3272

Egan J Chernoff

philosophy of mathematics education

2008

23

In this article the three dominant philosophical interpretations of probability in mathematics education (classical, frequentist, and subjective) are critiqued. Probabilistic explorations of the debate over whether classical probability is belief-type or frequency-type probability will bring forth the notion that common ranges, rather than common points, of philosophical reference are inherent to probability measurement. In recognition of this point, refinement of subjective probability, into the dual classification of intrasubjective and intersubjective, and frequentist probability into the dual classification of artefactual and formal objective, attempts to address the nomenclatural issues inherent to subjective and frequentist probability being both general classifiers and particular theories. More specifically, adoption of artefactual and intersubjective probability will provide a more nuanced framework for the field to begin to heed the numerous calls put forth over the last twenty-five years for a unified approach to teaching and learning probability. Furthermore, the article proposes that “artefactual period” be adopted as a first approximation descriptor for the next phase of probability education.