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597 INDEX Index This index includes the text of the full version of How Students Learn: History, Mathematics, and Science, which can be found on the CD attached to the back cover. A American Association for the Advancement of Science Absolute difference, 311 guidelines of, 398 Absolute thinking textbook review by, 16 as additive, 311 Analogs of number representations that Access to someone who saw for himself children can actively explore and textbook claims and the nature hands-on, 292â296 of sources, 93 Rosemaryâs Magic Shoes game, 295â Accounts, 59â61 296 of Colombian voyages, 192â193 Skating Party game, 292â295 different ideas about historical, 38â39 Analogy to understand the benchmark historical, 59â61 experience, 489â490 substantiated, 87 Ancient views of the Earth as flat or round, Actions at a distance 196â197 exploring similarities and differences the Atlas Farnese, 196 between, 492â493 the story of Eratosthenes and the Activity A1 worksheet, 483 Earthâs circumference, 196â197 Adams, John, 185 Anglo-Saxons, 117 Adaptive reasoning, 218 Anselm, St., 46 Adding It Up, 218, 233, 241 Arguments Additive reasoning, 311, 321 inadequacies in, 403 absolute thinking as, 311 Ashby, Rosalyn, 79â178, 591 Addressing preconceptions, 399â403 Assessment-centered, 415 Advantage Assessment-centered classroom selective, 542 environments, 13, 16â17, 267, 290, Adventure 292, 555â558 sense of, 71 examples of studentsâ critiques of Alternative instructional approaches, 321â their own Darwinian explanations, 322 558

598 INDEX sample exam question, and voyage of, 130â132 consistency between models, 557 working things out for ourselves, Assessment systems 133â138 DIAGNOSER, 513 Bridging Assessments. See also Self-assessment from understanding magnetic action formative, 16â17, 193 at a distance to understanding preinstruction, 495 gravitational action at a distance, âreflective,â 412 508â510 Assumptions âBridging context,â 324, 359 substantive, 127 Briefing sheets, 87, 91 Atlas Farnese, 194, 196 and textbook claims and the nature Authority, 135 of sources, 88â89 Award cards, 293 Building conceptual understanding, Awareness of how you are thinking, 135 procedural fluency, and connected knowledge, 364â369 3-slot schema for graphing a line, B 370â371 developmental model for learning Bain, Robert B., 23, 179â213, 591 functions, 365â366 Balzac, HonorÃ© de, 236 level 0, 364, 367 Barry, Tr., 578 level 1, 367â368 Barton, Keith, 45, 160 level 2, 368 Beakers level 3, 369 a new approach to rational-number Building on childrenâs current learning, 322â324 understandings, 267â279, 359â364 Bede, St., 58 administering and scoring the Bell jar experiment, 484, 489 Number Knowledge Test, 271 Benchmark lessons, 493â501, 512n mental counting line structure, 276 weighing in a vacuum, 480â483 Number Knowledge Test, 268â269 Black box approaches, 519â520 understandings of 4-year-olds, 270â âBlastoff!â, 298 273 Boorstin, Daniel, 198 understandings of 5-year-olds, 273â Bradford, William, 84â88, 96, 108â111 274 Bransford, John D., 1â28, 217â256, 397â understandings of 6-year-olds, 274â 419, 569â592 277 Brendan, St., 71, 82â83, 128â164, 171 understandings of 7-year-olds, 277â believing historical films when people 278 in them behave as we would, 151 understandings of 8-year-olds, 278â the deficit past, 154â155 279 explanation of words in the story, Building resourceful, self-regulating 132â133 problem solvers, 371â373 finding out what kind of story it is, an integrated understanding of 150â164 functions, 372 grid for evidence on, 173â174 the question, 128 C the shrinking past, 160â161 the story, 128â133 thinking from inside the story, 144â Cambridge History Project, 177n 150 Canada thinking from outside the story, 138â teaching history in, 151 144 âCandlesâ (unit), 456 Card games, 335â337

599 INDEX Carey, Susan, 592 Christian geography, 200 Cartier, Jennifer L., 23, 515â565, 592 Circle Land, 286â287 Cartoons, 143, 145â146, 148, 546â549 Claims Peanuts, 309 backing up, 58 sequencing activity, 546â547 Classroom environments Case, Robbie, 23 genetic inquiry in, 529â534 Causal models to account for patterns principles of learning and, 586â588 providing students with opportunities Classroom environments that support to develop, 524 learning with understanding, 555â Causes, 49â54 560 exploring the logic of the situation, assessment-centered classroom 50â51 environments, 13, 16â17, 267, 290, modeling, 562n 292, 555â558 as necessary conditions, 53 community-centered classroom âunderlying,â 35 environments, 13, 17â20, 301, Central conceptual structure hypothesis 559â560 bidimensional, for number, 279 knowledge-centered classroom dependence of future learning on the environments, 13â16, 267, 284, acquisition of this structure, 264â 292, 555, 587 265 learner-centered classroom importance of structure to successful environments, 13â14, 266, 292, performance on a range of tasks, 555 262â263 Clumping information, 69 for whole number, 261â262, 275 Codes Change, 43â46, 61 cracking, 335 direction of, 44 Cognitive Tutor Algebra, 355, 391 large-scale patterns of, 68 Colombian Exposition, 208 pace of, 44 Columbusâ voyages, 189â193, 195, 199, as progressive, rational, and limited in 204â205, 207â208, 587 time, 45 Common preconceptions about Cheese and the Worms, 185 mathematics, 220â222 Children as âfollowing rulesâ to guarantee engaging their emotions and correct answers, 220â221 capturing their imagination, as learning to compute, 220 embedding knowledge only some people have the ability to constructed in their hopes, fears, âdo math,â 221â222 and passions, 296â298 Community-centered classroom exposing to major forms of number environments, 13, 17â20, 301, 415, representation, 283â288 559â560 as ânaturalâ scientists, 421 learning with understanding, 559â560 Children passing the Number Knowledge organizing knowledge around core Test concepts, 18â19 and measures of arithmetic learning Comparing number worlds and control and achievement, 265 group outcomes, 304 and numerical transfer tests, 263 Competence developed by students, 1 Childrenâs Math World project, 219, 223, Comprehensive Test of Basic Skills, 412 227, 229, 231, 236, 241 Computing with percent, 329 Childrenâs thinking after instruction, 338â Concepts 340 substantive, 61â65 China Concepts of History and Teaching teaching of mathematics in, 15â16, Approaches (Project CHATA), 38â 18â19 39, 51â53, 56, 62, 82

600 INDEX Conceptual change, 400â403 suggested curricular sequence, 376â377 student conceptions of knowledge two different student solutions to an generation and justification in open-ended problem, 385 science, 402â403 Cut-and-paste, 167 Conceptual explanations Cycles of investigation without conceptual understanding, development of community 578 knowledge across cycles of Conceptual structure investigation, 460 bidimensional central, for number, development of conceptual 279 frameworks for light, 462â467 central, for whole number, 261â262, in guided-inquiry science, 427 275 supporting learning through, 460â467 Conceptual understanding, 218 of light, 423â424 D Conceptualization childrenâs problems with, 137 Dances with Wolves (film), 151 Connected knowledge, 15â16 Darwin, Charles, 542â545, 550â551, 556, Conquest of Paradise, 208 573 Consistency Darwinâs model of natural selection in high internal and external, 518 school evolution, 540â554 between models, 557 attending to significant disciplinary Constitution, 61 knowledge, 543â544 Context attending to student knowledge, 544â evidence in, 167 545 Continuity, 44 cartoon sequencing activity, 546â547 âControlled experiments,â 402 explanation written by students on Core concepts, 589 the monarch/viceroy case, 553 organizing knowledge around, 18â19 instruction, 545â554 organizing procedural knowledge and laying the groundwork, 545â549 skills around, 19 understanding, 550â552 Corne, Michael Felice, 90 Data âCounterintuitiveâ intuitions interpretation of, 403 in history, 33, 42 Data tables from initial recording and with Counting schema, 272 revisions for analysis, 445 Counting words Debugging as the crucial link between the world emphasizing, 239â240 of quantity and the world of Decimals, 332â334 formal symbols, 280â281 magnitude and order in decimal order of, 274 numbers, 333â334 Course outcomes, 181 and stopwatches, 332â333 Curriculum Decisions mandates in, 181 as to what knowledge to teach, 259â from Modeling for Understanding in 267, 281â282 Science Education, 555, 559 Deficit past, 154â155 âopeningsâ in, 245 Dependence, 234, 352 Curriculum for moving students through Design of instruction the model, 373â375 bridging instructional activities, 231 example lessons, 375â389 learning environments and, 12â20 learning slope, 378â381 Development learning y-intercept, 381â384 of community knowledge across operating on y = x2, 384â389 cycles of investigation, 460 sample computer screen, 386

601 INDEX of Darwinâs model of natural DNA, 517, 526 selection in high school evolution, âDoing,â 32, 48 540â554 âDoing mathâ of physical concepts in infancy, 4 only some people having the ability of understanding through model- for, 221â222 based inquiry, 515â565 Donovan, M. Suzanne, 1â28, 397â419, Development of conceptual frameworks 569â590, 592 for light, 462â467 Double-blind procedure, 302 community knowledge from the first Dragon Quest game, 297â298 cycle of investigation (first-hand), 463 E community knowledge from the fourth cycle of investigation (first- Earth as flat or round, ancient views of, hand), 467 196â197 community knowledge from the Earthâs circumference second cycle of investigation the story of Eratosthenes and, 196â197 (first-hand), 464 Effects of gravity, 510â511 community knowledge from the third explaining falling bodies, 510â511 cycle of investigation (second- explaining motion of projectiles, 511 hand), 465 Egan, Kieran, 592 Development of mathematical proficiency, 8-year-olds understandings of, 278â 232â236 279 inaccessible algorithms, 236 Elementary Science Study instruction to support mathematical Optics unit, 422, 468 proficiency, 233â236 âEmbroideringâ stories, 153 a learning path from childrenâs math Empathy, 46â49, 65, 112 worlds for single-digit addition Encouraging math talk, 228â231 and subtraction, 234â235 Encouraging the use of metacognitive Developmental model processes to facilitate knowledge for learning functions, 365â366 construction, 300â302 DIAGNOSER assessment system, 513 Engage phase, 428â434 Diagnosing preconceptions in physics, 404 Engagement of studentsâ preconceptions Diagnostic assessment, 491â492 and building on existing Diagnostic questions, 478 knowledge, 4â5, 223â231 Dialogue allowing multiple strategies, 223â227 internal and external, as support for designing bridging instructional metacognition, 241 activities, 231 Direction of change, 44 encouraging math talk, 228â231 Disciplinary knowledge, 32 Engagement of studentsâ problem-solving attending to significant, 543â544 strategies, 225â227 âsecond-order,â 61 Equipment Manager, 435 Disconfirmation, 415 Eratosthenes, 194, 196â197 Discrepant events European geographic knowledge providing students with opportunities the great interruption in, 200â201 to experience, 571â573 Everyday concepts Discussion history and, 33â61 guided, 579, 582 of scientific methods, argumentation, DiSessa, Andrea, 5 and reasoning, 400 Distinguishing among kinds of textbook of scientific phenomena, 399â400 claims and the nature of sources, 101â102

602 INDEX Evidence, 41, 54â58, 61, 65, 112, 120, 165 essential role of factual knowledge in context, 167 and conceptual frameworks in cutting-and-pasting, 167 understanding, 6â9 finding out about the past from importance of self-monitoring in, 10â received information, 56â58 12 historical, 134 âFlat earth,â 189â199 information as, 166 accounts of Colombian voyages, 192â in isolation, 167 193 model of progression in ideas about, ancient views of the Earth as flat or 166â167 round, 196â197 pictures of the past, 166 Formative assessments, 16â17, 193 questions at the heart of using, 124 Forms of representation testimony as, 166 4-year-olds understandings of, 270â Experiments on Plant Hybridization, 529 273 Experts remembering considerably more and the lands in which they appear, relevant detail than novices in 286 tasks within their domain, 8â9 Fourth cycle of investigation Explanations, 156 community knowledge from, 467 of words in the story, 132â133 Fourth gradersâ initial ideas about light, 431 Explanatory power, 518 Fractions and mixed representations of External consistency, 518 rational numbers, 334â337 External migration, 68 card games, 335â337 External testing, 181 cracking the code, 335 fractions and equivalencies, 334â335 Framework of How People Learn F seeking a balanced classroom environment, 242â243 Face value Frank, Anne, 109 going beyond, 134 Fundamental physics, 24 Factual knowledge Fundamentalism, 176 manipulating, 79â80 Fuson, Karen C., 23, 217â256, 593 Falling bodies Future real-world experience, 390 explaining, 510â511 Familiarity, 389â390 G the dangers of what appears to be familiar, 122 Feynman, Richard, 24, 403 Galapagos tortoises, 558 Filling the world with people GCK. See Genetics Construction Kit unit on, 169 General ideas, 162 First contacts General meaning of slope, 363 whether St. Brendan sailed from Generalizing and textbook claims and the Ireland to America, unit on, 171 nature of sources, 102â107 why the Norse colonists didnât stay in Genetics, 516â540 America, unit on, 172 attending to studentsâ existing First cycle of investigation knowledge, 517â526 community knowledge from, 463 metacognition and engaging students Fish story (Fish Is Fish), 2â12, 398, 414, 575 in reflective scientific practice, 5-year-olds understandings of, 273â 538â540 274 simple dominance homework engaging prior understandings in, 4â5 assignment, 539 student inquiry in, 526â538

603 INDEX H Genetics Construction Kit (GCK), 534â537 homework assignment, example of student work on, 535 âH(ac)â, 187â188 Genetics content Hall, G. Stanley, 177n learning, 524â526 Halsall, William Formsby, 87 Geographic knowledge Help Christian, 200 seeking and giving, 241â242 the great interruption in European, Heuristic for teaching and learning science 200â201 through guided inquiry, 427â455 Gibbon, Edward, 57 cycle of investigation in guided- GIsML Community of Practice, 470n inquiry science, 427 âGlobalization,â 169 data tables from initial recording and Gould, Stephen Jay, 198 with revisions for analysis, 445 Gragg, Charles, 236 engage phase, 428â434 Gravity and its effects, 477â511 fourth gradersâ initial ideas about activity A1 worksheet, 483 light, 431 analogy to magnetism, 508 investigate phase, 438â443 bridging from understanding investigative setup for studying how magnetic action at a distance to light interacts with solid objects, understanding gravitational action 437 at a distance, 508â510 prepare-to-investigate phase, 434â438 building an analogy to understand prepare-to-report phase, 443â448 the benchmark experience, 489â report phase, 448â455 490 âH(ev)â, 187 consensus discussion and summary of Higher-order knowledge structure, 276 learning, 490â491 Historical accounts, 59â61 defining, 477â510 different ideas about, 38â39 diagnostic assessment, 491â492 not copies of the past, 62â63 exploring similarities and differences âproblematizing,â 184â188 between actions at a distance, Historical evidence, 134 492â493 Historical films, 151 factors on which the magnitude of Historical lines of thinking, 182 gravitational force depends, 501â Historical problems 508 transforming topics and objectives finding out about studentsâ initial into, 181â199 ideas, 477â478 History, 29â213 identifying preconceptions, 478â480 applying the principles of How People opportunities for students to suggest Learn in teaching high school and test related hypotheses, 484â history, 179â213 489 âcounterintuitiveâ intuitions in, 33, 42 twisting a torsion bar, 493â501 âdoing,â 32, 48 weighing in a vacuum, 480â483 implications for planning, 164â176 Grids, 173â175 periods in, 42â43 Griffin, Sharon, 23, 257â308, 593 putting principles into practice, 79â Group work, 582â584 178 Guess My Number, 300 the reality test, 80â84 Guidance of student observation and significance in, 45 articulation that âworks,â 65â72 supporting metacognition, 584â585 understanding, 31â77 Guided inquiry, 495, 579, 582 working with evidence, 84â119

604 INDEX History and everyday ideas, 33â61 providing students with opportunities differences in the power of ideas, 36â to make public, 524 37 âsecond-order,â 32â33 grounds for caution, 40â41 time, 41â43 ideas we need to address, 41â61 Inaccessible algorithms, 236 the progression of ideas, 37â40 Information, 41, 124, 166 understanding the past and âclumping,â 69 understanding the discipline of finding, 121 history, 34â35 from history, 499 âHistory-as-account,â 187â188, 203 from the history of science, 499 âHistory-as-event,â 187, 203 inquiry based, 470n âHistory-considerateâ learning storing in memory, 180 environments Inheritance designing, 199â209 meiotic processes governing, 528 the great interruption in European Initial models geographic knowledge, 200â201 providing students with opportunities with tools for historical thinking, 199â to revise in light of anomalous 209 data and in response to critiques of others, 524 History of the Decline and Fall of the Roman Empire, The, 57 Inquiry based information, 470n Hitler, Adolf, 34â35, 59â60, 586 Instruction, 545â554 Holt, John, 218 to support mathematical proficiency, 233â236 How People Learn: Brain, Mind, Experience, and School, 1, 25, 31â32 Instruction in rational number, 319â340 cautions in, 199 alternative instructional approaches, design characteristics described in, 321â322 12â13, 20â22, 257â258, 359 childrenâs thinking after instruction, key findings of, 79â80, 171â173, 176 338â340 research summarized in, 241 curriculum overview, 325 violating principles of, 319 fractions and mixed representations How People Learn framework, 411â415 of rational numbers, 334â337 assessment-centered, 415 introduction of decimals, 332â334 community-centered, 415 introduction to percents, 325â332 knowledge-centered, 414 knowledge network, 340 learner-centered, 414 pie charts and a part-whole reflective assessment in ThinkerTools, interpretation of rational numbers, 412â413 320â321 Humor pipes, tubes, and beakers, 322â324 enlivening learning and helping build Instruction that supports metacognition, positive relationships with 239â242 students, 501 emphasizing debugging, 239â240 internal and external dialogue as support for metacognition, 241 I seeking and giving help, 241â242 Instructional lines of thinking, 182 Ideas, 41â61 Intellectual roles for students to adopt, 436 accounts, 59â61 Internal consistency, 518 cause, 49â54 Internal migration, 68 change, 43â46 Interpretation empathy, 46â49 anchoring themes in historical, 186 evidence, 54â58 of data, 403 progression of, 37â40

605 INDEX Interpreting sources in context and Knowledge claims textbook claims and the nature of in genetics, assessing, 523 sources, 100 Knowledge networks, 340 Intuitions in history new concepts of numbers and new âcounterintuitive,â 33, 42 applications, 312â316 Invented procedures, 329 new symbols, meanings, and Investigate phase, 438â443 representations, 313â314 Investigative setup for studying how light reconceptualizing the unit and interacts with solid objects, 437 operations, 315 Irving, Washington, 208 the subconstructs, 314â315 Isolation understanding numbers as evidence in, 167 multiplicative relations, 316 Italy âKnowledge packages,â 588n instruction about payment for work, Knowledge that should be taught, 259â267 66â67 central conceptual structure hypothesis, 262â265 children passing the Number J Knowledge Test, 263, 265 measures of arithmetic learning and Japan achievement, 265 teacher professional development in, numerical transfer tests, 263 244 Koedinger, Kenneth R., 351â393, 593â594 Jasper Woodbury series, 391 Kraus, Pamela, 23, 401, 475â513, 594 Jefferson, Thomas, 62â63 KWL charts, 199, 428â430 Johnson, Lyndon, 62 Jonassen, David, 181 L Judgments avoiding expressing, 498 Lamarck, Jean Baptiste de, 550, 573 Larson, Gary, 217 K Learner-centered classroom environments, 13â14, 266, 292, 414, 555 Kalchman, Mindy, 23, 217â256, 351â393, Learning 593 an active process, 476 Knowledge. See also Prior understandings humor enlivening, 501 building learning paths and networks Learning environments and the design of of, 258 instruction, 12â20 connected, 15â16 assessment-centered classroom disciplinary, 32, 543â544 environments, 13, 16â17, 267, 290, handed down through generations, 292, 555â558 93â94 community-centered classroom manipulating factual, 79â80 environments, 13, 17â20, 301, âmetahistorical,â 32 559â560 organized, 462 knowledge-centered classroom âsecond-order,â 32â33 environments, 13â16, 267, 284, secret, 72 292, 555, 587 student, 258, 544â545 learner-centered classroom of what it means to âdo science,â environments, 13â14, 266, 292, 403â407 414, 555 Knowledge-centered classroom perspectives on, 13 environments, 13â16, 267, 284, Learning goals for prekindergarten through 292, 414, 555, 587 grade 2, 284â285

606 INDEX Learning paths of knowledge Maps, 86, 140â141 building, 258 conceptual, 188 from childrenâs math worlds, for Marfanâs syndrome, 533 single-digit addition and Math words, 230 subtraction, 234â235 Mathematical proficiency, 218 Learning principles adaptive reasoning, 218 engaging resilient preconceptions, conceptual understanding, 218 569â575 procedural fluency, 218 organizing knowledge around core productive disposition, 218 concepts, 575â577 strategic competence, 218 principles of learning and classroom Mathematical thinkers environments, 586â588 building, 258 pulling threads, 569â590 Mathematical understanding, 217â256 revisiting the three, 567â590 computation without comprehension, supporting metacognition, 577â586 218 Learning rational number, 341â343 developing mathematical proficiency, metacognition, 342 232â236 network of concepts, 341â342 learning to use student thinking in prior understandings, 341 teacher video clubs, 244 Learning with understanding, 559â560 lesson study cycle, 244 supporting knowledge use in new a metacognitive approach enabling situations, 7 student self-monitoring, 236â243 Leather boats, 139â141 suggested reading list for teachers, Lee, Peter J., 23, 31â178, 576, 594 256 Lesson Study Research Group, 244 teachers as curriculum designers, 245 teachers engaging studentsâ Life and Voyages of Christopher Columbus, The, 208 preconceptions, 219â231 âLight catchers,â 437. See also Study of light understanding requiring factual Linkage knowledge and conceptual of formal mathematical understanding frameworks, 231â236 to informal reasoning, 354â355 Mathematics, 215â393 Lionni, Lee, 2, 4. See also Fish story as about quantity, not about numbers, Logic of the situation 280 exploring, 50â51 as âfollowing rulesâ to guarantee Lowenthal, David, 185 correct answers, 220â221 fostering the development of whole number sense, 257â308 M as learning to compute, 220 pipes, tubes, and beakers in, 309â349 Ma, Liping, 15â16, 18â19, 577â578 teaching and learning functions, 351â Magic Shoes game, 295â296 393 Magnetism Mathematics instruction analogy to gravity, 508 in China, 15â16, 18â19 Magnitude Mayflower, The in decimal numbers, 333â334 arrival of, 84, 87, 90, 92â95 of gravitational force, 501â508 Medawar, Peter, 406 Magnusson, Shirley J., 421â474, 594 Media Management of student activities, 435 technical and passive, 496 Mandates Meiotic processes curricular, 181 governing inheritance, 528 Manipulation of factual knowledge, 79â80

607 INDEX Mendel, Gregor, 406, 410, 517, 523, 525â Model-based inquiry, 515â565 529, 539 classroom environments that support model of simple dominance, 528 learning with understanding, 555â Mental counting line structure, 276 560 Metacognition, 10, 238, 407â411, 577â586 developing Darwinâs model of natural conceptual explanation without selection in high school evolution, conceptual understanding, 578 540â554 engaging students in reflective genetics, 516â540 scientific practice, 538â540 Modeling for Understanding in Science in evaluating the methods used in an Education (MUSE), 516, 548 experiment, 408â409 curricula from, 555, 559 guiding student observation and Models, 402â403 articulation, 584â585 consistency between, 557 of light, 426 of progression in ideas about in Mendelâs contribution to genetics, evidence, 166â167 410 providing students with opportunities questioning and explaining in high to revise in light of anomalous school science, 582â583 data and in response to critiques and rational number, 319, 342 of others, 524 supporting, 577â586 Monarch/viceroy case supporting skilled questioning and Darwinian explanation written by explaining in mathematics students on the, 553 problem solving, 580â581 Monitoring. See also Self-monitoring Metacognitive approaches to instruction, 2, metacognitive, 10 80 âMonster-free zone,â 295 enabling student self-monitoring, Moss, Joan, 23, 309â349, 595 236â243 Motion of projectiles framework of How People Learn, 242â explaining, 511 243 Multiple strategies, 223â227 instruction that supports allowing, 223â227 metacognition, 239â242 engaging studentsâ problem-solving seeking a balanced classroom strategies, 225â227 environment, 242â243 three subtraction methods, 224 supporting student and teacher Multiplicative operators, 315 learning through a classroom Multiplicative reasoning discourse community, 237 relative thinking as, 311 Metacognitive monitoring, 10 MUSE. See Modeling for Understanding in âMetahistoricalâ knowledge, 32 Science Education âMetamemory,â 11 Mystery Migration sense of, 71 internal and external, 68 âMystery Object Challenge,â 329 Miller Analogies Test, 404 âMindtools,â 181 N Minstrell, James, 23, 401, 475â513, 594â595 Minus Mouse, 290â291 Narrative accounts Misconceptions providing students with, 573â575 about momentum, 5 National Council of Teachers of about the scientific method, 414 Mathematics (NCTM), 221, 241, âMissing-term problem,â 317 259 Misunderstandings, 310 standards from, 305

608 INDEX National Curriculum for History, 177n providing opportunities to link the National Research Council, 1, 218, 221, 233 âworld of quantityâ with the guidelines of, 398 âworld of counting numbersâ and the âworld of formal symbols,â National Science Education Standards, 455, 561 288â292 Native Americans, 41, 82â83, 98, 105â106 Number Worlds program, 262, 283, 287â NCTM. See National Council of Teachers of 288, 292, 296, 300, 302â303 Mathematics Numeric answers, 372 Necessary conditions causes as, 53 O Neighborhood Number Line, 295 Networks Object Land, 284â286, 288 of concepts, and rational number, âOne worldâ revolution, 169 341â342 âOpeningsâ in the curriculum, 245 of knowledge, building, 258 Opportunities New conceptualizations to develop causal models to account understanding numbers as for patterns, 524 multiplicative relations, 316 to experience discrepant events that New ideas allow them to come to terms with development of, 470n the shortcomings in their everyday New rules models, 571â573 discovering, 588 to make ideas public, 524 New symbols providing students with, 523â524 meanings, and representations, 313â to revise initial models in light of 314 anomalous data and in response âNothingâ happening, 43 to critiques of others, 524 Number Knowledge Test, 260, 264, 267â to search for patterns in data, 524 269, 271, 279, 304â305 to use patterns in data and models to administering and scoring, 271 make predictions, 524 Number worlds, 282â302 to use prior knowledge to pose encouraging the use of metacognitive problems and generate data, 523â processes to facilitate knowledge 524 construction, 300â302 Opportunities for children to acquire engaging childrenâs emotions and computational fluency as well as capturing their imagination, 296â conceptual understanding, 298â300 298 Sky Land Blastoff activity, 298â299 exposing children to major forms of Opportunities for students to suggest and number representation, 283â288 test related hypotheses in the five forms of representation and elaboration activities, 484â489 the lands in which they appear, inverted cylinder in a cylinder of 286 water, 485â486 learning goals for prekindergarten inverted glass of water, 484â485 through grade 2, 284â285 leaky bottle, 486 providing analogs of number water and air in a straw, 486â488 representations that children can weighingâ an object in a fluid actively explore hands-on, 292â medium, 488â489 296 Opportunities to link the âworld of providing opportunities for children quantityâ with the âworld of to acquire computational fluency counting numbersâ and the âworld as well as conceptual of formal symbols,â 288â292 understanding, 298â300 Minus Mouse, 290â291

609 INDEX Plus Pup, 288â290 Periods in history, 42â43 Plus Pup meets Minus Mouse, 291â292 Physics Optics kit, 422, 468 fundamental, 24 Order instruction in, 16â17 of counting words, 274 Picture Land, 285â287, 297 in decimal numbers, 333â334 Pie charts and a part-whole interpretation Organized knowledge, 462 of rational numbers, 320â321 Organizing knowledge around core Pilgrim Fathers and Native Americans, 71, concepts 84â119 subtraction with regrouping, 18â19 exploring the basis for textbook Origin of Species, 551 claims and the nature of sources, Outcomes of courses, 181 84â111 grid for evidence on, 173, 175 ideas, beliefs, and attitudes, 112â118 P language of sources, interpretation, and other perspectives, 118â119 Pace of change, 44 teacher questions, 112â113, 115 Paley, William, 550â551, 573 whether people thought like us in the Palincsar, Annemarie Sullivan, 23, 421â474, past, 117 595 Pipes Park, Lesley, 455 a new approach to rational-number Part-whole relation, 314 learning, 322â324 Pass it on (game), 105 a representation for fullness, 325â326 Passive media, 496 Planning, 164â176 Passmore, Cynthia M., 23, 515â565, 595 of progression in ideas about Past evidence, 166â167, 174â175 finding out about, 56â58 unit on filling the world with people, pictures of, 166 169 Patterns in data unit on first contacts, whether St. providing students with opportunities Brendan sailed from Ireland to to search for, 524 America, 171 providing students with opportunities unit on first contacts, why the Norse to use to make predictions, 524 colonists didnât stay in America, Payment for work in history, 66â67 172 Peanuts cartoon, 309 unit on people going their separate Pedagogical words ways, 170 meaningful, 230 Plausibility, 138 People going their separate ways Plus Pup, 288â290 unit on, 170 meeting Minus Mouse, 291â292 Percents, 325â332, 340 Pocahontas (Disney film), 122 computing with, 329 Pory, John, 84â85, 90, 97, 100â104, 106â in everyday life, 325 108 âfamiliesâ of, 331 Positive relationships invented procedures, 329 humor helping to build with students, on number lines, 326â329 501 pipes and tubes, as representations Possible Worlds, 406 for fullness, 325â326 Power starting from, 322â324 explanatory and predictive, 518 string challenges, 329â331 Preconceptions, 1, 55, 399â403 Percy, George, 122 about people, society, and how the Performance world works, 127â128 need to assist, 203 conceptual change, 400â403

610 INDEX drawing on knowledge and âProblematizingâ historical accounts, 184â188 experiences that students Procedural fluency, 218 commonly bring to the classroom Productive disposition, 218 but are generally not activated Proficiency with regard to the topic of study, mathematical, 218 569â571 Progress, 44â45 engaging resilient, 569â575 Progression of ideas, 37â40 everyday concepts of scientific different ideas about historical methods, argumentation, and accounts, 38â39 reasoning, 400 Progressive change, 45 everyday concepts of scientific Project CHATA. See Concepts of History phenomena, 399â400 and Teaching Approaches importance of studentsâ, 79 Projectiles providing opportunities for students explaining motion of, 511 to experience discrepant events Proportion, 234, 340 that allow them to come to terms Pump Algebra Tutor. See Cognitive Tutor with the shortcomings in their Algebra everyday models, 571â573 providing students with narrative Q accounts of the discovery of (targeted) knowledge or the Quantity, 234 development of (targeted) tools, schema for, 272 573â575 Question Poser, 300â301 Preconceptions about how we know about Questioning and explaining in high school the past, 121â123 science common student assumptions about supporting metacognition, 582â583 how we know of the past, 123 Questions, 128 dangers of what appears to be diagnostic, 478 familiar, 122 at the heart of using evidence, 124 Predictive power, 518 many as yet unanswered, 492 Preinstruction assessments, 495 teachers modeling for students, 477 Prepare-to-investigate phase, 434â438 Quotient interpretation, 314 Prepare-to-report phase, 443â448 Principles of How People Learn applied to teaching high school history, 179â R 213 designing a âhistory-considerateâ Rational change, 45 learning environment, 199â209 Rational number, 341â343 transforming topics and objectives metacognition, 342 into historical problems, 181â199 network of concepts, 341â342 Prior understandings prior understandings, 341 development of physical concepts in Rational-number learning infancy, 4 and the knowledge network, 312â316 engaging, 4â5 metacognition and rational number, 319 of light, 425 new concepts of numbers and new misconceptions about momentum, 5 applications, 312â316 providing students with opportunities and the principles of How People to use to pose problems and Learn, 312â319 generate data, 523â524 studentsâ errors and misconceptions and rational number, 341 based on previous learning, 316â Problem solvers 319 building, 258

611 INDEX Real-world experience diagnosing preconceptions in physics, current and future, 390 404 Real-world words, 230 the How People Learn framework, Reality test, 80â84 411â415 â7-year gap,â 82 knowledge of what it means to âdo Reciprocal teaching, 11 science,â 403â407 Reconceptualizing the unit and operations, Scientific method 315 misconceptions about, 414 Recorder, 435 Scissors-and-paste approach and textbook Reflective assessments, 412 claims and the nature of sources, in ThinkerTools, 412â413 94 Regrouping Searchers, The (film), 151 subtraction with, 18â19 Second cycle of investigation Relative thinking as multiplicative, 311 community knowledge from, 464 Relativism, 176 Second-hand investigation, 455â459 Reliability, 126 âSecond-orderâ disciplinary concepts, 61, Religious practices, 113â118 73n Reporter, 301 âSecond-orderâ knowledge, 32â33, 41 Reporting phase, 427, 448â455 acquisition of, 40â41 Representations, 372 Secret knowledge, 72 anchoring themes in historical, 186 Seeing for yourself and textbook claims Reproductive success, 542 and the nature of sources, 93 Revolution, 61 Seixas, Peter, 151 Selective advantage, 542 Self-assessment, 12 S Self-monitoring importance of, 10â12 Sagan, Carl, 194, 196â197 metacognitive monitoring, 10 Sales, Kirkpatrick, 208 Sensitivity Schemas â7-year gap,â 82 2-slot and 3-slot, 370 7-year-olds understandings of, 277â counting and quantity, 272 278 Schools Council History Project, 40, 177n to studentsâ substantive assumptions, Science, 395â565 127 developing understanding through Severin, Tim, 139, 142â143 model-based inquiry, 515â565 Shemilt, Denis, 23, 56, 79â178, 595â596 guided inquiry in the science Shrinking past, 160â161 classroom, 475â513 Significance, 45 information from the history of, 499 historical, 45 leaving many questions as yet Simplicity, 389â390 unanswered, 492 6-year-olds understandings of, 274â teaching to promote the development 277 of scientific knowledge and Skating Party game, 292â295 reasoning about light at the Skills elementary school level, 421â474 defining, 40 unit on the nature of gravity and its Sky Land, 286â287 effects, 477â511 Blastoff activity, 298â299 Science classrooms Smith, John, 122 guided inquiry in, 475â513 Sources Scientific inquiry and How People Learn, access to someone who saw for 397â419 himself, 93 addressing preconceptions, 399â403 briefing sheet, 88â89

612 INDEX distinguishing among kinds of claims, initial GCK population for the final 101â102 GCK inquiry, 537 generalizing, 102â107 meiotic processes governing getting behind the record to concerns inheritance, 528 of the people who produced Mendelâs model of simple dominance, them, 107â108 528 interpreting sources in context, 100 Studentsâ errors and misconceptions based maintaining contact with an on previous learning, 316â319 eyewitness using knowledge Studentsâ existing knowledge, 517â526 handed down through assessing knowledge claims in generations, 93â94 genetics, 523 the nature of, 84â111 attending to, 544â545 scissors-and-paste approach, 94 black box, 520 seeing for yourself, 93 building on and connecting, 258 teacher questions, 92, 95â96, 99â101 learning genetics content, 524â526 trusting the source who was in a providing students with learning position to know, 96 opportunities, 523â524 understanding the purpose of the student conceptions of models, 518 source, 96â99 Studentsâ preconceptions understanding what is likely to get importance of, 79 recorded and under what Study of light, 422â426 circumstances, 108â111 conceptual understanding, 423â424 working out the facts from other metacognition, 426 sources or available knowledge, prior knowledge, 425 94â95 Study of light through inquiry, 426â459 Splitting, 323 heuristic for teaching and learning State of affairs science through guided inquiry, changes in, 44 427â455 Stearns, Peter, 210 second-hand investigation, 455â459 Stewart, James, 23, 515â565, 596 Subconstructs âStop-Start Challenge,â 333 the many personalities of rational Stopwatches number, 314â315 decimals and, 332â333 Subject-specific knowledge in effective Stories science instruction, 467â469 âembroidering,â 153 Substantiated accounts, 87 Strategic competence, 218 Substantive assumptions String challenges sensitivity to studentsâ, 127 guessing mystery objects, 329â331 Substantive concepts, 61â65 Student assumptions about how we know historical accounts not copies of the of the past, 123 past, 62â63 Student conceptions payment for work, 66â67 experimentation, 402 Subtraction with regrouping, 18â19 inadequacies in arguments, 403 Supporting learning through cycles of interpretation of data, 403 investigation, 460â467 of knowledge generation and Supporting skilled questioning and justification in science, 402â403 explaining in mathematics models, 402â403, 518 problem solving Student inquiry in genetics, 526â538 supporting metacognition, 580â581 example of student work on a GCK Supporting student and teacher learning homework assignment, 535 through a classroom discourse genetic inquiry in the classroom, 529â community, 237 534

613 INDEX T Teaching mathematics in the primary grades, 257â308 Table of values to produce a function, acknowledging teachersâ conceptions 353â358 and partial understandings, 279â Teacher professional development in 281 Japan, 244 building on childrenâs current Teacher questions, 112â113, 115 understandings, 267â279 and textbook claims and the nature the case of number worlds, 282â302 of sources, 92, 95â96, 99â101 comparing number worlds and Teachersâ conceptions and partial control group outcomes, 304 understandings, 279â281 deciding what knowledge to teach, acquiring an understanding of 259â267 number as a lengthy, step-by-step defining the knowledge that should process, 280â281 be taught, 281â282 counting words as the crucial link Teaching the rational number system, 309â between the world of quantity 349 and the world of formal symbols, additive and multiplicative reasoning, 280â281 311 math as not about numbers, but how students learn rational number, about quantity, 280 341â343 Teachers engaging studentsâ instruction in rational number, 319â preconceptions, 219â231 340 common preconceptions about rational-number learning and the mathematics, 220â222 principles of How People Learn, engaging studentsâ preconceptions 312â319 and building on existing Teaching to promote the development of knowledge, 223â231 scientific knowledge and Teaching reasoning about light at the reciprocal, 11 elementary school level, 421â474 Teaching and learning functions in the role of subject-specific knowledge mathematics, 351â393 in effective science instruction, addressing the three principles, 359â 467â469 373 the study of light, 422â426 building conceptual understanding, the study of light through inquiry, procedural fluency, and 426â459 connected knowledge, 364â369 supporting learning through cycles of building on prior knowledge, 359â investigation, 460â467 364 Technical media, 496 building resourceful, self-regulating Testimony, 41, 124, 135, 166 problem solvers, 371â373 Testing linking formal mathematical external, 181 understanding to informal Textbook claims reasoning, 354â355 access to someone who saw for making a table of values to produce a himself, 93 function, 353â358 briefing sheet, 88â89 teaching functions for understanding, distinguishing among kinds of claims, 373â389 101â102 teaching to achieve this kind of generalizing, 102â107 understanding, 358â359 getting behind the record to concerns Teaching as Story Telling, 574 of the people who produced Teaching functions for understanding, 373â them, 107â108 389 interpreting sources in context, 100

614 INDEX maintaining contact with an Turner, Frederick Jackson, 58 eyewitness using knowledge Twisting the truth, 105, 123 handed down through 2-slot schemas, 370 generations, 93â94 and the nature of sources, 84â111 U scissors-and-paste approach, 94 seeing for yourself, 93 âUnderlyingâ causes, 35 teacher questions, 92, 95â96, 99â101 Understanding trusting the source who was in a essential role of factual knowledge position to know, 96 and conceptual frameworks in, understanding the purpose of the 6â9 source, 96â99 experts remembering considerably understanding what is likely to get more relevant detail than novices recorded and under what in tasks within their domain, 8â9 circumstances, 108â111 learning with understanding working out the facts from other supporting knowledge use in new sources or available knowledge, situations, 7 94â95 Understanding of number Themes, 44 a lengthy, step-by-step process, 280â anchoring in historical representation 281 and interpretation, 186 Understanding the purpose of the source ThinkerTools, 407, 585 and textbook claims and the Third cycle of investigation nature of sources, 96â99 community knowledge from, 465 Understanding what is likely to get Third International Mathematics and recorded and under what Science Study, 243 circumstances 3-slot schema and textbook claims and the nature for graphing a line, 370â371 of sources, 108â111 Three subtraction methods, 224 Unit-level problem, 189â199 Time, 41â43 accounts of Colombian voyages, 192â change limited in, 45 193 periods in history, 43 ancient views of the Earth as flat or Time lines, 129, 159 round, 196â197 Timekeeper, 435 Unit on the nature of gravity and its Torsion bar, 493â501 effects, 477â511 Transforming topics and objectives into United Kingdom historical problems, 181â199 adjusting data from, 177n accounting for the âflat earth,â 189â Schools Council History Project, 40, 199 177n âproblematizingâ historical accounts, Units 184â188 on filling the world with people, 169 Transmission errors, 123 on first contacts, whether St. Brendan Trusting the source who was in a position sailed from Ireland to America, to know 171 and textbook claims and the nature on first contacts, why the Norse of sources, 96 colonists didnât stay in America, Truth 172 twisting, 105, 123 on people going their separate ways, Tubes 170 a new approach to rational-number learning, 322â324 a representation for fullness, 325â326

615 INDEX V Work payment for in history, 66â67 Verbal interpretations, 372 Working out the facts from other sources Visual proportional estimation or available knowledge starting from, and halving and and textbook claims and the nature doubling, 323â324 of sources, 94â95 Working things out for ourselves, 133â138 being aware of how we are thinking, W 135 going beyond face value, 134 War (card game), 336 how far a leather boat could have Warm-Up period, 298, 300 managed to sail, 139â141 Water and air in a straw, 486â488 Working through the task, 128â164 Website, 562n Working with evidence âWeighingâ an object in a fluid medium, Pilgrim Fathers and Native Americans, 488â489 84â119 Weighing-in-a-vacuum situation, 484, 489 preparing for the task, 121â128 Whole number the St. Brendanâs voyage task, 128â central conceptual structure for, 261â 164 262, 275 Worldâs Fair of 1892, 208 Wilson, Suzanne M., 596 Wrap-Up period, 301 Wineburg, Samuel S., 100 Written Arithmetic test, 264â265 Wisdom, 236, 238 Woodbury, Jasper, 391 Y Word Problems test, 264â265 Words versus notations, 230 Year-long historical questions, 184â188 Words in stories explaining, 132â133