Skip to main content

Philosophical and Pedagogical Remarks on the Concept “Abstract”

  • Chapter
  • 257 Accesses

Part of the book series: Boston Studies in the Philosophy of Science ((BSPS,volume 175))

Abstract

The nature of mathematical objects seems to be appropriately characterized by the concept “abstract.” Many theorists of education make use of this concept without giving it much thought. When used in this way, the concept “abstract” functions primarily as a metatheoretical concept. There is no mathematical definition of the concept. It is used when talking about mathematics.

Lecture delivered at the Institut für Didaktik der Mathematik der Universität Bielefeld, October 31, 1981.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. Aristotle: The Works of Aristotle, Vol. VIII, Metaphysica. Ed. by J. A. Smith and W. D. Ross. Oxford: Clarendon Press, 1908.

    Google Scholar 

  2. Arnauld, A.: The Port-Royal Logic. Trans. by T. S. Baynes. 8th ed., Edinburgh: William Blackwood and Sons, 1851.

    Google Scholar 

  3. Bauersfeld, H.: “Kommunikationsmuster im Mathematikunterricht—Eine Analyse am Beispiel der Handlungsverengung durch Antworterwartung.” In Bauersfeld, H. (Ed.): Fallstudien und Analysen zum Mathematikunterricht. Hannover: Schroedel, 1978, pp. 158–170.

    Google Scholar 

  4. Bauersfeld, H.: “Hidden Dimensions in the So-Called Reality of a Mathematics Classroom.” In Educational Studies in Mathematics, 11 (1), 1980, pp. 23–41.

    Google Scholar 

  5. Hegel, G. W. F.: Werke 2, Jenaer Schriften (1801–1807). Frankfurt a.M.: Suhrkamp, 1970.

    Google Scholar 

  6. Hopf, D.: Mathematikunterricht. Eine empirische Untersuchung zur Didaktik und Unterrichtsmethode in der 7. Klasse des Gymnasiums. Stuttgart: Kleff-Cotta, 1980.

    Google Scholar 

  7. Hume, D.: Enquiries Concerning Human Understanding and Concerning the Principles of Morals. Ed. by L. A. Selby-Bigge, 3rd ed. by P. Nidditch. Oxford: Oxford University Press, 1975.

    Google Scholar 

  8. Kant, I.: Critique of Pure Reason. Trans. by F. M. Müller. 2nd ed., New York: Macmillan, 1927.

    Google Scholar 

  9. Piaget, J.: Genetic Epistemology. New York: Columbia University Press, 1970.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Damerow, P. (1996). Philosophical and Pedagogical Remarks on the Concept “Abstract”. In: Abstraction and Representation. Boston Studies in the Philosophy of Science, vol 175. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8624-5_3

Download citation

  • DOI: https://doi.org/10.1007/978-94-015-8624-5_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4644-4

  • Online ISBN: 978-94-015-8624-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics