THE FORMALIST MATHEMATICAL TRADITION AS AN OBSTACLE TO
STOCHASTICAL REASONING
Maria Meletiou-Mavrotheris (Ministry of Education, Cyprus)
The research literature in the area of stochastics education indicates that most people,
even ones with substantive formal training, tend to think deterministically and to have
weak intuitions about the stochastic. In this paper, the argument is made 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. Deep-rooted beliefs about the nature
of mathematics are imported into statistics, affecting curricula and acting as a barrier
to instruction that provides students with the skills necessary to recognize uncertainty
and variability in the real world. The article first provides an overview of the literature
on the formalist view of mathematics and its impact on statistics curricula and
instructional approaches. It then reconsiders some well-known empirical findings on
students’ understanding of statistics, and forms some hypotheses regarding the link
between student difficulties and mathematical formalism. Next, it argues that in order
to move away from the formalist mathematical tradition and to improve people’s
impoverished probabilistic and statistical reasoning, statistics instruction must put
more emphasis on raising students’ awareness of variation and its relevance to
statistics. It conjectures that if we provided students with learning environments
where they experienced the omnipresence of variation and came to value statistical
tools as a means to describe and quantify it, they would develop statistical thinking
going beyond the superficial knowledge of terminology, rules and procedures. In
order to justify this conjecture, the article discusses the experiences and insights
gained from a teaching experiment in an introductory statistics course, which adopted
an alternative path to statistics instruction with variation at its core.