62, 65, 219
pre-school, 7, 8, 31, 32, 43, 44, 63, 70,
172, 194
see alsoFoundation stage
probability, 223
problem/problem-solving/problem-solving
approach, 5, 6, 9, 23, 108, 132, 138,
164, 174, 181, 185, 187, 196, 198, 234
process approach to writing, 67
see also emergent writing
progressive mathematisation, 4, 213
see alsoRealistic Mathematics Education
(REM), provocative mathematics, 68,
132quantity, 16, 17, 101, 175, 200, 202
questionnaires (teachers’ and
practitioners’, parents’), 7, 8, 81, 84,
194, 216, 221, 224, 239Realistic Mathematics Education (REM),4–6,
12
see alsoprogressive mathematisation
Reggio Emilia. 95
see alsoHundred Languages
repeated addition, 118, 150, 156,
181–185, 187, 188
see alsomultiplication,
RReepprreesseennttaattiioonn ooff qquuaannttiittiieess tthhaatt aarree
ccoouunntteedd,, 100–101, 131
RReepprreesseennttaattiioonnss ooff qquuaannttiittiieess tthhaatt aarree nnoott
ccoouunntteedd, 91, 102–103, 130, 131
see alsotaxonomy
resources, 3, 11, 34, 43, 45, 47, 49, 54, 92,
104, 106, 135, 140, 145, 149, 151,
152, 170, 171, 180, 181, 183, 185,
190, 191, 223
right angles, 52, 147, 168
Robert Owen Children’s Centre, xii,
166–167
role play, 17–19, 34, 73, 82, 23, 135, 139,
154, 166, 167–169, 178, 180–181,
187, 191,
area, 18, 40, 139, 145, 153, 234
and mark-making/writing, 139–140,
145, 178–181
see alsohome corner, symbolic play
Russia, 3, 4SATS (Standard Attainment Tasks), 234,
235, 239
scaffold/scaffolding, 11, 64, 137, 222
schemas, 10, 13, 21, 36–55, 59, 61, 91, 92,
94, 96, 99, 153, 178, 198, 199, 217,
223, 224, 225, 226, 238, 242
in school, 44–54, 153, 178, 180–181,
217, 224, 225, 226, 238observation of schemas,10, 44–49, 55,
57, 180
pattern of schemas, 51–54, 55, 58, 91,
242
supporting, 43–44
schematising/schematisation, 10
scribbles, 26, 58, 67, 86, 89, 90–91, 96,
227, 231, 241
second language learning (L2), 71, 77–79,
81, 119, 121, 212,
see alsoforeign language/foreign
language learning
semiotics, 72–73
SSeeppaarraattiinngg sseettss, 87, 108, 117–118, 130,
131
shape, 32, 34, 41, 48, 49, 55, 58, 60, 63,
88, 208, 209, 223, 225
space and shape, 153, 198, 227
shorthand, successive shorthand, 114, 122
Singapore, 14,
signs (abstract, conventional, formal,
mathematical), 10, 70, 71, 72, 115,
118, 123, 194, 212, 226, 242
addition, 74
children’s own, 134, 160
equals, 115, 122
invented,
minus, 124
operator, 125,
signs (labels, notices), 24, 141, 160, 166
situated learning, 5
Social constructivism, 11, 21, 22–33
Socio-culturalism/socio-cultural theory,
contexts, practices, 20, 21, 23–24,
31–32 33, 35, 242
social interaction, 11, 22, 23, 34, 220
social semiotic theory, 135
sorting, sets, matching and one-to-one
correspondence, 22, 37, 38, 65, 75,
219
standard abstract language, algorithms,
calculations, layout, methods, written
forms, written calculations, 4, 6, 41, 67,
75, 76, 79, 80, 82, 85, 89, 100
standard symbols, forms, letters,
numerals, 21, 24, 32, 33, 58, 67, 68,
70,79, 80, 88, 89, 96, 98
see alsostandard calculations,
SSttaannddaarrdd ssyymmbboolliicc ooppeerraattiioonnss wwiitthh ssmmaallll
nnuummbbeerrss, 123–125, 130, 131
structures (see generational structures)
subtraction, take away, 6, 9, 20, 70, 74,
77, 88, 108–110, 111, 112, 114, 115,
118, 121, 124, 125, 126, 127, 132,
203, 204, 213, 226, 231, 240, 241
sums,12, 69, 70, 75–76, 85, 203, 204, 226,
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