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1994 Book DidacticsOfMathematicsAsAScien
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Studies in Mathematics, 23, 213-230.
D'Ambrosio, U. (1991). Several dimensions of science education. A Latin American per- spective. Santiago de Chile: REDUC/CIDE. D'Ambrosio, U. (1992). Ethnomathematics: A research program on the history and philos- ophy of mathematics with pedagogical implications. Notices of the American Mathematical Society, 39(10), 1183-1185. D'Ambrosio, U. (1992). The history of mathematics and ethnomathematics. Impact of Science on Society, no. 160, 369-377. Flaubert, G. (1987). Bouvard et Pecuchet with the dictionary of received ideas. London: Penguin. (Original work published 1881) Gerdes, P. (1986). How to recognize hidden geometrical thinking? For the Learning of Mathematics, 5(1), 15 - 20. Gore, A. (1993). Earth in the balance. New York: A Plume Book. Knijnik, C. (in press). An ethnomathematical approach in mathematical education: A mat- ter of political power. For the Learning of Mathematics. Musil, R. (1953-1954). The man without qualities (Vols. 1-2). New York: Putnam. (Original work published 1952) Nietzsche, F. (1952). The birth of tragedy and the genealogy of morals. New York: Vintage. (Original work published 1872) Pompeu, G., Jr. (1992). Bringing ethnomathematics into the school curriculum: An investi- gation of teacher's attitude and pupil's learning. Doctoral dissertation, University of Cambridge, England. Reich, R. B. (1992). The work of nations, New York: Vintage. Saxe, G. (1991). Culture and cognitive development: Studies in mathematical understand- ing. Hillsdale, NJ: Erlbaum. CULTURAL FRAMING Suzuki, S. (1969). Nurtured by love: A new approach to education. New York: Exposition Press. Thom, R. (1990). Apologie du logos. Paris: Hachette. Weisskopf, V. (1992). Interview in Report of the Fifth Dialogue on the Preservation of Creation. Caux, Switzerland, 16-18 August 1992. Wiener, N. (1948). Cybernetics. Cambridge, MA: The Technology Press. Wigginton, E. (1988). Sometimes a shining moment. Garden City, NY: Anchor Press/Doubleday. 455 LIST OF AUTHORS Artigue, Prof. Dr. Michèle Université Paris 7 UFR de Mathématiques 2, Place du Jussieu, Tour 56 75251 Paris CEDEX 05 France artigue@mathp7.jussieu.fr Bartolini Bussi, Prof. Dr. Maria Universita degli Studi di Modena Dipartimento di Matematica pura ed applicata Via Campi, 213/B 41 100 Modena Italy dipmat@jmovx2.cineca.it Bauersfeld, Prof. Dr. Heinrich Universität Bielefeld IDM Postfach 100 131 33501 Bielefeld Germany hbauersf@post.uni-bielefeld.de Biehler, Dr. Rolf Universität Bielefeld IDM Postfach 100 131 33501 Bielefeld Germany rolf.biehler@post.uni-bielefeld.de Bromme, Prof. Dr. Rainer Johann Wolfgang Goethe-Universität Institut für Pädagogische Psychologie Postfach 111 932 60054 Frankfurt Germany bromme@paed.psych.uni-frankfurt.de Cooney, Prof. Dr. Thomas J. University of Georgia College of Education 105, Alderhold Hall Athens GA 30602 USA tcooney@uga.bitnet D' Ambrosio, Prof. Dr. Ubiratan Universidade Estadual de Campinas IMECC-UNICAMP Caixa Postal 1170 13.100 Campinas S.P. Brasil Dreyfus, Prof. Dr. Tommy Center for Technological Education P.O. Box 305 Holon 58102 Israel tommy@ilctehol.bitnet Ernest, Dr. Paul University of Exeter School of Education Heavitree Road Exeter EX1 2LU England ernest.p@exeter.ac.uk Fey, Prof. Dr. James T. University of Maryland Department of Curriculum and Instruction, Center for Mathematics Education College Park, MD 20472 USA 203196@umd.bitnet Fischbein, Prof. Dr. E. Tel-Aviv University School of Education Ramat-Aviv 6 99 78 Tel Aviv Israel Hanna, Prof. Dr. Gila Ontario Institute for Studies in Education Dept. of Measurement, Evaluation, and Computer Applications 252 Bloor Street West Toronto Ontario M5S 1V6 Canada g_hanna@utoroise 457 458 LIST OF AUTHORS Holland, Prof. Dr. Gerhard Justus-Liebig-Universität FB 12: Mathematik Institut für Didaktik der Mathematik Karl-Glöckner-Strasse 21 C 35394 Gießen Germany Jahnke, PD Dr. Hans Niels Universität Bielefeld IDM Postfach 100 131 33501 Bielefeld Germany njahnke@post.uni-bielefeld.de Kaput, Prof. Dr. James J. Southeastern Massachusetts University 473 Chase Road North Dartmouth, MA 02747 USA jkaput@umassd.edu Kelly, Dr. Anthony E. Graduate School of Education Rutgers The State University of New Jersey 10 Seminary Pl New Brunswick NJ 08903 USA akelly@zodiac.rutgers.edu Laborde, Prof. Dr. Colette LSDD Tour IMAG U.J. Fourier B.P.Nº 53 X 38401 Grenoble CEDEX France claborde@imag.fr Lesh, Prof. Dr. Richard Principal Research Scientist Educational Testing Service (MS 19T) Rosedale Road Princeton, NJ 08541 USA dlesh @rosedale.org Lompscher, Prof. Dr. Joachim Waldstraße 85 13 156 Berlin Germany Lorenz, PD Dr. Jens Holger Universität Bielefeld IDM Postfach 100 131 33501 Bielefeld Germany jens.lorenz@post.uni-bielefeld.de Nicol, Dr. Cynthia University of British Columbia Faculty of Education 2125 Main Mall Vancouver B.C.V6T IZ4 Canada Niss, Prof. Dr. Mogens Roskilde University IMFUFA Postbox 260 4000 Roskilde Denmark niss@jane.ruc.dk Noss, Dr. Richard University of London Institute of Education Department of Mathematics, Statistics & Computing 20, Bedford Way London WC1H OAL England noss@ioe.ac.uk Otte, Prof. Dr. Michael Universität Bielefeld IDM Postfach 100 131 33501 Bielefeld Germany michael.otte@post.uni-bielefeld.de Pimm, Prof. Dr. David Walton Hall The Open University Milton Keynes MK7 6AA England d.j.pimm@open.ac.uk LIST OF AUTHORS 459 Robitaille, Prof. Dr. David F. University of British Columbia Faculty of Education 2125 Main Mall Vancouver B.C.V6T IZ4 Canada david_robitaille@unixq.ubc.ca Scholz, Prof. Dr. Roland W. Universität Bielefeld IDM Postfach 100 131 33501 Bielefeld Germany and ETH-Zürich Environmental Science: Natural and Social Science Interface ETH-Zentrum VOD C14 8092 Zürich Switzerland Seeger, Dr. Falk Universität Bielefeld IDM Postfach 100 131 33501 Bielefeld Germany fseeger@post.uni-bielefeld.de Steinbring, Dr. Heinz Universität Bielefeld IDM Postfach 100 131 33501 Bielefeld Germany heinz.steinbring@post.uni-bielefeld.de Steiner, Prof. Dr. Gerhard Universität Basel Institut für Psychologie Bernoullistraße 14 4056 Basel Switzerland Sträßer, Dr. Rudolf Universität Bielefeld IDM Postfach 100 131 33501 Bielefeld Germany rstraess@hrz.uni-bielefeld.de Sutherland, Dr. Rosamund University of London Institute of Education Department of Mathematics, Statistics & Computing 20, Bedford Way London WC1H OAL England teuerjs@ioe.ac.uk Tall, Prof. Dr. David University of Warwick Mathematics Education Research Centre Coventry CV4 7AL England seral @csv.warwick.ac.uk Tietze, Prof. Dr. Uwe-Peter Georg-August Universtät Seminar für Didaktik der Mathematik, der Chemie und der Physik Waldweg 26 37073 Göttingen Germany Usiskin, Prof. Dr. Zalman The University of Chicago Department of Education 5835 Kimbark Avenue Judd Hall Chicago, IL 60637 USA z-usiskin@uchicago.edu Vollrath, Prof. Dr. Hans-Joachim Universität Würzburg Lehrstuhl für Didaktik der Mathematik Am Hubland 97074 Würzburg Germany 460 Winkelmann, Dr. Bernard Universität Bielefeld IDM Postfach 100 131 33501 Bielefeld Germany bwinkelmann @erasmus-nov.hrz.uni- bielefeld.de LIST OF AUTHORS SUBJECT INDEX accomodation 124, 229, 231, 247, 346 action - direct action 205 - research 123 - systems 332, 382, 389 activity theory 118, 119, 124-128, 135, 265-268, 272, 345, 346 adaptation 59, 103, 105, 111-112, 231 advance organizer 195 algebra 76, 180, 181-184, 332, 382-384, 391-393 - learning 25, 252-257 algebraic - analysis 420-422, 424-427 - mathematical network 247-258 algorithms 226, 231, 235, 241, 288 Allgemeinbildung 377, 417-420 applications (of mathematics) 337, 344, 368-373, 384-385, 400, 420-426 - direct versus indirect 400, 419-420, 427 -oriented teaching 45, 50-52 arithmetic 81-83, 95, 113, 318-319 artificial intelligence and education 213- 214, 217, 221-222, 396 assessment 108, 112-113 -design 55, 59, 281 assimilation 124, 229, 247 authentic performance 285 authority 103, 109-111, 345 automatization 296 BASIC 172, 178-179, 181 beliefs 55-56, 58, 106-108 black box issue 208-209 BLOCKS MICROWORLD 193-194 CABRI Géomètre 185, 192, 387 calculators 18, 316, 321, 345 calculus 46-48, 50-52, 57, 195-196, 197-198, 205-206, 325, 332, 391- 394, case studies 92, 113, 400, 415-429 categorical perception 83 channel of communication 160 citizenship 376-377 classroom interaction 97-100, 121-132 cognitive - appropriateness 210 - conflict 127 - development 227 - principles 215 - psychology 225-226, 295 - science 134, 142-144, 221 - tools 201-210, 222 collaboration (collaborative) 148, 152, 153 collective student 85 collectivist perspectives 136, 137, 139 combinatorical school 420-422 communication 90, 92-94, 97, 345 - analysis of 69, 117 communicative competence 164, 167 comparative studies (international) 311, 402, 403-413 - critique of 311, 406 complementarity 121, 128, 130 computer tool 201-210 - didactically based tools 172, 189- 199, 207, 209-210 - mathematically based tools 206-207, 209-210 computers 20, 34, 153-154, 171-173, 179, 186, 345, 384-385, 387-393, 435 concept image 207 concepts 57, 61-68, 96-97, 370-371 - central 49-50, 62, 65 - choice of 63 - elementary mathematical 266-269 461 462 SUBJECT INDEX - evaluation of 62-64 - figural 242-243 - meaning of 68 - personal shaping of 68-69 - reflection on 62-64 - theoretical 353 - understanding of 66-67 conflict (conflicting situations, conflicting processes) 148, 149, 152, 156 connectionism 119, 124, 141-144 constraints (epistemological, cognitive, didactical) 32 construction of knowledge 147, 148, 191 constructivism 105, 111, 119, 124-128, 138, 229, 286, 340 - social constructivism 329, 335, 338, 342-347 cooperation 91-94, 151-152 coordinate (coordination) 149, 156 counting strategies 81-82 creativity 45, 68, 110, 191, 209 culture 60, 287, 341, 343, 399-402, 406, 412, 415-416, 426-428, 435, 438-439 curriculum 43, 45, 204, 207, 208-209, 328, 400 -development 10-11, 15-16, 25-26, 35-37, 41-44 - naturalness of 431 - social context of 23-25, 42-43, 399- 402, 417-420, 427-428, 431, 433- 435,439-440 data 120, 137, 388, 407, 410, 411 Davis and Hersh's philosophy 342 decalage 248 decimals 98-100, 318 democracy 376 developmental psychology 226 devolution of the problem 148, 151 diagrams 95-96, 204-205 dialogue 89, 92-93, 97-101, 345 didactical - appropriateness 207 - consequences (of different philosophies) 339-347 - engineering 29-30 - situation 28, 117, 122, 127 - system 29 - thinking 61-62 - transposition 10, 27-28, 328, 331, 401, 435, 440 - triangle 4, 117 didactics of mathematics 1, 2, 11, 16, 61-62, 213 DIENES' MULTIBASE BLOCKS 193- 194, 387 discourse analysis 120, 137, 152-155, 161-162 discussion 152-155 discovery learning 218 display systems 382 dynamical systems 31-37, 201-203 ecology of knowledge 28 economy 368, 372, 404, 415, 434, 435, 447-448 education 445 - elementary 118, 127, 140-141 educational style 217 elementarization 10-11, 15, 25, 44, 45, 46-48 elementary teachers 107 enactive manipulation 192-193 encapsulation (of process as object) 189- 190 epistemological - dilemma 94, 97, 99 - obstacle 127, 329 - triangle 96, 97, 99 epistemology 91-94, 327-328 equations 25 error analysis 294 ethnomathematics 401, 449-453 exactification 46-47 SUBJECT INDEX 463 EXCEL 181-184, 203-204 experience 81, 83, 379 experimenting 184-185, 191-194 expert 58, 73 -rule 331, 376 extra-mathematical 367, 369, 371 feminist perspective 309 force 167-168 formal components 288 formal mathematics 383-385 formalism (formalistic) 68, 109, 336, 352 formation of concepts and theories 46- 48, 67 fractions 94-95, 98-99 frame 345 functions 47, 63, 77-78, 113, 181-182, 184-185, 384, 387, 389-394 - theoretical 167-168 fundamental - idea 10, 45, 48-50 - situation 35 gender differences in achievement 293, 298 generative teaching 256-258 generic organizer 195-196 Geneva School 124, 126, 149, 154, 225, 247, 263-271 GEOMETER'S SKETCHPAD 192, 387 geometrical figure 243 geometry 266, 324-325, 355, 387 gifted students 297 goal formation 270-274 goals for mathematics education 42-43, 172-173,446 goals-means argument 43 GRAPHIC CALCULUS 195-197, 205, 207, 209 Grice's conversational maxims 166 group work 148, 151-155 growth of knowledge 189-190, 194, 198 hedge 166 hierarchy in mathematics 205, 339 history (of mathematics) 57, 66, 92, 327-330,, 341-342, 337, 382-383, 415-428 holistic 417 Humboldtian reforms 416-426 ICMI 1, 7, 225 identity - in mathematics 355-362 - of the societal subject 357-360 ideology 400-401, 415, 431-441 IDM 5, 6 imitation 129 immaterial technology 370 implementation problem 10, 52, 374 in-service training 56, 91, 106, 108, 111 individualism 352, 355, 358, 362 individualistic perspectives 133-134, 139 individuation 355-358 inert medium 380 information -processing 237, 292-294 - technology 372 insight 198-199, 227, 229 - external, analogue, specific 194-195 instructional strategies 265-271 intelligent tutorial systems 213-214 interactionism (social) 119, 137-139 interactive media 380, 381 interiorization 264-265, 364 internalization 124, 126, 264-265 International Association for the Evaluation of Educational Achievement (IEA) 311, 406-411, 412-413 intuition 227, 332, 254 -geometrical 226 464 SUBJECT INDEX intuitionism 340 invariance 49 invisibility of mathematics 331, 371-373 I-R-F sequence 162 journal writing 161 justification problem 9, 43, 45, 373 Kant's philosophy 419 Kitcher's philosophy 342 Klein's reforms 426-427 knowledge 189-190, 191, 194, 351-356, 358-361, 363, 364 - formal 352, 353, 355, 356, 358 - mathematical 89-94, 96-100 - of teachers 55-59, 73-86, 106-108, 214 - structure 250-252 - theoretical 59, 93, 96, 330, 360 Lakatos'philosophy 341-342 language of mathematics 159-169, 438 languaging/language 120, 136-137, 141, 159-160, 341, 345 learning 138 - by discovery 218 - environment 217-218 lesson preparation 75 limit (of a sequence) 64-66,237 linearity 49 linking (of representation) 388, 389 literacy 351, 354, 355, 360, 363, 369 - mathematical 318-320, 375 local straightness 195-196, 205 logic 328 LOGO 172, 177, 178, 179, 180-181, 208, 209, 217, 388 macro (in computer language) 177 macro/micro didactic choices 34 math-worlds 342 mathematical - competence 375 - discussion 160 - knowledge 89-94, 96-100, 453-454 - microworld 217-218, 222 - model 330, 369 - modeling 45, 49, 50-51, 330-332, 369 - qualifications 369 - structures 16-17 - systems 325 - thinking 227, 288 mathematics - as a discipline 367 - foundations of 328, 336, 340 - history 57, 66, 92, 327-330, 337, 341-342, 382-383, 351, 353 - pure 367-368, 402, 417-420 - raw material of 437 - register 159 - teacher 89-93, 97-101 - teaching 351, 353, 360, 422-435 mathematization, pattern of 49 meaning 80, 105, 352, 353, 357, 359, 360-363 - delineated 401,436,440 - inherent 401, 436, 437 - of concepts 68 - of mathematics 92-97, 99-101, 138, 141, 330 media 55, 226, 345 mental activities 263-265, 380-381 meta-commenting 164-166 metacognition 20, 328 metaknowledge 79, 328, 351, 354, 361 methodology 104-106, 118, 402, 404- 405 Michigan studies 411-412 microworld 191-192, 217-218, 222, 345 milieu 155-156 misconceptions 234, 239 modality 166 model-eliciting problems 284 SUBJECT INDEX 465 models 277-278, 389-392 - validation of 330, 369 modes of knowledge construction 190 multiple-linked representations 204, 389 multiplication 234 music 401, 435-437 naturalism 335-338 neohumanist educational philosophy 416-420 neuropsychology 293 new math 17, 24, 41, 44, 117-118, 328 NEWTON (computer program) 191 noosphere 29 notations 385-388 novelty versus familiarity 306 numeracy 369, 375 objectivity 103, 105 operation 247-256 operative action systems 383 observer (detached) 118, 122, 123 observer (participant) 122, 123 organizer - 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