Educational Studies in Mathematics

, Volume 6, Issue 3, pp 339–350 | Cite as

The naive platonic approach as a teaching strategy in arithmetics

  • Shlomo Vinner


We tried to describe the i.a. of children and members of the naive group to the number realm. This i.a. was designated by means of an analogy between the concrete world and the world of mathematical objects. Admitting that the d.a. in mathematics is analogous to the modern philosophy of science we can sum up our series of analogies by the following scheme:

Assuming the analogies above we have recommended the n.P.a. as a teaching strategy. A success of this strategy will give us an indirect experimental support to our claim. However, such a success is not a thing that can be easily measured. One has to remember that we talk about very long periods of learning. Indeed, it can be measured if one tries to teach only a specific topic as, for instance, the complex numbers. But difficulties will arise also here. Namely, the n.P.a. strategy should be applied to students who have had the n.P.a. and nothing else. The d.a. strategy should be applied to students who have had the d.a. and nothing else. So the problem is how to find such two groups of students. Therefore, the best way in this case is to rely on teachers' expetience.


Specific Topic Complex Number Teaching Strategy Mathematical Object Experimental Support 
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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Copyright information

© D. Reidel Publishing Company 1975

Authors and Affiliations

  • Shlomo Vinner
    • 1
    • 2
  1. 1.Hebrew UniversityJerusalemIsrael
  2. 2.University of CaliforniaBerkeleyUSA

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