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OCR for page 229
597
Index
This index includes the text of the full vet sion of How SfudenfsLeatn: Hisfoty,
Mathematics, and Science, which can be found on the C19 attached to the
back cover
A
Absolute difference, 311
Absolute thinkmg
as additive, 311
Access to someone who saw for himself
and te2cchook c aims and the nature
of sources, 93
Accounts, 59 61
of Colombian voyages, 192-193
diffe ant ideas about h storical, 38 39
h stoncal, 59 61
substantiated, 87
Actions at a distance
explonog similarities and differences
between, 492 493
Activity Al worksheet, 483
Adams, John, 185
Adaptive teasonmg, 218
Addi,.g It Up, 218, 233, 241
Additive reason fig, 311, 321
absolute thinking as, 311
Add essmg preconceptions, 399 403
Advantage
selective, 542
Adventu e
sense of, 71
A ten sine inst uctiona approaches, 321-
322
An encdll Association for the Advancement
of Science
guide nes of, 398
textbook eview by, 16
Analogs of number rep esentations that
ch d en c m actively explo e
hands on, 292-296
Rosen a y's Magic Shoes game, 295-
296
Skating Pa ty game, 292-295
Analogy to al de stamd the benchmark
experience, 489 490
Ancient views of the Ea th as flat or roumd,
196 197
the Atlas Fa nese, 196
the sto y of E accost lot es and the
Ea th's ci cumference, 196 197
Anglo-Saxons, 117
Anselm, st, 46
A guments
inadequacies in, 403
Ashby, Rosa yn, 79 178, 591
Assessment centered, 415
Assessment centered c assroom
envi onments, 13, 16 17, 267, 290,
292, 555-558
examples of students' critiques of
thei own Darwinian explamations,
558
OCR for page 230
595 INDEX
sample exam question, and
consistency between models, 557
Assessment systems
DIAGNOSER, 513
Assessments See also Self-assessment
formative, 16 17, 193
preinst at loll, 495
"reflective," 412
Assumptions
substantive, 127
At as Fan use, 194, 196
Authonty, 135
Award cards, 293
Awareness of how you a e thinking, 135
B
Bain, Robe t B. 23, 179 213, 591
Balzac, Hol ore de, 236
Balrv,, Tr, 578
Ba ton, Keith, 45, 160
Beakers
a new approach to rations -number
learn ng, 322-324
Bede, st, 58
Bell jar expenment, 4 4, 489
Benchmark lessons, 493-501, 512n
weighing in a vacuum, 480 483
Black box approaches, 519 520
"Bbstoffl", 298
Boorstin, Daniel, 198
Bradford, Wi am, 84 88, 96, 108 111
Bramsfo d, John D, 1-28, 217-256, 397-
419, 569 592
Brendan, st, 71, 82 83, 128 164, 171
he ieving historica fi ms when people
in t em hchave as we won d, 151
the deficit past, 154 155
exp anation of words in the sto y,
132-133
fmding out what kind of sto y it is,
150 164
gad for evidence on, 173-174
the question, 128
the sh inking past, 160 161
the sto y, 128 133
thin ding from inside the sto y, 144
150
thin dn8 from outside the sto y, 138-
144
voyage of, 130 132
workmg d rigs out for on selves,
133-138
Budging
from al de standing magmetic action
at a distance to al de standing
g avxational action at a dixamce,
508 510
"Bridg rig context," 324, 359
Bnefmg sheets, 87, 91
and textbook c aims and dhe natu e
of son ces, 88 89
Bui ding conceptual unde stamding,
procedunal fluency, and
connected knowledge, 364 369
3-slot schema for grapEmg a line,
370 371
developmental model for lea n ng
functions, 365-366
level 0, 364, 367
level 1, 367-368
level 2, 368
level 3, 369
Building on chi d en's cur ent
umderstmdings, 267-279, 359 364
admmiste ing and sco ing dhe
Number Knowledge Test, 271
mental coumcmg ne st uctu e, 276
Number Knowledge Test, 268 269
unde standings of 4-year olds, 270
273
unde standings of 5-year olds, 273-
274
unde standings of 6-year olds, 274
277
unde standings of 7-year olds, 277-
278
unde standings of 8-year olds, 278
279
Bui ding esou cefu, self- egu atmg
problem solve s, 371-373
an mtegnated umderstand ng of
functions, 372
C
Cambridge Histo y Project, 177n
Canada
teaching histo y in, 151
"Camd es" (umt), 456
Ca d games, 335-337
OCR for page 231
INDEX 599
Carey, Susan, 592
Ca tier, Jennifer L, 23, 515-565, 592
Ca toons, 143, 145 146, 148, 546 549
Peamuts, 309
sequencing activity, 546 547
Case, Robbie, 23
Causa mode s to accoumt for patterns
providing students with oppo unities
to develop, 524
Causes, 49 54
explo ing the logic of the situation,
50-51
modeling, 562n
as necessary conditions, 53
"underlying,' 35
Cent al conceptua st uctu e hypothesis
bidimensiona, for number, 279
dependence of futu e learn rig on the
acquisition of this st uctu e, 264
265
impo lance of st uctu e to success u
performance on a ange of tasks,
262-263
for whole number, 261-262, 275
Change, 43 46, 61
di Action of, 44
la ge-sca e patterns of, 68
pace of, 44
as prog essive, rational, and limited in
time, 45
Cheese and the Worms, 185
Children
engaging their emotions and
captu ng thei imagination,
embedding knowledge
const acted m thei hopes, fea s,
and passions, 296 298
exposing to major fomms of number
rep esentation, 283-288
as "natu al" scientists, 421
Ch d en passing the Number Knowledge
Test
and measu es of ant m Eric learning
and ac ievement, 265
and numerical t amsfer tests, 263
Ch d en's Math World project, 219, 223,
227, 229, 231, 236, 241
Ch d en's thinking af er inst action, 338
340
China
teachmg of mathematics m, 15-16,
18-19
Christian geog aphy, 200
Ci cle Land, 286 287
Claims
backing up, 58
Classroom environments
genetic inquiry m, 529-534
principles of learning and, 586 588
Classroom environments that suppo t
learning with unde standing, 555-
560
assessment cente ed classroom
environments, 13, 16 17, 267, 290,
292, 555-558
community-cente ed classroom
environments, 13, 17-20, 301,
559-560
knowledge cente ed classroom
envi onments, 13-16, 267, 284,
292, 555, 587
learner cente ed c ass oom
envi onments, 13-14, 266, 292,
555
Clumping infommation, 69
Codes
c acking, 335
Cogmttive Tutor A gebra, 355, 391
Colombian Evposhtion, 208
Columbus' voyages, 189 193, 195, 199,
204 205, 207-20R, 587
Common p econceptions about
mathematics, 220 222
as "foDowmg ules" to gua antee
cor ect answers, 220 221
as leaming to compute, 220
on y some people have the ability to
"do math," 221-222
Community centered classroom
environments, 13, 17-20, 301, 415,
559-560
learn ng with understandmg, 559-560
o gamizmg knowledge around co e
concepts, 18 19
Comparing number worlds and control
g oup outcomes, 304
Competence developed by students, I
Comp ehensive Test of Basic Ski Is, 412
Computing wtth percent, 329
Concepts
substantive, 61 65
Concepts of History and Teaching
Approaches (Project CHATA), 38
39, 51-53, 56, 62, 82
OCR for page 232
600 INDEX
Conceptua chamge, 400 403
student conceptions of knowledge
gene ation and justification in
science, 402 403
Conceptua explanations
without conceptual umderxamding,
578
Conceptua st uctu e
bidimensiona cent al, for number,
279
cent a, for whole number, 261-262,
275
Conceptua unde standmg, 218
of light, 423 424
Conceptua ization
chid en's problems with, 137
Connected knowledge, 15-16
Conquest of Paradise, 208
Consistency
internal and external, 518
between models, 557
Constitution, 61
Context
evidence in, 167
Continuity, 44
"Controlled experiments," 402
Core concepts, 589
organizing knowledge around, 18-19
orgamzing procedu al knowledge amd
ski Is a ow d, 19
Come, Michael Felice, 90
Cowmre intuitive" intuitions
in history, 33, 42
Counting schema, 272
Counting wo ds
as the c octal link between the world
of quantity and the world of
fo ma symbols, 280 281
order of, 274
Con se outcomes, 181
Cu nculum
mandates in, 181
from Modelmg for Us de standing in
Science Education, 555, 559
"openings" m, 245
Cu nculum for moving students th Hugh
the model, 373-375
example lessons, 375-389
learning slope, 378 381
learning y-intercept, 381-384
operating on y = x', 384 389
sample computer screen, 386
suggested cu ncubr sequence, 376 377
two different student solutions to an
open ended problem, 385
Cut-and-paste, 167
Cycles of investigation
development of commumxy
knowledge across cyc es of
investigation, 460
development of conceptua
frameworks for light, 462 467
in guided-mquiry science, 427
suppo tmg learn rig through, 460 467
D
Dances ruith Woltes(fim), 151
Danvin, Charles, 542-545, 550-551, 556,
573
Danvin's model of Nate al selection in high
school evolution, 540 554
attending to significant disciplinary
knowledge, 543-544
attending to student knowledge, 544
545
ca toon sequencing activity, 546 547
explanation written by students on
the monarch/viceroy case, 553
ion action, 545-554
laying the groundwork, 545-549
us de standing, 550 552
Data
trite pretation of, 403
Data tables from initial reco ding and with
evisions for analysis, 445
Debugging
em p has iz fig, 2 39- 240
Decimals, 332-334
magnitude and order in decimal
numbers, 333-334
and stopwatches, 332-333
Decisions
as to what knowledge to teach, 259-
267, 281-282
Deficit past, 154 155
Dependence, 234, 352
Desigm of lost action
bndg rig lost uctional activities, 231
learn rig envi onments and, 12-20
Development
of con fllWnf y knowledge across
cyc es of investigation, 460
OCR for page 233
INDEX 601
of Danvin's model of natural
selection in high school evolution,
540 554
of physica concepts m infancy, 4
of us de standing th Hugh model-
based inquiry, 515-565
Development of conceptual hameworks
for light, 462 467
community knowledge from the fi st
cycle of investigation (fi stalk d),
463
community knowledge from the
fou th cyc e of investigation (fi x-
hamd), 467
community knowledge from the
second cycle of investigation
(fi st-1 and i, 464
community knowledge from the thi d
cycle of investigation (second-
hand), 465
Development of mathematical proficiency,
232-236
inaccessible algonthms, 236
lost action to suppo t mathematics
proficiency, 233-236
a learning path from children's math
worlds for single digit addition
and subtraction, 234-235
Developmental model
fo Iffimmg fimctions, 365-366
DIAGNOSER assessment system, 513
Diagmosing preconceptions in physics, 404
Diagmostic assessment, 491 492
Diagmostic questions, 478
Dialogue
intema and external, as suppo t for
metacogmrion, 241
Di action of c ange, 44
Disciplinary knowledge, 32
attending to sign ficant, 543-544
"second order," 61
Disconfirmation, 415
Discrepant events
providing students with oppo tumries
to expenence, 571-573
Discussion
guided, 579, 582
DiSessa, And ea. 5
Dist nguishmg among kinds of textbook
claims
and the natu e of son ces, 101-102
DNA, 517, 526
iDomg." 32, 48
"Doing math"
on y some people havmg the abi ity
for, 221-222
Donovan, M Suzamme, 1-28, 397-419,
569 590, 592
Double-b nd procedu e, 302
D agon Ouest game, 297-298
E
Ea th as flat or roumd, ancient views of,
196 197
Ea th's ci cumfe once
the Tory of Eratosthenes and, 196 197
Effects of g avity, 510 511
explainmg falling bodies, 510-511
explainmg motion of projectiles, 511
Egan, Kie an, 592
8-yea olds umderstmdings of, 278-
279
Elementary Science Study
OPTICS unit, 422, 4 8
"Embroidermg" stones, 153
Empathy, 46 49, 65, 112
Encouraging math ta k, 228 231
Encou ag ng the use of metacogmitive
processes to facilitate knowledge
const uction, 300 302
Engage phase, 426 434
Engagement of studentst p econceptions
amd bui ding on existing
knowledge, 4 5, 223-231
allow ng multiple x ategies, 223-227
desigmmg bndg ng inst uctiona
activities, 231
encou aging math ta k, 228 231
Engagement of studentst problffm-solvmg
st ategies, 225 227
Equipment Manag=, 435
E atosthenes, 194, 196 197
Eu opean geog aphic knowledge
the g eat inter uption in, 200 201
Everyd y concepts
hi xory and, 33 61
of scientific methods, a gumentation,
and reasonmg, 4 0
of scientific phenomena, 399 400
OCR for page 234
602 INDEX
Evidence, 41, 54 58, 61, 65, 112, 120, 165
in context, 167
cutting -and -pasting, 1 67
find ng out about the past from
received information, 56 58
histoncal, 134
information as, 166
in isolation, 167
model of prog e551011 in ideas about,
166 167
pick es of the past, 166
questions at the hea t of using, 124
test mony as, 166
L'xpenmt n Is on Plant Hyhtidizahon, 5 29
Expe ts emenlbe ing considerably mo e
relevant detail than novices m
tasks within their domain, 8 9
Explanations, 156
of words in the sto y, 132-133
Explamato y power, 518
Externa consistency, 518
Externa mid ation, 68
Externa testing, 181
Face va Be
going beyol d, 134
Factual knowledge
llUlllpU ating, 79 80
Falling bodies
exphi ng, 510 511
Fami in ity, 389 390
the d ngers of what appea s to be
fami ar, 122
Feymnan, Richa d, 24, 403
Filing the world with people
emit on, 169
FL st contacts
whether st Brend n sailed from
Ireland to Amenca, emit on, 171
why the No se colonists didn't stay in
Amenca, emit on, 172
FL st cycle of investigation
community knowledge from, 463
Fish sto y (Fish is Fish), 2 - 12, 398, 414, 575
5-year olds al de standings of, 273-
274
engaging prior understandings in, 4 5
essential role of actual knowledge
amd conceptual hameworks m
umderstmding, 6 9
impo tance of self-monitoring in, 10
12
"Flat ea th," 189-199
accounts of Colombian voyages, 192-
193
ancient views of the Ea th as h t or
roumd, 196 197
Formative assessments, 16-17, 193
Forms of representation
4-yea olds unde stamdings of, 270
273
and the lamds in which they appear,
286
Fou th cycle of investigation
commumty knowledge from, 467
Fou th g aders' initial ideas about light, 431
F actions and mixed rep esentations of
ationa numbers, 334 337
ca d games, 335-337
c acking the code, 335
fractions and equivalencies, 334 335
F amework of How P ople Learn
seeking a ba anced c ass oom
envi onment, 242-243
F ank, Amme, 109
Fumd mental physics, 24
Fumd menta sm. 176
Fuson, Ka en C, 23, 217-256, 593
Future eal-world experience, 390
G
Galapagos to toises, 558
GCK 5~e Genetics Construction Kit
General ideas, 162
General mean ng of slope, 363
Genera izing and textbook c aims and the
natu e of sou ces, 102 107
Genetics, 516 540
attending to students'existing
knowledge, 517-526
metacognition and engaging students
m reflective scientific practice,
538 540
simple dominance homework
assigmment, 539
student inquiry in, 526 538
OCR for page 235
INDEX 603
Genetics Con t action Kit (GCK), 534 537
homework assiEmment, example of
student work on, 535
Genetics content
teaming, 524 526
Geognaphic knowledge
Cll IttlAIl, 200
the g eat intenuption in European,
200 201
Gibbon, Edwa d, 57
GlsML Commumxy of Practice, 470n
"GIoba ization," 169
Gou d, Stephen Jay, 198
Gragg, Charles, 236
Gravity and as effects, 477-511
activity Al worksheet, 483
analogy to magnetism, 508
bridging from unde standing
magnetic action at a distance to
m de standing g avitational action
at a distance, 508 510
hut ding am analogy to umderxamd
the benchmark experience, 489-
490
consensus discussion and summa y of
learn fig, 490 491
defining, 477-510
diaEmostic assessment, 491 492
explonog similarities and di ferences
between actions at a distance,
492 493
facto s on which the maEmitude of
g avitationa force depends, 501-
508
fmding out about students' initial
ideas 477 478
identi ymg preconceptions, 478 480
oppo tumries for students to suggest
and test elated hypotheses, 484
489
twisting a to sion bar, 493-501
weighing in a vacuum, 180 483
Grids, 173-175
Griffin, Sharon, 23, 257-308, 593
Group work, 582-584
Guess My Number, 300
Guidance of student obse vation and
a ticu ation
suppo ring metacogmrion, 584 585
Guided inqui y, 495, 579, 582
H
-Hf:am~, 187-188
Hall, G. Stan ey, 177n
Halsall, William Formsby, 87
Help
seeking and giving, 241-242
Heuristic for teaching and learning science
th ough guided inqui y, 427 455
cyc e of love Ligation m guided-
mqui y science, 427
data tables from Nodal recording and
with evasions for ama ysis, 445
engage phase, 428 434
fou th gnade s' initial ideas about
light, 431
investigate phase, 438 443
investigative setup fo studymg how
ight mteracts with solid objects,
437
prepa e-to-investigate phase, 434 438
prepa e-to-repo t phase, 443 448
repo t phase, 448 455
`~H(ev)", 187
Higher o der knowledge st UCtu e, 276
Hixorica accoumrs, 59 61
di ferent ideas about, 38 39
not copies of the past, 62 63
"problematizing," 184 188
Hixorical evidence, 134
Hixorical fi ms, 151
Hixorical lines of thinking, 182
Hixorical problems
t ansforming topics and oh ectives
mto, 181-199
Hixo y 29-213
applymg the principles of How P ople
Learn in teaching high school
histo y, 179-213
"counte intuitive" mtuitions in, 33, 42
"domg," 32, 48
implications for plannmg, 164-176
periods m, 42 43
putting panciples into practice, 79-
178
the rea ity test, 80 84
sign ficance in, 45
that "works," 65-72
unde standing, 31-77
workmg with evidence, 84 119
OCR for page 236
604 INDEX
I
Histo y amd eve yday ideas, 33 61
diffe ences in the power of ideas, 36
37
groumds for caution, 40 41
ideas we need to add ess, 41 61
the prog ession of ideas, 37 40
understandmg the past and
us de standing the disciplme of
histo y, 34 35
"Histo y-as-account," 187-188, 203
"Histo y-as event," 187, 203
"Histo y considerate" learn rig
environments
design fig, 199 209
dhe g eat intenuption in En opean
geographic knowledge, 200 201
with tools for historical thinking, 199-
209
History of the DeeRne and Fall of the
Roman Empire, The, 57
Hider, Ado f, 34 35, 59 60, 586
Holt, John, 218
How Pe'2PIe Learn: Brain, Mind, Experi wee,
and School, 1, 25, 31-32
cautions in, 199
design cl araaenst~a described in,
12-13, 20 22, 257-258, 359
key findmgs of, 79 80, 171-173, 176
resea ch summarized in, 241
violating principles of, 319
How P opie L arn framework, 411 415
assessment centered, 415
community centered, 415
knowledge centered, 414
learner cente ed, 414
reflective assessment in ThinkerTools
412 413
Humor
en ivening lea n rig and helping bui d
positive elationships widh
students, 501
Ideas, 41 61
accoumrs, 59 61
cause, 49 54
chamge, 43 46
empadhy, 46 49
evidence, 54 58
prog ession of, 37 40
providmg students with oppo tunities
to make public, 524
"second o der," 32-33
time, 41 43
Inaccessible algondhms, 236
Information, 41, 124, 166
"c umping," 69
findmg, 121
from histo y, 499
from the histo y of science, 499
inqui y based, 470n
sto ing in memo y, 180
Inheritance
meiotic processes goveming, 528
Initial models
providmg students with oppo tunities
to revise in light of anomalous
data amd in tesPonse to c itiques
of others, 524
Inqui y based information, 470n
Inst uction, 545-554
to suppo t mathematical proficiency,
233-236
Instruction in ational number, 319-340
alternative inst uctiona approaches,
321-322
ch d en's dhinking af er inst uction,
338 340
cu nculum ove view, 325
fractions and mixed rep esentations
of national numbers, 334 337
introduction of decima s, 332-334
introduction to pe cents, 325-332
knowledge network, 340
pie cha ts and a pa t-whole
mterp etation of rationa numbe s,
320 321
pipes, tubes, amd beake s, 322-324
Inst uction dhat suppo ts metacogmrion,
239 242
emphasizmg debugging, 239 240
internal and external dialogue as
suppo t for metacognition, 241
seeking and giving help, 241-242
Inst uctional nes of dhmking, 182
Intellectua roles for students to adopt, 436
Internal consistency, 518
Internal mignation, 68
Interp etation
ancho ing dhemes in historica, 186
of data, 403
OCR for page 237
INDEX 605
Interpreting son ces m context and
textbook c aims amd the natu e of
son ces, 100
Lntuitions m histo y
~counterintuitive," 33, 42
Lnvented procedu es, 329
Lnvestigate phase, 438 443
Investigative setup for studying how light
interacts with solid objects, 437
I ving, Wash 112011, 208
Isolation
evidence in, 167
Italy
inst action about payment for work,
66 67
J
Japan
teacher professions development in,
244
Jasper Woodbu y senes, 391
Jeffe son, Thomas, 62 63
Johnson, Lyndon, 62
Jonassen, David, 181
Judgments
avoiding exp easing, 498
K
Kalchman, Mindy, 23, 217-256, 351-393,
593
Knowledge See also Pnor umderstandmgs
bui ding lea n rig paths amd networks
of, 258
connected, 15-16
discipline y, 32, 543-544
handed down th ough gene ations,
93-94
mampu atmg factual, 79 80
Swatch sto ical," 32
organized, 462
"second order," 32-33
see et, 72
student, 258, 544 545
of what it means to "do science,"
403 407
Knowledge centered crass ooll1
envi omments, 13-16, 267, 284,
292, 414, 555, 587
Knowledge c aims
in genetics, assessing, 523
Knowledge networks, 340
new concepts of numbe s and new
applications, 312-316
new symbols, meanings, and
presentations, 313-314
reconceptualizmg the unit and
operations, 315
the subconst acts, 314 315
w de standing nulllbe s as
multiplicative elations, 316
"Knowledge packages," 588n
Knowledge that shou d he taught, 259 267
cent al conceptual st uctu e
hypothesis, 262-265
ch d en passing the Number
Knowledge Test, 263, 265
measu es of a it metic learning amd
achievement, 265
llW1 encal t ansfer tests, 263
Koedinger, Kemmeth R. 351-393, 593-594
K aus, Pamela, 23, 401, 475-513, 594
KWL cha ts, 199, 428 430
L
Lama ck, Jean Baptists de, 550, 573
La son, Ga y, 217
Learner cente ed class oom envi onments,
13-14, 266, 292, 414, 555
Learn ng
an active p ocess, 476
humor en ivening, 501
Learning envi onments and the desi~,m of
mstruction, 12-20
assessment cente ed classroom
environments, 13, 16 17, 267, 290,
292, 555-558
community-cente ed classroom
environments, 13, 17-20, 301,
559-560
knowledge cente ed c ass oom
envi onments, 13-16, 267, 284,
292, 555, 587
learner cente ed c ass oom
envi onments, 13-14, 266, 292,
414, 555
perspectives on, 13
Learn ng goa s for prekinde ga ten th ough
g ade 2, 284 285
OCR for page 238
606 INDEX
Lea ning paths of knowledge
building, 258
from child en's math worlds, for
single digit addition and
subtraction, 234 235
Learning principles
engaging rest lent preconceptions,
569-575
organizing knowledge a ound core
concepts, 575-577
pnncip es of learning and class oom
environments, 586 588
pu ling th Cads, 569 590
revisiting the th Be, 567-590
suppo ring metacognition, 577-586
Learr[u g nations number, 341-343
metacoEmition, 342
network of concepts, 341-342
prior al de s[andulgs, 341
Lea llUlg with umderstamding, 559 560
suppo ring knowledge use in new
situations, 7
Leather boats, 139 141
Lee, PeterJ, 23, 31-178, 576, 594
Lesson Study Resea ch Group, 244
Lif e and Voyages of Christopher Colu mbus,
The, 208
"Light catchers," 437 See also Study of ight
Linkage
of forma mathematical w de sta 1dwg
to informs reason ng, 354 355
Liommi, Lee, 2, 4 See also Fish sto y
Logic of the situation
explo ing, 50 51
Lowenthal, David, 185
M
Ma, Lipmg, 15-16, 18 19, 577-578
Magic Shoes game, 295-296
MaEmetism
analogy to g avity, 508
Magmtude
in decimal numbers, 333-334
of gnavitationa force, 501-508
MaEmusson, ShirleyJ, 421 474, 594
M magement of student activities, 435
M mdates
cunicuar, 181
Mamipu ation of factua knowledge, 79 80
Maps, 86, 140 141
conceptual, 188
Marfan's synd on e, 533
Math words, 230
Mathematical proficiency, 218
adaptive reasonmg, 218
conceptual understandmg, 218
procedu al fluency, 218
productive disposition, 218
strategic competence, 218
Mathematica thi kers
buiding, 258
Mathematica undenstanding, 217-256
computation without comprehension,
218
developing mathematical proficiency,
232-236
learn ng to use student thinking in
teacher video c ubs, 244
lesson study cyc e, 244
a metacogmtive approach ff ab mg
studffnt se f-mowtommg, 236 243
suggested eadmg list fo tffchffs,
256
teachers as cuniculum desiEmffs, 245
teachers engagmg studffnts'
p econceptions, 219 231
undenstanding equi mg factua
knowledge and conceptua
hameworks, 231-236
Mathematics, 215-393
as ahout quanthty, not about numbens,
280
as "fohowing ules" to guanantee
cor ect answers, 220 221
fostenog the development of whole
number sense, 257-308
as leaming to compute, 220
pipes, tubes, amd beakens in, 309 349
teach ng and learn ng fimctions, 351-
393
Mathematics mst uction
in China, 15-16, 18 19
Mayflower, The
arnval of, 84, 87, 90, 92-95
Medawa, Peter, 406
Media
tec nica and passive, 496
Meiotic processes
goveming mberitance, 528
OCR for page 239
INDEX 607
Mendel, Gregor, 406, 410, 517, 523, 525-
529, 539
model of simple dominance, 528
Menta coming Ime St uctu e, 276
Metacogmrion, 10, 238, 407 411, 577-586
conceptual explanation without
conceptual umderstandmg, 578
engaging students in reflective
scientihc practice, 538-540
m eva Hating the methods used in an
experiment, 408 409
guidmg student obse vation and
a ticuation, 584 585
of light, 426
in Mendel's cont ibution to genetics,
410
questioning and explainmg in high
school science, 582-583
and nations number, 319, 342
suppo ting, 577-586
suppo ting ski led questioning amd
explainmg in mathematics
problem solving, 580 581
Metacognitive approaches to lost action, 2,
80
enab ng student self-monitoring,
236 243
fnamework of HOES Ptop)e Learn, 242-
243
inst action t at suppo ts
metacogmtion, 239 242
seekmg a balamced c assroom
environment, 242-243
suppo ting student and teacher
learning through a classmom
discos se community, 237
Metacognitive monitormg, 10
Metahisto ica " knowledge, 32
~Metamemo y," 11
Mig ation
intema and external, 68
Mider Analogies Test, 404
"Mindrools," 181
Mmst all, James, 23, 401, 475-513, 594 595
Mmus Mouse, 290 291
Misconceptions
about momentum, 5
ahout the scienti ic method, 414
"M ssing term problem," 317
Misunde stamdmgs, 310
Model-based mqui y, 515-565
cbssroom envi onments t at suppo t
lea n ng wxh unde standing, 555-
560
developing Da win's model of natu al
selection in high school evolution,
540 554
genetics, 516 540
Modeling for Understanding in Science
Education (MUSE), 516, 548
cu ncu a from, 555, 559
Models, 402 403
consistency between, 557
of progression in ideas about
evidence, 166 167
providmg students with oppo tunities
to revise in light of anomalous
data and in esponse to critiques
of others, 524
Mona ch/viceroy case
Da winian explanation w xten by
students on the, 553
Monitoring See also Self-monitormg
metacognitive, 10
"Monster-f ee zone," 295
Moss, Joan, 23, 309-349, 595
Motion of projectiles
explainmg, 511
Multiple st ategies, 223-227
allow ng, 223-227
engagmg xudentst problem-solving
st ategies, 225-227
th ee subt action methods, 224
Multiplicative operators, 315
Multiplicative reason ng
relative thmking as, 311
MUSE SeeModeling for Understanding in
Science Education
Myste y
sense of, 71
"Myste y Ohject Challenge," 329
N
Nanative accounts
providmg students with, 573-575
National Council of Teache s of
Mathematics (NCTM), 221, 241,
259
standa ds f om, 305
OCR for page 240
608 INDEX
National Can ice urn for Hitxoy, 177n
National Resea ch Coumci, 1, 218, 221, 233
guidelines of, 398
National Sconce Education Standands,
455, 561
Native Americans, 41, 82 83, 98, 105-106
NCTM Sac National Council of Teachers of
Mathematics
Necessary conditions
causes as, 53
Neighbo hood Number Lme, 295
Networks
of concepts, amd national number,
341-342
of knowledge, bui ding, 258
New conceptualizations
umderstandmg numbers as
mu tip icative relations, 316
New ideas
development of, 470n
New ules
discovermg, 588
New symbols
meanings, and epresentations, 313-
314
"Noth fig" happening, 43
Number Knowledge Test, 260, 264, 267-
269, 271, 279, 304 305
admmiste ing and scoring, 271
Number wo Ids, 282 302
ffncounagmg the use of metacoEmitive
processes to faci irate knowledge
const action, 300 302
engaging child en's emotions and
capturing their imagination, 296
298
exposing children to water forms of
number epresentation, 283-288
the five forms of rep esentation amd
the lands m which they appea,
286
learning goals for prekinde ga ten
th ough g ade 2, 284 285
providing analogs of number
rep esentations that children can
actively explore hands on, 292-
296
providing oppo unities for chi d en
to acqui e computations fluency
as well as conceptua
al de standing, 298 300
providmg opporhmities to link the
"world of quantity" with the
"world of coming numbers" and
the "world of formal symho s,"
288 292
Number Worlds program, 262, 283, 287-
288, 292, 296, 300, 302-303
Numenc al sue s, 372
o
Oh ect land, 284 286, 288
"One world" evolution, 169
"Openmgs" m the cuniculum, 245
Oppo tumities
to develop causal models to account
for pattems, 524
to experience discrepant events that
a low them to come to terms with
the sho tcomings in thei everyday
models, 571-573
to make ideas public, 524
providmg students with, 523 524
to revise initia mode s m ight of
amomalous data amd m esponse
to critiques of others, 524
to sea ch for patterns in data, 524
to use patterns in data amd models to
make p edictions, 524
to use prior knowledge to pose
problems and genenate data, 523-
524
Oppo tummies for chi d en to acqui e
computations fluency as well as
conceptual understanding, 298 300
Sky land Blastoff activity, 298 299
Oppo unities for students to suggest and
test related hypotheses in
elaboration activities, 484 489
love ted cylinder in a cylinder of
water, 485 486
love ted glass of water, 484 485
leaky bottle, 4 6
water and al in a st aw, 486 488
weighmg" an oh act m a fluid
medium, 488 489
Oppo tummies to li k the "world of
quamrity" with the "world of
counting numbers" and the "world
of formal symbols," 288 292
Minus Mouse, 290 291
OCR for page 241
INDEX 609
Plus Pup, 288 290
Plus Pup meets Minus Mouse, 291-292
Opticskit, 422, 4 8
Order
of coumring wo ds, 274
in decimal numbers, 333-334
O ganized knowledge, 462
O ganizing knowledge around core
concepts
subt action with regrouping, 18 19
Origin of Species, 551
Outcomes of con ses, 181
p
Pace of c ange, 44
Paley, Wi am, 550 551, 573
Palincsar, A 11 owe ie so hi an, 23, 421 474,
595
Park, Lesley, 455
Pa t-whole relation, 314
Pass it on game), 105
Passive media, 496
Passmo e, Cynth a M, 23, 515-565, 595
Past
fmding out about, 56 58
pick es of, 166
Patterns in data
providing students with oppo tumries
to sea ch for, 524
providing students with oppo tunities
to use to make predictions, 524
Payment for work in h sto y, 66 67
Peamuts ca toon, 309
Pedagogical wo ds
mean ngfu, 230
People going thei sepanate ways
emit on, 170
Pe cents, 325-332, 340
computing with, 329
in eve yday fe, 325
"fami ins" of, 331
invented procedu es, 329
on number lines, 326-329
pipes amd tubes, as rep esentations
fo fulness, 325-326
sta tmg f 0111, 322-324
st mg challenges, 329 331
Pe c, Geo ge, 122
Pe fo ma me
need to assist, 203
Penods in histo y, 42 43
Physics
fundamental, 24
inst uction in, 16 17
Picture Land, 285-287, 297
Pie c a ts and a pa t-whole inte p etation
of national numbers, 320 321
Pig im Fathe s and Native Amencans, 71,
84 119
explormg the basis for textbook
c aims and the natu e of sou ces,
84 111
gnd for evidence on, 173, 175
ideas, be iefs, amd atthtudes, 112-118
language of sou ces, inte pretation,
and other perspectives, 118 119
teacher questions, 112-113, 115
whether people thought like us in the
past, 117
Pipes
a new approach to national-number
lea n ng, 322-324
a rep esentation for fu~ness, 325-326
Plamn ng, 164 176
of progression in ideas about
evidence, 166 167, 174 175
umt on fi ng the world with people,
169
umt on fi st contacts, whether st
B endan sai ed from I eland to
America, 171
unit on fi st contacts, why the No se
colonists didn't stay in America,
172
unit on people gomg thei sepa ate
ways 170
PlausEhtity, 138
Plus Pup, 288 290
meeting Mmus Mouse, 291-292
Pocahontas (Disney fi m), 122
Po y, John, 84 85, 90, 97, 100 104, 106
108
Positive relationships
humor helping to bui d with students,
501
Possible Worlds, 4 6
Power
explanato y and predictive, 518
Pteconceptions, 1, 55, 399 403
ahout people, society, and how the
world works, 127-128
conceptual change, 400 403
OCR for page 242
610 INDEX
drawing on knowledge and
experiences that students
common y bang to the classroom
but are generally not activated
with regard to the topic of study,
569-571
engaging resi lent, 569-575
everyday concepts of scienti ic
methods, a gumentation, and
reason ng, 4 0
everyday concepts of scienti ic
phenomena, 399 400
IlllpO tance of students', 79
providing oppo tunities for students
to experience disc epant events
that allow them to come to terms
with the sho tcommgs in thei
everyday models, 571-573
providing students with nanative
accoumrs of the discovery of
(ta geted) 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
fami iar, 122
P edictive power, 518
P einst action assessments, 495
P epare-[o mvestigate phase, 434 438
Prepa e-to-repo t phase, 443 448
Principles of HOOP People Learn applied to
teaching high school history, 179-
213
designing a "history considerate"
learn rig envi onment, 199 209
t amsforming topics and objectives
into hi itorica problems, 181-199
Prior umderstandmgs
development of physica concepts m
infancy, 4
engaging, 4 5
of light, 425
misconceptions about momentum, 5
providing students with oppo tumries
to use to pose problems and
genenate data, 523-524
and nations number, 341
P Able SOIVffS
building, 258
"Problematizing' h stoncal accounts, 184 188
Procedu a fluency, 218
Productive disposition, 218
Prohciency
mathematical, 218
Prog ess, 44 45
Prog ession of ideas, 37 40
di ferent ideas about h stoncal
accounts, 38 39
Prog essive chamge, 45
Project CHATA See Concepts of History
and Teaching Approaches
Projectiles
explainmg motion of, 511
Propo tion, 234, 340
Pump Algebna Tutor See Cognitive Tutor
A gebna
Q
Quantity, 234
schema for, 272
Question Poser, 300-301
Question ng and explaming m high school
science
suppo tmg metacognition, 582-583
Questions, 128
diagnostic, 478
at the heart of using evidence, 124
mamy as yet unanswered, 492
teachers modelmg for students, 477
Quotient interpretation, 314
R
Rationa change, 45
Rationa number, 341-343
metacogmrion, 342
network of concepts, 341-342
prior umderst mdings, 341
Rationa -number lea n ng
and the knowledge network, 312-316
metacogmrion amd national number, 319
new concepts of numbe s and new
applications, 312-316
and the p inciples of HOEV Peop)e
Learn, 312-319
studentst errors and misconceptions
based on previous learn ng, 316
319
OCR for page 243
INDEX 611
Real-world expenence
cunent amd fate e, 390
Real-world words, 230
Rea ty test, 80 84
7-year gap," 82
Reciprocal teaching, 11
Reconceptua icing the unit and operations,
315
Reco der, 435
Reflective assessments, 412
in TbinkerToo 5, 412 413
Regrouping
subt action with, 18 19
Relative thinkmg as multiplicative, 311
Relativism, 176
Reliability, 126
Religious practices, 113-118
Repo ter, 301
Repo ring phase, 427, 44t 455
Rep esentations, 372
anchoring themes in histoncal, 186
Reproductive success, 542
Revolution, 61
S
Sagan, Ca 1, 194, 196 197
Sales, lii kpatack, 208
schemes
2-slot amd 3-s 01, 370
coming amd quantity, 272
Schools Counci Histo y Project, 40, 177n
Science, 395-565
developing understanding through
model-based inqui y, 515-565
guided inqui y m the science
c east 0111, 475-513
information from the histo y of, 499
leavmg many questions as yet
unanswe ad, 492
teachmg to promote the development
of scientific knowledge and
reasoning about light at the
elements y school level, 421 474
unit on the natu e of g avity and its
effects, 477-511
Science classrooms
guided inqui y m, 475-513
Scientific inqui y and How Prlplc Leant,
397 419
add easing p econceptions, 399 403
diagnosmg preconceptions in physics,
404
the HOEU People Lt~atn framework,
411415
knowledge of what it means to "do
science," 403 407
Scientific method
misconceptions about, 414
Scissors-amd-paste approach and lezlb ok
c aims and the natu e of son ces,
94
Ste~fn~hers, Thu(fim), 151
Second cycle of mvestigation
community knowledge from, 4 4
Second-hand investigation, 455 459
"Second o der' disciplma y concepts, 61,
73n
"Second o der' knowledge, 32-33, 41
acqu6ition of, 40 41
Sec et knowledge, 72
Seeing for you self and texthook c aims
amd the natu e of sou ces, 93
Seivas, Peter, 151
Selective advantage, 542
Self-assessment, 12
Self-monitormg
impo tance of, 10 12
metacogmrive mowto ing, 10
Sensitivity
7-year gap," 82
7-yea olds unde stamdings of, 277-
278
to students' substamrive assumptions,
127
Severin, Tim, 139, 142-143
shemilt, Denis, 23, 56, 79-178, 595-596
sh inking past, 160 161
sigmificance, 45
historica, 45
simplichty, 389 390
6-yea olds umderstmdings of, 274-
277
Skating Pa ty game, 292-295
Skil s
defming, 40
sky [and, 286 287
Bbstoff activity, 298-299
Smith, John, 122
sOu ces
access to someone who saw for
himself, 93
baefing sheet, 88 89
OCR for page 244
612 INDEX
distinguishmg among kinds of claims,
101-102
genera icing, 102-107
getting hch rid the ecord to concerns
of the people who produced
them, 107-108
interpreting son ces m context, 100
maintaining contact with am
eyewitness using knowledge
hamded down th Hugh
generations, 93 94
the natu e of, 84 111
scissors-amd-paste approach, 94
seeing for you self, 93
teacher questions, 92, 95-96, 99-101
t usting the son ce who was in a
position to know, 96
umderstandmg the pa pose of the
son ce, 96 99
umderstandmg what is likely to get
reco ded and under what
cicumstamces, 108 111
working out the facts from other
sources or avai able knowledge,
94-95
Splittmg, 323
State of affai s
changes in, 44
Stearns, Peter, 210
Stewa t, James, 23, 515-565, 596
"Stop-Sta t Challenge," 333
Stopwatches
decimals and, 332-333
Stories
"embroidering," 153
st ategic competence, 218
St ing challenges
guessmg myste y objects, 329-331
Student assumptions about how we know
of the past, 123
Student conceptions
expe imentation, 402
inadequacies in a guments, 403
interpretation of data, 403
of knowledge gene ation and
justi ication in science, 402 403
models, 402 403, 518
Student mqui y in genetics, 526 538
example of student work on a GCli
homework assignment, 535
genetic mqui y in the c dSS1110111, 529
534
initial GCli pope ation for the final
GCK mqui y, 537
meiotic processes governing
mberitance, 528
Mendel's model of simple dominance,
528
Students' enors and misconceptions based
on p evious teaming, 316 319
Students'existing knowledge, 517-526
assessmg knowledge c aims m
genetics, 523
attending to, 544 545
black box, 520
bui ding on and connecting, 258
learning genetics content, 524 526
providmg students wt h learn rig
oppo tumries, 523-524
student conceptions of models, 518
Studentst p econceptions
impo tance of, 79
Study of ight, 422 426
conceptual umderstandmg, 423 424
metacogmrion, 426
prior knowledge, 425
Study of light th ough mqui y, 426 459
heuristic for teaching and leaming
science th ough guided mqui y,
427 455
second-hand investigation, 455 459
Subconst ucts
the many pe sonaltties of nationa
number, 314 315
Subject-specific knowledge in effective
science mst uction, 467 469
Substantiated accounts, 87
Substantive assumptions
senshtivity to students', 127
Substantive concepts, 61 65
historica accoumrs not copies of the
past, 62 63
payment for work, 66 67
Subt action with regrouping, 18 19
suppo ting learning through cycles of
mvestigation, 460 467
suppo ting skilled questioning and
explaming in mathematics
problem solving
suppo tmg metacogmrion, 580 581
suppo ting student and teacher learn ng
th ough a c assroom discou se
commumtty, 237
OCR for page 245
INDEX 613
Table of va Yes to produce a function,
353-358
Teacher professional development in
Japan, 244
Teacher questions, 112-113, 115
and textbook c aims and the nature
of son ces, 92, 95 96, 99-101
Tffche st conceptions and pa tial
us de standings, 279 281
acqui ing an us de standing of
number as a lengthy, step-by- step
process, 280 281
coming words as the c ucial Imk
between the world of quantity
and the world of formal symho s,
280 281
math as not about numbe s, but
about qua itch, 280
Teache s ffngag rig students'
preconceptions, 219 231
common preconceptions about
mathematics, 220 222
engaging students' p econceptions
and building on existing
knowledge, 223-231
Teaching
recipmcal, 11
Teaching and learn rig fimctions m
mathematics, 351-393
add easing the th he principles, 359
373
bui ding conceptua understanding,
procedu al fluency, and
commented knowledge 364-369
bui dmg on pno knowledge, 359-
364
bui dmg esou cefu, self-regu at no
problem SOIVffS, 371 373
linkmg fom al mathematics
us de standing to informal
reasonmg, 354-355
making a table of values to produce a
fimction, 353-358
teachmg functions for umderstandmg,
373-389
teachmg to achieve this kind of
us de standing, 358 359
Teaching as Storv Telling, 574
Teaching functions for understanding, 373-
389
Teaching mathematics in the prims y
g ades, 257-308
acknowledging teachers' conceptions
amd pa tial umderstandmgs, 279-
281
bui ding on chi d en's cu rent
understandings, 267-279
the case of number worlds, 282-302
companog number worlds and
cont ol g cop outcomes, 304
deciding what knowledge to teach,
259 267
defming the knowledge that should
he taught, 281-282
Teaching the ational number wxem, 309-
349
additive and mu tiplicative easoning,
311
how students learn nations number,
341-343
me action in rational number, 319
340
rational-number lean mg and the
p inciples of HoEvPeop)eLeatn,
312-319
Teaching to promote the development of
scientific knowledge and
easoning about light at the
elements y school level, 421 474
the role of sub ect-speci ic knowledge
m effective science inst action,
467 469
the study of light, 422 426
the study of ight th ough mqui y,
426 459
suppo tmg learn rig through cyc es of
investigation, 460 467
Technica media, 496
Testimony, 41, 124, 135, 166
Testmg
external, 181
Textbook claims
access to someone who saw for
himself, 93
beefing sheet, 88 89
distmguish rig among kinds of c aims,
101-102
genenalizmg, 102-107
getting behind the record to concerns
of the people who produced
them, 107-108
interpreting son ces m context, 100
OCR for page 246
614 INDEX
maintaining contact with an
eyewitness using knowledge
hamded down th Bugle
generations, 93 94
and the natu e of son ces, 84 111
scissors-amd-paste approach, 94
seeing for you self, 93
teacher questions, 92, 95 96, 99 101
t usting the son ce who was in a
position to know, 96
umde standmg the pa pose of the
source, 96 99
understandmg what is likely to get
reco ded and under what
ci cumstances, 108 111
working out the facts from other
sources or avai able knowledge,
94-95
Themes, 44
anchoring m historical epresentation
and inte pretation, 186
Th nkerTools, 407, 585
Third cycle of investigation
community knowledge from, 465
Third International Mathematics and
Science Study, 243
3-slot schema
for g aphing a ne, 370 371
Th he subt action methods, 224
Time, 41 43
change limited in, 45
periods in histo y, 43
Time lines, 129, 159
Timekeeper, 435
Torsion bar, 493-501
Transforming topics and objectives into
historica problems, 181-199
accoumcmg for the "flat ea th," 189-
199
"problematizing" historica accoumrs,
184 188
Transmission enors, 123
T usting the son ce who was in a position
to know
and tomb ok c aims and the natu e
of son ces, 96
T uth
twistmg, 105, 123
Tubes
a new approach to rations -number
learn ng, 322-324
a epresentation for fu Iness, 325-326
Turner, F ederick Jackson, 58
Twisting the t uth, 105, 123
', or schemes, 370
U
"Underlying" causes, 35
Us de stamping
essentia role of factual knowledge
amd conceptual f an eworks in,
69
expe ts emembe ing considerably
more relevant detai t an novices
m tasks withm thei domain, 8 9
learn ng with umderstandmg
suppo ting knowledge use m new
Sttuations, 7
Unde standing of number
a lengthy, step-by-step process, 280
281
Unde stamding the pu pose of the sou ce
amd textbook c aims amd the
natu e of sou ces 96 99
Unde stamding what is kely to get
ecorded amd under what
ci cumstances
and te2ctbook c aims and the natu e
of sou ces, 108 111
Umt-level problem, 189 199
accounts of Colombian voyages, 192-
193
ancient views of the Ea th as fiat or
roumd, 196 197
Umt on the natu e of gnavity and its
effects, 477-511
United Kmgdom
adjusting data hom, 177n
Schoo s Coumci Histo y Project, 40,
177n
Units
on filling the world with people, 169
on fi st contacts, whether st Brendan
sai ed from I eland to Amenca,
171
on fi st contacts, why the No se
colon sts didn't stay in America,
172
on people gomg their separate ways,
170
OCR for page 247
INDEX 615
V
Verbal intem Stations, 372
Visual propo tional estimation
sta tmg from, and halving amd
doubling, 323-324
Wa (ca d game), 336
Wa m-Up period, 298, 300
Water and al in a straw, 486 488
Website, 562n
"Weighing" an oh ect in a fluid medium,
486 489
Weigh ng-in-a-vacuum situation, 484, 489
Whole number
cent a conceptual st uctu e for, 261-
262, 275
Wi son, Suzamne M, 596
Wmebu g, Samuel s, 100
Wisdom, 236, 238
Woodbury, Hasps, 391
Wo d P oblff s test, 264 265
Wo ds
tarsus notations, 230
Wo ds in stones
explaining, 132-133
Work
payment for in history, 66 67
Workmg out the facts from other son ces
or avai able knowledge
and textbook claims and the natu e
of soumes, 94 95
Workmg things out for on selves, 133-138
being awa e of how we are thin dng,
135
going beyond face value, 134
how far a leather boat con d have
managed to sail, 139 141
Workmg th ough the task, 128 164
Workmg with evidence
Pi g im Fathe s and Native An encd
64 119
prepa ing for the task, 121-128
the st Brand m's voyage task, 128
164
World's Fai of 1892, 208
Wrap-Up period, 301
Written A tthmetic test, 264 265
y
Year-long historical questions, 164-188
OCR for page 248
Representative terms from entire chapter:
suppo ting
