Second o der' disciplma y concepts, 61, 73n "Second o der' knowledge, 32-33, 41 acqu6ition of, 40 41 Sec et knowledge, 72 Seeing for you self and texthook c aims amd the natu e of sou ces, 93 Seivas, Peter, 151 Selective advantage, 542 Self-assessment, 12 Self-monitormg impo tance of, 10 12 metacogmrive mowto ing, 10 Sensitivity 7-year gap," 82 7-yea olds unde stamdings of, 277278 to students' substamrive assumptions, 127 Severin, Tim, 139, 142-143 shemilt, Denis, 23, 56, 79-178, 595-596 sh inking past, 160 161 sigmificance, 45 historica, 45 simplichty, 389 390 6-yea olds umderstmdings of, 274277 Skating Pa ty game, 292-295 Skil s defming, 40 sky [and, 286 287 Bbstoff activity, 298-299 Smith, John, 122 sOu ces access to someone who saw for himself, 93 baefing sheet, 88 89
|
From page 252... ...
612 INDEX distinguishmg among kinds of claims, 101-102 genera icing, 102-107 getting hch rid the ecord to concerns of the people who produced them, 107-108 interpreting son ces m context, 100 maintaining contact with am eyewitness using knowledge hamded down th Hugh generations, 93 94 the natu e of, 84 111 scissors-amd-paste approach, 94 seeing for you self, 93 teacher questions, 92, 95-96, 99-101 t usting the son ce who was in a position to know, 96 umderstandmg the pa pose of the son ce, 96 99 umderstandmg what is likely to get reco ded and under what cicumstamces, 108 111 working out the facts from other sources or avai able knowledge, 94-95 Splittmg, 323 State of affai s changes in, 44 Stearns, Peter, 210 Stewa t, James, 23, 515-565, 596 "Stop-Sta t Challenge," 333 Stopwatches decimals and, 332-333 Stories "embroidering," 153 st ategic competence, 218 St ing challenges guessmg myste y objects, 329-331 Student assumptions about how we know of the past, 123 Student conceptions expe imentation, 402 inadequacies in a guments, 403 interpretation of data, 403 of knowledge gene ation and justi ication in science, 402 403 models, 402 403, 518 Student mqui y in genetics, 526 538 example of student work on a GCli homework assignment, 535 genetic mqui y in the c dSS1110111, 529 534 initial GCli pope ation for the final GCK mqui y, 537 meiotic processes governing mberitance, 528 Mendel's model of simple dominance, 528 Students' enors and misconceptions based on p evious teaming, 316 319 Students'existing knowledge, 517-526 assessmg knowledge c aims m genetics, 523 attending to, 544 545 black box, 520 bui ding on and connecting, 258 learning genetics content, 524 526 providmg students wt h learn rig oppo tumries, 523-524 student conceptions of models, 518 Studentst p econceptions impo tance of, 79 Study of ight, 422 426 conceptual umderstandmg, 423 424 metacogmrion, 426 prior knowledge, 425 Study of light th ough mqui y, 426 459 heuristic for teaching and leaming science th ough guided mqui y, 427 455 second-hand investigation, 455 459 Subconst ucts the many pe sonaltties of nationa number, 314 315 Subject-specific knowledge in effective science mst uction, 467 469 Substantiated accounts, 87 Substantive assumptions senshtivity to students', 127 Substantive concepts, 61 65 historica accoumrs not copies of the past, 62 63 payment for work, 66 67 Subt action with regrouping, 18 19 suppo ting learning through cycles of mvestigation, 460 467 suppo ting skilled questioning and explaming in mathematics problem solving suppo tmg metacogmrion, 580 581 suppo ting student and teacher learn ng th ough a c assroom discou se commumtty, 237
|
From page 253... ...
INDEX 613 Table of va Yes to produce a function, 353-358 Teacher professional development in Japan, 244 Teacher questions, 112-113, 115 and textbook c aims and the nature of son ces, 92, 95 96, 99-101 Tffche st conceptions and pa tial us de standings, 279 281 acqui ing an us de standing of number as a lengthy, step-by- step process, 280 281 coming words as the c ucial Imk between the world of quantity and the world of formal symho s, 280 281 math as not about numbe s, but about qua itch, 280 Teache s ffngag rig students' preconceptions, 219 231 common preconceptions about mathematics, 220 222 engaging students' p econceptions and building on existing knowledge, 223-231 Teaching recipmcal, 11 Teaching and learn rig fimctions m mathematics, 351-393 add easing the th he principles, 359 373 bui ding conceptua understanding, procedu al fluency, and commented knowledge 364-369 bui dmg on pno knowledge, 359364 bui dmg esou cefu, self-regu at no problem SOIVffS, 371 373 linkmg fom al mathematics us de standing to informal reasonmg, 354-355 making a table of values to produce a fimction, 353-358 teachmg functions for umderstandmg, 373-389 teachmg to achieve this kind of us de standing, 358 359 Teaching as Storv Telling, 574 Teaching functions for understanding, 373389 Teaching mathematics in the prims y g ades, 257-308 acknowledging teachers' conceptions amd pa tial umderstandmgs, 279281 bui ding on chi d en's cu rent understandings, 267-279 the case of number worlds, 282-302 companog number worlds and cont ol g cop outcomes, 304 deciding what knowledge to teach, 259 267 defming the knowledge that should he taught, 281-282 Teaching the ational number wxem, 309349 additive and mu tiplicative easoning, 311 how students learn nations number, 341-343 me action in rational number, 319 340 rational-number lean mg and the p inciples of HoEvPeop) eLeatn, 312-319 Teaching to promote the development of scientific knowledge and easoning about light at the elements y school level, 421 474 the role of sub ect-speci ic knowledge m effective science inst action, 467 469 the study of light, 422 426 the study of ight th ough mqui y, 426 459 suppo tmg learn rig through cyc es of investigation, 460 467 Technica media, 496 Testimony, 41, 124, 135, 166 Testmg external, 181 Textbook claims access to someone who saw for himself, 93 beefing sheet, 88 89 distmguish rig among kinds of c aims, 101-102 genenalizmg, 102-107 getting behind the record to concerns of the people who produced them, 107-108 interpreting son ces m context, 100
|
From page 254... ...
614 INDEX maintaining contact with an eyewitness using knowledge hamded down th Bugle generations, 93 94 and the natu e of son ces, 84 111 scissors-amd-paste approach, 94 seeing for you self, 93 teacher questions, 92, 95 96, 99 101 t usting the son ce who was in a position to know, 96 umde standmg the pa pose of the source, 96 99 understandmg what is likely to get reco ded and under what ci cumstances, 108 111 working out the facts from other sources or avai able knowledge, 94-95 Themes, 44 anchoring m historical epresentation and inte pretation, 186 Th nkerTools, 407, 585 Third cycle of investigation community knowledge from, 465 Third International Mathematics and Science Study, 243 3-slot schema for g aphing a ne, 370 371 Th he subt action methods, 224 Time, 41 43 change limited in, 45 periods in histo y, 43 Time lines, 129, 159 Timekeeper, 435 Torsion bar, 493-501 Transforming topics and objectives into historica problems, 181-199 accoumcmg for the "flat ea th," 189199 "problematizing" historica accoumrs, 184 188 Transmission enors, 123 T usting the son ce who was in a position to know and tomb ok c aims and the natu e of son ces, 96 T uth twistmg, 105, 123 Tubes a new approach to rations -number learn ng, 322-324 a epresentation for fu Iness, 325-326 Turner, F ederick Jackson, 58 Twisting the t uth, 105, 123 ', or schemes, 370 U "Underlying" causes, 35 Us de stamping essentia role of factual knowledge amd conceptual f an eworks in, 69 expe ts emembe ing considerably more relevant detai t an novices m tasks withm thei domain, 8 9 learn ng with umderstandmg suppo ting knowledge use m new Sttuations, 7 Unde standing of number a lengthy, step-by-step process, 280 281 Unde stamding the pu pose of the sou ce amd textbook c aims amd the natu e of sou ces 96 99 Unde stamding what is kely to get ecorded amd under what ci cumstances and te2ctbook c aims and the natu e of sou ces, 108 111 Umt-level problem, 189 199 accounts of Colombian voyages, 192193 ancient views of the Ea th as fiat or roumd, 196 197 Umt on the natu e of gnavity and its effects, 477-511 United Kmgdom adjusting data hom, 177n Schoo s Coumci Histo y Project, 40, 177n Units on filling the world with people, 169 on fi st contacts, whether st Brendan sai ed from I eland to Amenca, 171 on fi st contacts, why the No se colon sts didn't stay in America, 172 on people gomg their separate ways, 170
|
From page 255... ...
INDEX 615 V Verbal intem Stations, 372 Visual propo tional estimation sta tmg from, and halving amd doubling, 323-324 Wa (ca d game) , 336 Wa m-Up period, 298, 300 Water and al in a straw, 486 488 Website, 562n "Weighing" an oh ect in a fluid medium, 486 489 Weigh ng-in-a-vacuum situation, 484, 489 Whole number cent a conceptual st uctu e for, 261262, 275 Wi son, Suzamne M, 596 Wmebu g, Samuel s, 100 Wisdom, 236, 238 Woodbury, Hasps, 391 Wo d P oblff s test, 264 265 Wo ds tarsus notations, 230 Wo ds in stones explaining, 132-133 Work payment for in history, 66 67 Workmg out the facts from other son ces or avai able knowledge and textbook claims and the natu e of soumes, 94 95 Workmg things out for on selves, 133-138 being awa e of how we are thin dng, 135 going beyond face value, 134 how far a leather boat con d have managed to sail, 139 141 Workmg th ough the task, 128 164 Workmg with evidence Pi g im Fathe s and Native An encd 64 119 prepa ing for the task, 121-128 the st Brand m's voyage task, 128 164 World's Fai of 1892, 208 Wrap-Up period, 301 Written A tthmetic test, 264 265 y Year-long historical questions, 164-188
|
Key Terms
This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More
information on Chapter Skim is available.