The Meaning and Understanding of Mathematics

The Case of Probability
  • Carmen Batanero
  • Carmen Díaz
Part of the Mathematics Education Library book series (MELI, volume 42)


We summarize a model with which to analyze the meaning of mathematical concepts, distinguishing five interrelated components. We also distinguish between the personal and the institutional meaning to differentiate between the meaning that has been proposed for a given concept in a specific institution, and the meaning given to the concept by a particular person in the institution. We use these ideas to analyze the historical emergence of probability and its different current meanings (intuitive, classical, frequentist, propensity, logical, subjective and axiomatic). We furthermore describe mathematical activity as a chain of semiotic functions and introduce the idea of semiotic conflict that can be used to give an alternative explanation to some widespread probabilistic misconceptions.


Probability history of probability proof semiotics misconceptions 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Carmen Batanero
    • 1
  • Carmen Díaz
    • 1
  1. 1.University of GranadaSpain

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