LEADER 04226nam 2200637 a 450 001 9910454672303321 005 20200520144314.0 010 $a1-280-20754-X 010 $a9786610207541 010 $a0-306-47203-1 024 7 $a10.1007/0-306-47203-1 035 $a(CKB)111056486601260 035 $a(EBL)3035371 035 $a(SSID)ssj0000097750 035 $a(PQKBManifestationID)11130874 035 $a(PQKBTitleCode)TC0000097750 035 $a(PQKBWorkID)10120816 035 $a(PQKB)10005269 035 $a(DE-He213)978-0-306-47203-9 035 $a(MiAaPQ)EBC3035371 035 $a(Au-PeEL)EBL3035371 035 $a(CaPaEBR)ebr10046992 035 $a(CaONFJC)MIL20754 035 $a(OCoLC)923695717 035 $a(EXLCZ)99111056486601260 100 $a19910816d1991 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aAdvanced mathematical thinking$b[electronic resource] /$fedited by David Tall 205 $a1st ed. 1991. 210 $aDordrecht ;$aBoston $cKluwer Academic Publishers$dc1991 215 $a1 online resource (310 p.) 225 1 $aMathematics education library ;$vv. 11 300 $aDescription based upon print version of record. 311 $a0-7923-1456-5 320 $aIncludes bibliographical references (p. 261-274) and index. 327 $aThe Psychology of Advanced Mathematical Thinking -- The Nature of Advanced Mathematical Thingking -- Advanced Mathematical Thinking Processes -- Mathematical Creativity -- Mathematical Proof -- Cognitive Theory of Advanced Mathematical Thinking -- The Role of Definitions in the Teaching and Learning of Mathematics -- The Role of Conceptual Entities and Their Symbols in Building Advanced Mathematical Concepts -- Reflective Abstraction in Advanced Mathematical Thinking -- Research into the Teaching and Learning of Advanced Mathematical Thinking -- Research in Teaching and Learning Mathematics at an Advanced Level -- Functions and Associated Learning Difficulties -- Limits -- Analysis -- The Role of Studients? Intuitions of Infinity in Teaching the Cantorian Theory -- Research on Mathematical Proof -- Advanced Mathematical Thinking and the Computer -- Epilogue -- Reflections. 330 $aAdvanced Mathematical Thinking has played a central role in the development of human civilization for over two millennia. Yet in all that time the serious study of the nature of advanced mathematical thinking ? what it is, how it functions in the minds of expert mathematicians, how it can be encouraged and improved in the developing minds of students ? has been limited to the reflections of a few significant individuals scattered throughout the history of mathematics. In the twentieth century the theory of mathematical education during the compulsory years of schooling to age 16 has developed its own body of empirical research, theory and practice. But the extensions of such theories to more advanced levels have only occurred in the last few years. In 1976 The International Group for the Psychology of Mathematics (known as PME) was formed and has met annually at different venues round the world to share research ideas. In 1985 a Working Group of PME was formed to focus on Advanced Mathematical Thinking with a major aim of producing this volume. The text begins with an introductory chapter on the psychology of advanced mathema- cal thinking, with the remaining chapters grouped under three headings: ? the nature of advanced mathematical thinking, ? cognitive theory, and ? reviews of the progress of cognitive research into different areas of advanced mathematics. 410 0$aMathematics education library ;$vv. 11. 606 $aMathematics$xStudy and teaching 606 $aMathematics$xPsychological aspects 608 $aElectronic books. 615 0$aMathematics$xStudy and teaching. 615 0$aMathematics$xPsychological aspects. 676 $a510/.71 701 $aTall$b David Orme$0931220 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910454672303321 996 $aAdvanced mathematical thinking$92094847 997 $aUNINA LEADER 01211nam 2200349Ia 450 001 996396414203316 005 20221108055918.0 035 $a(CKB)4330000000348133 035 $a(EEBO)2240962152 035 $a(OCoLC)12565789 035 $a(EXLCZ)994330000000348133 100 $a19850917d1693 uy | 101 0 $aeng 135 $aurbn||||a|bb| 200 12$aA sermon preached at Guild-Hall chapel, December the xi, 1692$b[electronic resource] $ebefore the Right Honourable the Lord Mayor, and Court of Aldermen /$fby W. Fleetwood .. 210 $aLondon $cPrinted for Thomas Newborough ...$d1693 215 $a[4], 5-29 p 300 $aHalf-title: Mr. Fleetwood's sermon before the Lord Mayor, &c. December xi, 1692. 300 $aReproduction of original in Cambridge University Library. 330 $aeebo-0021 606 $aSermons, English$y17th century 615 0$aSermons, English 700 $aFleetwood$b William$f1656-1723.$0745093 801 0$bEAA 801 1$bEAA 801 2$bm/c 801 2$bUMI 801 2$bWaOLN 906 $aBOOK 912 $a996396414203316 996 $aA sermon preached at Guild-Hall chapel, December the xi, 1692$92389191 997 $aUNISA