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Suggested Citation:"Index." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
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Index

A

Absolute difference, 311

Absolute thinking

as additive, 311

Access to someone who saw for himself and textbook claims and the nature of sources, 93

Accounts, 59–61

of Colombian voyages, 192–193

different ideas about historical, 38–39

historical, 59–61

substantiated, 87

Actions at a distance

exploring similarities and differences between, 492–493

Activity A1 worksheet, 483

Adams, John, 185

Adaptive reasoning, 218

Adding It Up, 218, 233, 241

Additive reasoning, 311, 321

absolute thinking as, 311

Addressing preconceptions, 399–403

Advantage

selective, 542

Adventure

sense of, 71

Alternative instructional approaches, 321–322

American Association for the Advancement of Science

guidelines of, 398

textbook review by, 16

Analogs of number representations that children can actively explore hands-on, 292–296

Rosemary’s Magic Shoes game, 295–296

Skating Party game, 292–295

Analogy to understand the benchmark experience, 489–490

Ancient views of the Earth as flat or round, 196–197

the Atlas Farnese, 196

the story of Eratosthenes and the Earth’s circumference, 196–197

Anglo-Saxons, 117

Anselm, St., 46

Arguments

inadequacies in, 403

Ashby, Rosalyn, 79–178, 591

Assessment-centered, 415

Assessment-centered classroom environments, 13, 16–17, 267, 290, 292, 555–558

examples of students’ critiques of their own Darwinian explanations, 558

Suggested Citation:"Index." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×

sample exam question, and consistency between models, 557

Assessment systems DIAGNOSER, 513

Assessments. See also Self-assessment formative, 16–17, 193

preinstruction, 495

“reflective,” 412

Assumptions

substantive, 127

Atlas Farnese, 194, 196

Authority, 135

Award cards, 293

Awareness of how you are thinking, 135

B

Bain, Robert B., 23, 179–213, 591

Balzac, Honoré de, 236

Barry, Tr., 578

Barton, Keith, 45, 160

Beakers

a new approach to rational-number learning, 322–324

Bede, St., 58

Bell jar experiment, 484, 489

Benchmark lessons, 493–501, 512n

weighing in a vacuum, 480–483

Black box approaches, 519–520

“Blastoff!”, 298

Boorstin, Daniel, 198

Bradford, William, 84–88, 96, 108–111

Bransford, John D., 1–28, 217–256, 397–419, 569–592

Brendan, St., 71, 82–83, 128–164, 171

believing historical films when people in them behave as we would, 151

the deficit past, 154–155

explanation of words in the story, 132–133

finding out what kind of story it is, 150–164

grid for evidence on, 173–174

the question, 128

the shrinking past, 160–161

the story, 128–133

thinking from inside the story, 144–150

thinking from outside the story, 138–144

voyage of, 130–132

working things out for ourselves, 133–138

Bridging

from understanding magnetic action at a distance to understanding gravitational action at a distance, 508–510

“Bridging context,” 324, 359

Briefing sheets, 87, 91

and textbook claims and the nature of sources, 88–89

Building conceptual understanding, procedural fluency, and connected knowledge, 364–369

3-slot schema for graphing a line, 370–371

developmental model for learning functions, 365–366

level 0, 364, 367

level 1, 367–368

level 2, 368

level 3, 369

Building on children’s current understandings, 267–279, 359–364

administering and scoring the Number Knowledge Test, 271

mental counting line structure, 276

Number Knowledge Test, 268–269

understandings of 4-year-olds, 270–273

understandings of 5-year-olds, 273–274

understandings of 6-year-olds, 274–277

understandings of 7-year-olds, 277–278

understandings of 8-year-olds, 278–279

Building resourceful, self-regulating problem solvers, 371–373

an integrated understanding of functions, 372

C

Cambridge History Project, 177n

Canada

teaching history in, 151

“Candles” (unit), 456

Card games, 335–337

Suggested Citation:"Index." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×

Carey, Susan, 592

Cartier, Jennifer L., 23, 515–565, 592

Cartoons, 143, 145–146, 148, 546–549

Peanuts, 309

sequencing activity, 546–547

Case, Robbie, 23

Causal models to account for patterns providing students with opportunities to develop, 524

Causes, 49–54

exploring the logic of the situation, 50–51

modeling, 562n

as necessary conditions, 53

“underlying,” 35

Central conceptual structure hypothesis bidimensional, for number, 279

dependence of future learning on the acquisition of this structure, 264–265

importance of structure to successful performance on a range of tasks, 262–263

for whole number, 261–262, 275

Change, 43–46, 61

direction of, 44

large-scale patterns of, 68

pace of, 44

as progressive, rational, and limited in time, 45

Cheese and the Worms, 185

Children

engaging their emotions and capturing their imagination, embedding knowledge constructed in their hopes, fears, and passions, 296–298

exposing to major forms of number representation, 283–288

as “natural” scientists, 421

Children passing the Number Knowledge Test

and measures of arithmetic learning and achievement, 265

and numerical transfer tests, 263

Children’s Math World project, 219, 223, 227, 229, 231, 236, 241

Children’s thinking after instruction, 338–340

China

teaching of mathematics in, 15–16, 18–19

Christian geography, 200

Circle Land, 286–287

Claims

backing up, 58

Classroom environments

genetic inquiry in, 529–534

principles of learning and, 586–588

Classroom environments that support learning with understanding, 555–560

assessment-centered classroom environments, 13, 16–17, 267, 290, 292, 555–558

community-centered classroom environments, 13, 17–20, 301, 559–560

knowledge-centered classroom environments, 13–16, 267, 284, 292, 555, 587

learner-centered classroom environments, 13–14, 266, 292, 555

Clumping information, 69

Codes

cracking, 335

Cognitive Tutor Algebra, 355, 391

Colombian Exposition, 208

Columbus’ voyages, 189–193, 195, 199, 204–205, 207–208, 587

Common preconceptions about mathematics, 220–222

as “following rules” to guarantee correct answers, 220–221

as learning to compute, 220

only some people have the ability to “do math,” 221–222

Community-centered classroom environments, 13, 17–20, 301, 415, 559–560

learning with understanding, 559–560

organizing knowledge around core concepts, 18–19

Comparing number worlds and control group outcomes, 304

Competence developed by students, 1

Comprehensive Test of Basic Skills, 412

Computing with percent, 329

Concepts

substantive, 61–65

Concepts of History and Teaching Approaches (Project CHATA), 38–39, 51–53, 56, 62, 82

Suggested Citation:"Index." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×

Conceptual change, 400–403

student conceptions of knowledge generation and justification in science, 402–403

Conceptual explanations

without conceptual understanding, 578

Conceptual structure

bidimensional central, for number, 279

central, for whole number, 261–262, 275

Conceptual understanding, 218

of light, 423–424

Conceptualization

children’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

organizing procedural knowledge and skills around, 19

Corne, Michael Felice, 90

“Counterintuitive” intuitions

in history, 33, 42

Counting schema, 272

Counting words

as the crucial link between the world of quantity and the world of formal symbols, 280–281

order of, 274

Course outcomes, 181

Curriculum

mandates in, 181

from Modeling for Understanding in Science Education, 555, 559

“openings” in, 245

Curriculum for moving students through the model, 373–375

example lessons, 375–389

learning slope, 378–381

learning y-intercept, 381–384

operating on y = x2, 384–389

sample computer screen, 386

suggested curricular sequence, 376–377

two different student solutions to an open-ended problem, 385

Cut-and-paste, 167

Cycles of investigation

development of community knowledge across cycles of investigation, 460

development of conceptual frameworks for light, 462–467

in guided-inquiry science, 427

supporting learning through, 460–467

D

Dances with Wolves (film), 151

Darwin, Charles, 542–545, 550–551, 556, 573

Darwin’s model of natural selection in high school evolution, 540–554

attending to significant disciplinary knowledge, 543–544

attending to student knowledge, 544–545

cartoon sequencing activity, 546–547

explanation written by students on the monarch/viceroy case, 553

instruction, 545–554

laying the groundwork, 545–549

understanding, 550–552

Data

interpretation of, 403

Data tables from initial recording and with revisions for analysis, 445

Debugging

emphasizing, 239–240

Decimals, 332–334

magnitude and order in decimal numbers, 333–334

and stopwatches, 332–333

Decisions

as to what knowledge to teach, 259–267, 281–282

Deficit past, 154–155

Dependence, 234, 352

Design of instruction

bridging instructional activities, 231

learning environments and, 12–20

Development

of community knowledge across cycles of investigation, 460

Suggested Citation:"Index." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×

of Darwin’s model of natural selection in high school evolution, 540–554

of physical concepts in infancy, 4

of understanding through model-based inquiry, 515–565

Development of conceptual frameworks for light, 462–467

community knowledge from the first cycle of investigation (first-hand), 463

community knowledge from the fourth cycle of investigation (first-hand), 467

community knowledge from the second cycle of investigation (first-hand), 464

community knowledge from the third cycle of investigation (second-hand), 465

Development of mathematical proficiency, 232–236

inaccessible algorithms, 236

instruction to support mathematical proficiency, 233–236

a learning path from children’s math worlds for single-digit addition and subtraction, 234–235

Developmental model

for learning functions, 365–366

DIAGNOSER assessment system, 513

Diagnosing preconceptions in physics, 404

Diagnostic assessment, 491–492

Diagnostic questions, 478

Dialogue

internal and external, as support for metacognition, 241

Direction of change, 44

Disciplinary knowledge, 32

attending to significant, 543–544

“second-order,” 61

Disconfirmation, 415

Discrepant events

providing students with opportunities to experience, 571–573

Discussion

guided, 579, 582

DiSessa, Andrea, 5

Distinguishing among kinds of textbook claims

and the nature of sources, 101–102

DNA, 517, 526

“Doing,” 32, 48

“Doing math”

only some people having the ability for, 221–222

Donovan, M. Suzanne, 1–28, 397–419, 569–590, 592

Double-blind procedure, 302

Dragon Quest game, 297–298

E

Earth as flat or round, ancient views of, 196–197

Earth’s circumference

the story of Eratosthenes and, 196–197

Effects of gravity, 510–511

explaining falling bodies, 510–511

explaining motion of projectiles, 511

Egan, Kieran, 592

8-year-olds understandings of, 278–279

Elementary Science Study

Optics unit, 422, 468

“Embroidering” stories, 153

Empathy, 46–49, 65, 112

Encouraging math talk, 228–231

Encouraging the use of metacognitive processes to facilitate knowledge construction, 300–302

Engage phase, 428–434

Engagement of students’ preconceptions and building on existing knowledge, 4–5, 223–231

allowing multiple strategies, 223–227

designing bridging instructional activities, 231

encouraging math talk, 228–231

Engagement of students’ problem-solving strategies, 225–227

Equipment Manager, 435

Eratosthenes, 194, 196–197

European geographic knowledge

the great interruption in, 200–201

Everyday concepts

history and, 33–61

of scientific methods, argumentation, and reasoning, 400

of scientific phenomena, 399–400

Suggested Citation:"Index." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×

Evidence, 41, 54–58, 61, 65, 112, 120, 165

in context, 167

cutting-and-pasting, 167

finding out about the past from received information, 56–58

historical, 134

information as, 166

in isolation, 167

model of progression in ideas about, 166–167

pictures of the past, 166

questions at the heart of using, 124

testimony as, 166

Experiments on Plant Hybridization, 529

Experts remembering considerably more relevant detail than novices in tasks within their domain, 8–9

Explanations, 156

of words in the story, 132–133

Explanatory power, 518

External consistency, 518

External migration, 68

External testing, 181

F

Face value

going beyond, 134

Factual knowledge

manipulating, 79–80

Falling bodies

explaining, 510–511

Familiarity, 389–390

the dangers of what appears to be familiar, 122

Feynman, Richard, 24, 403

Filling the world with people

unit on, 169

First contacts

whether St. Brendan sailed from Ireland to America, unit on, 171

why the Norse colonists didn’t stay in America, unit on, 172

First cycle of investigation

community knowledge from, 463

Fish story (Fish Is Fish), 2–12, 398, 414, 575

5-year-olds understandings of, 273–274

engaging prior understandings in, 4–5

essential role of factual knowledge and conceptual frameworks in understanding, 6–9

importance of self-monitoring in, 10–12

“Flat earth,” 189–199

accounts of Colombian voyages, 192–193

ancient views of the Earth as flat or round, 196–197

Formative assessments, 16–17, 193

Forms of representation

4-year-olds understandings of, 270–273

and the lands in which they appear, 286

Fourth cycle of investigation

community knowledge from, 467

Fourth graders’ initial ideas about light, 431

Fractions and mixed representations of rational numbers, 334–337

card games, 335–337

cracking the code, 335

fractions and equivalencies, 334–335

Framework of How People Learn

seeking a balanced classroom environment, 242–243

Frank, Anne, 109

Fundamental physics, 24

Fundamentalism, 176

Fuson, Karen C., 23, 217–256, 593

Future real-world experience, 390

G

Galapagos tortoises, 558

GCK. See Genetics Construction Kit

General ideas, 162

General meaning of slope, 363

Generalizing and textbook claims and the nature of sources, 102–107

Genetics, 516–540

attending to students’ existing knowledge, 517–526

metacognition and engaging students in reflective scientific practice, 538–540

simple dominance homework assignment, 539

student inquiry in, 526–538

Suggested Citation:"Index." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×

Genetics Construction Kit (GCK), 534–537

homework assignment, example of student work on, 535

Genetics content

learning, 524–526

Geographic knowledge

Christian, 200

the great interruption in European, 200–201

Gibbon, Edward, 57

GIsML Community of Practice, 470n

“Globalization,” 169

Gould, Stephen Jay, 198

Gragg, Charles, 236

Gravity and its effects, 477–511

activity A1 worksheet, 483

analogy to magnetism, 508

bridging from understanding magnetic action at a distance to understanding gravitational action at a distance, 508–510

building an analogy to understand the benchmark experience, 489–490

consensus discussion and summary of learning, 490–491

defining, 477–510

diagnostic assessment, 491–492

exploring similarities and differences between actions at a distance, 492–493

factors on which the magnitude of gravitational force depends, 501–508

finding out about students’ initial ideas, 477–478

identifying preconceptions, 478–480

opportunities for students to suggest and test related hypotheses, 484–489

twisting a torsion bar, 493–501

weighing in a vacuum, 480–483

Grids, 173–175

Griffin, Sharon, 23, 257–308, 593

Group work, 582–584

Guess My Number, 300

Guidance of student observation and articulation

supporting metacognition, 584–585

Guided inquiry, 495, 579, 582

H

“H(ac)”, 187–188

Hall, G. Stanley, 177n

Halsall, William Formsby, 87

Help

seeking and giving, 241–242

Heuristic for teaching and learning science through guided inquiry, 427–455

cycle of investigation in guided-inquiry science, 427

data tables from initial recording and with revisions for analysis, 445

engage phase, 428–434

fourth graders’ initial ideas about light, 431

investigate phase, 438–443

investigative setup for studying how light interacts with solid objects, 437

prepare-to-investigate phase, 434–438

prepare-to-report phase, 443–448

report phase, 448–455

“H(ev)”, 187

Higher-order knowledge structure, 276

Historical accounts, 59–61

different ideas about, 38–39

not copies of the past, 62–63

“problematizing,” 184–188

Historical evidence, 134

Historical films, 151

Historical lines of thinking, 182

Historical problems

transforming topics and objectives into, 181–199

History, 29–213

applying the principles of How People Learn in teaching high school history, 179–213

“counterintuitive” intuitions in, 33, 42

“doing,” 32, 48

implications for planning, 164–176

periods in, 42–43

putting principles into practice, 79–178

the reality test, 80–84

significance in, 45

that “works,” 65–72

understanding, 31–77

working with evidence, 84–119

Suggested Citation:"Index." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×

History and everyday ideas, 33–61

differences in the power of ideas, 36–37

grounds for caution, 40–41

ideas we need to address, 41–61

the progression of ideas, 37–40

understanding the past and understanding the discipline of history, 34–35

“History-as-account,” 187–188, 203

“History-as-event,” 187, 203

“History-considerate” learning environments

designing, 199–209

the great interruption in European geographic knowledge, 200–201

with tools for historical thinking, 199–209

History of the Decline and Fall of the Roman Empire, The, 57

Hitler, Adolf, 34–35, 59–60, 586

Holt, John, 218

How People Learn: Brain, Mind, Experience, and School, 1, 25, 31–32

cautions in, 199

design characteristics described in, 12–13, 20–22, 257–258, 359

key findings of, 79–80, 171–173, 176

research summarized in, 241

violating principles of, 319

How People Learn framework, 411–415

assessment-centered, 415

community-centered, 415

knowledge-centered, 414

learner-centered, 414

reflective assessment in ThinkerTools, 412–413

Humor

enlivening learning and helping build positive relationships with students, 501

I

Ideas, 41–61

accounts, 59–61

cause, 49–54

change, 43–46

empathy, 46–49

evidence, 54–58

progression of, 37–40

providing students with opportunities to make public, 524

“second-order,” 32–33

time, 41–43

Inaccessible algorithms, 236

Information, 41, 124, 166

“clumping,” 69

finding, 121

from history, 499

from the history of science, 499

inquiry based, 470n

storing in memory, 180

Inheritance

meiotic processes governing, 528

Initial models

providing students with opportunities to revise in light of anomalous data and in response to critiques of others, 524

Inquiry based information, 470n

Instruction, 545–554

to support mathematical proficiency, 233–236

Instruction in rational number, 319–340

alternative instructional approaches, 321–322

children’s thinking after instruction, 338–340

curriculum overview, 325

fractions and mixed representations of rational numbers, 334–337

introduction of decimals, 332–334

introduction to percents, 325–332

knowledge network, 340

pie charts and a part-whole interpretation of rational numbers, 320–321

pipes, tubes, and beakers, 322–324

Instruction that supports metacognition, 239–242

emphasizing debugging, 239–240

internal and external dialogue as support for metacognition, 241

seeking and giving help, 241–242

Instructional lines of thinking, 182

Intellectual roles for students to adopt, 436

Internal consistency, 518

Internal migration, 68

Interpretation

anchoring themes in historical, 186

of data, 403

Suggested Citation:"Index." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×

Interpreting sources in context and textbook claims and the nature of sources, 100

Intuitions in history

“counterintuitive,” 33, 42

Invented procedures, 329

Investigate phase, 438–443

Investigative setup for studying how light interacts with solid objects, 437

Irving, Washington, 208

Isolation

evidence in, 167

Italy

instruction about payment for work, 66–67

J

Japan

teacher professional development in, 244

Jasper Woodbury series, 391

Jefferson, Thomas, 62–63

Johnson, Lyndon, 62

Jonassen, David, 181

Judgments

avoiding expressing, 498

K

Kalchman, Mindy, 23, 217–256, 351–393, 593

Knowledge. See also Prior understandings building learning paths and networks of, 258

connected, 15–16

disciplinary, 32, 543–544

handed down through generations, 93–94

manipulating factual, 79–80

“metahistorical,” 32

organized, 462

“second-order,” 32–33

secret, 72

student, 258, 544–545

of what it means to “do science,” 403–407

Knowledge-centered classroom environments, 13–16, 267, 284, 292, 414, 555, 587

Knowledge claims

in genetics, assessing, 523

Knowledge networks, 340

new concepts of numbers and new applications, 312–316

new symbols, meanings, and representations, 313–314

reconceptualizing the unit and operations, 315

the subconstructs, 314–315

understanding numbers as multiplicative relations, 316

“Knowledge packages,” 588n

Knowledge that should be taught, 259–267

central conceptual structure hypothesis, 262–265

children passing the Number Knowledge Test, 263, 265

measures of arithmetic learning and achievement, 265

numerical transfer tests, 263

Koedinger, Kenneth R., 351–393, 593–594

Kraus, Pamela, 23, 401, 475–513, 594

KWL charts, 199, 428–430

L

Lamarck, Jean Baptiste de, 550, 573

Larson, Gary, 217

Learner-centered classroom environments, 13–14, 266, 292, 414, 555

Learning

an active process, 476

humor enlivening, 501

Learning environments and the design of instruction, 12–20

assessment-centered classroom environments, 13, 16–17, 267, 290, 292, 555–558

community-centered classroom environments, 13, 17–20, 301, 559–560

knowledge-centered classroom environments, 13–16, 267, 284, 292, 555, 587

learner-centered classroom environments, 13–14, 266, 292, 414, 555

perspectives on, 13

Learning goals for prekindergarten through grade 2, 284–285

Suggested Citation:"Index." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×

Learning paths of knowledge

building, 258

from children’s math worlds, for single-digit addition and subtraction, 234–235

Learning principles

engaging resilient preconceptions, 569–575

organizing knowledge around core concepts, 575–577

principles of learning and classroom environments, 586–588

pulling threads, 569–590

revisiting the three, 567–590

supporting metacognition, 577–586

Learning rational number, 341–343

metacognition, 342

network of concepts, 341–342

prior understandings, 341

Learning with understanding, 559–560

supporting knowledge use in new situations, 7

Leather boats, 139–141

Lee, Peter J., 23, 31–178, 576, 594

Lesson Study Research Group, 244

Life and Voyages of Christopher Columbus, The, 208

“Light catchers,” 437.

See also Study of light

Linkage

of formal mathematical understanding to informal reasoning, 354–355

Lionni, Lee, 2, 4.

See also Fish story

Logic of the situation

exploring, 50–51

Lowenthal, David, 185

M

Ma, Liping, 15–16, 18–19, 577–578

Magic Shoes game, 295–296

Magnetism

analogy to gravity, 508

Magnitude

in decimal numbers, 333–334

of gravitational force, 501–508

Magnusson, Shirley J., 421–474, 594

Management of student activities, 435

Mandates

curricular, 181

Manipulation of factual knowledge, 79–80

Maps, 86, 140–141

conceptual, 188

Marfan’s syndrome, 533

Math words, 230

Mathematical proficiency, 218

adaptive reasoning, 218

conceptual understanding, 218

procedural fluency, 218

productive disposition, 218

strategic competence, 218

Mathematical thinkers

building, 258

Mathematical understanding, 217–256

computation without comprehension, 218

developing mathematical proficiency, 232–236

learning to use student thinking in teacher video clubs, 244

lesson study cycle, 244

a metacognitive approach enabling student self-monitoring, 236–243

suggested reading list for teachers, 256

teachers as curriculum designers, 245

teachers engaging students’ preconceptions, 219–231

understanding requiring factual knowledge and conceptual frameworks, 231–236

Mathematics, 215–393

as about quantity, not about numbers, 280

as “following rules” to guarantee correct answers, 220–221

fostering the development of whole number sense, 257–308

as learning to compute, 220

pipes, tubes, and beakers in, 309–349

teaching and learning functions, 351–393

Mathematics instruction

in China, 15–16, 18–19

Mayflower, The

arrival of, 84, 87, 90, 92–95

Medawar, Peter, 406

Media

technical and passive, 496

Meiotic processes

governing inheritance, 528

Suggested Citation:"Index." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×

Mendel, Gregor, 406, 410, 517, 523, 525–529, 539

model of simple dominance, 528

Mental counting line structure, 276

Metacognition, 10, 238, 407–411, 577–586

conceptual explanation without conceptual understanding, 578

engaging students in reflective scientific practice, 538–540

in evaluating the methods used in an experiment, 408–409

guiding student observation and articulation, 584–585

of light, 426

in Mendel’s contribution to genetics, 410

questioning and explaining in high school science, 582–583

and rational number, 319, 342

supporting, 577–586

supporting skilled questioning and explaining in mathematics problem solving, 580–581

Metacognitive approaches to instruction, 2, 80

enabling student self-monitoring, 236–243

framework of How People Learn, 242–243

instruction that supports metacognition, 239–242

seeking a balanced classroom environment, 242–243

supporting student and teacher learning through a classroom discourse community, 237

Metacognitive monitoring, 10

“Metahistorical” knowledge, 32

“Metamemory,” 11

Migration

internal and external, 68

Miller Analogies Test, 404

“Mindtools,” 181

Minstrell, James, 23, 401, 475–513, 594–595

Minus Mouse, 290–291

Misconceptions

about momentum, 5

about the scientific method, 414

“Missing-term problem,” 317

Misunderstandings, 310

Model-based inquiry, 515–565

classroom environments that support learning with understanding, 555–560

developing Darwin’s model of natural selection in high school evolution, 540–554

genetics, 516–540

Modeling for Understanding in Science Education (MUSE), 516, 548

curricula from, 555, 559

Models, 402–403

consistency between, 557

of progression in ideas about evidence, 166–167

providing students with opportunities to revise in light of anomalous data and in response to critiques of others, 524

Monarch/viceroy case

Darwinian explanation written by students on the, 553

Monitoring.

See also Self-monitoring metacognitive, 10

“Monster-free zone,” 295

Moss, Joan, 23, 309–349, 595

Motion of projectiles

explaining, 511

Multiple strategies, 223–227

allowing, 223–227

engaging students’ problem-solving strategies, 225–227

three subtraction methods, 224

Multiplicative operators, 315

Multiplicative reasoning

relative thinking as, 311

MUSE. See Modeling for Understanding in Science Education

Mystery

sense of, 71

“Mystery Object Challenge,” 329

N

Narrative accounts

providing students with, 573–575

National Council of Teachers of Mathematics (NCTM), 221, 241, 259

standards from, 305

Suggested Citation:"Index." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×

National Curriculum for History, 177n

National Research Council, 1, 218, 221, 233

guidelines of, 398

National Science Education Standards, 455, 561

Native Americans, 41, 82–83, 98, 105–106

NCTM. See National Council of Teachers of Mathematics

Necessary conditions

causes as, 53

Neighborhood Number Line, 295

Networks

of concepts, and rational number, 341–342

of knowledge, building, 258

New conceptualizations

understanding numbers as multiplicative relations, 316

New ideas

development of, 470n

New rules

discovering, 588

New symbols

meanings, and representations, 313–314

“Nothing” happening, 43

Number Knowledge Test, 260, 264, 267–269, 271, 279, 304–305

administering and scoring, 271

Number worlds, 282–302

encouraging the use of metacognitive processes to facilitate knowledge construction, 300–302

engaging children’s emotions and capturing their imagination, 296–298

exposing children to major forms of number representation, 283–288

the five forms of representation and the lands in which they appear, 286

learning goals for prekindergarten through grade 2, 284–285

providing analogs of number representations that children can actively explore hands-on, 292–296

providing opportunities for children to acquire computational fluency as well as conceptual understanding, 298–300

providing opportunities to link the “world of quantity” with the “world of counting numbers” and the “world of formal symbols,” 288–292

Number Worlds program, 262, 283, 287–288, 292, 296, 300, 302–303

Numeric answers, 372

O

Object Land, 284–286, 288

“One world” revolution, 169

“Openings” in the curriculum, 245

Opportunities

to develop causal models to account for patterns, 524

to experience discrepant events that allow them to come to terms with the shortcomings in their everyday models, 571–573

to make ideas public, 524

providing students with, 523–524

to revise initial models in light of anomalous data and in response to critiques of others, 524

to search for patterns in data, 524

to use patterns in data and models to make predictions, 524

to use prior knowledge to pose problems and generate data, 523–524

Opportunities for children to acquire computational fluency as well as conceptual understanding, 298–300

Sky Land Blastoff activity, 298–299

Opportunities for students to suggest and test related hypotheses in elaboration activities, 484–489

inverted cylinder in a cylinder of water, 485–486

inverted glass of water, 484–485

leaky bottle, 486

water and air in a straw, 486–488

weighing” an object in a fluid medium, 488–489

Opportunities to link the “world of quantity” with the “world of counting numbers” and the “world of formal symbols,” 288–292

Minus Mouse, 290–291

Suggested Citation:"Index." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×

Plus Pup, 288–290

Plus Pup meets Minus Mouse, 291–292

Optics kit, 422, 468

Order

of counting words, 274

in decimal numbers, 333–334

Organized knowledge, 462

Organizing knowledge around core concepts

subtraction with regrouping, 18–19

Origin of Species, 551

Outcomes of courses, 181

P

Pace of change, 44

Paley, William, 550–551, 573

Palincsar, Annemarie Sullivan, 23, 421–474, 595

Park, Lesley, 455

Part-whole relation, 314

Pass it on (game), 105

Passive media, 496

Passmore, Cynthia M., 23, 515–565, 595

Past

finding out about, 56–58

pictures of, 166

Patterns in data

providing students with opportunities to search for, 524

providing students with opportunities to use to make predictions, 524

Payment for work in history, 66–67

Peanuts cartoon, 309

Pedagogical words

meaningful, 230

People going their separate ways

unit on, 170

Percents, 325–332, 340

computing with, 329

in everyday life, 325

“families” of, 331

invented procedures, 329

on number lines, 326–329

pipes and tubes, as representations for fullness, 325–326

starting from, 322–324

string challenges, 329–331

Percy, George, 122

Performance

need to assist, 203

Periods in history, 42–43

Physics

fundamental, 24

instruction in, 16–17

Picture Land, 285–287, 297

Pie charts and a part-whole interpretation of rational numbers, 320–321

Pilgrim Fathers and Native Americans, 71, 84–119

exploring the basis for textbook claims and the nature of sources, 84–111

grid for evidence on, 173, 175

ideas, beliefs, and attitudes, 112–118

language of sources, interpretation, and other perspectives, 118–119

teacher questions, 112–113, 115

whether people thought like us in the past, 117

Pipes

a new approach to rational-number learning, 322–324

a representation for fullness, 325–326

Planning, 164–176

of progression in ideas about evidence, 166–167, 174–175

unit on filling the world with people, 169

unit on first contacts, whether St. Brendan sailed from Ireland to America, 171

unit on first contacts, why the Norse colonists didn’t stay in America, 172

unit on people going their separate ways, 170

Plausibility, 138

Plus Pup, 288–290

meeting Minus Mouse, 291–292

Pocahontas (Disney film), 122

Pory, John, 84–85, 90, 97, 100–104, 106–108

Positive relationships

humor helping to build with students, 501

Possible Worlds, 406

Power

explanatory and predictive, 518

Preconceptions, 1, 55, 399–403

about people, society, and how the world works, 127–128

conceptual change, 400–403

Suggested Citation:"Index." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×

drawing on knowledge and experiences that students commonly bring to the classroom but are generally not activated with regard to the topic of study, 569–571

engaging resilient, 569–575

everyday concepts of scientific methods, argumentation, and reasoning, 400

everyday concepts of scientific phenomena, 399–400

importance of students’, 79

providing opportunities for students to experience discrepant events that allow them to come to terms with the shortcomings in their everyday models, 571–573

providing students with narrative accounts of the discovery of (targeted) knowledge or the development of (targeted) 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 familiar, 122

Predictive power, 518

Preinstruction assessments, 495

Prepare-to-investigate phase, 434–438

Prepare-to-report phase, 443–448

Principles of How People Learn applied to teaching high school history, 179–213

designing a “history-considerate” learning environment, 199–209

transforming topics and objectives into historical problems, 181–199

Prior understandings

development of physical concepts in infancy, 4

engaging, 4–5

of light, 425

misconceptions about momentum, 5

providing students with opportunities to use to pose problems and generate data, 523–524

and rational number, 341

Problem solvers

building, 258

“Problematizing” historical accounts, 184–188

Procedural fluency, 218

Productive disposition, 218

Proficiency

mathematical, 218

Progress, 44–45

Progression of ideas, 37–40

different ideas about historical accounts, 38–39

Progressive change, 45

Project CHATA. See Concepts of History and Teaching Approaches

Projectiles

explaining motion of, 511

Proportion, 234, 340

Pump Algebra Tutor. See Cognitive Tutor Algebra

Q

Quantity, 234

schema for, 272

Question Poser, 300–301

Questioning and explaining in high school science

supporting metacognition, 582–583

Questions, 128

diagnostic, 478

at the heart of using evidence, 124

many as yet unanswered, 492

teachers modeling for students, 477

Quotient interpretation, 314

R

Rational change, 45

Rational number, 341–343

metacognition, 342

network of concepts, 341–342

prior understandings, 341

Rational-number learning

and the knowledge network, 312–316

metacognition and rational number, 319

new concepts of numbers and new applications, 312–316

and the principles of How People Learn, 312–319

students’ errors and misconceptions based on previous learning, 316–319

Suggested Citation:"Index." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×

Real-world experience

current and future, 390

Real-world words, 230

Reality test, 80–84

“7-year gap,” 82

Reciprocal teaching, 11

Reconceptualizing the unit and operations, 315

Recorder, 435

Reflective assessments, 412

in ThinkerTools, 412–413

Regrouping

subtraction with, 18–19

Relative thinking as multiplicative, 311

Relativism, 176

Reliability, 126

Religious practices, 113–118

Reporter, 301

Reporting phase, 427, 448–455

Representations, 372

anchoring themes in historical, 186

Reproductive success, 542

Revolution, 61

S

Sagan, Carl, 194, 196–197

Sales, Kirkpatrick, 208

Schemas

2-slot and 3-slot, 370

counting and quantity, 272

Schools Council History Project, 40, 177n

Science, 395–565

developing understanding through model-based inquiry, 515–565

guided inquiry in the science classroom, 475–513

information from the history of, 499

leaving many questions as yet unanswered, 492

teaching to promote the development of scientific knowledge and reasoning about light at the elementary school level, 421–474

unit on the nature of gravity and its effects, 477–511

Science classrooms

guided inquiry in, 475–513

Scientific inquiry and How People Learn, 397–419

addressing preconceptions, 399–403

diagnosing preconceptions in physics, 404

the How People Learn framework, 411–415

knowledge of what it means to “do science,” 403–407

Scientific method

misconceptions about, 414

Scissors-and-paste approach and textbook claims and the nature of sources, 94

Searchers, The (film), 151

Second cycle of investigation

community knowledge from, 464

Second-hand investigation, 455–459

“Second-order” disciplinary concepts, 61, 73n

“Second-order” knowledge, 32–33, 41

acquisition of, 40–41

Secret knowledge, 72

Seeing for yourself and textbook claims and the nature of sources, 93

Seixas, Peter, 151

Selective advantage, 542

Self-assessment, 12

Self-monitoring

importance of, 10–12

metacognitive monitoring, 10

Sensitivity

“7-year gap,” 82

7-year-olds understandings of, 277–278

to students’ substantive assumptions, 127

Severin, Tim, 139, 142–143

Shemilt, Denis, 23, 56, 79–178, 595–596

Shrinking past, 160–161

Significance, 45

historical, 45

Simplicity, 389–390

6-year-olds understandings of, 274–277

Skating Party game, 292–295

Skills

defining, 40

Sky Land, 286–287

Blastoff activity, 298–299

Smith, John, 122

Sources

access to someone who saw for himself, 93

briefing sheet, 88–89

Suggested Citation:"Index." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×

distinguishing among kinds of claims, 101–102

generalizing, 102–107

getting behind the record to concerns of the people who produced them, 107–108

interpreting sources in context, 100

maintaining contact with an eyewitness using knowledge handed down through generations, 93–94

the nature of, 84–111

scissors-and-paste approach, 94

seeing for yourself, 93

teacher questions, 92, 95–96, 99–101

trusting the source who was in a position to know, 96

understanding the purpose of the source, 96–99

understanding what is likely to get recorded and under what circumstances, 108–111

working out the facts from other sources or available knowledge, 94–95

Splitting, 323

State of affairs

changes in, 44

Stearns, Peter, 210

Stewart, James, 23, 515–565, 596

“Stop-Start Challenge,” 333

Stopwatches

decimals and, 332–333

Stories

“embroidering,” 153

Strategic competence, 218

String challenges

guessing mystery objects, 329–331

Student assumptions about how we know of the past, 123

Student conceptions

experimentation, 402

inadequacies in arguments, 403

interpretation of data, 403

of knowledge generation and justification in science, 402–403

models, 402–403, 518

Student inquiry in genetics, 526–538

example of student work on a GCK homework assignment, 535

genetic inquiry in the classroom, 529–534

initial GCK population for the final GCK inquiry, 537

meiotic processes governing inheritance, 528

Mendel’s model of simple dominance, 528

Students’ errors and misconceptions based on previous learning, 316–319

Students’ existing knowledge, 517–526

assessing knowledge claims in genetics, 523

attending to, 544–545

black box, 520

building on and connecting, 258

learning genetics content, 524–526

providing students with learning opportunities, 523–524

student conceptions of models, 518

Students’ preconceptions

importance of, 79

Study of light, 422–426

conceptual understanding, 423–424

metacognition, 426

prior knowledge, 425

Study of light through inquiry, 426–459

heuristic for teaching and learning science through guided inquiry, 427–455

second-hand investigation, 455–459

Subconstructs

the many personalities of rational number, 314–315

Subject-specific knowledge in effective science instruction, 467–469

Substantiated accounts, 87

Substantive assumptions

sensitivity to students’, 127

Substantive concepts, 61–65

historical accounts not copies of the past, 62–63

payment for work, 66–67

Subtraction with regrouping, 18–19

Supporting learning through cycles of investigation, 460–467

Supporting skilled questioning and explaining in mathematics problem solving

supporting metacognition, 580–581

Supporting student and teacher learning through a classroom discourse community, 237

Suggested Citation:"Index." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×

T

Table of values to produce a function, 353–358

Teacher professional development in Japan, 244

Teacher questions, 112–113, 115

and textbook claims and the nature of sources, 92, 95–96, 99–101

Teachers’ conceptions and partial understandings, 279–281

acquiring an understanding of number as a lengthy, step-by-step process, 280–281

counting words as the crucial link between the world of quantity and the world of formal symbols, 280–281

math as not about numbers, but about quantity, 280

Teachers engaging students’ preconceptions, 219–231

common preconceptions about mathematics, 220–222

engaging students’ preconceptions and building on existing knowledge, 223–231

Teaching

reciprocal, 11

Teaching and learning functions in mathematics, 351–393

addressing the three principles, 359–373

building conceptual understanding, procedural fluency, and connected knowledge, 364–369

building on prior knowledge, 359–364

building resourceful, self-regulating problem solvers, 371–373

linking formal mathematical understanding to informal reasoning, 354–355

making a table of values to produce a function, 353–358

teaching functions for understanding, 373–389

teaching to achieve this kind of understanding, 358–359

Teaching as Story Telling, 574

Teaching functions for understanding, 373–389

Teaching mathematics in the primary grades, 257–308

acknowledging teachers’ conceptions and partial understandings, 279–281

building on children’s current understandings, 267–279

the case of number worlds, 282–302

comparing number worlds and control group outcomes, 304

deciding what knowledge to teach, 259–267

defining the knowledge that should be taught, 281–282

Teaching the rational number system, 309–349

additive and multiplicative reasoning, 311

how students learn rational number, 341–343

instruction in rational number, 319–340

rational-number learning and the principles of How People Learn, 312–319

Teaching to promote the development of scientific knowledge and reasoning about light at the elementary school level, 421–474

the role of subject-specific knowledge in effective science instruction, 467–469

the study of light, 422–426

the study of light through inquiry, 426–459

supporting learning through cycles of investigation, 460–467

Technical media, 496

Testimony, 41, 124, 135, 166

Testing

external, 181

Textbook claims

access to someone who saw for himself, 93

briefing sheet, 88–89

distinguishing among kinds of claims, 101–102

generalizing, 102–107

getting behind the record to concerns of the people who produced them, 107–108

interpreting sources in context, 100

Suggested Citation:"Index." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×

maintaining contact with an eyewitness using knowledge handed down through generations, 93–94

and the nature of sources, 84–111

scissors-and-paste approach, 94

seeing for yourself, 93

teacher questions, 92, 95–96, 99–101

trusting the source who was in a position to know, 96

understanding the purpose of the source, 96–99

understanding what is likely to get recorded and under what circumstances, 108–111

working out the facts from other sources or available knowledge, 94–95

Themes, 44

anchoring in historical representation and interpretation, 186

ThinkerTools, 407, 585

Third cycle of investigation

community knowledge from, 465

Third International Mathematics and Science Study, 243

3-slot schema

for graphing a line, 370–371

Three subtraction methods, 224

Time, 41–43

change limited in, 45

periods in history, 43

Time lines, 129, 159

Timekeeper, 435

Torsion bar, 493–501

Transforming topics and objectives into historical problems, 181–199

accounting for the “flat earth,” 189–199

“problematizing” historical accounts, 184–188

Transmission errors, 123

Trusting the source who was in a position to know

and textbook claims and the nature of sources, 96

Truth

twisting, 105, 123

Tubes

a new approach to rational-number learning, 322–324

a representation for fullness, 325–326

Turner, Frederick Jackson, 58

Twisting the truth, 105, 123

2-slot schemas, 370

U

“Underlying” causes, 35

Understanding

essential role of factual knowledge and conceptual frameworks in, 6–9

experts remembering considerably more relevant detail than novices in tasks within their domain, 8–9

learning with understanding supporting knowledge use in new situations, 7

Understanding of number

a lengthy, step-by-step process, 280–281

Understanding the purpose of the source and textbook claims and the nature of sources, 96–99

Understanding what is likely to get recorded and under what circumstances

and textbook claims and the nature of sources, 108–111

Unit-level problem, 189–199

accounts of Colombian voyages, 192–193

ancient views of the Earth as flat or round, 196–197

Unit on the nature of gravity and its effects, 477–511

United Kingdom

adjusting data from, 177n

Schools Council History Project, 40, 177n

Units

on filling the world with people, 169

on first contacts, whether St. Brendan sailed from Ireland to America, 171

on first contacts, why the Norse colonists didn’t stay in America, 172

on people going their separate ways, 170

Suggested Citation:"Index." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×

V

Verbal interpretations, 372

Visual proportional estimation starting from, and halving and doubling, 323–324

W

War (card game), 336

Warm-Up period, 298, 300

Water and air in a straw, 486–488

Website, 562n

“Weighing” an object in a fluid medium, 488–489

Weighing-in-a-vacuum situation, 484, 489

Whole number

central conceptual structure for, 261–262, 275

Wilson, Suzanne M., 596

Wineburg, Samuel S., 100

Wisdom, 236, 238

Woodbury, Jasper, 391

Word Problems test, 264–265

Words

versus notations, 230

Words in stories

explaining, 132–133

Work

payment for in history, 66–67

Working out the facts from other sources or available knowledge

and textbook claims and the nature of sources, 94–95

Working things out for ourselves, 133–138

being aware of how we are thinking, 135

going beyond face value, 134

how far a leather boat could have managed to sail, 139–141

Working through the task, 128–164

Working with evidence

Pilgrim Fathers and Native Americans, 84–119

preparing for the task, 121–128

the St. Brendan’s voyage task, 128–164

World’s Fair of 1892, 208

Wrap-Up period, 301

Written Arithmetic test, 264–265

Y

Year-long historical questions, 184–188

Suggested Citation:"Index." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×

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How do you get a fourth-grader excited about history? How do you even begin to persuade high school students that mathematical functions are relevant to their everyday lives? In this volume, practical questions that confront every classroom teacher are addressed using the latest exciting research on cognition, teaching, and learning.

How Students Learn: History, Mathematics, and Science in the Classroom builds on the discoveries detailed in the bestselling How People Learn. Now, these findings are presented in a way that teachers can use immediately, to revitalize their work in the classroom for even greater effectiveness.

Organized for utility, the book explores how the principles of learning can be applied in teaching history, science, and math topics at three levels: elementary, middle, and high school. Leading educators explain in detail how they developed successful curricula and teaching approaches, presenting strategies that serve as models for curriculum development and classroom instruction. Their recounting of personal teaching experiences lends strength and warmth to this volume.

The book explores the importance of balancing students’ knowledge of historical fact against their understanding of concepts, such as change and cause, and their skills in assessing historical accounts. It discusses how to build straightforward science experiments into true understanding of scientific principles. And it shows how to overcome the difficulties in teaching math to generate real insight and reasoning in math students. It also features illustrated suggestions for classroom activities.

How Students Learn offers a highly useful blend of principle and practice. It will be important not only to teachers, administrators, curriculum designers, and teacher educators, but also to parents and the larger community concerned about children’s education.

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