Four Decades of Conservation Research

What Do They Mean for Mathematics Education?
  • J. A. EasleyJr.


The context of this chapter is well put by Erich Wittmann in introducing one of his own papers:

The epistemology of natural numbers has been a subject of discussion since Helmholtz, Frege, Russell, Poincaré up to Hilbert, Brouwer and Weyl. This includes questions as to whether the ordinal or cardinal aspect is constitutive for number, whether number is an a priori entity as believed by Poincaré and the intuitionists, or reducible to logic as claimed by Frege and Russell. As a paradigm of long standing for the epistemological problem, that of natural number kept the status of a controversial question depending on different philosophical views, as long as it remained within philosophy—indeed philosophy does not know means to remove these differences. A way out was shown by J. Piaget’s genetic epistemology, which is based on the equality of developmental mechanisms both in the genesis of science and the individual, and consequently transforms the epistemological problem of natural number into an empirical problem, namely that of exploring the psychogenesis of the number concept. (Wittmann, 1975, p. 53)


Mathematics Education English Translation Category Theory Deductive Logic Logical Empiricist 
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Copyright information

© Plenum Press, New York 1978

Authors and Affiliations

  • J. A. EasleyJr.
    • 1
  1. 1.Committee on Culture and CognitionUniversity of IllinoisUrbanaUSA

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