19: Research In Probability and Statistics: Reflections and Directions

Some years ago, I happened to be teaching an introductory college level course on probability, combinatorics, and elementary statistical concepts. At the same time I was attending an interdisciplinary graduate seminar on research in problem solving, judgment, and decision making. Among the research we addressed in the seminar were some then-recent papers on judgment under uncertainty. What fascinated me about those papers was that the subjects in those studies could have used elementary probability and statistics concepts to estimate the likelihood of events in the research tasks they were given, but they didn’t. The mathematical concepts I was teaching to college freshman would have served them well, if only they had used them. Some of the subjects in those studies of judgment were even quite well schooled in statistics, and yet they still were caught using certain judgmental heuristics, rather than employing their hard- earned statistical knowledge. What was even more unnerving, from my point of view, was that I found myself falling prey to some of the same misconceptions that snared the subjects in the studies. Of course, my initial reaction as a mathematics teacher was that since most of the subjects in these studies were naive about probability and statistics, their nonmathematical ways of estimating likelihoods would disappear if only we could find the “right way” to teach them. So, I embarked on what has been a continually fascinating journey into research on the teaching and learning of probability and statistics. I soon found that the problem of getting people to use stochastics in their judgments and decisions, when appropriate, is not easily remedied just by “teaching them the right way.” (Stochastics is the common European term to include “probability and statistics.” This convenient abbreviation will be used throughout this chapter.) In tuitions, preconceptions, misconceptions, misunderstandings, nonnormative explanations—whatever one might call them— abound in the research on learning probability and statistics.