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Beyond realistic considerations: modeling conceptions and controls in task examples with simple word problems

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Abstract

Using simple word problems, we analyze possible teacher conceptions on the process of problem solving, its goals and the choices that a problem solver can make in problem mathematization. We identify several possible teacher conceptions that would be responsible for the different didactical contracts that teachers create in the mathematics class. Using especially chosen and designed task examples, we demonstrate the diagnosis of teacher own controls in solving problems and in evaluating problem solutions. We also discuss characteristics of task examples that might promote a shift from a problem solving perspective to a modeling perspective that goes beyond merely accepting alternative solutions due to realistic considerations. This shift in perspective would be exhibited through a new understanding of the process of fitting mathematical models in problem situations.

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Notes

  1. To use one of our reviewer’s terms, the three answers could represent a “socialist”, “almost socialist”, and “capitalist” approaches.

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Acknowledgments

This study was supported by a grant from the Israeli Science Foundation (59/06).

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Authors and Affiliations

  1. University of Haifa, Haifa, Israel

    Irit Peled

  2. Laboratoire d’Informatique de Grenoble, CNRS, Grenoble, France

    Nicolas Balacheff

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  1. Irit Peled
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  2. Nicolas Balacheff
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Correspondence to Irit Peled.

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Peled, I., Balacheff, N. Beyond realistic considerations: modeling conceptions and controls in task examples with simple word problems. ZDM Mathematics Education 43, 307–315 (2011). https://doi.org/10.1007/s11858-011-0310-0

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