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

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

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
Abel, N.H.      35
abstracting      36—38 41
Abstracting, relationships with representing      38—39
Abstraction      11—12 36 37 97 98 132 139 144 148—151 217
Abstraction as concept      11
Abstraction as process      11
Abstraction of properties      129
Abstraction, empirical      97 99 121
Abstraction, generic      12 13
Abstraction, processes in      34
Abstraction, pseudo-empirical      97 99
Abstraction, reflective      13 21 95—124 134 253
Abstraction, using a generic organizer      187
Accommodation      9 103
Acquisition of knowledge      132 133
Acquisition of specific concepts      134
Adler, C.      140
Advanced mathematical thinking as a process      26
Advanced mathematical thinking processes      25—41
Advanced mathematical thinking, differences from elementary mathematical thinking      20 26 127 133
Advanced mathematical thinking, full cycle of      42 132 136 252 259
Advanced mathematical thinking, Psychology of      3—22
Advanced mathematical thinking, taught as a finished theory      215
Affine approximation      173
Algebra      220
Algebra, learning difficulties      144
Algebraic permanence, principle of      10
Algorithm      5 43 61 104 137 163 193
Algorithm as a replacement for proof      186
Algorithm to solve a problem      125 131
Algorithm, algebraic differentiation      180
Algorithm, premature algebraic use      186
Algorithm, procedures in analysis      186
Algorithmisation      197
Alibert, D.      19 41 126 136 180 191 215—230 258
Analysis      167—198
Analysis of knowledge      15
Analysis of several variables      167
Analysis, arithmetization of      168
Analysis, complex      167
Analysis, constructive      5
Analysis, epistemological      118
Analysis, functional      167 168 170
Analysis, mathematical      125 153
Analysis, non-standard      6 172 187 196 197 202
Analysis, real      131
Analysis, Weierstrassian      162
Analytic thinking      147
Anton, H.      92
Anxiety      148—152
APL      242
Appel, K.      16 233
Appollonins of Pergs      174
Approximation in reasoning      182—183
Arbitrarily small      162
Arcavi, A.      32 37 142 145
Archimedes' axiom      256
Aristotle      200
Arithmetization of analysis      168
Arithmetization of mathematics      146
Artigue, M.      41 125 135 167—198 258
Assessment      130
Assimilation      9
Assimilation, generalizing      102
Athens, Georgia      144
Atiyah, M.F.      231
Attack phase of problem-solving      18—20
Attainment, variation in      131
Ausubel, D.P.      8
Authier, H.      180
Axiom of Choice      163
Axiomatic method      54
Ayers, T.      82 83 103 104 117 118 242
Bachelard, G.      134 154 158
Balacheff, N.      215 225
Ballistics      168
Barrier to advanced mathematical thinking      129
Barrier(limit)      155
BASIC      241 242
Bautier, E.      131
Beberman, M.      140
Begle, E.      140
Behaviourist psychology      7
Beke, E.      170 171
Ben-Chaim, D.      148
Ben-Gurion University      149
Berkeley, G.      169
Beth, E.W.      82 95 97 99
Bieberbach's conjecture      233
Biggs J.      8
Biological development      100
Birkhoff, G.D.      151
Bishop, A.      225
Bishop, E.      5 172
Blackett, N.      148
Blancmange function      188
Boas, R.      152
Bolzano, B.      200 208
Borasi, R.      201
Boschet, F.      131 132
Bourbaki      16 54 98 140 141 149
Boyer, C.B.      160 168
Bransford, J.D.      25
Breuer, S.      29
Brousseau, G.      133 134 159 224
Brown, A.      25
Brown, A.L.      141
Bruckheimer, M.      33 41
Buck, R.C.      141
Built-in knowledge generator      255
Bulletin of the American Mathematical Society      172
Cajori, F.      91 161
Calculus      8 16 27 105 107 142 147 148 153 160 161 163 165 220
Calculus, based on limits      169
Calculus, history of      168—198
Calculus, infinitesimal      168
Calculus, introduction into secondary education      170
Calculus, its metaphysical difficulties      161
Calculus, rigorously based on infinitesimals      172
Calculus, supplemented by programming in BASIC      241
Calculus, using graphic and symbol manipulating software      237
Calgary, Canada      144
Cambridge Conference      140
Campbell, R.      30
Campione, J.C.      25
Cantor — Bernstein theorem      230
Cantor, G.      4—6 200 201 208 214
Cantorian set theory      199 205 207 208 212
Cantorian set theory, constructing intuitive background      203
Cardinality of sets      105
Carter, H.C.      141
Case, R.      141
Category theory      98
Cauchy sequence      168
Cauchy, A.L.      10 35 56 129 160—162 168 169
Celestial mechanics      168
Cesaro's lemma      129
Chaos theory      232
Char, B.W.      235
checking      40 41
Cheshire, F.D.      241
Chunking complex ideas      88 252
Cipra, B.      148
Clark, C.      150
Clement, J.      122 205 214
Clements, M.A.      39 146 253
Cobb, P.      82
Codidactic situation      226
Cognitive characteristics of students      131
Cognitive conflict      134 206 236
Cognitive development      3 7—8
Cognitive mechanisms in learning      132
Cognitive obstacles      9—11 21 158—159 164 165 199 256
Cognitive re-construction      9 114 136 159 164
Cognitive root      136
Cognitive theory      63
Cohen, L.      141
Collis, K.      8
Commission Internationale, pour l'Enseignement de Mathematiques      170
Commission Internationale, pour l'Enseignement des Mathematiques      171
Commutativity of addition      100
Comparison of infinite quantities      203
Completeness axiom      6 196
Complex analysis      167
Complex number      5
complexity      151
Complexity of analysis      163
Complexity of function concept      140
Complexity, encountered by students      131 139
Comprehension of complex concepts      83
Comprehension of object-valued operators      86—88
Comprehension of point-wise operators      84
Compression of ideas      35
Computer      126
Computer algebra system      235
Computer and the need for finite algorithms      163
Computer as an experimental tool      29 166 189
Computer as environment for exploration of ideas      238—240
Computer for conceptual development      237
Computer for implementing processes      123
Computer for linking representations      33
Computer for programming      197 241—248
Computer for providing concrete representations      104 187
Computer for visualizing differential equations      193 239
Computer for visualizing graphic representations      193 232
Computer generated experiments      232
Computer in advanced mathematical thinking      231—248
Computer in mathematics education      234—235
Computer in mathematics research      231—234
Computer to construct solution of a differential equation      239
Computer to perform algorithms      236
Computer, aversion displayed by teaching staff      241
Computer, didactic advantages in analysis      197
Computer, used in mathematical proof      233
Concept acquisition      6
Concept definition      6—7 21 70—73 103 122 125 130 145 196—198
Concept definition in teaching and learning      65—80
Concept definition of a limit      156
Concept definition, operational deficiency      197
Concept definition, theory and practice      69
Concept formation      69
Concept formation, long term processes      71
Concept frame      68
Concept image      6—7 14 17 21 68—73 76 78 83 103 122 123 125 127 134 145 166 196—198
Concept image in geometry      134
Concept image of a function      74
Concept image of a function as a graph      146
Concept image of a limit      155 156
Concept image of a limit of a sequence      78 164
Concept image of a limit of a series      166
Concept image of a tangent      75—78 174—175
Concept image of continuity      156—158
Concept image of derivative      175 188
Concept image of infinity      156 199
Concept image of rigorous proof      197
Concept image, changing      70
Concept image, construction compatible with formal mathematics      187
Concept image, evoked      68 73 83 144
Concept image, evoked of a limit      155
Concept image, theory and practice      69
Concept image, three illustrations      73
Concept image, weakness of geometric image of differential      184
Conceptual entities      21 82 82—93 134 143 150 255
Conceptual entities and symbolism      88
Conceptual entities as aids to focus      88
Conceptual entities, construction of      83
Conceptual entities, three roles      83
Conceptual obstacles      133 153 251
Conceptualisation      197
Concrete operations      8
Concrete representations      38
Condensing power of creativity      50
Conflict      129 155
Conflict between actual infinity and finite experiences      201 205
Conflict between concept image and definition      125 158
Conflict between different student conceptions      175
Conflict between different theoretical paradigms      203
Conflict between differential and derivative      169—171
Conflict between infinity in limits and set theory      125 203
Conflict between limit as a process and its definition      156
Conflict between mathematics and cognition      65
Conflict between previous experience and formal theory      199 205
Conflict between secondary intuitions and primitive convictions      203
Conflict between spontaneous conceptions and definitions      158 196
Conflict between two conceptions of a differential      185
Conflict in comprehending cardinal infinity      206
Conflict in learning continuity      134
Conflict in learning limits      134 164
Conflict with infinity      199 204
Conflict, cognitive      134 206 236
Conflict, concerning limits and infinity      156
Conflict, lack of awareness of      180
Confusion in first year university      129
Conjecture      132 136 191 224—225 227 229 252 257 258
Constructivism      224
Constructivist psychology      7
Continuity      156—158 167
Continuity, conceptual difficulties      178
Continuous function, definition of Cauchy      160
Convergence of sequences and series      129
Convergence of series      159
Convergence, via epsilon-delta methods      129
Convincing      20 130
Coordination      103 104 106 114 143
Coordination of actions      97 99 101
Coordination of function schema      113
Coordination of processes      101 107 113 115 119
Coordination of quantifications      116
Coordination of schemas      104
Cornu, B.      9 17 41 103 122 125 134 153—166 177 255 258
Coset      87
Counter-example      226
Counter-example, generated by computer      232
Cours d'analyse (Cauchy)      160
Cramer, G., definition of tangent      174
Creative activities, absent in students      132
Creativity      21 42—53 257
Creativity, a tentative definition      46
Creativity, characteristics of      49
Creativity, fallibility      52
Creativity, ingredients      47
Creativity, motive power      47
Creativity, results of      50
Creativity, stages of development      42
Curriculum design      17 165
Cybernetic environment      236
D'Alembert, definition of tangent      174
D'Alembert, J.L.      160—162 169
D'Hallum, C.      189
Dalen, D.      See "Van Dalen D."
Dauben, J.      207
Davis, G.      82
Davis, P.J.      44 56 57 59 146 148
Davis, R.B.      27 68 73 78 94 164
de Branges, L.      233
Debating forum      56
Decapsulation      119
Dedekind cut      168
Dedekind, J.W.R.      200
Deep-end principle      15
1 2 3 4 5
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте