Placement: Does HS GPA Add EQUAL Value?

Many people are talking about ‘multiple measures’ placement, especially the option of using high school grade point average as an input variable. In some locations (like mine) ‘multiple measures’ is translated ‘HS GPA instead of placement test’, where ‘multiple’ means ‘alternative’. True multiple measures has some appeal. Conceptually, there is an advantage to using more than one variable as input when the variables measure different traits. The HS GPA involves several issues, with equity being high on my list.

As mathematicians, the first thing we should say about HS GPA is that this variable is a mis-use of the raw data. The grades in any class are barely ordinal in nature (rankings); the average used (mean) is based on ratio variables (equal intervals AND a 4 represents twice something compared to 2). When a variable has statistical flaws such as this, any further use in analysis should be suspect. Whatever the disadvantages of tests (ACT, SAT, or placement), at least they involve appropriate use of the measures from a statistical point of view.

High school GPA has a number of confounding variables, some of which are shared by most tests used today. In particular, economic level (SES) and ethnicity are both factors in the HS GPA picture (as they are in college GPA). This type of analysis is widespread and the results consistent; one such report is from the Educational Testing Services (see http://www.ets.org/Media/Research/pdf/RR-13-09.pdf ). Using HS GPA does not level the playing field, given the high correlations normally found between the measures. In fact, my view is that using HS GPA in addition to a test will benefit mostly majority students from comfortable homes … and will again place minority and poor students in lower levels.

As an anecdotal piece of data, I was at a conference session recently on co-requisite remediation where the placement method involved tests or HS GPA. Through the first year of their work, the co-requisite ‘add-on’ sections were almost totally minority … even more than their traditional developmental classes had been. [The institution used a co-requisite model where all students enroll in the college course, and those not meeting a cutoff were required to enroll in the add-on section as well.]

When people try to explain the predictive ‘power’ of HS GPA, they often use ill-defined phrases such as ‘stick-to-itness’. I suspect that our friends teaching high school would have a different point of view, where grades in the C+ to B range reflect not skills but attitudes (primarily compliance). How can we justify using an inappropriate statistic (grades are ordinal) which measures “who knows what”? Whatever the HS GPA measures, it is indirectly related to preparation for college mathematics. The connections are likely to be stronger for writing.

The arguments FOR using the HS GPA in placement are based on studies which indicate an equal or higher predictive validity, versus tests alone. One of the better studies within mathematics is one done by ACT (see http://www.act.org/content/dam/act/unsecured/documents/5582-tech-brief-joint-use-of-act-scores-and-hs-grade-point-average.pdf). Here is their graph:

$act math and hs gpa versus college algebra success 2016$

This graph is showing the probability of passing college algebra, with the 5 curves representing ACT Math levels (10-14, 15-19, etc). If a student’s ACT Math is below 20, their HS GPA does not improve their probability of success — until we get between 3.5 and 4.0. The 20 to 24 groups and above have a pattern indicating that it might help to include the GPA; since most of us use cutoffs in the 19 to 22 range, this shows some promise when using BOTH variables.

However, notice the negative indications … if the ACT math is high (over 25) and the GPA is low, the data indicates that we should place the student differently because the student has a dramatically lowered pass rate. Perhaps THIS is the place for co-requisite remediation! I would also point out the overall picture for HS GPA at the high end … the probability of success is varied, and depends upon the test score.

SUMMARY:
We know that both HS GPA and tests tend to reflect inequities, where the results tend to place more minorities in developmental courses. Although predictive value increases (correlation), we are using an inappropriate statistic (HS GPA) with little connection to preparation for college mathematics. The available research suggests some minor gains for using HS GPA:

for students just below the college math test cutoff with a very high HS GPA
those with high scores and low HS GPA
use of HS GPA alone results in an almost random assignment of students

Placement has never been a confident endeavor; even the best measures (tests or other) are incomplete and impacted by other variables. Placement Tests have taken a beating in recent years, a treatment which I think was not justified. Modernizing the placement tests is a more appropriate response … an idea which I will pursue in an upcoming post.

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placement | Jack Rotman | April 14, 2016 9:40 am

3 Comments

By Andrew Pitcher, April 15, 2016 @ 6:00 pm

I’m interested to see what you have to say in your upcoming post on modernizing the placement test. One of the major issues I have wondered about with curriculum redesign is that even if our placement tests did a good job of assessing algebra skills, they wouldn’t be appropriate for placing students into a course sequence that doesn’t focus on teaching algebra skills.
By Jack Rotman, April 18, 2016 @ 1:08 pm

I think the placement issue is more a matter of emphasis — of algebra, of skills, of reasoning, of communication. We live in an era of ‘non-algebraic’ when we are partially over-reacting: algebraic symbolism is not needed very much outside of math and sciences classes, but algebraic reasoning is needed. I’m working on a modern placement assessment (in early draft form) which seeks to assess a broader range of ‘skills’.
By Vernon, April 19, 2016 @ 2:53 pm

The State of Missouri is mandating multiple measures and with ACT out of the placement business via COMPASS we are reverting back to ACCUPLACER. It will be interesting to see how GPA is used in the system. The state is also mandating the ACT for every HS Student.

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