Commentary on Theories of Mathematics Education

662 Subject Index
234, 316, 324, 334, 355, 371, 374,
538, 567, 593
model, 51, 200, 215, 335
obstacle, 102
operator, 220
science, 10, 16, 40, 50, 66, 124, 147, 179,
235, 309, 315, 317, 397, 606, 610
tools, 221–223, 312, 538
Cognitive neuroscience, 305–306, 309–310,
312–316, 319–322, 324, 326, 334–
335
Cognitive psychology, 22–23, 114, 310, 316,
319–321, 538, 597
Cognitivist, 39, 40, 54, 78, 93, 316, 581
Complementarism, 193, 202, 205
Complex adaptive systems, 133–134, 564–565,
575–577, 579–581, 586
Complexity, ix, 10, 13, 22, 44, 65–66, 68, 122,
127, 217–218, 264, 268, 291–293,
335, 341, 371, 385, 397–398, 409,
424, 433, 438, 440, 480–481, 484,
489, 502, 508–510, 552–553, 563,
565, 569–573, 578–579, 583, 585–
587, 641
Compression of knowledge, 181, 183, 188–190
Computer-based mathematics teaching, 516,
519, 521–522, 527–528
Concept development, 142, 153, 196, 266–267,
270, 282, 297–298
Consilience of knowledge, 15
Constructivism, 8, 10, 13–15, 17, 36–37, 39–
43, 45–46, 49–51, 53–55, 57, 60, 71,
82, 101–103, 142, 306, 310, 316,
353, 384, 456–457, 471–472, 487,
583, 633
radical, 8, 10, 15, 39, 41–43, 46, 49–51, 53–
54, 60, 82, 101, 310, 384
social, 8, 10, 14–15, 36–37, 39, 40, 43, 46,
49–51, 53–54, 57, 60, 384, 471–472,
487, 633
Covert, 544, 596–597, 609–611, 614–615
Creativity, 107, 124, 269, 305, 313, 440, 470,
558, 593, 600, 609, 628, 632
Critical pedagogy, 623–624
CULTIS-model, 197–199
Culture, 11, 27, 65, 88, 114, 154, 201, 216–217,
226, 236, 255, 343, 398, 422, 433,
436, 440, 455, 467, 473–474, 487,
490, 614, 621, 630, 634–639, 641–
642
and mathematics cognition, 213
Curriculum, 3, 13–14, 20, 24, 40, 76–80, 105–
106, 122, 125–126, 128, 130, 132,
136–140, 148, 154–155, 161–163,
166, 179, 221–222, 228, 241, 246,
254, 261–264, 267–271, 273–275,
278, 282–283, 291, 294–295, 297–
298, 300–301, 311, 316, 324–325,
341, 371, 402, 404, 415, 431, 433,
436, 441, 443, 449–451, 489, 563,
565, 574, 585, 624, 628
development, 130, 132, 155, 163, 261–263,
271, 282, 298, 300
D
Data modeling, 299–301, 565
Democratic access, 462, 621
Democratization, 621
and curriculum, 622
and ideological debate, 627
and mathematical power, 623
and reform, 621
Design
research, 125, 147–149, 151, 153, 156, 159,
161, 166, 496
science, x, 25, 121–124, 127, 147, 151–152,
155, 159–167, 494
Device paradigm, 630–632, 639–640
Dialectic, 76, 381, 387, 487–488, 516
Dichotomies, 3, 27, 196, 252, 601, 610
Didactical situations, 22–23, 484, 486, 500
Didactics, 5, 18, 22–24, 112, 415, 483
Discrete mathematics, ix, 228, 241–243, 245–
249, 252–254
Diversity
of theoretical frameworks, 479
of theories, 99, 479–480, 483–484, 488–
491, 498, 502, 508–510, 515, 556
DNR-based instruction in mathematics, 341,
344–346, 373, 377
DNR premise, 354, 376
Domain of abstraction, 225–226
Dualism, 529–530
Duality Principle, 357–358, 362–364
Dynamic geometry, 225–226, 599
environment, 225, 230
Dynamic systems, 42, 50, 154, 567
E
Ecological validity, 306
Education, 105
Educational neuroscience, 264, 306, 309–311,
313, 315–321, 324–325, 334
Embodied cognition, 101, 112–113, 306, 309–
310, 313, 315–318, 320, 333–334,
597
Embodied mind, 42, 317
Embodiment, 27, 183–184, 188–190, 219, 310,
316–319, 321, 599, 610