Cooked Carrots and College Algebra

Perhaps your state or college is using high school grade point average (HS GPA) as a key placement tool in mathematics, in the style of North Carolina.  The rationale for this approach is studies showing a higher correlation between HS GPA and success in college mathematics, compared to standardized tests (SAT, Accuplacer, etc).  Is this a reasonable methodology?

Some of us are doing true multiple measures, where HS GPA is included along with other data (such as test scores).  However, North Carolina is using HS GPA as the primary determinant of college placement; see http://www.nccommunitycolleges.edu/sites/default/files/academic-programs/crpm/attachments/section26_16aug16_multiple_measures_of_placement.pdf .

This HS GPA movement reminds me of a specific class day in one of my classes — a graduate level research methods class.  On this day, the professor presented this scenario:

Data shows that students who liked cooked carrots are much more likely to succeed in college.  Should a preference for cooked carrots be included as a factor in college admissions?

The goal, of course, was to consider two basic statistical ideas.  First, that correlation does not equal explanation.  Second, most correlations have a number of confounding variables.  In the case of cooked carrots, the obvious confounding variable is money — families eating cooked carrots, as a rule, have more money than those who don’t.  Money (aka ‘social economic status’, or SES) is a confounding variable in much of our work.  We could even conjecture that liking cooked carrots is associated with a stable family structure as well as non-impoverished neighborhoods, which means that there will be a tendency for cooked-carrot-liking students to have attended better schools.  Of course, this whole scenario is bound up in the cultural context of that era (the 1970s in the USA).

In a similar way, proponents point out the high correlation between HS GPA and success in college mathematics.  That correlation (often 0.4 or 0.5) is higher than our test score correlations (often 0.2 or 0.3), which is often ‘proof enough’ for academic leaders who do not apply statistical reasoning to the problem.  Here is the issue:

If I am going to use a measure to sort students, I better have a sound rationale for this sorting.

That rationale is unlikely to ever exist for HS GPA … no explanation is provided beyond the statistical artifact of ‘correlation’.  Student A comes from a high-performing school and has a 2.5 GPA; do they need remediation?  Student B comes from a struggling school and has a 3.2 GPA; are they college ready?  Within a given school, which groups of students are likely to have low GPA numbers?  (Hint: HS GPA is not race-neutral.)

If you are curious, there is an interesting bit of research on HS GPA issues done by Educational Testing Service (ETS) in 2009; see https://www.ets.org/Media/Research/pdf/RR-13-09.pdf .  One of the findings:  HS GPA is “contaminated” by SES at the student level (pg 14).   Just like cooked carrots.

So, if you are okay with ‘cooked carrots’ being a sorting tool for college algebra, go ahead with HS GPA as a placement tool.

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