Math Education: Changes, Progress and the Club

What works?  How do we help more of our students … all students … achieve goals supported by understanding mathematics in college?  To answer those questions, we need to correct our confusion between measurements and objects; we need to develop cohesive theories based on scientific knowledge.  We are far from that stage, and policy makers tend to be just as ill-equipped.

Co-requisite remediation in mathematics has been broadly implemented.  The process which led to widespread use of a non-solution illustrates some of my points.

The rush towards co-requisite models is based on two patterns in ‘data’:

• Students who place into remedial mathematics courses tend to have significantly lower completion rates in programs
• Students who pass a college math course in their first year tend to have significantly higher completion rates in programs

These patterns in the data are not in dispute.  The reason I call co-requisite remediation a non-solution, however, is based on the faulty reasoning which bases a solution on these ‘facts’.  I find it surprising that our administrators accept this treatment for a problem which never addresses the needs of the students — it’s all about responding to the data.  That approach, in fact, is a political method for resolving a disagreement where people on one side hold the power to make decisions.

Eliminating stand-alone developmental math courses will not enable more students to complete their college program, beyond the 15% to 25% who were underplaced by testing — and then only to the extent that this group failed to complete their remedial math courses.  The data on this question usually shows that the issue is not failing remedial math courses; it’s retention or attempt.

Tennessee has been the most publicized ‘innovator’, and I have been addressed with the “club” that the leader of that effort was a mathematician — with the handle of the club saying “He’s a mathematician; and he thinks this is a good solution!”  Like mathematicians are never wrong :(.  Some evidence on related work in Tennessee is showing a lack of impact (https://www.insidehighered.com/news/2018/10/29/few-achievement-gains-tennessee-remedial-education-initiative).  I would expect that evidence to show that the main benefit of corequisite remediation is an increase in the proportion of students getting credit for a college math course in either statistics or quantitative reasoning (QR)/liberal arts (LAM).

When data shows that many students can pass a college math course in statistics, QR, or LAM I don’t see any evidence of corequisite working.  Many of my trusted colleagues believe that stat, QR and LAM have very minimal mathematics required; some believe that the only real requirement is a pulse as long as there is effort.

Why do students placed in remedial mathematics have lower completion rates?  The properties of this group of students is not homogeneous.  For some of them, they have reasonably solid mathematical knowledge that is ‘rusty’ … a short treatment, or just opportunity to review, is sufficient.  A significant portion have a combination of ‘rust’ and ‘absence’; the absence usually involves core ideas of fraction, percent, and basic algebraic reasoning.  Corequisite remediation presumes to address these needs via a ‘just in time’ approach; ‘rust’ responds well to short-term treatments — absence not so much.  Another portion of remedial math students have mostly ‘absence’ of mathematical knowledge.

I’ve written previously on the question of ‘when will co-requisites work’ (Co-requisite Remediation: When it’s likely to work).  My comments here are more related to the meaning of ‘work’ — what is the problem we are addressing, and what measures show the degree to which we are solving it?

One of the primary reasons we have today’s mess in college mathematics is … ourselves.  For decades, we presented an image of mathematics where calculus was the default goal as shown in the image at the start of this post.  This image is so flawed that external attacks had an easy time imposing a political solution to an educational problem:  avoidance.  Of course, courses not preparing students for calculus are generally ‘easier’ to complete.  That is not the problem.  The problem is our lack of understanding related to the mathematical needs of students beyond what we find in guided pathways.

To clarify, the ‘our’ in that last sentence is a reference to everybody engaged with both policy and curriculum.  As an example of the lack of understanding, consider the question of the mathematics needed for biology in general and future medical doctors in particular.  We hear comments like “doctors don’t use calculus” on the job; I’m pretty confident that my doctor is not finding derivatives nor integrating a rational function when she determines appropriate treatment options.  However, mastering modern biology depends on conceptual understanding of rates of change along with decent modeling skills.  The problem is not that doctors don’t use calculus on the job; the problem is that our mathematics courses do not address their mathematical needs.

So, back to the two data points mentioned earlier.  The second of these dealt with an observation that students who complete a college mathematics in their first year are more likely to complete their program.  This type of data is often used as a second rationale in the political effort to impose co-requisite remediation … get more students into that college math course right away.  Of course, the reasoning is based on confusing correlation with causation; do groups of similar students have better completion with a college math course right away compared to delays?  Historically, students who are able to complete a college math course in the first year have one or more of these advantages:

• Higher quality opportunities in their K-12 experience
• Better family support
• Lack of social risk factors
• Presence of enabling economic factors

If these factors are involved, then we would expect a ‘math in first year’ effort to primarily mean that more students complete a college math course — not that more students complete their program.  This is, in fact, what the latest Tennessee data shows.  I have not been able to find much research on the question of whether ‘first year math’ produces the results I predict versus what the policy marketing teams suggest.  If you know of any research on this, please pass it along.

We need to own our problems.  These problems include an antiquated curriculum in college mathematics combined with instructional practices which tend to not serve the majority of students.  Clubs with data engraved on the handle are poor choices for the forces needed to make changes; understanding based on long-term scientific theories provides a sustainable basis for progress which will serve all of our students.

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