Cognitive Science and Mathematics Education

By Alan H. Schoenfeld | Go to book overview

Subject Index

A
ABLE, 51-52
absolute value, 256
"accepting the given," 136
ACT, 137
Al. See artificial intellligence.
ALEX, 225
ALGEBRA ARCADE, 110
ALGEBRALAND, 81, 92, 111-114
algebra
arithmetic basis of, 181-182, 255-256
"bugs" in, 169-170, 176, 222-223
equation solving. See also equations.
Bundy's work on, 13-17, 226
computer programs for, 103, 227-228
"Generalized Substitution Principle," 232, 235, 238
inversing procedure in, 228
linear patterns in, 233, 235, 239
mixed cues in, 230-231, 235-236
planning in, 223, 234-235, 237
quadratic patterns in, 234, 239
radical as cue in, 233, 237
rote vs. planned, 233-235
Silver's work on, 226-227
skill in, 231-232
strategies for, 15-17, 229-232, 236-237, 239, 243
strategy errors in, 219, 223-224, 231, 236
student difficulties with, 192, 218-219
factoring, 150, 261
learning of, 181-182, 217-249
analysis of preconditions, 226-227, 237-238
knowledge organization and, 220
practice tasks and, 238-239, 241, 243
problem sequence and, 221
research in, 222-227, 246
role of examples in, 225-227, 228-229
student difficulties, 218-219, 223-224, 247
Wenger's theory of, 220-221
mathematicians' use of, 248
metacognition and, 192, 235, See also mathematical problem solving
problem schemata in, 47-48, 81, 83
word problems, 83
AM (Automated Mathematician), 132-133
arithmetic, 40, 110-111, 151-152, 181-182, 247
ARITHMEKIT, 110
artificial intelligence, 10, 18, 130, 133, 179
learning and, 51
mathematics learning and, 166, 180-181, 217, 222-228
equation solving, 222-228
planning in, 130
associationism, 2-3, 7

B
"back to basics," 6-7, 268
BANK STREET LAB, 105

-285-

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