M Meletiou-Mavrotheris, D.A.Stylianou 1 ON THE FORMALIST VIEW OF MATHEMATICS: IMPACT ON STATISTICS INSTRUCTION AND LEARNING

In the paper, we argue that the persistence of students ’ difficulties in reasoning about the stochastic despite significant reform efforts in statistics education might be the result of the continuing impact of the formalist mathematical tradition. We first provide an overview of the literature on the formalist view of mathematics and its impact on statistics instruction and learning. We then re-consider some well-known empirical findings on students ’ understanding of statistics, and form some hypotheses regarding the link between student difficulties and mathematical formalism. Finally, we briefly discuss possible research directions for a more formal study of the effects of the formalist tradition on statistics education. Wilensky (1993) has claimed that the failure in developing sound probabilistic intuitions is similar to other failures in mathematical understanding and is the result of deficient learning environments and reliance on “brittle formal methods”. It is, in our opinion, these same reasons that also cause the neglect of a number of other statistics concepts observed both in the curriculum and in the research literature. We argue here that deep-rooted beliefs about the nature of mathematics are imported into statistics, affecting instructional approaches and curricula and acting as a barrier to the kind of instruction that would provide students with the skills necessary to recognize and intelligently deal with uncertainty and variability. In this paper we give an overview of the literature on the formalist view of mathematics and its impact on statistics instruction and learning. While little empirical work has focused on examining the impact that formalism may have on student understanding, we use here examples from a number of studies in statistics that discuss student understanding in general and we illustrate how student difficulties may be related to mathematical formalism. Finally, we discuss possible directions for research on this important topic