Does the HS GPA Mean Anything?

In the context of succeeding in college-level mathematics, does the HS GPA have any meaning?  Specifically, does a high school grade point average over some arbitrary value (such as 3.2) indicate that a given student can succeed in college algebra or quantitative reasoning with appropriate support?

Statistically, the HS GPA should not exist.  The reason is the the original measures (semester grades on a scale from 0 to 4 with 0.5 increments) is an ordinal measure; higher values are greater than smaller values.  A mean of a measure depends upon a presumption of “interval measures” — the difference between 0 and 1 is the same as the difference between 3 and 4.  The existence of GPA (whether HS or college) is based on convenient ignorance of statistics.

Given the long-standing existence of the HS GPA, one can not hope for leaders to suddenly recognize the basic error.  Therefore, let’s assume that the HS GPA is a statistically valid measure of SOMETHING.  What is that something?  Is there a connection between that something and readiness for college mathematics?

The structure of the data used for the HS GPA varies considerably by region and state.  In some areas, the HS GPA is the mean of 48 values … 6 courses at 2 semesters per year for 4 years.  If the school schedule allows for 7 classes, then there are 56 values; that type of variation is probably not very significant for our discussion.  The meaning of the HS GPA is more impacted by the nature of the 6 (or 7) classes each semester.  How many of these courses are mathematical in nature?  In most situations, at the current time, we might see 8 of the 48 grades coming from a mathematics course with another 4 to 8 coming from a science course.  Although most students take “algebra II” in high school, a smaller portion take a mathematically intense science course (such as physics).

In other words, we have a measure which has approximately a 20% basis in mathematics alone.  The other 80% represent “english”, social science, foreign language, technology, and various electives.  Would we expect this “20% weighting” to produce useful connections between HS GPA and readiness for college mathematics?  If these connections exist, we should see meaningful relationships between HS GPA and accepted measures of readiness.

So, I have spent some time looking at our local data.  We have only been collecting HS GPA data for a short time (less than one year), and this data can be compared to other measures.  Here are the correlation coefficients for the sample (n>600 for all combinations):

  • HS GPA with SAT Math: r = 0.377
  • HS GPA with Accuplacer College Level Math: r = 0.164
  • HS GPA with Accuplacer Algebra:   r = 0.338

Compare this with the correlations of the math measures:

  • SAT Math with Accuplacer College Level Math: r = 0.560
  • SAT Math with Accuplacer Algebra: r = 0.627
  • Accuplacer College Level Math with Accuplacer Algebra: r = 0.526

Of course, correlation coefficients are crude measures of association.  In some cases, the measures can have a useful association.  Here is a scatterplot of SAT Math by HS GPA:

 

 

 

 

 

 

 

 

 

The horizontal lines represent our cut scores for college level mathematics (550 for college algebra, 520 for quantitative reasoning). As you can see from this graph, the HS GPA is a very poor predictor of SAT Math.  We have, of course, examined the validity of the traditional measures of readiness for our college math courses.  The overall ranking, starting with the most valid, is:

  1. Accuplacer Algebra
  2. Accuplacer College Level Math
  3. SAT Math

The order of the first two differs whether the context is college algebra or quantitative reasoning.  In all cases, the measures show consistent validity to promote student success.

Here is a display of related data, this time relative to ACT Math and HS GPA.  The curves represent the probability of passing college algebra for scores on SAT Math.

 

 

 

 

 

 

 

 

 

[Source:  http://www.act.org/content/act/en/research/act-scores-and-high-school-gpa-for-predicting-success-at-community-colleges.html ]

For math, this graph is saying that basing a student’s chance of success just on the HS GPA is a very risky proposition.  Even at the extreme (a 4.0 HS GPA), the probability of passing college algebra ranges from about 20% to about 80%.  The ACT Math score, by itself, is a better predictor. The data suggests, in fact, that the use of the HS GPA should be limited to predicting who is not going to pass college algebra in spite of their ACT Math score … ACT Math 25 with HS GPA below 3.0 means “needs more support”.

So, back to the basic question: What does the HS GPA mean? Well, if one ignores the statistical violation, the HS GPA has considerable meaning — just not for mathematics.  The HS GPA has long been used as the primary predictor of “first year success in college” (often measured by 1st year GPA, another mistake).  Clearly, there is an element of “academic maturity or lack thereof” in the HS GPA measure.  The GPA below 3.0 seems to indicate insufficient academic maturity to succeed in a traditional college algebra course (see the graph above).

We know that mathematics forms a minor portion of the HS GPA for most students.  Although a small portion of students might have 50% of their HS GPA based on mathematically intense courses, the mode is probably closer to 20%.  Therefore, it is not surprising that the HS GPA is not a strong indicator of readiness for a given college mathematics course.

My college has recently implemented a policy to allow students with a HS GPA 2.6 or higher to enroll in our quantitative reasoning course, regardless of any math measures.  The first semester of data indicates that there may be a problem with this … about a third of these students passed the course, compared to the overall pass rate of about 75%.

I suggest that the meaning of the HS GPA is that the measure can identify students at risk, who perhaps should not be placed in college level math courses even if their test scores qualify them. In some cases, “co-requisite remediation” might be appropriate; in others, stand-alone developmental mathematics courses are more appropriate.  My conjecture is that this scheme would support student success:

  • Qualifying test score with HS GPA > 3.00, place into college mathematics
  • Qualifying test score with 2.6≤HS GPA<3.0, place into co-requisite if available, developmental if not
  • Qualifying test score with HS GPA < 2.6, place into developmental math

This, of course, is not what the “policy influencers” want to hear (ie, complete college america and related groups).  They suggest that we can solve a problem by both ignoring prior learning of mathematics and applying bad statistics.  Our responsibility, as professionals, is to articulate a clear assessment based on evidence to support the success of our students in their college program.

 

categories placement, Research connected to practice | | datetime March 26, 2019 9:28 am

1 Comment

  • By Susan Jones, March 26, 2019 @ 2:49 pm

    I’m pretty sure Complete College is just a mask for Let’s Whack The Budget. Oh, and … “in the name of equity” we’re going to cut off opportunities to learn the math. Folks with a 2.0 should *not* have such dismal chances!
    (Can’t remember if I shared my little Thread On Developmental Math REform — https://twitter.com/geonz/status/1041091592919179265 )

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