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Wiskobas and Freudenthal Realistic Mathematics Education

  • A. Treffers
Chapter

Abstract

Freudenthal was the founder of so-called realistic mathematics education. In it reality does not only serve as application area but also as the source for learning. We take a newspaper article as an example of a rich context problem. It contains elements from all of the important areas of learning for mathematics education in primary school (grades 1 through 6). In the following these topics of learning are discussed. Historical comments will be indicated each time, in particular relating to the influence of Freudenthal. Freudenthal laid the foundation for this didactical realism and determined the development of various learning strands, but more indirectly than directly because he himself did not design or outline themes and learning strands. Attention is devoted briefly to the integral educational development of Wiskobas and Freudenthal’s contribution to it, especially in terms of developmental research. The summary, in conclusion, is given by way of a problem that was posed by Freudenthal — his last one.

Keywords

Mental Arithmetic Historical Comment Context Problem Developmental Research Realistic Mathematic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Brink, J. van den: 1991, `Realistic Arithmetic Education for Young children’, in Streefland, L. (ed.), Realistic Mathematics Education in Primary School, Freudenthai Institute/CD-ß, Utrecht, pp. 77–92.Google Scholar
  2. Ernest, P.: 1991, The Philosophy of Mathematics Education, Palmer, London.Google Scholar
  3. Freudenthal, H.: 1973, Mathematics as an Educational Task, D. Reidel Publ. Co., Dordrecht. Freudenthal, H.: 1977, `Wiskunde Onderwijs anno 2000–Afscheidsrede 1OWO’, Euclides 52, 290–295.Google Scholar
  4. Freudenthal, H.: 1978, `Oppervlakte als verschijnsel benaderd’, in R. de Jong (ed.), Oppervlakte, IOWO, Utrecht, pp. 109–120.Google Scholar
  5. Freudenthal, H.: 1983, Didactical Phenomenology of Mathematical Structures, D. Reidel Publ. Co., Dordrecht.Google Scholar
  6. Freudenthal, H.: 1987, Schrijf dat op Hans, Meulenhoff, Amsterdam.Google Scholar
  7. Freudenthal, H.: 1991, Revisiting Mathematics Education. China Lectures, Kluwer Acad. Publ., Dordrecht.Google Scholar
  8. Freudenthal, H., Janssen G.M. and Sweers, WE.J. (eds.): ‘1976, IOWO-snapshots’ Educational Studies in Mathematics 7 (3),188–367.Google Scholar
  9. Goffree, R: 1992, HF: Working on Mathematics Education. (paper).Google Scholar
  10. Gravemeijer, K., van den Heuvel, M. and Streefland, L.: 1990, Contexts, Free productions, Tests and Geometry in Realistic Mathematics Education, OW and OC, Utrecht.Google Scholar
  11. Gravemeijer, K.: 1989. Evaluatieonderzoek vanuit ontwikkelingsperspectief (paper).Google Scholar
  12. Heege, H. ter: 1985, `The acquisition of basic multiplication skills’, Educational Studies in Mathematics 16, 375–389.CrossRefGoogle Scholar
  13. Jong, R. de: 1986, Wiskobas in Methoden, OW and OC, Utrecht.Google Scholar
  14. Lange, J. de: 1979, ‘Contextuele problemen’, Euclides 55, 50–60.Google Scholar
  15. Lange, J. de: 1987, Mathematics, Insight and Meaning, OW and OC, Utrecht.Google Scholar
  16. Moor, E. de and Streefland, L.: 1991, Van Gogh in het graan’ Tijdschrii t voor Nascholing en Onderzoek van het Reken- Wiskundeonderwijs 10 (1), 61–64.Google Scholar
  17. Moor, E. de: ‘Geometry-instruction (age 4–14) in the Netherlands - the realistic approach; in L. Streefland (ed.), Realistic Mathematics Education in Primary School,Freudenthal Institute, Utrecht, pp. 119–139.Google Scholar
  18. Streefland, L.: 1991a, Fractions in realistic Mathematics Education, Kluwer Acad. Publ., Dordrecht. Streefland, L.: 1991b, `Fractions an integrated approach’, in Streefland, L. (ed.), Realistic Mathematics Education in Primary School, Freudenthal Institute/CD-ß, Utrecht, pp. 93–118.CrossRefGoogle Scholar
  19. Treffers, A.: 1987, Three dimensions. A Model of Goal and Theory Description in Mathematics Instruction - The Wiskobas Project, D. Reidel Publ. Co., Dordrecht.Google Scholar
  20. Treffers, A.: 1991a, `Meeting Innumeracy at Primary School’, Educational Studies in Mathematics, 22, 333–352.CrossRefGoogle Scholar
  21. Treffers, A.: 1991b, ‘Didactical Background of a Mathematics Program for Primary Education’, in Streefland, L. (ed.), Realistic Mathematics Education in Primary School, Freudenthal Institute/CD-ß, Utrecht, pp. 21–56.Google Scholar
  22. Treffers, A., De Moor E.: 1990, Proeve van een Nationaal Programma voor het Rekenwiskundeonderwijs op de Basisschool, (deel I I ), Zwijsen, Tilburg.Google Scholar
  23. Whitney, H.: 1988, Mathematical Reasoning, Early Grades, Princeton (paper).Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  • A. Treffers
    • 1
  1. 1.Freudenthal InstituteUtrecht UniversityThe Netherlands

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