Alignment of Remediation with Student Programs

My college is one of the institutions in the AACC Pathways Project; we’ve got a meeting coming up, for which we were directed to read some documents … including the famous (or infamous) “Core Principles” for remediation.  [See http://www.core-principles.org/uploads/2/6/4/5/26458024/core_principles_nov4.pdf]  In that list of Core Principles, this is #4:

Students for whom the default college-level course placement is not appropriate, even with additional mandatory support, are enrolled in rigorous, streamlined remediation options that align with the knowledge and skills required for success in gateway courses in their academic or career area of interest.

What does that word “align” mean?  It seems to be a key focus of this principle … and the principle also implies that colleges are failing if they can not implement co-requisite remediation.  In early posts, I have shared data which suggests that stand-alone remediation can be effective; the issue is length-of-sequence, meaning that we can not justify a sequence of 3 or 4 developmental courses (up to and including intermediate algebra).

The general meaning of “align” simply means to put items in their proper position.  The ‘align’ in the Core Principles must mean something more than that … ‘proper position’ does not add any meaning to the statement.  [It already said ‘streamlined’ and later says ‘required or’.]  What do they really mean by ‘align’?

In the supporting narrative, the document actually talks more about co-requisite remediation than alignment.  That does not help us understand what was intended.

The policy makers and leaders I’ve heard on this issue often use this type of statement about aligning remediation:

The remediation covers skills and applications like those the student will encounter in their required math course.

In other words, what ‘align’ means is “restricted” … restricted to those mathematical concepts or procedures that the student will directly use in the required math course.  The result is that the remedial math course will consist of the same stuff included in the mandatory support course in the co-requisite model.  The authors, then, are saying that we need to do co-requisite remediation … or co-requisite remediation; the only option is concurrent versus preceding.

If the only quantitative needs a student faced were restricted to the required math course, this might be reasonable.

I again find a basic flaw in this use of co-requisite remediation in two flavors (concurrent, sequential).  We fail to serve our fundamental charge to prepare students for success in their PROGRAM … not just one math course.  As long as the student’s program requires any quantitative work in courses such as these, the ‘aligned’ remediation will fail to serve student needs:

• Chemistry
• Physiology
• Economics
• Political science
• Psychology
• Basic Physics

Dozens of non-math courses on each campus have strong quantitative components.  Should we avoid remedial math courses just to get students through one required math course … and cause them to face unnecessary challenges in several other courses in their program?

In some rare cases, the required math course actually covers most of the quantitative knowledge a student needs for their program.  However, in my experience, the required math course only partially provides that background … or has absolutely no connection to those needs.

Whom does remediation serve?  Policy makers … or students?

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Equity and Stand-Alone Remedial Math Courses

One of the key errors that co-requisite (mainstreaming) advocates make is the treatment of ‘developmental mathematics courses’ as a single concept.  We would not expect college students who place into arithmetic to have comparable outcomes to those who place into intermediate algebra.  However, most ‘research’ cited with damning results uses that approach.  We need to have a more sophisticated understanding of our work, especially with respect to equity (ethnicity in particular).

A local study by Elizabeth Mary Flow-Delwiche (2012) looked at a variety of issues in a particular community college over a 10 year period; the article is “Community College Developmental Mathematics: Is More Better?“, which you can see at http://mipar.umbc.edu/files/2015/01/Flow-Delwiche-Mathematics-2012.pdf   I want to look at two issues in particular.

The first issue is the basic distribution of original placement by ethnicity.  In this study, ‘minority’ means ‘black or hispanic’; although these ethnicity identities are not equivalent, the grouping makes enough sense to look at the results.  The study covers a 10 year period, using cohorts from an 8 year period; partway through the 8 year period, the cutoffs were raised for mathematics.

Here is the ‘original’ distribution of placement by ethnicity using the data in the study:

After the cutoff change, here is the distribution of placement:

Clearly, the higher cutoffs did exactly what one would expect … lower initial placements in mathematics.  However, within this data is a very disturbing fact:

The modal placement for minorities is ‘3 levels below college’ (usually pre-algebra)

This ‘initial placement’ data appears to be difficult to obtain; I can’t share the data from my own college, because we do not have ‘3 levels below’ in our math courses.  However, the fact that minorities … black students in particular … place most commonly in the lowest dev math course is consistent with the summaries I have seen.

We know that a longer sequence of math courses always carries a higher risk, due to exponential attrition; see my post on that https://www.devmathrevival.net/?p=1685    Overall, the pass rates for minorities is less than the ‘average’ … which means that the exponential attrition risk is likely higher for minorities.

The response to this research is not ‘get rid of developmental mathematics’; the research, in fact, shows a consistent pattern of benefits for stand-alone remedial math courses.  This current study shows equivalent pass rates in college math courses, regardless of how low the original placement was (1-, 2-, or 3-levels below); in fact, the huge Achieve the Dream (ATD) data set shows the same thing.  See page 46 of the current research study.

The advocates of co-requisite (mainstreaming) focus on the fact that 20% or more of the students ‘referred’ to developmental mathematics never take any math AND the fact that only 10% to 15% of those who do ever pass a college math course.  The advocates suggest that a developmental math placement is a dis-motivator for students, and claim that placing them into college math will be a motivator.  Of all the research I’ve read, nothing backs this up — there are plenty of attitudinal measures, but not about placement; I suspect that if such studies existed, the advocates would be including this in their propaganda.

However, there is plenty of research to suggest that initial college courses … in any subject … create a higher risk for students; it’s not just mathematics.  So, the issue is not “all dev math is evil”; the issue is “can we shorten the path while still providing sufficient benefits for the students”.    This goes back to the good reasons to have stand-alone remedial math courses (see https://www.devmathrevival.net/?p=2461 ); although we often focus on just ‘getting ready for college math’, developmental mathematics plays a bigger role in preparing students.  The current reform efforts (such as the New Life Project with Math Literacy and Algebraic Literacy) provide guidance and models for a shorter dev math sequence.

Even if a course does not directly work on student skills and capabilities, modern developmental mathematics courses prepare students for a broad set of college courses (just like ‘reading’ and ‘writing’).  It’s not just math and science classes that need the preparation; the vast majority of academic disciplines are quantitatively focused in their modern work, though many introductory courses are still taught qualitatively … because the ‘students are not ready’.  Our colleagues in other disciplines should be up in arms over co-requisite remediation — because it is a direct threat to the success of their students.

Developmental mathematics is where dreams go to thrive; our job is to modernize our curriculum using a shorter sequence to give a powerful boost for all students … especially students of color.

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Open Educational Resources in Developmental Mathematics

Tired of your students paying over $100 for a textbook?  Frustrated by the cost of getting access to the online homework system that goes with the book?  It’s no news that “OER” is a general movement in colleges & universities.  At some institutions, including mine, there is a direct push for faculty to consider Open Educational Resources (OER) in an effort to save students money.

One concern with OER is that the materials available are almost always (perhaps always) designed for traditional courses, so that OER is a force opposing change in our curriculum.  For example, the “Open Stax” information (https://openstax.org/) information includes this:

“All textbooks meet standard scope and sequence requirements, making them seamlessly adaptable into existing courses.”  [in “About Our Textbooks”]

I’ve not seen any OER materials for Mathematical Literacy, nor for a modern pre-calculus course.  It is easy to understand why OER is traditional in orientation … the resources are judged by how many uses are tracked, and that can be done most easily by fitting materials to old courses.  What might not be as easily seen is the fact that OER is missing an element in the publishing business — the developmental editor, where ‘developmental’ refers to the creation of new textbooks for changing or new markets.  People say that OER is driven by users (faculty); that is not entirely true … I think OER is more driven by carrying on tradition in the name of saving students some money.

Of course, I know that some individual authors deliberately go someplace new.  For example,   see Schremmer’s work at http://www.freemathtexts.org/ where you’ll find nothing traditional.  The problem with this approach is that the materials … as interesting and high quality as they might be … remain on the fringes of the profession.  Perhaps the long-term benefit of these textbooks from the underground is more in the maturation of the profession, more than the particular materials themselves.

Within my college, “OER” even includes generic resources like the Khan Academy and Purple Math.  This inclusion is a bit humorous … math teachers have a strong tradition of connecting their students to such resources, but it has little to do with textbooks.  These free resources also represent a force which encourages us to maintain a traditional curriculum.

If our profession were content with the status quo, then there are few reasons to avoid using OER materials — you might get a traditional ‘book’ complete with online homework system for a lot less than a typical commercial textbook at full-retail price.  Faculty can even modify some of the material to represent their own well-founded (and not well-founded) views … like “never mention PEMDAS, because it’s an awful approach to mathematics”.

Almost everybody teaching developmental mathematics as part of their full-time load has been in contact with representatives of the main commercial publishers.  The publishers are sophisticated, in general, and know that they need to “do something” to keep our business in the face of the OER push, not to mention the presence of Amazon in the used-book market.  I’ve had conversations with field reps & editors from the big 3 (Pearson, McGraw Hill, Cengage); you can get a deal from the companies, though the discount rate appears to be inversely proportional to the company’s current market share.

With these discount deals, you can get a commercial textbook (as an e-book) with the online homework system for $50 to $80 per student.  The question might be:

Is the small savings ($10 to $40 less for OER with homework, compared to commercial book) a significant factor for students?

I think that the difference in cost between OER and commercial materials is relatively small now, and will tend to stay small.

So, I return to a prior statement, paraphrased:

OER materials tend to perpetuate the traditional math curriculum in colleges.

If you find OER materials that you are happy with, you might be able to save your current students some money (depending on how well your department can negotiate with publishers).  However, using OER will generally take you out of the process of basic improvements to your curriculum.  In my view, we should avoid using OER in both developmental mathematics and college mathematics so that we can maintain our focus on improving the curriculum first.

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Regional Accreditation and the Problems in Developmental Mathematics

This post is directed at my colleagues in community colleges and similar institutions … and the bodies that conduct our accreditation processes.  My conjecture is that the accreditation process contributes to the problems we have in developmental mathematics, and that this situation deserves corrective action on the part of the regional accreditation bodies.

The regional accreditation bodies use criteria for faculty credentials; in the case of the HLC, the specific wording is:

Faculty teaching general education courses, or other non-occupational courses, hold a master’s degree or higher in the discipline or subfield. If a faculty member holds a master’s degree or higher in a discipline or subfield other than that in which he or she is teaching, that faculty member should have completed a minimum of 18 graduate credit hours in the discipline or subfield in which they teach.
(see http://download.hlcommission.org/FacultyGuidelines_2016_OPB.pdf)

In all cases that I am aware of, remedial courses are not included in the ‘other non-occupational courses’ category.  The result is the common practice:

Anybody holding a bachelor’s degree, in any field, is qualified to teach developmental mathematics.

Within this common practice, a significant portion of faculty teaching developmental mathematics were original credentialed for high school teaching … usually in mathematics, but not always.  Teaching high school mathematics is a worthy profession, often undertaken by dedicated individuals who are either not-appreciated or blatantly disrespected.  However, the context for teaching developmental mathematics is fundamentally different from teaching high school mathematics.

Among those fundamental differences is the fact that developmental mathematics at an institution is directly connected to college-level math courses.  The developmental algebra courses are expected to prepare students for specific college-algebra or pre-calculus courses, with an expectation of content mastery and retention … those elements have a much lower priority in the high school setting.

Another critical difference between the high school and developmental math contexts is that the developmental math faculty need to interact positively with faculty teaching the college level courses.  Since so many of the developmental mathematics faculty have less qualifications, this presents a cultural and social problem:

How can faculty of college-level mathematics have professional respect for faculty of developmental math courses with ‘lower’ qualifications?

A typical developmental math course has a focus on procedural skills and passing, while the college-level math courses tend to emphasize application and theory … sometimes with a much lower emphasis on passing.  In many colleges, this difference in emphasis leads to either a de facto or official separation of developmental math from college math.

The biggest single problem we have in developmental mathematics is the emphasis on a long sequence of courses — 3 or 4 courses below college level.  The inertia for this structure is based, in large part, on the parallel to grade levels in K-12 work … arithmetic (K-6), pre-algebra (7-8), beginning algebra (9) and intermediate algebra (10 or 11).  I have found that many faculty in developmental mathematics have a difficult time letting go of this grade-level focus (courses in K-12).

The fact that the accreditation process ‘ignores’ developmental math teaching qualifications is the problem I think needs to be addressed.  Should faculty teaching developmental mathematics have the same credential requirement as college-level math faculty?  There are strong arguments for this approach.  Should faculty teaching developmental mathematics have credential requirements beyond that of K-12 math teachers?  In my view, definitely yes.

At this point in time, it is not realistic to hold developmental math faculty to the same credential requirement as college level math — we just don’t have enough people qualified at that level.  However, I think we can develop some reasonable standard which approaches that goal.  Perhaps  ‘masters in math education, or a minimum of 9 graduate credits in mathematics’ could be used as an alternative (in addition to the ‘regular’ credential for general education).  The professional organizations, primarily AMATYC, could develop such a criteria in collaboration with the accrediting bodies.

My purpose is more about pointing out the problem and need to develop a solution, rather than advocate a particular criteria.  Achieving a solution could be measured practically:

Can all mathematics faculty in a community college, regardless of normal teaching assignments, understand and contribute to all curricular discussions involving any math course at the institution?

Until we see this result, students will continue to experience a developmental math program that tends to be too long and overly connected to the K-12 ‘grade level’ structure.

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