Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Mason J., Burton B., Stacey K. — Thinking mathematically
Mason J., Burton B., Stacey K. — Thinking mathematically

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Thinking mathematically

Авторы: Mason J., Burton B., Stacey K.

Аннотация:

Every student doing a mathematics degree should read this book.' James Blowey, Durham University The ideas I encountered in Thinking Mathematically continue to influence the way in which I work today.' David J Wraith, National University of Ireland, Maynooth [This book] transformed my attitude to mathematics from apathy to delight' Nichola Clarke, Oxford University 'Thinking Mathematically has always been one of my favorite books. Expanded and updated, this version is a must for my bookshelf and should be for yours too.' Alan Schoenfeld, University of California, Berkeley


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1982

Количество страниц: 229

Добавлена в каталог: 23.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
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
1 2
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2019
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте