LEADER 04191nam  2200625 a 450 
001 9910780040503321
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(Au-PeEL)EBL3035371
035   $a(CaPaEBR)ebr10046992
035   $a(CaONFJC)MIL20754
035   $a(OCoLC)923695717
035   $a(MiAaPQ)EBC3035371
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
615  0$aMathematics$xStudy and teaching.
615  0$aMathematics$xPsychological aspects.
676   $a510/.71
701   $aTall$b David Orme$059114
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910780040503321
996   $aAdvanced mathematical thinking$93842327
997   $aUNINA