## Segregation in College Mathematics: Corequisites! Pathways?

So, this post will mostly apply to those of us located in urban colleges (more than rural). The idea is to remind of the societal costs of “separate and not equal”.

As a general statement, urban public schools have more challenges than suburban schools (and more than rural schools). The role of poverty in this situation appears substantial, and the burden of this poverty tends to fall on ‘minority’ students more than ‘majority’. In this post, I’m focusing on two categories — black/African American and white/Caucasian.

If you track the proportion of each course that is black, you are likely to get a chart like this one. Note that “0” represents a college-level math course (most commonly ‘college algebra’ … more on that later).

This comes from a college where black students represent about 10% of the population; the college does not have a “-3 course” (pre-algebra). The pattern in course enrollment is a similar pattern to the ‘placement levels’ of each group … the mean placement level for black students is about -1.4 compared to -0.6 for white students. If all students are in a sequence (‘path’) that produces an equal chance of succeeding to all college mathematics, there is ‘equality’ (given the unequal starting points).

However, two current trends break that ‘equality’ and produce a system of separate and unequal. In many co-requisite models, students who do not place into college mathematics are given only the option to take a non-STEM math course (statistics or quantitative reasoning aka ‘QR’). In general, colleges using a co-requisite model find that their ‘support sections’ (ones taken by non-placing students) are predominantly minority. I know some colleges have tried to use co-requisite models in college algebra (though more often ‘intermediate algebra’); these results are seldom published, and I think this is due to the much lower ‘results’ than statistics or QR. The result of this type of system is an unequal result for minority students — they are discouraged (or even prevented) from pursuing a STEM or high-tech program. A new segregation is being sold to colleges, in the name of ‘better results’; more on that later!

Some ‘pathways’ implementations also produce this same unequal pattern. Those placing ‘lowest’ and ‘struggling students’ are strongly encouraged to take a stat or QR pathway program; some of these programs actually do allow students to select a STEM or high-tech program, but many do not. The most common model is a side-by-side design … Math Literacy (or similar course) as an option to beginning algebra, where the Math Literacy course only leads to stat or QR. In the K-12 world, this is called “Tracking”. Pathways often create a segregated condition, due to the impacts of the lower-performing K-12 schools.

One argument is that the co-requisite models (and pathways) at least get students to complete a college math course, most commonly stat or QR. The question remains … so WHAT? There is an assumption that this stat/QR approach results in more students getting a degree (likely to be true). But … what good is the degree? Are there actually jobs for that program?

Obviously, the answer to that last question is ‘in some cases’. In some regions, nursing requires either statistics or QR for their associate degrees, and the employment outlook is often good. However, these health careers programs can be ‘selective admission’. My experience has been that students accepted in to a nursing program tend to be ‘whiter’ than the college population in general … which likely goes back to the urban school system problems. As a practical matter, I don’t think that a focus on stat or QR, in either co-requisite or pathways, results in ‘equal’. We are creating separate in a deliberate strategy, without ensuring that they are equal. [Of course, it’s also reasonable to say that we should avoid “separate” in the first place.]

Now, I’m not saying that co-requisite and pathways have no place in college mathematics. The concern deals with the ‘scaling up’ that is often sought with them, as well as the target population. Co-requisite remediation can be quite effective at the boundary … students who “just miss” qualifying for their college course (stat, QR, or college algebra); this system can be used to partially offset the negative impacts of lower-performing K-12 schools. Pathways keep our focus on getting out of the way as much as possible … get them to their college course quickly; however, all pathways should preserve student options. Any pathway that blocks student options is very likely to result in ‘unequal’ conditions.

Both of these efforts (co-requisites, pathways) remind me of the segregation caused by ‘school of choice’. Do we really want to institutionalize segregation in these new ways?

I think the better response is to modernize the entire mathematics curriculum in colleges. Start by replacing arithmetic and basic algebra courses with Math Literacy with an intentional design to provide students options at the next level. Replace intermediate algebra with Algebraic Literacy with its intentional design to prepare students for modern college mathematics courses. Replace college algebra with a course likewise designed to actually prepare students for calculus. Reduce the calculus curriculum to fewer courses while incorporating more numeric methods (see “Common Vision”).

We do not need to create separate conditions for students, not nearly as much as we need to modernize our curriculum.

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