Commentary on Theories of Mathematics Education

Subject Index 665
558, 569, 593–594, 596–599, 601–
602, 604–605, 607, 609–610, 613,
618, 621–625, 627, 629, 632, 639–
640, 642–643
Mediation, 44, 103, 211–213, 215, 223, 228,
538
Mental act, 355–358, 362
Meta-constructionist phenomenology, 381,
386, 389, 392–393
Meta-language, 511, 537, 549, 555, 558
Metaphor, 5, 15–16, 39–43, 49–51, 54, 108,
113, 139, 159–160, 201–202, 211–
213, 317, 404, 496–497, 510, 516,
528, 530–531, 538–539, 547, 552,
558, 596–600, 607, 609, 614
Methodology, 13, 19, 36, 75, 88, 97, 133, 148,
152, 156, 161–162, 164, 203, 206,
372, 386–387, 390, 392, 436, 498,
516, 533, 537, 553, 556–557
Micro-sociology, 551
Model, 4, 10, 18, 24, 26–27, 40, 42–45, 50–
51, 54, 67–68, 74, 81–83, 87, 89,
90, 100, 104, 107, 130, 133, 142–
145, 148, 153, 171–176, 178, 182–
183, 185–186, 190–193, 196–203,
211, 215, 217–219, 246–248, 253,
269, 274–275, 278, 281–282, 293,
299, 305, 321, 335, 343–344, 357,
373, 382, 384, 387, 421–423, 431–
433, 437, 439, 442–443, 445, 449,
451, 499, 555, 576–581, 584, 586–
587, 625–628
set, 218–219
Modeling, 79, 130, 144–145, 154, 219, 248,
252, 272, 356, 406, 442, 565–567,
570–571, 573, 584
Models
of learning, 11, 567, 582, 586
and modeling, 73
Modern mathematics, 3, 22, 608, 629
N
Necessity Principle, 359, 361–364
Need
for causality, 365
for certainty, 365
for communication, 365
for computation, 365
for connection and structure, 365
Networking strategies, 483, 492–493, 495–498,
500, 502, 507, 509, 515–516, 529,
553
Neurophenomenology, 315
New math, 3, 20–22, 629
Non-referential symbolic way of thinking, 356
Non-routine problems, 264–265, 271, 299
Normal science, 35, 201, 203
O
Objective knowledge, 36, 198, 471, 633
Objectivity, 27, 36, 126, 203–204, 214, 218,
220, 233, 235, 470, 625, 633
Ontology, 3, 116, 354, 385, 471
P
Paradigm, 3, 7, 8, 14, 19, 24, 42, 57, 67, 87,
115, 203, 305, 381, 393, 435–436,
445, 451, 498, 507, 510–511, 529,
569, 627, 630–632, 639–640
Paradigms for research
behaviorist, 581
critical theory, ix, 82, 103
epistemology, 3, 10, 19, 35, 42, 93, 171–
172, 230, 370, 382, 389, 391–392,
417, 471, 558, 626
metaphor, 16, 39, 40, 43, 51, 497, 596–597,
607, 614
psychometrics, 200, 315
qualitative research, 121, 165, 312, 384,
386–388, 392–393, 533, 610
quantitative research, 165, 533
social constructivist, 10, 14, 36–37, 43, 453,
642
Paradox, 202, 384–386, 388, 471, 543, 545–
547
Participatory, 54, 56–58
Pasteur’s quadrant, 81–82
Perspectives on doing mathematics, 500
Persuading, 355, 452
Phenomenology, 225, 319, 381–382, 384, 386,
389, 391–393, 524
Philosophy, 3, 7–10, 12, 16, 18–19, 27–37, 39,
49, 50, 54, 60–66, 75–76, 81, 83, 87–
89, 93, 105, 107, 116, 123, 202, 321,
341, 343, 383–385, 387, 391, 405,
417, 471, 479, 532, 594, 610, 613,
621, 633
of mathematics, 7–10, 35–37, 49, 50, 105,
107, 202, 405, 479, 621, 633
education, 7, 8, 10, 36–37, 49, 50, 479
Piagetian, 54, 103, 176–177, 203, 316, 384,
437, 582–583, 595
PISA, 266, 459, 461, 467–469
Platonism, 233
Pleasure, 249, 597, 599, 602, 606–607, 626
PME, ix, 10, 14, 39, 103–106, 114
Political, 3, 11, 14, 18, 24–26, 40, 53–54, 65,
67, 72, 80, 87, 142, 145, 162, 272,