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
David O.Tall — Advanced Mathematical Thinking
David O.Tall — Advanced Mathematical Thinking



Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Advanced Mathematical Thinking

Автор: David O.Tall

Аннотация:

Explores the psychology of thinking about post-secondary level mathematics, suggesting that the way it is taught does not correspond to the way it is learned. Addressed to mathematicians and educators in mathematics, considers the nature and cognitive theory of advanced mathematical thinking, and research into its teaching and learning in such areas as functions, calculus, and the Cantorial theory.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 291

Добавлена в каталог: 05.09.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
Hanna, G.      23 54—61 162 254
Hardy, T.      19
Harel, G.      12 31 37 63 82—93 142 255
Hart, K.M.      8
Hausdorff, F.      43 89
Heid, K.      237 238
Heller, J.L.      118
Helplessness      152
Henle, J.M.      172
Hermite, C.      13 253
Hersh, R.      44 146 149
Hess, P.      201 203
Heuristics      132 137 220
Hierarchy of concepts      256
Hilbert, D.      5 146 149 162 200 208
Hippocrates of Chios      159
Historical texts      138
History of analysis      168
Hodgson, B.R.      235
Hoffman, K.M.      29
Homotopy group      106
Horizontal growth of knowledge      83
Hubbard, J.H.      193 239
Humanistic mathematics movement      149
Hyperreal numbers      163
Illumination      50
Inbar, S.      147
Inconsistencies in comparing infinite quantities      204
Inconsistencies, raising students' awareness of      206—207
Induction, mathematical      38
Infinitely large and infinitely small      160—161
Infinitely small      160 168
Infinitesimal      6 160 161 198 199
Infinitesimal as 'banned' by Weierstrass      168
Infinitesimal as a carrier of paradoxes      169
Infinitesimal as an abreviation of an expression      169
Infinitesimal as defined by Cauchy      160
Infinitesimal in minds of mathematicians      162
Infinitesimal in non-standard analysis      162 168
Infinitesimal of Leibniz      161
Infinitesimal, decline in face of the limit notion      169
Infinitesimal, metaphysical haze      171
Infinitist      156
infinity      110 125 156 196 199—214
Infinity, actual      199 200
Infinity, actual, accepted by Galileo etc      200
Infinity, actual, rejected by Aristotle      200
Infinity, actual, rejected by Poincare      200
Infinity, actual, student experiences      202
Infinity, actual, student understanding      209—213
Infinity, cardinal      199 201 203
Infinity, comparing infinite quantities      199 203—205
Infinity, comparison between two infinite sets      199
Infinity, measuring      202 203
Infinity, non-standard      199
Infinity, ordinal      199
Infinity, potential      199 200 202
Infinity, student conceptions      201—205
Infinity, student difficulties      161
Infinity, teaching the Cantorian theory      199
Infinity, theoretical conceptions      200—201
INRC group      102
Institutionalization      135
Instrumental understanding      48
integral      85 151 167 176
Integral as a continuous linear form      175
Integral as a function      92
Integral as a process of measure      175 190
Integral as an inverse to differentiation      191
Integral as area under a curve      191
Integral as encapsulation and interiorization      105
Integral, Riemann      227
Integral, student conceptions      175
Integration      107 147 173 174
Integration in terms of the primitive      173
Integration in terms of the Riemann sum      173
Integration operation      82
Integration, algorithms      174
Intellectual development      100
Intelligent behaviour      131
Interiorization      103 104 106 113 143
Interiorization of a statement      115
Interiorization of actions      100 101 107 111 113 117
Intermediate Value Theorem      163 257
International Commission for Mathematical Instruction      170
Intuiting      40 41
Intuition      13—14 40 125 132 154
Intuition in mathematical creativity      47
Intuition in research using the computer      231
Intuition of actual infinity      201
Intuition of infinity      199—214
Intuition of infinity, origins in student experience      207
Intuition of infinity, via experiences of comparative size      202
Intuition, criteria for comparing infinite quantities      203—205
Intuition, developed with computer graphics      232
Intuition, primary      14
Intuition, primary, effects on thinking processes      207
Intuition, secondary      14 203 205
Intuitionism      55
Intuitionist school      54
Irrationality of $\sqrt{2}$      217
ISETL      242 244—248
Isomorphism      119
Isomorphism between vector spaces      82
Iterated limit      86
Iteration      114
Jacobian matrix      173 180 186
Janvier, C.      147
jargon      109
Jeeves, J.      15
Jensen, R.      144
Jordan's Theorem      146
Jordan, M.      48
Jurgens, H.      29
Jurin, J.      161
Kane, M.J.      141
Kantscluetsch, H.      38
Kaput, J.J.      31 39 41 63 82—93 255
Karplus, R.      147
Keisler, H.J.      172 238
Kepler, J.      10
King      151
Kitcher, P.      56
Klein, F.      14 17
Kleinberg, E.M.      172
Kleiner, I.      146
Kline, M.      141
Kline, W.      141
Kocak, H.      193 232
Kolata, G.      233
Kronecker, L.      4 5
Krutetskii, V.A.      146
L'Hospital, Marquis de      168
Laborde, C.      225
Lagrange, analysis without limits or infinitesimals      169
Lagrange, J.L.      161 163
Lakatos, I.      35 56
Lander, L.J.      232
Lane, K.D.      235
Laurent, H.      171
Learning difficulties in algebra      144
Learning theories and their deficiencies      142—144
Legrand, M.      19 137 191 216
Lehman, D.R.      141
Leibniz, G.W.      10 91 161 168 169
Leibniz, G.W., definition of tangent      174
Leibniz, G.W., notation for calculus      170
Leinhardt, G.      148
Lempert, R.O.      141
Leron, U.      19 41 216 220 221 223
Levels of understanding      143
Lewin, P.      82 143
LIMIT      106 125 134 154
Limit absence in Greek mathematics      160
Limit as a barrier      155
Limit as a concept      156
Limit as a formal definition      153
Limit as a procept      255
Limit as a process      156
Limit as being impassible      154
Limit as the basis for calculus      168
Limit in epsilon-delta terms      162
Limit in integration      105
Limit in the derivative concept      17
Limit is it attained?      161—162
Limit of a function      84 85 167
Limit of a sequence      73 78 167 177
Limit of a series      166
Limit of a staircase      163
Limit of polygons as a circle      159
Limit of secants      76
Limit, colloquial meaning      154
Limit, conceptual difficulty      178 188
Limit, conflicts in      134 176
Limit, defined as unencapsulated process      163
Limit, double      86
Limit, dynamic      155
Limit, generic      10 162 164
Limit, given by operations      153
Limit, iterated      86
Limit, metaphysical aspect      161
Limit, mixed      155
Limit, monotonic      155
Limit, obstacles in history      159
Limit, static      155
Limit, stationary      155
Limits      153—166
Linear function as conceptual entity      90
Linear functional      109 150
Linear transformation      150
Lisp      242
Local approximation      170
Local straightuess      136 187 238
Logic schema      111—113
Logical thinking      103
Logicism      55 56
Logicist school      54
Logico-mathematical thinking      100
LOGO      242
Lorenz, E.      232
MacLane, S.      50 82 141
Major, R.      150
Manin, Y.      59
Maple      235 236
Martin, G.      201 203
Maslow, A.H.      58
Masochism      232
Mason, A.      27 32 146
Mason, J.      18 20 25 37 41 138
Mathematica      28 236 242
Mathematical content      128
Mathematical gazette      171
Mathematical induction      102 106 109 110—113 120 123 139 See
Mathematical induction as a process      110
Mathematical induction, encapsulated as an object      110
Mathematical minds      4 63
Mathematical phobics      148
Mathematical practice      56
Mathematical Reviews      59
Mathematical theory structure of      46
Matrix      82 84 91 104
McCloakey, M.      205
Mean value theorem      218
Meaning of calculus concepts      237
Measure theory      167
Melamed, U.      201 214
Menis, Y.      241
Mental reconstruction      9
Meta-mathematical instruction      138
Meta-mathematical knowledge      131 138
Meta-mathematical reflection      136—138
Meta-mathematics      138
Metaphysical aspect of limit      161
Metaphysics of infinity      169
Method of exhaustion      168
Metric for aesthetics      151
Misconceptions      27 236
Misconceptions about "getting close", "growing large", etc      156
Misconceptions in learning about limits      164
Misconceptions of a function      74
Misconceptions of a limit of a sequence      79
Misconceptions of a tangent      76
Misconceptions of a variable      145
Modelling      34
Models of learning      142
modus ponens      113
Monadic number      221
Moore, R.L.      137
Movshovitz-Hadar, N.      216—218
Muir, A.      42
Multiple embodiment      141
Multiple embodiment, (picture, graph, formula)      189
Multiplication as addition of additions      100
Mundy, J.      147
Munroe, M.E.      86
Mutstion, mathematical      49
Nelson, E.      172
Nering      92
Newton, I.      56 160 168 169
Nicholas of Cusa      10
Nisbett, R.E.      141
Non-standard analysis      6 172 187 196—198 202
Non-Standard Analysis (Robinson)      172
Non-standard analysis, its weak impact on education      172—198
Notation      88 148—151 152
Notation as substitute for a concept      88 93
Notation in forming conceptual entities      88—91 93
Notation system      89
Notation to encapsulate entities      90
Notation to name a concept      89
Notation, elaborated      88 91 93
Notation, f(x) for a function      149
Notation, graphical      90
Notation, tacit      88 93
NUMBER      100 106
Number as concept      253
Number as process      253
Number, cardinal      200 202
Number, cardinal number of set of reals      212
Number, hyperreal      202
Number, infinite measuring      202
Number, monadic      221
Number, ordinal      200
Number, triadic      221
Numerical analysis      241
Numerical methods, used to solve problems      131
Object      102 106
Object-pivot in structural proof      221
Object-valued operator      83 87 93
Obstacle      9—11 166 175
Obstacle in learning calculus/analysis      196
Obstacle to construction of formal concepts      195
Obstacle, cognitive      11 21 165
Obstacle, conceptual      133 153
Obstacle, didactical      158
Obstacle, epistemological      103 134 158 162
Obstacle, epistemological, didactically transmitted      163—164
Obstacle, epistemological, important characteristics      158
Obstacle, epistemological, inability to overcome      165
Obstacle, genetic      158
1 2 3 4 5
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2024
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте