Category: politics of developmental mathematics

The Selfishness of the Corequisite Model

One of the major ‘things’ right now is “corequisite remediation”, referring specifically to the practice of placing (most or all) students in a college mathematics course with a requirement that certain students take a support class.  Over time, we will discover that this has sufficient promise to justify further exploration and use.  The problem is … the practice is very selfish on our part in many of the common implementations.

Most data on this practice comes from two college math courses — introductory statistics and liberal arts math.  For most offerings in those courses, few prior skills are needed for success; in both cases, the most common need is for expressing fractions as percents and some proportional reasoning.  Algebraic reasoning is seldom needed.  In both cases, the legacy prerequisite (usually intermediate algebra) was an artifact more related to establishing transfer than to course needs.  Few co-requisites structures have been done in college algebra nor in quantitative reasoning with an algebraic emphasis

My contention is that using co-requisite methods for a non-STEM math course amounts to a selfish decision on our part.  We place a higher priority on improving our ‘measures’ of completing that one math course … at the expense of preparing students for other quantitative needs in college.  This is especially an issue for our friends in science, who often depend on a variety of algebraic concepts in their courses (as they should).  The co-requisite model focuses almost totally on “What do they need for THIS terminal math class?” (which is a small set); ignored is the larger set “What do students need for college quantitative work?”.

Now, it is true that the traditional developmental mathematics courses do not deliver on that larger set — at least, not in an efficient manner or with good results.  Replacing developmental math courses with the co-requisite model (as is being suggested) is placing students at risk … just so a math course can ‘look better’.  Our response should be:  “How can we make fundamental improvements in the course content and design so that developmental mathematics works for almost all students across their college program?”

Our reason for existence in developmental mathematics is the whole student for their whole college experience.  We can achieve short term ‘better results’ for ourselves with co-requisite remediation.  This comes at the expense of leveling the playing field, equity, and student success in general.  Can we be that selfish?

I realize that I am attributing a personal motivation to a practice in the profession.  I’m okay with that … most of us are in this profession because of personal motivations.  I think large numbers of ‘us’ have a deep commitment to equity, as well as upward mobility.   Co-requisite remediation creates a system focused on the short-term ‘results’, often involving minority-heavy support classes, with few long-term benefits (if any).

Our responsibilities involve much more than “one math course”.  Let’s do our job.  Instead of taking the easy ‘out’ of co-requisite remediation, we should replace the traditional sequence of developmental math courses with a very short structure to serve all college students and all of their needs … Mathematical Literacy and Algebraic Literacy (or similar courses).

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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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Talking About Equity as an Avoidance

My department has begun a process which will (hopefully) lead to meaningful and sustained improvements in our equity picture.  Current, and historical, data makes it clear that our program is not serving all groups adequately.  Black students (aka “african american”) almost always have a pass rate significantly lower than other groups, after accounting for their level of preparation.

I am very pleased with my colleagues and their willingness to spend time working on a problem which involves some discomfort … it’s not always easy to talk about race and equity.  Much of our initial discussion focused on our point of view and problems that make sense to us … phrases like “student skills”, “role models”, and “tutoring” we very common.  “Compassion” and “empathy” were also used.  These are all good thoughts, but tend to focus on the surface and symptoms.

However, I am sure that our conversation will need to progress to deeper levels of understanding.  One reason to believe this is that this conversation has occurred hundreds of times in other institutions and organizations without producing an accepted basket of ‘best practices’ for eliminating the inequity as we generally would like.

One perspective that might help our profession actually make progress on this comes from Danny Martin (University of Illinois at Chicago).  Dr. Martin delivered a talk entitled “The Collective Black and Principles to Actions” (available at .  The ‘Principles to Actions” part of the title refers to the 2014 publication by NCTM of that name.  The “collective black” in the title refers to a way to understand a social structure in the United States.

A quote from near the end of that article is:

Does this document represent, symbolically and in spirit, the kind of disruptive violence to the
status quo that can move the last to first?  Can it truly help in improving the collective conditions
— not isolated examples of success — of African American, Latin@, Indigenous, and poor
students? By success, I do not mean slow growth and incremental gains.

The “disruptive violence” in this quote might bother some readers.  Remember that Dr. Martin is speaking of social institutions, not a personal philosophy of political change.

I think Dr. Martin’s point, perhaps shared by Dr. Martin Luther King as well, is that incremental change and “stuff around the edges” will not produce meaningful changes at the level necessary.  Our  problems are too well established in the existing structures, and even in the vocabulary we use to describe ‘the problem’.  For example, millions of white people have had “compassion” and “empathy” for a wide variety of students (including the group ‘black students’ my department is focused on).

Here is a point … Perhaps “white people” only support working on “equity” when this work does not involve any change in the white power relationships and social structure.  Are we willing to share power and authority to reach the lofty goals we seek?

Perhaps we will find that reaching equity in our department depends upon fundamental changes in the  local community.  The urban schools have old buildings, few resources, and other significant challenges; this district is heavily ‘minority’ (black students in particular) … because our state allows “school of choice’, where THOSE WITH RESOURCES can take their students to a ‘better’ school in the suburbs.   Can ‘separate and sort of equal’ ever allow us to achieve equity in higher education?  [The local condition amounts to sanctioned segregation of schools, especially at the high school level.]

We are likely to encounter large-size problems in our work to eliminate inequity in our courses.  We have only begun the conversation, and I’m proud that my colleagues are willing to begin this journey.  Our success will likely involve changes that would have been difficult to imagine prior to beginning the process.  So … I appreciate your “moral support”.

Is your department ready to face the challenges of doing effective work to reduce inequity?

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TBR and the Co-Requisite Fraud

Since many policy makers and academic leaders are telling us that we need to do (or consider) co-requisite remediation because of the results from the Tennessee Board of Regents (TBR), the TBR should release valid results … results which are consistent with direct observations by people within their system.  #TBR #Co-Requisite

Earlier this year, one of the TBR colleges shared their internal data for the past academic year, during a visit to my college.  This particular institution is not unusual in their academic setting, which is quite diverse.  Here is a summary of their data.

Foundations (intermediate algebra)          College: 61%

Math for Liberal Arts                                College: 52%

Statistics (Intro)                                      College: 40%

The TBR lists 51.7% as the completion rate for the same time period.  [See]

Recently, I was able to have a short conversation with a mathematics faculty member within the TBR system.  The college administrator who visited earlier this year said that their mathematics faculty “would never go back” now that they have tried co-requisite remediation, suggesting that most faculty are now supporters.  The faculty member I talked with had some very strong language about the validity of the TBR data; the phrase “cooked the books” was used.  This internal voice certainly does not sound like a strong supporter, and suggests that there is deliberate tampering with the data.

There are two direct indicators of fraud in the TBR data.

  1. Intermediate Algebra (Foundations) was used in the data, even though it does not meet any degree requirement in the system.  [It is “college level”, but does not count for an AA or AS degree.]  Foundations had the highest pass rate for the college visiting; however, TBR does not release course-by-course results.]
  2. “Passing” is a 1.0 or higher, even though the norm for general education is a 2.0 or higher.  Again, the TBR does not release actual grade distribution.  The rate of D/1.0-1.5 grades can vary but is often 10% or higher.

The data is presented as passing (implied 2.0) a college math course (implied not developmental); the TBR violates both of these conditions.  If the data was financial instead of academic, the condition is called fraud … as in a corporation which manages to report a large profit instead of the reality of a very small profit.

Perhaps the TBR did not intentionally commit this fraud.  However, given that the leaders involved are experienced academics, that does not seem likely.  The errors I am seeing are too fundamental.

Of course, it is possible that both views from internal sources are incorrect.  I do not think that is as likely as the TBR data being incorrect.

My estimate of the ACTUAL completion rate of college math courses (liberal arts math and statistics) with a 2.0/C or higher:

30% to 40%  completion of college mathematics in corequisite remediation … NOT 50% to 60% as claimed by the TBR.

Whether I am correct in claiming fraudulent data reporting from the TBR, I am sure that the TBR needs to provide much better transparency in its reporting. Developmental education is being attacked and fundamentally altered by policy makers and external influencers whose most common rationale consists of the statement “Co-requisite remediation has to be a good thing … that has been proven by the Tennessee data!”.

Some readers may suggest that my wording of this post is overly-dramatic and not in keeping with the norms of academic discourse.  I think the dramatic tone is quite warranted considering the manner in which the TBR data has been used by Complete College America and others.  I agree that this post is not within the norms of academic discourse, but I believe that the tone is totally within the norms of the new reality of higher education:

Instead of discourse, over time, building upon prior results, we have allowed external influencers to determine the agenda for higher education.

If policy makers and leaders seek to push us in the direction they prefer and then use selected data to support this direction, then those policy makers and leaders can expect us to call them out for fraud and other inappropriate behavior.

It is time for the Tennessee Board of Regents to report their data in a way that allows the rest of us to examine the questions of ‘what is working’ in ‘which course’ under ‘what conditions’.

Enough of the fraud; it’s time to show us the truth about what, which, and conditions.

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