Intuitive Conceptions of Probability and the Development of Basic Math Skills

Abstract

The idea of probabilities has been deseribed as a "Janus-f'aced" concept, which can be thought of either in terms of frequencies or in terms of subjective confidence. This dualism contributes to debates about the nature of human ratio? nality, and thcrefore the pedagogical assumptions and goals of education. For this reason, the present chapter explores the evidence regarding how quantitative inl'or? mation is intuitively understood in thc human mind over the course or elementary school education. Are particular interprctations of probability equally wcighted or cloes one interpretation prcclominate as mathematical conccpts are being acquired? We find multiple, converging lincs of evidence that indicate a frequency interpre? tation or probabilistic information is developmentally primary and privileged. This has implications l'or mathematics education, even bel'ore the introduction or actual probabilities, in areas such as learning fractions ancl clecimals. Eclucational prac? tices shoulcl work to bootstrap from these privilegecl representations (rather than fight them) and built towarcls a more inclusive and comprehcnsive model of proba? bility knowledge. We conclude that a fundamental issue is not just whether students think about probabilities as a frequentist or a. a subjectivist, but rathcr how they recognize