math class. As a student of one of us once wrote on remarkable that some of the music Mozart wrote at
the course evaluation form, “This course should be age 5 is still in the repertoire.
more like a math course, with everything you need Also, chess prodigies continue to appear.
laid out beforehand.” Sergey Karjakin is the youngest grandmaster ever
Mathematics has a long history of prodigies and at 12 years, 7 months. The infamous late Bobby
geniuses, with many of the most famous luminar- Fischer—who was youngest in 1958 when he
ies showing their genius at remarkably early ages. became a grand master at 15 years, 6 months, and
We’ve all heard at least one version of the famous 1 day—is now only 19th on that list.
story of young Carl Friedrich Gauss. A web search But there are only a few fields that develop
finds more than 100 retellings of the story, but prodigies, and all seem to be self-contained. For
an article by Brian Hayes in American Scientist’s example, as professor of English at the University
“Gauss’s Day of Reckoning” identifies a version of Connecticut, Thomas Dulack observed, “There
actually recounted at Gauss’ funeral. In that ver- are no child prodigies in literature.” Although one
sion, Gauss—age 7 and the youngest in the class— might argue that William Cullen Bryant, Thomas
summed the numbers from 1 to 100 in seconds, Chatterton, H. P. Lovecraft, or Mattie Stepanek
wrote the answer on his slate, and then threw it qualifies as a literary prodigy, that list doesn’t have
Carl Friedrich Gauss, a
down on the table mumbling “there it lies” in the quite the same panache as the others we’ve cited. It’s
math prodigy at the age of 7
local dialect. It was perhaps an hour later that the no easier to find prodigies in art, poetry, philosophy,
teacher discovered that his answer was, in fact, the or other endeavors that require life experience.
only correct one in the room. What does any of this have to do with statistics
Prodigies in math can develop at remarkably and how can it help us understand why introduc-
early ages because math creates its own self-con- tory statistics is so hard to teach? The challenge for
sistent and isolated world. Pascal had worked out the student (and teacher) of introductory statistics
the first 23 propositions of Euclid by age 12 when is that, as literature and art, navigating through
his parents, who wanted him to concentrate on and making sense of it requires not just rules and
religion, finally relented and presented him with a axioms, but life experience and “common sense.”
copy of Euclid’s Elements. Galois wrote down the Although working with elementary statistics
essentials of what later became Galois Theory the requires some mathematical skills, we ask so much
night before a fateful duel when he was 20, or so the more of the intro stats student than is required by,
legend has it. In the modern era, Norbert Weiner for example, a student in his or her first calculus
entered Tufts at age 11; Charles Pfefferman of course. A student in calculus I is not asked to com-
Princeton was, at 22, the youngest full professor in ment on whether a question makes sense, whether
Blaise Pascal was a French
American history; and Ruth Lawrence of Hebrew the assumptions are satisfied (e.g., Is the reservoir
mathematician, and a
University passed her A-levels in pure math at age from which the water pouring really a cone?), to
prodigy by the age of 12.
9 and became the youngest student ever to enroll at evaluate the consequences of the result, or to write
Oxford two years later. a sentence or two to communicate the answer to
Of course, mathematics isn’t the only field others. But, that’s exactly what the modern intro
that shows prodigies. Mozart, Schumann, and stats course demands.
Mendelssohn, among others, were young musical The challenge we face is that, unlike calculus I,
prodigies. Even though his music matured, it is we have a wide variety of skills to teach, and most of
them require judgment in addition to mathematical
manipulation. Judgment is best taught by example
and experience, which takes time. But, we’re sup-
posed to produce a student capable of these skills
in one term. It would be challenging enough
to teach the definitions, formulas, and skills
in the standard first course. To convey in
addition the grounds for sound judg-
ment is even more difficult. It should
Évariste Galois was a French
be no wonder that the first course in
mathematician and prodigy
statistics is widely acknowledged to
who finished the Galois Theory
be one of the most difficult courses
by the time he turned 20.
to teach in the university.
It is not merely that we hope to
teach judgment to sophomores; we
are actually asking our students to
change the way they reason about
SEPTEMBER 2008 AMSTAT NEWS 55
SEPTEMBER AMSTAT FINAL.indd 55 8/20/08 2:27:06 PM
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