Commentary on Theories of Mathematics Education

666 Subject Index
299, 300, 341, 385, 443, 448, 470,
473, 489, 509, 564, 621–625, 627,
629, 641
factors, 341
A posteriori knowledge, 382
Power (mathematical), 189, 214, 305, 624–625
Practice, 3–5, 13, 18, 23–25, 44–45, 55–58, 69,
71–72, 80, 89, 91–92, 100, 103, 107–
108, 111, 114–115, 129, 141–142,
147–148, 151–153, 155–156, 161–
162, 164, 166, 172, 174, 185, 198,
203, 212–213, 220–221, 233–235,
245, 247, 253–254, 256, 265, 267,
274, 292, 295, 310, 316, 325, 341–
342, 356, 359–360, 365, 369, 382,
386–387, 390, 392–393, 404, 421,
450, 452, 473, 487, 496–503, 511,
527, 529, 531, 533, 539–540, 543–
545, 547–548, 555–558, 570, 598,
608, 610, 630, 640, 642
Problem-solving, 90, 140–141, 242, 245, 248–
252, 254–256, 261–269, 271–273,
282–283, 297–301, 313, 355, 357,
360, 376, 422, 472, 586, 599
beyond the classroom, 266, 268, 273, 282,
298
concept development, 266–267, 282, 297–
298
heuristics and strategies, 264–266
Problem solving research, 140–141, 153, 253,
261–262, 266
Problem-solving, tools, 140, 265–269, 355
Problems, 13, 15–16, 23–24, 26, 36, 41, 57–
58, 70–75, 79, 83, 88–91, 108, 112,
122, 124, 126–130, 139, 141, 143,
147–149, 151, 153, 155, 159, 161–
164, 167, 176, 178, 181, 187, 199,
204, 213, 219, 225, 230, 241–247,
249, 252–255, 261, 263–265, 267–
274, 278–281, 283, 292–293, 297–
300, 315, 321, 324, 326, 341, 343–
344, 351, 354–357, 359–360, 362–
363, 432, 441, 452, 459, 469, 486–
487, 494, 498, 500, 510, 524, 526–
527, 532, 537, 539, 556, 565, 607–
608, 622, 627–628, 640
modeling (see mathematical modeling), 73,
219, 247, 261, 264, 270, 272, 299,
300, 565
non-routine, 264–265, 271, 299
word, 74, 112, 264–265, 267, 272–273
Procept, 172, 180–181, 184–185, 188, 194
Process-object encapsulation, 180
Proof, 9, 20, 37, 57–58, 87, 91–93, 183, 187,
189–190, 227–228, 230–231, 235,
245, 343–345, 355–356, 358, 362,
369–377, 436, 438, 441–444, 470,
599, 617, 632
scheme, 92, 355–356, 358, 362, 369
Proving, 355–358, 362, 369, 373, 444
Pseudo public debate, 365
Psychodynamics, 605
Psychophysiology, 309–310, 313, 322, 324
Q
Qualitative research, 121, 165, 312, 384, 386–
388, 392–393, 533, 610
Quantitative research, 165, 533
R
Reference field, 126, 216–217, 221
Referential symbolic way of thinking, 356
Reflexivity, 381–382, 388, 392
Refutations, 8–10, 35–36, 203–204, 312, 370,
372, 383, 633
Repeated reasoning principle, 360, 363–364
Representation, 27, 44–45, 50, 76, 79, 177, 183,
213–214, 217–218, 223–224, 227,
229, 231–234, 236, 243–248, 272,
360–362, 364, 388, 397, 532, 607,
615, 623
Representational systems (internal), 211, 220,
228, 233–235, 246–247, 253
affective, 246–247, 253
formal notational, 246
imagistic, 234, 246–247, 253
planning, monitoring and executive control,
246–247
verbal syntactic, 246
Research, ix, 10–15, 17–20, 22–25, 39, 42,
45–46, 49, 51, 55–59, 65–83, 87–
93, 97, 99, 100, 102–108, 111–116,
121–125, 127–130, 133, 139–142,
144, 147–149, 151–156, 159–166,
171–172, 184, 187, 189–193, 197,
199–203, 205–206, 215, 217, 221–
223, 227–228, 235, 248, 251–254,
256, 261–274, 279, 282–283, 291–
295, 297–300, 309–317, 319–320,
322, 324, 333–337, 341–344, 352,
357–358, 370, 374, 376–377, 381–
388, 391–393, 397–398, 401, 403,
405–406, 417, 422–424, 435, 444–
452, 455–456, 467, 472–473, 479–
481, 483–484, 486–490, 492–511,
515–517, 519–520, 522–524, 526–
530, 532–534, 537, 539–540, 542,
545, 547–548, 551–558, 567, 569,