Duality of probability and statistics teaching in French education

Abstract

In epistemological studies, two main interpretations of probabilities are the frequentist and the Bayesian. In this paper we first show that both interpretations are present in French Secondary schools, albeit the official curriculum only supports the frequentist approach. We then suggest a possible teaching situation to introduce teachers and students to the subjective-objective duality with some statistics training situations via the use of problem solving. We also give some characteristics and conditions useful to build situations fitted to this goal.

Rethinking mathematics teachers’ professional knowledge for teaching probability from the perspective of probabilistic reasoning: A proposed framework

“…This meets the demand to overcome individuals' deterministic thinking and admit the existence of chance in nature (Martignon, 2014). Furthermore, another critical issue for why probabilistic reasoning is appreciated in this study is the duality of the probability concept, which has statistical and subjective facets (Carranza & Kuzniak, 2008;Hacking, 1975).…”

The Meaning of Probability From a Foundational Perspective

“…This gives rise to investigating refined approaches towards teaching probability and statistics from a wider perspective on the range of meanings of probability apart from FQT. Carranza and Kuzniak (2008) provide evidence about shortcomings of educational approaches that ignore SJT aspects of probability, which lead to far-reaching misconceptions not only about the use of Bayes' formula but in the perception of probabilities at large. Anyway, we have argued that the concept of probability emerges from a mixture between APT, FQT, and SJT meanings, which are not easy to separate.…”

The Role of Probability for Understanding Statistical Inference

“…3) Bayesian ideas relate to thinking-as opposed to applying routinely mathematical conceptsand to conditional probability, integrating an impact that may be attached to an event under uncertainty. Carranza and Kuzniak (2008) have highlighted the problematic nature of conditional probability and the Bayes formula. Problems arise from the failure to extend the modes of meaning of probability to a subjectivist interpretation, which is a qualitative evaluation of a statement in terms of an abstract weight index.…”

“…It is a twist of the history of statistics education that in the attempt to expand the meaning of probability from the equally likely to a frequentist interpretation, it soon became clear that the methodology had to go beyond this and either integrate a subjectivist connotation or accept serious logical flaws (Hacking, 1965). This is precisely the dilemma that Carranza and Kuzniak (2008) have identified in relation to Bayes' formula. It mirrors the controversy in the foundations of probability (1930's-1980's), where the case of inference (either Bayesian or statistical) became the source of dispute over which meaning was superior to probability (see Hacking 1965).…”