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| Mason J., Burton B., Stacey K. — Thinking mathematically |
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| Предметный указатель |
Analogy and Mulling 140
Analogy, form of generalizing 86—87 89
Analogy, modifying question 124
Analogy, question acting as 173
Arithmagons 187
Atmosphere of mathematical thinking 176
Attack 29—42
Attack and monitor 133
Attack, conjecturing 71
Attack, justifying 105
Awareness of monitor's roles 132
Bee geneology 101—103 104
Being sceptical 145—7
Being sceptical and checking 146
Being sceptical to confirm insight 146
Belief and disbelief 7
Belief in pattern 11
Black friday 188
booklets 188
Cartesian chase 189
Checking conjectures 105
Checking, being sceptical 146
Chessboard squares 20—24 36 43 45 46 57 95 146
Circle and spots 91 111 129 146
classifying see “Specializing systematically”
Classifying information 35
Clocked 190
Coin slide 190
Confidence, cummulative effect of 164
Confidence, gained by specializing 34
Confidence, importance of 9 176
Confidence, sources of 162
Conjecturing and monitor 133
Conjecturing as process 11 30 171 178
Conjecturing distinct from hidden assumptions 114
Conjecturing, backbone of resolution 75
Conjecturing, challenging 110 170—179
Conjecturing, checking 105
Conjecturing, cyclic nature 77—78 84
Conjecturing, distrusting 110
Conjecturing, fixation 90
Conjecturing, how it arises 85
Conjecturing, justifying 105
Conjecturing, leading to sense of question 181
Conjecturing, recognizing pattern 10 89
Consecutive sums 76—85 87 88 89—90 120 125 140 142 146
Contemplating 147
Contemplating and growth of monitor 132
Contemplating as supreme generalizing 147
Convincing as process 171 172
Convincing based on structure 100—105
Convincing, emphasis on WHY 18 100
Convincing, leading to sense of questions 181
Convincing, self, friend, enemy 106—109
Creepy crawlies 48—50 137
Cube painting 191
Cubes cubed 40—41
Cut-away 121
Cycling digits 191
Desert crossing 192
Diagonals of a rectangle 192
Die rolling 193
Distilling and mulling 120
Distilling, good example of 121
Distilling, related activities 121
Divisibility 193
Eggs 194
Emotional snapshots as essence of monitor 134
Emotional snapshots for recalling key moments 135 46
Entry 31
Entry and monitor 133
Entry as response to STUCK 55
Entry, demands specializing 181
Entry, what can I INTRODUCE? 32 39—42
Entry, what do I KNOW? 32 33—36 55—57
Entry, what do I WANT? 32 36—39 55—57
Envelopes 38—39 137
Eureka sequences 111—112 114
Experience, learning from 131
Fare is fair 194
Faulty bricks 194—195
Fifteen 88 90 99 137
Fifteen, analogy with magic squares 124
Finger multiplication 195
Fixation in conjecturing 90
Fixation, hidden assumptions 126—127
Fixation, upsetting set 127
Flipping cups 195
Folding polygons 196
Fractious 37—38 141
Fred and frank 196
Full-length mirrors 197
Furniture 74—75 98—99 124 139 141 143
Generalizing and analogy 124 86 89
Generalizing and contemplating 147
Generalizing and monitor 133
Generalizing and mulling 140
Generalizing and specializing 10
Generalizing as removing constraints 125
Generalizing to produce subgoals 154
Generalizing to understand 17 138
Generalizing to wider context 47
Generalizing, artfully 18
Generalizing, increasing powers of 89
Generalizing, methods 18
Generalizing, process of 9—11 24—25 171 180 181
Generalizing, testing 11
Getting involved 138—140
Getting involved and RUBRIC writing 139
Getting involved and specializing 138
Getting involved and systematic specializing 139
getting started 136—138
Getting started, blocks to 137
Glaeser's dominoes 197
Goldbach's conjecture 71 95 105
Gossips 198
Half life 198—199
Half moon 199
handshakes 199—200
Helix of mathematical thinking 179—181
Hidden Assumptions 114 126
Hidden Assumptions, distinct from conjectures 114
Hundred squares 200
Information classifying 35
Information organizing 35
Information sorting 35
Ins and outs 200
Insight 143—145
Insight, being sceptical about 146
Insight, linking KNOW and WANT 144
Insight, partial 146
Insight, preparing for 123
Insight, writing down 2
Internal enemy see "Internal monitor"
Internal enemy as sceptic 128
Internal enemy, challenging conjectures 110
Internal enemy, convincing 107—109
Internal enemy, developing 109
Internal enemy, functioning of 106
Internal monitor and emotional snapshots 134
Internal monitor and keeping going 142
Internal monitor and mulling 141
Internal monitor as internal tutor 131
Internal monitor, growth with contemplating 147
Internal monitor, roles of 132—134 178
Internal monitor, to overcome stuck 172
Iterates 95 106 112—114 134 175
Jacobean locks 201
jobs 202
justifying 100 see "Structure"
| Justifying a conjecture 105—109
Kathy’s coins 202
Keeping going 141—143
Keeping going and internal monitor 142 144
Keeping going with particular plan 143
Key ideas 45—46 see "REVIEW"
Key ideas and reflecting 55 131
Key ideas as aid when stuck 55
Key ideas associated with emotions 171
Key ideas while reviewing 121
Key ideas, noticing and recording 135
Key moments 45—46
Key moments and internal monitor 134
Key moments and reflecting 55 131 135
Key moments as aid when stuck 55
Key moments as emotional snapshots 135
Key moments, clear and reliable 134—135
Key moments, noticing and recording 135
Key moments, photographing 46
Knotted 203
know 33—36
KNOW, extracting information 36
KNOW, gap with WANT 57 175
KNOW, insight links to WANT 144
KNOW, role in entry 32
KNOW, value of not knowing difficulties 62
Ladies luncheon 35—39 137
Leap birthday 203
Leapfrogs 63—67
Liouvlle 203
manipulating see "Specializing"
Manipulating as part of helix 179—181
Manipulating physical and mathematical objects 5 9 156
Manipulating to explore question 180
Manipulating, mentally 41 156
Manipulating, provoking a gap 181
Matches1 96—97 100 137
Matches2 97—98 100 137
math boxes 204
Medieval eggs 204
Mental screen extending 41
Milk cartons 205
Milkcrate 205
Monitor see "Internal monitor" "Internal
Moon struck 206
More consecutive sums 206
More furniture 207—208
Mulling 140—141
Mulling and analogy 140
Mulling and distilling 120
Mulling and generalizing 140
Mulling and monitor 141
Mulling and specializing 140
Mulling, doing and not doing 123
Multi-facets 128—129
Nine dots 126 129
Not cricket 207
Notation 39
Noticing key ideas and key moments 135
Noticing questions 153 160
Nullarbor plain 207
Number spirals 156—157 160
Odd divisors 208
One sum 208
organizing see "Specializing systematically"
Organizing information 39
Painted tyres 73—74 105 110 144 173 174
Palindromes 5—9 11 34 44—46 75 101 105 139 178
Pancakes 209
Paper bands 158 160
Paper knot 209
Paper strip 4 34 37 39—40 47 140
Patchwork 12—18 37 72 101 106 108 144
Pattern and generalizing 10
Pattern in special cases 2
Pattern, belief in 11 85
Pattern, conjecturing 89
Pattern, making space for 57
Pattern, seeking structure 103
Personal tutor see "Internal enemy"
Personal tutor, developing 46 56
Polya strikes out 210
Polygonal numbers 210—211
Quad-cut triangles 211
Questions see “Index of questions”
Questions as attitude 159 161 162
Questions as gap inside 175
Questions, acting as analogy 173
Questions, noticing 153 160
Questions, posed by others 151
Questions, posing own 48 153
Questions, sources of 32
Questions, spectrum of 153
Questions, subquestions 154
Quick and toasty 41 105 139
Quick and toasty, analogy with paper strip 124
recipes 212
recording see "RUBRIC" "Specializing"
Recording as opportunity to learn 18
Recording diagrams 39
Recording feelings 11—12 57
Recording ideas 11—12 57
Recording insights 2
Recording mathematical experience 11—12
Recording symbols 37
Recording, restating in own words 34
Recording, stimulating resonances 33
Recording, systematically 8
Rectangles on a chessboard 46—47
Reflecting on key moments and ideas 131 133 135
Reflecting on resolutions 134
Reflecting without embroidery 134—135
Reflecting without judgement 134—135
Reflecting, assisted by RUBRIC 135
Reflecting, requirements for 134
Reflecting, standing back from details 3
Repaint 213
Representation 39
Representation by diagram 140
Representation by physical object 5 8 156
Reversals 213
review 29 43—50
REVIEW and internal monitor 133
REVIEW, CHECK 43 44
REVIEW, EXTEND 43—44 46
REVIEW, key ideas 122
REVIEW, opportunity for 181
REVIEW, REFLECT 43—44 46
REVIEW, to appreciate a resolution 17
REVIEW, value of 173
Right angles 214
Rolling coins 214
RUBRIC 18—20 24 86 171 see
RUBRIC and getting involved 139
RUBRIC and internal monitor 133
RUBRIC as framework 24
RUBRIC, access to past experiences 33
RUBRIC, assisting reflection 135
RUBRIC, relation to review 122
RUBRIC, stimulus to resonances 33
RUBRIC, why recommended 55 57
Seesaw 155—156 160
Sense of, as part of helix 179—181
Sense of, pattern 9 180
Sense of, question 5 34
SEQUENCE 215
shadows 215
Sorting see "Specializing systematically"
Sorting information 35
Specializing and analogy 124
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