## Progression in Math — A Different Perspective

Much is made these days of the “7 percent problem” (sometimes 8%) — the percent of those placing in to the lowest math course who ever pass a college math course. This progression ‘problem’ has fueled the pushes for big changes … including co-requisite remediation and/or the elimination of developmental mathematics. The ‘problem’ is not as simple as these policy advocates suggest, and our job is to present a more complete picture of the real problem.

A policy brief was published in 2013 by folks at USC Rossier (Fong et al); it’s available at http://www.uscrossier.org/pullias/wp-content/uploads/2013/10/Different_View_Progression_Brief.pdf. Their key finding is represented in this chart:

The analysis here looks at actual student progression in a sequence, as opposed to overall counts of enrollment and passes. This particular data is from California (more on that later), the Los Angeles City Colleges specifically. Here is their methodology, using the arithmetic population as an example:

- Count those who place at a level: 15,106 place into Arithmetic
- In that group, count those who enroll in Arithmetic: 9255 enroll in Arithmetic (61%)
- Of those enrolled, count those who pass Arithmetic: 5961 pass Arithmetic (64%)
- Of those who pass Arithmetic, count those who enroll in Pre-Algebra: 4310 enroll in Pre-Algebra (72%)
- Of those who pass Arithmetic and enroll in Pre-Algebra, count those who pass Pre-Algebra: 3410 (79%)
- Compare this to those who place into Pre-Algebra: 68% of those placing in Pre-Algebra pass that course
- Of those who pass Arithmetic and then pass Pre-Algebra, count those who enroll in Elementary Algebra: 2833 enroll in Elementary Algebra (83%)
- Of those who pass Arithmetic, then pass Pre-Algebra, and enroll in Elementary Algebra, count those who pass Elementary Algebra: 2127 pass Elementary Algebra (75%)
- Compare this to those who place into Elementary Algebra: 70% of those placing into Elementary Algebra pass that course
- Of those who pass Arithmetic, then Pre-Algebra, and then Elementary Algebra, count those who enroll in Intermediate Algebra: 1393 enroll in Intermediate Algebra (65%)
- Of those who pass Arithmetic, then Pre-Algebra, and then Elementary Algebra, then enroll in Intermediate Algebra, count those who pass Intermediate Algebra: 1004 pass Intermediate Algebra (72%)
- Compare this to those who place directly into Intermediate Algebra: 73% of those placing into Intermediate Algebra pass that course

One point of this perspective is the comparisons … in each case, the progression is approximately equal, and sometimes favors those who came from the prior math course. This is not the popular story line!

I would point out two things in addition to this data. First, my own work on my institution’s data is not quite as positive as this; those ‘conditional probabilities’ show a disadvantage for the progression (especially at the pre-algebra to elementary algebra transition). Second, the retention rates (from one course to the next) are in the magnitude that I expect; in my presentations on ‘exponential attrition’ I often estimate this retention rate as being approximately equal to the course pass rate … and that is what their study found.

One of the points that the authors make is that the traditional progression data tends to assume that all students need to complete intermediate algebra (and then take a college math course). Even prior to our pathways work, this assumption was not warranted — in community colleges, students have many programs to choose from, and some of them either require no mathematics or basic stuff (pre-algebra or elementary algebra).

The traditional analysis, then, is flawed in a basic, fatal way — it does not reflect real student choices and requirements. For the same data that produced the chart above, this is the traditional analysis (from their policy brief):

This is what we might call a ‘non-trivial difference in analysis’! One methodology makes developmental mathematics look like a cemetery where student dreams go to die; the other makes it look like students will succeed as long as they don’t give up. One says “Stop hurting students!!” while the other says “How can we make this even better?”

So, I’ve got to talk about the “California” comment earlier. The policy brief reports that the math requirement changed for associate degrees, in California, during the period of their study: it started as elementary algebra, and was changed to intermediate algebra. I don’t know if this is accurate — it fits some things I find online but conflicts with a few. I do know that this requirement is not that appropriate (nor was elementary algebra) — these are variations of high school courses, and should not be used as a general education requirement in college. We can do better than this.

This alternate view of progression does nothing to minimize the penalties of a long sequence. A three-course-sequence has a penalty of about 60% — we lose 60% of the students at the retention points between courses. That is an unacceptable penalty; the New Life project provides a solution with Mathematical Literacy replacing both pre-algebra and elementary algebra (with no arithmetic either) and Algebraic Literacy replacing intermediate algebra (and also allowing about half of ‘elementary algebra students’ to start a course higher).

Let’s work on that question: “How can we make this even better?”

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