Research in probability and statistics: Reflections and directions

Handbook for Research in Mathematics Teaching and Learning.
Shaughnessy, J. M.
Grouws, D.
Macmillan Publishing
New York

Probability and statistics (stochastics) are viewed as necessary for all students no matter their ambitions. However, there are barriers to the effective teaching of both stochastics and problem solving: 1) getting stochastics into the mainstream of the mathematical science school curriculum; 2) enhancing teachers' background and conceptions of probability and statistics; 3) confronting students' and teachers' beliefs about probability and statistics. Psychologists and mathematics educators should work collaboratively to diminish misconceptions. Doing so combines the roles of observer, describer, and intervener. Research in stochastics suggests that heuristics that are used intuitively by learners impede the conceptual understanding of concepts such as sampling. This paper reviews the research on judgemental heuristics and biases, conditional probability and independence (i.e., causal schemes), decision schema (i.e., outcome approach), and the mean. Learners have difficulties in these areas, however, evidence is contradictory as to whether training in stochastics improves performance and decreases misconceptions. The conclusion emerging from this research is that probability concepts can and should be introduced into the school at an early age. Instruction that is designed to confront misconceptions should encourage students to test whether their beliefs coincide with those of others, whether they are consistent with their own beliefs about other related things, and whether their beliefs are born out with empirical evidence. Computers can be used to provide both an exploratory and representational aspect of the discipline. The role of teachers in this type of environment and the issue of whether stu- dents should use artificial or real data sets should be considered.

The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education