Index
A
activity system,
7, 11, 24–49, 223, 225, 228, 231–236
affordances,
11, 23, 158, 165, 166, 168–172, 174, 185, 191, 192, 198–202, 216, 218, 219, 224, 229, 244, 255, 256, 261, 267, 268, 278, 300, 302, 325, 328, 351, 352, 354, 367, 423, 434
analytical,
81, 330, 399, 406, 409, 414
approximation of practice,
228, 231–242, 244, 257, 276, 277, 291, 295, 297, 328
artefacts,
158, 263, 273, 274, 276–278, 346, 425
attend,
9, 11, 14, 39, 41–44, 49, 55, 88, 91, 92, 102, 149, 150, 157, 171, 205, 219, 224, 239, 240, 243, 273, 274, 289, 295, 298, 311, 316, 318, 320–323, 326, 329, 338, 340, 349–352, 361, 367, 369, 370, 372, 375, 376, 378, 383, 385, 399, 401, 430, 431
B
badge,
223–226, 228, 232, 233, 238, 243–246
becoming a mathematics teacher educator,
8, 92, 97, 98, 100, 149
blended courses,
10, 111, 122, 125, 127, 131, 132
C
communication technologies,
123, 134, 165, 224
complexity of practice,
292, 294, 299, 301–303
computational modelling,
11, 12, 197–220
computational thinking,
1, 9, 11, 197–201, 218
conceptual tools,
13–15, 24, 257–258, 264, 267, 276, 278, 279, 285, 286, 288, 289, 293, 301, 303, 367
conjecturing,
29, 81, 169, 374
continuum,
15, 16, 287, 394–399, 401–405, 408–415
controlled implementation,
5, 13, 14, 18, 285–303, 307–309
critical incidents,
7, 60–62, 66, 69, 70, 75, 78, 80
curriculum reform,
114–116
curriculum resource,
5, 9, 10, 12, 18, 128, 132, 134, 139–142, 146, 150, 152, 157, 158, 228, 311
D
de-brief conversation,
2, 4, 5–8, 85–106
decomposition of practice,
26, 257, 258, 263, 274–277, 289, 295
design dilemmas,
278
difficulty of reform teaching,
264, 266, 267, 269, 273, 275
digital resource,
139–159
digital technologies,
11, 131, 139, 140, 163–193, 432–434
document,
10, 25, 27, 142, 152, 163, 178, 290, 343
documentation work,
139, 142, 144, 145, 147–149, 150–159
documentational approach,
5, 10, 139–159
documentational genesis,
10, 142, 143
dynamic models,
11, 163, 169, 172–174, 176, 177, 187, 189, 191, 192, 201, 207, 212, 213
E
educative resource,
139–159
empirical, and formal arguments,
170
enactivism,
91
engagement with research,
260, 261, 279
F
facilitators,
6, 16, 24, 25, 27, 31, 33–35, 39–41, 44, 48, 129, 130, 200, 277, 290, 291, 298, 325, 421, 425, 429–431, 435, 436
formative assessment,
47, 155, 157, 307, 431, 432, 436
framework for teaching practice,
13, 285–294, 296, 301, 303
future mathematics teachers,
65, 67, 90, 146, 149, 150, 255, 279, 298, 329–331, 339, 393, 398
G
geometry,
29, 34, 35, 44, 47, 114, 115, 130, 131, 145, 146, 152, 166, 168–170, 172, 176, 179, 185, 191, 219, 223–236, 238, 240, 241, 244–246, 308
I
individual development,
80, 81
instructional exchanges,
11, 223, 226, 227, 229, 230, 243
instrumentalization,
16, 142, 148, 150–159, 422–424
instrumentation,
2, 5, 12–16, 142–157, 244, 346, 422–424, 435
interpret,
3, 58, 70, 89, 145, 167, 168, 230, 260, 265, 273, 275, 317, 340, 344, 346, 347, 349, 352, 373, 375
L
learning trajectories,
7, 60, 152, 157, 158, 226, 270, 327, 337, 338, 342–346, 354
low floor/high ceiling dimension of the activities,
11, 201, 203, 205, 210, 212, 219
M
Massive Open Online Courses (MOOCS),
10, 111, 122, 127–132, 134, 148
mathematical concepts,
63, 87, 100, 104, 164, 168, 169, 201, 219, 226, 272, 274, 341, 344, 346, 347, 350, 378, 432
mathematical problem solving,
34, 42, 48, 163–193
mathematical reasoning,
31, 148, 191, 351
mathematics teacher learning,
12, 139–159, 223–246, 308
meta-rules,
8, 88–90, 96, 104, 106
methodology,
115, 118, 274, 325, 381, 406, 428, 435
mini MOOCs,
10, 111, 122, 128–132, 134
N
narratives,
1, 7, 57, 60–62, 66, 68, 79, 80, 238, 328, 405, 421, 423, 424
notice,
77, 78, 141, 212, 213, 216, 218, 235, 277, 311–331, 337–355
noticing,
5, 7, 14, 17, 26, 28, 31–33, 40–44, 56, 57, 68, 72–75, 235–236, 239, 269, 288, 307, 311–332, 337–355
O
online platforms,
192
open educational resources,
10, 131, 141, 144, 150, 152, 153
P
pedagogical,
10
pedagogies of practice,
225, 257, 267, 273, 274, 278, 289, 303
pedagogy of enactment,
286
practice-based teacher education,
11, 224, 225, 231, 243, 328
praxis perspective,
120, 133
professional development,
5, 9, 10, 13, 15, 18, 23, 24, 27, 28, 34–36, 38, 39, 43, 44, 46, 47, 49, 57, 65, 87, 88, 90, 119, 126, 128, 145, 147, 149–150, 152, 153, 155–157, 163–165, 224, 261, 264, 285, 286, 288–303, 307–309, 322–324, 329, 330, 339, 341, 346, 351
professional identity,
395, 397, 398, 403, 415
professional learning communities of mathematics teachers,
16, 425–429, 431, 432, 436
professionalization,
397, 398
programme-level issues,
261–268
prospective and practicing teachers’ learning,
24
prospective teachers,
2, 3, 5–14, 16, 27, 28, 35–38, 40–46, 55–81, 85–96, 98–108, 119, 155, 167, 175, 209, 264–268, 271–276, 278, 286, 288, 293, 315, 320, 321, 323–328, 339–349, 351, 354
R
RaPID model: raveling, prompting, interpreting and deciding,
15, 362, 368, 371, 373, 374, 377–379, 381, 384, 385, 386, 389, 390
RaPID Framework for Lesson Analysis (RaPID FLA),
362, 369, 374, 378, 379, 381, 383–385
reflection of work of others,
66
reflective practice,
16, 37, 395, 398–401, 414
reflective skills,
2, 5–8, 29, 36, 55–81
representations of practice,
5, 9, 11, 12, 223, 237–240, 244, 245, 257, 258, 263, 273, 275, 287, 291, 302, 325, 342
resourcefulness,
44, 436
resources,
421–437
S
scheme of use,
148
school placement,
15, 85, 94, 258, 260, 264–267, 273, 276, 278
simulations,
40, 197, 199, 200, 209, 211–213, 231, 237, 238, 242–244, 287, 327
students’ thinking,
39, 46, 167, 232, 235–236, 257, 311, 314, 315, 323–325, 327, 339, 340, 342, 343, 348, 410
system-level issues,
258–261
T
tasks promoting reflection,
59–68
teacher education,
1–18, 57–58, 139–143, 146–150, 153, 157, 158, 163, 165, 167, 197–219, 223–228, 231, 232, 234, 235, 237, 243–245, 255–279, 285, 286, 288, 303, 312, 315
teacher educators,
1–27, 23–49, 80, 86–88, 90–93, 96–101, 149–152, 227, 230, 236, 237, 239, 243, 245, 246, 257, 260–268, 273, 286, 300, 330, 331, 396, 402–404
teacher knowledge,
28, 224, 225, 241, 243
teacher learning,
7, 12, 23–49, 139–159, 223–246, 292, 307, 339, 346
teacher-resource partnership,
368, 378
teachers collective work,
146, 153, 155
teachers community,
426–429
teaching experiments,
13, 255, 256, 268–278, 411
teaching mathematics,
13, 256, 268, 269, 273–278
teaching plans,
7, 56, 62–66, 79
teaching practices,
45, 124, 141, 148, 163–167, 171, 184, 192, 257, 258, 263–265, 269, 274, 289
technology,
111–134, 139–142, 146, 223–246
theoretical frameworks,
10, 12, 13, 24–27, 228–232, 244, 264, 270
theoretical lenses,
14, 18, 337–355
theory-practice,
256, 259, 261, 262, 266, 267, 273, 279
third space,
89, 264, 401, 402
three-point framework,
337, 338, 350, 351, 354
tools,
1–18, 223–246, 421–437
two-worlds paradigm,
262, 264, 266, 267
U
understanding teacher thinking,
274, 278
V
video analysis,
26, 27, 31, 32, 35, 39, 42, 43, 46–49, 326, 348
video intervention,
7, 55, 68–78
vision,
23, 26, 28, 33, 44–47, 116–118, 120, 132, 245, 269, 287, 288, 311–313, 325, 338
W
work-specific teacher education,
78, 264