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A brief historical comparison of tendencies in mathematics didactics/education in Germany and the United States

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You can imagine, Reader, to what lengths I might take this conversation on a subject which has been talked about written about so much for the last two thousand years without getting one step further forward. If you are not grateful to me for what I am telling you, be very grateful for what I am not telling you-Denis Direrot in Jacques the Fatalist

Abstract

In this paper we outline in macroscopic terms major tendencies in the mathematics education histories of Germany and the United States. In particular, we spell out periodic shifts in foucus of mathematics education over the last 100 years and in this process unravel common focal points in the parallel development of the field. In doing so we reflect and hypothesize on why certain trends seem to re-occur, sometimes invariantly, across time and geographic, location.

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References

  • http://www.didaktik.mathematik.uniwuerzburg.de/history/meg/index/html

  • Bauersfeld, H. (1988). Interaction, construction, and knowledge: alternative perspectives for mathematics education. In D. A. Grouws, T. J. Cooney & D. Jones (Eds.),Perspectives on research on effective mathematics teaching (pp. 27–46). Reston, VA: National Council of Teachers of Mathematics

    Google Scholar 

  • Bauersfeld, H. (1995). Theorien im Mathematikunterricht.Mathematica Didactica 18 (2), 3–19

    Google Scholar 

  • Becker, H. J. (1990). Mathematics and science uses of computer in American schools. 1989 data analyses from the U.S participation in the I.E.A Computers-In-Education Survey, Baltimore: Center for Social Organization of Schools. Johns Hopkins University.

    Google Scholar 

  • Becker, H. J. (1991. May). When powerful tools meet conventional beliefs and institutional constraintsComputing Teacher, pp. 6~9.

  • Beckmann, C. (1989). Effects of computer graphing use on student understanding of calculus concepts. Ph.D diss., Western Michigan University.Dissertation Abstracts International 50.

  • Belunke, Heinrich (1953). Der mathematische Unterricht und die Schulreformen.Math. Phys. Semesterberichte 3, 1–15.

    Google Scholar 

  • Behnke, Heinrich. (1961). Felix Klein und die heutige Mathematik.Math. Phys. Semesterberichte 7, 129–144.

    Google Scholar 

  • Betz, W. (1937).Algebra for today: First course. Boston: Ginn & Co.

    Google Scholar 

  • Bishop, A. J., et al. (1996).Intermational Handbook on mathematics education Dordrecht: Kluwer,Domain: A search for Identity (vol. 1). (pp. 105–116) Kluwer Academic Publishers: Great Britain.

    Google Scholar 

  • Burkhardt, H.; Schoenfeld, A. (2003). Improving Educational Research: Toward a more useful, more influential, betterfunded enterprise.Educational Researcher 32 (9), 3–14.

    Article  Google Scholar 

  • Burton, L. (2003).Which Way Social Justice in Mathematics education? Westport, CT: Praeger Publishers.

    Google Scholar 

  • Dick, T., (1992). Super calculators implications for calculus curriculum, instruction and assessmentCalculators in Mathematics Education, Yearbook (pp 145–57), Reston, VA: The Council.

    Google Scholar 

  • English, L. D. (2002). Priority themes and issues in international research in mathematics education. In English, L. D. (Ed.) (2002).Handbook of international research in mathematics education. (p. 3–15). Lawrence Erlbaum Associates: Mahwah, NJ.

    Google Scholar 

  • English, L. D. et al. (2002). Further issues and directions in international mathematics education research. In English, L. D. (Ed.) (2002)Handbook of international research in mathematics education, (p. 787–812). Lawrence Erlbaum Associates: Mahwah, NJ.

    Google Scholar 

  • Führer, L. (1997).Pädagogik des Mathematikunterrichts. Wiesbaden: Wieweg.

    Google Scholar 

  • Freudenthal, H. (1978).Vorrede zu emer Wissenschaft vom Mathematikunterricht. München: Oldenbourg.

    Google Scholar 

  • Harvey, J. (1993). Effectiveness of graphing technologies in a pre-calculus Course: The 1988~89 Field Test of the C PC Materials. Paper presented at the Technology in Mathematics Teaching Conference, Birmingham, England.

  • Hayden, R. W. (1983). A historical view of the “new mathematics. Eric Document. ED 228046.

  • Hiatt, D. B. (1986). Post Sputnik education reform era: to dream the impossible dream. Eric Document. ED 277160.

  • Hefendehl-Hebeker, L.; Hasemann, K.; Weigang, H.-G. (2004). 25 Jahre Journal für Mathematik-Didaktik aus der Sicht der amtierenden Herausgeber.Journal für Mathematikdidaktik 25 (3/4), 191–197.

    Google Scholar 

  • Huster, L. (1981). Dokumentation zur Entwicklung der Mathematik-Didaktik im 10. Jahrhundert; Ergebnisse der Pilotphase zum KID-Projekt: Heft 14. Bielefeld: Institut für Didaktik der Mathematik.

    Google Scholar 

  • Janke, H. N. (1990).Mathematik und Bildung in der Humboldtschen Reform. Göttingen: Vandenhoeck & Ruprecht.

    Google Scholar 

  • Kaiser, G. (1999).Unterrichtswirli chkeit in England und Deutschland. Vergleichende. Untersuchungen am Beispiel des Mathematikunterichts.—Weinheim: Deutscher Studienverlag.

    Google Scholar 

  • Kaiser, G. (2002). Educational philosophies and their influence on mathematics education—An ethnographic study in English and Geman classrooms.International Reviews on Mathematical Education (ZDM), 34(6), 241–257.

    Google Scholar 

  • Kilpatrick, J. (1992). A history of research in mathematics education. In D. A. Grouws (Ed.),Handbook of research on mathematics teaching and learning (pp. 3–38). New York: Simon & Schuster Macmillan

    Google Scholar 

  • Kilpatrick, J. & Davis, R. (1989). Computers and Curricuhum Change in Mathematics. In:Proceedings from the BACOMET III Conference. Berlin.

  • Lampert, M. (1988). Teachers' thinking about students' thinking about geometry: The effects of new teaching tools (Report No. TR88-1). Cambridge, MA: Educational Technology Center.

    Google Scholar 

  • Lampert, M. (1993). Teachers thinking about students' thinking about geometry: The effects of new teaching styles. In J. L. Schwartz, M. Yerushalmy, & B. Wilson (Eds.),The Geometric Supposer: What is it a case of? (pp. 143–177). Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Lenné, H. (1975).Analyse der Mathematikdidaktik in Deutschland. Stuttgart: Klett.

    Google Scholar 

  • Lesh, R. & Sriraman, B. (2005a). John Dewey Revisited-Pragmatism and the models-modeling perspective on mathematical learning. In: A. Beckmann et al [Eds.],Proceedings of the 1st International Symposium on Mathematics and its Comections to the Arts and Sciences. May 18~21, 2005, University of Schwaebish Gmuend: Germany Franzbeckert Verlag. pp. 32~51

  • Lesh, R. & Sriraman, B. (2005b). Mathematics Educations as a sciences.Zentralblatt für Didaktik der Mathematik, vol 37, no. 6 pp. 490–505.

    Article  Google Scholar 

  • Lietzmann, W. (1919).Methodik des mathematischen Unterrichts. 1. Teil. Leipzig: Quelle, & Meyer.

    Google Scholar 

  • Lietzmann, W. (1950). Felix Klein und die Schulreform.Math. Phys. Semesterberichte 1(3), 213–219.

    Google Scholar 

  • McKnight, C. C., Crosswhite, F. J., Dossey, J. A., Kifer, E., Swafford, J. O., Travers, K. J., Cooney, T. J. (1987).The underachieveing curriculum: Assessing U.S. school mathematics from an international perspective. IL: Stipes Publishing.

    Google Scholar 

  • Miller, J. W. (1990). Whatever happened to new math?American Heritage, 6, 76–83.

    Google Scholar 

  • Noss, R. & Hoyles, C. (1996).Windows on Mathematical Meanings. Dordrecht: Kluwer Academic Publishers.

    Google Scholar 

  • National Council of Teachers of Mathematics (1936).The Place of mathematics in modern education, (11th Yearbook), Teachers College: Columbia University.

  • National Council of Teachers of Mathematics (1970).A history of mathematics education in the United States and Canada (32nd Yearbook). Washington DC.

  • National Commission on Excellence in Education (1983).A nation at risk: The imperative for educational reform. Washington, D.C.: U.S. Government Printing Office.

    Google Scholar 

  • National Council of Teachers of Mathematics (1989).Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.

    Google Scholar 

  • Quesada, A. & Maxwell, M. (1992). The effect of using graphing calculators on, students': performance in pre-calculus.Proceedings of the Fourth International Conference on Technology in Collegiate Mathematics. (pp. 380~84). Addison-Wesley Publishing Company.

  • Reichel, H.-Chr., (1995). Hat die Stoffdidaktik Zukunft?Zentralblatt für Didaktik der Mathematik 27 (6), 178–187.

    Google Scholar 

  • Rich, B. (1991). The effect of using graphing calculators in learning function concepts in pre-calculus math. Ph. D., diss. University of Iowa.Dissertation Abstracts International 52.

  • Ruthven, K. (1990). The influence of graphing calculator use on translation from graphic to symbolic forms.Educational Studies in Mathematics 21 (pp 431–450).

    Article  Google Scholar 

  • Schoenfeld, A. (1999). Looking toward the 21st century: Challenges of educational theory and practice.Educational Researcher 28(7), 4–14.

    Google Scholar 

  • Schoenfeld, A. H. (2002). Research methods in (mathematics) education. In English, L. D. (Ed.) (2002),Handbook of international research in mathematics education. (p. 435–487. Lawrence Erlbaum Associates: Mahwah, NJ.

    Google Scholar 

  • Steen, L. A. (2001).Mathematics and Democracy: The Case for Quantitative Literacy. National Council on Education and the Disciplines.

  • Steiner, H.-G. (1982). Eine Entgegnung zu Herbert Zeitlers “Gedanken zur Mathematik”.Didaktik der Mathematik 10 (3), 233–246.

    Google Scholar 

  • Vollrath, H.-J. Fischer, R.; Kirsch, A. (2004). Zur Entstehung des Journals—Erinnerungen der ersten herausgeber.Journal für Mathematikdidaktik 25(3/4), 183–190.

    Google Scholar 

  • Weigand, H.-G. (1995). Steckt der Mathematikunterricht in der Krise?Mathematica didactica 18 (1), 3–20.

    Google Scholar 

  • Wilson, J. & Kilpatrick, J. (1983). Talking mathematics teaching seriously: Reflections on the teacher shortage. In J. L. Taylor (Ed.),Teacher shortages in science and mathematics: Myths, realities, and research. Washington: National Institute of Education.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, University of Duisburg-Essen, Duisburg Campus Lotharstr. 63/65, D-47048, Duisburg, Germany

    Günter Törner

  2. Dept. of Mathematical Sciences, The University of Montana, 59812, Missoula, MT, USA

    Bharath Sriraman (Editor. The Montana Mathematics Enthusiast)

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  1. Günter Törner
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  2. Bharath Sriraman
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Törner, G., Sriraman, B. A brief historical comparison of tendencies in mathematics didactics/education in Germany and the United States. Zentralblatt für Didaktik der Mathematik 38, 14–21 (2006). https://doi.org/10.1007/BF02655903

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