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Mathematics as part of technology

Elements of a philosophy of an applied oriented mathematical education

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Abstract

Competence in dealing with fundamental problems connected with mathematical model building requires three different forms of knowledge. Mathematical knowledge itself, technological knowledge about how to develop a model, and reflective knowledge relevant for evaluation of the model building process. We find that reflective knowledge cannot be reduced to technological knowledge, so that it is important for mathematical education that is to be consistent with a critical pedagogy to provide opportunities for development of that type of knowledge.

A general conceptual framework for identification of reflective knowledge is presented via a structural (synchronic) and a developmental (diachronic) perspective of a mathematical model.

The synchronic perspective includes relationships between the model, its object in reality, a complex of theories, a complex of interests, and a conceptual framework or system mediating the connection between model and object. The diachronic perspective includes the components: problem identification, structure of argumentation, basis for critique, and space of possible actions, all of them sensitive to the application of mathematics. In that sense mathematics is not a neutral tool in a technological investigation, a fact which mathematical education has to reflect.

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References

  1. Andrews, J. G. and R. R. McLone (eds.): 1976, Mathematical Modelling, Butterworths, London/Boston/Sydney/Wellington/Durban/Toronto.

  2. Aris, R.: 1978. Mathematical Modelling Techniques, Pitman Advanced Publishing Program, Boston/London/Melbourne.

  3. Beck, U.: 1979, Zur Didaktik der Anvendungen innerhalb eines ausgewogenen Mathematikunterrichts. PH Ruhr, Dortmund.

  4. Becker, G.: 1981, ‘Problems eines anwendungsorientierten Mathematikunterrichts’, Mathematica Didactica 4, 21–30.

  5. Becker, G.: 1979, ‘Über ein Konzept zum anwendungsorientierten Mathematikunterricht’, Mathematica Didactica 2, 45–53.

  6. Bender, E. A.: 1978, An Introduction to Mathematical Modelling, Wiley & Sons, New York/Chichester/Brisbane/Toronto.

  7. Braun, M.: 1975, Differential Equations and Their Applications, Springer, New York/Heidelberg Berlin.

  8. Burghes, D., I. Huntley, and J. McDonald: 1982, Applying Mathematics: A Course in Mathematical Modelling, Ellis Horwood, Chicester.

  9. Ewers, M. (Hrsg.): 1975, Naturwissenschaftliche Didaktik zwischen Kritik und Konstruktion, Beltz Verlag, Weinheim/Basel.

  10. Fischer, R. and G. Malle: 1985, Mensch und Mathematik, Bibliographisches Institut, Mannheim/Wien/Zürich.

  11. Fischer, R., E. Kotzmann, H. Jungwirth-Maass, and G. Ossimitz: 1986, Endbericht zum Project: Mathematik und Politische Bildung, Institut für Mathematik, Universität Klagenfurt.

  12. Ford, B. and G. G. Hall: 1970, Model building — an educational philosophy for applied mathematics’, International Journal of Mathematical Education in Science and Technology 1, 77–83.

  13. Forrester, J. W.: 1971, World Dynamics, Wright-Allen Press, Cambridge, Massachusetts.

  14. Freudenthal, H. (ed.): 1961, The Concept and the Role of the Model in Mathematics and Natural and Social Sciences, D. Reidel, Dordrecht.

  15. Goodwin, R. M.: 1972, ‘A growth cycle’, in E. K. Hunt and J. G. Schwartz, A Critique of Economic Theory, Penguin Books, Harmondsworth, pp. 442–449.

  16. Groth, C.: 1981, Cyklisk Kapitalakkumulation I–II, Økonomisk Institut, University of Copenhagen.

  17. Haberman, R.: 1977, Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow, Prentice-Hall, Englewood Cliffs, N.J.

  18. Habermas, J.: 1968, Erkenntnis und Interesse, Suhrkamp Verlag, Frankfurt-am-Main.

  19. Harré, R.: 1970, The Principles of Scientific Thinking, MacMillan, London/Basingstoke.

  20. Hickman, F. R.: 1986, ‘Didactic and pragmatic approaches to mathematical modelling’, International Journal of Mathematical Education in Science and Technology 17, 733–747.

  21. James, D. J. G. and J. J. McDonald (eds.): 1981, Case Studies in Mathematical Modelling, Stanley Thornes, Cheltenham.

  22. Jensen, J. H.: 1980, ‘Mathematiske modeller — vejledning eller vildledning’, Naturkampen 18, 14–22.

  23. Kaiser, G.: 1984, ‘Zur Realisierbarkeit von Zielen eines anvendungsorientierten Mathematikunterrichts’, Mathematica Didactica 7, 71–85.

  24. Kaiser, G., W. Blum, and M. Schober: 1982, Dokumentation ausgewählter Literatur zum anvendungsorientierten Mathematikunterricht, Fachinformationszentrum, Karlsruhe.

  25. Kapp, E.: 1977, Grundlinien einer Philosophie der Technik, Düsseldorf.

  26. Lakatos, I.: 1976, Proofs and Refutations, Cambridge University Press, Cambridge.

  27. Lighthill, J.: 1978: Newer Uses of Mathematics, Penguin Books, Harmondsworth.

  28. Lilienfeld, R.: 1978: The Rise of Systems Theory: An Ideological Analysis, John Wiley & Sons, New York/Chichester/Brisbane/Toronto.

  29. Meadows, D. L. et al.: 1974, Dynamics of Growth in a Finite World, Wright-Allen Press, Cambridge, Massachusetts.

  30. Münzinger, W. (Hrsg.): 1977, Projektorientierter Mathematikunterricht, Urbau & Schwarzenberg, München/Wien/Baltimore.

  31. Niss, M.: 1985, Applications and Modelling in the Mathematics Curriculum, IMFUFA, Roskilde University Centre.

  32. Niss, M. and K. Hermann: 1982, Beskæftigelsesmodellen i SMEC III, Nyt Nordisk Forlag Arnold Busck, Copenhagen.

  33. Ormell, C. P.: 1972a, ‘Mathematics, applicable versus pure-and-applied’, International Journal of Mathematical Education in Science and Technology 3, 125–131.

  34. Ormell, C. P.: 1972b, ‘Mathematics, science of possibility’, International Journal of Mathematical Education in Science and Technology 3, 329–341.

  35. Pinter, A.: 1981, ‘The concept “model” and its potential role in mathematics education’, International Journal of Mathematical Education in Science and Technology 12, 693–707.

  36. Pollak, H. O.: 1979, ‘The interaction between mathematics and other school subjects’, in UNESCO (1979), pp. 232–248.

  37. Rapp, F.: 1981, Analytical Philosophy of Technology, D. Reidel, Dordrecht.

  38. Reichenbach, H.: 1966, The Rise of Scientific Philosophy, University of California Press, Berkeley/Los Angeles.

  39. Skovsmose, O.: 1980, Forandringer i matematikundervisningen, Gyldendal, Copenhagen.

  40. Skovsmose, O.: 1981a, Matematikundervisning og kritisk pædagogik, Gyldendal, Copenhagen.

  41. Skovsmose, O.: 1981b, Alternativer i matematikundervisningen, Gyldendal, Copenhagen.

  42. Skovsmose, O.: 1984, Kritik, undervisning og matematik, Lærerforeningernes Materialeudvalg, Copenhagen.

  43. Skovsmose, O.: 1985, ‘Mathematical education versus critical education’, Educational Studies in Mathematics 16, 337–354.

  44. Skovsmose, O. and H. Siggaard Jensen: 1986, Teknologikritik, Systime, Herning.

  45. Smith, J. M.: 1974, Models in Ecology, Cambridge University Press, Cambridge/London/New York/Melbourne.

  46. Stachowiak, H.: 1973, Allgemeine Modelltheorie, Springer, Wien/New York.

  47. Stork, H.: 1977, Einführung in die Philosophie der Technik, Wissenschaftliche Buchgesellschaft, Darmstadt.

  48. UNESCO: 1979, New Trends in Mathematics Teaching 4, Paris.

  49. Volk, D.: 1975, ‘Plädoyer für einen problemorientierten Mathematikunterricht in emanzipatorischer Absicht’, in Ewers (1975), pp. 203–234.

  50. Volk, D. (Hrsg.): 1979a, Kritische Stichwörter zum Mathematikunterricht, Wilhelm Fink Verlag, München.

  51. Volk, D.: 1979b, Handlungsorientierende Unterrichtslehre am Beispiel Mathematikunterricht, Band A, Päd. extra Buchverlag, Bensheim.

  52. Volk, D.: 1980, Zur Wissenschaftstheorie der Mathematik: Handlungsorientierende Unterrichtslehre, Band B, Päd extra Buchverlag, Bensheim.

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Skovsmose, O. Mathematics as part of technology. Educ Stud Math 19, 23–41 (1988). https://doi.org/10.1007/BF00428383

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Keywords

  • Mathematical Model
  • Conceptual Framework
  • Problem Identification
  • Mathematical Education
  • Model Building