Mathematicians from the Greeks on have used simple physical or visual models to understand and create new mathematics. The history of innovation in geometry, probability and calculus is full of examples of commonplace or mundane models explicating and motivating new ideas. Modern research statisticians also use the same strategies. Ask an expert in experimental design what he knows about and how he thinks about an industrial experiment. Often you will get an extraordinarily naive answer. You discover that he has cheerfully ignored important, even critical, physical details of the industrial process., and yet industry amply compensates our apparently naive experimental design colleagues. Perhaps industry has learned some lessons that we as teachers of statistics have forgotten. In this paper we argue that our undergraduate students need to be able to view, construct and manipulate mundane models and that this is a critical part of undergraduate mathematics and statistics education. All this may seem obvious, but in the past decades a number of forces have contributed to a decline of our students ability to approach statistics using visual model approaches to mathematics.
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