The “...aftermath” column in the November 2011 issue of the MAA’s “Math Horizons” perfectly embodies The Big Mistake that some mathematicians commit when they teach introductory statistics courses: thinking of stat as a branch of math, teaching stat as though it were math, and seeing in stat only the math that's used. You can check out the full text at
http://horizonsaftermath.blogspot.com/2011/11/statistics-la-mode.html
The author comments that the intro stat course "seems oddly estranged from mathematics." Yeah. There's a good reason for that: stat is a different intellectual discipline. She longs for a so-called stat course based on sigma-algebras and probability spaces. Well, that has been tried many times over many years, and it fails miserably at helping students understand the important stat concepts. She also wants in her stat course "an exposition that glorifies its foundation in mathematics". Oops. The foundation of stat is in empirical science and in learning from observed data, not in math. And the reason she's not finding much substance in her stat text is probably because she's looking for math substance – which can be terribly beautiful, but which ain’t the same as stat substance.
Effective teaching in any discipline presumes an understanding of and appreciation for the issues and concepts that are deemed substantial in that field. Teaching should be entrusted only to those who have this understanding and appreciation, and ideally to those who have actually committed their entire lives’ professional energies to that very discipline. But we live in a world that’s far from ideal. For the foreseeable future, stat will continue to be taught by those without such depth of training in the field – partly because the supply of statisticians who are actually kooky enough to teach for a living meets only a fraction of the demand, partly because of entrenched folkways at most institutions, partly because of turf wars and staffing implications, etc. That’s the world we live in.
Fortunately, willing math folks with open minds can pick up enough of this understanding and appreciation to do a decent job. This past summer I led workshops for newly-minted math PhD’s assigned to teach intro stat, as part of the MAA’s Project NExT. From the participants’ reactions at the workshop and from the correspondence I’ve had with several of them since then, I feel comfortable with them teaching intro stat at their institutions. The MAA also has a Special Interest Group on stat education, the ASA and MAA have a joint committee on stat ed as well, and the ASA of course has oodles of outreach for all stat teachers, regardless of pedigree. There is no shortage of opportunities for mathematicians to learn enough about stat thinking to do a minimally sufficient job of teaching a non-majors intro course.
The “...aftermath” author, however, has openly declared that she wouldn’t recognize stat substance even if it walked into her office and said “hello”. She is exactly the sort of mathematician who should not be teaching stat. Fortunately, most mathematicians aren’t so woefully and unabashedly ignorant of stat thinking and concepts, especially once exposed to the crucial differences between math and stat. I’d take any of my green NExT workshop-ers over her in a heartbeat.