Does College Mathematics Have a Future?

I have been wondering about something over the past few months. The concerns originated much earlier, as it seems that people are trying to avoid algebra within college math classes for non-STEM students.  More concerns were added as policy experts suggest that we align mathematics requirements with programs and, ideally, contextualize math for non-STEM students.  #CCA #STEM #MathPaths

There seem to be two premises at work:

1. STEM students need lots of algebra, like we’ve been doing.
2. Non-STEM students are harmed by algebra, and need something less ‘challenging’.

You can see by my phrasing that I am not objective about these premises.  Many people — mathematics educators, policy experts, and more — presume that STEM students, especially those headed towards calculus, are well-served by a college algebra experience.  The problem is that (1) the typical college algebra experience lacks development of covariational reasoning needed in calculus, and (2) our client disciplines have a more diverse need than we work with.  We continue to dig deep into symbolic calculus (which is one of our great achievements) but we downplay the usefulness of numeric methods that are heavily used in engineering, biology, physics, and more.

The STEM life is much more than putting calculus on top of algebra.

A brief story:  At a recent state MAA meeting, I attended a student session on mathematical modeling in biology.  The presenters where all about to get the BS in biology, and reported on fitting models using Matlab (Matrix Laboratory).  After the session, I asked one of the presenters where they learned the techniques … in a math class?  Nope — their biology professor taught them mathematical modeling because their math courses did not.

The non-STEM students are being tracked into statistics or quantitative reasoning, with statistics having the bigger push.  Policy experts push statistics because it is ‘practical’, and people will ‘use it’; these statements are true to some extent.  The problem is that almost all mathematical fields are practical.  In particular, algebra is practical.  Mathematics courses have failed to present algebra as a practical tool for living and for basic science & technology.

Even in a quantitative reasoning courses, we tend to de-emphasize great mathematical ideas.  Sure, we cover finances and statistics, voting and logic; however, the symbolic work combined with the concepts for transfer to new situations tends not to be there.  We use one of the best QR books on the market, and I supplement heavily on functions and related concepts; still, I do not think it is enough.  Some QR courses only apply a couple of concepts (such as proportional reasoning, or math in the news); great components of a QR course … terrible foundations for a QR course.

The risk I see is this: At some point, mathematics will be eliminated.  Non-STEM students get tracked into statistics and weak QR courses; mathematics is thereby eliminated for these students.  STEM students outside of mathematics are only required to show some basic background, and then all of their mathematics is taught by other departments (see biology story above).  The only mathematics students around will be mathematical science majors, and (in most institutions) this is far too small to support mathematics.

We need to do two difficult things:

• Get our heads out of the sand, in terms of modern mathematics (what we should be teaching)
• Effectively argue against the decay of mathematics requirements (especially in two-year colleges)

Fortunately, we have resources from people wiser than I … such as the Mathematical Sciences 2025 material (http://www.nap.edu/catalog/15269/the-mathematical-sciences-in-2025 ).  Please take a look at the diverse nature of mathematics needed in STEM fields, and think about how narrow of a focus we have.

The major threat to mathematics requirements comes from policy influencers (CCA, JFF, Lumina, etc).  Just because they say it, and have ‘data’, does not mean the idea is good or safe.  The degree requirements in institutions are the responsibility of faculty (including mathematics faculty).  It is our job to honor that responsibility, which does not belong to these external agencies.

Let’s keep mathematics as a valid component in a college education.

 
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GPS Part II: Guided Pathways for Success, a Mathematician’s View (Part II)

Guided Pathways (GPS) is one of the current ‘movements’ in higher education, both at the associate degree and bachelors degree level.  A description of GPS is available at http://completecollege.org/the-game-changers/ (although quite a bit of this document is rhetoric designed to convince the reader of a point of view).

At the heart of GPS is the concept of one set of courses for the student to take for their program, starting (hopefully) in their first semester.  Mathematics is specifically addressed in the GPS model … “Math Alignment to Majors”, and this echos movements within the mathematics profession to create pathways leading to multiple end-points (college algebra/calculus, statistics, quantitative reasoning or QR).

This apparent congruence is a concern for me.  Here is the issue … math alignment is intended to divert students out of the college algebra path as early as possible.  This is somewhat true of pathways in general, but the GPS work tends to create rigid walls around the paths.  A student declares a major like nursing (which the CCA considers “STEM”, by the way) … and is likely to take statistics as their math course (possibly QR).  What happens when this student gets inspired to pursue a truly STEM field, such as biology or pre-med?  Actually, the student will not have much chance to be inspired in their math courses; the GPS work has a goal “as little as possible” when it comes to mathematics.

One of the reasons I believe so strongly in the QR course we offer is that it builds algebraic reasoning (as well as statistical reasoning and proportional reasoning).  If all QR courses did this, I would have fewer concerns about GPS paths … if QR was the default math path.  In many parts of the country, statistics has become the default math path (outside of STEM); I am concerned about a student’s only college math course being in one field of mathematics when the student’s program does not call for specialized or focused mathematics.

GPS also presents the idea of milestone courses; mathematics is likely to be on an institution’s short list of milestones, especially in the first year.  I do not want students to see that the world shares their desire to get math out of the way, nor do I want to see mathematics used as gatekeepers for programs.  Certainly, if the student’s program involves courses which will actually use the mathematics in their math course, by all means … require the math in semester #1.

Too often, however, our colleagues in other disciplines have de-quantified their subject … even STEM disciplines.  Intro science courses are often presented (at the associate degree level in particular) in a conceptual way, without the mathematical methods (or ideas, even) used in current work in those fields.

GPS holds promise, and our students can benefit if we do a good job.  We need to avoid the pressure to swallow the GPS pill whole; each component needs critical thinking and the professional expertise we can bring.

 
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Guided Pathways For Success: a Mathematicians View (part I)

The largest wave of external influence hitting colleges (especially community colleges) at this time is “Guided Pathways for Success” (GPS).  GPS is a package of talking points aimed at supporting degree completion at a higher (much higher) rate.

Here are the basic components of the GPS (see http://completecollege.org/the-game-changers/):

• Whole programs of study (as opposed to individual course selection)
• Informed choices and “meta majors“
• Default pathways (changing majors requires approval)
• Guaranteed milestone courses (each semester)
• Intrusive, just-in-time advising
• Math alignment to majors

GPS is one of the ‘game changers’ being advocated by Complete College America (co-requisite remediation is another).    One problem with the implementation of GPS is that the work is very complicated, which usually results in a lack of sufficient information for almost all of the people working on the program.  We’re starting ours this year, at my college, and a handful of people have a complete view of our work … the rest of us only know about parts of one of the 6 efforts.  It’s also true that colleges doing GPS often attempt to take on another ‘game changer’.

One specific issue where people often lack knowledge is the initial student choice … which program?  meta-major? Non-degree (and non-certificate)?  For students receiving financial aid through any federal program, they can choose a specific program leading to either transfer or employable occupation.  The idea of the meta majors is that these would be a shared starting point for clusters of eligible programs, designed to provide occupational information and specific program selection in the first year.

As a mathematician, I see several advantages to GPS … and some areas of concern.  This initial post will summarize some advantages and explore an area of concern.

So, here are some things I like (from a math point of view):

1. A strong emphasis on setting a goal (not much is worse than having students in class who have no idea what their goal is).
2. An established sequence of courses for the program.  [My college, like many ‘CC’, have drifted far away from structure for courses.]
3. A message that picking a major is a serious step, best done without a dart board but with sufficient information.
4. Putting an academic purpose in front of advising (completion).

Clearly, one area of concern related to GPS is the fact that other efforts (co-requisite remediation, for example) are often put into a ‘bundle’ of efforts for a college.  That is not a GPS issue; my first concerns with GPS relative to mathematics exist around the ‘milestone’ course idea.

Historically, mathematics has been used (and abused) as the ultimate gate keeper.  Students are required to take certain mathematics courses to prove that they are okay for the program.  Yes, mathematics is important for many careers; however, a gatekeeper context creates negative expectations for students.

If a program or meta-major requires mathematics (which they mostly will), what course will be most commonly selected for a milestone course in the first year?  Mathematics has already been mentioned for this role on my campus.  If the program is STEM or STEM-related, this is a great idea; students in these programs will have a sequence of mathematics to complete … and will also be using mathematics in other classes during most semesters.

Outside of those programs, I do not want students to (generally) take mathematics in the first year.  Many of these students currently wait until their very last semester to take mathematics, and this is a bad thing … but not as bad as being told that you must take that math course in the first (or second) semester.  I am concerned about student attitudes towards learning, combined with the challenges of starting college, within the mathematics classroom.

So, when a student looks at their program choices from among the non-STEM options, they might see “Math125” (or whatever) on their list of expected first semester courses.  The meta major option related to their program might not have a math course (because math is ‘aligned to majors’).  Likely result?  Students pick a meta major, in order to delay taking mathematics … or, we see reluctant (or resistant) students in math classes.

At least when students put off their math class until ‘late’, they come motivated to pass … perhaps not understanding what this means, but motivated.  First year CC students are likely to be reluctant and not especially motivated to pass mathematics.

Admittedly, this first concern discussed is not the best choice to begin the conversation.  The concern deals with the factors influencing student choice along with motivation.    I’ll try to do better next time!!

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Co-requisite Remediation: When it’s likely to work

A recent post dealt with the “CCA” (Complete College America) obsession with ‘corequisite remediation’.  In case you are not familiar with what the method involves, here is my synopsis:

Co-requisite remediation involves the student enrolling in both a credit course and a course that provides remediation, concurrently.  The method could be called ‘simultaneous’ remediation, since students are dealing with both the credit course and the remedial course concurrently.

The co-requisite models are a reaction to the sequential remediation done in the traditional models.  For mathematics, some colleges have from two to five remedial courses in front of the typical college course (college algebra, pre-calculus, or similar level).  The logic of exponential attrition points out the flaws in a long sequence (see https://www.devmathrevival.net/?p=1685 for a story on that).

The co-requisite models in use vary in the details, especially in terms of the degree of effort in remediation … some involve 1 credit (1 hour per week) in remedial work, others do more.  Some models involve adding this class time to the course by creating special sections that meet 5 or 6 hours per week instead of 4.

I do not have a basic disagreement with the idea of co-requisite remediation.  Our work in the New Life Project included these ideas from the start; we called it ‘just-in-time remediation’; this emphasis resulted in us not including any course before the Mathematical Literacy course.

The problem is the presumption that co-requisite remediation can serve all or almost all students.  For open-door institutions such as community colleges, we are entrusted with the goal of supporting upward mobility for people who might otherwise be blocked … including the portion needing remediation.  The issue is this:

For what levels of ‘remediation need’ is the co-requisite model appropriate?

No research exists on this question, nor am I aware of anybody working on it.  The CCA work, like “NCAT” (National Center for Academic Transformation) does not generally conduct research on their models.  NCAT actually did some, though the authors tended to be NCAT employees.  The CCA is taking anecdotal information about a new method and distributing it as ‘evidence’ that something works; I see that as a very dangerous tool, which we must resist.

However, there is no doubt that co-requisite remediation has the potential to be a very effective solution for some students in some situations.  Here is my attempt at defining the work space for the research question:  Which students benefit from co-requisite remediation?

Matching students to remediation model:

Here is the same information as text (in case you can’t read the image above):

The 3 by 3 grid is the problem space; within each, I have placed my hypotheses about the best remediation model (with the goal of minimizing the number of remedial courses for each student).

As you probably know, advocates like CCA have been very effective … some states have adopted policies that force extensive use of co-requisite remediation “based on the data”.  Of course the data shows positive outcomes; that happens with almost all reasonably good ideas, just because there is a good chance of the right students being there, and because of the halo and placebo factors.

What we need is some direct research on whether co-requisite remediation works for each type of student (like the 9 types I describe above).  We need science to guide our work, not politics directing it.

 
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