might be doing harm in reality. To raise awareness I perspired not because of the realization that I
of this phenomenon, I suggest it be recognized as committed an elementary error of extrapolation,
the “Off-Diagonal Paradox”, invoking a similar con- but rather because of the realization that if the
notation of “paradox” as in Simpson’s paradox to “turn-off” phenomenon is indeed more likely for
urge investigators to always keep in mind the need students at Harvard or Harvard-like institutions,
for comparing the two cells along the off-diagonal then our profession has an even deeper and per-
in Table 1. The word “off” should also serve as a haps more disturbing problem to worry about.
reminder that the effectiveness of the overall pro- Harvard undergraduates are undoubtedly a highly
gram for recruitment cannot be assessed by only selected group. But they are not so different from
asking those who are already in: we need also to ask undergraduates at many of Harvard’s peer insti-
those who are off or out. tutions, nor did they all come from one school
For AP statistics, the inequality P
OFF
> P
ON
district or one state. It is, however, quite possible
can hold even when P
ON
increases as long as P
OUT
that academically strong students have a higher
remains large (which is true, for example, for major- likelihood to walk away from a poorly taught sub-
ing in statistics), and when there are more poorly ject, statistics or not, than academically less able
taught AP courses than well taught ones; the latter ones. Other than the fact that the former will have
is one of the issues needing to be examined in any more choices at their disposal, it is not hard to
assessment of the overall impact of the AP program. imagine that the former are also more likely to
Not having enough well-qualified teachers is a well- be turned off by mechanical teaching emphasiz-
known problem, even at the college level, a situation ing memorization for testing, as alluded to in the
summarized so vividly by a college professor who aforementioned student’s email. Indeed, the latter
wrote to me: may even prefer such mechanical teaching because
it is less challenging than inspirational teaching
“While I am not losing sleep over the
which requires high-level creativity and indepen-
three “puzzles” you posed in your fine
dent thinking, the very traits we all look for when
article in the recent issue of the Amstat
we recruit students (and faculty). Therefore, if
News, I am losing sleep over the very
Harvard undergraduates can be viewed as a sam-
serious problem of not having competent
ple of high achieving high school students and if
classroom instruction in lower level
such students report more “turned-off” experi-
undergraduate courses. In particular, the
ences, then we must ask ourselves not only what
first and second introductory courses are
percentage of students are turned off by poorly
extremely problematic, as you have pointed
taught AP classes, but also what kind of students
out. Unfortunately, our mathematics
are more likely to be turned away.
colleagues think that “anyone” can
I perspired more when this was connected with
teach an introductory statistics course
the following anecdote, first heard from a Harvard
or, that having had one or two courses
undergraduate and then independently from a high
with emphasis in probability rather than
school student in California (the son of a friend).
statistical methodologies and thought,
In both cases, the student reported that his high
more than meets/surpasses any possible
school guidance counselor advised students that
qualifying criteria to teach introductory
they should consider taking AP stat courses only if
stats courses. As we know, this problem is
they cannot survive AP calculus courses. This sug-
not new, but it is reaching critical mass.”
gests that at least in some high schools AP statistics
is perceived as a “softer alternative” for students
An Even Harder Question: What Kind
who cannot yet handle calculus.
of Students Are We Turning Off?
Before we all get enraged by such a condescend-
An astute reader may have been wondering why
ing perception, let us collectively keep a cool head
I have not addressed an obvious question, that
and ask a deeper question. Should we then con-
is, could it be that the “turn-off” experience is
sider the impact of the AP program on the overall
unique to Harvard undergraduates? At the time
quality of students it helps to attract in addition
of writing my op-ed, Harvard undergraduates
to how many it attracts? Consider two versions of
were my targeted population, so this question was
Table 1, one for strong students and one for weak
of little interest. However, now that the “Harvard
students (the dichotomy, of course, is for simplic-
observation” is brought to the national level, I am
ity of illustration), labeled correspondingly with
indeed inspired by RPFHS to consider its general
a subscript S for strong and W for weak. Then
applicability. Coming with the inspiration, how-
arithmetically it is possible that we have
ever, is perspiration.
December 2009 AmstAt News 9
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