Research in Mathematics Education

  • Hans Niels Jahnke
  • Rolando Chuaqui
  • Gilles Lachaud
  • David Pimm
  • Gerald A. Goldin
  • Alan H. Schoenfeld
  • Elaine M. Bologna
  • Sadaharu Fujimori
  • Douglas E. Scott
  • Richard J. Shumway
  • George Booker
  • Jack Easley
  • Francois Pluvinage
  • R. W. Scholz
  • Leslie P. Steffe
  • Joan Yates
  • Annie Bessot
  • Leroy G. Callahan
  • Roy Hollands
  • Fredricka K. Reisman
  • Gert Schubring
  • Mahdi Abdeljaouad
  • Phillip Stanley Jones
  • Janine Rogalski
  • Gert Schubring
  • Derek Woodrow
  • Waclaw Zawadowski
  • Jeremy Kilpatrick
  • Horacio J. A. Rimoldi
  • Raymond Sumner
  • Ruth Rees
  • Karen C. Fuson
  • Shuntaro Sato
  • Claude Comiti
  • Thomas E. Kieran
  • Gerhard Steiner
  • Charles Taylor
  • A. P. French
  • Robert Karplus
  • Gerard Vergnaud
  • Edward Esty
  • Georges Glaeser
  • Heini Halbertstam
  • Yoshihiko Hashimoto
  • Thomas A. Romberg
  • Christine Keitel
  • B. Winklemann
  • Richard Lesh
  • Richard R. Skemp
  • Laurie Buxton
  • Nicolas Herscovics
  • Stanley J. Bezuszka
  • K. Hart

Abstract

The following is intended as an analysis of a specific conceptual change in mathematics during the early 19th century. From this some pedagogical conclusions are drawn. Analyzing a special example seems to be a more appropriate way of handling the relevance of historical and philosophical considerations for mathematical education than dealing with this question in general terms. My example refers to the fact that at the turn of the 19th century one began to distinguish more systematically between numbers and quantities than had been done before. The program of arithmetizing mathematics arose. Certainly this process had various causes. In the following I concentrate on one of these, namely, the relations of mathematics to experimental sciences.

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Copyright information

© Birkhäuser Boston, Inc. 1983

Authors and Affiliations

  • Hans Niels Jahnke
    • 1
  • Rolando Chuaqui
    • 2
  • Gilles Lachaud
    • 3
  • David Pimm
    • 4
  • Gerald A. Goldin
    • 5
  • Alan H. Schoenfeld
    • 6
  • Elaine M. Bologna
    • 7
  • Sadaharu Fujimori
    • 8
  • Douglas E. Scott
    • 9
  • Richard J. Shumway
    • 10
  • George Booker
    • 11
  • Jack Easley
    • 12
  • Francois Pluvinage
    • 13
  • R. W. Scholz
    • 14
  • Leslie P. Steffe
    • 15
  • Joan Yates
    • 16
  • Annie Bessot
    • 17
  • Leroy G. Callahan
    • 18
  • Roy Hollands
    • 19
  • Fredricka K. Reisman
    • 20
  • Gert Schubring
    • 1
  • Mahdi Abdeljaouad
    • 21
  • Phillip Stanley Jones
    • 22
  • Janine Rogalski
    • 23
  • Gert Schubring
    • 25
  • Derek Woodrow
    • 24
  • Waclaw Zawadowski
    • 25
  • Jeremy Kilpatrick
    • 26
  • Horacio J. A. Rimoldi
    • 27
  • Raymond Sumner
    • 28
  • Ruth Rees
    • 29
  • Karen C. Fuson
    • 30
  • Shuntaro Sato
    • 31
  • Claude Comiti
    • 32
  • Thomas E. Kieran
    • 33
  • Gerhard Steiner
    • 34
  • Charles Taylor
    • 35
  • A. P. French
    • 36
  • Robert Karplus
    • 37
  • Gerard Vergnaud
    • 38
  • Edward Esty
    • 39
  • Georges Glaeser
    • 40
  • Heini Halbertstam
    • 41
  • Yoshihiko Hashimoto
    • 42
  • Thomas A. Romberg
    • 43
  • Christine Keitel
    • 44
  • B. Winklemann
    • 45
  • Richard Lesh
    • 46
  • Richard R. Skemp
    • 47
  • Laurie Buxton
    • 48
  • Nicolas Herscovics
    • 49
  • Stanley J. Bezuszka
    • 50
  • K. Hart
    • 51
  1. 1.Institute fur Didaktik der MathematikBielefeldFederal Republic of Germany
  2. 2.Pontificia Universidad Catolica de ChileSantiagoChile
  3. 3.Universite de NiceFrance
  4. 4.Department of Science EducationUniversity of WarwickEngland
  5. 5.Northern Illinios UniversityDeKalbUSA
  6. 6.Hamilton CollegeClintonUSA
  7. 7.Summit SchoolWinston-SalemUSA
  8. 8.Keio Senior High SchoolYokohamaJapan
  9. 9.Amphitheater High SchoolTusconUSA
  10. 10.Ohio State UniversityColumbusUSA
  11. 11.Kelvin Grove College of Advanced EducationBrisbaneAustralia
  12. 12.University of Illinois at Urbana/ChampaignUSA
  13. 13.Universite Louis PasteurStrasbourgFrance
  14. 14.Institute fuer Didaktik der MathematikBielefeldFederal Republic of Germany
  15. 15.University of GeorgiaAthensUSA
  16. 16.University of BristolBristolEngland
  17. 17.IREM de GrenobleGrenobleFrance
  18. 18.State University of New YorkBuffaloUSA
  19. 19.Dundee College of EducationDundeeScotland
  20. 20.University of GeorgiaAthensUSA
  21. 21.Ecole Normale SuperieureTunisTunisia
  22. 22.University of MichiganAnn ArborUSA
  23. 23.Centre d’Etude des Processus Congnitifs et du LangageParisFrance
  24. 24.Manchester College of Higher EducationManchesterEngland
  25. 25.University of WarsawWarsawPoland
  26. 26.University of GeorgiaAthensUSA
  27. 27.CIIPMEBuenos AiresArgentina
  28. 28.National Foundation for Educational Research in England and WalesSloughEngland
  29. 29.Brunel UniversityUxbridgeEngland
  30. 30.Northwestern UniversityEvanstonUSA
  31. 31.Fukushima UniversityFukushimaJapan
  32. 32.Universite I de GrenobleGrenobleFrance
  33. 33.University of AlbertaAlbertaCanada
  34. 34.University of BaselBaselSwitzerland
  35. 35.University CollegeCardiffUK
  36. 36.Massachusetts Institute of TechnologyCambridgeUSA
  37. 37.University of CaliforniaBerkeleyUSA
  38. 38.Institut National de Recherche PedagogiqueParisFrance
  39. 39.National Institute of EducationUSA
  40. 40.IREM de StrasbougStrasbourgFrance
  41. 41.Unversity of NottinghamNottinghamEngland
  42. 42.National Institute for Educational ResearchTokyoJapan
  43. 43.University of WisconsinMadisonUSA
  44. 44.The Institut fuer Didaktik der Mathematik der UniversitatBielefeldFedaral Republic of Germany
  45. 45.The Institut fuer Didaktik der Mathematik der UniversitatBielefeldFederal Republic of Germany
  46. 46.Northwestern UniversityEvanstonUSA
  47. 47.University of WarwickWarwickEngland
  48. 48.Inner London Education AuthorityLondonEngland
  49. 49.Concordia UniversityMontrealCanada
  50. 50.Boston CollegeChestnut HillUSA
  51. 51.Chelsea CollegeLondon UniversityLondonEngland

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